Writing Science: Medical and Mathematical Authorship in Ancient Greece 9783110295122, 9783110295054

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Writing Science

Science, Technology, and Medicine in Ancient Cultures

Edited by Markus Asper Philip van der Eijk Mark Geller Heinrich von Staden Liba Taub

Volume 1

Writing Science

Medical and Mathematical Authorship in Ancient Greece

Edited by Markus Asper in collaboration with Anna-Maria Kanthak

DE GRUYTER

ISBN 978-3-11-029505-4 e-ISBN 978-3-11-029512-2 ISSN 2194-976X Library of Congress Cataloging-in-Publication Data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.dnb.de. © 2013 Walter de Gruyter GmbH, Berlin/Boston Typesetting: Meta Systems GmbH, Wustermark Printing: Hubert & Co. GmbH & Co. KG, Göttingen ♾ Printed on acid-free paper Printed in Germany www.degruyter.com

Preface For some years now, questions of authorship in ancient science, that is, of how and why scientists in ancient cultures write the way they do have become moderately popular among readers of ancient literatures. This is, I believe, one of the fields in ancient studies, comparative literature, and history of science and philosophy that can benefit most from exchange of all kinds. It is also an area of ancient literature that literary criticism has only just begun to discover in recent years. When the opportunity emerged in April 2009, I invited a group of scholars of ancient Greek science to come to New York University and give a talk about the topic ‘Writing Science: Medical and Mathematical Authorship in Ancient Greece’. The event was part of New York University’s Ranieri Colloquium on Ancient Studies series. Among the speakers invited were Reviel Netz and Mario Biagioli who gave a joint keynote, Philip van der Eijk, Heinrich von Staden, Alan Bowen, Serafina Cuomo, Brooke Holmes, and Paul Keyser. As someone in the know put it, this certainly was a “high-octane line-up”, and I would like to thank the speakers again for their impressive papers and the audience for vivid discussion. Besides the speakers, my thanks go to my colleagues David Sider and Alex Jones for chairing sessions, to Matthew Santirocco and Ken Kidd for organizing the conference, and to the Ranieri family for generously providing the funding. Quite soon after the conference, I asked some more scholars to provide additional papers with a view towards publication. To my amazement, by far the most of them said yes. I would like to thank especially Karine Chemla and Thorsten Fögen for greatly enriching the scope of the emerging collection. The collection in its current dimensions, however, took shape in Berlin. Maria Börno, Anna-Maria Kanthak, Saskia Lingthaler, and Konstantin Schulz have made great efforts to remove everything that might prove an obstacle on the way towards publication. Dave Lunt and Steve Kidd took, at different times and in different places, part in the process. I am especially grateful for the work Kanthak and Börno have put into the index. Special thanks go to Sabine Vogt who found a home for the volume among the rich and steadily unfolding landscapes of the de Gruyter program. I am most grateful, however, to the contributors who have put immense work into their papers. Markus Asper

Berlin, March 9th, 2013

Contents Markus Asper Introduction

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A. Comparisons Paul T. Keyser The Name and Nature of Science: Authorship in Social and Evolutionary 17 Context Karine Chemla Ancient Writings, Modern Conceptions of Authorship. Reflections on Some Historical Processes That Shaped the Oldest Extant Mathematical Sources from Ancient China 63 Thorsten Fögen Scholarship and Competitiveness: Pliny the Elder’s Attitude towards His Predecessors in the Naturalis Historia 83

B. Greek Medical Writing Heinrich von Staden Writing the Animal: Aristotle, Pliny the Elder, Galen

111

Philip van der Eijk Galen and the Scientific Treatise: a Case Study of Mixtures Ralph M. Rosen Galen on Poetic Testimony

145

177

Ineke Sluiter The Violent Scholiast: Power Issues in Ancient Commentaries

C. Greek Mathematical Writing Reviel Netz Authorial Presence in the Ancient Exact Sciences

217

191

viii

Contents

Serafina Cuomo Accounts, Numeracy and Democracy in Classical Athens

255

Steffen Bogen Diagrammatic Reasoning: the Foundations of Mechanics

279

Alan C. Bowen Three Introductions to Celestial Science in the First Century 

299

D. Science Writing as/and Literature Liba Taub On the Variety of ‘Genres’ of Greek Mathematical Writing: Thinking about 333 Mathematical Texts and Modes of Mathematical Discourse Apostolos Doxiadis and Michalis Sialaros Sing, Muse, of the Hypotenuse: Influences of Poetry and Rhetoric on the Formation of Greek Mathematics 367 Markus Asper Making up Progress – in Ancient Greek Science Writing

411

Brooke Holmes In Strange Lands: Disembodied Authority and the Role of the Physician in the 431 Hippocratic Corpus and Beyond Notes on Contributors General Index Index Locorum

477 485

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Introduction “Writing Science”? The title of this volume is ambiguous. In the term ‘writing science’, ‘science’ can function as the object, as in ‘writing novels’. The term claims that representation implies constructive aspects and that, to a certain extent, science is the product of these constructive aspects. But what is it to write ‘science’? Admittedly, historians of ancient science still debate whether what they investigate really is ‘science’ or something else.1 On the other hand, the object’s verb presents less of a challenge: whatever one names the object of practice for such individuals as Galen and Euclid, Geminus and Diogenes of Apollonia, Ptolemy and Diophantus, Hero and Dioscurides, ‘Hippocrates’ and Hippocrates, Apollonius of Perge and Apollonius of Citium, Ptolemais and Hypatia, to name but a few, these different individuals all can certainly be designated as writers. And, as writers, their study profits from perspectives that bring approaches from literary criticism, in its widest possible meaning. One can also understand ‘writing science’ as ‘the (part of) science that writes’, where ‘science’ is the subject and writing is one practice among others within the realm of science. Among the many myths of science there is the one, still widespread, that ‘writing up’ is not truly part of it. Thus, science writing has not been in the focus of traditional history or philosophy of science which both have largely concentrated on either practice or abstract argument. Things began to change, however, due to what has later been called ‘social constructionism’ and to some influential studies that have demonstrated that the representation of results is itself a constructive practice, which, sometimes, even fashions these results. It is fair to say, I believe, that writing is one representational practice in science among others.2 The contributions that follow will address both aspects of ‘writing science’. Science writing is a field that, except for a long-standing, but moderate interest by linguists, for the most time has found itself repeatedly on the wrong side of boundaries that have become permeable only in the more recent past. One such boundary is that between ‘literature’ and other forms of writing. Science writing has not been part of the traditional canon of literary criticism, ancient or modern. With regard to ancient Greek and Latin texts, things have admittedly been less strict, mainly because such a large chunk of extant ancient literature belongs to medicine, mathematics and astronomy, to name but a few fields of science, that even purely liter1 See, e.g., Lloyd 2009, 152–159; Ritter 2009, 83 f., and the contributions of E. Cancik-Kirschbaum and J. f. Quack in Pommerening & Imhausen 2010. Even in ancient studies, one feels the repercussions of the ongoing debate on how to demarcate ‘science’ (for which see Taylor 1996). 2 See two influential discussions of these questions in Holmes 1987, esp. 222–226, and Lynch & Woolgar 1990, 2–14.

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ary critics could not afford ignoring, e.g., Aristotle, Archimedes, or Galen. Nonetheless, the discussion of ancient science writing has suffered from certain problems that are specific to Classics: one is canonization which then provokes certain predispositions towards the canonized texts. Accordingly, in Classics and related disciplines, three approaches have dominated the study of such texts.3 The first, which we might call ‘textual’, has aimed at providing editions and translations, worked on textual traditions, dictionaries, has attempted to ascertain contextual meaning, etc. The second that has its roots in humanistic readings of ancient authorities is what we can call the ‘realist-humanist’: readers understand the texts as mere receptacles of facts and arguments, that is, they judge them according to their content of and relation to ‘reality’ or ‘truth’ as allegedly provided by modern science.4 If an ancient author is clearly wrong (e.g., Aristotle on the heart’s anatomy, Eratosthenes on the circumference of the earth),5 the realist-humanist either remains puzzled and passes over the lapse in embarrassed silence; or, often by seeking to excuse his author, he asks for possible cultural reasons of ‘getting it wrong’, which then leads into the third and last approach.6 The third approach that emerged in the 70s, and, thanks largely to the ground-breaking work of Geoffrey Lloyd as a scholar and a teacher, has increased in momentum ever since, one might call ‘cultural’. Ancient science writing is seen as a cultural practice that modern scholars can only understand in its social context, carefully avoiding anachronistic perspectives, but using any number and method of comparative approaches.7 All these approaches continue to thrive and, needless to say, they all contribute equally to our knowledge of and about this body of literature. Most scholarly work done today on ancient science probably combines elements of at least two of these three approaches. Compared, however, to contemporary discussion of, say, ancient historiography or epic, approaches that one might call ‘literary-aesthetic’ are, for the most part, missing. Mathematicians can discuss or, rather, acknowledge the beauty of Euclidean or Archimedean proof,8 but where is the classicist who would pin down the concept, and explain it in non-mathematical terms, comparing it with contemporary concepts of beauty in, say, visual art?9 Galen is a great and 3 A glance through the excellent bibliographical essay that concludes Cuomo 2007 (203–210) will provide an impression of how the three are inter-related with respect to the study of ancient technology. 4 Perhaps especially in Germany, where the disciplinary traditions of ‘Medizingeschichte’ and ‘Mathematikgeschichte’ have been institutionally annexed to the schools of medicine and mathematics, respectively. 5 On Aristotle’s anatomical concepts of hearts see Zierlein 2005, esp. 44 f.; on Eratosthenes see Geus 2002, 223–238. 6 See my brief discussion of emerging ‘error studies’ in history of science in Asper 2012, 47 f. 7 Cf. Lloyd’s programmatic outline of future comparative studies of ancient science (2001). 8 On mathematical beauty, see Hardy 1967, Rota 1997, and Sinclair 2006. 9 Netz 2009, esp. 174–229, has provided a brilliant attempt to do exactly this.

Introduction

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versatile writer and, whenever it suits his purposes, he will construct sparkling, usually somehow self-centered, stories about failure and success or about Greece and Rome, but until recently, these stories were not even collected, let alone analyzed, neither for themselves nor in the context of imperial prose.10 After all, these people are, to us, mainly writers, so why do we hesitate to apply to them the instruments we are accustomed to bring to reading Herodotus or Apollonius (of Rhodes)? Another problem that has made it difficult for a discourse about science writing to emerge is the modern institutional divide between literary, philosophical, medical, and mathematical traditions, scholarly communities, and even venues of publication. Scholars who specialize, even from a cultural point of view, in ancient mathematics, rarely compare their findings with research on ancient medicine, and vice versa. As writers, however, all these authors concerned had to face similar challenges and found certain responses to them that we can still compare. This volume will probably not change the course of ancient science studies, but it may show that among the most integrative and fruitful problems of the field is the one of writing science: it will not only provide approaches apt for addressing the whole range of ancient texts regardless of their thematic content, but also bring these research fields back in touch with what happens in literary studies. Therefore, this volume, which is part of a rather recent, but quickly developing sub-field of Classics that one could call ‘comparative studies in ancient science writing’, pleads for an integrated approach to these texts. Such an approach crosses the boundaries of discipline, ancient or modern, and borrows freely from, among others, comparative literature, history and philosophy of science, and STS (science and technology studies).11 What do these approaches add to the way ancient scientific texts have been read in the cultural mode as sketched out above? It is, I think, by now commonly accepted, that science writers ancient and modern seek to persuade their audiences and will employ whatever device comes handy to reach that goal.12 In addition to analyzing the design and impact of such textual devices which has been the focus of the rhetoric-of-science current within STS,13 there are especially two areas where approaches towards science writing in contemporary cultural studies could

10 Mattern 2008 has done much to fill this gap with respect to medical case histories. 11 For the last two and their programmatic differences see Hess 1997, 2 f. 12 Hankinson 1998, 69 (on Plato’s charge against the Sophists): “Scientists will seek to persuade people of the truth of their positions, and it is neither surprising nor intrinsically reprehensible if they employ rhetorical techniques to do so.” 13 Emerging in the late 70s, as seen, e.g., in Gusfield 1976 and Kelso 1980, ‘rhetoric of science’ was sketched out as a field and a research program by Gross 1990, esp. 202–205. Cf. his summary (2006, 3–45) with Zerbe’s (2007, 59–65) who has, however, a more practical concern: “Why is scientific discourse not a major concern of rhetoric and composition as a whole?” (37).

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help us to understand the ways in which ancient ‘rational-practice texts’14 work: first, authorial self-representation and the construction of authority, which is, naturally, somehow connected to the ways social authority in general is constructed in the society under investigation.15 Second, the workings of narrative as it impacts both the organization of empirical data and its representation in writing.16 A third potentially fruitful area is the impact of metaphor on terminology and, more generally, the ideology of terminology.17 Obviously, these areas partly overlap. Most of the following papers have a strong interest in what we might call ‘authorship studies’. The strategies and devices of authorship are neither wholly dependent on the objects of presentation nor wholly independent of them (genre, e.g., provides some constraints). When, however, contemporary mathematicians such as William Thurston or Michael Atiyah wonder about rhetorical strategies in mathematical writing,18 these strategies have nothing intrinsically mathematical to them. Authorship, that is, writing science as an aspect of ‘doing science’, seems to me to be a concept that could be capable of bridging the different aspects, practical and constructive, of writing science. Plus, it effortlessly puts writing science in the context of writing, even literature. Moreover, this might be the area where we and our students as (emerging) writers in the humanities can learn the most from ancient science writers. Finally, it may appear to some readers that notions such as ‘science’, ‘medicine’, ‘mathematics’, etc., come with some anachronistic baggage, because they are almost completely ‘etic’.19 Most, if not all, authors collected in this volume would agree. Cultural comparison, however, needs some over-arching frame which usually is the one of the observer who compares. In the cases of medicine and mathematics, and also of astronomy, there is, I believe, sufficient overlap of ancient practices with their modern namesakes to allow a commonsensical use of these notions without further qualms.20 ‘Science’, however, although it is certainly an etic concept through and through, when including mathematics and, partly,

14 I borrow the expression from Ritter 2009, who coined it for a number of ancient Mesopotamian domains that exhibit parallel formal structures, namely medicine, divination, mathematics, and law (93). 15 For modern scientific authority, see, e.g., Ziman 1984, 70–80. 16 On ‘authorial authority’ see, e.g., Gross 2006, 106 f.; on narrative in science and narratology in science studies see Merz 2010 and my 2011 essay on narrative and (ancient) mathematics (esp. 4); a specifically rich area is narrative medicine, for which see Mattern 2008, 27 f. 17 See, e.g., Graves 2005, 143–189. 18 Thurston 1994, 163: “I also threw out prize cryptic tidbits of insight, such as ‘the Godbillon-Vey invariant measures the helical wobble of a foliation’, that remained mysterious to most mathematicians who read them.”, thus providing illustration to Davis & Hersh 1987, especially p. 60 (quoting from a jocular list of different ways of proving, which at that time circulated among Yale’s graduate students). See also M. W. Hirsch (in Atiyah et al. 1994, 186 f.) on “narratives” in mathematics. 19 For the distinction of ‘emic’ vs. ‘etic’ see Goodenough 1970; Harris 1976. 20 See Lloyd 2009, chs. 2 and 4 and his use of the term ‘discipline’.

Introduction

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even philology, may appear sufficiently fuzzy to use it again. Fuzzy concepts have, at least in cultural studies, often proved to be the most productive ones. This volume collects fifteen essays from experts in the field of ancient science and/or its literature. In their respective areas, all offer approaches to questions of presentation and, especially, of authorship. The collection’s first section (“Comparisons”) opens with three papers that offer comparative perspectives on ancient Greek science and its literature. 1. In his introductory piece, Paul T. Keyser (“The Name and Nature of Science: Authorship in Social and Evolutionary Context”) gives an account of what ancient Greek science actually is, inspired by both Jacobs’s systematic approach and evolutionary theory, enriched by the enormous resources of Keyser’s recently published encyclopedia of ancient scientists.21 ‘Science’ emerges as a human tool in Darwinian struggles for survival, and thus comes itself under evolutionary pressure. Keyser explains his claim and its ramifications in three case studies, the first investigating the history of a mathematical problem, the second of wound-treatment in Egypt and Greece, and the third looking at artillery. One might wonder whether the emergence and change of established forms for writing about science would also be explainable by the same evolutionary framework,22 certainly with respect to the impersonal tradition of knowledge, but especially, when the literary success of individual scientists is concerned.23 Keyser’s account of Greek science calls for comparative accounts of non-Greek traditions. The two following contributions sketch out two very different areas in which such comparisons are highly rewarding: 2. Karine Chemla explains concepts of authorship and authority in ancient Chinese mathematical writing, and Thorsten Fögen discusses the clash of Greek and Roman knowledge-traditions in Pliny the Elder. Chemla’s contribution (“Ancient Writings, Modern Conceptions of Authorship. Reflections on Some Historical Processes that Shaped the Oldest Extant Mathematical Sources from Ancient China”) focuses on the notion of the ‘author’ in the Nine Chapters on Mathematical Procedures, and how this notion is actually a function of its two most ancient commentators’ concepts of canonicity. Chemla demonstrates that editing was the act which produced the mathematical classic. She extends her approach to Greek mathematical classics such as Euclid’s Elements. To see the commentator as the agent of retrospective authorship could also provide a fruitful perspective on medical and philosophical commentators in imperial Greece, as well as modern commentaries, especially of fragmentary authors. The resulting figure is an almost 21 Keyser & Irby-Massie 2008. 22 See my 2007a, 376 f., where, after a brief flirt with evolution I opt for the theoretically more inclusive frame-concept of differentiation à la Niklas Luhmann. 23 To a certain extent, Harold Bloom’s dire concept of what he calls ‘anxiety of influence’ (1973) seems to apply to at least some science writers in antiquity (see Asper 2007a, 360–363, on Galen).

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paradoxical one: the commentator constructs his author and, then, derives his own authority from the constructed classic. 3. Construction of authority is also the topic of Thorsten Fögen’s paper (“Scholarship and Competitiveness: Pliny the Elder’s Attitude towards His Predecessors in the Naturalis Historia”) who looks at Pliny the Elder’s comparative evaluation of Greek and Roman writers in botany and medicine. Since these are, at least in books XIX and XXX of the Naturalis historia, his predecessors, the piece becomes also a case-study of how to present oneself within the context of an already established field (one of the foremost challenges of modern scholarly writing, as well, although it usually is at least partly eased by formalization).24 Pliny emerges as a “shrewd strategist of self-advertisement” (Fögen) who stages his predecessors as sign-posts on the way to his own scholarly authority. Although often judged as inadequate and uncritical, in this respect Pliny is fully on a par with modern science writing. The second section is devoted to medical writing (“Greek Medical Writing”), the field which, within the confines of ancient Greek science, emerged quite early as one of literary and cultural studies, perhaps not least due to its amazing wealth of texts.25 4. Heinrich von Staden (“Writing the Animal: Aristotle, Pliny the Elder, Galen”) approaches the field from an unusual perspective, looking at how Aristotle, Pliny, and Galen write on animals. Analyzing non-human animals poses a host of problems, such as epistemological or linguistic challenges and questions of genre. Writers respond to these difficulties by developing different strategies, among them visualization, figurative responses to namelessness, impersonality or an authorial persona. Such a doubly comparative perspective brings out the characteristics of these three science writers very well: unlike Aristotle, Pliny and Galen need, on top of all the issues that counted for Aristotle as well, to construct authorial relations to political rulers, part of which might be a strong claim of originality. Pliny invents, e.g., a new category of authority, namely quantification of both sources and output. As is well acknowledged by now, Galen is a “master narrator … of the authorial self” (von Staden). Von Staden shows how this is true even when only Galen’s discourse on animals is concerned. 5. There is common agreement that the basic unit of modern communication in science, the research article, emerged in certain institutional contexts in the late 17th century.26 It seems that the closest one comes to an ancient equivalent is the

24 That is, abstract conventions that govern the distribution of content into separate areas of the text, such as footnotes, introductory passages on the ‘problem’s history’, IMRAD (‘Introduction, Methods, Results, and Discussion’, see, e.g. Zerbe 2007, 151 f.), formulaic deixis, etc. 25 The same holds for Latin medical literature which has been studied with an interest in the construction of authority; see, e.g., von Staden 1994 on Celsus, Doody 2009 on the Medicina Plinii, and in general Hine 2009 on Latin scientific and technical texts. 26 See, for example, the pivotal articles of Shapin 1984 and Dear 1985, focusing on Boyle and the Royal Society, and Holmes 1991, 167 ff., on the Académie des Sciences.

Introduction

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‘treatise’, a rather fuzzy genre. Philip van der Eijk who was among the first to think systematically (and comprehensively) about genre in ancient medical writing (see his often-quoted essay of 1997), gives an example of how a medical author makes his apparition in a treatise (“Galen and the Scientific Treatise: a Case Study of Mixtures”), thus both describing the genre and authorial practice of constructing a medical ego’s authority. Van der Eijk situates the problem within the longstanding discussions about Aristotle’s pragmateiai and the logoi of the Hippocratic Corpus, which both also often go under the name of ‘treatise’. Van der Eijk suggests that Mixtures has a definite Aristotelian ring, that is, it was crafted as part and product of an Aristotelianizing aesthetics that coincides with Galen’s attempt to appear as a true and worthy follower of Aristotelian doctrine. Among the many strategies of creating authorial presence in such texts is also a ‘rhetoric of confidence’ which, as the treatise proceeds, assures the reader with ever increasing suggestiveness that the author is right. Van der Eijk concludes by pointing out that Galen adds to the inherited tool-box of rhetorical devices that are typical for treatises, providing a whole new range of rhetorical tools which make the text much more personal than is typical for treatises both of Galen’s past and present. Galen thus emerges as a writer whose authorial practice is in harmony with his scientific claims. 6. Science writing in antiquity has a philological side which is the focus of papers by Ralph Rosen and Ineke Sluiter. Rosen (“Galen on Poetic Testimony”) opens up yet another aspect of the many-faceted Galen, namely his habit of quoting poets and criticizing the quotes of literature by others as parts of scientific argument. Put differently, besides writing ‘literature’ himself, how does Galen use ‘literature’ when discussing medico-philosophical issues? Rosen illustrates Galen’s ideas of how not to use poetic testimony, including allegorical readings of myth, with examples mostly taken from De Placitis Hippocratis et Platonis. Rosen shows how Galen betrays a clear concept of the rhetoric of science and argument as separate from its practice, and how he manipulates the divide according to the changing intentions of his criticism. 7. Sluiter’s paper (‘The Violent Scholiast: Power Issues in Ancient Commentaries’) leads us deeper into the struggles for meaning that ancient science writing exhibits when reading canonic authors. These struggles become most evident in the powerful tradition of writing commentaries, which is, I think, now so obsolete in science that it emerges as one of the major issues in understanding especially imperial and late-antique ‘science’.27 Sluiter approaches the commentator from how he wields his power to actually determine what the canonic and commentedupon author has to say. Besides showing the commentator’s power in action, Sluiter also explores how notions of power, violence and interpretation per se are

27 Netz 1998 has termed the phenomenon “deuteronomic culture” and has described it focusing on mathematical writers. His analysis, however, could be adapted to apply just as well to medicine and philology.

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connected. Here, the culture of commentary which still lives in modern Classics, comes alive as providing a frame for both science and literature (Sluiter culls her examples from commentaries on Homer and the Hippocratic Corpus). These two fields are, from the perspective of the commentator, not entirely different: after all, both provide knowledge-transmission in canonical mode. In many ways, Sluiter’s paper shows parallels to Chemla’s, and comparing Greek and Chinese commentaries on science might prove a fascinating object for further study.28 8. The third section (“Greek Mathematical Writing”) opens with a rich paper by Reviel Netz on mathematical authors (“Authorial Presence in the Ancient Exact Sciences”), which brings together topics many authors in this volume touch upon separately, not least medicine, mathematics and authoriality.29 Mathematical writing occupies a special position within Greek literature in many respects, but especially in that, unlike most of Greek literature, it is not performative. Despite presenting an impersonal surface to the reader, mathematical writing is nonetheless the product of rigorous authorial design which appears on several levels, not least in the narrative structure of mathematical composition. Netz sketches out the peculiarities of mathematical authorship by comparing it to a new concept of ancient authorship per se, analyzing it in terms of voice and competitiveness, involving issues of canonization, textuality, and communication. The key, however, towards understanding the peculiar genre of mathematical writing and its claim to authoriality, remains the lettered diagram, “the Troy and the Corinth of a Greek mathematical text” (Netz). Due to largely social-historical reasons, amply discussed here, mathematical and non-mathematical texts exhibit a complementary character concerning the issues of illustration and performance. As Netz shows, however, mathematicians opted for an opposite model of authoriality. From Netz’s article, one learns a great deal about non-scientific ancient (and, presumably, modern) literature, too. 9. Serafina Cuomo (“Accounts, Numeracy and Democracy in Classical Athens”) contributes a paper on authors and readers of inscriptions with ‘numeric’ content, that is, accounts such as tribute lists, building inscriptions, auction lists, etc. Mostly studied by epigraphists and historians for form, content, and historical context, these texts raise, however, complex questions concerning their symbolic and informative functions, among others, their audiences’ numeracy. Cuomo, however, investigates what authorship and readership mean with regard to such texts. When applied to public monumental inscriptions in an ancient Greek polis such as Athens, Cuomo argues, authorship means political participation and, thus, the authority constructed in these inscriptions differs from textual-authorial authority by a host of largely political implications. As for readership, Cuomo argues cogently that chosen formats are to be understood as choices of manipulation of the reader-

28 See Schwab & Gaeb 2011, on philosophical commentary (Ammonius, Philoponus, and Zhu Xi). 29 Providing amplification of Netz 2009, esp. ch. 2 “The telling of mathematics”.

Introduction

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ship of these texts (not completely unlike choices of formats available to a modern publisher).30 To me, this point seems to warrant application to ancient inscriptions in general. On a more general level, Cuomo demonstrates how inscriptional numbers, often taken to be ‘objective’, become a means of expressing political agendas. 10. In the two remaining contributions to mathematical authorship, the topic of authority enters, as it were, through the back door. Steffen Bogen (“Diagrammatic Reasoning: the Foundation of Mechanics”) discusses the function of diagrams in a context of reasoning, chiefly in mechanical texts by Ps.-Aristotle and Hero of Alexandria (diagrams play an important role also in Netz’s paper). Far from being mere illustrations, Bogen argues, diagrams provide immediate insight into the foundation of mechanics, namely the fact that enforced movements in space are related. On a rhetorical level, writing diagrams highlights an author’s claim to be more than just a craftsman, while reading diagrams discloses the secret workings that the machines seek to cover. Moreover, as Bogen shows, diagrams on paper also aim for an illusion, namely to convince the reader that the machine works smoothly. From such a perspective, mechanical diagrams turn, quite surprisingly, into “fantasies of power” (Bogen). 11. Alan C. Bowen (“Three Introductions to Celestial Science in the First Century ”) looks at introductory writing in hellenistic astronomy, especially at how Diodorus Siculus, Vitruvius, and Geminus present themselves to the reader as experts of theoretical knowledge regarding the heavens, and so, must navigate between astrological and astronomical concepts. Diodorus cleverly manoeuvers between Egyptian, ‘Chaldaean’, and Greek notions of such knowledge, for all of which he is his reader’s only reliable guide; Vitruvius mainly tries to convince Augustus to accept him as an expert. Both claim utility as their main purpose, but the beneficial effects of astrology (‘the Chaldean science’) are more important than the explanatory powers of Greek theoretical astronomy. In both cases, part of constructing an expert authority is the layout of a new kind of celestial science, namely a combination of native Greek and ‘Chaldaean’ elements, and their experts who are mainly seen as practitioners as opposed to traditional theoretical astronomy. Unlike Diodorus and Vitruvius, Geminus employs a rhetoric of impersonality which corresponds to his perspective on astronomy as a body not of useful, but of empirically true propositions about celestial phenomena. Here, just as in modern science writing,31 the rhetorical benefits of personal versus impersonal writing come well into view (see also Brooke Holmes’s paper, summarized below). The fourth and final section (“Science Writing as/and Literature”) cuts across disciplines. Its four contributions look at different fields of science writing by

30 Or to a Presocratic philosopher having a choice between either prose or poetry (see Asper 2007b, 98–100). 31 For impersonality in modern science writing, see, e.g., Gross 1990, 70–74 on “the support of privileged ontology” (quote 73), in ancient Greek mathematics, see Asper 2007a, 125–135.

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engaging issues taken from main-stream literary criticism and pursuing them in science writing: e.g., genre, narrative strategies, and fictionalization. 12. Liba Taub (“On the Variety of ‘Genres’ of Greek Mathematical Writing: Thinking about Mathematical Texts and Modes of Mathematical Discourse”) proceeds from the assumption that choosing a form for what the author has to say is one of the parallels of modern and ancient science writing. After giving short introductions into why both the classificatory notion of ‘mathematics’ and ‘genre’ as a category pose special problems for the literary-historical critic, among such choices she discusses an empirical taxonomy which includes Euclid-style ‘elements’ and their standard parts, question-and-answer texts, commentary, letters, and poems. What began as an investigation of form then ends as one of function, as she reads these forms into their cultural context. 13. Apostolos Doxiadis and Michalis Sialaros (“Sing, Muse, of the Hypotenuse: Influences of Poetry and Rhetoric on the Formation of Greek Mathematics”) first sketch out the uniqueness of ‘Greek-style’ mathematics as text, mainly by comparing it to Egyptian, Mesopotamian, and Chinese mathematics, and then discern a parallel in the development of Greek rhetorical practice. The two threads come together when proof in geometry or philosophy turns out to show remarkably similar structures to those of rhetorical demonstration. Some of these Doxiadis and Sialaros can even identify in earlier Greek traditions, especially regarding “Ringkomposition” and “Chiasmus”. Both mathematics and rhetoric thus emerge as specialist discourses, the unique features of which are based on pre-existing traditional communication, most importantly, story-telling. Suddenly, one sees very different forms of authority (narrative, scientific, juridical) as different aspects of one and the same cultural function. 14. My own contribution (“Making up Progress – in Ancient Greek Science Writing”) focuses on different ways of creating a narrative of progress. Among, chiefly, medical, mathematical, and technical writers I find three forms of such stories: the first tells of progress as a story of steady growth that continues, potentially, forever; the second constructs progress from its ending, which mostly consists in the achievements of the author himself; the third one tells a story of return, according to which true progress means going back to the achievements of the past. Writers tell these storied accounts of progress with certain agendas in mind, which ultimately have to do with the authors’ relation to their readers on the one hand and authority-granting points of reference on the other. In the realms of progress, it becomes instantly clear how narrative is a part of science and its presentation. 15. Proceeding from the impressive passage in Thucydides that describes how especially physicians died in the plague, Brooke Holmes (“In Strange Lands: Disembodied Authority and the Role of the Physician in the Hippocratic Corpus and Beyond”) analyzes the disembodied voice of Hippocratic treatises, mainly by comparing the Odyssey and didactic poetry. Just as Netz did concerning mathemati-

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cians, Holmes explains a silence. Medical authority rests on standing outside the physical forces described in Airs Waters Places, whereas Odysseus has “skin in the game” (Holmes). Holmes discusses the asymmetry of the clinical encounter as crucial for the bodiless authorial role. The Hippocratic Corpus, however, also mentions aspects of medical practice and practicing physicians both in the deontological treatises and beyond, where knowledge-based self-presentation is complemented by physical and ethical aspects. Holmes shows clearly how impersonality and authority are intertwined in ancient and, by implication, also in modern science writing. Authorial practice can also be seen as making choices; texts are sums and products of choosing between alternatives. Where choice is possible, temptation comes in which authors have to resist or give in to. I have always been especially bad in resisting authorial temptation, and thus I conclude by cheerfully repeating and adapting a quote which has already been used in this context:32 “Let a thousand writing-ancient-science flowers bloom!”*

Bibliography Asper, M. 2007a. Griechische Wissenschaftstexte. Formen, Funktionen, Differenzierungsgeschichten. Stuttgart. Asper, M. 2007b. “Medienwechsel und kultureller Kontext. Die Entstehung der griechischen Sachprosa“. In: J. Althoff (ed.), Philosophie und Dichtung im antiken Griechenland. Stuttgart, 67–102. Asper, M. 2011. Erzählungen in der (griechischen) Mathematik? Ein Survey. Berlin. Asper, M. 2012. “‘True’ and ‘False’ Errors in Ancient (Greek) Computation”. In: M. Geller and Κ. Geus (eds.), Productive Errors: Scientific Concepts in Antiquity. Berlin, 47–66. Bloom, H. 1973. The Anxiety of Influence. A Theory of Poetry. Oxford. Brodie Graves, H. 2005. Rhetoric in(to) Science: Style as Invention in Inquiry. Creskill, NJ. Cuomo, S. 2007. Technology and Culture in Greek and Roman Antiquity. Cambridge. Davis, Ph. J., and R. Hersh 1987. “Rhetoric and Mathematics”. In: J. S. Nelson et al. (eds.), The Rhetoric of the Human Sciences. Language and Argument in Scholarship and Public Affairs. Madison, WI, 53–68. Dear, P. 1985. “Totius in Verba: Rhetoric and Authority in the Early Royal Society”. In: Isis 76, 144–161. Doody, A. 2009. “Authority and Authorship in the Medicina Plinii”. In: Taub & Doody 2009, 93– 105.

32 By Cuomo in her 2007 (p. 166). That Mao Zedong in his original slogan only spoke of a hundred flowers, does not need to concern us. It seems perfectly reasonable to raise the number, both because the actual campaign’s function and turnout was anything but cheerful (see Meisner, M. 2007. Mao Zedong: A Political and Intellectual Portrait. Cambridge, 130–134) and because a hundred writing-ancient-science flowers would be far too few. * Thanks to Anna-Maria Kanthak and Stephen Kidd who have greatly improved this text.

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van der Eijk, Ph. J. 1997. “Towards a Rhetoric of Ancient Scientific Discourse […]”. In: E. J. Bakker (ed.), Grammar as Interpretation. Greek Literature in its Linguistic Contexts. Leiden, 77–129. Geus, K. 2002. Eratosthenes von Kyrene. Studien zur hellenistischen Kultur- und Wissenschaftsgeschichte. München. Goodenough, W. H. 1970. “Describing a Culture”. In: idem, Description and Comparison in Cultural Anthropology. Cambridge, 104–119. Gross, A. G. 1990. The Rhetoric of Science. Cambridge, MA. Gross, A. G. 2006. Starring the Text. The Place of Rhetoric in Science Studies. Carbondale, IL. Gusfield, J. 1976. “The Literary Rhetoric of Science: Comedy and Pathos in Drinking Driver Research”. In: American Sociological Review 41, 16–34. Hankinson, R. J. 1998. Cause and Explanation in Ancient Greek Thought. Oxford. Hardy, G. H. 1940. A Mathematician’s Apology. Reprinted, with a foreword by C. P. Snow. Cambridge, 1967. Harris, M. 1976. “History and Significance of the Emic/Etic Distinction”. In: Annual Review of Anthropology 5, 329–350. Heintz, B. 2000. Die Innenwelt der Mathematik. Zur Kultur und Praxis einer beweisenden Disziplin. Wien/New York. Hess, D. J. 1997. Science Studies. An Advanced Introduction. New York. Hine, H. 2009. “Subjectivity and Objectivity in Latin Scientific and Technical Literature”. In: Taub & Doody 2009, 13–30. Holmes, F. L. 1987. “Scientific Writing and Scientific Discovery”. In: Isis 78, 220–235. Holmes, F. L. 1991. “Argument and Narrative in Scientific Writing”. In: P. Dear (ed.), The Literary Structure of Scientific Argument. Historical Studies. Philadelphia, 164–181. Imhausen, A., and T. Pommerening (eds.) 2010. Writings of Early Scholars in the Ancient Near East, Egypt, Rome, and Greece. Translating Ancient Scientific Texts. Berlin. Kelso, J. A. 1980. “Science and the Rhetoric of Reality”. In: Central States Speech Journal 31.1, 17–29. Keyser, P. T, and G. L. Irby-Massie 2008 (eds.). The Encyclopedia of Ancient Natural Scientists. The Greek Tradition and Its Many Heirs. London. Lloyd, G. E. R. 2001. “Is There a Future for Ancient Science?”. In: Proceedings of the Cambridge Philological Society 47, 198–210. Lloyd, G. E. R. 2009. Disciplines in the Making. Cross-Cultural Perspectives on Elites, Learning, Innovation. Oxford. Lynch, M., and S. Woolgar 1990: “Introduction: Sociological Orientations to Representational Practice in Science”. In: idem (eds.), Representation in Scientific Practice. Cambridge, MA, 1– 18. Mattern, S. P. 2008. Galen and the Rhetoric of Healing. Baltimore. Merz, M. 2010. “Bildkomplexe als Geschichten: Naturwissenschaftler erzählen”. In: B. Engler (ed.), Erzählen in den Wissenschaften. Positionen, Probleme, Perspektiven. Fribourg, 211–215. Netz, R. 1998. “Deuteronomic Texts: Late Antiquity and the History of Mathematics”. In: Revue d’histoire des mathématiques 4, 261–288. Netz, R. 2009. Ludic Proof. Greek Mathematics and the Alexandrian Aesthetic. Cambridge. Ritter, J. 2009. “Science and Reason in Ancient Mesopotamia”. In: X. Faivre et al. (eds.), Et il y eut un esprit dans l’Homme. Jean Bottéro et la Mésopotamie. Paris, 83–103. Rota, G.-C. 1997. “The Phenomenology of Mathematical Beauty”. In: Synthese 111, 171–182. Schwab, A., and S. Gaeb 2011. “Der Kommentar als Medium der Philosophie? Eine vergleichende Untersuchung zu den Philosophen Ammonios, Philoponos and Zhu Xi”. In: G. Wöhrle (ed.), Form und Gehalt in Texten der griechischen und chinesischen Philosophie. Stuttgart, 113– 131. Shapin, S. 1984. “Pump and Circumstance: Robert Boyle’s Literary Technology”. In: Social Studies of Science 14, 481–520.

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Sinclair, N. 2006. “The Aesthetic Sensibilities of Mathematicians”. In: eadem et al. (eds.), Mathematics and the Aesthetic. New Approaches to an Ancient Affinity. New York. von Staden, H. 1994. “Author and Authority. Celsus and the Construction of a Scientific Self”. In: M. E. Vázquez Buján (ed.), Tradición e innovación de la medicina latina de la antigüedad y de la alta edad media. Santiago de Compostela, 103–117. Taub, L., and A. Doody (eds.) 2009. Authorial Voices in Greco-Roman Technical Writing. Trier. Taylor, Ch. A. 1996. Defining Science. A Rhetoric of Demarcation. Madison, WI. Thurston, W. 1994: “On Proof and Progress in Mathematics”. In: Bulletin of the American Mathematical Society 30.2, 161–177. Zerbe, M. J. 2007. Composition and the Rhetoric of Science: Engaging the Dominant Discourse. Carbondale, IL. Zierlein, St. 2005. “Aristoteles’ anatomische Vorstellung vom menschlichen Herzen”. In: Antike Naturwissenschaft und ihre Rezeption 15, 43–71. Ziman, J. 1984. An Introduction to Science Studies. The Philosophical and Social Aspects of Science and Technology. Cambridge.

A. Comparisons

Paul T. Keyser

The Name and Nature of Science: Authorship in Social and Evolutionary Context Abstract: Two quandaries confront those who study “science” – why do we call some things “science” and others not? – and, how can we say, if we can, that “science” makes progress? I will argue that we can simultaneously address both those quandaries by considering under what circumstances science evolves. Science, with technology, exists in some form in every culture, and consists at a minimum of collections of recipes held to be efficacious; typically, we find that the collections of recipes are organized and systematic, and come with principles conceived to explain them. Evolution is a substrate-neutral algorithm, and occurs in any system exhibiting variation and replication moderated by differential fitness – thus recipes and explanations evolve through trial and error as people employ them. Any instance of Popperian falsification may be understood as a demonstration of lack of fitness, i.e., as a demonstration that the given explanation is internally incoherent or else that the given recipe does not conform to the knowable world. Unconsciously-selective evolution can become conscious – especially in a polity that provides a rich context of debate and challenge. Jacobs has argued that polities manifesting the “commercial” syndrome will provide a greater degree of debate and challenge in contrast to those manifesting the “guardian” syndrome. Historically, we observe that the rise and decline of science during 13 centuries of Greco-Roman society correlates very well with the degree of freedom of debate and thought manifested, i.e., with the degree of “democracy” exhibited. Democracy increases the selection pressure on theories and thus accelerates the evolution of science. We may conclude that science is that set of practices (recipes) plus theories (explanations) which evolves in a suitably robust ecology of debate and challenge, and that the evolution of science constitutes progress.

I Introduction: the Problem In the study of the science of any place or era, a confounding question is “where to begin?” Rather than beginning, like the Muse in the Odyssey (I 5), “somewhere or other”, or even arguing for my starting point, let me simply confess an outlook, and proceed from there.1 I take it that: (a) the world that we observe indeed exists, 1 I am indebted to many hearers and readers for useful suggestions of many kinds, from passages and vocabulary to matters of presentation: Larissa Bonfante, Laurel M. Bowman, Alexander Jones, David Levene, Sarah Lowengard, Michèle Lowrie, Kurt Raaflaub, Ralph Rosen, Ian Simmonds, and Matthew Stanley and the NYU History of Science Working Group, to whom I presented a version of this paper (2009 December 4th), but above all to Markus Asper who invited me to speak at the conference in April 2008, and who has steadfastly encouraged this work. None but myself should

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and is knowable; moreover, (b) knowledge about the world is shareable; and finally, (c) there is a way that the world is, and it is both possible and meaningful to say that some model or models of the world better represent that way than do others. One classic example is the spherical-earth theory, namely that the earth is not a flattish expanse on whose top we live, but rather a globular mass, with no preferred ‘top’, on whose outside we live. In using the label ‘science’, I mean to pick out the common features of individual sciences, and do not by using the singular intend any suggestion that there is some necessarily unified underlying discourse or method, other than that implied by the hypothesis that there is in fact an observable world. Among the ancient Greeks, no single label designated all science(s), although phusiologia, tekhnē, pragmateia, theōria or theōrēma, epistēmē, and ‘natural philosophy’ were terms commonly used that often covered nearly the same semantic range as our ‘science’.2 We can label the work of ancient mathematicians, astronomers, doctors, mechanicians, and the like as ‘science’, on the basis of shared goals, namely the comprehending, explaining, and sometimes even predicting the phenomena of the natural world. Moreover, we regularly map ancient practices onto modern categories, in order to be able to think about them at all. It is no more anachronistic to employ the modern term ‘science’ than it is to use any modern term – such as ‘book’ or ‘city,’ or even ‘food’ or ‘school’ – to refer to a corresponding ancient Greek concept or practice. We also normally use modern terms, such as ‘astronomy’, to encompass what ancient Greeks included in their study of the heavens, and so also for ‘mathematics’ or ‘medicine’ or the rest. This outlook, as exclusive as it is of many claims, still leaves a large open field in play. I would like to focus on what is special or particular about the way in which scientific authors write – how they present material, relate to their tradition, and innovate. That immediately raises two queries: first, what is science, i.e., why do we call some kinds of knowledge or activities by the name ‘science’ and others not? (Above I gave what amounts to an ostensive definition – now I am seeking a more intrinsic answer.) Secondly, what is innovation in science, and why does science seem to flourish in some times and places more actively or vigorously than in others?3 My argument is that those questions have a deep connection, and will be clarified from the point of view to be described here. What I am attempting is a kind of meta-hypothesis that alters the way in which we see science. We have now, and for a long time have had, more the status of ‘insiders’ with respect to ancient Greek science than did members of other ancient cultures in contact with the Greeks. It is salutary to refresh our minds briefly with the outlook be held accountable for the views presented here. This paper was submitted in its final form on 2012 May 5th. 2 Schaerer 1930 (for tekhnē and epistēmē before Plato) and Cuomo 2007, 7–40 (for tekhnē in classical Athens), show the wide semantic range of the terms they study. 3 I have addressed this issue briefly in Keyser 2010a, and broadly in Keyser 2010b.

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of those outsiders, in order to remind ourselves of the uncanny oddity that is science. Moreover, as I will argue, their perceptions point us to a disclosing feature of Greek science. I am unaware of any explicit statement from ancient Egyptian texts, but one can hardly imagine that they eagerly welcomed Greek ideas.4 Persians rarely adopted or even discussed Greek thought, it seems,5 although I can offer no Achaemenid texts. I focus on the two ancient cultures from which such reproaches are preserved, Rome and Israel. As Horace famously remarked to Augustus (Epistles II 1.156–157), the Romans, in conquering Greece, were in turn mastered by Greek culture: Graecia capta ferum uictorem cepit et artis / intulit agresti Latio. Horace was not unhappy with this outcome, but earlier Romans generally believed that the proper observance of custom maintained the integrity and continuity of the Roman people and state, as Ennius asserts: moribus antiquis res stat Romana uirisque (“ancient rules and men sustain the state of Rome”).6 Such Romans saw a more dangerous and destabilizing Greece, and thus saw Greek wisdom, including science, as working against Roman order and stability.7 For example, Cato banished Greeks from Rome, explicitly because of the danger of their philosophical disputes.8 One of the earliest extant Roman writers to refer to Greek thought, the author of the Ad Herennium, portrays it as empty boasting and a pretense of great knowledge, as if to say “full of sound and fury, signifying nothing” (I 1): illa, quae Graeci scriptores inanis adrogantiae causa sibi adsumpserunt … nam illi, ne parum multa scisse uiderentur, ea conquisierunt, quae nihil adtinebant (“those topics which Greek writers have adopted because of vain arrogance … fearing to appear to know too little, they have sought out irrelevancies”). Even Cicero, who wrested from Greece, and transferred to Rome, much of their thought (Tusculan Disputations II 2.5: Graeciae eripiant et transferant in hanc urbem), repeatedly portrayed Greek philosophy and science as endlessly disputatious.9 Cicero acknowledges that debate strengthens philosophy: in ipsa enim Grae4 Cf. Herodotus II 41.3. Hecataeus of Abdera (ca 305 ) records the Egyptian expulsion of all foreigners, including Greeks: Jacoby 1923–1958, 264, fr. 6 = Diodorus of Sicily, book XXXX, fr. 3.1– 2, from Photius, Bibl. § 244 (p. 380a); cf. Kaplan in Keyser & Irby-Massie 2008, s.v. Hekataios of Abdera, 360. Egyptian texts, beginning in the first dynasty, manifest such potent and persistent disdain for foreigners that Egyptologists describe it as xenophobia: Loprieno 1988, 22–40; Nunn 1996, 8; and Wilkinson 2000, 28–29, deriving it from an ideology of nationalism. 5 Herodotus III 131–137 records a Greek prisoner of war serving as physician in Persia; and Ktesias of Knidos served as physician to Artaxerxes II: Kaplan in Keyser & Irby-Massie 2008, s.v. Ktesias of Knidos, 496. The letters of Darius and Heraclitus in Diogenes Laertius IX 12–14 are an amusing fiction. 6 Ennius, Ann., Book V, fr. 156 Skutsch, from Augustine, Civ. II 21. 7 Jehne 1999. 8 Pliny VII 113, XXIX 14 (cf. Livy XXV 1.9–11); Astin 1978, 189–203; Gruen 1992, 52–83; Roman & Roman 1994, 77–90. 9 Cicero’s response is variously evaluated by Guite 1962, 151–152, 154–155; Urban 1983, 168–170; and Zimmermann 1999.

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cia philosophia tanto in honore numquam fuisset, nisi doctissimorum contentionibus dissensionibus uiguisset (II 2.4). For Roman purposes, however, he would rather have settled conclusions than endless debates and the making of many books: Quod si haec studia traducta erunt ad nostros, ne bibliothecis quidem Graecis egebimus, in quibus multitudo infinita librorum propter eorum est multitudinem, qui scripserunt.10 Cicero brings on his friend Atticus to report the anecdote about L. Gellius (consul and censor) arranging a ‘peace conference’ among the philosophers at Athens (ca 93 ), in order to make them concur on their doctrine.11 Likewise, he impugns Carneades (one of the philosophers expelled by Cato) for debating on both sides of a philosophical question.12 Excess debate was like mob rule, where any fool or knave could raise his voice or hand, a liberty that destroyed Greece.13 Vergil seems to summarize the Roman feeling, when he brings Aeneas’ father on to say: let “others” debate and practice philosophy, art, and science (Aeneid VI 847–850) – as for we Romans, we will rule (851–853). Given that the arts mentioned are marble and bronze figural sculpture, and that the sciences mentioned concern “causes” and the paths of the stars, the “others” can hardly be anyone but Greeks and their scientists. Likewise, the Jews, when confronted by Greek philosophia or even sophia, portrayed it as unsound because mutable. Around 130 , Jesus ben Sira translated into Greek his grandfather’s book in praise of wisdom,14 which defines the true Jewish sophia as fear of god and obedience to god’s commands (19.20), and rejects debate as simply evil (28.9). The Pharisee Saul of Tarsos (ca 60 ), although educated in Greek philosophy, continued to identify himself not as Greek, but as Jewish, e.g., in his first (extant) letter to the Corinthian church.15 In that same letter, Saul/Paul rejects the σοφίαν τοῦ κόσμου (“wisdom of the kosmos”), presumably Greek (and not, say, Roman or Persian), as does he or his imitator elsewhere.16 The author of the Acts of the Apostles, who seems to have accompanied Paul on some of his travels,17 describes the Athenians as liking nothing better than to say or hear something new: εἰς οὐδὲν ἕτερον ηὐκαίρουν ἢ λέγειν τι ἢ ἀκούειν τι καινóτερον (Acts 17.21). The renegade Zionist (‘Galilean’) Yosef ben Mattathias, writing in Greek as Josephus, defends the Jewish culture and religion in the work now entitled Against Apion.18 In contrast to the Greeks, whose histories are unreliable and 10 M. Tullius Cicero, Tusc. II 2.6; cf. Citroni 2003, 150–155. 11 M. Tullius Cicero, Leg. I 53; cf. Gotter 2003. 12 M. Tullius Cicero, Nat. deor. III 43–44; Rep. III 8, and book III, fr. 9, from Lactantius, Div. inst. V 14.3–5; and De orat. II 161. Cf. Ferrary 1977. 13 M. Tullius Cicero, Pro Flacc. 15–18; see esp. Ste. Croix 1981, 310. 14 Hengel 1988, 241–275. 15 I Cor 9.20–21; see also II Cor 11.22, Gal 1.13–14, Phil 3.4–7, and Rom 2.28–29, 11.1; Dunn 1999; Perkins 2009. 16 I Cor 1.20–22, cf. 2.1–8; cf. Col 2.8 “deceit”, Eph 4.14 “wind of teaching”. 17 Porter 1999, 10–46; Wolter 2008, 7–9 (§ 2.1.3). 18 Schäublin 1982.

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discordant,19 the Jews have changed nothing in their law ever (I 8.42), and unlike Greek philosophia, make no contradictory statements about god, having only εἷς δὲ λόγος, ὁ τῷ νόμῳ συμφωνῶν (“one account, harmonizing with the law”, II 19.181). Apion is quoted as saying the Jews have no inventors of tekhnai, unlike the Greeks (II 13.135), which Josephus accepts with pride, denying the existence of any Jewish καινῶν εὑρετάς (“discoverers of novelties”, II 20.182–183). Not all Greeks at all times were fond of innovation and debate, and particularly in our sources the Spartans are seen as manifesting the antithesis of Athenian Neugier. So much so, that Jewish sources could view the Spartans as long-lost cousins, a connection confirmed by Spartan steadfastness in maintaining their ancient laws, and in excluding foreign influence.20 The oligarchic author of the Constitution of the Athenians explains that although Greeks in general keep to their old ways, the Athenians adopt behaviors from everywhere (2.7–8). Thucydides brings on a Corinthian to explain that unlike the Spartans, the Athenians are always νεωτεροποιοί (“revolutionary”); later, he reports that the Athenian Kleon said much the same.21 Aristophanes in the Clouds and in the Women Politicians (“Ecclesiazusae”) mocks the Athenian lust for the New,22 as later Demosthenes also does (Philippic 1.10). Nevertheless, Thucydides I 6 contrasts innovative Greeks as a whole with conservative barbarians.

II The Cultural Context of Greek Science It is on that openness to novelty that I wish to focus in exploring the cultural context of Greek science. I will be offering a model that deploys concepts from several fields, and which I argue explains the rise and decline of ancient science, and can be used also to explain several other cultural milieus in which science also flourished. I will first describe that model, show how it explains the course of Greek science, and then turn to three example cases from ancient science. My model is based on two broad considerations, first the nature of the social contexts that promote science, and second the way in which those contexts could operate to promote science.

19 Contra Ap. I 3.15–5.27; cf. Hecataeus of Miletos, Jacoby 1923–1958, # 1, fr. 1. 20 I Macc 12.5–23, 14.16–23. Laws: Josephus, Contra Ap. II 31.225–231; cf. Thucydides I 18.1. Foreigners: Josephus, Contra Ap. II 36.259–261. Cf. Cardauns 1967; Schäublin 1982, 331; Katzoff 1985. 21 Thucydides I 70, cf. I 102.3; Kleon: III 38.5, 7. Gomme 1956 / 1962, 230–232 offers parallels from Euripides, Suppl. 339–345, 576–577, Heracl. 329–332, as well as in Thucydides II 37.1–2, 40.2, 41.1, VI 18.6–7, 87.3, and VIII 96.5; and Raaflaub 2006 points to Thucydides VI 9.3, 18.3, and VIII 96 as confirming parallels to Thucydides’ depiction in I 70. Cf. Meier 1978, 282 / 1980, 456 / 1990, 198. 22 Aristophanes, Nub. 896–898 and Eccl. 218–220, 456–457, 577–580 (if not meta-theater), and 586– 587. See Meier 1978, 276–280 / 1980, 447–450 / 1990, 194–195.

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We are relatively well-informed about the development of science in Greece in the sixth and fifth centuries , and Geoffrey Lloyd has argued that Greek political culture (especially democracy), because of its practice of free debate and its disregard for traditional authority, promoted the initial rapid development of science, as thinkers competed to build theories.23 Lloyd shows that Greek scientific and political discourse are alike replete with challenges to particular claims, to basic assumptions, and even to the fundamental nature of the inquiries, and are characterized by an agonistic approach. Both discourses opened up the prospect of radical innovations, they promoted the ‘habit of scrutiny’, they expected a rational account or justification, and they allowed an open forum, where all might enter the debate. It is precisely the pervasiveness of this mode of thought and discourse that, Lloyd argues, promoted the relatively rapid flourishing of science. However, the political developments and modes of thought referred to by Lloyd are not restricted to the democratic movements of the sixth and fifth centuries, but indeed appear in the seventh century.24 Already Greek cities sought autonomy and changed their constitutions, and Greek individuals expressed themselves in new ways, as shown by extensive, if fragmentary evidence. For example, Xenophanes opened up a debate about the very nature of the gods, whose exact scope is still disputed, but was in any case more extensive than anything found in any other ancient culture.25 Likewise, the very existence of such poets as Archilochus of Paros, Terpander of Antissa, Alcaeus of Mytilene, Mimnermus of Kolophon, Alcman of Sparta, and especially Sappho of Lesbos, attests to an open social space, in which individuals expressed themselves in novel ways, re-examining and reimagining traditions. The world they depict seems agonistic, innovative, and open. Greeks themselves referred to these aspects of their thought, both in their political writings and in their scientific writings. They were very aware that they often and overtly innovated – rather than rarely, and only on the authority of gods or ancient authorities, as in other cultures of which they knew. They were likewise aware that they themselves contested their own traditions, not only in politics or science, but in many other areas, to a degree not found in other cultures of which they knew. Lloyd cites much evidence from the Hippocratic corpus, of which a few examples may be given. The author of the Hippocratic work On the Art of Medicine says that “the aim and function of intelligence to discover what was unknown before, wherever such a discovery confers a benefit over ignorance”.26 Another

23 Lloyd 1979, 234, 258, 264; he is building upon three works: Vernant 1957 / 1965 / 1983; Vernant 1962 / 1982; and Detienne 1967 / 1996. Note that Vernant 1957 / 1965 / 1983 himself cites Schuhl 1949, 151–175, as formative. 24 Raaflaub 1985, § 2.1–2 (pp. 29–54), Raaflaub 2004, § 2.1–2 (pp. 23–45). 25 Xenophanes Diels-Kranz B 11, B 12, B 14, B 16, and B 23 especially. See Lesher 2010. Note: the fragments of Anaxagoras, Anaximander, Antiphon, Democritus, Protagoras, Xenophanes, and Zeno are cited within from “Diels-Kranz”, i.e., Diels & Kranz 1952. 26 Ars 1: Heiberg et al. 1927, 9.

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theoretical work, On Ancient Medicine, optimistically declares that whatever remains to be discovered will be discovered, given what is already known.27 The author of a more practical Hippocratic work, On Regimen, claims that his discovery is one that “none of my predecessors attempted to understand”,28 and the author of the Airs, Waters, Places asserts that those who live in more open polities will have more tendency to try new things.29 Outside the Hippocratic corpus, we have already seen how Thucydides portrays Greeks in general and the Athenians in particular (I 6, 70, 102.3). He recalls that portrait of Athens twice again, in Pericles’ speech (discussion is no impediment to action, but a requirement for wise action), and in the debate about Mytilene.30 In that debate, Kleon sneers at democrats for being open to reconsidering questions and eager to show their wisdom and declare their opinions (III 37.2–4); whereas Diodotos, whose argument prevails, insists that good decisions come not from haste and passion, but rather that words are guides to action (III 42.1–2). The speech of Aristagoras of Syracuse states that “the many” are best at evaluating arguments, which is an argument for open debate and the possibility of innovation (VI 35–40). Although Herodotus is usually seen as more traditional and less rational than Thucydides, he provides extensive evidence of a commitment to rational inquiry, and both records and engages in contentious debate.31 The debate in Herodotus III 80–82 regarding the ideal form of government is hardly Persian (as Herodotus pretends), and is not even composed from a ‘neutral’ point of view, but emanates from a debate about democracy that was likely similar to the conceptual context of Euripides’ Supplices 403–455, especially on the topic of the citizen’s right to speak, 438–441. Indeed, Herodotus makes it explicit, the Athenians achieved greatness through freedom (V 78), and in general one distinguishes the better choice through opposing ideas (VII 10a.1). Like the Hippocratic medical writers, Herodotus makes extensive use of the language of proof, engages critically with predecessors, and steps forward to enter the dispute in his own voice.32 For Herodotus, Euripides, and Thucydides, the openness of Athens and of Greek cities generally was a marvel.33 Isocrates praises his Athens in the same

27 Vet. med. 2: Heiberg et al. 1927, 37. 28 Vict. III 69 (6.606 Littré). 29 Aer. 16.3–5 (2.64–66 Littré = Jouanna 1996, 228–230) and 23.4 (2.86 Littré = Jouanna 1996, 243– 244) 30 Pericles’ speech: II 40.2; cf. II 37.2–3. Mytilenian debate: Thucydides III 37–48, on which see Andrews 2000, 50–58; Gil 2007, 165–174. 31 Thomas 1997; Keyser 2008a. 32 Thomas 2000, 168–212, 213–239, and 239–247 respectively. 33 Raaflaub 1985, § 2.3 (pp. 54–70), § 3.2 (pp. 108–125), and § 6.1–3 (pp. 258–312); Pope 1988; Raaflaub 1989; Raaflaub 2004, § 2.3 (pp. 45–57), § 3.2 (pp. 89–102), § 6.1–3 (pp. 203–249); Raaflaub 2006; Ober 2008.

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terms, as a city open to outsiders, i.e., novelty,34 and even Aristotle asserted that everyone prefers what is good to what is ancestral,35 thus allowing for novelty. Some of these texts seem to show a belief in progress, a topic to which I return below (§ VIII). I have argued elsewhere that these same features – contentious public debate, constantly shifting politics, and multiple autonomous states – are just what promoted the further development of Greek science in the Hellenistic era.36 That cultural space provided a wide variety of intellectual marketplaces, and if some of the rulers were autocratic, there were still many free cities, and a mercantile world of free travel and trade. For several generations after the death of Alexander the Great, the various ‘successors’ and their kingdoms struggled to control the fragments of his empire, and in that context, there was widespread opportunity to gain power, as ‘friends’ of the kings, or as mercenaries, or as technical experts. Many Greek cities not wholly controlled by any of the kingdoms formed federated states, and frequent embassies and envoys traveled across the Greek world. The ruling classes were everywhere mobile – even if the kingships themselves were securely hereditary. Let me now summarize what I see as the key characteristics of the social context of ancient science: first, disregard for traditional authority, at least as to matters investigated by science; second, openness to innovation and dissent; third, a relatively high status accorded to mercantile activity; and fourth, a relatively low level of xenophobia. This stew of debate and innovation provides a constant flux of new ideas and new facts, which is just the sort of thing Cyrus the Persian and Plato the aristocrat feared from a port city37 – but for science, it is the ideal ecology. Jane Jacobs analyses societies as manifesting two sets of correlated ethical precepts or behaviors, which she calls “syndromes”.38 Each set or syndrome consists of precepts that emerge as a codification of the behaviors advantageous to the two primary modes of subsistence in society, which she designates as “trading” (or commerce) and “extraction”. Most societies manifest both sorts of behavior, within different groups or even within the same group at different times. The two sets do not exhaust the whole universe of human behavior, but only refer to the behaviors specific to the modes of subsistence. Societies whose mode of economic activity is primarily extractive will perceive the need to control and defend territo-

34 Isocrates 4.41–43. 35 Aristotle, Pol. II 8 (1269a3–4). 36 Keyser 2002. 37 Cyrus, according to Herodotos I 153; Plato, Leg. IV (705ab), XII (949e-950a); and also M. Tullius Cicero, Rep. II 7–9. In contrast, the anonymous (Ps.-Xenophon) Ath. Pol. 2.7–8, Thucydides II 38.2, and (somewhat equivocally) Aristotle, Pol. VII 6 (1327a18–28), all speak of the benefits of a port city. Note Popper’s insight that sea-commerce tends to open up the “closed” society: Popper 1945 / 1963, § 10.2 (p. 177); see also Momigliano 1944. 38 Jacobs 1992.

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ry39 – and the syndrome associated with extraction Jacobs also designates as the “guardian” syndrome; moreover, prosperity within an “extractive” economy is tightly coupled to stability (social as well as ecological), thus suppressing change. Within Plato’s ideal politeia, these two syndromes defined two of the classes,40 and indeed Jacobs drew from Plato her term “guardian”. There is no absolute dichotomy between the two modes of subsistence and their attendant syndromes, and any actual society will manifest both, to varying degrees. Greek society transformed from a primarily guardian mode to a highly commercial mode, consciously preferring innovation, dissent, and collaboration with outsiders. “Guardian” “Commercial” Shun trading Exert prowess Be obedient and disciplined Adhere to tradition Respect hierarchy Be loyal Take vengeance Deceive for the sake of the task Make rich use of leisure Be ostentatious Dispense largesse Be exclusive Show fortitude Be fatalistic Treasure honor

Shun force Compete Be efficient Be open to innovation Use initiative and enterprise Come to voluntary agreements Respect contracts Dissent for the sake of the task Be industrious Be thrifty Invest for productive purposes Collaborate easily with outsiders Promote comfort and convenience Be optimistic Be honest

Table : Jacobs’ Two Syndromes ( Precepts)

Jacobs’ analysis has been productively used to analyze the problems attendant upon health care, which is a social function involving activities that are both “commercial” and “guardian”.41 Moreover, her insight regarding two primary forms of society can be recognized as parallel to the insights of Bergson and Popper, both of whom distinguish between a “closed” and an “open” society, where in each case the “closed” society corresponds to Jacobs’ “guardian” society. Bergson describes the closed society as caring nothing for outsiders and perpetually alert for war, held together through traditional and unquestioned myths.42 Popper sees the essential difference between the “closed” and “open” societies as the ability of the latter to distinguish between the “natural” and the “normative”, and to 39 Cf. Campbell 1991. 40 Plato, Res publ. IV (433a–434c). 41 Rachlis & Kushner 1994, 17–21, 80–84, 248–281; and Guidotti 2005. 42 Bergson 1932 / 2007, 287–290, in transl. pp. 255–257.

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accept new ideas, so that members of an “open” society are confronted with personal decisions and develop a tradition of challenging theories and beliefs.43 Moreover, the ruling class of Popper’s “closed” society has a monopoly on arms but is excluded from commerce, and such societies avoid trade with outsiders and seek self-sufficiency.44 The societies designated “closed” by Bergson and Popper, and “guardian” or “extractive” by Jacobs, have also been studied from another point of view, as “oral” or “traditional” or “indigenous” societies, although no agreed non-controversial term seems to exist for societies studied from this point of view.45 Here the approach has been to characterize modes of thought in various small-scale, nonliterate, non-industrial societies, that display minimal specialization in the division of labor, and then to identify common modes. Hallpike, starting from a Piagetian perspective, has identified, among others, some common modes of indigenous

“indigenous”

“oral”

“open”

Complexive classification

Additive, aggregative, redundant –

Analytic classification

Change is: metamorphosis Causes: essences and concrete qualities Stable world: essences & relations persist Vitalism (soul / body unity) Wisdom: concrete and contextual

–

Language: solely social Words powerful, Names inherent

Empathetic / participatory Agonistic

Homeostatic and conservative Seamless human life Situational

Change involves: conservation Causation: series of stages Dynamic world: of multiple perspectives Mind distinct from world Knowledge: abstract and general Language: a conceptual tool Words and Names relative

Table : Indigenous / Oral Societies and Open Societies

societies, shown in Table 2 (where I add the contrasts to ‘open’ societies).46 Ong is analyzing the transition from an “oral” society to a “literate” society,47 and elicits

43 Popper 1945 / 1963, §§ 5.2 (pp. 59–60), 10.1 (pp. 173–175), 10.2 (p. 183), and 10.4 (p. 188). 44 Popper 1945 / 1963, § 6.1 (pp. 86–87). 45 The implicit contrast of the term ‘traditional’ is with ‘modern’, and of the term ‘indigenous’ is with ‘invasive’, as for example in the cases of the primarily British occupation of Australia, Hawai’i, and New Zealand during the late 18th and early 19th centuries. 46 Hallpike 1979; Oesterdiekhoff 1992 performs a similar analysis, with reference to traditional and modern European society, and with a focus on law and ethics. Hallpike and Oesterdiekhoff start from Piaget, but the results of their analysis do not require adopting a Piagetian perspective. 47 Ong 1982, 37–57.

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a number of characteristics of oral societies that are closely parallel to those of Hallpike (although Ong does not examine ideas of causation or change). Hawke has shown very thoroughly how early Greek numeracy developed in the seventh to sixth centuries , in a series of stages that move from an indigenous mode to the mode of an open society;48 this exactly parallels the development of Greek political culture described above.

III First Test: Decline of Ancient Science The analysis I have given, in terms of social structures, suggests that we could explain not only contexts in which science flourishes, but also those in which science weakens or stagnates, i.e., not just the rise of science, but even its decline. In particular, the decline of ancient Greek science in late antiquity is amenable to this analysis. Let me now turn to that, beginning with the Roman assimilation of Greek science.49 The early Roman involvement in south Italy, Greece, and the eastern Mediterranean led to political settlements that preserved distinctions between states and were selfishly arbitrated by the Romans. That itself gave new stimulus to public debate and political activity, especially via competing embassies to Rome – and Rome’s policy was generally to allow client states to regulate their own internal affairs.50 The initial Roman assimilation of science, from about 200 , was marked by a desire to master Greek learning in a manner that protected the auctoritas of the Roman rulers. Roman wisdom, both scientific and otherwise, was based on personal auctoritas, itself based upon publicly validated accomplishment, per se leaving few openings for assimilation of foreign ideas.51 Roman assimilation of Greek science was not uniform, and displays several distinct stages, including the man of auctoritas demonstrating his wisdom in writing, by selective translation or presentation, or else by patronage, as well as works dedicated to leading men, especially the princeps. Much of what they assimilated was of practical benefit, especially medicine, military technology, and agronomy. One typical product of Greek scientific writing was the doxography, collecting and collating disparate answers to various questions (a form not practiced by Romans), whereas one typical product of Roman scientific writing was the encyclopedia, that is, collections of established results for specified problems (cf. Varro, Vitruvius, Celsus, Pliny the Elder) – and these are rare or absent from Greek scientific writing.

48 Hawke 2008. 49 I have treated this at greater length in Keyser 2010c. 50 Oligarchies were more often preferred: Ste. Croix 1981, 519–521. 51 Görler 1974, 154–171.

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Until almost 100 , the Roman polity was an articulated whole, composed of political entities of many sorts. There were client kingdoms (such as Nabataea, Commagene, and Armenia Minor), client leagues (such as the Lycian League), and various city-states, designated “free” or “confederate” (such as Athens, Marseilles, Rhodes, and Sparta).52 Such entities, though subordinate to Rome in foreign policy, were both in theory and practice free to regulate their internal affairs according to their own desires and beliefs. It was not the Roman conquest that stifled Greek science, but the later reorganization of the Empire (primarily due to Hadrian), transforming it from an articulated complex, including many free Greek cities and client kingdoms, into a single centralized hierarchy.53 Provincials internalized the Imperial ideology of a direct relationship with the emperor, as the guarantor of imperial benefits. As the orator Aelius Aristides proclaimed ca 150 , in his panegyric To Rome § 60, the Roman emperors made the empire into “a single city, a single house, a single family”. Similarly, the historian Appian describes the unity of the empire as subject to the emperor (praef. 24–28). There was a growing imperial tendency for direct and invasive management in local administration.54 The full story is complex, and beyond the scope of this paper, but the pattern is clear – and consistent with Jacobs’ model. The Roman polity was always “extractive”, and valued tradition, respected hierarchy, loyalty, and obedience, and rejected trade. Thus, once Hadrian’s reforms were securely established, and persisted in their effect, the necessary intellectual context, in which theories could evolve and be falsified, scarcely existed. Consistent with that model, the decline of scientific activity occurs by the middle of the second century , as shown in Figure 1.55 The timing of this decline coincides rather closely with the decline of trade, as shown by ship-wreck evidence.56 That correlation is consistent with a model of the transformation of Roman society from “commercial” to “extractive”, per Jacobs.

52 Jones 1940, 129–146. 53 Ste. Croix 1981, § V.iii, pp. 300–326 (notes pp. 609–617), esp. 308, 310, 313, 323, and cf. Appendix IV (pp. 518–537, notes 659–660); Alföldy 1988, 158–164, 170–171, 181; Grant 1994, 41, 152, 154–155, etc.; Griffin 2000, 117–123 (on the “imperial paternalism” of Trajan); Eck 2000a; and Eck 2000b; cf. Keyser 2002. 54 Jongmann 2009; Vervaet 2009; Zuiderhoek 2009. 55 The data of Keyser 2008b, but presented in a single graph; scientists with date-ranges greater than the bin-width of 60 years are distributed proportionately into the relevant bins. 56 Parker 1992, fig. 3 and 5, pp. 549 and 551; data pp. 10–14. Wilson 2009, 219–229 graphs the data in narrower bins (20 and 25 years; wrecks with date-ranges greater than the bin-width are distributed proportionately into the relevant bins), which shows that the decline may have begun earlier in the second century.

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Figure 1: Distribution in Time of Ancient Scientists.

IV An Evolutionary Perspective on Science So, if I am right, the ‘open’ society, as delineated above, is the sort of society that promotes the flourishing of science. That claim is simply an observational claim, purporting to have noticed a correlation between certain social forms and the flourishing of science, and even between the ‘opposite’ social forms and the decline of science. Let me now turn to the theory by which I propose to explain how a context like that could operate to promote science. Above, in sketching the course of Greek science, I have been implicitly using a rather broad, and rather ostensive, definition of science. That is, I have taken all those fields of activity that normally are called science with greater or lesser certainty, such as mathematics, astronomy, geography, mechanics, biology, medicine, etc., and simply lumped them together. To make that a little more precise, let me suggest that we may usefully consider as science any and all systematic collections of effective recipes, with principles conceived to explain such collections. The definition is broad enough to include much that has been called applied science or even technology. Should we have some need to distinguish ‘pure’ from ‘applied’ science, we may file the recipes as applied science and the principles as pure science, considering science as concerned with discovery and technology as concerned with construction. But there is really no separation, and

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we are faced not with two distinct species, but with a continuum.57 In any case, science and technology will exist in some form in every culture, and the success of the theories and practices will initially be measured primarily by immediate efficacy. Recipes that are efficacious are generally preferred, and recipes will rarely be static: practitioners again and again adjust and fit them to new conditions and circumstances. We are familiar with the theory of biological evolution, by which populations of living beings, through blind variation and selective reproduction, evolve into the manifold forms that we observe. But evolution is a substrate-neutral algorithm, and occurs in any system exhibiting variation and replication moderated by differential fitness.58 Thus, numerous systems, from the chordate adaptive immune system,59 to cultural phenomena such as language itself,60 and cultural activities generally,61 display evolutionary behavior. My proposal is that scientific recipes and explanations will evolve through trial and error, as people employ and alter them, and that social forces more strongly manifested in ‘commercial’ societies augment the ordinary evolution of science. The units of selection, as with biological evolution, have no precise boundaries,62 and in both cases selection proceeds with no need for such boundaries. The hypothesis that science can be seen as an evolutionary process, in which variation and selection produce changes, in a less or more strict sense, has been often raised.63 Several recent offerings should be mentioned, especially: Hull’s study of the evolution of modern zoology,64 Cziko’s model of the evolution of science as a generalization of Darwinian selection,65 Sanderson’s exposition of scientific change within his quasi-Marxist materialist theory of social evolution,66

57 Ziman 1968, 23–26; Price 1975, 117–135; McMullin 1985, who points to secrecy as the mark of technology in contrast to the openness of science; Niiniluoto 1993; and Kitcher 2001, esp. 85–108. The long tradition of distinguishing science from technology reaches back at least to Aristotle, Phys. II 1–2 (192b8–194b15). 58 Lewontin 1970; Hull 1988, esp. 397–476; Dennett 1995. 59 On the adaptive immune system, see: Jerne 1955; Janeway 1993; Cziko 1995, 39–48; and Coico, Sunshine, & Benjamini 2003, 79–87. 60 Evolution of Indo-European: Jones 1786 / 1970; Poser & Campbell 1992. Evolution of Algonquian: Edwards 1787; Campbell 1997. On evolutionary approaches to language in general, see: Cziko 1995, 179–211; Bichakjian 2002, with analogy to the alphabet; Ritt 2004, a survey; Croft 2006, an “evolutionary model of language change”; Mufwene 2008, with special reference to creoles and pidgins; Pagel 2009; and Greenhill et al. 2010, examining the relative rate of “typological” (phonology, grammar, etc.) and lexical evolution. 61 For “memes”, see Blackmore 2002; Dawkins 1999, 180 finds a trace of memes in Darwin. 62 O’Hara 1994; Dawkins 1999, 81–96. 63 Campbell 1974 gives a thorough survey up to that date; add Keller 1915 / 1931, 198–208. 64 Hull 1988. 65 Cziko 1995, 151–178. 66 Sanderson 1999.

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Blackmore’s account explaining science through memes,67 and Knudsen’s neo-Darwinian formulation.68 Moreover, just as in biological evolution, the selection process can be conscious or unconscious. The process of conscious, or ‘artificial’, selection in biological evolution is also familiar – for example, in the way that humans bred dogs from wolves, or created corn and other cultivars. The distinction between conscious and unconscious selection is no dichotomy, but a matter of degree. As we pay more and more attention to some process of selection that we are performing, we become more and more conscious that we are indeed selecting. Thus, within science, people select from among the recipes available to accomplish a particular goal, and also select from among available principles those that are the most productive, or else explanatory, of effective recipes. Even the creation of variations may be deliberate and conscious. For example, in order to make water boil we may try different kinds of fires or different kinds of pots, and similarly, to harden or soften metals, or to cast colors onto cloth or clay, we may try various techniques, and infer various principles. Recipes that are less effective are rejected – and principles that produce less effective recipes are abandoned. (Of course, practices may persist if no variation produces sufficient differential outcome.) To abandon or reject a recipe or a principle is to declare it unfit. To vary a recipe or a principle is to mutate it, or to produce an innovation. To reject or abandon is to falsify. No test, no argument, no means at all can ever be found to prove a recipe or principle true. Rather, recipes and principles are tested, and they may fail. In saying that, I am of course describing something like Popper’s model of falsification.69 Any instance of the falsification of a recipe or principle may be understood as a demonstration of the lack of fitness of the recipe or principle. Principles are unfit when they generate ineffective or less effective recipes, or are internally incoherent. Recipes are unfit when they do not conform to the knowable world. Thus, unlike other cultural phenomena that evolve, science evolves under a much more severe constraint. Science may be demarcated as the set of all recipes and principles that can be falsified: that insight into demarcation is gained by considering science from the perspective of evolution. A second valuable insight gained is the understanding of the common ground on which there occur episodes of relative stasis as well as relatively rapid change: ‘punctuated equilibria’ are common both in biological evolution and in the evolution of science. Biological species may display little change despite demonstrable selection pressures, when suitable mutations have not arisen, and no competing species (or allele) is “better suited”70 – likewise with scientific theories or technological practices, which may 67 68 69 70

Blackmore 2002. Knudsen 2003. García 2006. Dawkins 1999, 30–54.

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persist for long periods in the absence of better alternatives. (I return to this point below.) Thirdly, we are enabled the better to understand why it is that the ‘open’ or ‘commercial’ societies are those in which science flourishes: because those societies augment the evolutionary process of science. Biological evolution may be studied at a macroscopic level, of populations and selection pressure, as well as at a microscopic level, of genes, alleles, and DNA. A like possibility exists for studying evolution in other systems, and my account is clearly macroscopic, taking no account one way or the other of the many important ‘microscopic’ procedural details of scientific work. That is, nothing in the model of openness and evolution addresses or constrains the ‘context of discovery’, i.e., the working methods, particular circumstances, or conceptual sources of individual scientists. That we can validly and effectively contemplate a ‘macroscopic’ model of human behavior, without direct regard for the ‘microscopic’ chains of causation, is seen in other important models of behavior, that purport to show how the behavior of an individual in some social or cultural context is conceptualized by that individual in an incomplete or partial way. Again, the topic is too large for the scope of this paper, but I need only mention two such models to explain the issue. First, the theories of Freud, according to which pervasive sexual or other “unconscious” motives are “hidden” from the actors, and yet have observable and demonstrable effects on behavior.71 Secondly, the theories of Smith or Marx, according to which individual economic motives operating collectively produce collective results, for which Smith’s short-hand was the “invisible hand”,72 and to Marx was the “class struggle”.73 The cause of the variations in biological evolution is random, but even if it were not (as in artificial selection), the same constraints of fitness would determine survival. That is also true for the evolution of science, where the variations are presumably quite deliberate, but nevertheless the same constraints of falsifiability apply, no matter what the origin of the variations. Some macroscopic patterns that are observed in biological evolution appear also in the evolution of science. For example, flight independently evolved among insects, among theropods, and among mammals, and sight independently evolved among arthropods, among molluscs, and among chordates – an outcome called ‘convergent evolution’.74 The same pattern is observed in science, when the science of different cultures or practitioners arrives at equivalent results – then we can say that science displays convergent evolution, rather than interpreting the presence of equivalent results as evidence of influence or diffusion.

71 72 73 74

Freud 1899, ch. 7 / 1913, 403–493 / 1972, 488–588. Smith 1776 § 4.2.9 / 1976, v. 2a, p. 456. Marx & Engels 1848, 3–11 / 1976, 477–485 / 1995, 3–11. Serb & Eernisse 2008.

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Another pair of patterns are, first, punctuated equilibria, and second the seeming stasis of certain species. A scientific theory or biological species may persist so long as its fitness is unchallenged – that is, so long as there has occurred neither any specific event or test demonstrating relative unfitness, nor any variation manifesting greater fitness. Popper refers to this as the “stableness” of a theory, and in biology we may think of such stable species (‘living fossils’) as the ginkgo tree or the coelacanth fishes, the horseshoe crabs or the tuatara. Such species at least manifest the slow tail of “a normal distribution of evolutionary rates” (a circumstance named bradytely).75 For some of these species, more rapid molecular evolution has been demonstrated, indicating a decoupling from phenotypic evolution.76 In any case, the evolution of biological species often involves long periods of approximate stasis interrupted – or ‘punctuated’ – by brief spasms of radical change. There is no dichotomy, but rather a continuum along which the rate of evolutionary change varies greatly over time. Thus the two phenomena are two aspects of one pattern, and the long intervals of apparent stasis, the equilibria, are precisely what is observed in such cases as the ginkgo or tuatara. In the evolution of science, the periods of rapid evolution correspond to what Kuhn referred to as “paradigm shifts”.77 The periods of stasis within the evolution of science are those during which anomalies endure, because no betterfitted variation has yet appeared. Here one can think especially of the fourelement theory of matter, or the four-humor theory of health, or Aristotle’s theory of natural places. Now let me turn to three case-studies, chosen from domains of science in which success and failure are strongly marked – that is, in which falsification is readily apparent. First, a mathematical example, the summing of an ‘infinite’ series, as attempted by pre-Socratics, Aristotle, Euclid, and Archimedes. Second, a medical example, the diagnosis, care, and healing of wounds to the head, in Old Kingdom Egypt and Hippocratic medicine. Third, an example from applied science, the technology of artillery; the Greek writers on artillery whom I will consult are primarily Philo of Byzantium and Hero of Alexandria.

75 Eldredge & Stanley 1984, 2, which treats over 30 cases, mostly metazoans (animals, i.e., chordates, insects, mollusks, rotifers, sponges, etc.), including the Comorian coelacanth 166–169, and the horseshoe crabs 196–213, but not the tuatara, for which see Hay et al. 2008. On the ginkgo tree, see Gong et al. 2008. Gess, Coates, & Rubidge 2006 suggest the lamprey is a living fossil. 76 Avise, Nelson, & Sugita 1994 (horseshoe crabs); and Hay et al. 2008 (tuatara). The two living species of coelacanth are genetically distinct, diverging ca 1.3 Mya: Pouyaud et al. 1999; but the Wollemi pine shows “exceptionally low genetic diversity”: Peakall et al. 2003. 77 Kuhn 1962 / 1970 / 1996.

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V Case-Study: Summing a Series78 Anaximander is attested to have formally introduced the Boundless into Greek cosmological thought (Diels-Kranz B 1), and Zeno of Elea argued that change was illusory, since it involved going all the way through a boundless series. Early Greek thinkers dealt with unbounded entities in various ways, generally rejecting ‘actual’, i.e., physical infinities, but often accepting endless series. For example, there was no greatest number, so the series of numbers was endless. Nonetheless, some did accept actual infinity, such as Xenophanes’ boundless roots of Earth (Diels-Kranz B 28), Anaxagoras’ boundless seeds (Diels-Kranz B1, B4), or the boundless number of worlds of the atomists (Diogenes Laertius IX 31). Mathematical puzzles about endlessness existed, such as: was the series of prime numbers endless? what would it mean to measure the area of a circle by means of an endless series of polygons? Scholars since Aristotle have engaged in argument with those issues, but I would instead like to examine how the Greek approach to such problems evolved over time, from Zeno to Aristotle, and especially from Aristotle through Euclid to Archimedes, and furthermore how those alterations in outlook led to certain specific results. I will discuss how the understanding of what we call ‘infinite series’ gradually evolved, from Zeno to Archimedes, in the twin contexts of finding areas and volumes by the ‘method of exhaustion’ and of summing a series of magnitudes. Zeno advanced arguments against the reality of change, and in one such argument he focused on an endless series of actions, crossing half the interval or reaching the slow runner, without considering that one could complete the acts by taking them otherwise than one by one. That is, Zeno had been puzzled to understand how an endless series of finite quantities could reach any finite total or limit.79 Aristotle replied that the intervals, being shorter and shorter, take less and less time to traverse, and therefore that the whole series can be covered in a finite time (Physics VI 2 (232a23–233a21)). That is true, but involves a transition to a different set of concepts, which does not meet but evades – or transforms – Zeno’s puzzle, as Aristotle himself elsewhere admits.80 Democritus considered truncations of a cone, made parallel to its base, and asked if the adjacent surfaces created in one such truncation were equal or not: if they were, then the cone would be a cylinder, but if they were not, then the cone would be a pile of disks of uniformly decreasing size (Diels-Kranz B 155). He also

78 This case-study was originally conceived in a reading group at the University of Alberta (with Heidi Northwood and Janet Sisson, 1992), and then given as a paper at the American Philological Association annual meeting in Boston (2005 January 8th); the abstract is available online: http:// www.apaclassics.org/AnnualMeeting/05mtg/abstracts/Keyser.html. 79 Zeno Diels-Kranz A 25–26 in Aristotle, Phys. VI 2 (233a21–32) and VI 9 (239b9–30); cf. McKirahan 1999. 80 Aristotle, Phys. VIII 8 (263a4-b9); White 1992, 169–173.

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is said to have found the volume of a cone to be one-third that of the circumscribed cylinder.81 Antiphon attempted to square the circle by inscribing it with an endless series of polygons, arguing that the polygons will eventually coincide with the circle, or at least measure it. The fragments (Diels-Kranz A 13), preserved in Simplicius and others, do not explain his intent or approach, and give no ground for supposing that Antiphon employed hypothetical infinitesimal straight line segments to measure the curved circumference.82 Plato, in refuting the fourth attempt of Theaitetos to define knowledge, allows that a sextet is equinumerous with a quartet plus a pair, but worries whether a sum is identical with its constituents (Theaetetus 203–205). His worry is expressed in the context of the problem of how an account can be given of a composite whole in terms of its parts. The difficulty into which the argument falls is the pair of claims, that a sum is an aggregate whole, and also that what is true of a whole is true of all its parts. If so, then the parts of a sextet cannot be the same as the parts of a pair joined with those of a quartet.83 Aristotle indicates that Plato accepted the combination of lengths, saying that Plato proposed two infinities, by increase and by subtraction. That evidence is somewhat confirmed by Simplicius, who quotes from Porphyry and from Alexander of Aphrodisias, each reporting on Plato’s “On the Good”, to show that Plato considered how a finite length could be composed from an endless series of successive divisions and additions.84 Worries about combinability and about endless addition also engaged Aristotle, who argued that the non-combinability of the units of numbers would cause insurmountable difficulties, and was therefore to be rejected.85 He also rejected as ill-founded Antiphon’s attempt to square the circle, and scholars infer that Aristotle meant to reject the use of hypothetical infinitesimal straight line segments to measure the curved circumference.86 But – and here is where I begin my detailed tracing – Aristotle did allow for a certain kind of endless addition in the Physics, III 6 (206b). He draws a parallel between infinity by addition and infinity by division (lines 3–6), which Plato also did (27–33). But Aristotle firmly rejects an actual infinity by addition, for several reasons – or at least, he makes several rejections. First (9–12), endlessly adding the same quantity will produce a magnitude that exceeds any finite quantity. Second (16–20), an addition that has potential infinity in the same way as division does, is an addition that does not actually exceed any finite magnitude, i.e., that does not grow without bound. The bound to addition, he says (20–24), is not 81 82 83 84 85 86

Seide 1981. Pendrick 2001, 108–125, 261–275. Burnyeat 1987; Bostock 1988, 211–222. Simplicius, In Arist. Phys. 3.4: Diels 1882, 453–455. Aristotle, Metaph. Μ 6–8 (1080a12–1085a2). Aristotle, Phys. I 2 (185a14–18) and Soph. el. 11 (172a3–9); Knorr 1982.

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infinite, since there is no infinitely large thing in the kosmos (so there cannot even potentially be the infinitely large, like infinite matter). Now (24–27), since there is no actual infinitely large thing, there can be no infinity by addition, except in the inverse sense to that of division above. Aristotle, Physics III 6 (206b), writes:87 (3) In a way, the kind of infinity that depends upon addition is the same as that which depends upon division. Any finite magnitude can include infinity inversely by addition: for just as we see division proceeding infinitely, so addition proceeds to a terminus (ὡρισμένον). (7) I mean: if, in a finite magnitude, you took a (7) ἐν γὰρ τῷ πεπερασμένῳ μεγέθει ἂν determinate amount and added to it, taking the λαβών τις ὡρισμένον προσλαμβάνῃ τῷ αὐτῷ same proportion (of what remains), not taking λόγῳ, μὴ τὸ αὐτὸ τι τοῦ ὅλου μέγεθος περιthe same fraction of the whole, you would never λαμβάνων, οὐ διέξεισι τὸ πεπερασμένον. exceed the finite quantity. (9) But, if you increase the proportion so as always to add the same magnitude, you will pass it, because any finite magnitude is exhausted by any determinate quantity. (12) Thus, the sole way for the infinite to exist is potentially and by subtraction. It has actuality only in the way we say a day or a game does (there’s always another), and it has potential just as does matter, and does not exist on its own as does the finite. (16) That’s how the infinity by addition has potential, just as we say that that by division does: you can always take more, and it will never pass any determinate magnitude, whereas in division it passes any determinate magnitude and there’s always something lesser. (20) But it is impossible for the infinity that passes every determinate magnitude by addition to exist even potentially, unless by accident there exists an actual infinity – such as how the phusiologoi claim the body outside the kosmos, whose substance is air or whatever, is infinite. (24) But if an actually infinite body like this cannot exist, it is clear that the infinite by addition cannot exist even potentially, unless, as stated, inversely to division. (27) After all, even Plato proposed two infinities for this reason, because it seems possible to pass (any magnitude) and proceed to infinity, both by increase and by subtraction. (30) Though having proposed them, he doesn’t use them, since in numbers there is no infinity by subtraction – for the monad is the least, nor by increase – for he proposed numbers only up to the decade.

Thus Aristotle is attempting to describe the endless addition of successively smaller pieces (in the same ratio), Figure 2, and calling that process “infinite”, in the sense that one can always take another piece, in the same ratio, just as one can for

Figure 2: Infinite Addition in Aristotle, Physics III 6 (206b3–33).

87 I have altered the translation of Waterfield 1996, 72–73.

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division. Aristotle mentions that this is almost exactly what Plato said, which Simplicius’ sources confirm. Furthermore, and this is the first key point, Aristotle must know that such a sum is indeed finite, since he has argued that it cannot be infinite. But the other key point is that Aristotle never explicitly states that there is any particular length such that the sum is always less than that length: i.e., he offers no finite upper bound to the sum. Nor does Aristotle explicitly state, for a given set of lengths in a given ratio, that one can find the least upper bound of the sum (the least upper bound is the smallest quantity that the sum does not exceed).88 Euclid, however, does both – though not for a sum that is strictly infinite. In book IX of the Elements, as a lemma to his proof about the “perfect” or “complete” numbers,89 Euclid establishes a formula for the sum of an arbitrarily lengthy series of numbers (IX 35). Euclid, or his source, established a theorem valid for numbers or lengths in continued proportion, as in his diagram, so long as the series was finite. The procedure of the proof does assume that the proportion is greater than 1:1, but the result is not restricted to proportions greater than 1:1, as could be shown by modifications of the proof that are straightforward and in a Euclidean style. Moreover, the proof is evidently not restricted to numbers, and is valid for arbitrary magnitudes. Furthermore, since his sum exists in a definite proportion to a finite magnitude, i.e., to the difference of the first and last terms, Euclid had available the least upper bound of an infinite addition of the sort discussed by Plato and Aristotle. Euclid, Elements IX 35, writes:90 If arbitrarily (ὁσοιδηποτοῦν) many numbers be in continued proportion, and numbers equal to the first are subtracted from the second and last, then, as the excess (ὑπεροχή) of the second (after subtraction) is to the first, so will the excess of the last (after subtraction) be to all those before it. Let there be arbitrarily (ὁποσοιδηποτοῦν) many numbers in continued proportion, Α, ΒΓ, Δ, ΕΖ, starting from Α as least, and let there be subtracted from ΒΓ and ΕΖ the numbers ΒΗ, ΖΘ each equal to Α. Then, as ΗΓ is to Α, so is ΕΘ to Α, ΒΓ, Δ (summed). For let ΖΚ be equal to ΒΓ, and ΖΛ equal to Δ. Then, since ΖΚ is equal to ΒΓ, and of these (the part) ΖΘ is equal to (the part) ΒΗ, therefore the remainder ΘΚ is equal to the remainder ΗΓ. And since, as ΕΖ is to Δ, so is Δ to ΒΓ, and ΒΓ to Α (7.13), while Δ is equal to ΖΛ and ΒΓ to ΖΚ and Α to ΖΘ (by construction), therefore as ΕΖ is to ΖΛ, so is ΛΖ to ΖΚ, and ΖΚ to ΖΘ. Separando (διελόντι), as ΕΛ is to ΛΖ, so is ΛΚ to ΖΚ, and ΚΘ to ΖΘ (7.11, 13). Therefore also, as one of the antecedents is to one of the consequents, so are all the antecedents to all the consequents (7.12); and therefore as ΚΘ is to ΖΘ, so are ΕΛ, ΛΚ, ΚΘ (summed) to ΛΖ, ΖΚ, ΘΖ (summed). But ΚΘ is equal to ΓΗ, and ΖΘ to Α, and ΛΖ, ΖΚ, ΘΖ (summed) to Δ, ΒΓ, Α (summed); therefore as ΓΗ is to Α so is ΕΘ to Δ, ΒΓ, Α (summed).

88 Charleton 1991; White 1992, 8–14, 208–209; Kouremenos 1995. 89 Nicomachus, Ar. I 16, lists as known perfect numbers 6, 28, 496, and 8128; on Euclid, Elem. IX 35 see Mueller 1991, 101–106; on the origin of the concept see Acerbi 2005. 90 I have altered the translation of Heath 1926, 2.420.

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Figure 3: Infinite Addition in Euclid, Elements IX 35. Therefore, as the excess of the second is to the first, so is the excess of the last to all those before it: Q.E.D.

Moreover, in book X of the Elements, he shows that, if given two magnitudes, a greater and a lesser, then one can successively subtract parts of the greater, in the same proportion, until the remainder of the greater is less than the original lesser magnitude (X 1). That is in effect a proof, by the ‘method of exhaustion’, that one can come arbitrarily close to any given magnitude. So, Euclid has shown that he can find an upper bound to either of the infinite series discussed by Plato and Aristotle. In book XII, he builds upon this result in proving that the area of a circle is proportional to the square on its diameter (XII 2). He inscribes a square, and by using the lemma that a triangle inscribed in the arc of a circle is greater than half the area of that segment of the circle, he shows that the series of inscribed polygons – square, octagon, hexadecagon, etc. – exhausts more than half the remainder at each step. Euclid then argues, by contradiction, that the areas of two circles are in proportion just as are the squares on their diameters. The contradiction used by Euclid is established in part by the method of exhaustion. Euclid’s method of proof here (XII 2) is similar to that in his proof that the volume of a cone is onethird of the circumscribed cylinder (XII 10), a result that Archimedes attributes to Eudoxus.91 What Aristotle and Plato did was to consider two specific cases of the infinite, and to show that, in a certain way, each one was tractable. The “infinite by division” can be managed by considering it as a way to produce an arbitrarily small magnitude, whereas the “infinite by addition” can be managed so long as the parts added are in continued proportion, and their proportion is less than 1:1, which Aristotle does not say explicitly. Now Euclid, or his source, took another step of abstraction beyond Aristotle’s position, and developed a way to compute the sum of any arbitrary sequence of numbers in continued proportion. This development, abstracted from considerations of infinity and questions of physical possibility, 91 Archimedes, Sphaer. cyl. I praef. (p. 5 St.); Mueller 1991, 234–236; White 1992, 293–306.

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was taken in the context of proving a theorem about factors of numbers. Euclid, or his source, also developed further the method of exhaustion, showing that one could come arbitrarily close to a given magnitude, and also showing how the method can be used to find proportions between curvilinear figures. In the case of infinities, Archimedes responds to earlier work by Aristotle, and others, as he often does. Democritus, Antiphon, and probably Eudoxus sought to compute the area or volume of curvilinear figures using an endless series of rectilinear figures, e.g., to ‘square’ the circle. I have discussed how Aristotle and Euclid responded to that work. Archimedes, explicitly building upon the work of Democritus and Eudoxus, dealt with limits in two works, Sphere and Cylinder (I praef.; I 1–6) and Measurement of the Circle, and he explained in his Method the heuristic by which he achieved many of those results. To return to the issue of the sum of an infinite series, in another early work, the Quadrature of the Parabola, Archimedes establishes that the area of any parabolic segment is to the inscribed triangle as 4 is to 3. Archimedes’ penultimate proof in that work is a variant of the proof by Euclid for the sum of a series in continuous proportion, in the particular case of a quadruplicate ratio, and starting from the greatest term rather than the least. Archimedes has shown that triangles inscribed in successive parabolic segments are in quadruplicate ratio – in , segment AΔBEΓ is succeeded by the pair of smaller segments AΔB and BEΓ, etc. He now uses that result to argue, in a way exactly analogous to the cited proofs in book XII of Euclid’s Elements, that the area of the parabolic segment is neither greater nor lesser than is 4 to 3. Moreover, since Archimedes is dealing with magnitudes, rather than numbers, and with an arbitrary quantity of them, he has shown in effect how to determine the sum of an infinite series of quantities in continuous decreasing proportion. Archimedes does not say explicitly that his result applies to such an infinite series, but no change in the proof would be required to do so, and scholars debate whether he meant to imply so.92 Archimedes, Quadrature of the Parabola, 23–24, writes:93 23. Given a series of magnitudes in quadruplicate ratio, then the sum of all the magnitudes, plus a third part of the least, will be the four-thirds of the greatest. Let there be given arbitrarily (ὁποσαοῦν) many magnitudes in series Α, Β, Γ, Δ, Ε, each being the quadruplicate of the next, and let the greatest be A. And let there be Z the third of B, and H the third of Γ, and Θ the third of Δ, and I the third of E. Then, since Z is the third part of B, and B is the fourth part of A, both B and Z (added) together will be the third part of A. In like manner, H and Γ will be (the third part) of B, and Θ and Δ (the third part) of Γ, and I and E (the third part) of Δ. So the total B, Γ, Δ, E, Z, H, Θ, I is the third part of the total A, B, Γ, Δ. But the sum Z, H, Θ is the third part of the sum B, Γ, Δ: and the remaining sum B, Γ, Δ, E, I (i.e., the total without

92 No: Stamatis, 1963; García de la Sienra 1983, 69, 73; White 1992, 135–148; and Christianidis & Demis 2010. Yes: Dijksterhuis 1987, 320–321; Knorr 1996; and Netz, Saito, & Tchernetska 2001–2002. 93 The translation is my own, but cf. Mugler 1971, 192–195.

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Z, H, Θ) is the third part of the remaining A. So it is clear that the total A, B, Γ, Δ, E, plus I, which is the third part of E, is equal to the four-thirds of A. 24. Every segment bounded by a straight line and a ‘square section’ of a cone (i.e., a parabola) is the four-thirds of the triangle having the same base and equal in height.

Figure 4: Infinite Addition in Archimedes, Quadr. parab. 23–24.

Let there be a segment AΔBEΓ bounded by a straight line and ‘square section’ of a cone, and let there be a triangle ABΓ having the same base as the segment and equal in height, and let the area K be the four-thirds of the triangle ABΓ. It is to be shown that K is equal to the segment AΔBEΓ. Now if it is not equal, either it is greater or lesser. First let it be, if possible, that the segment AΔBEΓ is greater than the area K. Now, I have inscribed the triangles AΔB, BEΓ, as stated, and I have inscribed also in the leftover segments other triangles having the same base as the segments and equal in height, and I will inscribe into every successively appearing segment two triangles having the same base as the segments and equal in height. Now (eventually) the leftover segments will be less than the excess by which the segment AΔBEΓ exceeds the area K. So that the inscribed polygon (formed by the union of all the inscribed triangles) will be greater than K: which is impossible. I mean, since the given areas are in quadruplicate ratio, first the triangle ABΓ is the quadruple of the triangles AΔB, BEΓ (proposition 21), and then these are the quadruple of those inscribed in the next segments, and so on, thus it is clear that the sum of the areas is less than the four-thirds of the greatest, but the area K is the four-thirds of the greatest area. So then the segment AΔBEΓ is not greater than the area K. Well, let it be, if possible, less (than K). Now let the triangle ABΓ be given equal to area Z, and let the area H be set as the fourth part of Z, and likewise the area Θ the fourth part of Z, and so on, until the last area is less than the excess by which the area K exceeds the segment, and let the last be I. Now the areas Z, H, Θ, I, plus the third of I, is the four-thirds of Z. But the area K is also the four-thirds of Z. So K is equal to the areas Z, H, Θ, I (summed) plus the third part of I. Now since the area K exceeds that of Z, H, Θ, I (summed) by less than I, and exceeds the area of the segment by more than the area of I, it is clear that the areas Z, H, Θ, I (summed) are greater than the segment: which is impossible. I mean, it was shown that if arbitrarily many areas be given in continuous quadruplicate proportion, and the greatest be equal to the triangle inscribed in the segment, the total area will be less than the segment. Therefore the segment AΔBEΓ is not less than the area K. But it was also shown not to be greater: therefore it is equal to K. And the area K is the fourthirds of the triangle ABΓ. So then, the segment AΔBEΓ is the four-thirds of the triangle ABΓ.

The development of thought on this issue was evolutionary and driven by ad hoc concerns. Aristotle and Plato, by focusing on additions and divisions of lengths, argued that certain kinds of infinity were tractable. Euclid, or his source, in focus-

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ing on the specific issue of perfect numbers, found a way to determine the sum of numbers in continued proportion. Moreover, Euclid or his source showed how to treat rigorously the method of exhaustion. Archimedes, in squaring the parabola, extended the Euclidean result to an arbitrary number of lengths in decreasing proportion, and (at least implicitly) to an infinite series. So, in moving to more and more narrowly-defined problems, more and more concrete results were possible. We observe an evolution from speaking of infinity as a paradox to speaking of certain infinities as tractable, then to handling exhaustion and handling sums of arbitrarily many terms in continuous proportion, and thirdly to determining the area of a curvilinear figure by means of exhaustion, employing sums of arbitrarily many terms in continuous decreasing proportion. Evolutionary steps are not of course teleological. But the results obtained, although in one way the product of narrower focus, in another way cover more and more of the conceptual space, so that one can validly speak of observing a trend to greater and greater complexity. That is, focusing on a particular problem resulted in a finite addition to the sum of mathematical knowledge, and that increment itself allowed for further ramification of what could be done and known.

VI Case-Study: Wounds of the Head Let us turn now to the head, and surgeries performed on it. Cranial surgery that creates a hole in the skull, known as trepanation or trephination,94 is attested archaeologically from Neolithic Eurasia and from the pre-Columbian Americas.95 Extant writings on the subject are no earlier than the bronze age, in archaic Egyptian surgery, namely the Edwin Smith papyrus, ca 1550  (recording a much earlier work),96 which I will first consider, and then turn to the Hippocratic On Head Wounds, ca 400 . The Edwin Smith papyrus contains 48 surgical cases, arranged from head downwards, each with examination, diagnosis, and prescription. Each diagnosis includes a triage, assessing the ailment as one that can be “handled”, or one against which the physician can “contend”, or else one for which “nothing can be done”. Fifteen of the 48 cases concern wounds to the head of the sort considered in the Hippocratic text. They are arranged by location, the head being divided into three regions: first skull, then face-and-jaw, and third temple.97 The kinds of wounds are classified by the sort of damage done to the underlying bone,

94 95 96 97

Kaufman, Whitaker, & McTavish 1997. Arnott, Finger, & Smith 2003, see the articles on pp. 55–188, 203–221, and 223–249. Breasted 1930; Nunn 1996, 25–30; Allen 2005. Iversen 1953; Branawski 2001; Branawski 2006.

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Figure 5: P. Edwin Smith (col. 7R, line 9).

either no damage (four cases: 1, 2, 10, 18), a “split” (two cases),98 a “perforation” (four cases),99 or worst of all a “smash” (five cases).100 The Egyptian word for “split” is peshen, the word for “perforation” is tehem, and for “smash” it is śed – all three may be seen, listed in order, in case 18 (col. 7R, line 9): Figure 5. Several observations are pertinent. The three names for damage indicate increasing degrees of damage, “smash” being worse than “perforation”, and that in turn worse than a mere “split”. The “smash” is clearly a compound fracture (described in Cases 5 and 6), and the “perforation” seems to mean a separation at the sutures of the skull – Case 7 establishes the connection. Moreover, four of the five cases of “smash” / śed are diagnosed as cases “for which nothing can be done” (Cases 5, 6, 8, and 22), and only once is a lighter ailment so diagnosed (Case 20, a “perforation”). The therapeutic interventions are minimal – simple

98 The “split” / peshen: Case 4 (col. 2R, line 2) and Case 21 (col. 8R, lines 6, 7bis); cf. Case 3 (col. 1R, line 18) where the flesh is split and the bone is perforated; also: Case 16, a split in the cheek, Case 38, split in upper arm. 99 The “perforation” / tehem: Case 3 (col. 1R, line 18), Case 7 (col. 3R, line 2), Case 19 (col. 7R, lines 14–15 & 17), and Case 20 (col. 7R, line 23 and 8R, line 3); also Case 15, apparently a perforation in the cheek. 100 The “smash” / śed: Case 5 (col. 2R, line 11), Case 6 (col. 2R, lines 18, 23, 24 bis), Case 8 (col. 4R, line 5), Case 9 (col. 4R, line 19), and Case 22 (col. 8R, line 9); also: Case 13, of the nose; Case 17, of the cheek. On all three, see Nunn 1996, 57–58.

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Figure 6: P. Edwin Smith (col. 8R, line 9).

poultices, but no bandages,101 plus bed rest, and in several serious cases, resting in a seated position.102 Archaeological evidence from Egypt confirms that head wounds of these kinds were mostly fatal, and that the therapies applied did not involve invasive surgery, but only wound cleaning and fragment removal.103 In general, Egyptian medicine eschewed surgery.104 Finally, in four of the most serious cases, the physician is advised to await the “turning point” (the rekhet), Figure 6, when one can tell whether the patient will recover or not.105 This corresponds rather closely to the Hippocratic concept of the krisis.106 Egyptian medical theory was cardiocentric, regarding the heart as the source of life and motion, and explaining its control of the body as mediated by the vessels running out from it to all parts of the body.107 Each of the “seven holes” of the head (eyes, ears, nostrils, and mouth) was of great importance, and the head itself was symbolically in the first place (as often in many cultures) – so much so, that in the fable of the dispute of the organs about who shall lead the body (from the ‘Libyan’ 22nd dynasty, i.e., ca 850 ), the final decision between heart and

101 Iversen 1953, 167. 102 Seated: Cases 4, 7b, and perhaps 20. 103 Nerlich et al. 2003. 104 Nunn 1996, 165–169. 105 The “turning point” / rekhet: Case 4 (col. 2R, line 8), Case 6 (col. 2R, line 23), Case 7ab (col. 3R, lines 7, 8, 15), and Case 21 (col. 8R, line 9). 106 See, e.g., Langholf 1990, 79–135. 107 Nunn 1996, 55, 60–62; Westendorf 1999, 1.108–138.

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head is left to a god (contrast Livy II 32).108 Perhaps the cardiocentric focus of Egyptian medical theory and the observable dangers of cranial surgery dissuaded Egyptian doctors from invasive cranial procedures. Turning now to the Hippocratic corpus, let us examine the work On Head Wounds, which advises the physician on the treatment of fractures of the skull.109 Rather than a list of cases, with analyses and prescriptions, the Hippocratic work offers general rules of treatment, instruction on procedures, and anatomical analysis. The focus of the work on the head, and the care with which the procedures are performed, recall the capitocentric view of the Hippocratic Sacred Disease, arguing that thought and sensation reside in the head.110 Moreover, the procedure is advised in the Places in Man,111 is recorded in four or more of the cases in the Epidemics,112 and is archaeologically attested in the Greek world.113 As for the Egyptian text, the kinds of wounds are classified by the sort of damage done to the underlying bone, and the three basic types are the rhōgmē or “break”, the phlasis or “crush”, and the eisphlasis or “depressed crush” (further refinements of the categories are offered).114 The rhōgmē is explained as damage to the sutures (rhaphai), and is perceived as less problematic than the phlasis, a simple fracture.115 There is thus a close but not exact correspondence between the two classification schemes, an instance of convergent evolution:116

108 Westendorf 1999, 1.138–171. On the legend see Brunner-Traut 1959, 158–159, 174; and Kammerzell 1995, 951–954. 109 Hanson 1999; Panourias et al. 2005; Dimopoulos, Robinson, & Fountas 2008. 110 Morb. sacr. 14–17 (6.386–394 Littré = Jouanna 2003, 25–31); see Jouanna 2003, LIII–LXX, 122– 127 for commentary. 111 Loc. hom. 32 (6.324 Littré = Craik 1998, 70–71); see Craik 1998, 187–188 for commentary, noting the similarity to the system in Vuln. cap. 112 Epid. V 16 (5.214–216 Littré): forehead fracture, survived; V 27 (5.226 Littré): wound on sutures of bregma, died; V 28 (5.226–228 Littré): phlasis and ῥήγνυσι (“broke”, cf. rhōgmē), died; and the several patients in VII 35 (5.402–404 Littré), cf. V 97 (5.256 Littré): bone laid bare, died. In addition, it is prescribed for several diseases in Morb. II 23–25 (7.38–40 Littré = Jouanna 1983, 157–159), on which see Jouanna 1983, 231–232. 113 Agelarakis 2006; Liston & Day 2009; and Fabbri et al. 2010. 114 Vuln. cap. 4–6 (3.194–204 Littré = Hanson 1999, 66–68). Iversen 1953, 168–169, wrongly substitutes hedra for eisphlasis. See Hanson 1999, 101–103 for discussion. The three terms are listed as fundamental kinds in 3 (3.194 Littré = Hanson 1999, 66) and again 9 (3.210–212 Littré = Hanson 1999, 70–72), and the refinements given in 7 (3.194–210 Littré = Hanson 1999, 68–70), with what may be “contrecoup” injuries 8 (3.210 Littré = Hanson 1999, 70), cf. Breasted 1930, 202, 205; Iversen 1953, 169; Hanson 1999, 104–105; and Panourias et al. 2005, 183. 115 Vuln. cap. 12 (3.222–228 Littré = Hanson 1999, 76–78). 116 Iversen 1953, 168–169, creates a different correspondence, also close but not exact: peshen (1) to (1) rhōgmē; then śed (3) to (2) phlasis; and tehem (2) to (3) hedra.

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Egyptian Greek “perforation” / tehem:  : rhōgmē / “break” “split” / peshen:  : phlásis / “crush” “smash” / śed:  : eísphlasis / “in-crush” Table : Egyptian and Greek Classification of Head Wounds

But the relation between them is not one of influence117 – note the inversion of the order of the two lesser forms of damage. What we see here is that the basic kinds of damage were all observed, in both cultures, but organized within different systems. For the Greek, a break at an existing fissure seemed less extreme than any form of crack where bone had been continuous, whereas for the Egyptian, any opening, whether at a suture or not, seemed worse than a new seam that did not open. Moreover, three of the symptoms reported are very similar:118 apoplexy,119 hemiplegia,120 and facial edema.121 However, the Greek generalizes these as signs of impending fatality, whereas the Egyptian simply lists them, in two of the cases. The therapeutic interventions prescribed by the Hippocratic writer are far bolder and more invasive than those of the Egyptian. First, the Hippocratic knows that poultices on the skull or scalp are of little use122 – that is, he rejected the false analogy that poultices aided all wounds. On the other hand, he advises surgical removal of damaged flesh and bone, in order the better to examine the wound – that is, in order the better to diagnose.123 A rasp for removing bone, and a dye or ink solution for finding cracks are prescribed. Furthermore, he prescribes interventions even for eisphlasis, the dangerous and difficult depressed skull fracture: notably including prisis – using a kind of circular saw to remove the section of damaged bone.124 Finally, like the Egyptian, he is alert to the prospect of untreatable cases,

117 Even later, when Greek medicine was practiced and studied extensively in Alexandria near Egypt, there is little or no evidence of Greek adoption of Egyptian theories, see von Staden 1989, 1–31. 118 Iversen 1953, 168–169. 119 P. Edwin Smith, Case 8 (col. 4R, lines 7–9) and Vuln. cap. 19.3 (3.254 Littré = Hanson 1999, 88). 120 P. Edwin Smith, Case 8 (col. 4R, lines 6–7) and Vuln. cap. 19.3 (3.254 Littré = Hanson 1999, 88). 121 P. Edwin Smith, Case 7 (col. 3R, lines 9–10) and Vuln. cap. 20 (3.254–256 Littré = Hanson 1999, 88–90). 122 Vuln. cap. 13.1–2 (3.228–230 Littré = Hanson 1999, 78); cf. Iversen 1953, 169, and see Hanson 1999, 110 for discussion. 123 Vuln. cap. 13.3–14 (3.232–242 Littré = Hanson 1999, 78–84). See Hanson 1999, 110–113 for discussion. 124 Vuln. cap. 9, 21 (3.210–212, 256–260 Littré = Hanson 1999, 70–72, 90–92). See Hanson 1999, 106, 117–119 for discussion. On trepanation in ancient Greek medicine, see Rocca 2003.

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but offers a precise set of signs based on which the physician should recognize that nothing can be done and death is coming.125 The two texts mark two stages in the evolution of surgical procedure for head wounds, and show how practitioners elicit principles from recipes, and how they augment their range of recipes. Moreover, we see how independent medical understanding evolves to converge upon a similar characterization of wounds. We also see how the theoretical context can enable further developments, if indeed the Hippocratic text was using a capitocentric model (similar to that in the text On the Sacred Disease).

VII Case-Study: Artillery Ancient artillery provides another suggestive case-study, in which the evolution of ancient science was relatively rapid. Ancient artillery, in the west, begins when a well-funded governmental research program in weapons technology created very large bows firing very large arrows.126 Notable is the emphasis of our witness that no expense was spared, and thus the engineers (τεχνῖται) worked with unsurpassable (ἀνυπέρβλητον) devotion to invent (προσεπενοοῦντο) all sorts of devices (Diodorus of Sicily XIV 42.2). Hero confirms this, writing that the construction of artillery took its start from bows, as men were “forced” to fire larger arrows at greater range, and thus began to construct larger bows.127 They looked something like Figure 7. The further evolution of artillery is traced by the two technical treatises of Hero (ca 60 ) and his predecessor Philo (ca 200 ). The selection-pressure driving the evolution was, as Hero said, the desire to shoot bigger and farther. Hero explains that once the bow had grown enough that cocking by lever no longer sufficed, another variation was tried: a rotating winch that drew back the bow using pulleys, the poluspaston.128 Next, the bow having grown so large that it could no longer easily be aimed or even cocked, a further variation was made which Hero describes, the universal joint or karkhēsion, allowing aiming in both azimuth and elevation.129 Now, an instance of ‘punctuated equilibrium’: the gastraphetēs was rather stable as a species, but still war demanded bigger guns. Thus did someone invent the torsion-catapult, as Hero tells, in which the propulsive force was supplied, not via

125 Vuln. cap. 19 (3.252–254 Littré = Hanson 1999, 86–88). 126 Diodorus of Sicily XIV 41–43.4, probably from Philistos of Syracuse; Marsden 1969; Keyser 1994; Rihll 2007. 127 Hero, Belop. p. 75 Wescher; Marsden 1969, 7–8, 48–49; Rihll 2007, 144. 128 Hero, Belop. pp. 84–86 Wescher; Marsden 1969, 13; Rihll 2007, 145. 129 Hero, Belop. pp. 86–90 Wescher; Marsden 1969, 13.

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Figure 7: Zopyros’ Gastraphetēs

the bend of a bow, but through the twist of a bundle of fibers – probably sinew, or hemp, or hair.130 The date of this innovation is uncertain but must have been ca 360 . However, the new species, though successful, did not wholly and immediately displace the gastraphetēs, which was recorded in use two centuries later.131 The new torsion-artillery itself evolved, a tale told by Philo, who himself produced one of the later innovations. The earliest innovations were: (a) the development of stone-throwers, by ca 355 ;132 and then (b) their evolution into machines large enough to destroy city walls, by 307 .133 The dual-purpose arrow-and-stone thrower was invented by Bromios of Athens around the same time, but is not otherwise attested, suggesting an unsuccessful variation.134 In each case, the variation was created under the pressure of military need, and then survived or became extinct based on its success in meeting that need. Moreover, an instance of conver-

130 Hero, Belop. pp. 81–83 Wescher; Marsden 1969, 16; Rihll 2007, 78–80, 277–279. Rihll 2007, 73– 74, speaks of this development as “evolution”. 131 Lewis 1999; note that the artificer Zopyros of Taras, creator of two kinds of gastraphetēs, is likely to have been working ca 215 : see Keyser in Keyser & Irby-Massie 2008, s.v., 851. 132 Because used by Onomarkhos of Phokis against Philip of Macedon: Polyaenus, Strat. 2.38.2. Cf. Rihll 2007, 60, but contrast 116–117, citing Polybius book XI, fr. 12.4. 133 Keyser 1994, 45–46; cf. Rihll 2007, 120, 135–136, but contrast 161–163. Brun 1994, Karlsson 1994, and Winter 1994, find securely-dated walls built to resist large stone-throwers no earlier than ca 300 , and emphasize the difficulty of dating walls, as well as the occurrence of later walls not resistant to large stone-throwers. Probably the invention was due to an engineer under Demetrius Poliorcetes, thus perhaps Epimakhos of Athens, cf. Irby-Massie in Keyser & Irby-Massie 2008, s.v., 293. 134 On Bromios see Keyser in Keyser & Irby-Massie 2008, s.v., 199.

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gent evolution is found in the design of the “hole-carrier” (a bronze fitting at the ends of the fiber-bundles).135 Philo records that engineers working in Alexandria and Rhodes sought to optimize the design of the torsion catapult by trial and error (πεῖρα and ἡμαρτημένον) from which they elicited principles and a formula.136 These engineers must have been working in the early third century , and Philo tells us that, like those in Syracuse, they were well-funded.137 The ecology was fertile enough that one of those engineers, Ctesibius of Alexandria, invented the bronze-spring engine, which Philo himself recreated and improved – the goal was a more reliable spring than fibers could provide.138 But contemporary metallurgy could not reliably produce suitable springs, and the device became extinct. Another soon-extinct species, also by Ctesibius, was the piston-powered catapult, whose ‘spring’ was the air compressed in a pair of pistons – but contemporary machine technology could not create sufficiently smooth yet tight pistons.139 In both the bronze-spring and the piston-powered catapults, the variation was made to the ‘spring’ in attempt to improve on fibers. The third new species was the repeating catapult, a kind of Gatling gun invented by Dionysius of Alexandria working in Rhodes, and possibly still extant two centuries later.140 Philo’s own contribution was to create a novel method by which the tension of the fibers could be adjusted more easily and smoothly, and which also made the construction of the torsion catapult simpler.141 Finally, under siege conditions, the one-armed torsion catapult (μονάγκων) was favored – perhaps because it was easier to set up and calibrate, albeit perhaps harder to re-aim when very large. Although hardly attested in earlier texts or sites, by late antiquity, known as the onager, it came to dominate all other species.142

VIII Past and Future Progress Thus the ‘commercial’ society of the Greeks provided a context within which, for several centuries, three aspects of science evolved: mathematics handling infini135 Rihll 2007, 111–112. 136 Philo, Belop. pp. 50–51 Thévenot; cf. Hero, Belop. pp. 112–113 Wescher; Marsden 1969, 25; Rihll 2007, 108, 146, 149–150. 137 Cf. Diodorus of Sicily XIV 41–43.4, and compare Claus 1975: Achilles cannot be bought but must be rewarded. 138 Philo, Belop. pp. 56, 67–73 Thévenot; Marsden 1969, 41–42; Rihll 2007, 154–157. 139 Philo, Belop. pp. 77–78 Thévenot; Marsden 1969, 41–42; Rihll 2007, 159–160. 140 Philo, Belop. pp. 73–77 Thévenot; Marsden 1969, 75, 89, 94; Foley et al. 1982; Rihll 2007, 157– 159. 141 Philo, Belop. pp. 56–67 Thévenot; Marsden 1969, 42; Rihll 2007, 153–154. 142 Marsden 1969, 249–265; Rihll 2007, 76–77, arguing that the device was a 4th-century  invention, and 247–249.

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ties, surgery for cranial trauma, and a variety of successful species of artillery. Cases could be greatly multiplied, in those areas and in others, such as (1) ancient pharmacy,143 in which effective analgesics, contraceptives, and even antiseptics were developed, or (2) ancient alchemy, in which effective imitations of silver were produced,144 or (3) ancient water-lifting machines, from the shadoof to the pistonpump.145 Yet we can also see that cultural conservatism, especially in the fourth century , opposed the adoption of the new science and technology of artillery, and attempted to adhere to the tradition of the hoplite warrior.146 Likewise, in medical science, we do not always find that innovation prevails over tradition. A ‘commercial’ society amplifies the evolution of science, but when societies turn back toward a ‘guardian’ mentality, the amplifying effect correspondingly weakens. So if the socio-evolutionary model here advocated is correct, we should expect to find many instances of evolution and development, especially in ‘open’ societies, ancient and later (a matter to be further investigated).147 Moreover, in an ‘open’ society, we would expect to find an awareness of that development – that is, we would expect to find authors, whether scientific or not, recognizing the greater and greater diversity of scientific thought, and the closer and closer fit of the scientific models to the world. That is, we would expect members of an ‘open’ society to observe and remark upon what we may call scientific progress. Using that word raises a host of muchdebated and complex issues around the nature of ‘progress’. These too, like the issues raised above, constitute a topic of sufficient magnitude that it cannot be thoroughly considered here. Any theory of the general progress of human society ipso facto implies a theory of the progress of science, but one can propose that science and technology make progress without necessarily claiming any other kind of progress. Some Greeks were quite aware that their society and its practices promoted innovation, and those Greeks refer to that innovative character positively. Already in the sixth century , Xenophanes wrote that: … the gods did not reveal all things to mortals at the start, But in time they seek and find out better148

143 Keyser 1997. 144 Keyser 1990; Keyser 1995/6. 145 Oleson 1984; Wikander 2000; Wilson 2002; and Stein 2004. 146 Keyser 1994; Lendon 2005, 5–13, 156–161, and 2010, 6–13, argues that the conservative response in Greek warfare was strong in the late fifth century (431–420 ) and weaker in the Hellenistic period. 147 I have begun that task, in Keyser 2010b. 148 Xenophanes Diels-Kranz B 18 preserved in Ioannes Stobaeus, Anth. I 8.2; see Kirk, Raven, & Schofield 1983, 179.

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Plato presents, in his eponymous dialog, a version of Protagoras’ theory of the growth of human society, that scholars seem to agree more or less accurately represents what Protagoras wrote: if so, Protagoras argued for progress in human affairs, including science – and even if not, Plato was willing to portray Protagoras as having done so, implying at least that the fiction was meaningful.149 The hymn to progress in the first stasimon of Sophocles’ Antigone has been widely discussed, though some scholars suspect some kind of dramatic irony, and deny that the text should be read as praise of progress, or even constitutes evidence for a belief in progress.150 In Thucydides, scholars are agreed, there is an idea of progress, and indeed, it is hard to imagine a reading of the ‘archaeology’ that would conclude otherwise.151 Isocrates briefly refers, in his own voice, to a theory of human progress very similar to that attributed to Protagoras by Plato;152 another writer from the same period (ca 380–350 ), the fragmentary tragedian Moskhion, hymns the instruction that long practice brings.153 The historian Polybius, writing in the mid-second century , opines that “The natural human love of innovation (φιλόκαινον) is itself sufficient for any change”,154 describes the evolution of signaling techniques as progress;155 and concludes that “all our sciences (θεωρήματα) have achieved such advances (προκοπάς) that in most ways the sciences (ἐπιστήμας) are systems”.156 Diodorus of Sicily, in the mid-first century , manifests a wide-ranging belief in human progress of many kinds, especially in the learning of “useful arts”, i.e., technology.157 Although, as argued above, Roman social mores ultimately stifled Greek science, some Romans (from the era ca 100  to ca 100 ) reflected a more open and Hellenic appreciation of science, and of progress. Lucretius, rendering Epicurus into Latin, proclaims the advance of technology and science (V 332–336):158 149 Plato, Prot. 320c8–323a4, cf. Protagoras Diels-Kranz A 1.55 = Diogenes Laertius IX 55; de Romilly 1966, 147, 151–155; McNeal 1986; Manuwald 1996. 150 Sophocles, Ant. 332–375; see Jebb 1900 / 2004, 69–77; Müller 1967, 83–89; Meier 1978, 283– 284 / 1980, 457–459 / 1990, 199–200; and Benardete 1999, 40–49. 151 Thucydides I 4–18 especially; Gomme 1962, 99–100, 105–106, 120–122, 129–130, 232; de Romilly 1966; Hunter 1982, 17–49; Hornblower 1987, 129–131. 152 Isocrates 4.32, 40. 153 Snell & Kannicht 1986, Trag. Graec. Frag. 97, fr. 6, preserved in Ioannes Stobaeus; see Stephanopoulos 1988, 23–29. 154 Book XXXVI, fr. 13.3, as preserved in the Excerpta de Sententiis § 153 (ca 910 ), see BüttnerWobst 1904, xvi–xvii. 155 Book X, frr. 43–47, as preserved in the Excerpta de Legationibus (ca 910 ), see Büttner-Wobst 1893, iii–vi, and cf. Büttner-Wobst 1905, iv–vii. 156 Book X, fr. 47.12; cf. book IX, fr. 2.5 (as preserved in the Excerpta de Legationibus), saying μάλιστα δὲ νῦν ὑπάρχειν, τῷ τὰς ἐμπειρίας καὶ τέχνας ἐπὶ τοσοῦτον προκοπὴν εἰληφέναι καθ᾽ ἡμὰς (“especially as things are now, when experience and technology have achieved so much progress among us”). 157 Especially I 8, but Sacks 1990, 55–82, lists dozens of other passages, mainly in books I to VI. 158 The “organ” is the musical hydraulis invented by Ctesibius, ca 260 .

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Quare etiam quaedam nunc artes expoliuntur Nunc etiam augescunt: nunc addita nauigiis sunt Multa; modo organici melicos peperere sonores; Denique natura haec rerum ratioque repertast Nuper, …

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Thus even now some technologies are being refined and augmented: much is now added to ships, recently organs made melodies, and finally the nature of things, and this account, has just been discovered, …

Later in the same book, he reconstructs the evolution of technology (V 1241–1378), which he then summarizes, explicitly naming it progress (V 1452–1453): Usus et impigrae simul experientia mentis Paulatim docuit pedetemtim progredientis.

Practice and experience together slowly taught the active mind stepwise progressing.

Cicero, within an attempt to determine the limits and parameters of proper behavior, offers a myth of human origins very like that of Protagoras (in Plato), describing the gradual attainment of human technical skill as due to human effort.159 Vitruvius offers yet another version of such a myth (II 1), speaking of people adding novelty to their thoughts, adicientes suis cogitationibus res nouas (II 1.2), and how from the technology of building houses they progressed to other technologies (artes) and sciences (disciplinas) step-by-step: gradatim progressi ad ceteras artes et disciplinas (II 1.6).160 Among modern scholars considering the issue of progress, many and varied opinions have been expressed, not all on the issue of scientific progress, and a thorough study would demand much greater space than here. Several scholars have investigated whether the idea of progress in some form existed in antiquity. Spoerri traces the idea of the progress of human society from Diodorus of Sicily through the Greco-Roman period, offering much evidence from the two centuries after Diodorus, and very little after that.161 Guthrie finds a strong notion in scattered places in the fifth and fourth centuries .162 Dodds concludes that “the most explicit statements of the idea refer to scientific progress and come from working scientists or from writers on scientific subjects”.163 Blumenberg, even under a more restrictive definition, identifies an explicit notion of progress in ancient Greek astronomy.164 Meier, using “ability” to cover the Greek semantic range of sophia and tekhnē, identifies a concept of the increase of human “ability”

159 M. Tullius Cicero, Off. II 12–15. 160 Note also the remarks of Seneca, Nat. quaest. VII 25.4–5; and much later, the anonymous De rebus bellicis (“Military Matters”), prol. 4 (ca 370 ); and Procopius, Bell. VIII 11.28 (ca 555 ), whose personal name itself refers to progress. 161 Spoerri 1959, 1–163. 162 Guthrie 1969, 79–84. 163 Dodds 1973, 24. 164 Blumenberg 1974.

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in the fifth century .165 Blundell, in discussing ancient Greek and Roman theories of the origins of society, argues that theories of progress were widespread albeit not universally accepted, from the fifth century  through the first century .166 Certainly many thinkers in societies that are ‘extractive’ or traditional will oppose most change, scientific or other, implicitly or explicitly denying the prospect that progress is possible or desirable. Among modern thinkers troubled by ‘progress’, foremost is Nietzsche, who in Jenseits 1.14 asserts that modern physics and biology is plebeian and joyless;167 he has been interpreted as denying causality and explaining the appearance of scientific development as merely power-struggles between differing schools of thought.168 Max Weber, greatly under the influence of Nietzsche, while acknowledging that science does make progress, indicated that the progress of science accomplishes the disenchanting (Entzauberung) of the world and that science itself conveys no humanistic meaning (Sinn).169 Kuhn is often read as having argued that distinct paradigms are incommensurable, and thus that no notion of progress can exist – but in fact he himself suggested that regarding science as an evolutionary process would explain the evident progress of science across paradigm-shifts.170 More recent work has demonstrated a wide variety of ways to observe in detail various senses of progress in science.171 Returning to the topic of evolution, we see that biological evolution produces over time a greater and greater diversity of species, filling more and more ecological niches. That same sort of growth is observed in science, in the form of the evergrowing size of the collection of recipes, as well as in the wider and wider reach of the principles. This way of regarding the progress of science avoids many of the pitfalls of the debate on ‘progress’ sketched above. Coupling that with the Popperian notion of testable theories, we would expect that over time, those theories and practices, that are less well fitted to the world as it is, would be rejected in favor of those that fit better. I began with observations on Roman and Jewish views of the Greeks, seeing Greeks as prone to innovate and debate. Greeks themselves stressed that aspect of their cultural self-understanding, and I argue that by widening Lloyd’s approach to Greek science, and taking into account the persistent Greek tendency for debate and openness, we can explain the growth and decline of Greek science as alike

165 Meier 1978 / 1980 / 1990. 166 Blundell 1986, 165–202. 167 Nietzsche 1886 / 1988 / 1998, 28–29 (1988 ed.). 168 Schutte 1984, 48–53; Babich 1994, 136–146; Poellner 1999; Rehberg 1999. 169 Weber 1919 / 1992, 14, 16, and 20 respectively (= 85, 87, 92 of the 1992 ed.), translated in Owen, Strong, & Livingstone 2004, 11, 13, 16, respectively. Owen and Strong further discuss Weber’s remarks on progress, pp. xxix–xxx, and on meaning, pp. xxx–xxxiv. The speech was given in 1917, and first published in 1919: Weber, ed. Mommsen et al. 1992, 43–46. 170 Kuhn 1962 / 1970 / 1996, 170–173. 171 Niiniluoto 2009.

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due to those social forms and behaviors: openness and debate foster growth through the production of novel theories and practices, and their absence allows decline. The perspectives of Jacobs and Popper, in considering societies as more or less “open”, allow us to see how it is that Greek society would especially promote the growth of science – and how Roman society, especially as their empire became ever more centralized and authoritarian, would stifle science. The three case studies I have presented cover a wide range of scientific endeavor, mathematics, medicine, and mechanics, and could be greatly multiplied. The causal linkage from openness and debate to the flourishing of science is provided by the evolutionary algorithm, in which novel forms of theory and practice are selected for survival so long as they are not refuted. It is of course my hope that the model and hypothesis that I have presented here will itself be tested against the world as it is, whether ancient or later, to determine how well fitted is this theory. I have argued here that this theory can explain a number of observations not otherwise explained, and that it draws together observations into a useful, because productive, framework. The greatest use of this model will be if it can alter the way in which we view science. That can only be determined through open debate, and free inquiry, and the testing of this hypothesis against the historical data. In the end, this theory will survive if and only if it performs more effectively than all those other theories that have been invented from time to time.

Bibliography Texts quoted Aristotle, Phys.: Waterfield, R. 1996. Aristotle: Physics. New York. Archimedes: Heiberg, J. L., & E. S. Stamatis. 1972–1975. Archimedis Opera Omnia. Stuttgart; Mugler, C. 1971. Archimède. Vol. 2. Paris. Diodorus of Sicily: Marsden, E. W. 1969 / 1971. Greek Artillery. 2 vols. Oxford. Ennius, Ann.: Skutsch, O. 1985. The annals of Q. Ennius. Oxford. Euclid, Elem.: Heath, T. L. 1926. The thirteen books of Euclid’s Elements, translated from the text of Heiberg. 2nd ed., 3 vols. Cambridge. FGrHist: Jacoby, F. 1923–1958. Die Fragmente der griechischen Historiker. Berlin. Hero of Alexandria: Marsden, E. W. 1969 / 1971. Greek Artillery. 2 vols. Oxford. Corp. Hipp.: Heiberg, J. L., J. Mewaldt, E. Nachmanson, & H. Schoene 1927. Hippocratis Opera. Leipzig; Littré, É. M. P. 1839–1861. Œuvres complètes d’Hippocrate. Paris. Corp. Hipp., Morb.: Jouanna, J. 1983. Hippocrate v. 10.2: Maladies II. Paris. Corp. Hipp., Aer.: Jouanna, J. 1996. Hippocrate v. 2.2: Airs, Eaux, Lieux. Paris. Corp. Hipp., Morb. sacr.: Jouanna, J. 2003. Hippocrate v. 2.3: La Maladie Sacrée. Paris. Corp. Hipp., Loc. hom.: Craik, E. 1998. Hippocrates: Places in Man. Oxford. Corp. Hipp., Vuln. cap.: Hanson, M. 1999. On head wounds / Hippocrates: edition, translation, and commentary. Berlin.

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P. Edwin Smith: Breasted, J. H. 1930. The Edwin Smith Surgical Papyrus. 2 vols. Chicago. Philo of Byzantium: Marsden, E. W. 1969 / 1971. Greek Artillery. 2 vols. Oxford. Plato, Theaet.: Bostock, D. 1988. Plato’s Theaetetus. Oxford. Polybius: Büttner-Wobst, Th. 1893–1905. Polybii Historiae. 4 vols. Leipzig 1893–1905. Poliorcetics: Wescher, C. 1867. La Poliorcétique des Grecs. Paris. Pre-Socratics: Diels, H., & W. Kranz 1952. Die Fragmente der Vorsokratiker, griechisch und deutsch. 6th ed. Berlin. Simplicius, In Phys.: Diels, H. 1882. Simplicii In Aristotelis Physicorum Libros Quattuor Priores Commentaria. Berlin. Sophocles, Ant.: Jebb, R. C. 1900 / 2004. Sophocles: plays. Antigone. Ed. P. E. Easterling and R. Blondell. London. Trag. Graec. Frag.: Snell, B. & R. Kannicht 1986. Tragicorum Graecorum fragmenta. 2nd ed., vol. 1. Göttingen.

Works quoted Acerbi, F. 2005. “A Reference to Perfect Numbers in Plato’s Theaetetus”. In: Archive for History of Exact Sciences 59, 319–348. Agelarakis, A. P. 2006. “Early Evidence of Cranial Surgical Intervention in Abdera, Greece: A Nexus to On Head Wounds of the Hippocratic Corpus”. In: Mediterranean Archaeology and Archaeometry 6.1, 5–18. Alföldy, G. 1988. The Social History of Rome. Transl. D. Braund and Fr. Pollock. Baltimore. Allen, J. P. 2005. The Art of Medicine in Ancient Egypt. New York. Andrews, J. A. 2000. “Cleon’s Hidden Appeals (Thucydides 3.37–40)”. In: Classical Quarterly, New Series 50, 45–62. Arnott, R., S. Finger, & C. U. M. Smith 2003. Trepanation: discovery, history, theory. Lisse. Astin, A. E. 1978. Cato the Censor. Oxford / New York. Avise, J. C., W. S. Nelson, & H. Sugita 1994. “A Speciational History of «Living Fossils»: Molecular Evolutionary Patterns in Horseshoe Crabs”. In: Evolution 48, 1986–2001. Babich, B. E. 1994. Nietzsche’s Philosophy of Science: Reflecting Science on the Ground of Art and Life. Albany. Babich, B. E., & R. S. Cohen 1999. Nietzsche, Epistemology, and Philosophy of Science = Nietzsche and the Sciences. Vol. 2. Dordrecht. Benardete, S. 1999. Sacred transgressions: a reading of Sophocles’ Antigone. South Bend, IN. Bergson, H. 1932 / 2007. Les Deux Sources de la morale et de la religion (orig. Paris 1932). Transl. R. A. Audra, C. Brereton, & W. Horsfall Carter 1935 / 1954. The two sources of morality and religion (orig. New York 1935). Repr. Notre Dame, IN, 1977. Bichakjian, B. H. 2002. Language in a Darwinian perspective. Frankfurt am Main. Blackmore, S. 2002. “Meme”. In: M. Pagel (ed.), Encyclopedia of Evolution. Oxford. http://www.oxfordreference.com/views/ENTRY.html?sub-view=Main&entry=t169.e264 Blumenberg, H. 1974. “On a Lineage of the Idea of Progress”. Transl. E. B. Ashton. In: Social Research 41, 5–27. Blundell, S. 1986. The Origins of Civilization in Greek and Roman Thought. London. Bowman, A. K., P. Garnsey, & D. Rathbone (eds.) 2000. The High Empire, AD 70–192. Cambridge Ancient History, vol. 11. 2nd ed., Cambridge. Bowman, A. K., & A. Wilson (eds.) 2009. Quantifying the Roman Economy: Methods and Problems. Oxford. Braund, D. C. (ed.) 1988. The Administration of the Roman Empire (241 BC-AD 193). Exeter.

The Name and Nature of Science: Authorship in Social and Evolutionary Context

55

Brawanski, A. 2001. “Die Fälle 1–8 des Papyrus Edwin Smith («Schädelhirntraumafälle»)”. In: Studien zur Altägyptischen Kultur 29, 7–39. Brawanski, A. 2006. “Mittelgesichtsverletzungen in Pap. Smith (Fälle 9–14)”. In: Studien zur Altägyptischen Kultur 35, 43–60. Brun, P. 1994. “Les fortifications d’Hyllarina, Philon de Byzance et Pleistarchos”. In: Revue des Études Anciennes 96, 193–204. Brunner-Traut, E. 1959. “Altägyptische Tiergeschichte und Fabel. Gestalt und Strahlkraft”. In: Saeculum: Jahrbuch für Universalgeschichte 10, 124–185. Burnyeat, M. 1987. “Platonism and Mathematics: A Prelude to Discussion”. In: A. Graeser (ed.), Mathematics and Metaphysics in Aristotle / Mathematik und Metaphysik bei Aristoteles. Bern, 213–240. Campbell, D. T. 1974. “Evolutionary Epistemology”. In: P. A. Schilpp (ed.), The Philosophy of Karl Popper. La Salle, IL, 413–463. Campbell, D. T. 1991. “A Naturalistic Theory of Archaic Moral Orders”. In: Zygon: Journal of Religion and Science 26.1, 91–114. Campbell, L. 1997. American Indian Languages: The Historical Linguistics of Native America. Oxford. Cardauns, B. 1967. “Juden und Spartaner: Zur hellenistisch-jüdischen Literatur”. In: Hermes 95, 317–324. Charlton, W. 1991. “Aristotle’s Potential Infinities”. In: L. Judson (ed.), Aristotle’s Physics: A collection of essays. Oxford, 129–149. Christianidis, J., & A. Demis 2010. “Archimedes’ Quadratures”. In: S. A. Paipetis and M. Ceccarelli (eds.), The Genius of Archimedes – 23 Centuries of Influence on Mathematics, Science and Engineering, Proceedings of an International Conference held at Syracuse, Italy, June 8–10, 2010. Dordrecht, 57–68. Citroni, M. 2003. “I proemi delle Tusculanae e le costruizione di un immagine della tradizione litteraria romana”. In: Citroni, M. (ed.), Memoria e identità: la cultura romana costruisce la sua immagine. Firenze, 149–184. Claus, D. B. 1975. “Aidôs in the Language of Achilles”. In: Transactions of the American Philological Association 105, 13–28. Coico, R., G. Sunshine, & E. Benjamini 2003. Immunology: A Short Course. 5th ed. Hoboken. Croft, W. 2006. “The Relevance of an Evolutionary Model to Historical Linguistics”. In: O. N. Thomsen (ed.), Competing Models of Linguistic Change. Amsterdam, 91–132. Cuomo, S. 2007. Technology and culture in Greek and Roman antiquity. Cambridge. Cziko, G. 1995. Without Miracles: universal selection theory and the second Darwinian revolution. Cambridge, MA. Dawkins, R. 1999. The Extended Phenotype. Oxford. Dennett, D. C. 1995. Darwin’s Dangerous Idea. New York. De Romilly, J. 1966. “Thucydide et l’Idée de Progrès”. In: Annali della Scuola Normale Superiore di Pisa. Classe di lettere, storia e filosofia s. 2, vol. 35, 143–191. Detienne, M. 1967 / 1996. Les Maîtres de Vérité dans la Grèce Archaïque. Paris, 81–105 (“Le procès de laïcisation”). Transl. J. Lloyd. The Masters of Truth in Archaic Greece. New York, 89–106 (“The Process of Secularization”). Dijksterhuis, E. J. 1987. Archimedes: With a new bibliographic essay by Wilbur R. Knorr. Princeton. Dimopoulos, V. G., J. S. Robinson III, & K. N. Fountas 2008. “The Pearls and Pitfalls of Skull Trephination as Described in the Hippocratic Treatise «On Head Wounds»”. In: Journal of the History of the Neurosciences 17.2, 131–140. Dodds, E. R. 1973. “The Ancient Concept of Progress”. In: Dodds, E. R., The Ancient Concept of Progress and other Essays on Greek Literature and Belief. Oxford, 1–25. Dunn, J. D. G. 1999. “Who did Paul Think he was? A Study of Jewish-Christian Identity”. In: New Testament Studies 45, 174–193.

56

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Eck, W. 2000a. “The Growth of Administrative Posts”. In: Bowman, Garnsey, & Rathbone 2000, 238–265. Eck, W. 2000b. “Provincial Administration and Finance”. In: Bowman, Garnsey, & Rathbone 2000, 266–292. Edwards, J. Jr. 1787. Observations on the Language of the Muhhekaneew Indians, in Which the Extent of that Language in North America is Shewn, its Genius is Grammatically Traced, Some of its Peculiarities, and Some Instances of Analogy between that and the Hebrew are Pointed out. New Haven, CT. Eldredge, N., & S. M. Stanley (eds.) 1984. Living fossils. New York. Fabbri, P. F., N. Lonoce, M. Masieri, D. Caramella, M. Valentino & S. Vassallo 2010. “Partial Cranial Trephination by Means of Hippocrates’ τρύπανον (Trypanon) from 5th Century BC Himera (Sicily, Italy)”. In: International Journal of Osteoarchaeology 20 (http://dx.doi.org/10. 1002/oa.1197). Ferrary, J.-L. 1977. “Le discours de Philus (Cicéron, De Republica, III, 8–31) et la philosophie de Carnéade”. In: Revue des Études Latines 55, 128–156. Foley, V., W. Soedel, J. Turner, & B. Wilhoite 1982. “The Origin of Gearing”. In: History of Technology 7, 101–129. Freud, S. 1899/1913/2001. Die Traumdeutung (Leipzig & Vienna 1899); English transl. A. A. Brill as The Interpretation of Dreams (New York 1913); ed. A. Mitscherlich, A. Richards, & J. Strachey (Frankfurt am Main 1972, repr. 2001). García, C. E. 2006. Popper’s theory of science: an apologia. London. García de la Sienra, A. 1983. “El Metodo de Arquimedes”. In: Dianoia 29, 53–80. Gess, R. W., M. I. Coates, & B. S. Rubidge 2006. “A lamprey from the Devonian period of South Africa”. In: Nature 443, 981–984. Gil, L. 2007. “Terror e imperialismo: el caso de Mitilene”. In: Cuadernos de filología clásica: Estudios griegos e indoeuropeos 17, 163–181. Görler, W. 1974. Untersuchungen zu Ciceros Philosophie. Heidelberg, 154–171. Gomme, A. W. 1956 / 1962. A Historical Commentary on Thucydides. Vol. 1. Oxford. Gong, W., C. Chen, C. Dobeš, C.-X. Fu, & M. A. Koch 2008. “Phylogeography of a living fossil: Pleistocene glaciations forced Ginkgo biloba L. (Ginkgoaceae) into two refuge areas in China with limited subsequent postglacial expansion”. In: Molecular Phylogenetics and Evolution 48, 1094–1105. Gotter, U. 2003. “Ontologie versus Exemplum: Griechische Philosophie als politisches Argument in der späten römischen Republik”. In: K. Piepenbrink (ed.), Philosophie und Lebenswelt in der Antike. Darmstadt, 165–185. Grant, M. 1994. The Antonines: The Roman Empire in Transition. London. Greenhill, S. J., Q. D. Atkinson, A. Meade, & R. D. Gray 2010. “The shape and tempo of language evolution”. In: Proceedings of the Royal Society B: Biological Sciences 277, 2443–2450. Griffin, M. 2000. “Nerva to Hadrian”. In: Bowman, Garnsey, & Rathbone 2000, 84–131. Gruen, E. 1992. Culture and National Identity in Republican Rome. Ithaca, NY. Guidotti, T. L. 2005. “Ethics and Skeptics: What Lies Behind Ethical Codes in Occupational Health”. In: Journal of Occupational and Environmental Medicine 47, 168–175. Guite, H. 1962. “Cicero’s Attitude to the Greeks”. In: Greece and Rome 9, 142–159. Guthrie, W. K. C. 1969. A history of Greek philosophy v. 3: The Fifth Century Enlightenment. Cambridge. Hallpike, C. R. 1979. The Foundations of Primitive Thought. Oxford. Hawke, J. 2008. “Number and Numeracy in Early Greek Literature”. In: Syllecta Classica 19, 1–76. Hay, J. M., S. Subramanian, C. D. Millar, E. Mohandesan, & D. M. Lambert 2008. “Rapid molecular evolution in a living fossil”. In: Trends in Genetics 24, 106–109. Hengel, M. 1988. Judentum und Hellenismus. 3rd ed. Tübingen.

The Name and Nature of Science: Authorship in Social and Evolutionary Context

57

Hornblower, S. 1987. Thucydides. Baltimore. Hull, D. L. 1988. Science as a process: an evolutionary account of the social and conceptual development of science. Chicago. Hunter, V. 1982. Past and Process in Herodotus and Thucydides. Princeton. Iversen, E. 1953. “Wounds in the Head in egyptian and hippocratic Medicine”. In: Studia orientalia Ioanni Pedersen septuagenario A.D. VII id. nov. anno MCMLIII a collegis discipulis amicis dicata. Copenhagen, 163–171. Jacobs, J. 1992. Systems of Survival. New York. Janeway, C. A. Jr. 1993. “How the Immune System Recognizes Invaders”. In: Scientific American 269.3, 73–79. Jehne, M. 1999. “Zum Spannungsverhältnis zwischen mos maiorum und griechischer Kultur in zweiten Jahrhundert v. Chr.”. In: Vogt-Spira & Rommel 1999, 115–134. Jensen, H. S., L. M. Richter, & M. T. Vendelø 2003. The Evolution of Scientific Knowledge. Cheltenham (UK). Jerne, N. K. 1955. “The natural-selection theory of antibody formation”. In: Proceedings of the National Academy of Sciences 41, 849–857. Jones, A. H. M. 1940 The Greek City from Alexander to Justinian. Oxford. Jones, W. 1786 / 1970. “The Third Anniversary Discourse”. In: Asiatic Researches (Feb 2nd). Ed. P. J. Marshall. In: British Discovery of Hinduism in the Eighteenth Century. Cambridge, 246–261. Jongmann, W. 2009. “Archaeology, Demography, and Roman Economic Growth”. In: Bowman & Wilson 2009, 115–126. Kammerzell, F. 1995. “Vom Streit zwischen Leib und Kopf”. In O. Kaiser and R. Borger (ed.), Texte aus der Umwelt des Alten Testaments 3.5: Mythen und Epen 3. Gütersloh, 951–954. Karlsson, L. 1994. “Thoughts about Fortifications in Caria from Maussollos to Demetrios Poliorketes”. In: Revue des Études Anciennes 96, 141–153. Katzoff, R. 1985. “Jonathan and Late Sparta”. In: American Journal of Philology 106, 485–489. Kaufman, M. H., D. Whitaker & J. McTavish 1997. “Differential Diagnosis of Holes in the Calvarium: Application of Modern Clinical Data to Palaeopathology”. In: Journal of Archaeological Science 24, 193–218. Keller, A. G. 1915 / 1931. Societal Evolution: A Study of the Evolutionary Basis of the Science of Society. Rev. ed. New Haven. Keyser, P. T. 1990. “Alchemy in the Ancient World: from Science to Magic”. In: Illinois Classical Studies 15, 353–378. Keyser, P. T. 1994. “The Use of Artillery by Philip II and Alexander the Great”. In: Ancient World 25.1, 27–59. Keyser, P. T. 1995/6. “Greco-Roman Alchemy and Coins of Imitation Silver”. In: American Journal of Numismatics 7/8, 209–234, plates 28–32. Keyser, P. T. 1997. “Science and Magic in Galen’s Recipes (Sympathy and Efficacy)”. In: A. Debru (ed.), Galen on Pharmacology: Philosophy, History, and Medicine, Leiden, 175–198. Keyser, P. T. 2002. “Introduction”. In: G. L. Irby-Massie and P. T. Keyser, Greek Science. London, 1–17. Keyser, P. T. 2008a. “(Un)Natural Accounts in Herodotos and Thucydides”. In: Mouseion s. 3. Vol. 6, 323–351. Keyser, P. T. 2008b. “Time-Line”. In: Keyser & Irby-Massie 2008, 937–988. Keyser, P. T. 2010a. “Science”. In: M. Gagarin (ed.), The Oxford Encyclopedia of Ancient Greece and Rome. Vol. 6. Oxford, 229–234. Keyser, P. T. 2010b. “The Name and Nature of Science: Insights from Jane Jacobs and GrecoRoman Society”. In: International Journal of Science in Society 1.4, 65–84. Keyser, P. T. 2010c. “Science”. In: A. Barchiesi & W. Scheidel (eds.), Oxford Handbook of Roman Studies. Oxford, 859–881.

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Keyser, P. T., & G. L. Irby-Massie (eds.) 2008. Encyclopedia of Ancient Natural Scientists. London. Kirk, G. S., J. E. Raven, & M. Schofield 1983. The Presocratic Philosophers: A Critical History with a Selection of Texts. 2nd ed. Cambridge. Kitcher, P. S. 2001. Science, Truth, and Democracy. Oxford. Knorr, W. R. 1982 “Infinity and Continuity: The Interaction of Mathematics and Philosophy in Antiquity”. In: N. Kretzmann (ed.), Infinity and Continuity in Ancient and Medieval Thought. Ithaca, NY, 112–145. Knorr, W. R. 1996. “The Method of Indivisibles in Ancient Geometry”. In: Ronald Calinger (ed.), Vita Mathematica: historical research and integration with teaching. Providence, RI, 67–86. Knudsen, T. 2003. “A neo-Darwinian model of science”. In: Jensen, Richter, & Vendelø 2003, 79– 119. Kouremenos, T. 1995. Aristotle on Mathematical Infinity. Stuttgart. Kuhn, T. S. 1962 / 1970 / 1996. The Structure of Scientific Revolutions. 1st / 2nd / 3rd ed. Chicago. Langholf, V. 1990. Medical theories in Hippocrates. Early texts and the “Epidemics”. Berlin. Lesher, J. H. 2010. “Xenophanes”. In: E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Fall 2010 Edition). URL = http://plato.stanford.edu/archives/fall2010/entries/xenophanes/. Lendon, J. E. 2005. Soldiers and Ghosts: a history of battle in classical antiquity. New Haven. Lendon, J. E. 2010. Song of wrath: the Peloponnesian War begins. New York. Lewis, M. J. T. 1999. “When was Biton?” In: Mnemosyne 52, 159–168. Lewontin, R. C. 1970. “The Units of Selection”. In: Annual Review of Ecology and Systematics 1, 1–18. Liston, M. A. & L. P. Day 2009. “It Does Take a Brain Surgeon: A Successful Trepanation from Kavousi, Crete”. In: L. A. Schepartz, S. C. Fox, & C. Bourbou (eds.), New directions in the skeletal biology of Greece. Princeton, 57–73. Lloyd, G. E. R. 1979. Magic, Reason, and Experience. Cambridge. Lloyd, G. E. R. 1987. The Revolutions of Wisdom: Studies in the Claims and Practice of Ancient Greek Science. Berkeley, 50–108. Lloyd, G. E. R. 1997. “The Comparative History of Pre-Modern Science: The Pitfalls and the Prizes”. In: Studies in History and Philosophy of Science A 28, 363–368. Loprieno, A. 1988. Topos und Mimesis: zum Ausländer in der ägyptischen Literatur. Wiesbaden. McKirahan, R. D. 1999. “Zeno”. In: A. A. Long (ed.), Cambridge Companion to Early Greek Philosophy. Cambridge, 134–158. McMullin, E. 1985. “Openness and Secrecy in Science: Some Notes on Early History”. In: Science, Technology, & Human Values 10.2, 14–23. McNeal, R. A. 1986. “Protagoras the Historian”. In: History and Theory 25, 299–318. Manuwald, B. 1996. “Platon oder Protagoras? Zur großen Rede des Protagoras (Plat. Prot. 320C8– 328 D2)”. In: C. Mueller-Goldingen & K. Sier (eds.), ΛΗΝΑΙΚΑ: Festschrift Carl Werner Müller. Stuttgart. Marx, K., & Fr. Engels 1848/1976. Manifest der kommunistischen Partei (London 1848); English transl. in Karl Marx and Friedrich Engels: Collected Works 6 (New York 1976) 477–517; ed. Thomas Kuczynski (Trier 1995). Meier, C. 1978 / 1980 / 1990. “Ein antikes Äquivalent des Fortschrittsgedankens: Das «KönnensBewußtsein» des 5.Jahrhunderts v. Chr.”. In: Historische Zeitschrift 226, 265–316. Repr. in: Die Entstehung des Politischen bei den Griechen, Frankfurt am Main, 435–499. Transl. D. McLintock. The Greek Discovery of Politics. Cambridge, MA, 186–221, 286–300. Momigliano, A. 1944. “Sea-Power in Greek Thought”. In: Classical Review 58, 1–7. Müller, G. 1967. Sophokles. Antigone. Heidelberg. Mueller, I. 1991. Philosophy of Mathematics and Deductive Structure in Euclid’s Elements. Cambridge, MA. Mufwene, S. S. 2008. Language Evolution: Contact, Competition and Change. London.

The Name and Nature of Science: Authorship in Social and Evolutionary Context

59

Nerlich, A. G., A. Zink, U. Szeimies, H. G. Hagedorn, & F. W. Rösing 2003. “Perforating Skull Trauma in Ancient Egypt and Evidence for Early Neurosurgical Therapy”. In: Arnott, Finger, & Smith 2003, 191–202. Netz, R., K. Saito, & N. Tchernetska 2001 / 2002. “A new reading of Method Proposition 14: preliminary evidence from the Archimedes palimpsest”. In: SCIAMVS 2, 9–30 and 3, 109–126. Nietzsche, F. W. 1886 / 1988 / 1998. Jenseits von Gut und Böse: Vorspiel einer Philosophie der Zukunft. Leipzig. Ed. G. Colli & M. Montinari, Sämtliche Werke: kritische Studienausgabe. 2nd ed., vol. 5. Berlin, 9–243. Transl. M. Faber. Beyond good and evil: prelude to a philosophy of the future. Oxford. Niiniluoto, I.1993. “The Aim and Structure of Applied Research”. In: Erkenntnis 38, 1–21. Niiniluoto, I. 2009. “Scientific Progress”. In: E. N. Zalta (ed.), The Stanford Encyclopedia of Philosophy (Spring 2009 Edition). URL = http://plato.stanford.edu/archives/spr2009/entries/ scientific-progress/ Nunn, J. F. 1996. Ancient Egyptian Medicine. Norman, OK. Ober, J. 2008. Democracy and Knowledge: Innovation and Learning in Classical Athens. Princeton. Oesterdiekhoff, G. W. 1992. Traditonales Denken und Modernisierung: Jean Piaget und die Theorie der sozialen Evolution. Opladen. O’Hara, R. J. 1994. “Evolutionary History and the Species Problem”. In: American Zoologist 34, 12–22. Oleson, J. P. 1984. Greek and Roman mechanical water-lifting devices: the history of a technology. Toronto. Ong, W. J. 1982. Orality and Literacy: the technologizing of the word. London. Repr. London 1988. Owen, D., & T. B. Strong (eds.), R. Livingstone (transl.) 2004. Max Weber: The Vocation Lectures. Indianapolis. Panourias, I. G., P. K. Skiadas, D. E. Sakas, & S. G. Marketos 2005. “Hippocrates: A Pioneer In The Treatment Of Head Injuries”. In: Neurosurgery 57, 181–189. Pagel, M. 2009. “Human Language as a Culturally Transmitted Replicator”. In: Nature Reviews: Genetics 10, 405–415. Parker, A. J. 1992. Ancient Shipwrecks of the Mediterranean and the Roman Provinces. Oxford. Peakall, R., D. Ebert, L. J. Scott, P. F. Meagher, & C. A. Offord 2003. “Comparative genetic study confirms exceptionally low genetic variation in the ancient and endangered relictual conifer, Wollemia nobilis (Araucariaceae)”. In: Molecular Ecology 12, 2331–2343. Pendrick, G. J. 2001. Antiphon the Sophist. Cambridge. Perkins, P. 2009. “«To the Jews as a Jew» (1 Cor 9:20): Paul and Jewish Identity”. In: Studies in Christian-Jewish Relations 4.1 (http://escholarship.bc.edu/scjr/vol4). Poellner, P. 1999. “Causation and Force in Nietzsche”. In: Babich & Cohen 1999, 287–297. Pope, M. 1988. “Thucydides and Democracy”. In: Historia: Zeitschrift für Alte Geschichte 37, 276–296. Popper, K. 1945 / 1963. The Open Society and its Enemies. 4th ed. Princeton (orig. London 1945). Popper, K. 1979. Objective Knowledge: An Evolutionary Approach. Rev. ed. Oxford. Porter, S. E. 1999. The Paul of Acts. Tübingen. Poser, W. J. & L. Campbell 1992. “Indo-European Practice and Historical Methodology”. In: Proceedings of the annual meeting of the Berkeley Linguistics Society 18, 214–236. Pouyaud, L., S. Wirjoatmodjo, I. Rachmatika, A. Tjakrawidjaja, R. Hadiaty, & W. Hadie 1999. “Une nouvelle espèce de cœlacanthe. Preuves génétiques et morphologiques”. In: Comptes Rendus de l’Académie des Sciences, Série III: Sciences de la vie 322, 261–267. Price, D. d. S. 1975. Science Since Babylon. New Haven. Raaflaub, K. 1985. Die Entdeckung der Freiheit: Zur historischen Semantik und Gesellschaftsgeschichte eines politischen Grundbegriffes der Griechen. München.

60

Paul T. Keyser

Raaflaub, K. 1989. “Contemporary Perceptions of Democracy in Fifth-Century Athens”. In: Classica et Mediaevalia 40, 33–70. Raaflaub, K. 2004. The discovery of freedom in ancient Greece. Chicago. Raaflaub, K. 2006. “Thucydides on Democracy and Oligarchy”. In: A. Rengakos & A. Tsakmakis (eds.), Brill’s Companion to Thucydides. Leiden, 189–222. Rachlis, M., & C. Kushner 1994. Strong Medicine: How to Save Canada’s Health Care System. Toronto. Rehberg, A. 1999. “Nietzsche’s Transvaluation of Causality”. In: Babich & Cohen 1999, 279–286. Rihll, T. E. 2007. The Catapult: a history. Yardley, PA. Ritt, N. 2004. Selfish Sounds and Linguistic Evolution: A Darwinian Approach to Language Change. Cambridge. Rocca, J. 2003. “Galen and the Uses of Trepanation”. In Arnott, Finger, & Smith 2003, 253–272. Roman, D., & Y. Roman 1994. Rome, l’identité romaine et la culture hellénistique (218–31 avant J.-C.). Paris. Sacks, K. S. 1990. Diodorus Siculus and the First Century. Princeton. Ste. Croix, G. E. M. d. 1981. The Class Struggle in the Ancient Greek World from the Archaic Age to the Arab Conquests. Ithaca. Sanderson, S. K. 1999. Social Transformations: A General Theory of Historical Development. Oxford, 317–332. Schaerer, R. 1930. ΕΠΙΣΤΗΜΗ et ΤΕΧΝΗ: Étude sur les Notions de Connaissance et d’Art d’Homère à Platon. Macon. Schäublin, C. 1982. “Josephus und die Griechen”. In: Hermes 110, 316–341. Schuhl, P.-M. 1949. Essai sur la formation de la pensée Grecque. 2nd ed. Paris. Schutte, O. 1984. Beyond Nihilism: Nietzsche without Masks. Chicago. Seide, R. 1981. “Zum Problem des geometrischen Atomismus bei Demokrit”. In: Hermes 109, 265–280. Serb, J. M., & D. J. Eernisse 2008. “Charting Evolution’s Trajectory: Using Molluscan Eye Diversity to Understand Parallel and Convergent Evolution”. In: Evolution: Education and Outreach 1, 439–447. Smith, A. 1976. An Inquiry into the Nature and Causes of the Wealth of Nations. Ed. R. H. Campbell, A. S. Skinner, & W. B. Todd. Oxford (original London 1776). Spoerri, W. 1959. Späthellenistische Berichte über Welt, Kultur, und Götter. Basel. von Staden, H. 1989. Herophilus: The art of medicine in early Alexandria. Cambridge. Stamatis, E. S. 1963. “Genikeusis enos theorēmatos tou Archimēdous”. In: Platon 15, 165–168. Stein, R. 2004. “Roman wooden force pumps: A case-study in innovation”. In: Journal of Roman Archaeology 17, 221–250. Stephanopoulos, Th. K. 1988. “Tragica II”. In: Zeitschrift für Papyrologie und Epigraphik 75, 3–38. Thomas, R. 1997. “Ethnography, Proof and Argument in Herodotus’ Histories”. In: Proceedings of the Cambridge Philological Society 43, 128–148. Thomas, R. 2000. Herodotus in Context: ethnography, science and the art of persuasion. Cambridge. Toulmin, S. E. 1967. “The Evolutionary Development of Natural Science”. In: American Scientist 55, 456–471. Urban, R. 1983. “Die Griechen aus der Sicht des Advokaten, Politikers und Privatmannes Cicero”. In: Heinz Heinen (ed.), Althistorische Studien: Hermann Bengtson zum 70. Geburtstag dargebracht von Kollegen und Schülern. Wiesbaden, 157–173. Vernant, J.-P. 1957 / 1965 / 1983. “Du mythe à la raison: La formation de la pensée positive dans la Grèce archaïque”. In: Annales: Économies, Sociétés, Civilisations 12, 183–206. Repr. in: Mythe et Pensée chez les Grecs: Études de psychologie historique. Paris, 285–314. Transl. in: Myth and Thought among the Greeks. London, 343–374 (“The Formation of Positivist Thought in Archaic Greece”). French repr. 1985, 373–402.

The Name and Nature of Science: Authorship in Social and Evolutionary Context

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Vernant, J.-P. 1962 / 1982. Origines de la Pensée Grecque. Paris. Transl. The Origins of Greek Thought. Ithaca, NY. Vervaet, Fr. J. 2009. “The Reappearance of the Supra-Provincial Commands in the late second and early third centuries C.E.: Constitutional and Historical Considerations”. In: Bowman & Wilson 2009, 125–139. Vogt-Spira, G., & B. Rommel (eds.) 1999. Rezeption und Identität: die kulturelle Auseinandersetzung Roms mit Griechenland als europäisches Paradigma. Stuttgart. Weber, M. 1919 / 1992. Wissenschaft als Beruf. München. Ed. W. J. Mommsen, W. Schluchter, & B. Morgenbrod, Max Weber: Studienausgabe. Vol. 1.17. Tübingen, 71–111. Westendorf, W. 1999. Handbuch der altägyptischen Medizin. 2 vols. Leiden. White, M. J. 1992. The continuous and the discrete: ancient physical theories from a contemporary perspective. Oxford. Wikander, Ö. (ed.) 2000. Handbook of ancient water technology. Leiden. Wilkinson, T. A. H. 2000. “What a King Is This: Narmer and the Concept of the Ruler”. In: Journal of Egyptian Archaeology 86, 23–32. Wilson, A. 2002. “Machines, Power and the Ancient Economy”. In: Journal of Roman Studies 92, 1–32. Wilson, A. 2009. “Approaches to Quantifying Roman Trade”. In: Bowman & Wilson 2009, 213–249. Winter, F. E. 1994. “Problems of Tradition and Innovation in Greek Fortifications in Asia Minor, Late Fifth to Third century B.C.”. In: Revue des Études Anciennes 96, 29–52. Wolter, M. 2008. Das Lukasevangelium. Tübingen. Ziman, J. M. 1968. Public Knowledge: An Essay Concerning the Social Dimensions of Science. Cambridge. Ziman, J. M. 2000. Technological Innovation as an Evolutionary Process. Cambridge. Zimmermann, B. 1999. “Cicero und die Griechen”. In: Vogt-Spira & Rommel 1999, 240–248. Zuiderhoek, A. 2009. “Government Centralization in Late Second and Third Century A.D. Asia Minor: A Working Hypothesis”. In: Classical World 103.1, 39–51.

Karine Chemla

Ancient Writings, Modern Conceptions of Authorship. Reflections on Some Historical Processes That Shaped the Oldest Extant Mathematical Sources from Ancient China Abstract: The oldest extant mathematical writing in Chinese handed down through the written tradition is the book The Nine Chapters on Mathematical Procedures, probably compiled in the 1st century . Two facts about it are puzzling. First, there is no material evidence that the book existed as separate from later commentary, especially the one of Liu Hui, completed in 263, and the annotations compiled by Li Chunfeng, completed in 656. Second, the earliest testimony attributes its compilation to two authors who lived more than a century apart. The first part of this paper is an attempt to account at least partly for these facts. I show that the scriptural act that produced The Nine Chapters was not that of writing, but that of editing. I suggest that its early editors conceived of the text as a Canon, the text of which had been damaged through transmission. In their view, editing was the act appropriate to restore the scripture to its original state. The text of the medical Canon, the Internal Classic of the Yellow Emperor, provides a parallel. As a result, for the book The Nine Chapters as we have it today, it may be anachronistic to look for an author. This result invites comparison with Greek mathematical texts such as Euclid’s Elements or Apollonius’ Conica. In a second part, I argue that the 7th century commentary testifies to a shift in the conception of authorship and consequently in the way of handling writings of the past in the editorial work.

To the dear memory of Barbara Bray, whose generosity will remain with me forever

The oldest writing in Chinese devoted to mathematics that has been handed down through the written tradition is the book The Nine Chapters on mathematical procedures. This book, whose title I shall abbreviate below as The Nine Chapters, has probably reached the form in which we can read it today in the first century .1 In the 20th century, the book has been the object of much historical research and 1 This is the thesis for which I argue in my introduction to chapter 6, in Chemla & Guo Shuchun 2004, 475–478. Guo Shuchun, in Chapter B of the same book, presents various theses about the datation of the book and argues in favor of dating the completion of The Nine Chapters to the first century . Compare Chemla & Guo Shuchun 2004, 43–46.

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was translated into several foreign languages.2 Given the fact that it was handed down without the name of any author attached to it, historians have regularly discussed the question of its plausible author(s). One of the issues that this chapter aims at addressing is to wonder whether this is a meaningful question. Two facts will be essential for our discussion. First, in fact, there is no ancient material evidence available today that attests to the existence of the book as such. What I mean by this statement is simple: all the ancient editions on the basis of which we know the content of The Nine Chapters include the commentary on it completed by Liu Hui in 263 as well as the annotations compiled under the supervision of Li Chunfeng and presented to the throne in 656. I have presented elsewhere historical evidence that shows the cohesion that these three layers of text possessed in the eyes of Chinese actors of the past (Chemla 2010). Somehow, as far as our material evidence goes, the book The Nine Chapters as a writing standing on its own is an artifact which may have been a fiction created by historians in the 19th century.3 What is important for us here is that these two layers of commentary contain evidence regarding how, in the eyes of the earliest readers that we can observe, the text of The Nine Chapters was produced and which attitudes these early readers reveal vis-à-vis the book. It is precisely in the earliest of these two commentaries that we can read the second fact that will be of interest for our discussion. The earliest testimony available regarding those who took part in the shaping of The Nine Chapters itself, namely the preface of Liu Hui’s commentary, attributes the composition of the book to two scholars who lived more than a century apart from each other. The question on which we focus, that is, whether it makes sense to ask who were the

2 The first translation of The Nine Chapters ever was the translation into Russian, in Biérëzkina 1957. It was the basis for the translation into German: Vogel 1968. Kawahara Hideki 川原秀城 1980 contains a translation into Japanese; Shen Kangshen, Crossley & Lun 1999 a translation into English; and Chemla & Guo Shuchun 2004a translation into French. Several translations into modern Chinese also appeared since 1990: Bai Shangshu 白尚恕 1990; Shen Kangshen 沈康身 1997; Guo Shuchun 郭書春 1998; Li Jimin 李繼閔 1998. These translations reflect the intense research activity that developed since the 1950s on that book. I refer the reader to their bibliographies for a more complete overview of the publications on that topic. 3 If we except the translations into Russian and German mentioned in the preceding footnote, all the other translations also provide the texts of commentaries. The translation into Japanese extends to Liu Hui’s commentary whereas all the other translations provide a translation of the two layers of commentaries with which The Nine Chapters was handed down. Li Jimin 李繼閔 1993, Chemla & Guo Shuchun 2004 contain a critical edition of the book and its two commentaries. Other critical editions by Guo Shuchun were published in relation to the joint project that was concluded by the publication of Chemla & Guo Shuchun 2004. In what follows, we shall refer to the commentary composed under Li Chunfeng’s supervision as “Li Chunfeng’s commentary”. This commentary was in fact carried out within the framework of a larger project, that of editing and commenting upon a set of Ten Classics of Mathematics. The Nine Chapters was one of them. More on this later. In recent years, two critical editions of the Ten Classics of Mathematics appeared: Qian Baocong 錢寶琮 1963; Guo Shuchun 郭書春 and Liu Dun 劉鈍 1998.

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authors of The Nine Chapters, is thus connected to a second question. How can we interpret the fact that the production of the book was a process that lasted more than a century? I shall deal with these questions in two parts. In a first part, I shall show that for Liu Hui, the third century commentator, the scriptural act that shaped The Nine Chapters was not that of ‘authoring’, but rather that of ‘editing’. The two scholars to whom Liu Hui attributes the shaping of The Nine Chapters as he inherits it are thus ‘editors’ who, in turn, worked on editing the text on the basis of earlier documents. This fact explains why they could live a century apart from each other. We shall see that Liu Hui seems to conceive of his own work on The Nine Chapters as carrying on the editing further. In doing so, he describes how editing was done. Moreover, he testifies to the connection between editing and commenting upon the book. At the end of this first part, our suggestion will be that for someone like Liu Hui, the question that makes sense is not so much that of determining the author as it is that of naming the ‘editors’ of The Nine Chapters. In correlation with this approach, the text of the book is perceived as having to be restored on the basis of sources, according to criteria and through operations on each of which Liu Hui sheds light. The second part of this chapter argues that the attitude towards earlier texts demonstrated by the seventh-century commentary betrays a radical shift. The received version of both The Nine Chapters and Liu Hui’s commentary are at the time treated as historical documents and given to read as such in the new edition. When Li Chunfeng has doubts about the received texts, in that edition he expresses them in his subcommentary, without altering the text as he sees it in his sources. His commentary provides evidence for this new attitude. This thesis for which I shall argue runs counter to a general opinion, which holds that the group of scholars working under Li Chunfeng’s supervision modified the text.4 As a consequence of a treatment of historical documents different in the seventh century from what it was in Liu Hui’s time, Liu Hui is turned into the ‘author’ of what for him was part of his editing of The Nine Chapters. One could argue that it was in the seventh

4 This opinion was for instance expressed in Wagner 1978, 212. In the conclusion of his excellent paper, Donald Wagner suggests: “There were numerous other commentaries (i.e., other than Liu Hui) available to Li Chunfeng when he compiled his edition, and it would be logical for him to include all of these which were of high quality. In particular there is good reason to believe that Tsu Ch’ung-chih wrote a commentary, and that this was included in Li Chunfeng’s edition.” I shall come back to this point in conclusion. In an essay review on Chemla & Guo Shuchun 2004, Volkov 2010, 282 writes: “It is generally assumed that all the parts of the received commentary not signed by Li Chunfeng and his team were authored by the elusive mathematician of the third century.” By the latter clause, he means Liu Hui. At the end of this remark, Volkov adds in footnote 6: “The scale and nature of the emendations done by Li Chunfeng’s team remains unknown.” On p. 298, Volkov comes back again to the question of “the scope and the nature of the editorial work done by Li Chunfeng and his team”. In what follows, I shall suggest conclusions on that point, on the basis of the evidence discussed.

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century, in Li Chunfeng’s edition of the Ten Classics of Mathematics, that Liu Hui became an author, one of the very first ‘authors’ in the history of mathematics written in Chinese.

1 The book as the product of edition and not of authorship The third-century commentator Liu Hui’s preface is the earliest extant document in which we can find names attached to the making of The Nine Chapters as a book. More generally, in this text, Liu Hui describes his view of the emergence of mathematical knowledge within a wider cosmogonical scheme. The scheme is taken from a key passage of the canonical literature, the “Great commentary” of the Yijing (Book of changes). This passage sketches an account of how the main cultural institutions came into being in Antiquity. Liu Hui modifies the quotation, in particular by inserting mathematics in the picture. At the end of this outline, Liu Hui evokes the process whereby mathematical knowledge took the shape of The Nine Chapters. Let us read this opening section of his preface:5 In times past there was Baoxi, who, first, drew the eight trigrams to enter into communication with the capacities of clairvoyance and illumination, to classify the essentials of the myriad things, and then created the procedure of the multiplication table so that it be in concordance with the mutations of the six lines (of the hexagrams). Huangdi metamorphosed them [by working at the level of] the unfathomable, increased [their extension] by elongating them, and hence established the structure of the calendar, tuned the musical tubes, and used them to inquire into the source of the Way (dao). Hence the essential and minute qi of the two exemplars and of the four models could model themselves on them. Records tell that Li Shou created mathematics6 (…). It is only when the Duke of Zhou established the Rites that [we know that] the nine parts of mathematics existed. The development (liu) of these nine parts is precisely The Nine Chapters.

5 In Chemla & Guo Shuchun 2004, 126–129, the reader can find a critical edition and a translation into French of the whole preface. For detailed explanations of the text and the interpretation for which I opt, making explicit references to which Liu Hui alludes, see my footnotes to the translation in ibid., 747–759. I cannot enter into any detail here. Chemla 2008a analyzes the vision of antiquity sketched here and the part granted to mathematics in this context. 6 Li Shou is given by late sources to have been a minister of the first legendary Emperor Huangdi and to have created mathematics. When in the next sentence quoted, Liu Hui mentions the Duke of Zhou and the differentiation of mathematics into nine branches, his account arrives to the time of history and the foundation of Zhou dynasty in the 11th century .

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Formerly, the cruel Qin burnt the books.7 The procedures of the canon got scattered and damaged. After that time, the Bei Ping Marquis Zhang Cang8 and the Assistant of the Grand Minister of Agriculture Geng Shouchang9 both acquired a universal reputation for their excellence in mathematics. On the basis of scraps of the old text (wen) that were handed down, Zhang Cang and others made both excisions (shan) and completions (to restore the damaged text of The Nine Chapters). (Chemla & Guo 2004, 126; my emphasis)

Without entering into all details, what do we learn from this opening section of Liu Hui’s preface in relation to the issue of authorship? For Liu Hui, mathematical knowledge appears in the earliest antiquity, in parallel with the gradual creation by the Sages of the most fundamental cultural artifacts, that is, the trigrams, the hexagrams, the structure of the calendar, the musical tubes and so on. The passage of the “Great commentary” that Liu Hui evokes here explains how most common cultural artifacts were later on progressively introduced by the Sages who had taken the hexagrams as models to carry out these tasks. In Liu Hui’s mind, moreover, mathematical knowledge appears as the result of a process of unfolding that starts from the “multiplication table”. Deriving from that root, mathematics was created as an undifferentiated whole by a Minister of the first legendary Emperor Huangdi, and it later received its structuring into “nine branches”, at the time when the cultural hero whose name is associated with the establishment of the Zhou dynasty in the 11th century, the Duke of Zhou, was active. It is this structure of mathematics that The Nine Chapters embodies. More precisely, the book appeared as a development of these “nine parts of mathematics”. To sum up, mathematical knowledge is the creation of Sages. Accordingly, the book which grew out of this process of structuring with respect to mathematics, The Nine Chapters, was later on to be perceived as a ‘classic’ (jing). We shall come back to this characterization. Note that up to this point in Liu Hui’s account, nobody is mentioned as the author of the book. Even more importantly, the book is not given as produced by an act of writing, the question of its author in a sense

7 Liu Hui attributes to the burning of books ordered by the first Emperor who unified the Chinese empire in 221 , Qin Shihuangdi, the interruption of what he presents as an unproblematic transmission of the text of The Nine Chapters, until this point. According to the historical records, the Emperor’s aim in doing so was to get rid of writings that could offer a basis to criticize his rule, compare Bodde 1986, 69–70. 8 Zhang Cang (ca 250 −152 ) was a civil servant who held quite important positions in the administration of the Qin Empire and then the Han Empire since its beginnings. His domains of expertise included mathematics, calendar making, harmonics, bookkeeping, management of finance and exegesis of some canons. See Guo Shuchun, chapter B, in Chemla & Guo Shuchun 2004, 54. 9 Geng Shouchang was a civil servant active in the years 57–49. Like Zhang Cang, but, in the first century , he contributed to the administration of finance and to settling astronomical questions. See Guo Shuchun, chapter B, in ibid., 54–55. A translation of sources documenting his activities in the administration is given in Swann 1950, 192–196.

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not appearing to be meaningful. The Nine Chapters emerges somehow at the end of a global process of generation of all the cultural artifacts given by Sages to humans. In the story recounted by Liu Hui, it is only later that human actors intervene in relation to the book. They occur after a disruption in the process of transmission of the book. Liu Hui attributes this break to a major cultural event: the burning of the books by the first emperor Qin. The point is not here to wonder whether Liu Hui is right or not when he believes that The Nine Chapters suffered from this destruction. Let us simply notice that in asserting the fact, he discloses his understanding that the mathematical canon was associated with a kind of scholarship which the Qin Emperor attempted to eradicate. What matters more for us is that for Liu Hui it is in relation to the problem of having access to a correct and complete version of The Nine Chapters that he feels the need to mention the names of two scholars in the history of the book. Zhang Cang, before his death in 152 , was a high official in the Qin and Han administrations, whereas historical records mention Geng Shouchang’s activities around 54 , especially for the management of grains in the Empire. Both were well known for their excellence in mathematics, a fact that Liu Hui recalls in his preface, before explaining how they both undertook to ‘restore’ the text of The Nine Chapters. It appears at this point that The Nine Chapters as the book he had in his hands was for Liu Hui produced by an act of ‘editing’. The text of The Nine Chapters from high Antiquity was no longer available and it was only through attempts at ‘restoring’ it that ‘editors’, among whom Liu Hui mentions Zhang Cang and Geng Shouchang, were able to shape an access to it. Such is the scriptural act that, according to Liu Hui’s account, yields the text. It is characterized by the fact of being a scriptural act that calls for regular revision. Such a thesis regarding the textual practices linked to the making of a canon can account for the fact that the production of the text could extend along centuries. This would explain why those who established its text could form a sequence of editors who operated at different times. Moreover, as we shall see, Liu Hui himself will resume the activity of ‘editing’.10 How was editing of The Nine Chapters carried out at the time of Zhang Cang and Geng Shouchang? The only evidence we have comes from Liu Hui’s description

10 The fact that editing was the main operation yielding The Nine Chapters may incidentally account for another fact, that is, the multiplicity of names attached to the title The Nine Chapters in the various bibliographical chapters of the official histories that came down to us. Li Yan 李儼 1958, 25–26 (vol. 1, second edition) lists all these titles. He remarks that, once The Nine Chapters with Liu Hui’s commentary and Li Chunfeng’s subcommentary appeared as evidenced in these bibliographies, the other Nine Chapters seem to have vanished. One may contrast this situation with the case of ancient medical texts, for which apparently several compilations of the same basic set of texts seem to have survived, compare Unschuld 2003, chapter III.

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in his preface.11 The basis for their work, he tells us, consisted of documents that had partially survived the burning of the books. Moreover, Liu Hui describes Zhang’s and Guo’s editorial activity with two terms: they “made both excisions (shan) and completions” on the basis of these sources. The first operation, “excising”, evokes the edition of the Confucian classics as viewed in the Han dynasty. In fact, from at least the second century  onwards emerged the view that Confucius had been the ‘editor’ of the canons associated to his name – a set of scriptures which were canonized during the Emperor Wu’s reign (141–87 ). Moreover, as an editor of the canons, Confucius’s main operation, according to a view that also took shape in the second century , had been that of ‘expurgating’ the received documents from inauthentic material accumulated in them through the process of transmission.12 Liu Hui thus describes the edition of The Nine Chapters as starting in the Western Han dynasty more or less at the same time as the edition of the corpus of texts to be associated with Confucius, a task made difficult also because of the burning of the books. Moreover, he views The Nine Chapters as produced through edition like the canonical corpus. Lastly, he designates one of the main operations for this editing with a term that Western Han scholars associated with Confucius’s editing of the so-called “Confucian canons”, namely “excising (shan)”. These facts all betray Liu Hui’s perception of The Nine Chapters as being a ‘canon’. The second operation Liu Hui attributes to Zhang Cang and Geng Shouchang in their editing of The Nine Chapters is to have “made completions”. What this operation may have meant at the time and why it was used is not clear. However, Liu Hui’s preface sheds light of what it meant in the mind of the third-century commentator. Indeed, the preface expresses dissatisfaction with respect to the state of the text available to Liu Hui precisely in relation to the question of its completeness. The commentator mentions the problem of measuring the distance between the earth and the sun as one that was raised in the Rites of the Zhou (Zhouli), one of the three pieces of the canonical corpus devoted to ritual and traditionally associated precisely with the Duke of Zhou. However, he observes that “(in The Nine Chapters as restored by the Han editors) there is nothing of the category (lei) of (…the problem introduced…)” (Chemla & Guo 2004, 128). Earlier in the preface, Liu Hui had emphasized the reason why, again according to the Rites of the Zhou, the “nine

11 I have dealt with this topic from a different angle and placed emphasis on different points in Chemla 2008a, 197–202. 12 On Confucius’ operation of excising the superfluous to restore the original text of the canons, see Henderson 1991, 26ff. In the first piece of literary criticism devoted to “canons” (Wenxin diaolong, chapter “Revering the Canons (Zong jing)”), at the turn of the sixth century, Liu Xie refers to Confucius’ editing with the same word: “excising shan” (Owen 1992, 194–196.) On the formation of the canonical corpus during Emperor Wu’s time and the emphasis placed during the former Han dynasty on the idea of Confucius as the editor of the Classics, compare Nylan 2001.

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parts of mathematics” had been selected as one of the topics with which the offspring of the grandees should be trained. He had written: “Although one speaks of “the nine parts of mathematics”, they have the capacity to exhaust the subtle (xian) and to penetrate the minute (wei), to fathom what knows no bounds (what has no location – the shen)” (Chemla & Guo 2004, 126). Such a belief made the failure to cover the problem mentioned an indication that the edition provided by the Han editors required fixing. Liu Hui concluded: “Therefore the procedures made by Zhang Cang and the others do not yet suffice to exhaust extensively all mathematics (bo jin qun shu)”. (Chemla & Guo 2004, 128) Two points are important here. On the one hand, Liu Hui discloses his belief in the fact that The Nine Chapters in its original state encompassed all mathematics.13 This belief serves as a criterion to judge the editorial work carried out by Zhang Cang and Geng Shouchang. On the other hand, on the basis of his diagnosis of the Han edition, Liu Hui describes in his preface the procedure he follows to make a new completion to the text of the canon, thereby carrying on further the edition of The Nine Chapters. Here is how his procedure reads (Chemla & Guo 2004, 128): Within the nine parts of mathematics, I investigated the one named ‘double difference’. I examined (yuan) its essential points (zhiqu) so as to make them extend to/be efficient for (shi) this (problem). … (Here follows the statement of procedures allowing solving problems of this class) I elaborated the ‘double difference’ and wrote a commentary on it so as to explore the meaning/intention (yi) of the ancients. I joined it after (the chapter) “ base and height ” (gougu, i.e.: the last chapter).

Without again entering into any detailed explanation of what this passage means, let us stress the points that are important for us here. First, Liu Hui, like he said his predecessors did, goes back to sources in which he can have access to the “nine parts of mathematics”. We remember that this expression designates the body of knowledge from which the original The Nine Chapters derived as a book. Therefrom, Liu Hui’s treatment of the difficulty raised with respect to the Han edition consists of several steps. He begins by analyzing the procedure he finds in ways that are reminiscent of his activity as a commentator. Having derived from that analysis a solution for problems of the category not covered by the Han edition, he then composes a piece of text based on his source as well as a commentary. Lastly he appends that composition after the last chapter of The Nine Chapters as handed down to him from the Han dynasty. As a result, the gap that had been uncovered in the Han edition is filled.

13 What it may mean for a book to be all-encompassing and how this belief relates to the fact that Liu Hui composed a commentary of The Nine Chapters are the two main issues addressed in Chemla 2008b. My claim there is that this belief is another property attached to The Nine Chapters that derives from its being considered a canon.

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Clearly, Liu Hui goes on with the edition of the text as initiated by Zhang Cang and Geng Shouchang, on the basis of the belief that The Nine Chapters was originally complete – in a sense that can be determined. When he discovers a lacuna in the Han edition, he feels free to modify its text according to the loose procedure summarized above. No other modification that he may have carried out in the edition is mentioned. To recapitulate what I have shown so far, I argue in favor of the hypothesis that the successive editors conceived of The Nine Chapters as a canon, the text of which had been produced by Sages in early antiquity and had then suffered damage through transmission. It was the belief that The Nine Chapters was scripture which lent it authority, and focused on its text the efforts of a sequence of editors. In their view, editing was the act that was appropriate to restore the scripture to its original state. The text of the canon was by no means sacred, in the sense that its edition could be challenged and modified. That tradition of editing went on until at least the third century. The textual operations editing involved seem to demonstrate a form of stability between the Western Han dynasty and the time period during which Liu Hui operated. This may be due to the fact that Liu Hui’s testimony is the only one available regarding how editing was carried out before his time. We must therefore remain cautious before projecting his own practice of editing back onto the Han editors. Moreover, we can identify some links between Liu Hui’s composition of a commentary and his analysis of the editorial work. If Liu Hui’s edition had been handed down as such, the commentator could have been considered at the present day as the editor of The Nine Chapters, whose edition was completed in 263. In fact, this edition may well be the item listed in the bibliographical monograph of the History of the Sui, under the title: “The Nine Chapters on mathematical procedures. 10 chapters/rolls, compiled by Liu Hui. (Jiu zhang suanshu. Shi juan. Liu Hui zhuan.)”14 The same bibliographical monograph mentioned another title that it related to Liu Hui: “Diagrams of The Nine Chapters and ‘Double difference’. One chapter/roll. Compiled by Liu Hui. (Jiu zhang chongcha tu. yi juan. Liu Hui zhuan)”.15 The bibliographical chapter in question was one of the monographs appended to the History of the Sui [dynasty]. This official history of the dynasty that had preceded the Tang dynasty and had reigned over China between 581 and 618 had been completed in 636, without, however, the monographs. In 641, a small commission was appointed to make up for this lacuna. It presented the results of its work

14 Li Yan 李儼 1958, 45, footnote 1, notes that the scholar Wang Xiaotong, who was active in the 620s, mentions The Nine Chapters with a last chapter by Liu Hui in the preface of his Mathematical Classic Continuing the Ancient (Qigu suanjing). The latter book, composed only a few decades before the compilation of the Ten Classics of Mathematics was also included in that anthology. Its preface presents many themes similar to Liu Hui’s (Qian Baocong 錢寶琮 1963, vol. 2, 493). 15 Li Yan 李儼 1958, 25–26 (vol. 1, second edition) analyzes the various mentions of related titles in the bibliographical monographs of the various dynastic histories.

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to the throne in 656, including the bibliographical monograph quoted above. One of the members of the commission, Li Chunfeng, is believed to have taken care of the monographs connected to heavenly and cosmological matters.16 We have, however, met him earlier in this chapter, as the person in charge of the group of scholars who presented their annotations on the Ten Classics of Mathematics to the throne also in 656. What we know of how they approached the text of The Nine Chapters and Liu Hui’s commentary manifests a shift in the attitude towards the received documents. Their edition, carried out with apparently new principles, may well be what shaped for the future The Nine Chapters in a form closer to that it had taken in the hands of Han editors named above. Moreover, I shall argue that their new treatment of historical documents was what shaped Liu Hui as an ‘author’. Let us turn to their approach to texts.

2 Evidence of a new attitude towards texts and authorship As was mentioned earlier, the commentary on The Nine Chapters composed under Li Chunfeng’s supervision was written as part of a wider project that yielded, in 656, an annotated edition of Ten Classics of Mathematics. In fact, as regards The Nine Chapters, what we call “Li Chunfeng’s commentary” is a subcommentary on The Nine Chapters and Liu Hui’s commentary, composed within the framework of the compilation of the whole anthology. The first act of the seventh-century editors that can be perceived through our sources is interesting from the point of view of authorship. They detached Liu Hui’s addition to the Han edition of The Nine Chapters and turned it into a book: Mathematical Classic of the Sea Island (Hai dao suanjing), whose authorship was attributed to Liu Hui. Let us provide some evidence for this fact. We have seen (footnote 14) that as late as the first decades of the seventh century, Wang Xiaotong still referred to Liu Hui’s addition as the final chapter of The Nine Chapters. The bibliographical monograph of the History of the Sui [Dynasty], presented to the throne in 656, also contained an item which can be interpreted as Liu Hui’s edition of, and commentary on, The Nine Chapters in ten chapters. In these sources, there is no evidence of a book entitled Mathematical Classic of the Sea Island. However, soon after the compilation of the anthology in the seventh century, the Ten Classics of Mathematics were used as textbooks in the College of Mathematics (Suan xue). In the list of textbooks studied by the students, as listed in The Six Codes of the Tang [Dynasty], (Tang liu dian, compiled in ca 739), as well as in the New History of the Tang [Dynasty], (Xin Tang shu, compiled 16 On the composition of the monographs of the History of the Sui [Dynasty], compare McMullen 1988, 167–168.

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in 1060), one finds the title Mathematical Classic of the Sea Island. These administrative documents make clear that the latter book is studied with The Nine Chapters during three years.17 In addition, the bibliographical monograph of the New History of the Tang [Dynasty] contains the following items: “Liu Hui, Mathematical Classic of the Sea Island, one chapter/roll; in addition, Diagrams of The Nine Chapters and ‘Double difference’. one chapter/roll. (Jiu zhang chongcha tu. yi juan)” as well as: “Li Chunfeng comments on …; in addition, comments on The Nine Chapters on mathematical procedures, nine chapters/rolls (…), comments on the Mathematical Classic of the Sea Island, one chapter/roll” (see vol. 5 of the monographs, in Ouyang Xiu 歐陽脩 and Song Qi 宋祁, 1546–1547). We see that in all these sources, the Mathematical Classic of the Sea Island is treated as a separate book. In fact, it is one of the Ten Classics of Mathematics. In addition, the new format under which the monograph of the New History of the Tang [Dynasty] lists bibliographical items promotes the name of the author at the beginning of the clause.18 This first operation carried out within the framework of the preparation of an annotated edition of the Ten Classics of Mathematics betrays an attitude towards ancient documents different from that Liu Hui demonstrated in the third century. What had been added by Liu Hui in 263 is no longer considered a missing part of The Nine Chapters.19 Rather, it is clearly considered a piece composed in the third century and to which an author, that is Liu Hui, can be attributed. It is therefore separated from the text of The Nine Chapters, the intention appearing to be to restore the latter book to the form it had during the Han dynasty. Through this fact, one can perceive the editors’ intention to determine the status of the documents they have in their hands in a way in which agency can be attributed in the

17 Compare Siu & Volkov 1999, who analyze the curriculum and the institutions of mathematical teaching. 18 The confusion as to whether the Mathematical Classic of the Sea Island was a separate book or not and whether it had been written by Liu Hui lasted until the second printing of the Ten Classics of Mathematics at the beginning of the 13th century. The editor of this new edition, Bao Huanzhi, signs his postface of the Mathematical Classic of the Sea Island in 1200. In this postface, he relies on the documents mentioned above – in particular, the New History of the Tang [Dynasty] –and on catalogues of books compiled in the 11th century to establish what this book is. On the one hand, he determines how the Mathematical Classic of the Sea Island was detached from The Nine Chapters. On the other, he establishes that it was a book authored by Liu Hui (and not by Zhen Luan), that this book had been detached from Liu Hui’s commentary on The Nine Chapters and in turn commented upon by Li Chunfeng. See the version of the postface probably copied, as Yan Dunjie has shown, from the Grand Classic of the Yongle Reign period, and inserted in the nineteenth century in the manuscript entitled Zhujia suanfa ji xuji 諸家算法及序記 “Mathematical methods and records of prefaces from all schools”; see its reproduction and the introduction in Guo Shuchun 郭書春 (ed.) 1993, 1451–1452. 19 In the postface mentioned in the preceding footnote, Bao Huanzhi also attributes Liu Hui’s addition of this text to The Nine Chapters to the commentator’s intention to restore the canon as it was mentioned in the Rites of the Zhou.

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production of texts. In this sense, the different attitude towards received documents relates to another attitude towards authorship. Other hints confirm this conclusion. Twice, the text that the editors acting under Li Chunfeng’s supervision find in their sources as being the formulation of Liu Hui’s commentary is clearly corrupted. On these two occasions, the received text of Liu Hui’s commentary is kept in the seventh-century edition as it was handed down, a note in Li Chunfeng’s commentary mentioning the error and how to rectify the text. Let us observe these two passages. The first example of such a mistake occurs in Liu Hui’s commentary on the “rule of three”, that is, in the Chinese terminology of The Nine Chapters, the “procedure of ‘suppose’”. This piece of text is placed in the opening section of chapter 2, before the formulation of any problem. The algorithm is described in abstract terms in The Nine Chapters. Its text opposes a “quantity of what one has” to the quantity sought for, the one which the “rule of three” will determine. To do so, the procedure will also rely on a pair of values determining the equivalence between “what one has” and “what one seeks”. These values are referred to as “lü of what one has” and “lü of what one seeks”, the qualification as lü indicating that these two values can be multiplied or divided by the same factor without damaging the equivalence they express. The “rule of three” is thus formulated as follows: Suppose Procedure: One multiplies, by the quantity of what one has, the lü of what one seeks, what makes the dividend; one takes the lü of what one has as divisor. Dividing the dividend by the divisor makes the result.20

Liu Hui’s commentary accounts for the correctness of the procedure, by interpreting its steps with respect to a paradigm, provided by the first problem. The text of the latter reads as follows: Suppose that, having 1 dou of foxtail millet, one wants to make coarsely husked grain. One asks how much it yields. Answer: it makes 6 sheng of coarsely husked grain.

Additional data had been given at the beginning of chapter 2, that is, the values of 50 and 30 as expressing the equivalence between, respectively, foxtail millet and coarsely husked grain. These are the values to be designated as lü and to be accordingly simplified into 5 and 3. 5 is, with respect to the problem mentioned, the “lü of what one has” whereas 3 is the “lü of what one seeks”. Liu Hui first accounts for the correctness of the 20 My emphasis. The critical edition and translation into French of the passage of The Nine Chapters, Liu Hui’s commentary and Li Chunfeng’s subcommentary can be found in Chemla & Guo Shuchun 2004, 224–225. The footnotes to the translation direct the reader towards the appropriate entries of the glossary, in which all technical terms are explained.

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“rule of three” on the basis of these values. He then explains that this equivalence could be expressed with integers, as it is the case with 5 and 3, or by means of fractions. One could then say that 1 unit of measure of foxtail millet is equivalent to 3/5 unit of measure of coarsely husked grain. 5, the “lü of what one has”, then is taken as denominator whereas the 3, the “lü of what one seeks”, is taken as numerator. Liu Hui’s commentary concludes with the following statement: When, having foxtail millet, one looks for coarsely husked grain, one multiplies by the numerator and the corresponding denominator divides in return. If this is so, then the lü of what one seeks makes constantly the denominator.

Li Chunfeng’s edition keeps the text as clearly it is to be found in the received versions and the subcommentary notices: One should say “the lü of what one has makes constantly the numerator, the lü of what one seeks makes constantly the denominator”. If, now, it is said that “the lü of what one seeks makes constantly the denominator”, this is a mistake by omission.

This passage discloses how the seventh-century editors behaved with respect to the documents on the basis of which they established their edition. They clearly kept the received text, even in cases when, in their eyes, it was obviously mistaken, keeping for their own commentary the mention and correction of that mistake. Note that their formulation does not allow here to determine whether they attribute the mistake to Liu Hui himself or to the transmission. A similar case occurs elsewhere in the edition. In that other case, clearly they attribute the mistake to the transmission of the text. Let us read Li Chunfeng’s commentary on the “procedure for extracting the circular root”: In this commentary (by Liu Hui), the six characters “If one divides this by extraction of the square root, this gives the diameter” that occurs in the method for looking for the circumference with (Liu) Hui’s procedure (i.e.: values for π) are of no use. Among the present day books, those having them (these characters) contain an interpolation.21

Again, some documents on the basis of which the edition of Liu Hui’s commentary is made have characters that do not make sense. Even though apparently this is not the case for all documents through which one can attempt to establish the text of Liu Hui’s commentary, the seventh-century editors keep the interpolated text in the edition of this passage of the commentary and designate it as mistaken in their subcommentary. These two cases manifest the editors’ intention to transmit Liu Hui’s text as they find it in their sources as extensively as possible. On the one hand, these examples shed light on their attitude towards documents. On the other hand, they betray an interest in conveying as accurately as possible the third-century commen21 See ibid., 368–369.

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tator’s formulation, even when they have doubts regarding the transmission. This is the point where the interest in a genuine text meets with the question of authorship.22 These examples are all the more important that they contradict a widespread idea about the seventh-century edition, namely that the Tang editors manipulated the text, for instance by adding to the third-century passages taken from other, later, sources.23 I have exemplified two versions of that idea in footnote 4. If that were the case, Li Chunfeng’s team would be more interested in having ‘a’ commentary to The Nine Chapters that they would be interested in recovering Liu Hui’s text as that of a given author. I shall now examine anew the three main passages of Liu Hiu’s commentary and Li Chunfeng’s subcommentary that have nourished the doubts of present day historians vis-à-vis the reliability of the seventh-century edition. My aim is to find out whether, against the backdrop of the evidence adduced above, these passages may not be read in an entirely different way. The first passage that has cast doubt about the text of Liu Hui’s commentary as provided by Li Chunfeng’s edition relates to the question of the area of the circle. At the end of a long commentary on that topic, the commentary that one could think is attributed to Liu Hui mentions the Jin dynasty, which was established in 265, whereas Liu Hui is supposed to have completed his commentary under the Wei dynasty in 263. In fact, I have established elsewhere that the passage starting at this point in the commentary is not written by Liu Hui.24 However, we do not know where, in the text attributed to Liu Hui on that topic, the text starts that was not written by him. I will come back to that issue below. If we take for granted the fact that the passage mentioned above is not of Liu Hui’s hand, one may be tempted to conclude with Don Wagner that, under Liu Hui’s name, Li Chunfeng compiled several writings that he could see. Yet it is interesting to examine Li Chunfeng’s commentary on that section. Li Chunfeng’s subcommentary reads (Chemla & Guo 2004, 184–186):

22 As far as I know, Li Chunfeng’s commentary provides no example of a similar case with respect to the text of The Nine Chapters. This does not mean, however, that in the seventh-century editors’ eyes this text stands above criticisms. The eighth problem of chapter 6 and its procedure appear to be problematic for them, since one cannot make use of the same reasoning for any value that the data of the problem could take. Li Chunfeng’s commentary explains why, concluding the reasoning by the following judgment: “Therefore, one knows that the lü of that procedure (i.e., the one contained in The Nine Chapters to solve the problem) are contrary to reason.” Ibid., 510–511. 23 Exactly the same conclusion holds true for Li Chunfeng’s subcommentary on the other Han canon, The Gnomon of the Zhou, and its two commentaries. Li Chunfeng’s subcommentaries signal several mistakes in Zhen Luan’s subcommentary, without modifying the text. 24 Wagner 1978 voiced the problem most clearly. For all references to the discussion among historians on that vexed issue, I refer the reader to the detailed footnotes (133–140 as well as 146– 149) that I devoted to this question in Chemla & Guo Shuchun 2004, 774–778. In them, I present evidence supporting my conclusion.

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Liu Hui (…) was not able to exhaust the corresponding minute (parts, that is the fractional parts of the circumference with respect to the diameter, or of the area of the circle). Zu Chongzhi (i.e., a fifth century practitioner of mathematics), finding that all this was not accurate enough, explored further their values, following the same method. At the present day, we have compiled and selected (writings, values, or computations) of the various schools and we have assessed their correctness. [Zu] Chongzhi’s are the most precise. Therefore, we made them appear after Liu Hui’s procedure to help scholars make up their mind on this (matter). 徽(…)不能究其纖毫也。祖沖之以其不精, 就中更推其數。今者修撰, 攈摭諸家, 考其是非, 沖之為密。故顯之于徽術之下, 冀學者知所裁焉。

Exactly like above, the subcommentary therefore describes the operation carried out on the text, that is, appending another piece of text to Liu Hui’s. We thus observe once more that the seventh-century editors, on the one hand, respected Liu Hui’s text, but, on the other hand, made explicit an addition they made to it. Note that, here too, the author of the addition is mentioned, confirming the interest we already underlined above in having texts corresponding to authors. A second passage incited present-day historians to assume that the seventhcentury editors had applied important transformations to their sources to carry out their editorial work. It is the very first passage of Li Chunfeng’s subcommentary, in which one reads: The present-day commentary keeps what is excellent and deletes what is wrong. It coarsely evaluates and selects, passing this on to the scholars to come (今者注釋, 存善去非, 略為科簡, 遺諸後學.)25

Placed at the end of the first piece of subcommentary, this passage is certainly essential to understand Li Chunfeng’s project and thus, for the purpose of this paper, his attitude towards Liu Hui as an author. The key point here is, in particular, to interpret to what part of the edition was applied the operation of “keeping what is excellent and deleting what is wrong”. This statement has to be understood in its context, that is, on the one hand, in the context of the evidence brought forward above, and, on the other hand, in the context of the piece of subcommentary that it concludes.

25 My emphasis. Compare Chemla & Guo Shuchun 2004, 152–153. Note that this fragment has been interpreted quite differently by those who provided translations. The translation into modern Chinese in Shen Kangshen 沈康身 1997, 83, understands as follows: “When one makes a commentary, one should keep the true and eliminate the wrong. I outline my understanding for reference to future scholars.” Shen Kangshen, Crossley & Lun 1999, 62, translate: “In providing commentaries, we should retain nothing but the truth. Here I contribute my modest opinion just for reference.” Guo Shuchun 郭書春 1998, 49, interprets as follows: “The present-day commentary keeps what is correct and deletes what is wrong, slightly adding judgments and selection, offering its contribution to future students.” As for Li Jimin 李繼閔 1998, 231, he suggests understanding: “When one writes a commentary at the present day, one should keep what is good and deletes what is wrong. Here we only did some screening and more detailed and deep analysis, leaving it to scholars of the future generations to complete it.”

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To begin with, let us outline the context in which Li Chunfeng makes this statement. This declaration concludes a long development placed after Liu Hui’s commentary on the first procedure of The Nine Chapters. The details do not matter.26 The point is that, commenting on a concept that The Nine Chapters introduces, Liu Hui gives it as equivalent to another concept. At least, this is how Li Chunfeng interprets Liu Hui’s statement. This leads Li Chunfeng to a long development explaining why the two concepts should be distinguished. He thus concludes that Liu Hui is wrong, and continues with the statement that we now analyze. Something is clear. Li Chunfeng explains why he believes Liu Hui is wrong, but he keeps the statement which he believes wrong as part of Liu Hui’s commentary. Such an attitude does not fit with the idea that he would “delete what is wrong” from the third-century commentary. By contrast, the fact that the edition includes Liu Hui’s suspect statement conforms with what we deduced above from Li Chunfeng’s attitude towards the ‘mistakes’ in the text attributed to Liu Hui: he records them as ‘Liu Hui’s text’ as it was handed down and only then exposes them. So, in front of this bunch of evidence, it seems difficult to conclude that Li Chunfeng applied the operation of “keeping what is excellent and deleting what is wrong” to Liu Hui’s text. Moreover, in the statement which we discuss, note that Li Chunfeng speaks of his own subcommentary as “keeping what is excellent and deleting what is wrong”.27 This conclusion derives quite naturally if one compares this statement to Li Chunfeng’s own discussion of what he does with Zu Chongzhi’s treatment of the area of the circle, analyzed above. As we recall, there Li Chunfeng explains that Liu Hui’s treatment of the topic is not the best one available. He then goes on explaining how he compared several sources that improved over Liu Hui and kept the best one to make it appear after Liu Hui’s commentary. The two passages fit quite nicely with each other, making it natural to understand the former as a general description of what happens specifically in the latter. We should thus understand that Li Chunfeng’s subcommentary compiled several sources and preserved part of them, and not that this compilation was made under Liu Hui’s name. This conclusion fits nicely with what we can read in this subcommentary. It is true, as I stressed earlier, that, when speaking of the commentary on the area of the circle, we do not know where the text that should be attributed to Zu Chongzhi starts. Nothing in the text seems to indicate that the author changed at some point, except for what Li Chunfeng explains. Does this mean that Li Chunfeng added to Liu Hui’s commentary without distinguishing the additions from Liu 26 I refer the reader to the footnotes to the French translation to understand the concepts involved in this context. 27 The various translations of the passage in question show that this point is disputed. The statement appears to me quite clearly to refer to Li Chunfeng’s commentary, especially if one compares its formulation and its structure to that of the previous passage quoted. I develop this comparison in what follows.

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Hui’s text, or even in some cases without mentioning them? This question leads me to the third passage of the subcommentary that has cast doubt about the text of Liu Hui’s commentary as provided by Li Chunfeng’s edition. In the commentary attributed to Liu Hui after problem 5.28,28 one finds again a mention to the Jin dynasty. In fact, this is not the only problem of that kind in this passage. It also mentions a unit of measure posterior to Liu Hui’s time. Accordingly, at the present day, most historians agree that this passage was not written by Liu Hui. Li Chunfeng’s subcommentary on that piece as it was handed down is extremely brief and does not mention any addition. It is thus tempting to believe that the exact extension of Li Chunfeng’s subcommentary in this case was not handed down correctly. The actual subcommentary composed by Li Chunfeng covered more text than what the extant evidence shows. I can at this point recapitulate my conclusions. I believe that we have strong evidence that Li Chunfeng’s edition took special care of transmitting Liu Hui’s text as handed down by the written tradition. Moreover, we also have evidence that Li Chunfeng mentioned in his subcommentary the additions he made when it so happened. However, we also have indications that the distinction between Liu Hui’s commentary and Li Chunfeng’s subcommentary was not handed down as it once was in the seventh century.29 This set of remarks leads me to distinguish the question of the principles according to which Li Chunfeng’s edition was prepared in the seventh century from the question of determining the history of the received versions of Li Chunfeng’s edition. I believe we have evidence to describe ‘the scale and the nature’ of the editorial work carried out in the seventh century. This does not mean, however, that the received editions of that work perfectly reflect that ‘editorial work’. We know that an edition of the Ten Classics of Mathematics was prepared and printed by state institutions in 1084, followed by another state enterprise of the same type completed in 1213. However, we know next to nothing of the editorial work carried out at that time.30 How did these enterprises affect our perception of the seventh-century edition is extremely hard to determine. If we focus on the evidence we have of Li Chunfeng’s attitude towards Liu Hui’s text, we see the interest manifested in keeping Liu Hui’s formulations as they were, even when they appeared to Li Chunfeng to be mistaken, whether conceptually or mathematically. I read this new attitude towards the text as an indication

28 Compare Chemla & Guo Shuchun 2004, 456–457. For the statements made without any argumentation below, I refer the reader to the footnotes to the translation, especially footnote 159, p. 832. 29 I summarize my reasons for this conclusion in my introduction to Chapter 6, in ibid., 472–473. I suggested there that the new objective of research on The Nine Chapters should be to find means to distinguish the text of Liu Hui’s commentary from that of Li Chunfeng’s subcommentary. 30 For details about these editions, I refer the reader to Chemla 2010. In contrast to this situation, it seems that we can describe in much greater detail the editorial work carried out in the eighth century by the commentator Wang Bing on the medical classic Su wen, thanks to the information given by the eleventh-century editors of medical canons, compare Unschuld 2003, chapter III.

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of an awareness of that text as authored by someone. The same awareness is in my view manifest with the attribution to Zu Chongzhi of the piece of text appended to Liu Hui’s commentary. By contrast, Liu Hui’s commentary does not contain any evidence of that kind vis-à-vis the text commented upon. To the contrary, he reveals an assumption that the text of The Nine Chapters is an ideal to be achieved and the concrete documents are tools to improve the down-to-earth versions of the canon.

Conclusion We can now go back to the questions we raised at the beginning of this chapter. With respect to the issue of ascribing an author to The Nine Chapters, I think it is now clear why, for the book as we have it today, it may be anachronistic to look for an author in a modern sense of the term, at least regarding how ancient scholars approached the issue. In the eyes of Liu Hui who wrote the first account on the production of the text, the canon appeared as a text in high antiquity, reflecting a body of knowledge that had emerged without the action of any ‘author’. For him, the text of The Nine Chapters that he had in his hands was the result of an ‘editing’ carried out in the Han dynasty. Moreover, the edition could be improved by reference to criteria of which he believed that that kind of literature should satisfy them. When we come to Li Chunfeng, we have evidence that the perception of how texts were produced has changed, the agency of actors now playing a key part in this process. Such an awareness is reflected in two kinds of operations. On the one hand, Liu Hui’s addition to The Nine Chapters is detached from the text and turned into a separate book, to which an author is ascribed. On the other hand, the way of handling the edition of the commentary reflects an attitude that considers Liu Hui as the author of his commentary. Through these two operations, Liu Hui is definitely made an author. Such considerations shed light on the history of the text of The Nine Chapters and its two commentaries, without, for sure, exhausting the whole story of our sources. However, considering without further ado that Li Chunfeng placed under Liu Hui’s name what in fact was a compilation of a multitude of sources might not fit all the evidence we have about the seventh-century edition. Shadows remain on what the received versions of The Nine Chapters evidence. Yet we can gain some understanding of what Li Chunfeng was doing, which is indeed quite important if we are to use the evidence he left us. This remark, however, should not hide an even more important fact. Dissecting The Nine Chapters, Liu Hui’s commentary and Li Chunfeng’s annotations into three layers to account for their production separately may conceal the fact that what was really meaningful for actors of the past who read The Nine Chapters was the collection as a whole. This is the point

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where too strong an emphasis on the question of authorship might prevent us of seeing the sources of the past as actors used them.

Bibliography Texts quoted Bai Shangshu 白尚恕 1990. Jiuzhang suanshu jinyi (Modern Translation of The Nine Chapters on Mathematical Procedures) 九章算術今譯. Jinan. Biérëzkina, E. I. 1957. “Matiématika v diéviati knigakh (Mathematics in Nine Books). Annotated translation of The Nine Chapters on mathematical procedures.” In: Istorikomatiématitchiéskiié issliédovaniia (Studies in the history of mathematics) 10, 439–584. Chemla, K., & Guo Shuchun 2004. Les neuf chapitres. Le Classique mathématique de la Chine ancienne et ses commentaires. Paris. Guo Shuchun 郭書春 (ed.) 1993. Zhongguo kexue jishu dianji tonghui. Shuxue juan 中國科學技術典籍通彙.數學卷. Volume 1. Zhengzhou. Guo Shuchun 郭書春 1998. Yi zhu Jiuzhang suanshu 譯注九章算術 (Translation and commentary on The Nine Chapters on Mathematical Procedures). Shenyang. Guo Shuchun 郭書春 & Liu Dun 劉鈍 1998. Suanjing shishu 算經十書. Guo Shuchun, Liu Dun dianjiao 郭書春, 劉鈍 點校. Shenyang. Kawahara Hideki 川原秀城. 1980. “Ryûki chû Kyûshô sanjutsu (Liu Hui’s Commentary on The Nine Chapters) 劉徽注九章算術.” In: Yabuuti Kiyosi (ed.), Chôgoku tenmon gaku sûgaku shû 中國天文學, 數學集 (Collection of Chinese Astronomical and Mathematical Texts) Tokyo, 75–264. Li Jimin 李繼閔 1993. Jiuzhang suanshu jiaozheng 九章算術校證 (Critical edition of The Nine Chapters on Mathematical Procedures). Xi’an. Li Jimin 李繼閔 1998. Jiuzhang suanshu daodu yu yizhu 九章算術導讀與譯註 (Guidebook and Annotated Translation of The Nine Chapters on Mathematical Procedures). Xi’an. Ouyang Xiu 歐陽脩 & Song Qi 宋祁. New History of the Tang [Dynasty] Xin Tang shu 新唐書. Beijing. Qian Baocong 錢寶琮 1963. Suanjing shishu 算經十書 (Qian Baocong jiaodian 錢寶琮校點) (Critical punctuated edition of The Ten Classics of Mathematics). Beijing 北京.

Works quoted Bodde, D. 1986. “The State and Empire of Ch’in.” In: D. Twitchett & M. Loewe (eds.), The Cambridge History of China. Volume I: The Ch’in and Han Empires. Cambridge, 20–102. Chemla, K. 2008a. “Antiquity in the Shape of a Canon. Views on Antiquity from the Outlook of Mathematics.” In: D. Kuhn & H. Stahl (eds.), Perceptions of Antiquity in Chinese Civilization. Heidelberg, 191–208. Chemla, K. 2008b. Classic and Commentary: An Outlook Based on Mathematical Sources. Preprint/ Max-Planck-Institut für Wissenschaftsgeschichte Vol. 344. Berlin.

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Chemla, K. 2010. “A Chinese Canon in Mathematics and its two Layers of Commentaries: Reading a Collection of Texts as Shaped by Actors.” In: F. Bretelle-Establet (ed.), Looking at it from Asia: The Processes that Shaped the Sources of History of Science. Dordrecht, 169–210. Henderson, J. B. 1991. Scripture, Canon and Commentary. A Comparison of Confucian and Western Exegesis. Princeton. Li Yan 李儼 1958. Zhongguo shuxue dagang. Xiuding ben 中國數學大綱. 修訂本 (An Outline of Chinese Mathematics. Revised edition). Beijing. McMullen, D. 1988. State and Scholars in T’ang China. Cambridge (UK). Nylan, M. 2001. The Five “Confucian” Classics. New Haven. Owen, S. 1992. Readings in Chinese Literary Thought. Cambridge (Mass.). Shen Kangshen, J. N. Crossley & A. W.-C. Lun 1999. The Nine Chapters on the Mathematical Art. Companion and Commentary. Oxford. Shen Kangshen 沈康身 1997. Guide for the Reading of The Nine Chapters 九章算術導讀. Hankou. Siu, M.-K. & A. Volkov 1999. “Official Curriculum in Traditional Chinese Mathematics: How did Candidates Pass the Examinations?” In: Historia scientiarum 9, 85–99. Swann, N. L. 1950. Food and Money in Ancient China. Princeton. Unschuld, P. 2003. Huang Di nei jing su wen. Nature, Knowledge, Imagery in an Ancient Chinese Medical Text. Berkeley. Vogel, K. 1968. Neun Bücher arithmetischer Technik. Braunschweig. Volkov, A. 2010. “Commentaries upon Commentaries: The Translation of the Jiu zhang suan shu 九章算術 by Karine Chemla and Guo Shuchun.” In: Historia Mathematica 37, 281–301. Wagner, D. B. 1978. “Doubts Concerning the Attribution of Liu Hui’s Commentary on “Chiu-chang suan-shu”.” In: Acta Orientalia. Societates Orientales Danica Fennica Norvegica Svecica 39, 199–212.

Thorsten Fögen

Scholarship and Competitiveness: Pliny the Elder’s Attitude towards His Predecessors in the Naturalis Historia Abstract: This article examines the strategies of self-presentation that Pliny the Elder uses in his “Natural History”. It investigates the linguistic, stylistic and narrative techniques which Pliny employs to support his predecessors’ views or to distance himself from them. The analysis focuses on representative passages from the preface of the “Natural History”, from Book II on cosmology, Book XIV on viniculture, and the beginning of Book XXV on the history of pharmacology.

1 Introduction With his “Natural History” in 37 books, Pliny the Elder (c.  23–79) composed the most comprehensive assemblage in Latin of ancient knowledge about nature. Most classicists have exploited his work for antiquarian information (Realia), without any real appreciation for its specific character. Numerous rather negative judgments about Pliny, such as those of Arthur Schopenhauer, Theodor Mommsen, Gottfried Bernhardy and Eduard Norden,1 seem to have prevented many scholars from analyzing the “Natural History” for its own sake. Walter C. Summers, who in his 1920 study The Silver Age of Latin Literature dedicated about ten pages to Pliny, found his style gruesome (1920, 306): His Latinity is perhaps the worst that has reached us from any man with pretensions to culture before the fourth and fifth centuries. Almost all the rules that made Rome’s language the clear and elegant vehicle of expression it was he habitually breaks (…).

At least he acknowledged that the work is “not wholly devoid of interest” and added: “It also contains a mass of really valuable information” (Summers 1920, 308). Apparently, he recognized the “Natural History” as an important source not only for the reconstruction of lost texts of other authors but also for useful insights into ancient culture in general. But he did not view Pliny’s text as a literary product that deserves to be examined in its own right. As late as 1982, F. R. D. Goodyear wrote in the second volume of the widely used Cambridge History of Classical Literature (1982, 670–671): Pliny is one of the prodigies of Latin literature, (…) wide-ranging and narrow-minded, a pedant who wanted to be a popularizer, (…) and an aspirant to style who could hardly frame a coher-

1 See Fögen 2009, 201–203 for details and bibliographical references.

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ent sentence. (…) Instead of adopting the plain and sober style appropriate to his theme, he succumbs to lust for embellishment.

In the spirit of nineteenth-century scholarship, both Pliny’s style as well as the content and conception of the “Natural History” are utterly condemned here.2 These and similar assessments have been propagated for a long time and until recently met with relatively sparing dissent.3 It was not until the beginning of the 1990s that some scholars made serious attempts to scrutinize the character of Pliny’s monumental encyclopaedia, with particular emphasis on the narrative structure of the “Natural History”, its use of anecdotes, its paradoxical elements (mirabilia) and its moral agenda. A glance at the works that have been published especially during the last two decades shows that there is hardly any other Roman technical writer on whom a similarly large number of studies has been written.4 In accordance with recent work, we no longer read Pliny the Elder simply in order to extract Realia, although it cannot be denied that he is an invaluable source for understanding the parameters of ancient scientific enquiry. Instead, we have come to look at the “Natural History” from a more differentiated perspective, which leads to a better understanding as to why Pliny wrote the way he wrote. Of special interest is the question of what sort of strategy Pliny uses to present himself, especially in comparison with his predecessors with whose works he constantly engages in the “Natural History”. In his table of contents, which follows the preface, he lists for every single book of the “Natural History” the authors whom he used and to whom he wants to pay appropriate tribute. Throughout his work he continues to refer to positions of his predecessors, partly in a very general way (Graeci, antiqui, sunt qui etc.), partly with explicit mention of their names. It is the aim of this article to investigate the linguistic, stylistic and narrative strategies which Pliny employs to support his predecessors’ views or to distance himself from them. I should emphasize that I am not concerned here with the issue as to which sources Pliny in fact used and to what extent he relied upon them. In this paper, I consciously refrain from any kind of “Quellenkritik”, which was so popular among classical scholars of the nineteenth and early twentieth centuries,5 and I 2 Wallace-Hadrill 1990, 80–81 offers a thoughtful response to Goodyear and also to Norden. 3 For Köves-Zulauf 1973, 156, who is a fierce advocate of Pliny’s rehabilitation, he is still “ein Sonderling, in gewisser Weise ein Pedant”. For further evidence, see e.g. Schilling 1978, 281–282, Serbat 1986, 2102–2107, Healy 1999, 79–81, 97, 99, 111–112, Naas 2002, 4–5, and Borst 21995, 3–5, 11– 12. However, some writers of the twentieth century have had a much more positive view of Pliny, as for example Jorge Luis Borges and Italo Calvino (see Borst 21995, 336–339). 4 See especially the monographs by Citroni Marchetti 1991, Beagon 1992, Healy 1999, Naas 2002, Carey 2003 and Murphy 2004, each with further literature (see also Fögen 2009, 201–264, 319–324). König & Winkler 1979 present no more than a short introduction. There are particularly important contributions by Serbat 1986 and Conte 1994; see also French 1994, 196–255. 5 See especially Detlefsen 1881, 1901, 1908, 1909 and Münzer 1897, further e.g. Kalkmann 1898, Klotz 1906 and Rabenhorst 1907. On the goal and methodology of this focus of research see e.g. Detlefsen 1869, 702: “Das endziel der hier zu leistenden arbeit muss sein im einzelnen festzustellen, was Plinius jedem dieser schriftsteller verdankt, seinen mosaikartig zusammengesetzten text in

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believe to have good reasons for doing so, especially since the great majority of Pliny the Elder’s sources has either not been preserved or exists only in fragmentary form, thereby precluding a satisfactory solution to this problem from the start.6 Instead, I intend to pay particular attention to his self-stylization as an imparter of knowledge, whom the reader is supposed to perceive as a weighty authority ranging above other writers, who are categorized as less reliable or even untrustworthy. The textual basis of my analysis will be representative passages from the preface of the “Natural History”, from Book II on cosmology, Book XIV on viniculture, and the beginning of Book XXV on the history of pharmacology.

2 The praefatio of the Naturalis historia In his extensive preface, which is stylized as a letter dedicated to the emperor Vespasian’s son Titus (regn.  79–81), Pliny claims among other things that he has utilized about 20,000 excerpts from roughly 100 selected authors for his own account.7 Yet importantly enough, he also notes that he has amplified the information which he found in these sources with facts that were unknown to his informants, without however being able to guarantee absolute completeness (Nat. hist. praef. 17–18): viginti milia rerum dignarum cura – quoniam, ut ait Domitius Piso, thesauros oportet esse, non libros – lectione voluminum circiter duorum milium, quorum pauca admodum studiosi attingunt propter secretum materiae, ex exquisitis auctoribus centum inclusimus XXXVI voluminibus, adiectis rebus plurimis, quas aut ignoraverant priores aut postea invenerat vita. nec dubitamus multa esse quae et nos praeterierint. homines enim sumus et occupati officiis subsicivisque temporibus ista curamus, id est nocturnis, ne quis vestrum putet his cessatum horis.

diese bruchstücke zu zerlegen, eine arbeit die einerseits durch unmittelbaren nachweis der aus noch erhaltenen schriftstellern entlehnten stellen zu beschaffen ist, andrerseits aber, so weit dies nicht möglich, nur durch verwickelte combination zu ende geführt werden kann.” Sallmann 1971 took up the discussion of Pliny the Elder’s sources and provided a useful overview of earlier approaches. 6 Kroll 1930, 1 already referred to the problematic nature of “Quellenforschung”: “Eine Quellenuntersuchung zu Plinius hat mit großen Schwierigkeiten zu kämpfen. Er ist kein gewöhnlicher Kompilator, sondern hat eigene schriftstellerische Prätentionen, und Leute dieser Art lassen sich nur selten mit der Schere so glatt zerschneiden, wie es der ‘Quellenforscher’ von Profession am liebsten täte. Am ehesten gelingt es natürlich da, wo die Auswahl unter den möglicherweise benutzten Autoren begrenzt ist (…).” 7 It is noteworthy that in the table of contents, which follows the preface, Pliny lists more than 450 writers (146 Roman and 327 ‘external’). See Michael von Albrecht, Geschichte der römischen Literatur, München etc. 1994, 1004: “Vermutlich hat Plinius einen aus relativ wenigen, vorzugsweise römischen Autoren – z.B. Varro – gewonnenen Grundstock laufend durch Exzerpte aus anderen Quellen ergänzt.” Sallmann 1971, 171 translates Pliny’s phrase exquisiti auctores (§ 17) as “Vorzugsquellen”; but see Ferraro 1975, esp. 527–530 and 533.

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As Domitius Piso says, it is not books but store-houses that are needed; consequently by perusing about 2,000 volumes, very few of which, owing to the abstruseness of their contents, are ever handled by students, we have collected in thirty-six volumes 20,000 noteworthy facts obtained from one hundred authors that we have explored, with a great number of other facts in addition that were either ignored by our predecessors or have been discovered by subsequent experience. Nor do we doubt that there are many things that have escaped us also; for we are but human, and beset with duties, and we pursue this sort of interest in our spare moments, that is at night – lest any of your house should think that the night hours have been given to idleness.8

With this passage, Pliny accentuates primarily two points: first, the vast array of sources that he has consulted for writing his own work; the fact that he studied these texts is presented as a remarkable achievement insofar as their often esoteric subject matter (propter secretum materiae) is rarely dealt with even by experts. By referring to the painstaking task of making accessible a wide range of rather complicated information, he wants to make it obvious that he has done an invaluable service to the user of his “Natural History”; he thus portrays it as a text which, much to the advantage of the reader, focuses on convenience and usefulness (utilitas). Second, Pliny underscores here the novel character of his work, as he has already done at the beginning of the preface (§ 1: novicium Camenis Quiritium tuorum opus) and also in a later passage (praef. 14–15): Praeterea iter est non trita auctoribus via nec qua peregrinari animus expetat. nemo apud nos qui idem temptaverit, nemo apud Graecos qui unus omnia ea tractaverit. magna pars studiorum amoenitates quaerimus; quae vero tractata ab aliis dicuntur inmensae subtilitatis, obscuris rerum tenebris premuntur. iam omnia attingenda, quae Graeci τῆς ἐγκυκλίου παιδείας vocant, et tamen ignota aut incerta ingeniis facta; alia vero ita multis prodita, ut in fastidium sint adducta. res ardua vetustis novitatem dare, novis auctoritatem, obsoletis nitorem, obscuris lucem, fastiditis gratiam, dubiis fidem, omnibus vero naturam et naturae sua omnia. itaque etiam non assecutis voluisse abunde pulchrum atque magnificum est. Moreover, the path is not a beaten highway of authorship, nor one in which the mind is eager to range: there is not one person to be found among us who has made the same venture, nor yet one among the Greeks who has tackled single-handedly all departments of the subject. A large part of us seek agreeable fields of study, while topics of immeasurable subtlety treated by others are drowned in the shadowy darkness of the theme. Deserving of treatment before all things are the subjects included by the Greeks under the name of ἐγκύκλιος παιδεία; and nevertheless they are unknown, or have been obscured by subtleties, whereas other subjects have been published so widely that they have become stale. It is a difficult task to give novelty to what is old, authority to what is new, brilliance to the commonplace, light to the obscure, attraction to the stale, credibility to the doubtful, but nature to all things and her properties to nature. Accordingly, even if we have not succeeded, it is honourable and glorious in the fullest measure to have resolved on the attempt.

As he points out himself, the innovative nature of his work, which he circumscribes by using the long-established image of the untrodden path (see Fögen 2000: 72, 8 All translations of Pliny the Elder given in this article are from the Loeb edition by Rackham, Jones and Eichholz 1938–1962. In certain instances, I have slightly modified them.

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with n. 33, quoting further literature), consists of his universalist approach: there may be several other treatises which cover specific areas also considered by Pliny; what is, however, missing in these other works is a comprehensive and sufficiently wide-ranging overview. Pliny furthermore emphasizes that not only no Roman, but also no Greek ever dared to commit himself to a similarly sizeable encyclopaedic project – a statement that gains momentum through its strict syntactic parallelism (nemo apud nos qui idem temptaverit, nemo apud Graecos qui unus omnia ea tractaverit).9 It is true that the reference to innovation frequently occurs in ancient technical literature, especially in the prefaces where it can be seen as a rhetorical commonplace.10 However, by repeatedly and forcibly underscoring the novel character of his “Natural History”, Pliny seems to have been very eager to avoid the impression of using merely topical elements. He wanted to come across as an author who was truly convinced of the novelty of his work. And indeed, there is no similar storehouse of information on nature written in Latin. To be sure, Celsus’ (c. 25  – c.  50) encyclopaedia with its books on agriculture, military affairs, rhetoric, philosophy, law and medicine encompassed a much wider thematic spectrum than Pliny’s “Natural History”, but only Celsus’ books on medicine have been preserved. A similar case is the polyhistor Varro (116–27 ), although a full comparison with Pliny is difficult to make, since no more than a fraction of his writings have survived; we can, however, claim with some certainty that he did not produce a work similar in content and structure to Pliny’s.11 What also differentiates him from others, as he asserts, is his use of sources (auctores) that he consulted for the composition of his own work. In contrast to usual custom, he not only wants to show an appropriate amount of respect by listing his sources in a table of contents, which he places right after his preface; he also wishes to make the academic tradition on which he relied transparent for his readers. He regards this as a convincing way of demonstrating both his scholarly sincerity and moral integrity, which have prevented him from misusing others’ intellectual property. At the same time, he wants to avoid the impression of being ambitious (ambitio) at the cost of others. From the more than three paragraphs in which he sets out his position, I will single out no more than the following passages (praef. 21–23): argumentum huius stomachi mei habebis quod in his voluminibus auctorum nomina praetexui. est enim benignum, ut arbitror, et plenum ingenui pudoris fateri per quos profeceris, non ut

9 Pliny’s claim to occupying a special status within the scholarly tradition can also be detected at the very end of his work (Nat. hist. XXXVII 205): salve, parens rerum omnium natura, teque nobis Quiritium solis celebratam esse numeris omnibus tuis fave. 10 See Fögen 2009, esp. 27–34; Fögen 2005, 3–4. 11 For a short introduction to Celsus, see, for example, Grimal 1965, 475–477, and in particular Langslow 2000, 41–48; on Varro see Grimal 1965, 468–474.

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plerique ex iis, quos attigi, fecerunt. scito enim conferentem auctores me deprehendisse a iuratissimis ex proximis veteres transcriptos ad verbum neque nominatos (…). obnoxii profecto animi et infelicis ingenii est deprehendi in furto malle quam mutuum reddere, cum praesertim sors fiat ex usura. You will deem it a proof of this pride of mine that I have prefaced these volumes with the names of my authorities. I have done so because it is, in my opinion, a pleasant thing and one that shows an honourable modesty, to own up to those who were the means of one’s achievements, not to do as most of the authors to whom I have referred did. For you must know that when collating authorities I have found that the most professedly reliable and modern writers have copied the old authors word for word, without acknowledgement. (…). Surely it marks a mean spirit and an unfortunate disposition to prefer being detected in a theft to repaying a loan – especially as interest creates capital.

This quotation proves that Pliny was at great pains to discuss the importance of scholarly honesty. However, his emphatic indignation about plagiarism also serves to present himself in an even more favorable light to his readers. This conscious self-advertisement as a superior exemplar is reinforced stylistically. Pliny employs a number of morally tinged terms which let plagiarism appear as a vicious theft. He not only sharply distances himself from such trespasses, but also casts himself as the one to have discovered them (deprehendisse) – in particular in cases where authors seemed to be very reliable at first sight. By using this kind of language, Pliny suggests to his readers that they can fully trust him without any scruple. After such a preface the reader must necessarily have deemed it impossible that he would be found guilty of any inappropriate and unacknowledged treatment of his sources. But one may go even further than that: Pliny’s self-advertisement also implies that the reader who has gone through the preface has been warned against other writings and is well advised to stay away from them. The only consequence for the reader, if he wants to be on the safe side, would be to rely fully upon the “Natural History” and simply ignore other works on similar topics, above all contemporary studies. That Pliny had especially his contemporary competitors in mind is shown in the quoted passage by his explicit reference to the present or at least the most recent past (a iuratissimis ex proximis). His polemics remain, however, rather general, since he does not mention the names of the authors whom he intends to criticize. But it is precisely this vagueness that seems to motivate the reader all the more to disregard other works that deal with nature. Another important issue that Pliny brings up in his preface is the choice of an unpretentious and modest title for his own work which is contrasted with those of other Greek and Roman compilations whose authors are said to have put greater emphasis on the originality or wittiness of their titles than on the solid content of their treatises.12 In contrast to their rather exalted and often pompous titles, Pliny 12 See esp. Nat. hist. praef. 24: inscriptionis apud Graecos mira felicitas: κηρίον inscripsere, quod volebant intellegi favum, alii κέρας Ἀμαλθείας, quod copiae cornu, ut vel lactis gallinacei sperare possis in volumine haustum; iam ἴα, Μοῦσαι, πανδέκται, ἐγχειρίδια, λειμών, πίναξ, σχεδίων: inscrip-

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stresses that he decided for a simple title, which he compares to inscriptions made by painters and sculptors of classical Greece on their works of art. He interprets a lapidary remark such as Apelles faciebat not only as a sign of the artist’s modesty (verecundia), but also as a way of showing a certain non-committal attitude which is supposed to save him from criticism (Nat. hist. praef. 26–27). By positioning himself in this way, Pliny once more reaffirms how much value he, in his function as a scientific writer, attributes to both integrity and practicality. These high standards that Pliny claims for himself are meant to converge with his preceding remarks about the supposedly straightforward and simple structure of his work which, as he maintains, deliberately refrains from digressions and the interweaving of phantastic elements.13 However forcefully Pliny introduces the reader to his own agenda and principles as a writer, one cannot overlook that it is one of his intentions to disparage authors of other works which deal with similar topics. Even though their names may not be mentioned, it is obvious that he contrasts his self-presentation with that of others who purportedly do not subscribe to the same standards and values. The fact that he attempts to convince his readers that the “Natural History” meets the highest scholarly as well as ethical standards is also suggested by the dedication of his preface to Titus as a future emperor. By accentuating his excellent connections with political power, he signals his authority, which sets him even more apart from his predecessors. In order to strengthen his argument further, he tiones, propter quas vadimonium deseri possit; at cum intraveris, di deaeque, quam nihil in medio invenies! Aulus Gellius follows a similar strategy in the preface to his Noctes Atticae (praef. 4–10), where he criticizes, among other things, the ‘overly recherché titles’ (praef. 5: titulos … exquisitissimos; cf. praef. 4: festivitates inscriptionum) of many of his predecessors and contrasts them with his own rather simply title: Nos vero, ut captus noster est, incuriose et inmediate ac prope etiam subrustice ex ipso loco ac tempore hibernarum vigiliarum Atticas noctes inscripsimus tantum ceteris omnibus in ipsius quoque inscriptionis laude cedentes, quantum cessimus in cura et elegantia scriptionis (praef. 10). See Fögen 2005, 4: “Schon der Titel eines Fachtextes, mit dessen Wahl sich ein Autor in eine bestimmte Linie stellt, erzeugt beim potentiellen Leser eine bestimmte Erwartungshaltung.” 13 Nat. hist. praef. 12–13: (…) levioris operae hos tibi dedicavi libellos. Nam nec ingenii sunt capaces, quod alioqui in nobis perquam mediocre erat, neque admittunt excessus aut orationes sermonesve aut casus mirabiles vel eventus varios, iucunda dictu aut legentibus blanda sterili materia: rerum natura, hoc est vita, narratur, et haec sordidissima sui parte ut plurimarum rerum aut rusticis vocabulis aut externis, immo barbaris etiam, cum honoris praefatione ponendis. It has often been noticed by modern scholarship (e.g. Fögen 2007) that this statement runs counter to the actual structure of the Naturalis historia. However, with regard to praef. 12, Naas 1997, 150 remarks: “On peut penser que le merveilleux ne se réfère pas tant, dans ce passage, aux merveilles de la nature qu’aux événements fictifs, aux récits d’aventure. Ce que Pline refuse, c’est la fiction, ou encore le hasard (casus, euentus); (…) ce qui déplaît à Pline et dont il se démarque, ce ne sont pas tant les informations elles-mêmes que leur cadre et leur présentation. Pline refuse la paradoxographie en tant que littérature d’agrément.” On mirabilia in Pliny the Elder see e.g. Schilling 1978, 280–281, Isager 1991, 44–47, Beagon 1992, 8–11, 128–133, 151–152, 158; 2001, 743–745, Naas 1997; 2002, 237– 393, and Healy 1999, 63–70.

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calls attention to the fact that his relationship with Titus is of a special kind: not only is the emperor’s son extraordinarily cultivated, rhetorically gifted and himself a literary writer;14 what is also remarkable is the fact that their old friendship stems back from their time in the military service, which entitles Pliny to speak of their close association and comradeship.15 The praise of the prince is so extensive and panegyrical16 that plenty of shine falls back on the laudator himself. The deduction the reader is expected to make from all this is that an author like Pliny who enjoys the full trust and friendship of one of the most powerful figures in the state must be a similarly trustworthy and reputable person, whose work is as reliable as his reputation. Pliny thus follows a sociocultural practice which can frequently be observed in ancient technical literature. A comparison with Vitruvius’ earlier work De architectura or with Vegetius’ much later Epitoma rei militaris proves this. Both writers include a direct address to the emperor in the prefaces of their works: Vitruvius turns to Augustus (see Fögen 2009, 107–151), Vegetius probably speaks to Theodosius I (regn.  379–395) or perhaps to Valentinian III (regn.  425– 455).17 This also supports Pamela Long’s view that Roman technical writers usually belonged to the social elite, who had close contact with the highest political rulers (Long 2001, 35–38). Pliny concludes his prefaces by resuming his remarks about the table of contents that immediately follows the dedicatory epistle (praef. 21–23, see above).18 14 See Nat. hist. praef. 5: fulgurare in nullo umquam verius dicta vis eloquentiae, tribunicia potestas facundiae. Quanto tu ore patris laudes tonas! Quanto fratris amas! Quantus in poetica es! O magna fecunditas animi! Quam ad modum fratrem quoque imitareris excogitasti! See also Nat. hist. praef. 11: Te quidem in excelsissimo generis humani fastigio positum, summa eloquentia, summa eruditione praeditum, religiose adiri etiam a salutantibus scio (…). In Nat. hist. II 89 Pliny mentions a (lost) poem by Titus on the comet of the year  76. Pliny’s characterization of Titus is similar to that of other sources, especially Suetonius, Titus 3: in puero statim corporis animique dotes explenduerunt, magisque ac magis deinceps per aetatis gradus: forma egregia et cui non minus auctoritatis inesset quam gratiae, praecipuum robur, quanquam neque procera statura et ventre paulo proiectiore; memoria[e] singularis, docilitas ad omnis fere tum belli tum pacis artes. armorum et equitandi peritissimus, Latine Graeceque vel in orando vel in fingendis poematibus promptus et facilis ad extemporalitatem usque; sed ne musicae quidem rudis, ut qui cantaret et psalleret iucunde scienterque. E pluribus comperi, notis quoque excipere velocissime solitum, cum amanuensibus suis per ludum iocumque certantem, imitarique chirographa quaecumque vidisset, ac saepe profiteri maximum falsarium esse potuisse. – That Titus’ father Vespasian, with whom Pliny the Elder had close professional contact (Pliny the Younger, Epist. III 5.7: ante lucem ibat ad Vespasianum imperatorem), had a keen interest in scholarship and the arts is documented, for example, in Suetonius, Vespasian 18–19. See Franchet d’Espèrey 1986. 15 Nat. hist. praef. 3: nobis quidem qualis in castrensi contubernio, nec quicquam in te mutavit fortunae amplitudo, nisi ut prodesse tantundem posses et velles. 16 Janson 1964, 102 speaks of a “prolonged and immoderate praise of the Emperor”. 17 Neither the question of the addressee of Vegetius’ Epitoma rei militaris nor its exact date have been fully elucidated by modern scholarship (see Fögen 2009, 57). 18 On the usefulness of Pliny’s index, see Doody 2001, who also discusses various aspects of the history of textual editions; see further Naas 2002, 171–195.

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This time, however, he does not so much highlight his scholarly sincerity, discernible from the transparent way of dealing with his sources, as the practical usefulness of the “Natural History” for its readers. By consulting the table of contents, a busy man like Titus can easily identify where to find information on what topic, and thus save a lot of time. Pliny presents the economical method of providing a full list of the topics that are dealt with in a technical work as something outstanding and almost unique: he asserts that, apart from his own work, it can only be found in Quintus Valerius Soranus’ (c. 130–82 ) Ἐποπτίδες,19 a poem that was probably about female divinities,20 but of which we have no more than the beginning of a hymn to Jupiter (Fr. Poet. Lat. fr. 2 Morel/Büchner/Blänsdorf). Let us examine briefly to what extent Pliny’s claim is justified. One has to admit that his tables of contents to each book of the “Natural History” offer more than just an overview of the thematic structure of the work. As mentioned before, he also lists the names of predecessors who are relevant for the individual topics. It is noteworthy that, in doing so, he throughout separates Roman and non-Roman authors (externi), the latter of whom, predominantly represented by Greeks, always come second, even though it would have made more sense from a chronological perspective to list them before the Roman sources. In Books XX to XXVII, which are concerned with herbal remedies, and in some of Books XXVIII to XXXII, which thematize animal remedies, Pliny adds medical doctors (medici) as a third group of sources. As far as I can see, the cataloging of his predecessors does not follow any coherent principle; it is neither alphabetical nor chronological. While the names of authors often occur in the same order in the index as they actually appear in the individual books, this is not a scheme that Pliny follows very rigorously. From a modern point of view, one may also find it remarkable that titles of works consulted are never given, although this was by no means unusual in antiquity. For the first century , the recipe-book Compositiones by Scribonius Largus, probably written between  43 and 48,21 indicates that Pliny was not the only technical writer to place an index at the beginning of his work.22 However, unlike Pliny, Scribonius does not supply any precise documentation of his sources,

19 Nat. hist. praef. 33: quia occupationibus tuis publico bono parcendum erat, quid singulis contineretur libris, huic epistulae subiunxi summaque cura, ne legendos eos haberes, operam dedi. tu per hoc et aliis praestabis ne perlegant, sed, ut quisque desiderabit aliquid, id tantum quaerat et sciat quo loco inveniat. hoc ante me fecit in litteris nostris Valerius Soranus in libris, quos ἐποπτίδων inscripsit. 20 Köves-Zulauf analyzes the exact meaning of the title Ἐποπτίδες and comes to the following conclusion: “Gemeint sind offensichtlich gewisse dämonische Wächterinnen, die Menschheit bewachende Göttinnen” (1970, 342). 21 Thus Schonack 1913, xiv, Deichgräber 1950, 856, and Langslow 2000, 50. The Compositiones are dedicated to C. Iulius Callistus, an influential freedman of the emperor Claudius. 22 Sconocchia 1987 scrutinizes the sequence of praefatio, index and text, which is typical of Roman technical treatises. Apart from Scribonius Largus, he also takes into account Vitruvius, Columella und Frontinus as examples from the first century .

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although his index is rather extensive (Comp. praef. 15, p. 6–16 Sconocchia). Modern scholarship has not fully elucidated why Pliny does not refer to Scribonius; suffice it here to say that Scribonius is mentioned nowhere throughout the entire “Natural History” (see Sconocchia 1987, 310, with n. 7). In the second century , Aulus Gellius in his Noctes Atticae uses the same structuring principle. He also underscores the usefulness of this method, albeit in a much more terse fashion than Pliny does.23 It is interesting to note that Gellius mentions neither Pliny nor Valerius Soranus as his models, although he was clearly very familiar with the “Natural History”, as can be seen from the numerous similarities between his preface and Pliny’s. It is time to draw some conclusions from my analysis of the preface of the “Natural History”. In a short article published in 1889, Ludwig von Urlichs called Pliny’s prefatory epistle “one of the most charming pieces of Silver Latin literature (…): a graceful combination of liberal pleasantry and serious scholarship”.24 Noone will be likely to deny that the letter is indeed intricately designed and aspires to an elevated stylistic level.25 Yet this well-calculated rhetorization is not simply supposed to provide a sample of Pliny’s skills as a writer. It goes far beyond l’art pour l’art, since, as is so often the case in other ancient technical literature, Pliny’s proclaimed modesty and unpretentiousness co-exist with the vigorous claim to his considerable scholarly achievement, which for him consists of the reduction of the complexity of the material that he has digested and its resulting usefulness for the reader. His repeatedly emphasized conviction that he is a genuine scholarly as well as moral authority is part of the preface reminiscent of an appeal which seeks to forcefully advertise the “Natural History” to its audience26 and to dismantle a great number of predecessors in the same field, even without naming them explicitly. Pointedly speaking, the reader who has perused Pliny’s introduction is given no real choices in terms of an alternative. If he is still willing to consult works other than the “Natural History” despite Pliny’s warnings, he will incur the risk of getting blamed for not being circumspect enough and for being too credulous. It would actually mean acting against one’s better judgment and all too readily allowing oneself to be deceived by less reputable writers on nature. Pliny’s laudatio of his own persona and his accomplishments has a strongly suggestive character which proposes to establish a consensus between author and reader. Whoever reads Pliny and disregards other authors with lower standards, stands on the right side or, to put it in sociological terms, belongs to the in-group. By carefully constructing the

23 Aulus Gellius, Noct. Att. praef. 25: capita rerum, quae cuique commentario insunt, exposuimus hic universa, ut iam statim declaretur, quid quo in libro quaeri inveniri possit. 24 See Urlichs 1889, 259: “[e]ines der reizendsten Stücke der silbernen Latinität (…): eine anmuthige Verbindung von freimüthigem Scherz und ernster Gelehrsamkeit”. 25 See Köves-Zulauf 1973, 141–144. 26 The reference to his historical work A fine Aufidii Bassi (praef. 20) and to his grammatical books De dubio sermone (praef. 28) are also part of his self-advertisement.

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presumed savviness of his readership, Pliny wanted to make it as attractive as possible for his audience to devote full attention to his “Natural History”.27

3 Pliny’s cosmology (Book II of the Naturalis historia) The second book of Pliny’s “Natural History” is fundamental for his view of the world.28 He discusses heaven with its planets and portents in the skies (Nat. hist. II 1–101), meteorological features (II 102–153) and general aspects of geography (II 154–211), and then moves on to hydrography (II 212–234) and the attributes of terrestrial fire (II 235–241). At the end of Book II, there is a transition to the subsequent geographical books (Nat. hist. III-VII), which thematizes distances and dimensions (II 242–248). Posidonius (135–51 ) has often been identified as Pliny’s main source for his second book, but already in 1930 Wilhelm Kroll correctly observed that it cannot be determined with certainty whether Pliny used Posidonius directly or via other writers such as Varro.29 For the question pursued in this article, one of the most illuminating passages in Book II is his section on the eclipses of moon and sun (Nat. hist. II 51–55). As Pliny says, among the Romans it was the former consul C. Sulpicius Gallus who first dealt with these phenomena. In his function as military tribune, he not only motivated his soldiers before the battle of Pydna (168 ) by predicting an eclipse of the moon as a sign of the defeat of king Perses of Macedonia; thereafter, he also wrote a book about this phenomenon. Pliny adduces the example of Sulpicius Gallus in order to demonstrate how science can serve public and even governmental interests: in this particular case, proper knowledge, applied at the right moment, led to a political victory of the Romans.30 It is striking that Thales of Miletus (6th/5th cent. ), the Greek scholar who must be considered as the protagonist in the field of research on lunar and solar eclipses,31 is mentioned only after

27 One may therefore argue that Pliny’s praefatio is “virtually unique in the history of the Latin encyclopedia during antiquity and the middle ages” (Howe 1985, 562). However, the reason for that lies not, as Howe thinks, in “Pliny’s elaborate self-deprecation” (ibid.), but rather in his selfconfidence and conscious self-advertisement. 28 Campbell 1936 offers a commentary on Book II; Kroll 1930 is comparable, but focuses very much on the question of Pliny’s sources. See also Stahl 1962, 107–116. 29 Kroll 1930, 1; Serbat 1986, 2109–2111 reviews several findings which, pace Kroll 1930, question Posidonius’ direct influence on Pliny’s cosmology. On the importance of Posidonius for the philosophical and scientific literature of Rome, see the short remarks in Stahl 1962, 45–51. 30 Pliny’s emphasis on the aspect of science and scholarship as forms of service to the state is dealt with by Grüninger 1976, esp. 87–91. 31 See also Diogenes Laertius I 23: δοκεῖ δὲ κατά τινας πρῶτος ἀστρολογῆσαι καὶ ἡλιακὰς ἐκλείψεις καὶ τροπὰς προειπεῖν, ὥς φησιν Εὔδημος ἐν τῇ Περὶ τῶν ἀστρολογουμένων ἱστορίᾳ· ὅθεν αὐτὸν καὶ Ξενοφάνης καὶ Ἡρόδοτος θαυμάζει. Μαρτυρεῖ δ’αὐτῷ καὶ Ἡράκλειτος καὶ Δημόκριτος.

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the Roman Sulpicius Gallus. Apart from Thales, Pliny also refers to the later Hipparchus of Nicaea (2nd cent. ), who is said to have foretold the course of the sun and the moon for 600 years (Nat. hist. II 53). Pliny does not reveal the extent to which the Roman Sulpicius Gallus relied upon Thales and Hipparchus. Instead, he emphatically praises the impressive cognitive faculties of all three scholars. In contrast to poets such as Stesichorus or Pindar, they made a vital contribution through their understanding of the workings of nature: it was because of their influence that lunar and solar eclipses were no longer interpreted in a superstitious manner, thereby assuaging the fears of many people. Pliny’s eulogy takes on a solemn and almost religious tone when he says (Nat. hist. II 54):32 macte ingenio este, caeli interpretes rerumque naturae capaces, argumenti repertores, quo deos hominesque vicistis! All hail to your genius, you that interpret the heavens and grasp the facts of nature, discoverers of a theory whereby you have vanquished gods and men!

Stylistically, one notes the affective character of his sentences which combine an amplifying succession of parallel syntactic elements with the form of an exclamation.33 In terms of content, Pliny elaborates upon the idea that scientific progress, in this particular case the grasp of nature and its functioning, can eradicate delusion and superstition. He strongly believes in the idea of progress and repeatedly illustrates his opinion to his readers. Pliny may imply that theories of earlier scholars sometimes need to be revised, but this does not minimize their accomplishments, as he declares later on in his section on the movements of planets (Nat. hist. II 62): In quibus aliter multa quam priores tradituri fatemur ea quoque illorum esse muneris, qui primi vias quaerendi demonstraverint; modo ne quis desperet saecula proficere semper. And although our account of these matters will differ in many points from that of our predecessors, we confess that credit for these points also must be given to those who first demonstrated the methods of investigating them: only nobody must abandon the hope that the generations are constantly making progress.

32 Pliny sings similar praise in his section on earthquakes, where he extols Anaximander and Pherecydes for their talent to predict earthquakes (Nat. hist. II 192): quae si vera sunt, quantum a deo tandem videri possunt tales distare, dum vivant? However, by the phrase quae si vera sunt Pliny indicates that the reports about the two scholars may be exaggerated. Rather cautiously formulated is also the following sentence in the preceding chapter (Nat. hist. II 191): praeclara quaedam et inmortalis in eo, si credimus, divinitas perhibetur Anaximandro Milesio physico. 33 Müller 1883, 118–119 argues that stylistically there is nothing more characteristic of Pliny’s narrative than his tendency towards affective insertions, and provides further examples from the Naturalis historia. While this opinion is very plausible, it should not be explained with Pliny’s supposed proneness to a ‘sentimental view of nature’. – With regard to Nat. hist. II 54, Beaujeu 1957, 9 speaks of Pliny’s “enthousiasme lyrique et un peu puéril”.

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His position, namely that he contributes to the constant growth of learning with his own work, results not only from his collection and discussion of established knowledge, but also from his analysis of a number of details that had never been dealt with by anyone before him. His examination of the movements of the lower planets (Nat. hist. II 72–76) is just one example of this, and it is a topic that he consciously designates as difficilior (Nat. hist. II 71 fin.), since he wants to create the impression that he, in contrast to others, is not afraid of any intellectual challenge. His claim for being an innovator in many respects is part of his self-advertisement. In the context of his more general remarks on winds and their origin, Pliny mentions that more than twenty older Greek authors wrote on this topic. He finds this intriguing, since in former times the circumstances under which meteorological and geographical research was conducted were more unfavorable because of wars and assaults than in Pliny’s own era, which is characterized by secure peace and greatly benefits from a ruler who has a vigorous interest in the sciences and arts (Nat. hist. II 117). He thus argues that the writings of earlier scholars need to be evaluated as even higher achievements. This observation also forms the basis of his vehement criticism of all those who do not make any use of the benign political conditions for doing proper research, but instead use the opportunity to travel anywhere safely only for their personal financial advantage. By contrast, scholars of former times were not concerned about monetary gain, but about the intellectual and practical rewards that their insights would yield for their own time as well as for later periods (Nat. hist. II 118). Only by assuming such an altruistic and noble attitude would it be possible to expand current research on meteorology. It becomes obvious from such passages how much emphasis Pliny puts on the right scholarly ethos: according to him, science and scholarship can only flourish and progress if researchers have a serious interest in them and are not focused on any financial profit that may result from their investigations. Without these high moral standards, which are oriented towards making knowledge readily available to others, he believes that scholarship is doomed to remain a dubious business. It is thus fitting that Pliny concludes this section by adding for whom he has primarily written his paragraphs on winds: they are meant to be especially useful to sailors.34

4 Pliny’s viniculture (Book XIV of the Naturalis historia) The moral integrity and professional competence of certain former scholars is accentuated in a similar way at the beginning of Book XIV, which focuses on viniculture and comprises one part of the section of his “Natural History” devoted to botany. In his introduction, Pliny bewails the frequent loss of knowledge about 34 Nat. hist. II 118: quapropter scrupulosius, quam instituto fortassis conveniat operi, tractabo ventos, tot milia navigantium cernens.

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certain trees and their names, even though this information has been compiled by earlier authors. Drawing upon an argument from Book II, he finds this irritating in view of the fact that the world is now under Roman rule and that the advantageous political situation greatly facilitates safe travelling and thereby gaining easy and thorough first-hand knowledge of trees and other plants. For him, early science is characterized by a greater degree of care and productivity (cura fertilior) as well as diligence (industria felicior), whereas during his time a pronounced tendency towards slackness (desidia) endangers the preservation of knowledge.35 He locates the reasons for this development in the loss of established moral convictions (Nat. hist. XIV 4): Quis alias quam publicas mundi invenerit? Nimirum alii subiere ritus circaque alia mentes hominum detinentur et avaritiae tantum artes coluntur. Who can discover other causes than the general movement of affairs in the world? The fact is that other customs have come into vogue, and the minds of men are occupied with other matters: the only arts cultivated are the arts of avarice.

He believes that no-one can afford idleness since the scope of information to be handled has grown immensely over the centuries (Nat. hist. XIV 3). The storing and transmission of knowledge thus requires an enormous effort which, according to Pliny, hardly anyone among his contemporaries is able to make. This assessment serves as a motive for Pliny to reflect at greater length on the situation of the artes and compare it with that of the past (Nat. hist. XIV 4–6). Most deplorable from his point of view is the misguided use of the great size of the Roman empire, which resulted from its territorial expansion, as well as the marked fixation on material wealth, which seems to have developed into the most decisive motivation for those involved in political life. It fits well with his recurrent criticism of luxuria36 when he finally says: ergo, Hercules, voluptas vivere coepit, vita ipsa desiit (Nat. hist. XIV 6).37 He reinforces his genuine indignation not only by the interjected appeal to Hercules, but also by the parallel syntax, which with regard to both structure and content exhibits the characteristics of a proverb. In conclusion, he contrasts this scenario of the decline of serious scholarship with his own view of what proper research ought to look like (Nat. hist. XIV 7): Sed nos oblitterata quoque scrutabimur, nec deterrebit quarundam rerum humilitas, sicuti nec in animalibus fecit, quamquam videmus Vergilium praecellentissimum vatem ea de causa horto-

35 In Nat. hist. X 20 Pliny speaks of a desidia rerum omnium: supposedly, certain species of birds have not been spotted in Rome for a longer period of time. However, according to Pliny, this is not due to the fact that these birds have indeed disappeared from Rome; rather, it must be ascribed to a widespread tendency towards a lack of thorough scientific observation. 36 See esp. Citroni Marchetti 1991, passim, further e.g. Serbat 1986, 2093–2095, and Wallace-Hadrill 1990, 85–92. 37 Similarly Nat. hist. XXII 14: addidere vivendi pretia deliciae luxusque, numquam fuit vitae cupido maior nec minor cura.

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rum dotes fugisse et in his, quae rettulit, flores modo rerum decerpsisse, beatum felicemque gratiae quindecim omnino generibus uvarum nominatis, tribus oleae, totidem pirorum, malo vero tantum Assyrio, ceteris omnibus neglectis. We, however, will carry our researches even into matters that have passed out of notice, and will not be daunted by the lowliness of certain subjects, any more than we were when dealing with the animals, although we see that Virgil, the prince of poets, was led by this consideration to make omissions among the resources of the garden and in those which he has recorded has only culled out the flower of his subject, happy and gracious as he is: he has only named fifteen kinds of grapes in all and three of olives and as many pears, and of apples only the Assyrian citron, neglecting all the rest.

As he avers in this passage, he does not want to provide a brilliant, yet cursory, overview of selected highlights; rather, he strives for the most representative38 comprehensiveness possible by incorporating copious details and thus incurring the risk of potentially alienating his readership. That even Virgil’s account on fruittrees in the Georgics does not evade Pliny’s stern judgment stems from the latter’s desire to extol the qualities of his own work. The poet is certainly not ranged on the same level as those nameless contemporaries whom he criticized for their lack of diligence; this can be seen from the fact that he pays tribute to Virgil by calling him praecellentissimum vatem. Nonetheless, Pliny suggests that he surpasses Virgil with his own books on fruit-trees and thus commends himself once more to his readers, to whom he endeavors to present as much useful material as possible.39 Pliny’s thoughts on the decline of contemporary scholarship were by no means original. There are comparable passages towards the end of Seneca’s Naturales quaestiones (Nat. quaest. VII 31.1–32.4), which posit moral depravation (nequitia) and extravagance (luxuria) as the reasons for the sparse contemporary interest in the sciences. He argues that most people in his own time prefer to indulge in effeminate behavior (mollitia) and invidious forms of entertainment such as pantomime dancing. He therefore does not find it surprising that there is hardly any

38 That Pliny does not intend to be completely exhaustive is shown by the example of the types of vines about which he remarks the following (Nat. hist. XIV 20): Genera vitium numero conprehendi posse unus existimavit Democritus, cuncta sibi Graeciae cognita professus; ceteri innumera atque infinita esse prodiderunt, quod verius apparebit ex vinis. nec omnia dicentur, sed maxime insignia, quippe totidem paene sunt quot agri, quam ob rem celeberrimas vitium aut quibus est aliqua proprietate miraculum ostendisse satis erit. As his thematic spectrum is very broad, he cannot and does not want to offer a work which covers all the details related to a certain theme or object. Rather, his goal is an overview which is focused on the essentials. At the same time, this does not mean that the structure of his text is absolutely straightforward. Instead, his factual accounts are often intervowen with anecdotes and similar digressions (see e.g. Fögen 2007). 39 Pliny is bitter about the fact that the usefulness of scholarly accounts, assembled through an enormous amount of work, is not always acknowledged, as can be seen from the following excerpt (Nat. hist. XXII 15): immo vero plerisque ultro etiam inrisui sumus ista commentantes atque frivoli operis arguimur; magno quamquam inmensi laboris solatio sperni cum rerum natura, quam certe non defuisse nobis docebimus (…).

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striving for real wisdom (sapientia), the ultimate goal of serious and intense philosophical studies. He summarizes the resulting problems as follows (Nat. quaest. VII 32.4): Philosophiae nulla cura est. Itaque adeo nihil invenitur ex his quae parum investigata antiqui reliquerunt ut multa quae inventa erant oblitterentur. At mehercule, si hoc totis membris premeremus, si in hoc iuventus sobria incumberet, hoc maiores docerent, hoc minores addiscerent, vix ad fundum veniretur in quo veritas posita est, quam nunc in summa terra et levi manu quaerimus. There is no interest in philosophy. Accordingly, so little is found out from those subjects which the ancients left partially investigated that many things which were discovered are being forgotten. But, by Hercules, if we applied ourselves to this with all our might – if youth soberly applied itself to it, if the elders taught it and the younger generation learned it –, we would scarcely reach to the bottom where truth is located, which we now seek on the surface of the earth and with slack effort.40

With this rather gloomy statement, Book VII of the Naturales quaestiones ends. Unlike Pliny, Seneca is less concerned here with advertising his own scholarly merits, although it is certainly also important to him to be perceived as an authority in the natural sciences. Furthermore, he is less optimistic than Pliny as far as the discovery of scientific knowledge is concerned, especially in the area of cosmology: for him, nature is full of almost impenetrable secrets which often produce severe challenges for human minds. At the same time, this fact is proof of the bewildering greatness and complexity of the world. In particular, doing research on planets and stars requires a certain amount of modesty and reverence for nature and the gods. For Seneca, the accumulation of knowledge about nature is a gradual and very slow process which requires extreme patience on the part of the researcher; even a concerted and most vigorous effort seldom leads to fully enlightening results.41 But it is also clear enough to Seneca that his own generation is too effete to make a sufficient effort to increase knowledge about nature, and this is a conviction that Pliny shares with him. As for his praise of former scholars who travelled around for their research despite the numerous difficulties they faced, one may refer to similar passages in Polybius’ “Histories” (III 58–59). He shows a similarly high respect as Pliny does for earlier generations of geographers, although he admits that they were mistaken 40 Translation from the Loeb edition (Seneca: Naturales quaestiones. With an English translation by Thomas H. Corcoran, vol. 2, London & Cambridge, Mass. 1972). 41 Seneca, Nat. quaest. VII 30, esp. VII 30.5–6: Quam multa animalia hoc primum cognovimus saeculo, quam multa negotia ne hoc quidem! Multa venientis aevi populus ignota nobis sciet; multa saeculis tunc futuris cum memoria nostri exoleverit reservantur. Pusilla res mundus est, nisi in illo quod quaerat omnis mundus habeat. Non semel quaedam sacra traduntur: Eleusin servat quod ostendat revisentibus; rerum natura sacra sua non semel tradit. Initiatos nos credimus, in vestibulo eius haeremus. Illa arcana non promiscue nec omnibus patent; reducta et interiore sacrario clausa sunt, ex quibus aliud haec aetas, aliud quae post nos subibit aspiciet.

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in many respects, a fact that he cannot overlook. But instead of criticizing them for something for which they cannot really be blamed, Polybius is grateful to them for their accomplishments, since they considerably advanced geographical knowledge. For his own generation, he points out the necessity of making use of the favorable political climate and the territorial expansion of the Alexandrian and Roman empires for personal observations (αὐτοψία) that might improve or even correct the findings of former scholars.42 This is what Polybius himself attempts to do in his own work (III 59.6–8) with the obvious goal of commending himself to his readers, as he does in so many other instances throughout the “Histories”.43 In this particular passage, however, he does so without detracting from the reputation of other writers. Unlike Pliny, he also does not attack them for being primarily concerned about financial matters.

5 Pliny’s history of herbal medicine (Book XXV of the Naturalis historia) The beginning of Book XXV of the “Natural History”, which offers an outline of herbal medicine in Greece and Rome, provides a plethora of evidence regarding Pliny’s position towards his predecessors. This book is introduced by three paragraphs which express a reverence for earlier pharmacologists (prisci), who are said to have excelled not only in their indefatigable search for remedies, but also in passing on their knowledge to others in the most generous fashion. Their high scholarly ethos is sharply contrasted with the dishonourable attitude of those experts of his own times who wilfully hide their insights from others, either out of ill-will or in order to augment their personal reputation. Pliny condemns such a strategy since it impedes the transmission of valuable knowledge and thus reduces the possibilities for improving the quality of human life.44 42 Polybius III 59.3–5: ἐν δὲ τοῖς καθ’ ἡμᾶς τῶν μὲν κατὰ τὴν Ἀσίαν διὰ τὴν Ἀλεξάνδρου δυναστείαν, τῶν δὲ λοιπῶν τόπων διὰ τὴν Ῥωμαίων ὑπεροχὴν σχεδὸν ἁπάντων πλωτῶν καὶ πορευτῶν γεγονότων, ἀπολελυμένων δὲ καὶ τῶν πρακτικῶν ἀνδρῶν τῆς περὶ τὰς πολεμικὰς καὶ πολιτικὰς πράξεις φιλοτιμίας, ἐκ δὲ τούτων πολλὰς καὶ μεγάλας ἀφορμὰς εἰληφότων εἰς τὸ πολυπραγμονεῖν καὶ φιλομαθεῖν περὶ τῶν προειρημένων, δέον ἂν εἴη καὶ βέλτιον γινώσκειν κἀληθινώτερον ὑπὲρ τῶν πρότερον ἀγνοουμένων. 43 See e.g. Fögen 1999. 44 Nat. hist. XXV 1–2: Ipsa quae nunc dicetur herbarum claritas, medicinae tantum gignente eas tellure, in admirationem curae priscorum diligentiaeque animum agit. nihil ergo intemptatum inexpertumque illis fuit, nihil deinde occultatum quodque non prodesse posteris vellent. at nos elaborata iis abscondere ac supprimere cupimus et fraudare vitam etiam alienis bonis. ita certe recondunt qui pauca aliqua novere, invidentes aliis, et neminem docere in auctoritatem scientiae est. tantum ab excogitandis novis ac iuvanda vita mores absunt, summumque opus ingeniorum diu iam hoc fuit, ut intra unumquemque recte facta veterum perirent. (…) Pliny’s criticism of the conscious hiding of knowledge is resumed in Nat. hist. XXV 16.

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This harsh criticism of common practice among contemporary researchers is followed by a synopsis of those authors who have significantly contributed to advances in herbal pharmacology (Nat. hist. XXV 4–15). Roman specialists are listed before Greek writers, which is noteworthy also insofar as Pliny himself concedes that, quite in contrast to their general orientation towards practicality and utilitarianism, the Romans have not sufficiently appreciated this area of science (Nat. hist. XXV 4: minus hoc quam par erat nostri celebravere, omnium utilitatium et virtutum rapacissimi). The list of experts begins with Marcus Porcius Cato (234– 149 ), who is said to have dealt with herbal pharmacology only briefly, although he remained the only one to do so among the Romans for a long time. Next in line came the freedman Pompeius Lenaeus (1st cent. ), educated as a grammarian, and later on, in the Augustan period, Gaius Valgius Rufus. According to Pliny, serious interest in herbal pharmacology among Romans was not discernible until Pompeius’ defeat of the Pontic king Mithridates (66 ), who had engaged in major research in this area. It is particularly intriguing to see how Pliny assesses Mithridates’ scholarly accomplishments. In three full paragraphs (Nat. hist. XXV 5–7) he acknowledges his intellectual capacity, which is also evidenced by Mithridates’ astounding mastery of foreign languages.45 That Mithridates was one of Rome’s former arch-enemies seems to be almost irrelevant for Pliny, although he was active in politics and the military himself (Nat. hist. XXV 5): namque Mithridates, maximus sua aetate regum, quem debellavit Pompeius, omnium ante se genitorum diligentissimus vitae fuisse argumentis, praeterquam fama, intellegitur. For it was Mithridates, the greatest king of his time, whom Pompeius vanquished, and who was, we know by evidence as well as by report, a more attentive investigator of life’s problems than any of those born before him.

He obviates possible resentments against the Pontic king by taking his exalted reputation as a learned man absolutely for granted. The exceptional results achieved in his pharmacological research make his worthiness beyond any doubt, whereas any other than the scholarly aspects of Mithridates’ personality are secondary and negligible for Pliny. The political victory of the Romans over Mithridates interests Pliny only insofar as it enabled Pompeius’ freedman Pompeius Lenaeus to translate into Latin the notes left behind by the Pontic king.46 Thus it is first and foremost the 45 Nat. hist. XXV 6: illum solum mortalium certum est XXII linguis locutum, nec e subiectis gentibus ullum hominem per interpretem appellatum ab eo annis LVI, quibus regnavit. Similarly Nat. hist. VII 88; see also Quintilian, Inst. XI 2.50 and Aulus Gellius, Noct. Att. XVII 17.2. 46 Nat. hist. XXV 7: is ergo in reliqua ingeni magnitudine medicinae peculiariter curiosus et ab omnibus subiectis, qui fuere magna pars terrarum, singula exquirens scrinium commentationum harum et exemplaria effectusque in arcanis suis reliquit, Pompeius autem omni praeda regia potitus transferre ea sermone nostro libertum suum Lenaeum grammaticae artis iussit vitaeque ita profuit non minus quam reipublicae victoria illa. In this passage it is noteworthy that it is Pompeius himself, not his freedman, who is seen as the benefactor, although he simply commissioned the translation

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scholarly profit that the Romans derived from this conquest that matters most to Pliny. One may therefore argue that, for Pliny, Mithridates is much more important as a fruitful source of scientific information than as a political enemy of Rome. A similar case is the Carthaginian Mago with his agronomical treatise in 28 books, written in Punic.47 As both Pliny (Nat. hist. XVIII 22) and Columella (De re rust. I 1.13) report, there existed an official Latin version of his work, which had been commissioned by senate decree after the victory of the Romans over Carthage in 146 . As in the case of Mithridates, Pliny is not concerned here with Mago as a member of a nation that was Rome’s enemy; most important for him is the progress of knowledge for the Romans which resulted from the fact that Mago’s treatise was now available in Latin and thus readily accessible to those without any knowledge of Punic. With comments like these, Pliny suggests that he has not selected the sources upon which he relies for his own work on the basis of considerations of political expediency, but merely with regard to the superior quality of their factual accounts. Indeed, for highly innovative writings, the origin of their author does not play any significant role. Pliny therefore portrays himself to be as practical-minded and utilitarian as one could possibly expect from a Roman (cf. Nat. hist. XXV 4; quoted above). In the ensuing eight paragraphs, he considers Greek writers on herbal pharmacology (Nat. hist. XXV 8–15). This section consists not just of an enumeration of names, but also puts forward a fundamental methodological critique of authors such as Crateuas,48 Dionysius and Metrodorus, who are censured for not having provided particularly lucid accounts, since they preferred to describe medicinal plants with pictorial instead of verbal sketches and just wrote their (medicinal) effects underneath the pictures. Pliny finds this method questionable for various reasons: (1) The colors of plants can never be depicted as realistically as they occur in nature.49 (2) Pictorial representations are often reproduced inaccurately by copyists. (3) Graphical sketches do not make allowance for the fact that plants change their shape and appearance over the course of time.50 All of his arguments into Latin without being directly involved. On Pompeius in the Naturalis historia see Grüninger 1976, 71–76. 47 See Fögen 2009, esp. 72–73. 48 On Crateuas see esp. Wellmann, who thinks that his illustrated herbarium cannot be identical with his Ῥιζοτομικόν (1897, 5); rather, it must have been “eine mehr für das Bedürfnis des Volkes bestimmte, populäre Form der ῥιζοτομικά” (1897, 21). On illustrations in ancient botanical and pharmacological writings see Stückelberger 1994, 78–83. 49 Comparable with this argumentation is Nat. hist. XXI 2 (on the coronamenta): sed ne pictura quidem sufficiente imagini colorum reddendae mixturarumque varietati (…). 50 Nat. hist. XXV 8: praeter hos Graeci auctores prodidere, quos suis locis diximus, ex his Crateuas, Dionysius, Metrodorus ratione blandissima, sed qua nihil paene aliud quam difficultas rei intellegatur. pinxere namque effigies herbarum atque ita subscripsere effectus. verum et pictura fallax est coloribus tam numerosis, praesertim in aemulationem naturae, multumque degenerat transcribentium socordia. praeterea parum est singulas earum aetates pingi, cum quadripertitis varietatibus anni faciem mutent.

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amount to a plea for a precise verbal description of the morphology of medicinal plants, which can be adequately supplied only by those who devote themselves to a meticulous analysis (cognitio) of plants through autopsy. Pliny himself claims to have counteracted this deficit of many of his predecessors by gaining first-hand knowledge of plants from thorough study conducted under the guidance of Antonius Castor, who owned a garden with a great number of specimens and was a highly regarded specialist in the field of botany (Nat. hist. XXV 9). By associating himself with this established authority, Pliny makes it obvious to his readers that he was well-acquainted with the scholarly elite and had direct contact with them. He becomes an authority himself by virtue of his membership in this elite. What is more, he also substantiates his entitlement to be equipped with true expert knowledge by referring to his personal observation of plants.51 He is eager to avoid the impression of himself as an armchair scholar who confines himself to a compilation of what he found in other people’s books, and wants to come across as an intellectual who is actively involved in research, wherever possible. Autopsy was considered to be absolutely vital for conducting proper research especially in botany and pharmacology, as can be seen, for example, in the preface to Pedanius Dioscurides’ Materia medica (Περὶ ὕλης ἰατρικῆς), in which the author repeatedly emphasizes that his own descriptions of plants are for the most part based upon direct personal investigation. He could practise αὐτοψία during the numerous journeys that he undertook during his military career.52 The possibility that Pliny was influenced by Dioscurides’ concept cannot be dismissed, although he never refers to his contemporary or his work.53 Similarly, Scribonius Largus, another of Pliny’s contemporaries, highlights in the preface to his recipe-book Compositiones the great value of personal experience and autopsy (see Deichgräber 1950, 865). I find it more likely that these first-century authors found the methodological postulate of αὐτοψία 51 Nat. hist. XXV 18: in eadem provincia cognovi in agro hospitis nuper ibi repertum dracunculum appellatum cualem pollicari crassitudine, versicoloribus viperarum maculis (…). Further Nat. hist. XXV 116: mihi et tertia cyclaminos demonstrata est cognomine chamaecissos, uno omnino folio, radice ramosa, qua pisces necabantur. In Nat. hist. XXV 27 Pliny refers to a report of an eyewitness whom he personally consulted. 52 Pedanius Dioscurides, Mat. med. praef. 4: ἡμεῖς δὲ ὡς εἰπεῖν ἐκ πρώτης ἡλικίας ἄληκτόν τινα ἔχοντες ἐπιθυμίαν περὶ τὴν ἐπίγνωσιν τῆς ὕλης καὶ πολλὴν γῆν ἐπελθόντες – οἶσθα γὰρ ἡμῖν στρατιωτικὸν τὸν βίον – συναγηόχαμεν τὴν πραγματείαν ἐν πέντε βιβλίοις (…). Further Mat. med. praef. 3 and esp. praef. 7–8: τὸν δὲ βουλόμενον ἐν τούτοις ἐμπειρίαν ἔχειν δεῖ κατά τε τὴν ἀρτιφυῆ βλάστησιν ἐκ τῆς γῆς καὶ ἀκμάζουσι καὶ παρηκμακόσι παρατυγχάνειν· οὔτε γὰρ ὁ τῇ βλαστήσει ἐντετυχηκὼς μόνον δύναται τὸ ἀκμάζον γνωρίσαι οὔτε ὁ ἑωρακὼς τὰ ἀκμάζοντα τὸ ἀρτιφυὲς ἐπιγνῶναι. παρὰ γὰρ τοὺς μετασχηματισμοὺς τῶν φύλλων καὶ τὰ μεγέθη τῶν καυλῶν καὶ ἀνθῶν καὶ καρπῶν καί τινας ἄλλας ἰδιότητας μεγάλη πλάνη γίνεται ἐπ’ ἐνίων τοῖς μὴ οὕτω τὴν θέαν ποιησαμένοις. (…) ὁ δὲ πολλάκις ἐντετευχὼς αὐτοῖς καὶ ἐν πολλοῖς τόποις μάλιστα τὴν ἐπίγνωσιν ποιήσεται. 53 According to Riddle 1985, 13 and Touwaide 2000, 462–463, this indicates that Dioscurides’ Περὶ ὕλης ἰατρικῆς had not been finished or sufficiently widely disseminated when the Naturalis historia was being written. Therefore Pliny was unable to take it into account for his own work.

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in earlier medical and botanical writers, especially those, like Aristotle and Theophrastus, who subscribed to empiricism.54 The influence of historiography should not be underestimated either, especially that of Herodotus and Thucydides,55 the latter of whom provides the basis for the development of a so-called “pragmatically oriented historiography” (πραγματικὴ ἱστορία) as endorsed both by Polybius56 and, later on, in Lucian’s treatise “How to write history” (Πῶς δεῖ ἱστορίαν συγγράφειν, see esp. Hist. conscr. 47). But apart from botany and pharmacology, there are other instances in Pliny’s “Natural History” in which he makes a point of noting his autopsies of the objects in question and how these autopsies informed the facts described. There are at least four examples in Book VII on anthropology57 and various others in Book XVII on agriculture, to name but a few.58 It may be true that many classicists have a hard time trusting some of his supposed eyewitness accounts. But what is important for the purposes of this article is the fact that he stresses autopsy as part of his selfstylization as a scholar. This has been overlooked by modern scholarship which, since Gottfried Bernhardy’s verdict in the nineteenth century,59 has tended to view Pliny as someone who more or less completely refrained from first-hand observations.60

54 Theophrastus starts from the premise that the description of plants must be based upon θεωρία; see e.g. Hist. plant. I 1.1 (εὐθεωρητότεραι) and I 14.4 (αἴσθησις κοινοτέρα, further συνθεωρεῖν). In particular for the sake of botanical studies, the Lyceion send out researchers to collect first-hand information (see e.g. Hist. plant. III 12.4 on Satyrus). 55 Thucydides explains his method in I 20–23. On αὐτοψία see I 22.1–3, esp. I 22.2: τὰ δ’ ἔργα τῶν πραχθένθων ἐν τῷ πολέμῳ οὐκ ἐκ τοῦ παρατυχόντος πυνθανόμενος ἠξίωσα γράφειν οὐδ’ ὡς ἐμοὶ ἐδόκει, ἀλλ’ οἷς τε αὐτὸς παρῆν καὶ παρὰ τῶν ἄλλων ὅσον δυνατὸν ἀκριβείᾳ περὶ ἑκάστου ἐπεξελθών (see also V 26.5). On the significance of eyewitness reports in Herodotus and Thucydides see Schepens 1980. 56 On the role of αὐτοψία in Polybius and on his polemics against historiographers who in his view do not follow this methodological principle and are thus to be blamed for a βιβλιακὴ ἕξις, see e.g. Fögen 1999, with further literature. 57 Nat. hist. VII 35, VII 36 fin., VII 76 (the son of Cornelius Tacitus as ἐκτράπελος) and VII 83 (Athanatus dressed with an extremely heavy leaden cuirass). 58 A selection of further references to Pliny’s autopsy can be found in König & Winkler 1979, 22– 23. 59 Bernhardy 41865, 827–828: “häufiger als man erwartet ist offenbar daß Plinius nicht aus unmittelbarer Anschauung und selbständiger Forschung berichtet. Er spricht vielmehr als Buchgelehrter, als kompilirender [sic] Chronist des menschlichen Wissens, der sich zum Beruf macht ein Maximum von Denkwürdigkeiten aphoristisch und in kurzen Summen aufzuzeichnen; durch die Gewohnheit des unablässigen Lesens und Ausziehens ist ihm die Freiheit des Blicks getrübt worden und die Lust am Organisiren verloren gegangen.” 60 Most secondary literature mentions Pliny’s eyewitness reports only in passing, as for example Grüninger 1976, 45, with n. 45, Schilling 1978, 279, and Nikitinski 1998, 341, with n. 3. But see the short remarks in Serbat 1986, 2104–2105.

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6 Conclusions The traditional analysis of Pliny’s sources (“Quellenanalyse”), as practised mainly in the nineteenth century, pursued the question of which authors he really used and to what extent he did so. This often led to a degradation of Pliny to a mere compiler of his sources. In my own inquiry, I have focused on the ways in which the author of the “Natural History” deals with his predecessors in order to demonstrate that he employs a shrewd strategy of self-advertisement as a scholarly authority to his readers. His work is full of passages in which he reflects on his own scientific as well as literary methods and goals and contrasts them with those of others who have written on similar topics. By his differentiated comments on his predecessors and the character of their works, he develops a coherent picture of himself as a writer, which commends him to his audience. The target of his critique is not a uniform group of scholars; rather, it is quite diverse: it comprises contemporaries as well as earlier figures, Romans as well as non-Romans, some of whom are named explicitly, and some of whom are not.61 Some scholars have imputed a negative view of Greek authors to Pliny and attempted to explain this with his anti-Hellenism (see e.g. Grüninger 1976, 92–127). As my analysis demonstrates, this position cannot be fully substantiated, since Pliny comments rather approvingly on many of his Greek sources and even demonstrates a great deal of admiration for some of them; to quote Guy Serbat (1986, 2092–2093): “Pline éprouve une admiration sans limite pour les savants grecs authentiques; mais une vive hostilité à l’égard de tous les charlatans hellénophones”. Therefore, it is not the origin or nationality of an author alone which forms the basis for Pliny’s assessment, but rather the quality of the scholar’s work.62 On the other hand, it cannot be disputed that there are passages where Pliny does employ negative stereotypes towards the Greeks as a whole and where he praises the Romans for their virtues (see esp. Fögen 2009, 259–262). However, in this respect, he is not very different from Cicero and other Roman authors’ similar views of the Greeks: while these writers sometimes make negative remarks about their moral qualities in general, they are all too aware of their debt to Greek knowledge. Pliny’s evaluation of his predecessors’ accomplishments is a crucial part of his tactic to accentuate his high scholarly ethos by which he sets himself apart from 61 See Grüninger 1976, 48: “Kritik ist für ihn an jedermann möglich. Sie wird ausgesprochen gegenüber nicht namentlich genannten Autoren wie gegenüber bekannten und angesehenen, gegenüber Einzelmeinungen wie gegenüber der communis opinio, gegenüber heimischen Autoren wie fremden, gegenüber Früheren und Zeitgenossen. Er ist grundsätzlich weder laudator temporis acti noch Anbeter der Neuen.” 62 On this more extensively Serbat 1987; see also Schilling 1978, 280, Serbat 1986, 2092–2093, 2105– 2106, French 1994, 218–225, and Carey 2003, 23–25. The complex problem of Rome’s relationship to Greece, especially with regard to the arts and sciences, is discussed in Fögen (2000, passim), with further references (2000, esp. 90). Wallace-Hadrill’s hypothesis that in the Naturalis historia “Greek science in general is characterized by misplaced ingenuity and vanity” (1990, 93) cannot be sustained.

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numerous other technical writers. He conceives his “Natural History” not only as a comprehensive panorama of knowledge in the natural sciences, but also as a way to reflect on his own persona as a scholar. Pliny the Younger said that, for his uncle, no book was so bad that it did not bring at least some reward for the reader.63 We may add to this dictum that it was Pliny the Elder who saw himself as the one fully capable of judging to what extent a book was indeed useful. This is exactly what he does throughout the “Natural History”, and from his own perspective, it was precisely by demonstrating his capacity to distinguish between ‘good’ and ‘bad’ that he intended to corroborate his scholarly competence and authority.64

Bibliography Texts quoted Campbell, D. J. 1936. C. Plini Secundi Naturalis historiae Liber Secundus. A Commentary. Aberdeen. König, R., G. Winkler, K. Bayer, J. Hopp & K. Brodersen (eds.). 1973–2007. C. Plinius Secundus: Naturkunde in 37 Büchern (Lateinisch – deutsch). München etc. Rackham, H., W. H. S. Jones & D. E. Eichholz (eds.). 1938–1962. Pliny: Natural History. With an English translation (10 vols.). Cambridge, Mass.

Works quoted Beagon, M. 1992. Roman Nature. The Thought of Pliny the Elder. Oxford. Beagon, M. 2001. “Plinio, la tradizione enciclopedica e i mirabilia.” In: Storia della scienza, Roma, 735–745. Beaujeu, J. 1957. La vie scientifique à Rome au premier siècle de l’empire (Les Conférences du Palais de la Découverte D 51). Paris. Bernhardy, G. 41865. Grundriss der Römischen Litteratur. Braunschweig. Borst, A. 21995. Das Buch der Naturgeschichte. Plinius und seine Leser im Zeitalter des Pergaments. Heidelberg. Carey, S. 2003. Pliny’s Catalogue of Culture. Art and Empire in the “Natural History”. Oxford.

63 Pliny the Younger, Epist. III 5.10: Nihil enim legit, quod non excerperet; dicere etiam solebat nullum esse librum tam malum, ut non aliqua parte prodesset. 64 Versions of this paper, the arguments of which are much more fully developed in the chapter on Pliny the Elder contained in my book on knowledge, communication and self-stylization in ancient technical writers (Fögen 2009, 201–264), were presented at Humboldt University of Berlin, the University of California Los Angeles, Bryn Mawr College, the University of California Santa Barbara and the University of Cambridge. I am very grateful to the various audiences for sharing their ideas with me. Special thanks are due to Erik G. Huneke and Peter J. Heslin for invaluable help with the final draft.

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Citroni Marchetti, S. 1991. Plinio il Vecchio e la tradizione del moralismo romano. Pisa. Conte, G. B. 1994. “The inventory of the world. Form of nature and encyclopedic project in the work of Pliny the Elder.” In: Id., Genres and Readers. Lucretius, Love Elegy, Pliny’s Encyclopedia. Baltimore, 67–104. Deichgräber, K. 1950. Professio medici. Zum Vorwort des Scribonius Largus (Abhandlungen der Akademie der Wissenschaften und der Literatur in Mainz. Geistes- und sozialwiss. Klasse 1950, Nr. 9). Wiesbaden. Detlefsen, D. 1869. “Die Indices der Naturalis Historia des Plinius.” In: Philologus 28, 701–716. Detlefsen, D. 1881. Kurze Notizen über einige Quellenschriftsteller des Plinius (Programm des Königlichen Gymnasiums zu Glückstadt 1881). Glückstadt. Detlefsen, D. 1901. Die Beschreibung Italiens in der Naturalis historia des Plinius und ihre Quellen. Leipzig. Detlefsen, D. 1908. Die Geographie Afrikas bei Plinius und Mela und ihre Quellen. Berlin. Detlefsen, D. 1909. Die Anordnung der geographischen Bücher des Plinius und ihre Quellen. Berlin. Doody, A. 2001. “Finding facts in Pliny’s encyclopaedia. The summarium of the Natural history.” In: Ramus 30, 1–22. Ferraro, V. 1975. “Il numero delle fonti, dei volumi e dei fatti nella Naturalis historia di Plinio.” In: Annali della Scuola Normale Superiore di Pisa. Classe di Lettere e Filosofia III 5, 519–533. Fögen, T. 1999. “Zur Kritik des Polybios an Timaios von Tauromenion.” In: Listy filologické 122, 1–31. Fögen, T. 2000. “Patrii sermonis egestas”: Einstellungen lateinischer Autoren zu ihrer Muttersprache. Ein Beitrag zum Sprachbewußtsein in der römischen Antike. München & Leipzig. Fögen, T. 2005. “Antike Fachtexte als Forschungsgegenstand.” In: Id. (ed.), Antike Fachtexte – Ancient Technical Texts. Berlin & New York, 1–20. Fögen, T. 2007. “Pliny the Elder’s animals. Some remarks on the narrative structure of Nat. hist. 8–11.” In: Hermes 135, 184–198. Fögen, T. 2009. Wissen, Kommunikation und Selbstdarstellung. Zur Struktur und Charakteristik römischer Fachtexte der frühen Kaiserzeit. München. Franchet d’Espèrey, S. 1986. “Vespasien, Titus et la littérature.” In: Aufstieg und Niedergang der römischen Welt II 32.5, 3048–3086. French, R. 1994. Ancient Natural History. Histories of Nature. London & New York. Goodyear, F. R. D. 1982. “Pliny the Elder.” In: E. J. Kenney & W. V. Clausen (eds.), The Cambridge History of Classical Literature. Vol. 2: Latin Literature. Cambridge, 670–672. Grimal, P. 1965. “Encyclopédies antiques.” In: Cahiers d’Histoire Mondiale 9, 459–482. Grüninger, G. 1976. Untersuchungen zur Persönlichkeit des älteren Plinius. Die Bedeutung wissenschaftlicher Arbeit in seinem Denken. Diss. Freiburg im Breisgau. Healy, J. F. 1999. Pliny the Elder on Science and Technology. Oxford. Howe, N. P. 1985. “In defense of the encyclopedic mode. On Pliny’s Preface to the Natural History.” In: Latomus 44, 561–576. Isager, J. 1991. Pliny on Art and Society. The Elder Pliny’s Chapters on the History of Art. London. Janson, T. 1964. Latin Prose Prefaces. Studies in Literary Conventions. Stockholm. Kalkmann, A. 1898. Die Quellen der Kunstgeschichte des Plinius. Berlin. Klotz, A. 1906. Quaestiones Plinianae geographicae. Berlin. König, R., & G. Winkler 1979. Plinius der Ältere. Leben und Werk eines antiken Naturforschers. Darmstadt. Köves-Zulauf, T. 1970. “Die Ἐποπτίδες des Valerius Soranus.” In: Rheinisches Museum für Philologie 113, 323–358. Köves-Zulauf, T. 1973. “Die Vorrede der plinianischen ‘Naturgeschichte’.” In: Wiener Studien 86 (= N.F. 7), 134–184.

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Kroll, W. 1930. Die Kosmologie des Plinius (Abhandlungen der Schlesischen Gesellschaft für vaterländische Cultur. Geisteswissenschaftliche Reihe 3). Breslau. Langslow, D. R. 2000. Medical Latin in the Roman Empire. Oxford. Long, P. O. 2001. Openness, Secrecy, Authorship. Technical Arts and the Culture of Knowledge from Antiquity to the Renaissance. Baltimore & London. Müller, J. 1883. Der Stil des älteren Plinius. Innsbruck. Münzer, F. 1897. Beiträge zur Quellenkritik der Naturgeschichte des Plinius. Berlin. Murphy, T. 2004. Pliny the Elder’s Natural History. The Empire in the Encyclopedia. Oxford. Naas, V. 1997. “Extraordinaire et merveilleux dans l’Histoire naturelle. Réflexions sur la définition de l’‘encyclopédie’ plinienne.” In: J. Bouffartigue & F. Mélonio (eds.), L’Entreprise encyclopédique (= Littérales 21). Nanterre, 139–168. Naas, V. 2002. Le projet encyclopédique de Pline l’Ancien. Roma. Nikitinski, O. 1998. “Plinius der Ältere. Seine Enzyklopädie und ihre Leser.” In: W. Kullmann, J. Althoff & M. Asper (eds.), Gattungen wissenschaftlicher Literatur in der Antike. Tübingen, 341–359. Rabenhorst, M. 1907. Der ältere Plinius als Epitomator des Verrius Flaccus. Eine Quellenanalyse des siebenten Buches der Naturgeschichte. Berlin. Riddle, J. M. 1985. Dioscorides on Pharmacy and Medicine. Austin, Texas. Sallmann, K. G. 1971. Die Geographie des älteren Plinius in ihrem Verhältnis zu Varro. Versuch einer Quellenanalyse. Berlin & New York. Schepens, G. 1980. L’ ‘autopsie’ dans la méthode des historiens grecs du Ve siècle avant J.-C. (Verhandelingen van de Koninklijke Academie voor Wetenschappen, Letteren en Schone Kunsten van België. Klasse der Letteren 42, Nr. 93). Bruxelles. Schilling, R. 1978. “La place de Pline l’Ancien dans la littérature technique.” In: Revue de philologie 52, 272–283. Schonack, W. 1913. Die Rezepte des Scribonius Largus. Zum ersten Male vollständig ins Deutsche übersetzt und mit ausführlichem Arzneimittelregister versehen. Jena. Sconocchia, S. 1987. “La structure de la NH dans la tradition scientifique et encyclopédie romaine.” In: Helmantica 38, 307–316. Serbat, G. 1986. “Pline l’Ancien. État présent des études sur sa vie, son œuvre et son influence.” In: Aufstieg und Niedergang der römischen Welt II 32.4, 2069–2200. Serbat, G. 1987. “Il y a Grecs et Grecs! Quel sens donner au prétendu antihellénisme de Pline?” In: Helmantica 38, 273–282. Stahl, W. H. 1962. Roman Science. Origins, Development, and Influence to the Later Middle Ages. Madison, Wisconsin. Stückelberger, A. 1994. Bild und Wort. Das illustrierte Fachbuch in der antiken Naturwissenschaft, Medizin und Technik. Mainz. Summers, W. C. 1920. The Silver Age of Latin Literature. From Tiberius to Trajan. London. Touwaide, A. 2000. s. v. “Pedanios Dioskurides”. In: Der Neue Pauly (vol. 9). Stuttgart, 462–465. Urlichs, L. von 1889. “Pliniana.” In: Rheinisches Museum für Philologie 44, 259–266. Wallace-Hadrill, A. 1990. “Pliny the Elder and man’s unnatural history.” In: Greece & Rome 37, 80–96. Wellmann, M. 1897. Krateuas (Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen. Philosophisch-historische Klasse N.F. Bd. 2.1). Berlin.

B. Greek Medical Writing

Heinrich von Staden

Writing the Animal: Aristotle, Pliny the Elder, Galen 1

Abstract: This article provides a comparative examination of Aristotle, Pliny, and Galen’s writing about animals. Among the works examined are the five zoological works of Aristotle, books 9–10 of the Elder Pliny’s Natural History, and Galen’s Anatomical procedures and On the Uses of Parts. In their ways to grapple with textualizing zoology, profiles of the three authors as science writers, their textual methods, their self-representation and respective rhetoric emerge. Special attention will be devoted to writing on primates and the construction or destabilization of boundaries between man and animal.

I Introduction Formidable difficulties confront authors who write about non-human animals. One of these, widely discussed in recent decades, is epistemological. The incommensurability of human cognitive structures, categories and capacities with many features of non-human animals frequently led to scientific texts based on principles, categories and questions that make demands of animals that animals could answer only by becoming negative or positive mirror images of humans. Many ancient technical texts too describe the diverse cognitive, social and moral lives of animals in all too human terms, even when they recognized that non-human animals differ to varying degrees not only from the human animal but also from one another in their biological complexity, in their cognitive and emotional lives, in their degrees of sociability and collaborative activity, in their systems of communication,2 and in their moral characteristics. Pliny the Elder, for instance, opened the first of his books on non-human animals in the Natural History as follows: Let us move on [from the human animal] to the rest of the animals, and first to terrestrial animals. The largest of these is the elephant, and it is closest to humans in its faculties of perception, inasmuch as it comprehends the language of its own fatherland, obeys orders, remembers duties it has learned, and takes pleasure in love and honor. In fact, it possesses integrity, wisdom, and fairness – all of which are rare even among humans – and it also worships the sun and the moon and has reverence for the stars. There are authorities according to whom in the mountainous regions of Mauretania, when the new moon is shining bright,

1 I am grateful to other participants in this volume for useful suggestions and, in particular, to Markus Asper, whose work and insights have been a source of inspiration since our first discussion in 1996. 2 See Fögen 2007b.

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herds of elephants descend to a river called Amilo, and there they purify themselves with due ritual by spraying themselves all around with water. Having thus hailed the heavenly body [the authorities report], they turn back to the forests carrying in front of them those of their calves that have tired. Elephants are also believed to have an understanding of the religion of others…3

Pliny thus is a writer who ‘knows’ elephants, but his knowledge of them is conceived almost exclusively in all too familiar human categories: human cognitive capacities, human pleasures, human virtues, human religion, human parenting. This passage vividly illustrates a second obstacle that is closely related to the epistemological hurdles: language. An author trying to write ‘scientifically’ about animals faces at least three linguistic challenges: the inability of the non-human animal to respond in human language to the human investigator’s interrogation of the subject; the inadequacy of the tool-kits of human language to account for some features of non-human animals; and the gap between the nature of ordinary language and the nature of the claims made by science. In short, the at times intractable endeavor of trying to force the investigated organism – the observed exterior and the seen or inferred interior of the animal – into words, descriptions, arguments and narratives that will meet the demands of textualized science, including precision, logic, clarity, and a lack of ambiguity, presents the writer of science with notorious prolesm, as some ancients recognized. A third challenge to writing the animal ‘scientifically’ is the choice of literary form. Different authors resorted to different literary forms, and some freely experimented by interlacing several traditional forms with a single work.4 An awareness of the literate culture’s generic habits entails stylistic, rhetorical, and socio-linguistic expectations on the part of both author and audience. Such expectations can, however, deflect the author’s and reader’s attentiveness to scientific truth, to scientific ‘facts’, and to a rigorous interpretation of these ‘facts’. Some ancients responded to the threat of such deflections by trying to write what the art historian James Elkins in a different context called “beautiful, dry, 3 Nat. hist. VIII 1–3: Ad reliqua transeamus animalia et primum terrestria. Maximum est elephans proximumque humanis sensibus, quippe intellectus illis sermonis patrii et imperiorum oboedientia, officiorum quae didicere memoria, amoris et gloriae uoluptas, immo uero, quae etiam in homine rara, probitas, prudentia, aequitas, religio quoque siderum, Solisque ac Lunae ueneratio. Auctores sunt in Mauretaniae saltibus ad quendam amnem, cui nomen est Amilo, nitescente luna noua greges eorum descendere ibique se purificantes sollemniter aqua circumspergi, atque ita salutato sidere in siluas reuerti uitulorum fatigatos prae se ferentes. Alienae quoque religionis intellectu creduntur… On Pliny’s account of elephants (VIII 1–34) see French 1994, 216–218; Bona 1991, 42–69; Giebel 2003, 87–94; Mastrorosa 2003; Fögen 2007a, 185–188, and 2007b, 53–54. 4 On ‘technical treatises’ and their literary forms in antiquity, see Fuhrmann 1960; Nicolet and Gros 1996; van der Eijk 1997; Asper 1998, 2001, 2003, and 2007; Kullmann et al. 1998; von Staden 1998; Meißner 1999; Wöhrle 1999; Netz 1999 and 2004; Formisano 2001; Mastrorosa et al. 2002; Celantano 2003; Horster and Reitz 2003; Rodríguez Alfageme 2004; Fögen 2005 and 2009; Diederich 2007; Taub & Doody 2009; Montero Cartelle 2010. For cross-cultural perspectives see Chemla 2004; on modern scientific writing see e.g. Holmes 1987 and 1991; Dear 1991.

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and distant texts”:5 seemingly transparent, dispassionate textual vehicles for the transmission of scientific facts and explanations concerning animals (see especially section II below). Others, however, yielded to writing as an expressive medium, exploiting the fact that writing has a capacity not only for scientific abstraction and cool reflection but also for emotion – that is, both for representing authorial affect and for provoking audience affect – and they freely incorporated a strong affective dimension in their strategies of narration and representation (see, in particular, section IV below). To the latter contexts belongs a fourth challenge for the ancient writer of animal science: how to navigate the relation between scientific authorship and scientific authority and, in particular, how to construct forms of authorial self-presentation appropriate to the writing of science. Within the scope of a single article it obviously is impossible to address all these issues. This contribution therefore will try to shine a spotlight briefly on only two issues: the problems posed by language for ancient attempts to textualize the animal, and the authorial shaping of the author and his authority. The principal examples are drawn from Aristotle (part II below), with brief comparative glances at Pliny the Elder (part III) and Galen (part IV).

II Aristotle, the animal, and language In Aristotle’s voluminous writings on animals he signals his awareness of the challenges presented by language in several ways. Three are singled out here (II.a– c below): the use of non-verbal, mainly visual aids (II.a); the emphasis on the namelessness of numerous zoological phenomena (II.b); and the nameless author fending off ambiguity and equivocity (II.c).

II.a Visualizing and textualizing the animal Apparently in recognition of the limitations of a verbal representation of animals, Aristotle has recourse to visual means for the communication of his science more frequently in the works on animals than in any other part of his œuvre. While he introduces visual diagrams in some of his non-biological works too, it is particularly in his representations of animal anatomy that he explicitly brings into play the complementarity of the visual and the verbal. Yet with a few notable exceptions,6 his recurrent emphasis on the profoundly visual foundations of his animal science, and his use of visual means to aid visualization on the part of the reader have been relegated to footnotes or passing remarks, perhaps because modern 5 Elkins 1997. 6 E.g., Stückelberger 1993; 1994, 74–78; 1998, 287–293; Kullmann 1998, 130–131.

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scholarship has been more interested in the theoretical and classificatory superstructures of Aristotle’s enormous biological project than in his authorial strategies of communicating his science.7 Aristotle was, of course, neither the first nor the last ancient scientist to use visual aids.8 Diagrams were widely used in various kinds of technical writing, and especially in the exact sciences and in works on mechanical technology.9 In addition, astronomers used two- and three- dimensional objects as aids for calculating and visualizing the positions, sizes and movements of celestial bodies;10 geographers used armillary spheres and maps;11 authors of surgical treatises developed a range of images to illustrate the use of various instruments and the proper way of positioning the patient’s body in various operations,12 and treatises on medicinal substances used illustrations, especially of plants and animal substances, as did texts on venomous animals, etc.13 Illustrations accompanying written texts, like objects that aided visualization, were not the only visual means of communicating science. The private or public showing of the scientific investigation of a living or dead animal – a visual performance of animal science accompanied by the scientist’s oral commentary – had become a well attested medium no later than the second century .14 Such visual showing and its verbal accompaniment, that is, oral exegesis of the observed, while very significant, are fleeting, transient modes of demonstrating and transmitting science: performed at a given moment and place, shown and then gone, they 7 With rare exceptions, modern accounts of visual aids in ancient science have tended to remain descriptive, i.e., the relation between visual images, visualization, explanation, argument, and narrative in ancient technical texts has not yet been subjected to the in-depth analyses that have enhanced our understanding of, for example, the role of visualization in ancient and modern mathematics (see e.g. Mancosu et al. 2005). See also Mazzolini 1993. 8 On Greek and Latin illustrated texts see Weitzmann 1947, 47–49; 1959 and 1977; Kadar 1978; Grmek 1984; Blanck 1992, 102–112; Stückelberger 1993, 1994 and 1998; Gros 1996; Marganne 2004, 35–58. On the controversial ‘Artemidorus Papyrus’ and its illustrations, see Gallazzi & Kramer 1998; Canfora 2008; Gallazzi et al. 2008; Brodersen & Elsner 2009. 9 See Netz 1999 and 2004; Asper 2003; 2007, 75, 103–104, 108 (nn. 102 and 106), 113, 123 n. 205, 126 n. 224, 139–140, 149, 279–280, 284–287, 347–348, 365, 370, 373. 10 See Ptolemy, Almagest I 5, and Geography I 2.2, I 3.3; Neugebauer 1949, 240–256; Segonds 1981; Stückelberger 1988, 59–60 and plates III-IV; Stückelberger 1994, 27–46. 11 E.g., Ptolemy, Geography VII 5–7, VIII 1–28; Stückelberger & Graßhoff 2006, vol. II, pp. 742–907. 12 Apollonius of Citium, in his extant first-century  surgical manual (known as his ‘commentary’ on the Hippocratic treatise On Joints), repeatedly refers to illustrations (ζωγραφία, ζωγραφικὴ σκιαγραφία, ὑπόδειγμα, ὑπογραφή, ὑπογράφω) that accompanied his text. Whether and to what extent Apollonius’ illustrations resembled those transmitted with his text in a tenth-century Florentine manuscript (Cod. Laurentianus 74.7), remains disputed. See Weitzmann 1959, 21 and fig. 26; 1970, 108–109; Kudlien 1960; Kollesch et al. 1965, plates I–XXX; Grmek & Gourevitch 1998, 306– 308; Stückelberger 1994, 88–90. Cf. Grmek 1984. 13 See Pliny, Nat. hist. XXV 8 (on Crateuas’ botanical illustrations); Weitzmann 1959, 11–18; 1947, 9–10, 94–95; Marganne 2004, 37–42. 14 See Debru 1994; von Staden 1995a and 1997; Gleason 2009.

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are present yet instantly absent, stored only in memory fragments. For all the challenges that writing science entails, writing therefore became the norm for some ancient scientists who did research on animals,15 even if they underscored the complementarity of the visual and written. In his surviving treatises on animals and in some of his psychophysical writings, Aristotle repeatedly refers to visual representations in his work Dissections (Anatomai). No longer extant, this work may have consisted of six to eight books.16 In the opening book of his most extensive extant work on animals, his Researches on Animals (Historia Animalium), for instance, he says: All [the above-mentioned parts, including the heart, lung, diaphragm, kidneys, and bladder] are naturally arranged the same way in the female [as in the male]; for there is no difference in the internal parts except the uterus, the visual appearance (opsis) of which should be studied from the diagram in [my treatise] Dissections.17

So too, in this excerpt from On Generation of Animals: These things [i.e., how embryos receive nourishment, and details concerning the uterus of certain ambidentate hornless animals] should be studied both on the basis of the drawings [paradeigmata] in the Dissections and on the basis of the written descriptions in the Researches [Historia animalium].18

My translation of paradeigmata as ‘drawings’ perhaps requires brief comment, given that most modern translators have taken it to mean ‘examples’ (which is of course a widely attested meaning of paradeigma). First, from the classical period on, paradeigma also is used to refer to an architectural ‘plan’, ‘model’ or ‘drawing’, or to a ‘model’ made by a sculptor in preparation for executing a larger sculpture, or to a ‘sketch’ or ‘outline’ made by a painter before executing a painting, etc.19 Secondly, in all other instances in which Aristotle draws a direct contrast between

15 I say ‘some’, because others did not commit their results to writing, e.g. the illustrious secondcentury anatomist Quintus; see Galen, Anat. adm. XIV 1 (Simon I, 231; Duckworth 183; Garofalo 1991, III, 1039–1040); In Hipp. Nat. hom. I 27 and II 6 (Kühn 15.68, 136; Mewaldt, Corp. Med. Graec. V 9.1, 36.19–23, 70.11–13). 16 See Gigon 1987, 492b31 (treatise no. 103). 17 Aristotle, Hist. anim. I 17.497a30–32: τὸν αὐτὸν δὲ τρόπον καὶ ἐν τῷ θήλει πάντα πέφυκε· διαφέρει γὰρ οὐθενὶ τῶν ἔσω πλὴν ταῖς ὑστέραις, ὧν ἡ μὲν ὄψις θεωρείσθω ἐκ τῆς διαγραφῆς τῆς ἐν ταῖς ἀνατομαῖς. 18 Aristotle, Gen. anim. II 7.746a14–15: δεῖ δὲ ταῦτα θεωρεῖν ἔκ τε τῶν παραδειγμάτων τῶν ἐν ταῖς ἀνατομαῖς καὶ τῶν ἐν ταῖς ἱστορίαις γεγραμμένων. 19 For παράδειγμα in the sense of architectural ‘model’ or ‘plan’, or ‘drawing’, see e.g., Herodotus V 62; Inscr. Graec. II2.1667.95 and XI(2).161 A 43, 75, 203 B 95 al. (Delos, 3rd cent. ). For παράδειγμα as sculptor’s or painter’s ‘model’, see Plato, Tim. 28c, Res publ. 500e; Inscr. Graec. I2.374.248 and II2.1675.23 (pl.). Cf. Herodotus II 86 (‘samples’ of mummies made from wood); Pap. Soc. Ital. 5.485 (3rd cent. ); Pap. Cair. Zen. 445.9, 665.2 (3rd cent. ). See Gros 1996, 38. As is well known, Aristotle uses παράδειγμα in the sense of ‘argument’, ‘example’ or ‘proof from example’ too.

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the content of his Dissections and that of his other biological works, the contrast is between visual images and verbal accounts. These two considerations do not preclude the possibility that paradeigmata here might mean ‘examples’, but contextually the more plausible interpretation here seems to be ‘drawings’. Aristotle’s Researches on Animals is especially rich in references to the illustrations in his lost treatise Dissections, as these further examples illustrate: The [female] cuttlefish has two sacs and inside them numerous eggs that resemble white hailstones. The position of each of these parts should be studied on the basis of the diagram in the Dissections.20 There are also other differences between the ducts for spermatic excretions [in the male Selachia, including dogfish, angel-fish, torpedo-fish, sting-ray, etc.] and the passages of the uterus … But the arrangement of the ducts in the males should be studied from the diagrams drawn in the Dissections.21 The differences between the uteri of these animals [scil. dogfish and selachians], compared both with one another and with the rest of the fishes, could be studied more accurately by means of the figures from the Dissections.22

Some passages that modern scholars have been taken to be references to the Dissections but that do not explicitly refer to diagrams, figures or drawings are, however, less conclusive, for instance: “What the shape of the uterus in fishes looks like should be studied from the Dissections [or: ‘from dissections’?].”23 In such cases, ‘from the dissections’ (ἐκ τῶν ἀνατομῶν) could refer either to Aristotle’s illustrated work Dissections or simply to what could be observed by doing dissections and vivisections (ἀνατομαί).24 It nevertheless is abundantly attested that Aristotle had recourse to illustrations in his Dissections, and that he repeatedly drew attention to these as a necessary complement to his written accounts of animals.

20 Hist. anim. IV 1.525a6–8: ἡ δὲ σηπία δύο τε τὰ κύτη καὶ πολλὰ ᾠὰ ἐν τούτοις, χαλάζαις ὅμοια λευκαῖς. ἕκαστα δὲ τούτων ὡς κεῖται τῶν μορίων, θεωρείσθω ἐκ τῆς ἐν ταῖς ἀνατομαῖς διαγραφῆς. 21 Hist. anim. VI 11.566a10–15: ἔχουσι δὲ διαφορὰς καὶ ἄλλας μὲν πρὸς ἄλληλα οἵ τε θορικοὶ πόροι καὶ οἱ ὑστερικοί, καὶ ὅτι οἱ μὲν προσπεφύκασι τῇ ὀσφύϊ, οἱ δὲ τῶν θηλειῶν πόροι εὐκίνητοί εἰσι καὶ λεπτῷ ὑμένι προσειλημμένοι. θεωρείσθωσαν δὲ καὶ οἱ τῶν ἀρρένων πόροι, ὡς ἔχουσιν, ἐκ τῶν ἐν ταῖς ἀνατομαις διαγεγραμμένων (the variant reading ἐκ τῶν ἀνατομῶν is adopted by Balme in his edition, 2002). 22 Hist. anim. III 1.511a11–14: αὐτῶν δὲ τούτων πρὸς ἄλληλά τε καὶ πρὸς τοὺς ἄλλους ἰχθῦς ἡ διαφορὰ τῶν ὑστερῶν ἀκριβέστερον ἂν θεωρηθείη τοῖς σχήμασιν ἐκ τῶν ἀνατομῶν. 23 Hist. anim. VI 10.565a12–13: τὸ μὲν οὖν σχῆμα τῆς ὑστέρας ὡς ἔχει, ἐκ τῶν ἀνατομῶν θεωρείσθω. 24 Stückelberger 1998, 286–293, and Gigon 1987, fr. 297–324 (pp. 494b–502b), seem to assume that all Aristotle’s references to αἱ ἀνατομαί are to Aristotle’s lost illustrated work, and in many cases they might be right, but I share the more differentiating approach adopted by Kullmann 1998, 130 n. 33. Many of the following passages, included by Gigon among the ‘fragments’ from the Anatomai, seem to provide inconclusive evidence: Respir. 8.474b9; 16.478a26-b2. Hist. anim. III 1.509b21–24; IV 4.529b18–19; IV 4.530a30–31. Part. anim. II 3.650a31–32; III 4.666a8–10; III 6.668b28–30; III 14.674b15–17; IV 2.677a8–10; IV 5.679b32–680a2; IV 8.684b1–5; IV 10.689a16–20; IV 13.696b14–16. Gen. anim. II 4.740a23–24; IV 1.764a33–36; IV 4.771b32–33; V 1.779a7–11.

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Indeed, it has been argued that the apparently sizable work Dissections consisted mainly or exclusively of anatomical illustrations of the parts of various animals,25 though other scholars have suggested that it contained a text too.26 Aristotle’s use of visual images to convey what words alone cannot, is, however, not confined to his lost Dissections. Illustrations were also imbedded in several of his extant works on animals. In his account in Researches on Animals of the embryonic development of the baby cuttlefish from an egg, for example, Aristotle says: At first the eyes appear very large in cuttlefish embryos too, as in the other animals. The egg is where Α is, the eyes where Β and Γ are, the baby cuttlefish itself [still attached to the egg] where Ε is, and the cuttlefish itself is Δ. It conceives in the spring and gives birth after fifteen days.27

Here alpha, beta, gamma, etc. seem to refer to various points in a visual figure – a figure to which Aristotle also appears to allude in On Generation of Animals: While being formed, the female is attached to the egg by its front part, because only there can it be attached. You see, only in this animal do the back part and the front part face in the same direction. But the figure representing how the parts are positioned during their formation must be examined in the Researches [i.e., Historia animalium]28.

Aristotle’s lengthy account of the male genitalia in viviparous animals that have feet likewise was accompanied by a schematic figure: The things that have been described should be studied from this diagram [sketch?]: Α marks the starting point of the passages from the aorta; Κ marks the heads of the testicles and the passages that come down [into them]; ΩΩ mark the [two] passages that come from these and

25 Louis 1964–1969, I, xxx n. 5 (“ce receuil…ne comportait que des figures”); Stückelberger 1994, 76–77; 1998, 289; Kullmann 1998, 130. 26 Sharples 1995, 34–37, follows earlier scholars in characterizing the Anatomai as a compilation of textual material from different sources. Cf. Kullmann 1998, 130 n. 31. 27 Hist. anim. V 18.550a23–27: μέγιστοι δὲ φαίνονται πρῶτον, ὥσπερ καὶ ἐν τοῖς ἄλλοις, καὶ ἐν τούτοις οἱ ὀφθαλμοί. ᾠὸν ἐφ’ οὗ τὸ Α, ὀφθαλμοὶ ἐφ’ οὗ τὸ ΒΓ, τὸ σηπίδιον αὐτὸ τὸ Ε, τὸ δ’ ἐφ’ οὗ τὸ Δ. κύει δὲ τοῦ ἔαρος, ἀποτίκτει δ’ ἐν ἡμέραις πεντεκαίδεκα. Peck 1970, 168–169, note a, athetizes the sentence referring to the diagram, while Balme 2002 retains it; the manuscript tradition provides good evidence for a diagram here (see Balme’s app. crit.). Most earlier editors also accepted the presence of a diagram in this passage, e.g. J. C. Scaliger (in: Schneider 1811, I 205); Schneider 1811, II 216 and III 340 n. 5; Bekker 1831; Aubert & Wimmer 1868, 502; Dittmeyer 1907; Louis 1964–1969, II 36. 28 Gen. anim. III 8.758a21–25: προσπέφυκε δ’ ἡ γιγνομένη σηπία τοῖς ᾠοῖς κατὰ τὸ πρόσθιον· ταύτῃ γὰρ ἐνδέχεται μόνον· ἔχει γὰρ μόνον ἐπὶ ταὐτὸ τὸ ὀπίσθιον μέρος καὶ τὸ πρόσθιον. τὸ δὲ σχῆμα τῆς θέσεως ὃν ἔχει γιγνόμενα τρόπον δεῖ θεωρεῖν ἐκ τῶν ἱστοριῶν.

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sit closely next to the testicles; ΒΒ mark the passages that bend back in which the white fluid is; Δ the penis, Ε the bladder, ΨΨ the [two] testicles.29

In On the Movement of Animals Aristotle likewise refers to imbedded diagrams: If one of the parts [of an animal] moves, another of its parts must be at rest. And for this reason animals have flexing joints. In fact, they use their joints just like a center, and the entire part in which the joint is becomes both one and two, both straight and bent, changing potentially and actually thanks to the joint. And when [the part] is being bent and moved, one point in the joints is moved while another remains still, as if, on a diameter ΑΔ, it were to remain fixed while Β is moved and ΑΓ come about. But there [in geometry] the center seems indivisible in every way (for, as they say, in those cases the notion that motion takes place, is their fictive notion, since none of the mathematical entities moves). In the flexing joints, by contrast, the [center] becomes, both potentially and actually, at times one and at other times divided.30 The middle part of the body necessarily is one in potentiality but becomes more than one in actuality. You see, the limbs are set in motion simultaneously from the origin, and when either of the two limbs is at rest, the other is moved. I mean, for example, in the [figure] ΑΒΓ, Β is moved, while Α sets in motion. But something must be at rest, if one [part] is to be moved, the other to set in motion; Α then, though it is one in potentiality, will be two in actuality, so that it necessarily is not a point but a magnitude.31 It is, however, possible that Γ is moved simultaneously with Β, so that both of the origins in Α necessarily impart movement while being moved. There must therefore be another thing besides these that sets in motion but is not moved. Otherwise the extremities and the origins which are in Α would rest on one another when they are moved, just like people who, while leaning their backs against one another, move their legs.32

29 Hist. anim. III 1.510a29–35: θεωρείσθω δὲ τὰ εἰρημένα ταῦτα καὶ ἐκ τῆς ὑπογραφῆς τῆσδε. τῶν πόρων ἀρχὴ τῶν ἀπὸ τῆς ἀρτηρίας, ἐφ’ οἷς Α· κεφαλαὶ τῶν ὄρχεων καὶ οἱ καθήκοντες πόροι, ἐφ’ οἷς Κ· οἱ άπὸ τούτων πρὸς τῷ ὄρχει προσκαθήμενοι, ἐφ’ οἷς τὰ ΩΩ· οἱ δ’ ἀνακάμπτοντες, ἐν οἷς ἡ ὑγρότης ἡ λευκή, ἐφ’ οἷς τὰ ΒΒ· αἰδοῖον Δ, κύστις Ε, ὄρχεις δ’ ἐν οἷς τὰ ΨΨ. 30 Mot. anim. 1.698a16-b1: δεῖ γάρ, ἂν κινῆταί τι τῶν μορίων, ἠρεμεῖν τι· καὶ διὰ τοῦτο αἱ καμπαὶ τοῖς ζῴοις εἰσίν. ὥσπερ γὰρ κέντρῳ χρῶνται ταῖς καμπαῖς, καὶ γίνεται τὸ ὅλον μέρος, ἐν ᾧ ἡ καμπή, καὶ ἓν καὶ δύο, καὶ εὐθὺ καὶ κεκαμμένον, μεταβάλλον δυνάμει καὶ ἐνεργείᾳ διὰ τὴν καμπήν. καμπτομένου δὲ καὶ κινουμένου τὸ μὲν κινεῖται σημεῖον τὸ δὲ μένει τῶν ἐν ταῖς καμπαῖς, ὥσπερ ἂν εἰ τῆς διαμέτρου ἡ μὲν Α καὶ ἡ Δ μένοι, ἡ δὲ Β κινοῖτο, καὶ γίνοιτο ἡ ΑΓ. ἀλλ’ ἐνταῦθα μὲν δοκεῖ πάντα τρόπον ἀδιαίρετον εἶναι τὸ κέντρον (καὶ γὰρ τὸ κινεῖσθαι, ὡς φασί, πλάττουσιν ἐπ’αὐτῶν· οὐ γὰρ κινεῖται τῶν μαθηματικῶν οὐδέν), τὰ δ’ ἐν ταῖς καμπαῖς δυνάμει καὶ ἐνεργείᾳ γίνεται ὁτὲ μὲν ἓν ὁτὲ δὲ διαιρετά. 31 See e.g. Aristotle, Physics VI 10.240b8–9, VIII 6.258b25: a mathematical point is without parts (ἀμερές) i.e., indivisible, and “that which is without parts cannot be moved”. 32 Mot. anim. 9.702b25–703a1: τὸ δὲ μέσον τοῦ σώματος μέρος δυνάμει μὲν ἕν, ἐνεργείᾳ δ’ ἀνάγκη γίνεσθαι πλείω· καὶ γὰρ ἅμα κινεῖται τὰ κῶλα ἀπὸ τῆς ἀρχῆς, καὶ θατέρου ἠρεμοῦντος θάτερον κινεῖται. λέγω δ’ οἷον ἐπὶ τῆς ΑΒΓ, τὸ Β κινεῖται, κινεῖ δὲ τὸ Α. ἀλλὰ μὴν δεῖ γέ τι ἠρεμεῖν, εἰ μέλλει τὸ μὲν κινεῖσθαι, τὸ δὲ κινεῖν. ἓν ἄρα δυνάμει ὂν τὸ Α, ἐνεργείᾳ δύο ἔσται, ὥστ’ ἀνάγκη μὴ στιγμὴν ἀλλὰ μέγεθός τι εἶναι. ἀλλὰ μὴν ἐνδέχεται τὸ Γ ἅμα τῷ Β κινεῖσθαι, ὥστ’ ἀνάγκη ἀμφοτέρας τὰς ἀρχὰς τὰς ἐν τῷ Α κινουμένας κινεῖν. δεῖ τι ἄρα εἶναι παρὰ ταύτας ἕτερον τὸ κινοῦν καὶ μὴ κινούμενον. ἀπερείδοιντο μὲν γὰρ ἂν τὰ ἄκρα καὶ αἱ ἀρχαὶ αἱ ἐν τῷ Α πρὸς ἀλλήλας κινουμένων, ὥσπερ ἂν εἴ τινες τὰ νῶτα ἀντερείδοντες κινοῖεν τὰ σκέλη.

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The final chapter of On the Movement of Animals seems to refer back to this figure: One must conceive of Α as the origin. Then the movements go to the origin from each of the letters [of the alphabet] that have been drawn, and from the origin when it is moved and changes (you see, it is potentially many), the movement of Β to Β, that of Γ to Γ, that of both to both.33

Aristotle’s short work On the Locomotion of Animals likewise resorts to diagrams, as in the following passage: A sign [evidence] that snakes move themselves like quadrupeds is this: they change, in turn, the concave to convex and the convex to concave. You see, when in turn the left of their forward parts is leading, the concavity in its turn becomes reversed, for the right again becomes the inner. The right front point is Α, the left front Β; the left hind is Γ, the right hind Δ.34 Of the land animals, snakes move themselves this way, and of the aquatic animals, eels, conger-eels and lampreys, and of the rest all those that have a snake-like form.35

Both through the illustrations in his Dissections and through his use of diagrammatic figures in most of his extant treatises on animals, Aristotle thus gives strong signals that, while words can do much of the work of scientific description and explanation, visual images are an essential complement to language in his communication of his animal science.36 33 Mot. anim. 11.703b29–33: δεῖ γὰρ νοῆσαι τὸ Α ἀρχήν. αἱ οὖν κινήσεις καθ’ ἕκαστον στοιχεῖον τῶν ἐπιγεγραμμένων ἐπὶ τὴν ἀρχὴν ἀφικνοῦνται, καὶ ἀπὸ τῆς ἀρχῆς κινουμένης καὶ μεταβαλλούσης, ἐπειδὴ πολλὰ δυνάμει ἐστίν, ἡ μὲν τοῦ Β [ἀρχή secl. Nussbaum] ἐπὶ τὸ Β, ἡ δὲ τοῦ Γ ἐπὶ τὸ Γ, ἡ δ’ ἀμφοῖν ἐπ’ ἄμφω. Farquharson, in: Smith & Ross 1912, translates καθ’ ἕκαστον στοιχεῖον τῶν ἐπιγεγραμμένων as “from each letter in the diagram we have drawn,” referring the reader to 702b29; identically, Nussbaum 1985, 54; similarly, Torraca 1958, 37: “conforme a ogni lettera del diagramma inanzi disegnato.” More cautious is Kollesch 1985, 22,50: “im Bereich jedes einzelnen von den eingetragenen Buchstaben”. See also Michael of Ephesus, in: Comm. Arist. Graec. 22.2, Berlin 1904, 125.14–126.25, 130.8–26. 34 The manuscripts PSU reverse ‘left hind’ and ‘right hind’; Louis (Budé ed. 1973) prefers the reading of PSU, whereas Jaeger (Teubner ed. 1913) prefers the reading of ΥΖ (and Michael of Ephesus), which is adopted here. 35 Inc. anim. 7.707b22–30: σημεῖον δ’ ὅτι ὁμοίως κινοῦνται τοῖς τετράποσιν· ἐν μέρει γὰρ μεταβάλλουσι τὸ κοῖλον καὶ τὸ κυρτόν. ὅταν γὰρ τὸ ἀριστερὸν πάλιν τῶν προσθίων ἡγήσηται, ἐξ ἐναντίας πάλιν τὸ κοῖλον γίνεται· τὸ γὰρ δεξιὸν ἐντὸς πάλιν γίνεται. σημεῖον δεξιὸν πρόσθιον ἐφ’ οὗ Α, ἀριστερὸν ἐφ’ οὗ Β, ὀπίσθιον ἀριστερὸν ἐφ’ οὗ Γ, δεξιὸν ἐφ’ οὗ Δ. οὕτω δὲ κινοῦνται τῶν μὲν χερσαίων οἱ ὄφεις, τῶν δ’ ἐνύδρων αἱ ἐγχέλεις καὶ οἱ γόγγροι καὶ αἱ σμύραιναι, καὶ τῶν ἄλλων ὅσα ἔχει τὴν μορφὴν ὀφιωδεστέραν. 36 It is worth noting that Aristotle’s zoological illustrations seem to have been known in the Hellenistic period. In the late third or early second century  Aristophanes of Byzantium, who succeeded Eratosthenes as head of the Alexandrian Library about 194 , composed a lengthy abridgement of Aristotle’s works on animals, in which he refers to drawings of the uterus in Aristotle’s Dissections: ἡ δὲ θέσις αὐτῆς (scil. τῆς ὑστέρας) μεταξὺ ἀρχοῦ καὶ κύστεως, μικρὸν ὑπεράνω τῆς ἥβης. τὸ δὲ σχῆμα αὐτῆς ἐκ τῶν ὑπογραφῶν τῶν ἐν ταῖς ἀνατομαῖς θεωρεῖται (Aristophanes Byz., Epitome Historiae Animalium 2.29 (Suppl. Arist. 1.1 [1885], p. 41.9–11 Lambros; Gigon 1987, fr. 269, p. 456a3–6). See Kullmann 1998, 126–135; 1999.

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II.b Anonyma: Biologizing the nameless A second recurrent signal of the difficulties that language entails for Aristotle is his frequent emphasis on the lack of words for numerous phenomena in the animal kingdom. While recognizing the rich signifying capacities of the Greek language, he nevertheless in his attempts to differentiate, to describe and to explain animal phenomena repeatedly runs into the obstacle of the namelessness of many of these phenomena. The issue of things for which there are no words (the ἀνώνυμα) is of course addressed in some of Aristotle’s non-biological works too, notably in his Ethics37 and in On the Soul,38 but in his Researches on Animals it is singled out as a challenge at least as often as in any other extant treatise of Aristotle’s.39 Four zoological contexts in which he draws attention to this problem of anonymity are particularly prominent: anonymous natural kinds (genos, eidos) at various levels of generality; anonymous parts of animal bodies; nameless substances that are processed and moved within animal bodies; and nameless animals within a single natural kind (whether at the level of what we call ‘species’ or at a different level). A few examples will illustrate each of these different strands in his evocation of the problem of namelessness in his works on animals. The namelessness of many of the natural kinds (γένη, εἴδη40) in the animal kingdom appears in diverse contexts, as the four examples cited below from the opening book of Researches on Animals illustrate. After drawing a distinction between three kinds of animals that can fly – those with feathered wings (τὰ πτερωτά), those with membranous wings (τὰ πτιλωτά), and those with leatherlike wings (τὰ δερμόπτερα) – Aristotle remarks that “the kind (genos) of animal with feathered wings is called ‘bird’, whereas there is no single name in the case 37 E.g., Eth. Nic. II 7.1107b1–2: τῶν δ’ ὑπερβαλλόντων ὁ μὲν τῇ ἀφοβίᾳ ἀνώνυμος (πολλὰ δ’ ἐστῖν ἀνώνυμα); II 7.1107b28–31: λέγεται δ’ ὁ μὲν ὑπερβάλλων ταῖς ὀρέξεσι φιλότιμος, ὁ δ’ ἐλλείπων ἀφιλότιμος, ὁ δὲ μέσος ἀνώνυμος. ἀνώνυμοι δὲ καὶ αἱ διαθέσεις. See also Aristotle’s references to namelessness in Eth. Nic. II 7.1108a4–6, 1108a16–19; III 6.1115b24–26; IV 4–5.1125b17–29; IV 6– 7.1127a11–14. Cf. Eth. Eud. II 3.1221a3, 1221a28–31, 1221a38–40; II 8.1224a18–20; III 2.1231a39-b2; III 6.1233a38–39; III 7.1233b19–22. 38 On the Soul II 5.417b32–418a3; II 7.418a26–29, 419a2–6, 419a30–32; III 2.426a11–15. See also the ‘nameless’ in Aristotle, Physics V 2.226a29-b1; VII 4.249b22–26. On Interpretation 10.19b5–12. Posterior Analytics I 5.74a8–10; II 13.96b6–8. Metaphysics Ζ 7.1033a8–16; Ι 5.1056a24–25. Rhetoric I 2.1357b3–5; III 2.1405a34-b5; III 3.1406a35–36. Poetics 1.1447a28-b2; 21.1457b25–33. Politics I 3.1253b8–11, III 1.1275b29.32. 39 In response to my presentation of some of these observations at Stanford University, Josiah Ober raised the question whether the relative frequency with which Aristotle uses anonymos in different treatises can be correlated with the extent to which he is making claims of innovation or of exploring terra incognita. A preliminary scrutiny of the evidence suggests that there is no simple or straightforward answer, but the question merits further examination. 40 For the debate about the meaning and role of γένος and εἶδος in Aristotle’s works on animals see Lloyd 1961 and 1991, 1–26; Balme 1962; Pellegrin 1985, 1986 and 1990. Cf. also Lennox 2001a, 131–181; 2001b, 309, on “the ‘context sensitivity’ of Aristotle’s concepts of ‘kind’ and ‘form’.”

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of the other two kinds.”41 Similarly, after listing “the most extensive kinds of animals” (birds, fishes, cetaceans) and stating that these all are blooded, he adds: “Another kind (genos) belongs to the hard-shelled animals, and it is called oyster; still another kind is that of the soft-shelled animals – it has no single name – such as crayfish and certain kinds of crabs and lobsters.”42 Furthermore, of some animals, “the kinds (γένη) are not large, for one kind (εἶδος) does not contain many kinds (εἴδη), but one kind is simple and itself admits no differentiation, such as (the species) human being, while others do admit of differentiation, but their kinds (εἴδη) are nameless.”43 In the case of viviparous quadrupeds (or, as Lennox prefers,44 “live-bearing four-footed animals”) the kinds or forms (εἴδη) “are numerous but nameless.”45 The problem of namelessness extends not only to ‘natural kinds’ and ‘forms’ of varying levels of generality in the animal kingdom. It also surfaces repeatedly in attempts to name parts of animal bodies. Already in the first book of his Researches on Animals, Aristotle threads the theme of the anonymity of parts into his text: “One sense, and one alone, is common to all animals: the sense of touch, so that the part in which touch by nature occurs is without a name. You see, in some animals it is the same but in others analogous.”46 Similarly, “one part of the ear is nameless, while another is [called] the lobe.”47 Other parts of bodies for which Aristotle has claims to have no word include the foreskin,48 the back or 41 Hist. anim. I 5.490a12–13: τὸ μὲν οὖν πτερωτὸν γένος τῶν ζῴων ὄρνις καλεῖται, τὰ δὲ λοιπὰ δύο ἀνώνυμα ἑνὶ ὄνοματι. See also 490a6–11. 42 Hist. anim. I 6.490b7–12: γένη δὲ μέγιστα τῶν ζῴων, εἰς ἃ διῄρηται τἆλλα ζῷα, τάδ’ ἐστίν, ἓν μὲν ὀρνίθων, ἓν δ’ ἰχθύων, ἄλλο δὲ κήτους. ταῦτα μὲν οὖν πάντα ἔναιμά ἐστιν. ἄλλο δὲ γένος ἐστὶ τὸ τῶν ὀστρακοδέρμων, ὃ καλεῖται ὄστρεον· ἄλλο τὸ τῶν μαλακοστράκων, ἀνώνυμον ἑνὶ ὀνόματι, οἷον κάραβοι καὶ γένη τινὰ καρκίνων καὶ ἀστακῶν. 43 Hist. anim. I 6.490b15–20: τῶν δὲ λοιπῶν ζῴων οὐκ ἔστι τὰ γένη μεγάλα· οὐ γὰρ περιέχει πολλὰ εἴδη ἓν εἶδος, ἀλλὰ τὸ μέν ἐστιν ἁπλοῦν αὐτὸ οὐκ ἔχον διαφορὰν τὸ εἶδος, οἷον ἄνθρωπος, τὰ δ’ ἔχει μὲν, ἀλλ’ ἀνώνυμα τὰ εἴδη. 44 Lennox 2001b, xii, 362, 364, 373, 378, and passim in his translation. 45 Hist. anim. I 6.490b31–32: τοῦ δὲ γένους τοῦ τῶν τετραπόδων ζῴων καὶ ζωοτόκων εἴδη μέν ἐστι πολλά, ἀνώνυμα δέ. 46 Hist. anim. I 3.489a17–19: πᾶσι δὲ τοῖς ζῴοις αἴσθησις μία ὑπάρχει κοινὴ μόνη ἡ ἁφή, ὥστε καὶ ἐν ᾧ αὕτη μορίῳ γίνεσθαι πέφυκεν ἀνώνυμόν ἐστι· τοῖς μὲν γὰρ ταὐτὸ τοῖς δὲ τὸ ἀνάλογόν ἐστιν. 47 Hist. anim. I 11.492a13–16: ἔστι δὲ κεφαλῆς μόριον, δι’ οὗ ἀκούει, ἄπνουν τὸ οὖς· Ἀλκμαίων γὰρ οὐκ ἀληθῆ λέγει, φάμενος ἀναπνεῖν τὰς αἶγας κατὰ τὰ ὦτα. ὠτὸς δὲ μέρος τὸ μὲν ἀνώνυμον, τὸ δὲ λοβός· ὅλον δ’ ἐκ χόνδρου καὶ σαρκὸς σύγκειται. 48 Hist. anim. I 13.493a25–30: καὶ τοῦ ἄρρενος αἰδοῖον…διμερές, τὸ μὲν ἄκρον σαρκῶδες καὶ ἀεὶ ὡς εἰπεῖν ἴσον, ὃ καλεῖται βάλανος, τὸ δὲ περὶ αὐτὴν ἀνώνυμον δέρμα, ὃ εὰν διακοπῇ, οὐ συμφύεται (οὐδὲ γνάθος οὐδὲ βλέφαρις). κοινὸν δὲ τούτου καὶ τῆς βαλάνου ἀκροποσθία. Aristotle’s remark about the namelessness of the prepuce and his subsequent use of ἀκροποσθία are puzzling for several reasons. First, several Greek words were used to designate the foreskin: πόσθη, πόσθιον, ποσθία, ἀκροπόσθιον, ἀκροποσθία (in this passage cited here Aristotle seems to be using the latter term to refer to the frenulum). Although the semantic field of some of these terms was wide, from ‘prepuce’ and ‘tip of the prepuce’ to ‘penis’ (and ‘stye’ on the eyelid), words for ‘foreskin’ were

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outside of the hand (as opposed to the palm),49 and the outer or upper part of the foot, at its top (as opposed to the sole and the ball of the foot underneath).50 So, too, in his account of the parts of sea urchins (ἐχῖνοι), Aristotle says that “certain dark things that have no name are spread around in a circle from the mouth of the sea urchin, as if pouring out in a flood.”51 In the case of all hard-shelled animals (ὀστρακόδερμα, ‘pottery-skinned’), human language is even worse off: “All have a head but, with the exception of the receptacle of nutriment, the other parts of their bodies are nameless.”52 The problem of nameless parts of animals seems to be more acute when Aristotle tries to give accounts of features of bloodless animals. In On Respiration, for instance, he argues that life and the presence of soul involve some heat, and that not even digestion can occur without soul and heat. The ‘first nutritive soul’ therefore must be in the first part and region of the body in which the principle of heat resides, that is, in the region between the part that receives food and the part that discharges waste; yet, Aristotle adds, “in bloodless animals it has no name, but in blooded animals it is the heart.”53 At times, a substance processed in the body of bloodless animals is also labeled ‘nameless’, for instance: “Since it is necessary that animals take in their food from outside, and that from this food in turn the final nutriment comes to be, from which it then is right away distributed to the parts (and in bloodless animals this [final nutriment] is nameless, but in blooded animals it is called ‘blood’), there must be something through which the nutriment will travel, as if through roots, from the stomach into the blood vessels.”54 Furthermore, on occasion Aristotle refers more generally to unspecified animals that are nameless, for instance in a discussion of insects: “Some of the coleoptera and

available. Second, Aristotle himself appears to use ἀκροποσθία for ‘prepuce’ in a similar context in Part. anim. (II 13.657b3–4); see Schneider 1811, III 41; Kullmann 2007, 461; Lennox 2001b (who here translates ἀκροποσθία with ‘foreskin’). Third, these two Aristotelian passages are close echoes of Corp. Hipp., Aph. VI 19 (Littré 4.568.4), which uses ἀκροποσθίη of the prepuce and probably is the source of Coan Prognoses 494 (Littré 5.696.20). See also Corp. Hipp., On Ulcers 12.4, 14.3 (Littré 6.412.23, 6.418.3 = Duminil 60.24, 53.16), On Diseases IV 55 (Littré 7.604.6); Dioscurides, Mat. med. IV 153.4 (Wellmann II, 300.6); Rufus of Ephesus, On the Nomenclature of the Parts of the Human Body 101–102 (Daremberg/Ruelle, p. 146.7–12). 49 Hist. anim. I 15.494a2–3: τὸ δὲ ἔξω τῆς χειρὸς νευρῶδες καὶ ἀνώνυμον. 50 Hist. anim. I 15.494a13–14: τὸ δ’ ἄνωθεν (sc.τοῦ ποδὸς) ἐν τοῖς πρανέσι νευρῶδες καὶ ἀνώνυμον. 51 Part. anim. IV 5.680a14–15: καὶ κύκλῳ ἀπὸ τοῦ στόματος μέλαν’ ἄττα διεσπαρμένα χύδην, ἀνώνυμα. 52 Part. anim. IV 7.683b22–24: ἔχει δὲ κεφαλὴν μὲν πάντα (sc.τὰ ὀστρακόδερμα), τὰ δὲ τοῦ σώματος μόρια παρὰ τὸ τῆς τροφῆς δεκτικὸν ἀνώνυμα τἆλλα. 53 Respir. 8.474b2–3: τοῖς μὲν οὖν ἀναίμοις ἀνώνυμον, τοῖς δ’ ἐναίμοις ἡ καρδία τοῦτο τὸ μόριόν ἐστιν. 54 Part. anim. IV 4.678a6–11: ἐπεὶ γὰρ ἀναγκαῖον τὰ ζῷα τροφὴν λαμβάνειν θύραθεν, καὶ πάλιν ἐκ ταύτης γίνεσθαι τὴν ἐσχάτην τροφήν, ἐξ ἦς ἤδη διαδίδοται εἰς τὰ μόρια (τοῦτο δὲ τοῖς μὲν ἀναίμοις ἀνώνυμον, τοῖς δ’ ἐναίμοις αἷμα καλεῖται), δεῖ τι εἶναι δι’ οὗ εἰς τὰς φλέβας ἐκ τῆς κοιλίας οἷον διὰ ῥιζῶν πορεύσεται ἡ τροφή.

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some small nameless animals make small holes of mud on grave-stones or on walls, and there they bring forth their grubs.55 Namelessness requires naming, but naming the nameless in turn risks generating polysemy (πολλαχῶς λεγόμενα or λέγεται, πλεοναχῶς λεγόμενα, πλείω σημαίνει, etc.). Aristotle recognized that, even when namelessness is not an issue, some of the most fundamental technical terms of his biology, such as hot and cold,56 dry and moist,57 and biologically ‘possible’ and ‘impossible’,58 are destabilized by polysemy and therefore require assiduous semantic fencing in and fencing off. In his Rhetoric, he famously signals that one way of solving the problem of anonymity is figuration, notably using metaphors to create names for the nameless.59 But Aristotle is fully aware that, for all its power in poetry and for all its rhetorical utility, metaphor, like other forms of figuration, entails ambiguity. Instead of an overt use of metaphor to deal with the lack of a zoological terminology, he therefore coins numerous technical neologisms and a cumbersome phrasal nomenclature – or, as is not uncommon in his non-zoological works, he simply draws attention to the namelessness of an entity, without trying to solve the problem. This does not mean that Aristotle ignores the recurrent threat that ambiguity poses to his project of writing a science of animals. On the contrary, in his writings on animals too, he makes clear that he is constantly trying to ward off ambiguity, and this is a third signal he gives that writing the animal faces significant obstacles. A useful, if at first glance circuitous, way of exploring this feature of his approach will be to step back from the problem of language in order to take a brief comparative look at authorial self-presentations on the part of Aristotle and other ancient writers of technical treatises on animals. In particular, a comparative glance at how Aristotle, Pliny the Elder, and Galen launched their works is a useful starting point.

55 Hist. anim. V 20.552b30–553a2: ἔνια δὲ τῶν κολεοπτέρων καὶ μικρῶν καὶ ἀνωνύμων ζῴων τοῦ πηλοῦ τρώγλας ποιοῦται μικρὰς ἢ πρὸς τάφοις ἢ τειχίοις, καὶ ἐνταῦθα τὰ σκωλήκια ἐκτίκτουσιν. 56 Part. anim. II 2.648a31-b1: ἔτι δ’ αἷμα καὶ χολὴν οἱ μὲν θερμὸν ὁποτερονοῦν εἶναί φασιν αὐτῶν, οἱ δὲ ψυχρόν. εἰ δ’ ἔχει τοσαύτην τὸ θερμὸν καὶ τὸ ψυχρὸν ἀμφισβήτησιν, τί χρὴ περὶ τῶν ἄλλων ὑπολαβεῖν; ταῦτα γὰρ ἡμῖν ἐναργέστατα τῶν περὶ τὴν αἴσθησιν. ἔοικε δὲ διὰ τὸ πολλαχῶς λέγεσθαι τὸ θερμότερον ταῦτα συμβαίνειν. See also next note and Part. anim. II 2.648b10–649b9. 57 Part. anim. II 2–3.649b5–11: λεγομένου δὲ τοῦ θερμοῦ πολλαχῶς, ἀκολουθήσει δῆλον ὅτι καὶ τὸ ψυχρὸν κατὰ τὸν αὐτὸν λόγον … ἐχόμενον δὲ καὶ περὶ ξηροῦ καὶ ὑγροῦ διελθεῖν ἀκολούθως τοῖς εἰρημένοις. λέγεται δὲ ταῦτα πλεοναχῶς, οἷον τὰ μὲν δυνάμει, τὰ δ’ ἐνεργείᾳ. See also Gen. anim. II 3.649b12–28); Gen. corr. II 2.330a12. 58 Gen. anim. IV 1.765b35–766a4. 59 Rhet. III 2.1405a33-b5.

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II.c A nameless, faceless author? Aristotle begins his most extensive extant work on animals, Researches on Animals – that is, the work he regarded as a necessary, if massive, prelude to the work of biological explanation – as follows: Of the parts of animals, some are uncompounded (asyntheta), namely all those that divide into uniform parts (homoiomerē), such as flesh into flesh, whereas others are composite (syntheta), namely all those that divide into non-uniform parts (anhomoiomerē), for instance the hand does not divide up into hands, nor the face into faces.60

No preface, no proem, no captatio beneuolentiae, no address to any real or imagined audience or reader opens the work – and no author, no ego. Only basic scientific facts, expressed in a dry technical language, await his audience: ‘uncompounded’ or ‘incomposite’ (asynthetos, apparently coined by Plato61), ‘uniform’ (homoiomerēs, possibly coined by Anaxagoras62) and ‘non-uniform’ (anhomoiomerēs, not attested before Aristotle). Rather than relying on personalized claims of authorship and authority, of originality and innovation, Aristotle achieves much of his effect by means of a strategy of authorial distance combined with systematicity, and, on the whole, of orderly, transparent expository structure – a structure shaped by a specified purpose and method in each work on animals. Keeping the focus quite consistently on animals, not on himself or on any real or putative audience, he leaves little room for the intrusion of an authorial ego. The author remains faceless and nameless. It might of course be objected that the biological works, unlike Aristotle’s dialogues or his Protreptic, are esoteric works which might not owe their current form to Aristotle himself. For all the ink that generations of scholars have spilled on this hypothesis, it remains a hypothesis. What is more certain, is that even in the most theoretical and polished of Aristotle’s treatises on animals, On the Parts of Animals, where the study of even the lowliest of animals is passionately defended, the authorial first person singular rarely intrudes into his text (but for a significant exception see below). The basic facts that Aristotle presented in the opening sentence of his monumental Researches on Animals might seem simple and obvious, but he casts them 60 Hist. anim. I 1.486a5–8: τῶν ἐν τοῖς ζῴοις μορίων τὰ μέν ἐστιν ἀσύνθετα, ὅσα διαιρεῖται εἰς ὁμοιομερῆ, οἷον σάρκες εἰς σάρκας, τὰ δέ σύνθετα, ὅσα εἰς ἀνομοιομερῆ, οἷον ἡ χεὶρ οὐκ εἰς χεῖρας διαιρεῖται οὐδὲ τὸ πρόσωπον εἰς πρόσωπα. 61 Plato, Phaedo 78c3–8; Theaetetus 205c7; Politicus 288e5. The adjective σύνθετος, however, is also attested in Aeschylus (?), Prometheus Bound 686; Lysias, fr. 101a, line 10 Carey (authenticity disputed); Xenophon, Cyropaedia IV 3.20; Corp. Hipp., Acut. 64.1 (Littré 2.364.3; Joly 65.3), and, less certain, Coac. 109 (Littré 5.606.4). See also Herodotus III 86.2: ὥσπερ ἐκ συνθέτου, “as if in agreement”? 62 Though ὁμοιομερής and ὁμοιομέρεια are often attributed to Anaxagoras in the testimonia, neither word seems to appear in his extant fragments.

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in a technical language and in a succinct, transparent generalizing form, complete with a pertinent example for each of the two complementary claims, without inserting himself overtly into the text as author – neither as the author of this generalization nor as the author of its textual rendering. It is a scientific truth that matters, not its author. This might serve as an example of ‘dry and distant’ scientific writing, of a depersonalized, dispassionate science writing, devoid of explicit authorial intrusions, without first-person singulars: no ego, no ‘I’. This Aristotelian practice had a long afterlife. In the preface to his early 17th-century Instauratio Magna, for example, Francis Bacon explicitly adopts it, saying, “Of myself I shall say nothing” (de nobis ipsis silemus) – a statement in turn used by Immanuel Kant as a motto in the second edition of his Critique of Pure Reason.63 The irony that Bacon talks about himself in order not to talk about himself will not escape any reader; Aristotle, by contrast, simply remains silent about himself. Each in his own way, Aristotle, Bacon and Kant appear to suggest, as did numerous later writers on science, that autobiography provides no framework for the discovery of method or for the communication of the trans-subjective, trans-temporal truths to which science should aspire. First-person singular pronouns – ego, (e)me, (e)moi, emos, etc. – do not seem to appear in Aristotle’s treatises on animals, and verb forms in the first person singular are used only sparingly, with one major exception. This exception is prompted precisely by the problem of the polysemous nature of ordinary language: it is the present tense verb form λέγω (lego), in the sense ‘I mean’, used repeatedly precisely when Aristotle recognizes a need to clarify the meaning of a technical biological term, whether a neologism or a polysemous or unclear term or expression. These ‘I mean’ attempts at semantic clarification resort to diverse strategies in order to remove the menace of misunderstanding due to polysemy or obscurity. One is to introduce technical differentiations among the possible meanings of the term and then to specify which of the meanings is intended in the relevant instance. Another is to elaborate by a definition or a descriptive narrowing of the semantic field of the term. A third is to clarify the meaning by providing examples of entities – often zoological entities – denoted by the term (when this strategy is used, Aristotle often but not invariably resorts to λέγω οἷον (“I mean for instance”), to introduce his examples (see below nn. 64, 65, 70, 73, 79)). Among the technical biological terms susceptible to ambiguity but clarified with an ‘I mean’ clause are ‘soft-shelled’ (μαλακόστρακα, clarified by two exam-

63 See O’Neill 1989, 6–7. I am grateful to Gideon Manning for this reference.

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ples: crayfish and crabs);64 modes of γεννᾶν;65 κύημα;66 ἄχρηστος τροφή;67 σύντηγμα and περίττωμα;68 τῶν μερῶν σύμφυσις;69 ὀργανικὰ μέρη;70 ὁλόχροος and μονόχροος;71 ἔσχατον περίττωμα;72 ἀτελής;73 δίθυρος and μονόθυρος (univalved);74 and πάθημα.75 In his works on animals not only technical biological terms but also fundamental philosophical notions that are deployed throughout Aristotle’s extant corpus are frequently clarified by one of the ‘I mean’ (λέγω)

64 On Respiration 12.476b30–32: διὰ ταὐτὸ δὲ τοῦτο δέχεται καὶ τὰ μαλάκια τὸ ὕδωρ καὶ τὰ μαλακόστρακα, λέγω δ’ οἷον τοὺς καλουμένους καράβους καὶ τοὺς καρκίνους. 65 Gen. anim. III 10.759a15–20: καὶ γεννᾶν ἢ ὀχευομένας ἢ ἀνοχεύτους· καὶ ὀχευομένας γεννᾶν ἤτοι ἕκαστον γένος καθ’ αὑτό, ἢ ἕν τι αὐτῶν τἆλλα, ἢ συνδυαζόμενον ἄλλο γένος ἄλλῳ, λέγω δ’ οἷον μελίττας μὲν γίγνεσθαι ἐκ μελιττῶν συνδυαζομένων, κηφῆνας δ’ ἐκ κηφήνων καὶ τοὺς βασιλεῖς ἐκ τῶν βασιλέων. 66 Gen. anim. I 20.728b32–36: ἐν ὅσοις μὲν οὖν τῶν ζωὴν ἐχόντων μὴ κεχώρισται τὸ θῆλυ καὶ τὸ ἄρρεν, τούτοις μὲν τὸ σπέρμα οἷον κύημά ἐστιν. λέγω δὲ κύημα τὸ πρῶτον μίγμα ἐκ θήλεος καὶ ἄρρενος. διὸ καὶ ἐξ ἑνὸς σπέρματος ἓν σῶμα γίγνεται οἷον ἐξ ἑνὸς πυροῦ εἷς πυθμήν, ὥσπερ ἐξ ἑνὸς ᾠοῦ ἓν ζῷον. 67 Gen. anim. I 18.725a3–7: ἀλλὰ μὴν περίττωμά γε πᾶν ἢ ἀχρήστου τροφῆς ἐστιν ἢ χρησίμης. ἄχρηστον μὲν οὖν λέγω ἀφ’ ἧς μηθὲν ἔτι συντελεῖται εἰς τὴν φύσιν, ἀλλ’ ἀναλισκομένου πλέονος μάλιστα κακοῦται, τὴν δὲ χρησίμην τὴν ἐναντίαν. 68 Gen. anim. I 18.724b23–28: ἀνάγκη δὴ πᾶν ὃ ἂν λαμβάνωμεν ἐν τῷ σώματι ἢ μέρος εἶναι τῶν κατὰ φύσιν, καὶ τοῦτο ἢ τῶν ἀνομοιομερῶν ἢ τῶν ὁμοιομερῶν, ἢ τῶν παρὰ φύσιν οἷον φῦμα, ἢ περίττωμα ἢ σύντηγμα ἢ τροφήν. λέγω δὲ περίττωμα μὲν τὸ τῆς τροφῆς ὑπόλειμμα, σύντηγμα δὲ τὸ ἀποκριθὲν ἐκ τοῦ αὐξήματος ὑπὸ τῆς παρὰ φύσιν ἀναλύσεως. 69 Inc. anim. 6.706b25–28: πάντα ταῦτα κοινὴν ἀρχὴν ἔχει κατὰ τὴν τῶν εἰρημένων μερῶν σύμφυσιν, λέγω δὲ τῶν τε δεξιῶν καὶ τῶν ἀριστερῶν καὶ τῶν ἄνω καὶ κάτω καὶ τῶν ἔμπροσθεν καὶ τῶν ὄπισθεν. 70 Inc. anim. 4.705b22–23: ὅσα μὲν γὰρ ὀργανικοῖς μέρεσι χρώμενα (λέγω δ’ οἷον ποσὶν ἢ πτέρυξιν ἤ τινι ἄλλῳ τοιούτῳ). 71 Gen. anim. V 6.785b16–21: τῶν δὲ ζῴων τὰ μέν ἐστι μονόχροα (λέγω δὲ μονόχροα ὧν τὸ γένος ὅλον ἓν χρῶμα ἔχει, οἷον λέοντες πυρροὶ πάντες, καὶ τοῦτο καὶ ἐπ’ ὀρνίθων καὶ ἐπ’ ἰχθύων ἐστὶ καὶ τῶν ἄλλων ζῴων ὁμοίως), τὰ δὲ πολύχροα μέν, ὁλόχροα δέ (λέγω δὲ ὧν τὸ σῶμα ὅλον τὴν αὐτὴν ἔχει χρόαν, οἷον βοῦς ἐστιν ὅλος λευκὸς ἢ ὅλος μέλας), τὰ δὲ ποικίλα. While πολύχροος is attested before Aristotle (e.g., Empedocles fr. B23.3 Diels-Kranz), μονόχροος, δίχροος (so too δίχροια) and ὁλόχροος seem to be Aristotle’s coinages. 72 Gen. anim. IV 1.766b7–12: ἀναλαβόντες δὲ πάλιν λέγομεν ὅτι τὸ μὲν σπέρμα ὑπόκειται περίττωμα τροφῆς ὂν τὸ ἔσχατον (ἔσχατον δὲ λέγω τὸ πρὸς ἔκαστον φερόμενον. διὸ καὶ ἔοικε τὸ γεννώμενον τῷ γεννήσαντι· οὐθὲν γὰρ διαφέρει ἀφ’ ἑκάστου τῶν μορίων ἀπελθεῖν ἢ πρὸς ἕκαστον προσελθεῖν – ὀρθότερον δ’ οὕτως). 73 Respir. 17.478b28–31: ἔστι δὲ θάνατος καὶ ἡ φθορὰ πᾶσιν ὁμοίως τοῖς μὴ ἀτελέσιν· τούτοις δὲ παρομοίως μέν, ἄλλον δὲ τρόπον. ἀτελῆ δὲ λέγω οἷον τά τε ᾠὰ καὶ τὰ σπέρματα τῶν φυτῶν, ὅσα ἄρριζα. 74 Hist. anim. IV 4.528a11–13: τῶν δ’ ἄλλων (sc. τῶν ὀστρακοδέρμων) τὰ μέν ἐστι δίθυρα τὰ δὲ μονόθυρα· λέγω δὲ δίθυρα τὰ δυσὶν ὀστράκοις περιεχόμενα, μονόθυρα δὲ τὰ ἑνί. 75 Gen. anim. V 1.778a16–20: περὶ δὲ τῶν παθημάτων οἷς διαφέρουσι τὰ μόρια τῶν ζῴων θεωρητέον νῦν. λέγω δὲ τὰ τοιαῦτα παθήματα τῶν μορίων οἷον γλαυκότητα ὀμμάτων καὶ μελανίαν, καὶ φωνῆς ὀξύτητα καὶ βαρύτητα, καὶ χρώματος [ἢ σώματος secl. Bekker] καὶ τριχῶν ἢ πτερῶν διαφοράς.

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strategies identified above. Such notions include ἀρχή,76 αἰτία,77 τρόπος,78 πρότερον – ὕστερον,79 and the adjective λογική.80 Against the background of Aristotle’s tendency to eschew overt intrusions of an authorial ‘I’, ‘me’ and ‘my’ into his text, the frequency with which he uses the first-person singular ‘I mean’ (λέγω) in his treatises on animals to signal the need to clarify an ambiguous term or expression is a further indication of the difficulty of constituting a language adequate to the task of giving a scientific account of animals. Indeed, the only authorial ‘I’ that is liberally accommodated in Aristotle’s writings on animals is the ‘I’ who is a guardian against polysemy, a semantic clarifier who delimits countless meanings in the name of fending off ambiguity and equivocity. I hasten to add that the first person plural, ‘we’, is not uncommon in Aristotle’s treatises on animals. A self-referential use of ‘we’, to refer to Aristotle as the author, is however largely restricted to two purposes: cross references to points made in earlier parts of the text (‘as we said elsewhere or earlier’),81 or to mark the end of one section and the beginning of another (‘about x, let this much be said by us’).82 76 Gen. anim. IV 1.765b8–14: ἀλλ’ ἐπεὶ τὸ ἄρρεν καὶ τὸ θῆλυ διώρισται δυνάμει τινὶ καὶ ἀδυναμίᾳ· τὸ μὲν γὰρ δυνάμενον πέττειν καὶ συνιστάναι τε καὶ ἐκκρίνειν σπέρμα ἔχον τὴν ἀρχὴν τοῦ εἴδους ἄρρεν (λέγω δ’ ἀρχὴν οὐ τὴν τοιαύτην ἐξ ἧς ὥσπερ ὕλης γίγνεται τοιοῦτον οἷον τὸ γεννῶν, ἀλλὰ τὴν κινοῦσαν πρώτην, ἐάν τ’ ἐν αὐτῷ ἐάν τ’ ἐν ἄλλῳ τοῦτο δύνηται ποιεῖν. 77 Gen. anim. I 1.715a1–4: ἐπεὶ δὲ περὶ τῶν ἄλλων μορίων εἴρηται τῶν ἐν τοῖς ζῴοις καὶ κοινῇ καὶ καθ’ ἔκαστον γένος περὶ τῶν ἰδίων χωρίς, τίνα τρόπον διὰ τὴν τοιαύτην αἰτίαν ἐστὶν ἕκαστον, λέγω δὲ ταύτην τὴν ἕνεκά του· ὑπόκεινται γὰρ αἰτίαι τέτταρες… 78 Gen. anim. II 4.740b18–24: ἀλλ’ ὅτι τὸ περίττωμα τὸ τοῦ θήλεος δυνάμει τοιοῦτόν ἐστιν οἷον φύσει τὸ ζῷον, καὶ ἔνεστι δυνάμει τὰ μόρια, ἐνεργείᾳ δ’ οὐθέν, διὰ ταύτην τὴν αἰτίαν γίγνεται ἕκαστον αὐτῶν, καὶ ὅτι τὸ ποιητικὸν καὶ τὸ παθητικὸν ὅταν θίγωσιν, ὃν τρόπον ἐστὶ τὸ μὲν ποιητικὸν τὸ δὲ παθητικόν (τὸν δὲ τρόπον λέγω τὸ ὣς καὶ οὗ καὶ ὅτε), εὐθὺς τὸ μὲν ποιεῖ τὸ δὲ πάσχει. 79 Gen. anim. II 1.734a23–29: μείζων γὰρ τὸ μέγεθος ὢν ὁ πνεύμων τῆς καρδίας ὕστερον φαίνεται τῆς καρδίας ἐν τῇ ἐξ ἀρχῆς γενέσει. ἐπεὶ δὲ τὸ μὲν πρότερον τὸ δ’ ὕστερον, πότερον θάτερον ποιεῖ θάτερον, καὶ ἔστι διὰ τὸ ἐχόμενον, ἢ μᾶλλον μετὰ τόδε γίγνεται τόδε; λέγω δ’ οἷον οὐχ ἡ καρδία γενομένη ποιεῖ τὸ ἧπαρ, τοῦτο δ’ ἕτερόν τι, ἀλλὰ τόδε μετὰ τόδε, ὥσπερ μετὰ τὸ παῖς ἀνὴρ γίγνεται ἀλλ’ οὐχ ὑπ’ ἐκείνου. 80 Gen. anim. II 8.747b27–30: ἴσως δὲ μᾶλλον ἂν δόξειεν ἀπόδειξις εἶναι πιθανὴ τῶν εἰρημένων λογική – λέγω δὲ λογικὴν διὰ τοῦτο ὅτι ὅσῳ καθόλου μᾶλλον πορρωτέρω τῶν οἰκείων ἐστὶν ἀρχῶν. 81 E.g., Part. anim. III 4.666b16–17: ἡ δὲ καρδία, καθάπερ εἴπομεν καὶ πρότερον, οἷον ζῷόν τι πέφυκεν ἐν τοῖς ἔχουσιν. Inc. anim. 8.708a12–14: ἔτι δὲ καὶ τὸ πρότερον ἡμῖν εἰρημένον, τὸ τῶν ἐναίμων μηθὲν οἷόν τ’εἶναι πλείοσι κινεῖσθαι σημείοις ἢ τέτταρσιν. Similarly, Inc. Anim. 16.713a26– 27: τὰ δ’ ἄναιμα τῶν ὑποπόδων ὅτι μὲν πολύποδά ἐστι καὶ οὐθὲν αὐτῶν τετράπουν, πρότερον ἡμῖν εἴρηται. For καθάπερ (or ὥσπερ) εἴπομεν, πρότερον εἰρήκαμεν, and similar cross-references in the first person plural within Aristotle’s zoological works see also Gen. anim. I 2.716a4, I 18.723b22, I 21.730a3, I 23.731b7–8, II 6.743b16, III 3.754b33, IV 4.771a36, V 1.779a6. Hist. anim. I 15.494a23–24, V 14.545a14–15. Inc. anim. 15.713a2–3. Mot. anim. 8.702a12–13, 11.704b2. Part. anim. I 1.640a13–14, I 5.645b11, II 8.654a27, II 16.659a14–15, 659a34, 659b21–22, 659b36, II 17.661a30, III 1.661b16, 662a19, III 3.664b20, III 4.666b25, 667a8, III 5.668a10, III 7.670a3–4, IV 11.692a20. 82 E.g., Part. anim. I 5.646a1–2: καὶ περὶ μὲν τοῦ τρόπου τῆς μεθόδου τοσαῦθ’ ἡμῖν εἰρήσθω.

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Even in these two contexts, however, impersonal constructions in the passive voice are more common, for instance: ‘as was said earlier’, ‘as was said in section x or in work y’, or ‘let this much be said about x’.83 Less frequently, Aristotle puts the first person plural to several other uses too. Four of these, all of which seem to refer to a collectivity of which Aristotle is a member rather than to Aristotle as the authorial individual, are noteworthy. First, he uses ‘we’ to refer to all members of the human species, especially to biological and other features that all of us, as members of the human species, share;84 secondly, he uses ‘we’ or ‘among us’ to distinguish between the celestial, supralunary sphere and our earthly sphere, that is, to refer to what is the case ‘here among us on earth, in this sublunary world of ours’;85 third, Aristotle deploys ‘we’ to draw a distinction between various precursors (notably Democritus) and ‘us’ who disagree with them (especially followers of Plato);86 and finally, he resorts to ‘we’ to invite the reader into complicity with the author (‘if x, we – i.e., you and I – see that y’).87 Aristotle’s use of ‘we’ in crossreferences and in boundary markers which serve to orient the reader or audience within his often complex exposition, is, however, more amply attested than the other four uses. This suggests an author who wants to convey the well-structured, well-ordered nature of his reasoning, of his theories, and of his exposition, without asserting an authorial ego.

83 For ὥσπερ ἐν τοῖς ἄνω ἐλέχθη, ὥσπερ ἐλἐχθη ἐπὶ (x or y), ὥσπερ ἐλέχθη περὶ (x or y), ὥσπερ ἐλέχθη πρότερον ἐν τοῖς ἄλλοις, ὥσπερ εἴρηται (or ἐλέχθη) πρότερον, καθάπερ εἴρηται (or ἐλέχθη) πρότερον, εἴρηται δὲ πρότερον, εἴρηται δ’ έν έτέροις περὶ τούτων, ὥσπερ εἴρηται (or ἐλέχθη), ὥσπερ ἐλέχθη κατ’ ἀρχάς and similar depersonalized cross-references in Aristotle’s treatises on animals, see e.g. Hist. anim. I 16.494b20, II 1.499b21, II 8.502a26, II 17.507a1–2, IV 3.527b7, IV 6.531a28–29, V 5.541a5–6, V 11.543b10, V 22.554b2–3, V 32.557b1–2, VI 10.564b18–19, 565a6–7, VI 11.566a9–10, VI 13.567a18, VI 29.578b6–7, VII 10.587a24–25, VIII 1.588b11–12, VIII 17.600b18–19, IX 1.608b15. Part. anim. I 1.640a2–3, I 5.645b3–4, III 4.665b31, IV 5.678b23, 682a2–3. Gen. anim. I 2.716a21, I 5.717b33, I 13.720a24, I 15.720b19–20, I 16.721a26–27, I 18.726a9, I 19.726b2–3, 726b34, 727a33–34, II 1.733b17–18, II 2.736a18, II 6.741b25, 742b36–37, II 7.745b23, II 8.748a13, III 9.758a30– 31, V 1.778b1–2, 779b22. 84 See e.g., Gen. anim. II 6.743a33: what ‘we’ do, as opposed to what nature does; IV 1.763b28: ‘our’ – human – sense-perception. Hist. anim. II 11.503a24: the relation of the human thumb to the rest of the human hand. Mot. anim. 4.699b20: human sight. Hist. anim. I 6.491a22: of the animals, the human is most familiar to us. Cf. Hist. anim. VI 5.563a8. See also Part. anim. II 2.648a35: ταῦτα ἡμῖν ἐναργέστατα; II 10.656a8: τῶν ἡμῖν γνωρίμων ζῴων. 85 Part. anim. I 1.641b19–20: what appears ἐν τοῖς οὐρανίοις as opposed to περὶ ἡμᾶς, i.e., περὶ τὰ θνητά; I 5.645a2–3: terrestrial things are closer to us, πλησιαίτερα ἡμῶν, than celestial things. – In a similar context: I 5.644b24–645a5: ἡμῖν ὑπάρχειν, ποθοῦμεν, ἐφαπτόμεθα, τὰ παρ’ ἡμῖν ἅπαντα, τὸ φαινόμενον ἡμῖν, all to refer to ‘our’ sublunary sphere which is subject to generation and decay. 86 Anim. I 3.406b22: in response to Democritus’ views “we will ask whether…”. Gen. anim. I 18.725a22: ‘the ancients’ said x, we will maintain y, I 18.723a22 to say that some of the seed is sinew and bone is ‘beyond us’, i.e., it is going too far beyond what we who engage in rational thinking will say; so too Empedocles’ views are ‘beyond us’, II 8.747b8. 87 E.g., Gen. anim. I 19.726b19: from the distinctions that have been drawn, it is not yet clear to us…

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As Geoffrey Lloyd has pointed out, a number of Greek writers of technical texts eagerly inserted an authorial ego into their writings, often linking it to claims of innovation, of originality, of privileged scientific or technical knowledge, and of scientific superiority over rivals,88 and many Latin authors of technical treatises likewise displayed no reluctance to insert an authorial ego conspicuously into their texts, though not always with the same aims as Greek authors.89 Not so Aristotle. This is not to underplay Aristotle’s extensive criticisms of precursors in his works on animals too (for instance Democritus, Diogenes of Apollonia, Empedocles, Anaxagoras, Polybus, and Syennesis of Cyprus), but it is striking that, unlike the authors discussed by Lloyd in this context, Aristotle tries to refute his adversaries without insisting on the authorial ‘I’, ‘me’, and ‘my’.

III Pliny the Elder: the author, the Emperor, and the animal When one turns from Aristotle to two other prolific ancient writers on animals – Pliny the Elder and Galen – for a comparative perspective, un-Aristotelian strategies of positioning the author emerge. The opening sentences of Pliny’s Natural History, eight books of which are devoted to non-human animals, offer an instructive example: Plinius Secundus to his dear Vespasian [i.e. Titus, Emperor 79–81], greetings. These books of natural history, born of my most recent gestation – a new work for the native Muses (Camenae) of your Roman citizens – are what I have decided to tell you about in this rather presumptuous letter, most delightful Emperor. For let this be your title, a very well-founded title – even while the title ‘Greatest’ grows old with your father – since, to be sure, ‘it was always your way to deem my trifles (nugas) worth something,’ to give a passing touch of polish to my ‘fellow territorial’ Catullus (you’ll recognize this military camp jargon).90

In this lengthy preface, Pliny continues in a similar vein, enumerating Titus’ many offices and honors, while eagerly reminding the future Emperor of the author’s 88 Lloyd 1987, 56–70. 89 On ego in Latin technical treatises see e.g. Hine 2009; von Staden 1994. 90 Pliny, Nat. hist. praef. 1: Plinius Secundus Vespasiano Caesare suo s. Libros Naturalis Historiae, nouicium Camenis Quiritium tuorum opus, natos apud me proxima fetura licentiore epistula narrare constitui tibi, iucundissime Imperator; sit enim haec tui praefatio, uerissima, dum maximi consenescit in patre, namque tu solebas nugas esse aliquid meas putare, ut obiter emolliam Catullum conterraneum meum (agnoscis et hoc castrense uerbum). The appropriative allusion that beginning with namque tu solebas is of course to Catullus 1.3–4: Corneli, tibi: namque tu solebas / meas esse aliquid putare nugas, on which Pliny pointedly claims to have improved by rearranging the word order. For detailed analyses of Pliny’s preface see Köves-Zulauf 1973, especially 144–157; Howe 1985; Fögen 2009, 205–215. See also Beagon 1992. Further bibliography in Sallmann 1975; Römer 1978; Serbat 1986. On prefaces to Latin technical texts cf. Santini & Scivoletto 1990–1992.

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impudence and of their close comradeship in military camp. More interesting for present purposes than the floridity, stylized flattery, and attempt at literary oneupmanship are the accumulation of authorial first-person singulars (apud me; constitui; meas; emolliam; meum) and the emphatic establishment of the author’s personal relation with the future emperor (narrare constitui tibi; haec tui praefatio; tu solebas nugas esse aliquid meas putare; agnoscis et hoc castrense uerbum). These contribute to a highly personalized construction of the author of a monumental technical treatise as an elite socio-political phenomenon. This is far from the first or last time that an author of a technical treatise evoked his relation with a powerful, autocratic ruler.91 But Pliny is not content just to insert himself as the author of natural history into a constellation of imperial power and social status, close to the Emperor himself. He also resorts to several strategies to present himself as an expert – a competent, erudite connoisseur of nature, including the animal kingdom, who deserves to be taken seriously by the reader. One such strategy is to make strong claims of originality. At first glance this might seem paradoxical in an author who openly concedes that most of the ‘scientific’ information he offers is derivative, including the ‘facts’ presented in the eight books of his Natural History devoted to non-human animals (VIII–XI, XXVIII–XXX, XXXII). Yet it is perhaps precisely the derivative nature of his work that necessitates staking out claims of originality. Aristotle was enormously original but, if we take his extant texts to reflect his own approach to writing about animals, he did not make an authorial fuss about his stunning new empirical investigations and his innovative theories, let alone about his ownership of numerous zoological discoveries.92 Pliny, by contrast, explicitly describes his Natural History as unique and unprecedented: “Not one person could be found among us [Romans] who has attempted this journey, and not one among the Greeks who has single-handedly tackled all of this.”93 His originality, he claims, lies in his unprecedented encyclopaedism, in the comprehensiveness of his account of the natural world in all its aspects. Pliny repeatedly reverts to this theme – ‘I am the first’, ‘I am unique’ – in his Natural History, for instance in the opening of one of his four books on drugs derived from animals: “The nature of the remedies [from animals] and the great

91 In the Hellenistic period, for instance, Apollonius of Citium (1st cent. ; see above n. 12) directly addressed ‘King Ptolemy’ in the opening sentence of each of the three books of his On Joints, while Biton (probably 3rd cent. ) addressed ‘King Attalus’ in the opening sentence of his Construction of War Engines and Artillery. 92 On the contrary, Aristotle acknowledges his indebtedness to fishermen, eel-farmers, hunters, peasants, ethnographers, and historians for some of his data. 93 Pliny, Nat. hist. praef. 14: praeterea iter est non trita auctoribus uia nec qua peregrinari animus expetat: nemo apud nos qui idem temptauerit, nemo apud Graecos qui unus omnia ea tractauerit. In the second nemo… clause, the qualification expressed by unus omnia ea is a tacit acknowledgement of his indebtedness to diverse Greek predecessors, including Aristotle. See Fögen 2009, 231–232.

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number of those that are about to be discussed or have been discussed compel me to say more about the ars of healing itself, although I am not unaware that no one has yet composed a work about it in Latin…”.94 This claim conveniently overlooks the fact that he himself (in Book I) had listed a dozen Latin authors on whose works he drew for this book (XXIX),95 among them Aulus Cornelius Celsus, whose eight books on medicine include extensive accounts of animal-derived drugs.96 Pliny likewise passes in silence over Scribonius Largus’ Compositiones (composed during the reign of the Emperor Claudius). A second move made by Pliny is to quantify the authority of the author. Already in the preface he depicts himself as having collected 20,000 facts worthy of the reader’s attention in the course of reading 2,000 volumes in both Greek and Latin, very few of which, he claims, have ever been used by other scholars.97 Furthermore, he claims that his work includes what he learned from a hundred different authors, both Latin and Greek.98 To this project of quantifying his erudition also belongs the enormous parade of sources, both Roman and foreign (auctores externi), enumerated, book by book, in the first book of the Natural History,99 where he also tallies the number of ‘facts’ or ‘remedies’, ‘investigations, and observations’ (res/medicinae, historiae, observationes) recorded in each book of his treatise. For the eight books on non-human animals, for instance, Pliny announces in

94 Pliny, Nat. hist. XXIX 1: naturae remediorum atque multitudo instantium ac praeteritorum plura de ipsa medendi arte cogunt dicere, quamquam non ignaros nulli ante haec Latino sermon condita, ancepsque, lubricum esse rerum omnium nouarum initium et talium, utique tam sterilis gratiae tantaeque difficultatis in promendo. 95 Pliny, Nat. hist. I, on his Roman sources for Book 29: ex auctoribvs: M. Varrone. L. Pisone. Flacco Verrio. Antiate. Nigidio. Cassio Hermina. Cicerone. Plauto. Celso. Sextio Nigro qui Graece scripsit. Caecilio medico. Metello Scipione. Ouidio poeta. Licinio Macro. externis: Palaephato. Homero. Aristotele. Orpheo. Democrito. Anaxilao. medicis: Botrye. Apollodoro. Archedemo. Aristogene. Xenocrate. Democrate. Diodoro. Chrysippo philosopho. Oro. Nicandro. Apollonio Pitanaeo. 96 See especially Celsus, Medicina V–VI. Cf. von Staden forthcoming. 97 Pliny, Nat. hist. praef. 17: viginti milia rerum dignarum cura …lectione voluminum circiter duorum milium, quorum pauca admodum studiosi attingunt propter secretum materiae, ex exquisitis auctoribus centum inclusimus triginta sex voluminibus, adiectis rebus plurimis quas aut ignoraverant priores aut postea invenerat vita. 98 See previous n. In Book I, however, Pliny lists more than 450 authors (146 Roman and 327 foreign [externi], the latter mostly Greek) as sources for his Nat. hist. See Fögen 2009, 205 n. 11. 99 According to Book I, the distribution of sources in Pliny’s books on non-human animals is as follows. Book VIII (on terrestrial animals): 19 Roman and 40 foreign auctores. Book IX (on aquatic animals): 19 Roman and 9 foreign auctores. Book X (mostly on birds): 23 Roman and 40 foreign authors. Book XI (on insects, animal parts; varia): 20 Roman and 24 foreign authors. Book XXVIII (remedies from humans and terrestrial animals): 16 Roman and 34 foreign auctores. Book XXIX (mostly on remedies from animals): 15 Roman and 18 foreign. Book XXX (remedies from animals): 6 Roman and 20 foreign. Book XXXII (remedies from aquatic animals): 8 Roman and 8 foreign auctores. That neither the number of sources listed nor the names of these sources accurately reflect Pliny’s use of sources has been recognized at least since Münzer 1897. On Pliny’s books on animals see Bodson 1986.

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Book I that he’ll be presenting the reader with a total of 9,078 of such ‘facts’, etc. concerning animals.100 And in Book XVII he remarks that he aims “not to pass knowingly over anything that I have discovered anywhere”.101 About this statement – unthinkable in Aristotle – Gian Biagio Conte remarks: “Pliny disseminates along his path a number of not always consistent statements of [authorial] principle, but this is one of the most sincere and heartfelt ones”.102 “Sincere and heartfelt” might be too generous, but there is little doubt that the quantification of authorial knowledge is a recurrent strand in Pliny’s projection of erudite authority. Even as he draws non-stop on a motley array of sources, he continues to quantify himself and his achievement. Conte has rightly highlighted Pliny’s affective exploitation of a rhetoric of enumeration – enumerations of sources, of scientific ‘facts’, and of curiosities. But Pliny was not only the great self-quantifier and enumerator of nature. He also presented himself as an author who engaged in an encyclopedic imposition of order on nature, including the animal kingdom. In part it is a hierarchical order, with human beings at the top of all living organisms (Book VII), immediately followed by non-human animals in a clearly marked sequence (see above n. 99), even if here too Pliny could not resist numerous digressions. Trevor Murphy has plausibly argued that “the sheer persistence of the book’s tendency to digress … is both deliberate and artistic, an aesthetic choice… of poikilia, intricacy”.103 The initially announced structure of Pliny’s Natural History and its narrative progress are indeed repeatedly deflected by Pliny’s taste for digressive mini-narratives about the grotesque, the exotic, or the marvelous within the animal kingdom. Italo Calvino and Gian Biagio Conte have both emphasized that Pliny proceeds by networks of associative analogies, and Conte has suggested that the propensity for analogy in part ‘authorizes’ the digressions.104 The overall structure announced in Book I nevertheless is largely maintained, and it very much belongs to Pliny’s self-presentation as a disciplined, meticulous, orderly author.105

100 According to Nat. hist. I the total number of ‘facts, investigations and observations’ for each book on non-human animals is as follows: 787 facts, etc. in Book VIII; 650 in Book IX; 794 in Book X; 2,700 in Book XI; 1,682 in Book XXVIII; 621 in Book XXIX; 854 in Book XXX; 990 in Book XXXII (for the principal contents of each of these books see n. 99). These tallies do not accurately reflect the number of ‘facts’, etc. that Pliny introduces in each of these books, but the conceit of quantitative ‘precision’ belongs to his strategy of quantifying the erudition and thus the authority of the author. 101 Pliny, Nat. hist. XVII 137: … ne quid sciens quidem praeteream quod usquam inuenerim. On Pliny’s ‘problem of totality’ and on ‘the desire for totality’ inherent in the process of collecting see Carey 2003, 75–101; cf. Murphy 2004, 11, 53, 71. 102 Conte 1994, 68. 103 Murphy 2004, 38. 104 Calvino 1986, 321; Conte 1994, 101. 105 Norden 1922, 293 n. 1, was taken in by this Plinian strategy (even though he despised Pliny’s style): “Die Disposition der NH ist ja nach einem ganz bestimmten Plane eingerichtet, das einzelne

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The originality of the derivative, the quantification of the author’s erudition and authority, and the orderly structure of the digressively disorderly thus all belong to Pliny’s strategies for positioning his authorial self. So do minimizing his own achievement by self-deprecatory gestures and self-irony, while maximizing his self-valorization by means of an elaborately charged insertion of the author into an elite socio-political constellation in his preface. All these stratagems aim to legitimate both the author and his claim to have composed an exceptional work of exceptional authority. If language presented a multi-dimensional challenge for Aristotle’s attempt to textualize the animal, and if some Latin authors who depended heavily on Greek sources acknowledged that the Latin language presented a particular set of challenges to their attempts to import Greek technical knowledge into the Latin language,106 Pliny seems to be less concerned with such challenges. While he does point out the frequent lack of a Latin equivalent for Greek terms,107 he usually does so without problematizing the lack and without lamenting the poverty of the Latin language – a poverty famously deplored by other Latin authors.108 In many cases, he simply cites the Greek term first, as though Greek is the unproblematic nomenclative norm, and then adds the Latin term without further comment.109 Signs of linguistic unease do, however, surface occasionally in Pliny’s text too. Thus he suggests that the Romans have not been sufficiently diligent about developing a Latin nomenclature for things in the natural world.110 At times he also refers to disputes about whether a Latin word for a Greek term exists, for instance: “Some think that there is an animal like a locust but without wings, which is called trixallis in Greek; but it does not have a Latin name. Not a few authorities say that this is what is called grylli.”111 Furthermore, Pliny sometimes admits uncertainty about a Latin term, for example: “There is a bird called icterus [Greek ἴκτερος, “jaundice”] from its color; they say that, if a patient with jaundice durch Rückverweisungen so straff unter sich verbunden wie kaum in einem anderen Werk des Altertums.” See also Sallmann 1971, 30 n. 25, who quotes Norden approvingly. 106 See e.g., Langslow 2000; Fögen 2000a; von Staden 1991. 107 E.g., Nat. hist. XXI 50, XXIV 90, XXIV 91, XXVI 100, XXXIV 65; cf. XXVIII 22. 108 See especially Fögen 2000a and 2000b. 109 E.g. Nat. hist. X 68; XVIII 159; XXIV 29; XXIV 130; XXII 147; XXXII 140. For an example of the reverse (a Latin technical term followed by the Greek) see Nat. hist. XXXII 154. Occasionally, Pliny adds an anecdote to explain the origins of a Latin equivalent for a Greek term, e.g. Nat. hist. XXVI 2. 110 E.g., Nat. hist. XXI 52: “There are other kinds [of foliage for wreathes] that can be indicated only by their Greek names, because attention to nomenclature has been lacking in our countrymen for the most part” (sunt et alia genera nominibus Graecis indicanda, quia nostris maiore ex parte huius nomenclaturae defuit cura). 111 Nat. hist. XXX 49. Cf. XXX 117: trixallidum (‘ash of trixallis’), among animal ingredients used to treat ulcerations. Trixallis may be from τρωξαλλίς, ‘locust’, or ‘grasshopper’, attested in Alexis, fr. 15.12 (PCG II, p. 32); Aelian, Nat. anim. VI 19; Dioscurides, Mat. med. II 52. See Leitner 1972, 132– 133, s. v. ‘Gryllus’.

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watches this bird, the disease is healed, while the bird dies. I think (puto) this bird is called galgulus in Latin”.112 In other cases, he hints that some, but not all, authorities agree on a Latin name, for instance in the case of a miraculously powerful little fish called echenais (ἐχενηΐς, “ship-detainer”), to which people attribute powers such as preventing a ship from moving, arresting a miscarriage, and aiding human parturition: “Among our countrymen, certain people (quidam) have named it mora [“delay”] in Latin.”113 These diverse glimpses of uncertainty, unease and vacillation about his own technical language suggest that his confident claims of mastery and order conceal the difficulties that arise when knowledge migrates across linguistic and cultural boundaries.114 If for Aristotle two of the principal problems posed by language (namelessness and the difficulty of communicating visual information) arose in large measure from venturing into new terrain, both theoretically and empirically, for Pliny the main linguistic issues therefore are the Greek provenance of most of his material and the Romans’ lack of adequate attention to nomenclature.

IV Galen of Pergamum: author, animal, audience, and language Galen of Pergamum (129 – ca 216 ) wrote extensively on animals and recorded, often in great detail, his numerous experiments on animals and his systematic dissections and vivisections of animals. He was a master narrator not only of the other – the human other as well as the animal other – but also of the authorial self.115 In his works, including those in which animals feature most prominently, the scientific author to a remarkable degree becomes both narrator and narratee, both the writing subject and the written object; both an agent of scientific investigation and a dramatic performer in his own texts. Furthermore, in his texts, Galen evokes himself as an author keenly aware of his diverse audiences, often linking his choice of a given literary form to his target audience. He distinguished not only between his writings for beginners, for experts, and for a general readership but

112 Nat. hist. XXX 94. Cf. X 73. See Leitner 1972, 85–86 (s. v. ‘Chlorion’). 113 Nat. hist. XXXII 1–6. On this fish see also Nat. hist. IX 79; Aristotle, Hist. anim. II 14.505b18–22; Oppian, Hal. I 212; Leitner 1972, 114–115. For another apparent reference to a lack of Roman unanimity about nomenclature see Nat. hist. XVI 67. 114 See Langslow 2000; von Staden 1991 and 1996. Cf. Quintilian, Inst. I 1.12–14, on training in Greek and Latin. Bilingualism was so important to some social niches that even birds are said to have been trained to imitate both Greek and Latin words and sentences; see Pliny, Nat. hist. X 120. Cf. especially Adams et al. 2002 and Adams 2003 on bilingualism in antiquity. 115 See Nutton 2009.

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also between his ‘private’ and his ‘public’ writings,116 just as he distinguished between his ‘private’ and ‘public’ dissections and vivisections.117 The ‘private’ writings, composed for one or a few individuals, often display a lesser degree of literary polish and have a lower density of literary references; by contrast, the ‘public’ texts, intended for wider circulation (πρὸς ἔκδοσιν), are more polished, often teeming with references to predecessors and with quotations from various authors, including poets, philosophers and physicians.118 Agile in deploying differently nuanced authorial personae as he moved between different literary forms, he was not averse to claiming authorship of transgressive innovations in his uses of form, including a frequent, innovative contamination of generic conventions.119 Furthermore, he was attentive to a textual staging of his own scientific authority, of his originality, and of his philological and historiographic authority in matters concerning science, medicine, and philosophy. Moreover, perhaps to a greater degree than any other ancient writer of technical treatises, Galen also staged himself as a scientific performer who is taken seriously by powerful intellectual and political elites with whom he claims personal familiarity in a number of treatises, but before whom he does not engage in the self-deprecation and flattery that characterize Pliny’s prefatory epistle to the future Emperor Titus.120 The latter point is illustrated by the opening sentences of Galen’s monumental work in 15 books called On Dissecting Procedures (De anatomicis administrationibus): Previously too I have written about dissecting procedures, namely, when I came to Rome for the first time [162 ], at the beginning of the reign of our present Emperor, Antoninus [Marcus Aurelius, Emperor 161–180]. But for two reasons I think it now is fitting to write these further [books on] dissecting procedures. One is that [in those early days,] when Flavius Boethus, a Roman consul, was about to leave Rome [165 ] for his native Ptolemais, he urged me to record my earlier dissections and vivisections for him, because, if any human being who has ever lived has had a fierce passion for observational investigation through dissection, it was Boethus… [At that time, I yielded to Boethus’ request and composed two books on dissecting procedures for him, but now there are no copies of that work, and Boethus has died without leaving a trace of it…] So, at the urging of my friends, I decided it would be better to write further such works. The second reason is that the work I now will compose will be a much better demonstration than the previous work, … since I have discovered many additional things through observations made possible by my dissections and vivisections… [though even at the time when Boethus was still in Rome,] I had made numerous dissections for him, at which

116 On Galen’s conceptions of the audiences, real or imagined, of his writings see Manetti & Roselli 1994, 1532, 1539, 1558–1562, 1589, 1592; Asper 1998, 331–335; 2007, 304–311, 323–367; von Staden 2009. 117 On private and public dissections and vivisections see von Staden 1995a and 1997. 118 For three distinct meanings of ἔκδοσις in Galen’s writings see von Staden 2006, 23–25, and 2009, 135–144. 119 See von Staden 1998. 120 See Gleason 2009; von Staden 1995a and 1997.

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were always present Eudemus the Peripatetic philosopher, Alexander of Damascus, who now is the official public teacher of Peripatetic doctrines in Athens, and frequently also other holders of high office, such as Sergius Paulus, currently the governor of Rome, a man distinguished in all respects, both in his deeds and in philosophical theories…121.

This opening to Galen’s principal anatomical treatise is a far cry from the opening sentences in Aristotle’s Researches on Animals cited above (Part II). Galen here inserts not only himself as author but also his scientific performances of animal dissection and vivisection into an elite socio-political and intellectual nexus. Immediately after this passage, he proceeds to a highly technical discussion of the structure of animal bodies and of non-human primates as the ideal subjects for systematic dissection.122 In short, once he has situated the author as a socio-political and scientific phenomenon in the opening section, he immediately turns to textualizing his scientific investigation of animals. In the course of this treatise, Galen proceeds to present himself as an expert on a remarkable array of animal species. The animals he discusses include birds, ranging from sparrows, larks, chickens and ducks to hawks, eagles, cranes and ostriches; aquatic animals from crabs and lobsters to small and large fish, seals, dolphins, and whales; and terrestrial animals, from mice and snakes to weasels, martens, rabbits, cats, dogs, wolves, sheep, goats, pigs, deer, donkeys, horses, mules, oxen, and even many exotic species, such as monkeys, baboons, camels, 121 Galen, Anat. adm. I 1 (2.215–218 Kühn; 1.1–5 Garofalo 1986–2000): ἀνατομικὰς ἐγχειρήσεις ἔγραψα μὲν καὶ πρόσθεν, ἡνίκα τὸ πρῶτον ἀνῆλθον εἰς Ῥώμην, ἔναγχος ἄρχειν ἠργμένου τοῦ καὶ νῦν ἡμῖν ἄρχοντος Ἀντωνίνου, γράφειν δ’ αὖθις ἄλλας ἔοικα ταύτας διὰ διττὴν αἰτίαν. ἑτέραν μὲν τήνδε· ὅτι Φλάβιος Βοηθὸς ἀνὴρ ὕπατος Ῥωμαίων, ἐξιὼν ἐκ Ῥώμης εἰς τὴν ἑαυτοῦ πατρίδα Πτολεμαΐδα, παρεκάλεσέ με τὰς ἐγχειρήσεις ἐκείνας αὐτῷ γράφειν, δριμὺν ἔρωτα τῆς ἀνατομικῆς ἐρασθεὶς θεωρίας, εἴπερ τις καὶ ἄλλος τῶν πώποτε γεγενημένων ἀνθρώπων. τούτῳ τῷ Βοηθῷ καὶ ἄλλας μὲν ἔδωκα πραγματείας ἐξιόντι, καὶ μέντοι καὶ τὴν τῶν ἀνατομικῶν ἐγχειρήσεων ἐν δυοῖν ὑπομνήμασιν· ἐπεὶ γάρ τοι ἐτεθέατο πάνυ πολλὰ παρ’ ἡμῖν ἐν ὀλίγῳ χρόνῳ δεδιὼς δέ, μὴ λάθοιτό ποτε τῶν ὀφθέντων, ἐδεήθη τοιούτων ἀναμνήσεων. ἐπεὶ δ’ ἐκεῖνος μὲν ἤδη τέθνηκεν, ἐγὼ δὲ οὐκ ἔχω τῶν γενομένων ὑπομνημάτων ἀντίγραφα διδόναι τοῖς ἑταίροις, ἀπολομένων ὧν εἶχον ἐν Ῥώμῃ, διὰ τοῦτο παρακαλεσάντων αὐτῶν, ἔδοξεν ἄμεινον εἶναι γράφειν ἕτερα. δευτέραν δ’ αἰτίαν, διὰ τὸ βελτίω μακρῷ τῆς τότε τὴν νῦν μοι γενησομένην ἀποδειχθήσεσθαι πραγματείαν, ἅμα μὲν εἰς διέξοδον ὑπομνημάτων πλειόνων ἐκταθεῖσαν ἕνεκα σαφηνείας, ἅμα δ’ ἀκριβεστέραν ἐκείνης ἐσομένην, ὡς ἂν πολλῶν ἐν τῷ μεταξὺ προσεξευρημένων μοι θεωρημάτων ἀνατομικῶν… καὶ τῷ Βοηθῷ παμπόλλας ἐποιησάμην ἀνατομάς, παρόντων αὐταῖς ἀεὶ μὲν Εὐδήμου τε τοῦ περιπατητικοῦ καὶ Ἀλεξάνδρου τοῦ Δαμασκηνοῦ, τοῦ νῦν Ἀθήνησιν ἀξιουμένου τοὺς περιπατητικοὺς λόγους διδάσκειν δημοσίᾳ, πολλάκις δὲ καὶ ἄλλων ἀνδρῶν ἐν τέλει, καθάπερ καὶ τοῦδε τοῦ νῦν ἀπάρχου τῆς Ῥωμαίων πόλεως, ἀνδρὸς τὰ πάντα πρωτεύοντος ἔργοις τε καὶ λόγοις τοῖς ἐν φιλοσοφίᾳ, Σεργίου Παύλου [ὑπάτου del. Garofalo]. 122 Anat. adm. I 2 (2.218–219 Kühn; 1.5 Garofalo 1986–2000): ὁποῖόν τι ταῖς σκηναῖς οἱ καλούμενοι κάμακές εἰσί, καὶ ταῖς οἰκίαις οἱ τοῖχοι, τοιοῦτον ἐν τοῖς ζῴοις ἥ γε τῶν ὀστῶν οὐσία. συνεξομοιοῦσθαι γὰρ αὐτῇ τἆλλα καὶ συμμεταβάλλεσθαι πέφυκεν. οἷον, εἰ τῷ ζῴῳ κρανίον εἴη στρογγύλον, ἀνάγκη καὶ τὸν ἐγκέφαλον τοιοῦτον εἶναι, ὥσπερ γε καί, εἰ πρόμηκες, προμήκης τούτῳ τῷ ζῴῳ καὶ ὁ ἐγκέφαλος…διὰ τοῦτο γοῦν καὶ ὁ πίθηκος ἁπάντων τῶν ζῴων ὁμοιότατος ἀνθρώπῳ καὶ σπλάγχνοις, καὶ μυσί, καῖ ἀρτηρίαις, καὶ φλεψί, καὶ νεύροις, ὅτι καὶ τῇ τῶν ὀστῶν ἰδέᾳ.

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bears, and crocodiles, hippopotami, lions, and the elephant. If some of Galen’s lost treatises, such as On the Dissection of the Living in two books, On the Dissection of the Dead in one book, and perhaps a further work On Animals, had survived, we might have been even better informed about the extent of Galen’s investigation of animals.123 Only rarely does Galen concede that there are species which he did not investigate, for instance: “I have never at all tried to dissect [vivisect?]124 ants, gnats, fleas and all the other small animals, but I have often dissected animals that creep, like weasels and mice, and ones that crawl, like snakes, as well as many kinds of birds and fishes, and so too all the other marine kinds”.125 Modern scholarship has tended to emphasize Galen’s use of animals only as a road map to the human body, at the expense of exploring the multiplicity of motives Galen himself cited for his dissections and vivisections of numerous animals. However, had Galen been interested only in learning about the structure, anatomical geography, and biological functions of the human body, he might have confined his investigations to what he frequently described as the six classes of animals closest to the human animal, one version of which is, in increasing distance from the human animal: (1) non-human primates; (2) bear; (3) swine (wild and domestic); (4) ‘saw-toothed’ animals (καρχαρόδοντες, i.e., quadruped carnivores, such as the lion); (5) horned cloven-footed ruminants; and (6) hornless quadrupeds with uncleft feet and undivided hooves.126 But so intrigued did Galen become by the enormous diversity of living organisms, and by the differences and similarities between them, that he investigated numerous other species, from the largest mammals to insects and small marine animals. Indeed, at times he admitted that he had to force himself to redirect his attention to the human body, so engrossed had he become in his research on non-human animals. In his voluminous descriptions of non-human animals, Galen identifies several distinct motivations for writing about them so extensively: (1) to obtain a verifiable knowledge of nature is invaluable for its own sake; (2) a knowledge of animals increases our understanding of nature’s intricately purposive workings in even the smallest parts of all living organisms; (3) an experimental investigation of living animals, in particular, yields a better understanding of biological functions and their causes; (4) animal dissection and vivisection provide invaluable practice for 123 For the treatises On Dissection of the Living and On Dissection of the Dead see Galen, Lib. prop. 4.38 (Boudon-Millot 154.1–2); Ord. lib. prop. 2.6 (19.55 Kühn; Boudon-Millot 93.1–3); Ars med. 37.9 (1.408.15–16 Kühn; Boudon 389.11–12); Anat. adm. III 9 (2.396.6–7 Kühn; 1.189.7–8 Garofalo 1986– 2000). For the far from certain view that Galen composed a sizable treatise On Animals, see Orth 1934. 124 It should be kept in mind that ἀνατέμνειν, without further specification, can refer to either dissection or vivisection. 125 Galen, Anat. adm. VI 1 (2.537 Kühn; 2.343.2–7 Garofalo 1986–2000). 126 Galen, Anat. adm. IV 3 (2.430–431 Kühn; 1.223.7–20 Garofalo 1986–2000). Cf. Anat. adm. VI 1, VI 3, VI 7, X 1, X 7, XI 2, XI 8, XI 12, XIII 4, XIV 1 and XV 2 for various versions of these six classes of animals.

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surgery on human patients. His motivations thus included using non-human animals as a useful theoretical and practical road map to the human body, but they went considerably beyond this single motive. Textualizing the animals he investigated and the scientific harvest they yielded was, however, not unproblematic in Galen’s view. He obviously does not adopt Aristotle’s detached, largely depersonalized style. Rather, compared to the style of most other ancient technical texts, Galen’s stands out for its emotional, personal, autobiographical, unusually robust, dialectical, and historically aware qualities. He nevertheless shares Aristotle’s view that one of the main hurdles to communicating a science of human and non-human animals is language. Galen seems to believe that one of the more treacherous difficulties faced by the scientist writing about living organisms is that language constantly threatens to ambush the scientist. He therefore repeatedly presents himself both as a master of animal science and as a theoretician of language who, while building on theories of language developed by Aristotle and the Stoics, grapples authoritatively with the relation of science to language, also as it pertains to writing about animals. Less concerned than Aristotle about the namelessness of many zoological phenomena and about the need for visual supplements to verbal accounts, Galen instead picks up on Aristotle’s recognition of the need for univocity in scientific writing. The figurative tendencies of language, Galen too claims, deprive language of the univocity required for a precise, clear articulation of scientific truths.127 Inconsistencies between this theory and Galen’s practice are hardly surprising: he resorts to numerous tropes and figures of speech throughout his vast œuvre. In On Dissecting Procedures, for instance, he begins his discussion of animal bodies with technological similes: “As so-called poles are to tents and walls to houses, so is the substance of the bones in animals.”128 Galen recognizes that the concept ‘figurative’ depends on the polarity ‘literal-figurative’, and that the ‘figurative’ covers a vast and varied domain, but, like ancient writers in the rhetorical tradition, he singles out one trope as a paradigm case of the ‘figurative’, namely metaphor. The polarity ‘literal-figurative’ in his writings thus becomes usurped by the opposition ‘literal-metaphorical’. The metaphoric proclivity of language, he thought, is a particularly stubborn obstacle to the avoidance of ambiguity and obscurity in the communication of a science of living bodies. So preoccupied did Galen become with this problem that he engaged in extensive discussions of metaphor, though these are scattered across several treatises.129 With an optimism that seems unwarranted from a modern perspective, he argues that the solution is to recuperate a literal language for science. The literal, he claims, is primary and univocal, 127 Von Staden 1995b. On Galen’s theory of language see also Hankinson 1994; Barnes 1997; Morrison 2008. 128 See above n. 122. 129 The most extensive extant remarks are in Galen’s On the Differences between Pulses (De pulsuum differentiis) III 6–7 (8.670–694 Kühn); see Deichgräber 1957 and n. 127 above.

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whereas the figurative is secondary and polysemous. The literal, however, has largely been lost, whereas the metaphorical is omnipresent. Yet the recovery of the literal, he believes, is essential for a scientific writing of the animal, as it is for all scientific writing, for such a language alone would meet the demands that science makes of language. How, then, does one recover the literal? In Galen’s optimistic view, this could be accomplished by recognizing the historical dimensions of language and engaging in semantic archaeology. To put it perilously briefly, one has to excavate an original ordinary language, the original ordinary, literal meanings. For this purpose, it often is necessary to journey many centuries into the past, to texts of the classical period that represent ‘ordinary’ people speaking ‘ordinary’ language, for instance Greek comedy and ‘colloquial’ parts of Plato’s dialogues.130 To write the animal scientifically, one accordingly must not only conduct extensive, systematic investigations of animals according to proven logical and methodological principles but also identify and expose the metaphors of precursors, recent and remote. But, in Galen’s view, this can be done only by first securing the ‘literal’ through extensive forays into the history of linguistic usage. Galen positions himself as a scientific authority capable of writing the animal, human and non-human, in part because he has undertaken and continues to undertake this linguistic excavation in addition to his anatomical and physiological investigations. As indicated above, his writings in fact reveal him to be a master of metaphor and other tropes and figures, whom the animal kingdom too serves as a source of numerous kinds of figuration; his quest for literalness is itself marked by his dense deployment of metaphors. But central to his authorial selfpresentation remained not only the socio-political and historiographic construction of Galen the matchless scientist and scientific performer frequented by the elite, but also the presentation of himself as exceptionally well equipped to write the animal, thanks to his understanding of language and, in particular, to his exercises in semantic archaeology. Aristotle, Pliny the Elder, and Galen thus offer instructive examples of the diverse ancient styles of ‘knowing’ and writing the animal, of strategies of authorial self-presentation in technical texts on animals, and of responses to the linguistic hurdles faced by those who try to write the animal ‘scientifically’.

130 To this context several of Galen’s lost works on the language of comedy seem to belong, such as Ordinary Words in Aristophanes, Ordinary Words in Eupolis, and Ordinary Words in Cratinus; see Galen, Lib. prop. 20.1 (19.48 Kühn; Boudon-Millot 173) .

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Bibliography Texts quoted Aubert, H., & F. Wimmer 1868. Aristoteles Thierkunde. 2 vols. Leipzig. Balme, D. M. 2002. Aristotle. Historia animalium, vol. I: Books I-X: Text. Prepared for publication by A. Gotthelf. Cambridge. Bekker, I. 1831. Aristotelis opera. 5 vols. Berlin (repr. 1960). Bona, I. 1991. Natura terrestrium (Plin. Nat. hist. VIII). Genoa. Canfora, L. 2008. Il papiro di Artemidoro. Bari. Gallazzi, C. et al. 2008. Il Papiro di Artemidoro (P. Artemid). Milan. Garofalo, I. 1986–2000. Galenus. Anatomicarum Administrationibus libri qui supersunt novem earundem interpretatio Arabica Hunaino Isaaci filio ascripta, 2 vols. Naples. Gigon, O. 1987. Aristotelis opera, vol. III: Librorum deperditorum fragmenta (in: 2nd rev. ed. of I. Bekker et al., Aristotelis opera, 1831–1870). Berlin. Kollesch, J. 1985. Aristoteles Über die Bewegung der Lebewesen, Über die Fortbewegung der Lebewesen. Aristoteles Werke in deutscher Übersetzung 17.II/III. Berlin. Kollesch, J. et al. 1965. Apollonios von Kition. Kommentar zu Hippokrates über das Einrenken der Gelenke. Corp. Med. Graec. XI 1,1. Berlin. Kullmann, W. 2007. Aristoteles Über die Teile der Lebewesen. Aristoteles Werke in deutscher Übersetzung 17. Berlin. Lennox, J. G. 2001. Aristotle On the Parts of Animals I-IV. Oxford. Louis, P. 1964–1969. Aristote. Histoire des animaux, 3 vols. Paris. Louis, P. 1973. Aristote. Marche des animaux, Mouvement des animaux. Paris. Nussbaum, M. C. 1985. Aristotle’s De motu animalium (reprint, with corrections, of 1st ed. 1978). Princeton. Santini, C., & N. Scivoletto 1990–1992. Prefazioni, prologhi, proemi di opere tecnico-scientifiche latine. 2 vols. Rome. Schneider, J. G. 1811. Aristotelis De animalibus historiae libri X. 4 vols. Leipzig. Segonds, A. P. 1981. Jean Philopon, Traité de l’astrolabe. Paris (reprint, with an introduction, appendix and corrections, of H. Hase (ed.) 1839, Ioannis Alexandrini cognomina Philoponi De usu astrolabii, Bonn). Stückelberger, A., & G. Graßhoff 2006. Klaudios Ptolemaios. Handbuch der Geographie. Griechisch–Deutsch. Einleitung, Text und Übersetzung, 2 vols. Basel. Torraca, L. 1958. Aristotele De motu animalium. Naples.

Works quoted Adams, J. N. et al. (eds.) 2002. Bilingualism in Ancient Society. Language Contact and the Written Test. Oxford. Adams, J. N. 2003. Bilingualism and the Latin Language. Oxford. Asper, M. 1998. “Zu Struktur und Funktion eisagogischer Texte.” In: Kullmann et al. 1998, 309– 340. Asper, M. 2001. “Stoicheia und Gesetze. Spekulationen zur Entstehung mathematischer Textformen in Griechenland.“ In: Antike Naturwissenschaft und ihre Rezeption 11, 73–106. Asper, M. 2003. Review of Netz 1999. In: Gnomon 75, 7–12.

Writing the Animal: Aristotle, Pliny the Elder, Galen

141

Asper, M. 2007. Griechische Wissenschaftstexte. Formen, Funktionen, Differenzierungsgeschichten. Stuttgart. Balme, D. M. 1962. “ΓΕΝΟΣ and ΕΙΔΟΣ in Aristotle’s biology.” In: Classical Quarterly NS 12, 81–98. Barnes, J. 1997. “Logique et pharmacologie. À propos de quelques remarques d’ordre linguistique dans le De simplicium medicamentorum temperamentis ac facultatibus de Galien.” In: A. Debru (ed.), Galen on Pharmacology. Philosophy, History and Medicine. Leiden, 3–33. Beagon, M. 1992. Roman Nature. The Thought of Pliny the Elder. Oxford. Blanck, H. 1992. Das Buch in der Antike. Munich. Bodson, L. 1986. “La zoologie romaine d’après la NH de Pline.” In: Helmantica 37, 107–116. Brodersen, K., & J. Elsner (eds.) 2009. Images and Texts in the “Artemidorus Papyrus.” Working Papers on P. Artemid. Stuttgart. Calvino, I. 1986. “Man, the Sky, and the Elephant.” In: I. Calvino, The Uses of Literature. Essays, translated by P. Creagle. San Diego, 315–330 (Italian original 1982). Carey, S. 2003. Pliny’s Catalogue of Culture: Art and Empire in the Natural History. Oxford. Celantano, M. S. (ed.) 2003. Ars/Techne. Il manuale tecnico nelle civiltà greca e romana. Atti del Convegno Internazionale Università ‘G. d’Annunzio’ di Chieti-Pescara, 29–30 ottobre 2001. Alessandria. Chemla, K. (ed.) 2004. History of Science, History of Text. Dordrecht. Conte, G. B. 1994. Genres and Readers. Baltimore (transl. by G. W. Most; Italian original: Generi e Lettori, Milan 1991). Dear, P. (ed.) 1991. The Literary Structure of Scientific Argument: Historical Studies. Philadelphia. Debru, A. 1994. “Les démonstrations médicales à Rome au temps de Galien.” In: van der Eijk et al. 1995, vol. I, 69–81. Deichgräber, K. 1957. Parabasenverse aus Thesmophoriazusen II des Aristophanes bei Galen. Sitzungsberichte, Akademie der Wissenschaften zu Berlin, Klasse für Sprachen, Literatur und Kunst 1956.2. Diederich, S. 2007. Römische Agrarhandbücher zwischen Fachwissenschaft, Literatur und Ideologie. Berlin. van der Eijk, P. J. 1997. “Towards a Rhetoric of Scientific Discourse. Some formal characteristics of Greek Medical and Philosophical Texts.” In: E. J. Bakker (ed.), Grammar as Interpretation. Greek Literature in its linguistic Context. Leiden, 77–129. van der Eijk, P. J. et al. (eds.) 1995. Ancient Medicine in its Socio-cultural Contexts. 2 vols. Amsterdam. Elkins, J. 1997. Our Beautiful, Dry, and Distant Texts. Art History as Writing. University Park, PA. Fögen, T. 2000a. “Patrii sermonis egestas”: Einstellungen lateinischer Autoren zu ihrer Muttersprache. Ein Beitrag zum Sprachbewußtsein in der römischen Antike. Munich. Fögen, T. 2000b. “Patrii sermonis egestas und dichterisches Selbstbewußtsein bei Lukrez.” In: A. Haltenhoff & F.-H. Mutschler (eds.), Hortus litterarum antiquarum. Festschrift für Hans Arnim Gärtner am 70. Geburtstag. Heidelberg, 125–141. Fögen, T. (ed.) 2005. Antike Fachtexte. Ancient technical texts. Berlin. Fögen, T. 2007a. “Pliny the Elder’s animals: some remarks on the narrative structure of Nat. hist. 8–11.” In: Hermes 135, 184–198. Fögen, T. 2007b. “Antike Zeugnisse zu Kommunikationsformen von Tieren.” In: Antike und Abendland 53, 39–75. Fögen, T. 2009. Wissen, Kommunikation und Selbstdarstellung. Zur Struktur und Charakteristik römischer Fachtexte der frühen Kaiserzeit. Munich. Formisano, M. 2001. Tecnica e scrittura. Le letterature tecnico-scientifiche nello spazio letterario tardolatino. Rome. French, R. 1994. Ancient Natural History. Histories of Nature. London.

142

Heinrich von Staden

Fuhrmann, M. 1960. Das systematische Lehrbuch. Ein Beitrag zur Geschichte der Wissenschaften in der Antike. Göttingen. Gallazzi, C., & B. Kramer 1998. “Artemidor im Zeichensaal: eine Papyrusrolle mit Text, Landkarte und Skizzenbüchern aus späthellenistischer Zeit.” In: Archiv für Papyrusforschung 44, 189– 208. Giebel, M. 2003. Tiere in der Antike. Von Fabelwesen, Opfertieren und treuen Begleitern. Stuttgart. Gill, C. et al. (eds.) 2009. Galen and the World of Knowledge. Cambridge. Gleason, M. 2009. “Shock and awe: the performance dimension of Galen’s anatomy demonstrations.” In: Gill et al. 2009, 85–114. Grmek, M. D. 1984. “Vestigia della chirurgia greca: il Codice di Niceta et i suoi discendenti.” In: Kos I.5, 52–60. Grmek, M. D., & D. Gourevitch 1998. Les maladies dans l’art antique. Paris. Gros, P. 1996. “Les illustrations du De architectura de Vitruve. Histoire d’un malentendu.” In: Nicolet & Gros 1996, 19–44. Hankinson, R. J. 1994. “Usage and Abusage: Galen on Language.” In: S. Everson (ed.), Language. Cambridge, 166–187. Hine, H. M. 2009. “Subjectivity and Objectivity in Latin Scientific and Technical Literature.” In: Taub & Doody 2009, 13–30. Holmes, F. L. 1987. “Scientific Writing and Scientific Discovery.” In: Isis 78, 220–235. Holmes, F. L. 1991. “Argument and Narrative in Scientific Writing.” In: Dear 1991, 164–181. Horster, M., & C. Reitz (eds.) 2003. Antike Fachschriftsteller: Literarischer Diskurs und sozialer Kontext. Wiesbaden. Howe, N. P. 1985. “In defense of the encyclopaedic mode.” In: Latomus 44, 561–576. Kadar, Z. 1978. Survivals of Greek zoological illuminations in Byzantine manuscripts. Budapest. Köves-Zulauf, Th. 1973. “Die Vorrede der plinianischen Naturgeschichte.” In: Wiener Studien N.F. 7 (86 Bd.), 134–184. Kudlien, F. 1960. Die handschriftliche Überlieferung des Galenkommentars zu Hippokrates De articulis. Berlin. Kullmann, W. 1998. “Zoologische Sammelwerke in der Antike.” In: Kullmann et al. 1998, 121–139. Kullmann, W. 1999. “Zoologische Sammelwerke in der Antike.” In: Wöhrle 1999, 181–198. Kullmann, W., et al. (eds.) 1998. Gattungen wissenschaftlicher Literatur in der Antike. Tübingen. Langslow, D. 2000. Medical Latin in the Roman Empire. Oxford. Leitner, H. 1972. Zoologische Terminologie beim älteren Plinius. Hildesheim. Lennox, J. G. 2001a. Aristotle’s Philosophy of Biology. Studies in the Origins of the Life Sciences. Cambridge. Lloyd, G. E. R. 1961. “The development of Aristotle’s theory of classification of animals.” In: Phronesis 6, 59–81 (repr. with a response to his critics in: Lloyd 1991, 1–26). Lloyd, G. E. R. 1987. The Revolutions of Wisdom. Studies in the Claims and Practice of Ancient Greek Science. Berkeley. Lloyd, G. E. R. 1991. Methods and Problems in Greek Science. Cambridge. Mancosu, P., et al. (eds.) 2005. Visualization, Explanation, and Reasoning Styles in Modern Mathematics. Dordrecht. Manetti, D., & A. Roselli 1994. “Galeno commentatore d’Ippocrate.” In: Aufstieg und Niedergang der römischen Welt II.37.2, 1529–1635, 2071–2080. Marganne, M.-H. 2004. Le livre médical dans le monde gréco-romain. Liège. Mastrorosa, I. 2003. “Proximumque humanis sensibus. Gli elefanti fra etiologia e aneddotica storico-geografica.” In: F. Gasti & E. Romano (eds.), “Buoni per pensare”. Gli animali nel pensiero e nella letteratura del antichità. Atti del II Giornata Ghisleriana di filologia classica (Pavia, 8–19 aprile 2002). Como, 125–146.

Writing the Animal: Aristotle, Pliny the Elder, Galen

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Mastrorosa, I., & A. Zumbo, with C. Santini (eds.) 2002. Letteratura scientifica e tecnica di Grecia e Roma. Rome. Mazzolini, R. G. (ed.) 1993. Non-verbal communication in science prior to 1900. Florence. Meißner, B. 1999. Die technologische Fachliteratur der Antike. Struktur, Überlieferung und Wirkung technischen Wissens in der Antike (ca. 400 v. Chr.–ca. 500 n. Chr.). Berlin. Montero Cartelle, E. 2010. Tipologia de la Literatura Médica Latina. Antigüedad, Edad Media, Renacimiento. Porto. Morison, B. 2008. “Language.” In: R. J. Hankinson (ed.), A Companion to Galen. Cambridge, 116– 156. Münzer, F. 1897. Beitrage zur Quellenkritik der Naturgeschichte des Plinius. Berlin. Murphy, T. 2004. Pliny the Elder’s Natural History. The Empire in the Encyclopedia. Oxford. Netz, R. 1999. The Shaping of Deduction in Greek Mathematics: A Study in Cognitive Science. Cambridge. Netz, R. 2004. “The Limits of Text in Greek Mathematics.” In: Chemla 2004, 161–176. Neugebauer, O. 1949. “Studies in Ancient Astronomy IX: The early history of the astrolabe.” In: Isis 40, 240–256. Nicolet, C., & P. Gros (eds.) 1996. Les littératures techniques dans l’Antiquité romaine. Vandœuvres-Genève. Norden, E. 1922. Die germanische Urgeschichte in Tacitus Germania, 2nd ed. Leipzig (repr. Darmstadt 1959). Nutton, V. 2009. “Galen’s Authorial Voice: a Preliminary Enquiry.” In: Taub & Doody, 53–62. Orth, E. 1934. “Eine unbekannte Schrift Galens.” In: Philologische Wochenschrift 54, 846–848. Pellegrin, P. 1985. “Aristotle: a zoology without species.” In: A. Gotthelf (ed.), Aristotle on Nature and Living Things. Philosophical and Historical Studies presented to David M. Balme. Pittsburgh, 95–115. Pellegrin, P. 1986. Aristotle’s Classification of Animals. Biology and the Conceptual Unity of the Aristotelian Corpus. Berkeley. Pellegrin, P. 1990. “Taxonomie, moriologie, division: réponses à G. E. R. Lloyd.” In: D. Devereux & P. Pellegrin (eds.), Biologie, logique et métaphysique chez Aristote. Actes du séminaire C.N.R.S.-N.S.F. Paris, 37–47. Rodríguez Alfageme, I. 2004. Literatura científica griega. Madrid. Römer, F. 1978. “Plinius der Ältere, III. Bericht.” In: Anzeiger für die Altertumswissenschaft 31, 129–206. Sallmann, K. G. 1971. Die Geographie des älteren Plinius in ihrem Verhältnis zu Varro. Berlin. Sallmann, K. 1975. “Plinius der Ältere 1938–1970.” In: Lustrum 18, 5–299, 345–352. Serbat, G. 1986. “Pline l’Ancien. État présent des études sur sa vie, son œuvre et son influence.” Aufstieg und Niedergang der römischen Welt II.32.4, 2069–2200. Sharples, R. 1995. Theophrastus of Eresus. Sources for his Life, Writings, Thought and Influence. Commentary, vol. 5: Sources on Biology. Leiden. von Staden, H. 1991. “Apud nos foediora verba. Celsus’ reluctant construction of the female body.” In: G. Sabbah (ed.), Le latin médical. La constitution d’un langage scientifique. SaintÉtienne, 271–296. von Staden, H. 1994. “Author and Authority. Celsus and the Construction of a Scientific Self.” In: M. E. Vázquez Buján (ed.), Tradición e Innovación de la Medicina Latina de la Antigüedad y de la Alta Edad Media, Santiago de Compostela, 103–117. von Staden, H. 1995a. “Anatomy as Rhetoric: Galen on dissection and persuasion.” In: Journal of the History of Medicine and Allied Sciences 50, 48–67. von Staden, H. 1995b. “Science as text, science as history. Galen on metaphor.” In: van der Eijk et al. 1995, vol. II, 499–518. von Staden, H. 1996. “Liminal Perils. Early Roman Receptions of Greek Medicine.” In: F. Rager & S. P. Ragep (eds.), Tradition, Transmission, Transformation with S. Livesey. Leiden, 369–418.

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von Staden, H. 1997. “Galen and the Second Sophistic.” In: R. Sorabji (ed.), Aristotle and After. London, 33–54. von Staden, H. 1998. “Gattung und Gedächtnis. Galen über Wahrheit und Lehrdichtung.” In: Kullmann et al. 1998, 65–94. von Staden, H. 2006. “Interpreting ‘Hippokrates’ in the 3rd and 2nd centuries ”. In: C. W. Müller et al. (eds.), Ärzte und ihre Interpreten. Medizinische Fachtexte der Antike als Forschungsgegenstand der Klassischen Philologie. Fachkonferenz zu Ehren von Diethard Nickel. München, 15–47. von Staden, H. 2009. “Staging the past, staging oneself: Galen on Hellenistic exegetical traditions”. In: Gill et al., 132–155. von Staden, H. forthcoming. “The Living Environment: Animals and Humans in Celsus’ Medicina.” In: N. Palmieri (ed.), L’environnement dans la médecine antique et médiévale. Saint Étienne, 69–94 (in press). Stückelberger, A. 1988. Einführung in die antiken Naturwissenschaften. Darmstadt. Stückelberger, A. 1993. “Aristoteles illustratus. Anschauungshilfsmittel in der Schule des Peripatos.“ In: Museum Helveticum 50,131–143. Stückelberger, A. 1994. Bild und Wort: das illustrierte Fachbuch in der antiken Naturwissenschaft, Medizin und Technik. Mainz. Stückelberger, A. 1998. “Vom anatomischen Atlas des Aristoteles zum geographischen Atlas des Ptolemaios: Beobachtungen zu wissenschaftlichen Bilddokumentationen.” In: Kullmann et al. 1998, 287–307. Taub, L., & A. Doody (eds.) 2009. Authorial Voices in Greco-Roman Technical Writing. Trier. Weitzmann, K. 1947. Illustrations in Roll and Codex. A Study in the Origin and Method of Text Illustration. Princeton (2nd print. with addenda 1970). Weitzmann, K. 1959. Ancient Book Illumination. Cambridge, MA. Weitzmann, K. 1977. Late antique and early Christian book illumination. New York. Wöhrle, G. (ed.) 1999. Geschichte der Mathematik und der Naturwissenschaften, I: Biologie. Stuttgart.

Philip van der Eijk

Galen and the Scientific Treatise: a Case Study of Mixtures 1

Abstract: Galen of Pergamum was a prolific and versatile author, using a great variety of genres or types of writing. In producing these various forms of scientific output, he was well aware of earlier practices by other authors, and he self-consciously positions himself in relation to the relevant literary and scientific traditions. This paper examines Galen’s use of a specific kind of writing that is often designated as ‘treatise’. Using the case study of his pragmateia peri kraseôn (De temperamentis, Mixtures), we will consider to what extent Galen conforms to, or departs from, the characteristics of this type of writing as these had been established by predecessors, notably Aristotle.

Introduction Galen of Pergamum was great at multi-tasking. Not only was he a wide-ranging thinker and practitioner, combining medical theory, philosophy, literary criticism and linguistics with a busy practice as a high society physician and public intellectual, debater and dissector. He was also a prolific and versatile author, confidently using a large number of different forms of writing. In what has been preserved of his immense œuvre, we find ‘isagogic’ works introducing the reader to various aspects of medical theory and practice; prolegomena to the study of his own writings; systematic expositions of the medical art (technai); an ‘exhortation’ to the arts (protreptikos logos); more specialized ‘treatises’ (pragmateiai) on medical and philosophical topics; synopses, epitomes, summaries and compendia; commentaries on other medical or philosophical texts; theses; letters, advisory and consolatory texts; glossaries; and texts in the form of questions and answers or lists of definitions.2 1 I am grateful to the Alexander von Humboldt Foundation for funding the research from which this project has arisen. This paper has benefited from feedback given by audiences at the University of Bamberg (Workshop on ‘Ancient Scientific and Technical Texts’, March 2010), the University of Oslo (Conference on ‘The Texts of the Medical Profession in Antiquity: Genres and Purposes’, September 2010) and the Humboldt University at Berlin (Ancient Medicine Colloquium, February 2011). 2 Examples of the types of text mentioned: Bones for Beginners; The Order of My Own Books; The Constitution of the Medical Art; Exhortation to the Arts; Mixtures; Synopsis on the Pulse; Compendium of Plato’s Timaeus; the commentaries on several works of Hippocrates; Thrasybulus; Avoidance of Distress; Glossary of Hippocratic Terms; Medical Definitions (although the latter work is probably not by Galen). This survey of types of writing does not include the numerous works by Galen that are lost. For a study of Galen’s usages of a number of these genres see Curtis 2009, with extensive bibliography of more specialized investigations of Galen’s use of specific genres and forms of

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In practicing all these various forms of output, Galen was well aware of earlier usages of these types of writing by other authors. Indeed, in his evaluations of the contributions made by earlier medical and scientific writers, he sometimes explicitly addresses their use of language, style and argument, and he positions his own work in relation to that of his predecessors not only in doctrine but also in form and style of presentation.3 In this paper, we will examine an example of a kind of writing practiced by Galen that, for lack of a better term, we usually designate as ‘treatise’; and we will consider how Galen uses this form of scientific output, to what extent he adheres to any existing conventions associated with it (as far as these can be retrieved from ancient scientific writing practice) or puts his own stamp on it.4 To give a strict definition of the treatise may not be so easy, but we can certainly list some features commonly attributed to it and that distinguish it from other, perhaps equally elusive forms of writing (such as the ‘essay’). In modern usage, we associate the treatise with systematicity, rigorous and sober reasoning about a well-defined subject or question, with the inquiry proceeding through rational argument from premises to conclusions, sometimes presented in the form of a series of theses with demonstrations. A treatise is usually impersonal and dispassionate in tone or mode of address; the presence of the author in the text (the authorial ego) tends to be minimal, as the argument is supposed to speak for itself; and the audience likewise tends to be, on a textual level, invisible or anonymous – at any rate no allowances are made for the non-expert.5 Consequently, and contrary to texts that are intended for beginners or lay people, a treatise can be characterized by ruthlessly specialized and complicated discussion of the subject matter, by exhaustive coverage and by a relentlessly high degree of technical detail and precision.6 When we look for examples from the ancient world illustrating these characteristics, we often associate the term ‘treatise’ with Aristotle’s pragmateiai, well known – if not notorious – for their dry, sober, impersonal style of writing and uncompromising presentation. In Aristotle’s case, it has long been believed that

writing, e.g. Oser-Grote 1998 on Galen’s isagogic texts, or von Staden 2002 and 2006 on Galen’s commentaries. 3 See von Staden 1995 and 1998; Sluiter 1995. 4 Earlier studies into Galen’s use of the ‘treatise’ are Asper 2007, 323–364 (on the ‘Systempragmatie’) and Curtis 2009, 149–177. 5 This, for instance, is a defining feature used by Markus Asper in his 2007, 315, distinguishing texts that have no clear designation of the intended audience (‘Adressatenbegrenzung’) from texts that address specific audiences such as students or beginners or lay people or specialists, or are intended for specific occasions, such as teaching, public demonstration, etc. On the relationship between the idea of an ‘auditoire universel’ and claims to scientific, universal truth see Perelman & Olbrechts-Tyteca 1970, 40–46. 6 Cf. Curtis 2009, 152: “A scientific treatise … is a written work which provides a detailed treatment of a subject by linking a series of related topics together using a variety of different types of discourse to convey its message.”

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these features were at least partly motivated by considerations of the function, occasion, usage or audience for which they were intended: according to the traditional view, the pragmateiai were ‘school’ treatises not meant for public consumption, perhaps even ‘lecture notes’ meant for private use, as opposed to the more polished literary dialogues Aristotle is also reported to have written but which have not survived. Yet, as recent scholarship has shown, it is too superficial to define ancient pragmateiai simply by the absence of the more striking, ‘literary’ features characteristic of the dialogue, the letter, the didactic poem or the other genres just mentioned,7 rather than by any positive characteristics of their own.8 And to regard this perceived absence as a sign of carelessness, or lack of consideration with a potentially wider future readership than originally envisaged, fails to do justice to the evidence of careful crafting that many ancient pragmateiai, even Aristotle’s ‘esoteric’ writings, undeniably display. After all, the allegedly characteristic ‘dryness’ and dispassionate tone of the pragmateia can be seen, in specific contexts, as a virtue rather than a defect, and as such it can be cultivated and become, in the hands of a skilful author, an effective rhetorical instrument in creating a certain posture or ethos vis-à-vis the audience; and it can be projected as an expression of the sober search for truth and thus enhance an author’s impression of integrity, honesty and transparency in presentation, devoid of any rhetorical point-scoring or attempts to manipulate the audience. Furthermore, not all works we tend to regard as treatises correspond to the associations mentioned above to the same extent. For example, among the medical writings attributed to Hippocrates (the so-called ‘Hippocratic Corpus’), we find many works in which the authorial ego is prominently present; and these are not just the rhetorically crafted master pieces such as The Sacred Disease or Regimen, but also seemingly less polished or less argumentative works such as the Epidemics or Nature of the Child.9 Even Aristotle’s writings display considerable formal vari-

7 For examples of such ‘genres’ of scientific and philosophical texts in the ancient world, and the Greek and Latin terms used to refer to them, see Untersteiner 1980, 51–103 (distinguishing aphorisms, apophthegmata, gnōmai, didactic poetry, humnoi, symposium literature, dialogues, apomnēmoneumata, chreiai, diatribes, protreptic texts, consolationes, problēmata, letters, and isagogic texts). See also Schenkeveld 1997. 8 On Aristotle’s pragmateiai see Lengen 2002, with references to older literature, and Untersteiner 1980, 33–44. 9 It is, of course, possible that this variety is related to a distinction between Hippocratic works intended for oral delivery and works meant to be read (see van der Eijk 1997, 93–99, with references to further discussion) or that between works intended for specialists and apprentices and works intended for a wider audience (see van der Eijk 1997, 79 n. 9, on the distinction made by Jouanna 1984 between ‘cours’ and ‘discours’). Yet while these distinctions may be functional in some cases, it is not always possible to assign specific works to the former or the latter category; and as we shall see below, some features commonly associated with ‘oral’ presentation are found in works designated as pragmateiai as well.

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ety, e.g. in the alternation between rhetorically elaborate exploratory sections and more ‘dogmatic’ or ‘schoolmasterly’ passages,10 or some displaying lively, dialectical and even ‘dialogic’ features, rhetorical questions and the like.11 Clearly, then, within what we usually call treatises there is a considerable degree of variation and flexibility; and this could give rise to the question to what extent our concept of the ‘treatise’ is actually appropriate or helpful to the study of ancient scientific texts, or whether we should classify them differently. I would certainly not wish to suggest that, throughout antiquity, the treatise was recognized as a rigid genre with well-defined rules, conventions and features signalling to an audience what kind of things it could expect, as there is no evidence to suggest that this was the case.12 I rather see it, more pragmatically, as a mode of writing that scientists in antiquity developed in dealing with their subject matter, in communication with their colleagues and students and in reaction to their predecessors, and that gradually acquired a certain, distinct shape. That mode of writing was apparently very successful and managed to establish itself in antiquity and beyond, setting a standard as one of the most suitable ways for a scientist to express his views. And since it was obviously so influential in the subsequent history of science, it is well worth trying to describe its various features and development and to explain why it was deemed so suitable, considering that it is by no means the only possible or self-evident mode of scientific output – not even within the tradition of Western science, let alone in comparison with non-Western civilizations.13 A further question one might raise in this connection is that of the relationship between our word ‘treatise’ and the Greek pragmateia (or the Latin tractatus). To answer this question properly would require a comprehensive examination of the semantics and various usages of pragmateia in Greek literature. Such an examination would be very desirable, as it could provide us with a clearer idea of what ancient authors had in mind when using the term pragmateia; and this would be relevant to Galen as well, since Galen has strong views on the formal aspects of scientific discourse, on the use of language and style, on the kinds of argument

10 Cf. the distinction made by G. E. R. Lloyd between ‘dogmatism’ and ‘uncertainty’ in the manner in which scientific writers in the ancient world presented their ideas and arguments (Lloyd 1987). A modern equivalent, taken from discourse analysis, would be Kinneavy’s distinction between ‘assertory’ and ‘exploratory’ modes of discourse, which can occur at different places in one and the same text (Kinneavy 1971). 11 See Lengen 2002. 12 Of course, Aristotle’s observations on dialectics (and, to some extent, rhetoric) reflect a strong awareness of several of the issues mentioned, especially concerning the types of argument allowed in specific contexts, but they do not give rise (at least not explicitly) to the articulation of an ideal ‘genre’. For the influence of ancient dialectics and rhetorical theory on the later development of scientific writing (e.g. in the Early Modern Period) and on modern argumentation theory see Pera 1994 and Perelman & Olbrechts-Tyteca 1970. 13 See Crombie 1995.

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allowed in specific contexts, on the extent to which poetry and metaphor are permitted in scientific prose and on the most effective and most appropriate modes of ‘scientific instruction’ (epistēmonikē didaskalia).14 Such an examination would perhaps also shed light on the question – which needs to be faced open-mindedly – whether Galen used pragmateia as a genre term demarcating certain types of text from others (such as hupomnēmata or sungrammata),15 or more loosely in the sense of ‘discussion’, ‘treatment’, ‘occupation’, without further indication of the nature of such discussion – and there may, of course, be instances of both, and possibly further, usages.16 This question is prompted both by the wide variety of texts that Galen refers to as pragmateiai17 and by a similar difficulty surrounding the word hupomnēmata, which Galen uses in a number of different ways, sometimes referring to his commentaries on Hippocrates and Plato (hence it is often translated ‘commentary’ by modern scholars) but sometimes also to other works that are neither in the form of a commentary nor exegetical in nature; and while Galen sometimes seems to use the term hupomnēmata in opposition to sungramma for works not intended for publication (hence the translation ‘notes’),18 there are also cases where he applies the word to works for which there is no reason to assume that they were meant for private use only, and where it seems best translated just ‘work’ or ‘writing’.19 Yet in the absence of such a comprehensive semantic examination of the word pragmateia (which would be a project of great size and complexity), it would be premature to make definitive claims about the relationship between our concept of ‘treatise’ and the Greek pragmateia or to suggest that the term pragmateia actually did serve as a genre category in the ancient world in the way I referred to

14 See Sluiter 1995; von Staden 1998; Vogt 2005. 15 These terms are used frequently in Galen’s writings, and sometimes all three are found within the same context, as in the Commentary on Hippocrates’ Nature of Man p. 7,10–13 Mewaldt (15.9 Kühn) where, however, he does not seem to use them as genre terms demarcating them from each other or from other designations (and where sungramma is used to refer to the actual commentary he is writing). 16 See von Staden 1998, 72–73. 17 Even a superficial, impressionistic survey of Galen’s auto-references bears this out: cf. My Own Books 19.20, 28, 30, 31, 32, 33, 37 and 41 Kühn. For further examples see von Staden 1998, 72 n. 31– 32. 18 E.g. Difficulty of Breathing 7.825 Kühn, 7.854 Kühn; Commentary on Hippocrates’ Regimen in Acute Diseases 15.515 Kühn; Commentary on Hippocrates’ Prorrheticon I 16.532 Kühn; Commentary on Hippocrates’ Epidemics VI 17A.822 Kühn. For a discussion see Dorandi 2007, 70–81. 19 Cf. von Staden 1998, 73: “Wenn ὑπόμνημα ähnlich wie “memoir” ursprünglich das Verhältnis zwischen Text und Gedächtnis betonte, so gibt es jedenfalls m.W. bei Galen, bei dem das Wort häufiger bezeugt ist als bei allen anderen griechischen Schriftstellern, kaum Hinweise auf ein lebendiges Bewusstsein oder gar eine bewusste Verwendung dieses etymologischen Zusammenhangs. Beide Begriffe, πραγματεία und ὑπόμνημα, bezeichnen eher einen Text, der seinen Gegenstand systematisch wissenschaftlich behandelt, doch kann ein solcher Text im Gewand zahlreicher verschiedener literarischer Formen erscheinen.”

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above. In this paper, I therefore prefer to start, so to speak, from the bottom up by concentrating on one specific text, viz. Galen’s Mixtures. This choice is motivated by the following considerations. First of all, the work presents, on the face of it, a paradigmatic case of what we would call a treatise: it is one of the most rigorous and tightly argued works in the Galenic corpus; it lacks the anecdotes and biographical touches we find in many other Galenic works; and, contrary to some other Galenic writings, it is not addressed to a named individual, nor is there any reference to a particular reason why the work was written (e.g. because someone had asked Galen to write it) or a particular occasion for which the work was produced. Secondly, as we shall see shortly, it is in many respects a very Aristotelian, or maybe one should say Aristotelianizing work, not only in doctrine but also, at least at first sight, in manner of presentation – and this is why I dwelt on Aristotle’s style just a while ago. Furthermore, it is a work that Galen himself regarded as one of his most important and fundamental scientific writings, occupying a central position in his œuvre and underlying, in its doctrine, his physiology, pathology, therapeutics, dietetics and pharmacology; and this sense of the work’s importance was shared by later generations of readers, among whom it was very influential. Finally, for what it is worth, Galen himself refers to the work as a pragmateia on several occasions,20 so it seems we are on relatively safe ground.

Aristotelianism in Mixtures Mixtures (Περὶ κράσεων, in Latin usually referred to as De temperamentis or De complexionibus) is a work in three books. It deals with elementary physiology, with the role of the four qualities hot, cold, dry and wet in the constitution of the bodies of living beings, and especially with the so called ‘mixtures’ or kraseis, the specific combinations of the four qualities in their varying proportions and the way in which these variations constitute the differences in physical make-up between human and animal bodies and between individual human beings. In the text, Galen arrives at this theory through a typically Aristotelian, ‘dialectical’ discussion of the views of other, unnamed thinkers, and with the aid of Aristotelian terminology and examples.21 He begins with a statement of the subject 20 Elements 1.489 Kühn; Mixtures 1.544 Kühn; 1.571 Kühn; Health 6.372 Kühn; Good and Bad Juices 6.800 Kühn; Fulness 7.552 Kühn; Therapeutic Method 10.15 Kühn; 10.531 Kühn; Treatment by Venesection 11.257 Kühn; Simple Medicines 11.379 Kühn; Commentary on Hippocrates’ Nature of Man 15.188 Kühn. 21 E.g. the use of μουσικός in the analysis of coming to be (γένεσις) and alteration (ἀλλοίωσις) in 4,23 (1.515 Kühn), or the use of ἁπλῶς (“simply, without qualification”) as opposed to πρός (“in relation to”) in 20,8–21,9 (1.542 Kühn). All quotations from the Greek text are based on the edition by G. Helmreich (Leipzig 1914) and referred to by page and line number in this edition, followed by the corresponding reference to the volume and page number in the edition by Kühn.

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matter and its relationship to his other work, Elements according to Hippocrates, where certain premises of the present investigation have been established: That the bodies of living beings consist of a mixture of hot, cold, dry and wet and that there is not an equal portion of all these in the mixture was adequately demonstrated by ancient authors, the best of both philosophers and doctors;22 and the appropriate things on these matters have been stated by us, too, in a separate work, in which we made an inquiry into the elements according to Hippocrates. Now, then, I shall do what follows on from that, namely go through in the present work the discovery of all the different varieties of mixture, how many there are, and of what kind, as one distinguishes them by genus and species.23

He adds some preliminary terminological clarifications about the various ways in which the terms ‘hot, cold, dry and wet’, are used, and then he starts his discussion proper with a statement of “the most widespread belief (doxa), among the most distinguished doctors and philosophers”,24 namely that there are four mixtures. This statement is subsequently qualified: some have accepted the existence of two mixtures only, Galen says, but their arguments have been criticized by other thinkers, and in two different ways.25 He rehearses the views of these latter two groups and then concludes this report at the end of ch. 2 by moving on to an analysis of their mistakes: “Such are the positions of the most admired of our predecessors, both doctors and philosophers. It is now time to say what I think to be their omissions…”26 He engages in an imaginary debate between them, in which 22 As Singer notes: “Each of the three books of Mixtures begins with a near-identical syntactic structure: in each case, (1) a sentence beginning with ὅτι μέν summarises a proposition that has already been proved or shown (in the present case, by the ‘ancients’, in the subsequent cases, in the preceding books of this very work); and this status is described by a perfect passive verb (here, ἀποδέδεικται; in book II διείρηται (40,3, 1.572 Kühn); in book III εἴρηται (86,5, 1.646 Kühn); (2) a supplementary proposition that has been shown or stated is then introduced, with the word καί, and this proposition is also expressed by a perfect passive verb (here, εἴρηται; in book II, δέδεικται; in book III, δέδεικται); (3) a sentence with the adversative particle δέ introduces the argument which ‘follows’ (ἐφεξῆς), here and book II (40,11, 1.573 Kühn) or ‘remains’ (λοιπόν, book III, 86,6, 1.646 Kühn), and will be treated in the present book. The formal similarity is interesting both as a feature of Galen’s sequential ordering of his material in intellectual terms, and as a reflex of the rhetorical training and orally-related literary genres that underlie Galen’s work” (Singer & van der Eijk in press). 23 1,1–10 (1.509 Kühn): Ὅτι μὲν ἐκ θερμοῦ καὶ ψυχροῦ καὶ ξηροῦ καὶ ὑγροῦ τὰ τῶν ζῴων σώματα κέκραται καὶ ὡς οὐκ ἴση πάντων ἐστὶν ἐν τῇ κράσει μοῖρα, παλαιοῖς ἀνδράσιν ἱκανῶς ἀποδέδεικται φιλοσόφων τε καὶ ἰατρῶν τοῖς ἀρίστοις· εἴρηται δὲ καὶ πρὸς ἡμῶν ὑπὲρ αὐτῶν τὰ εἰκότα δι' ἑτέρου γράμματος, ἐν ᾧ περὶ τῶν καθ' Ἱπποκράτην στοιχείων ἐσκοπούμεθα. νυνὶ δ', ὅπερ ἐστὶν ἐφεξῆς ἐκείνῳ, ἁπάσας ἐξευρεῖν τῶν κράσεων τὰς διαφοράς, ὁπόσαι τ' εἰσὶ καὶ ὁποῖαι κατ' εἴδη τε καὶ γένη διαιρουμένοις, ἐν τῷδε τῷ γράμματι δίειμι. All English quotations from Mixtures are taken from the translation by P. N. Singer, revised by P. N. Singer & P. J. van der Eijk, to appear in Galen, Works on Human Nature, Cambridge in press. 24 2,5ff. (1.510 Kühn). 25 2,22ff. (1.511 Kühn) and 5,20ff. (1.516 Kühn). 26 7,3–5 (1.518 Kühn): Ἃ μὲν οὖν οἱ χαριέστατοι τῶν πρὸ ἡμῶν ἰατρῶν τε καὶ φιλοσόφων εἰρήκασι, ταῦτ' ἐστίν. ἃ δ’ ἐγὼ παραλιπεῖν αὐτοὺς νομίζω, λέγειν ἤδη καιρός.

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he argues that they have left out an account of the ‘best mixture’, and he addresses his opponents in the second person plural before continuing to describe their errors in the third person: But in that case how is it that you are talking of four rather than of five mixtures, if you are making reference to the best one? There are only two possible explanations: either one of the poor mixtures must have been omitted, or the well-mixed one. In fact I know perfectly well on the basis of their stated opinions that they are omitting the latter.27

The debate remains unresolved and further thinkers enter the stage, this time identified by name: the pupils of Athenaeus of Attalia, followed by Aristotle, Theophrastus and the Stoics.28 Thus the impression is created of a whole host of ‘witnesses’ (martures) gathering against Galen’s own theory. Yet Galen argues that these people are deceiving themselves and that Aristotle is, in fact, on his side.29 A long, again dialectical argument follows, with frequent citations of Hippocrates,30 concluded by a devastating diagnosis of the cause of Galen’s opponents’ errors: It is clear from this what great harm is done to medical treatment by reasoning about nature which fails to hit the truth; and one would be well advised to adopt one of two solutions: either to have no truck with such arguments at all, but rely entirely on experience (peira), or to undergo a preliminary training in the study of logic (logikē theōria). To ignore experience, and to embark upon the study of natural philosophy (theōria phusikē) without a proper previous discipline in the kind of reasoning by which we might discover it, cannot but lead to such fallacies. It then follows that people engage in debate about matters which are evident to the senses as if they themselves did not have use of the senses, and call upon Aristotle, whose teachings they misunderstand, as a witness. For Aristotle knows that the terms hot, cold, dry and wet are used in a multiplicity of senses; yet these people do not understand him as using them in different senses, but always in the same sense. Aristotle himself even explained how ‘to be hot’ does not mean the same thing when it is by virtue of the individual’s own innate hot, or by virtue of that acquired from an external source. Even this, though, they misunderstand. Furthermore Aristotle, and similarly Theophrastus, gave an accurate account of the criteria by reference to which one should establish whether an object is well-mixed or illmixed. But these people do not realize this either; instead, they read some statement in those authors that animals are wet and hot, or that the mixture of children is wet and hot, and without understanding the particular sense in which those terms are used there, transfer the argument idiotically to the seasons, as if it were the same thing – and not, in fact, very different indeed – to say that our own mixture is wet and hot and that the air that surrounds

27 7,24–28 (1.520 Kühn): καὶ πῶς οὐχὶ πέντε λέγετε τὰς πάσας εἶναι κράσεις, ἀλλὰ τέτταρας, εἴπερ τῆς ἀρίστης μέμνησθε; δυοῖν γὰρ θάτερον, ἢ τῶν δυσκράτων ἀνάγκη παραλελεῖφθαι μίαν ἢ τὴν εὔκρατον. ἐγὼ μὲν δὴ σαφῶς οἶδα τὴν εὔκρατον αὐτοὺς παραλιπόντας ἐξ ὧν ἀξιοῦσιν. A slight variation of this pattern is found in 88,20–21 (1.650 Kühn): “So how is it, as some people object (φασίν), that they do not appear hot to the touch? I have no idea (οὐκ οἶδα) why they say this (λέγουσιν).” 28 9,1–26 and 9,27–28 (1.522–523 Kühn). 29 10,1–5 (1.523–524 Kühn). 30 13,26ff. and 15,1ff. (1.530 and 531 Kühn).

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us is wet and hot. For it is not the same thing; nor are the terms wet and hot applied in the same way to the mixture of an animal and to the mixture of the air.31

Galen goes on to point out his opponents’ confusing use of terminology which, again, shows strong similarities with similar conceptual distinctions and clarifications on the different usages of terms such as ‘hot’, ‘cold’, ‘dry’ and ‘wet’ as Aristotle carries these out in the transitions between his critical discussion of other people’s views and the setting out of his own ideas. After this dialectical stage of the inquiry,32 Galen sets out his own theory of nine mixtures, one of which is the perfect, ‘well-tempered’, evenly balanced eukrasia, followed by eight duskrasiai, in which one quality, or a particular combination of qualities, predominates.33 Extending the range of his discussion to include nonhuman animals and even plants, he points out how the variations that may occur here determine the variations in physical constitution between human and animal and plant bodies as well as the variations between individuals (or sub-species) of one and the same kind. He identifies ‘the middle’ (to meson) – again a characteristically Aristotelian concept – between two extreme qualities as the standard and point of reference; and he dwells at considerable length on the ideal physiology of the ‘well-fleshed human being’ (eusarkos anthrōpos), analogous to the artistic representation of the ideal human body as set out by the sculptor Polyclitus in his famous ‘Canon’.34 In book two, Galen proceeds to the methodology of determining the mixture of an individual body or bodily part. He dwells at considerable length on what he calls the gnōrismata, the diagnostic ‘indicators’ on the strength of which one can

31 16,24–17,21 (1.534–536 Kühn): Ὧι καὶ δῆλον, εἰς ὅσον οἱ περὶ φύσεως λογισμοὶ σφαλέντες τῆς ἀληθείας εἰς τὰς ἰάσεις βλάπτουσι καὶ βέλτιόν ἐστι δυοῖν θάτερον, ἢ μηδ' ὅλως ἅπτεσθαι τῶν τοιούτων λόγων, ἀλλ' ἐπιτρέψαι τῇ πείρᾳ τὸ πᾶν, ἢ πρότερον ἐν τῇ λογικῇ θεωρίᾳ γυμνάσασθαι. τὸ δὲ μήτε τῇ πείρᾳ προσέχειν τὸν νοῦν ἐπιχειρεῖν τε θεωρίᾳ φυσικῇ πρὸ τοῦ τὸν λογισμόν, ᾧ μέλλοιμεν εὑρίσκειν αὐτήν, ἀσκῆσαι πρεπόντως εἰς τὰ τοιαῦτ' ἀναγκαῖον ἀπάγειν σοφίσματα, καὶ περί τε τῶν φαινομένων ὡς ἀναισθήτους ἀναγκάζει διαλέγεσθαι μάρτυρά τε καλεῖν Ἀριστοτέλην παρακούοντας ὧν διδάσκει. πολλαχῶς γὰρ ἐκεῖνος οἶδε καὶ τὸ θερμὸν λεγόμενον καὶ τὸ ψυχρὸν καὶ τὸ ξηρὸν καὶ τὸ ὑγρόν· οἱ δ' οὐκ ἀκούουσιν αὐτοῦ πολλαχῶς ἀλλ' ὡσαύτως ἀεί. καὶ μὲν δὴ καὶ ὡς οὐ ταὐτόν ἐστιν ἢ οἰκείῳ τινὶ καὶ συμφύτῳ θερμῷ θερμὸν ὑπάρχειν ἢ ἐπικτήτῳ τε καὶ ἀλλοτρίῳ διῆλθεν Ἀριστοτέλης· οἱ δὲ καὶ τούτου παρακούουσιν. ἔτι δὲ πρὸς τούτοις ὁ μὲν Ἀριστοτέλης, ὡσαύτως δὲ καὶ ὁ Θεόφραστος, εἰς ὅ τι χρὴ βλέποντας ἢ εὔκρατον ἢ δύσκρατον ὑπολαμβάνειν εἶναι τὴν φύσιν, ἀκριβῶς εἰρήκασιν· οἱ δ' οὐδὲ τοῦτο γιγνώσκουσιν, ἀλλ' ὅταν ἀκούσωσί που λεγόντων αὐτῶν ὑγρὸν εἶναι καὶ θερμὸν τὸ ζῷον ἢ τὴν τοῦ παιδὸς κρᾶσιν ὑγρὰν καὶ θερμήν, οὔθ' ὅπως εἴρηται ταῦτα συνιᾶσιν ἐμπλήκτως τε μεταφέρουσι τὸν λόγον ἐπὶ τὰς ὥρας ὥσπερ ταὐτὸν ὂν ἀλλ' οὐ μακρῷ διαφέρον ἢ τὴν οἰκείαν κρᾶσιν ὑγρὰν εἶναι καὶ θερμὴν ἢ τὴν τοῦ περιέχοντος ἡμᾶς ἀέρος. οὔτε γὰρ ταὐτόν ἐστιν οὔθ' ὁμοίως ὑγρὰ καὶ θερμὴ ζῴου κρᾶσις ἀέρος ὑγρᾷ καὶ θερμῇ κράσει λέγεται. 32 17,22 (1.536 Kühn). 33 31,28–32,4 (1.559 Kühn). 34 36,8–37,8 (1.566–567 Kühn).

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determine an individual’s krasis. In a long epistemological, and again partly polemical discussion (directed against various kinds of sceptics), Galen shows that these indicators vary from straightforward empirical observation, especially through the sense of touch, to various modes of theoretical and inferential reasoning. And while throughout the treatise, krasis is used as a physiological term, Galen here ventures also into the psychological domain, where he makes a number of physiognomical observations connecting corporeal characteristics with psychological character traits,35 with the latter providing the clues for inferential reasoning about the internal mixtures. The third and final book of the work is devoted to dietetics and pharmacology: it discusses the elementary mixtures of substances such as foods, drinks and drugs, and thus paves the way for Galen’s theoretical pharmacology as expounded in his monumental work Simple Medicines. Once again, in his distinctions between different modes of presence and activity of the four qualities within organic and anorganic substances, Galen makes frequent use of Aristotelian concepts such as ‘potentiality’ versus ‘actuality’ (dunamei and energeiai) and ‘by itself’ versus ‘incidentally’ (kath’ hauto and kata sumbebēkos). Thus in contents and programme, as well as methodology and terminology, Mixtures has a strong Aristotelian flavour to it. It fits in closely with Aristotle’s doctrine of the four elements and the four elementary qualities as expounded in book II of Parts of Animals, book II of Coming to Be and Passing Away, and the ‘chemical’ book IV of the Meteorologica – all works of which Galen was well aware.36 The elementary physiology that Galen develops in this work is, fundamentally, Aristotelian, and so is the terminology, with repeated usage of distinctions such as dunamis vs. energeia, kath’ hauto vs. kata sumbebēkos and, on one occasion, the typically Aristotelian use of the definite article followed by a noun or adjective in the dative and the infinitive einai.37 Furthermore, its teleological approach to the analysis of bodily features and parts in relation to the purposes they are meant to serve, for instance the example of the human hand in relation to human intelligence (34,24–25; 1.564 Kühn), faithfully reflects Aristotelian doctrine.

35 This connection will be developed further in Galen’s later work That the Faculties of the Soul follow the Mixtures of the Body and has given rise to our psychological use of the term ‘temperament’. There is, again, an Aristotelian heritage here, for the statement that “dispositions” (διάνοιαι) of the soul “follow” (ἕπονται) the states of the body is also found at the beginning of the (Pseudo?-)Aristotelian Physiognomonica. 36 Van der Eijk 2009, 264 (with references to older literature). 37 109,26–27 (1.685 Kühn): τοῦτο γὰρ ἦν αὐτῷ τὸ δυνάμει θερμῷ εἶναι τὸ ταχέως μεταβάλλειν εἰς τὸ ἐνεργείᾳ θερμόν. I have found only two other instances of this usage in Galen: in The Doctrines of Hippocrates and Plato, p. 92,25–26 De Lacy (5.202 Kühn) we find the expression τὸ ὀφθαλμῷ εἶναι in a context in which Galen is critically engaging with Aristotle and asking him questions; and in the Commentary on Hippocrates’ Fractures (18B.548 Kühn) we find καὶ τοῦτ’ ἔστιν αὐτῷ τῷ πυρετῷ εἶναι τὸ θερμασίαν ἔχειν καπνώδη.

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It therefore comes as no surprise that in Mixtures, Aristotle is prominently present as an authority, mentioned at least as often as Hippocrates, and without exception in favourable terms.38 Apart from these two authors, references to other named authors are sparse in Mixtures: there are occasional references to Theophrastus, Plato, Archimedes, Athenaeus of Attalia (the Pneumatist), Eudemus the Peripatetic, Erasistratus and more generally ‘the ancients’ (hoi palaioi),39 but most of the time when referring to other authors, Galen uses anonymous expressions such as ‘some people’, or ‘those who have written about the mixtures’.40 This Aristotelianizing aspect of the work is the more remarkable, for when one studies Galen’s work at large one has to say that, on the whole, Galen’s attitude to Aristotle is not unqualifiedly sympathetic. Indeed, Galen is often openly hostile to Aristotle; and while he is more indebted to Aristotelian philosophy than he would like to admit, one often gets the impression that he tries to play down the significance of Aristotle’s thought for his own work. I have dealt with this attitude of Galen in a different paper, and have suggested various possible reasons for this; they are complicated, but need not concern us here.41 In Mixtures, however, Galen is much more sympathetic to Aristotle and only too ready to admit his fundamental debt to the philosopher. This very positive evaluation of Aristotle in Mixtures becomes even more striking when we compare the work with three other writings of Galen roughly on the same topic, Elements according to Hippocrates, the Commentary on Hippocrates’ On the Nature of Man and Natural Faculties. In these works, too, Aristotle is mentioned in favourable terms, but he is just one among the many ‘ancients’ (palaioi) alongside Hippocrates, Plato, Diocles, Praxagoras and others, who are called upon by Galen as authorities to back up his own position. And in Elements according to Hippocrates, Aristotle is presented as a follower of Hippocrates: he is the natural philosopher (phusikos) providing logical demonstration (apodeixis) of what the physician had already stated correctly before him.42 By contrast, in Mixtures, Aristotle is an authority in his own right.43 Indeed, even in a few cases where Galen 38 Aristotle is mentioned twelve times, though three occurrences are in one and the same context (17,4.10.11, 1.535 Kühn); for examples of the nature of these references see note 46 below. Hippocrates is mentioned twelve times as well, though once in a reference to a Galenic work (1,6, 1.509 Kühn), and twice we find two occurrences in one and the same context: 12,6.12 (1.527 Kühn) and 28,20.22 (1.554 Kühn). 39 See Helmreich 1914, 116 for an index. 40 82,11 (1.640 Kühn). 41 See van der Eijk 2009 and 2010; see also Flemming 2009, 77–78. 42 Jouanna 2003. 43 One might explain the prominent role of Aristotle in Mixtures by arguing that it is a work of ‘natural philosophy’ or ‘natural science’ – or what we would call ‘physiology’ – rather than a medical work. And indeed, Galen positions the text very accurately in relation to the more medical works such as the Therapeutic Method and Simple Medicines. Yet that still does not account for the difference between Mixtures and Elements, Natural Faculties and the Commentary on Hippocrates’ Nature of Man, which are likewise physiological in scope.

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uses the vague expression ‘the ancients’ (hoi palaioi), there is good reason to believe that it is especially, if not exclusively, Aristotle he is thinking of.44 Thus in 72,19 (1.624 Kühn) Galen first refers in general terms to what “the student of nature” (ho phusikos anēr) does, and then a few lines further down mentions Aristotle as the model for this (72,24);45 and a little later, once again lavish praise is given to Aristotle (75,3; 1.628 Kühn).46 Furthermore, in Mixtures Galen presents him on several occasions as trying to preserve sound Aristotelian teaching against the doctrines of other (unnamed) thinkers who have either ignored or misinterpreted the works of the great natural philosopher. The first example occurs early on in the text: Such, then, are the arguments of the followers of Athenaeus. The same belief would appear to be shared by the philosopher Aristotle and, among his followers, by Theophrastus, at least, and also by the Stoics; so that we are embarrassed by the multitude of the witnesses. But I may, perhaps, if required, demonstrate the views of Aristotle regarding hot wet mixture as the argument progresses; for the others appear to me have misunderstood (παρακούειν) his opinion.47

This distinction between what Aristotle really meant and what later interpreters (sometimes within the Peripatetic school) erroneously read into his works is a feature of Galen’s Aristotelianism that occurs also in contexts that are much more

44 Thus in 61,28 (1.607 Kühn), the doctrine of habit as a second nature goes back to Aristotle; and in 51,10–11 (1.589–590 Kühn), a reference is given to “the best sect in philosophy … that posits hot, cold, dry and wet as the principles and elements of things”. 45 “These things have for the most part been discussed well by Aristotle” (περὶ μὲν δὴ τούτων Ἀριστοτέλει καλῶς ἐπὶ πλεῖστον εἴρηται). 46 “This, too, has for the most part been distinguished very well by Aristotle” (Καὶ γὰρ δὴ καὶ τοῦτο κάλλιστα πρὸς Ἀριστοτέλους ἐπὶ πολλῶν διώρισται). Similar praise is found in other passages, such as 46,10 (1.581 Kühn): “Aristotle rightly compares old age to a waning plant” (καὶ καλῶς Ἀριστοτέλης εἰκάζει τὸ γῆρας αὐαινομένῳ φυτῷ); 98,23–24 (1.666 Kühn): “This, along with many other things, has been correctly discussed by Aristotle” (ὀρθῶς οὖν καὶ τοῦτο σὺν πολλοῖς ἄλλοις ὑπ' Ἀριστοτέλους εἴρηται) and 102,15–16 (1.672 Kühn): “The solution to this problem is found when one distinguishes between what is cold by itself and what is cold accidentally, as Aristotle taught” (λύσις δὲ τῆς ἀπορίας, εἰ διορισθείη τὸ καθ' αὑτὸ ψυχρὸν τοῦ κατὰ συμβεβηκός, ὡς Ἀριστοτέλης ἐδίδαξεν). Explicit agreement between Aristotle and Galen is noted in 36,3–6 (1.565–566 Kühn): “That it is proper for the activities of the body to be suited to the character of the soul has been demonstrated both by Aristotle in his Parts of Animals, and it has been demonstrated no less by us too” (καὶ μέν γε καὶ ὡς τὰς τοῦ σώματος ἐνεργείας οἰκείας εἶναι προσήκει τῷ τῆς ψυχῆς ἤθει, δέδεικται μὲν καὶ πρὸς Ἀριστοτέλους ἐν τοῖς περὶ ζῴων μορίων, δέδεικται δὲ καὶ πρὸς ἡμῶν ὑπὲρ αὐτῶν οὐδὲν ἧττον). 47 9,26–10,3 (1.523 Kühn): οἱ μὲν δὴ τῶν ἀμφὶ τὸν Ἀθήναιον λόγοι τοιοίδε. δοκεῖ δέ πως ἡ αὐτὴ δόξα καὶ Ἀριστοτέλους εἶναι τοῦ φιλοσόφου καὶ Θεοφράστου γε μετ' αὐτὸν καὶ τῶν Στωϊκῶν, ὥστε καὶ τῷ πλήθει τῶν μαρτύρων ἡμᾶς δυσωποῦσιν. ἐγὼ δὲ περὶ μὲν Ἀριστοτέλους, ὅπως ἐγίγνωσκεν ὑπὲρ θερμῆς καὶ ὑγρᾶς κράσεως, ἴσως ἄν, εἰ δεηθείην, ἐπὶ προήκοντι τῷ λόγῳ δείξαιμι· δοκοῦσι γάρ μοι παρακούειν αὐτοῦ.

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aggressively polemical, such as the discussion on the male and female contribution to reproduction in Seed, where Galen is strongly opposed to the Aristotelian position as such.48 Yet even within the domain of elementary physiology, where Aristotle is the unassailable authority, Galen presents him as being in need of defence (by Galen) against those who misinterpret his opinions, as we have seen in the passage 16,24–17,21 (1.534–536 Kühn) on the relationship between theory and experience quoted above. There is just one case in Mixtures where Galen expresses a shade of reservation about Aristotle’s position: Both these schools of thought are wrong, for one common reason, namely that they both are so bold as to base an assertion about the whole body on a single part; a second mistake is that they do not regard the power in nature that shapes us as a craftsmanlike power, which shapes the parts in a way which is a consequence of the character traits of the soul. On this point even Aristotle raised a query (ἠπόρησε): whether this power may not derive from some more divine cause, rather than that found in the hot, the cold, the dry and the wet. Those who make a rash assertion on this greatest of issues, attributing the shaping to the physical qualities alone, seem to me to act wrongly. For surely these latter are only the instruments by which it takes place, while the actual shaper is something else. Yet even without engaging in enquiries of this kind, it is still possible, as we have already shown, to find out whether a mixture is wet, dry, cold or hot. Where these individuals go wrong is that they ignore the specific indicators, but move on to broader questions – and ones which have already been the subject of a great deal of enquiry, continuing to baffle the best of philosophers up to the present day.49

Aristotle is said to have wavered between a physical explanation in terms of elementary qualities and a metaphysical explanation in terms of a divine power of force. A similar point was raised, but without mentioning Aristotle, earlier on in the work.50 Galen clearly states that the former type of explanation is wrong and confidently sides with the latter, but he does not pursue the issue here and he does not openly criticize Aristotle for failing to apply his own teleological principles in

48 See van der Eijk 2009, 276–278. 49 79,18–80,6 (1.635–636 K.): ἀμφότεροι δὲ διαμαρτάνουσι τῆς ἀληθείας ἑνὶ μὲν καὶ κοινῷ λόγῳ, διότι περὶ παντὸς τοῦ σώματος ἐξ ἑνὸς ἀποφαίνεσθαι τολμῶσι μορίου· κατὰ δεύτερον δὲ τρόπον, ὅτι τῆς διαπλαστικῆς ἐν τῇ φύσει δυνάμεως οὐ μέμνηνται τεχνικῆς τ' οὔσης καὶ τοῖς τῆς ψυχῆς ἤθεσιν ἀκολούθως διαπλαττούσης τὰ μόρια. περὶ ταύτης γάρ τοι καὶ ὁ Ἀριστοτέλης ἠπόρησε, μή ποτ' ἄρα θειοτέρας τινὸς ἀρχῆς εἴη καὶ οὐ κατὰ τὸ θερμὸν καὶ ψυχρὸν καὶ ξηρὸν καὶ ὑγρόν. οὔκουν ὀρθῶς μοι δοκοῦσι ποιεῖν οἱ προπετῶς οὕτως ὑπὲρ τῶν μεγίστων ἀποφαινόμενοι καὶ ταῖς ποιότησι μόναις ἀναφέροντες τὴν διάπλασιν. εὔλογον γὰρ ὄργανα μὲν εἶναι ταύτας, τὸ διαπλάττον δ' ἕτερον. ἀλλὰ καὶ χωρὶς τῶν τηλικούτων ζητημάτων ἐνὸν ἐξευρίσκειν, ὡς ἔμπροσθεν ἐδείξαμεν, ὑγρὰν καὶ ξηρὰν καὶ ψυχρὰν καὶ θερμὴν κρᾶσιν ἁμαρτάνουσιν οἱ τῶν οἰκείων μὲν ἀμελοῦντες γνωρισμάτων, ἐπὶ δὲ τὰ πόρρω τε καὶ ζητήσεως ἱκανῆς τετυχηκότα καὶ μέχρι τοῦ δεῦρο καὶ παρ' αὐτοῖς τοῖς ἀρίστοις φιλοσόφοις ἀπορούμενα μεταβαίνοντες. 50 34,6–7 (1.562 Kühn); 36,16–17 (1.566 Kühn).

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the way in which Galen does so, for example, in his main work on teleology, The Usefulness of the Parts.51

The presence of the author and the audience in the text Let us now turn to a more formal feature of the work, i.e. the question of audienceorientedness and the presence of the author in the text. As already mentioned, Mixtures is not addressed to a particular named individual or well-specified audience,52 nor is there any reference to a particular reason why the work was written or an occasion for which the work was produced. And although, as we have seen, there are several references to rival thinkers, they are hardly ever identified,53 so the details of the ‘discourse community’ or ‘setting’ that Galen creates remain vague. This fits in well with the features of the treatise as we sketched these above, and with the general Aristotelian style of reasoning. In the opening statement of Mixtures quoted above (p. 151), Galen uses the first person plural (ἡμῶν) in order to involve his audience or his students into a joint intellectual exercise or systematic discussion or examination. This ‘inclusive’ use of the first person plural (‘we researchers’, ‘we observers’, ‘we humans’),54 or in cross-references, announcements and statements of intent (‘as we have seen above’, ‘as we will see later’, ‘let us now turn to the next topic’),55 is a standard

51 Van der Eijk 2009, 274–276. 52 The only explicit indication of the kind of audience for whom the work is intended, and for its place in Galen’s ‘curriculum’, occurs towards the end of book II, discussed below on p. 106. 53 We find one reference to “the followers of Athenaeus of Attalia” (9,1.16, 1.522–523 Kühn) and one to “the followers of Erasistratus” (57,11, 1.599 Kühn), but other holders of rival views are referred to by expressions such as οἱ μέν…, οἱ δέ, τινές, ἔνιοι. 54 E.g. 88,15–16 (1.650 Kühn): “for those drugs which are readily ignited by contact with fire evidently also heat us” (ὅσα πυρὸς ἁπτόμενα φάρμακα ῥᾳδίως ἐκπυροῦται, ταῦτα καὶ ἡμᾶς θερμαίνοντα); 103,6–14 (1.674 Kühn): “It is hardly remarkable, then, that opium, a drug so opposed to our nature (ἡμῶν), is very swiftly cooled, even when drunk hot, and that the body is simultaneously cooled with it. It cannot retain its acquired heat because it is cold in its original nature; but since its substance is not altered by us (ἡμῶν) but rather itself alters and transforms us (ἡμᾶς), it does not become in any way heated by us (ἡμῶν), but itself affects us according to its own nature. But being naturally cold, it then cools us (ἡμᾶς)”. For distinctions of various usages of first person singular and plural in ancient technical literature see von Staden 1994 and Hine 2009. 55 Cross references in Mixtures are found both in the first person singular and plural active and in passive constructions, either with indication of the agent (e.g. 63,3, 1.609 Kühn: ἐπιδέδεικται γὰρ ἡμῖν; 64,7, 1.610 Kühn: ταῦτ’ εἴρηταί μοι) or without (e.g. 75,22, 1.629 Kühn: ὡς εἴρηται καὶ πρόσθεν), and both in past, present, perfect and future tenses, e.g. 100,2 (1.668 Kühn): “as we discussed (ἐλέγομεν) in the above”; 69,19 (1.619 Kühn): “as is shown (δείκνυται) in The Usefulness of the Parts”; 99,8–9 (1.667 Kühn): “as will be discussed in Drugs” (ὡς ἐν τοῖς περὶ φαρμάκων εἰρήσεται);

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feature in Greek (and Latin) treatises, and it is found in Aristotle as well. Yet, interestingly, and less characteristically Aristotelian, it is combined here with a usage of the first person singular (δίειμι), thus differentiating between the collective intellectual enterprise in which Galen involves his audience and his own individuality as the lead-investigator: Now, then, I shall do what follows on from that, namely go through in the present work the discovery of all the different varieties of mixture, how many there are, and of what kind, as one distinguishes them by genus and species.56

Such usage of the first person singular to refer to Galen’s own role as the author and stage-manager of the text is also found elsewhere in Mixtures, e.g. in 17,22–23 (1.536 Kühn)57 and in 84,18 (1.643 Kühn, quoted on p. 167 below).58 The first person singular is further used in Mixtures in argumentative contexts, where Galen distinguishes his own views from those of rival thinkers: In fact I know perfectly well on the basis of their stated opinions that they are omitting the well-balanced mixture.59 I, however, so far from asserting that spring is hot and wet, or indeed from agreeing that anything which is well-mixed is hot and wet, assert on the contrary…60

90,29–91,1 (1.654 Kühn): “the demonstration of which we will state in Natural Faculties” (οὗ τὴν μὲν ἀπόδειξιν ἐν τοῖς Περὶ φυσικῶν δυνάμεων ἐροῦμεν). 56 1,7–10 (1.509 Kühn): νυνὶ δ', ὅπερ ἐστὶν ἐφεξῆς ἐκείνῳ, ἁπάσας ἐξευρεῖν τῶν κράσεων τὰς διαφοράς, ὁπόσαι τ' εἰσὶ καὶ ὁποῖαι κατ' εἴδη τε καὶ γένη διαιρουμένοις, ἐν τῷδε τῷ γράμματι δίειμι. 57 Τί δὴ τὸ τούτων ἁπάντων αἴτιον, ἤδη διηγήσομαι καὶ δείξω σαφῶς τοῖς προσέχειν τὸν νοῦν βουλομένοις. 58 See also 10,4–7 (1.524 Kühn): “For the moment, I shall first attempt to indicate to the proponents of these arguments the precise way in which they are engaged in fallacious reasoning, and after that proceed to give a demonstration of the whole argument, drawing it together in a single summary” (Τὸ δέ γε νῦν ἔχον πειράσομαι πρῶτον ἐνδείξασθαι τοῖς λέγουσι ταῦτα, πῇ ποτε σοφίζονται σφᾶς αὐτούς, εἶτ' ἐφεξῆς ἀποδεῖξαι τὸν ἅπαντα λόγον εἰς ἓν ἀθροίσας κεφάλαιον); 17,22–25 (1.536 Kühn): “I shall now explain the reason for all these errors; and I shall show quite clearly – to anyone who is prepared to pay attention – that small mistakes at the stage of initial instruction in logical science are responsible for very great errors” (Τί δὴ τὸ τούτων ἁπάντων αἴτιον, ἤδη διηγήσομαι καὶ δείξω σαφῶς τοῖς προσέχειν τὸν νοῦν βουλομένοις, ὡς μικρὰ πταίσματα τῶν ἐν ἀρχῇ τῆς λογικῆς θεωρίας διδασκομένων αἴτια μεγίστων ἁμαρτημάτων γίγνεται); 114,27–29 (1.692 Kühn): “Now, however, with a reminder of what I said previously, I shall attempt to put the fitting conclusion to the present argument.” (Νυνὶ δὲ πάλιν ἀναμνήσας ὧν ἤδη καὶ πρόσθεν εἶπον ἐπιθεῖναι πειράσομαι τῷ παρόντι λόγῳ τὴν προσήκουσαν τελευτήν); Other instances are in 37,25 (1.568 Kühn) and 39,10 (1.571 Kühn). On Galen’s use of the first person singular see Nutton 2009; for a more general study differentiating various usages of the first person see Hine 2009; for a case study of Celsus see von Staden 1994. On the Hippocratic background see Roselli 2006. 59 7,27–28 (1.520 Kühn): ἐγὼ μὲν δὴ σαφῶς οἶδα τὴν εὔκρατον αὐτοὺς παραλιπόντας ἐξ ὧν ἀξιοῦσιν. 60 13,20–22 (1.529 Kühn): ἐγὼ δὲ τοσοῦτον ἀποδέω ἢ θερμὸν καὶ ὑγρὸν ἀποφαίνειν τὸ ἔαρ, ἢ ὅ τί περ ἂν εὔκρατον ᾖ, θερμὸν καὶ ὑγρὸν εἶναι συγχωρεῖν, ὥστε πᾶν τοὐναντίον ἀποφαίνομαι.

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Yet the first person plural, too, is used for this purpose: “We thus assert the complete opposite of the view of those who assume spring to be wet and hot.”61 As we have seen (p. 152), these opponents are sometimes addressed in the second person plural. Alternatively, Galens also challenges them by using the third person imperative: “If they have a conception or recognition of hot and cold from some other source, let them tell us what it is”.62 Usually, however, Galen refers to them in the third person indicative, as in 82,11–12 (1.640 Kühn), where he speaks of “those who have written works (hupomnēmata) about mixtures”. The first person singular is further used by Galen to refer to his own insights, experience and observations, sometimes made in the past: I have observed many naturally thin people become thickened, and naturally thick people thinned…63 I have known cases of very phlegmatic individuals in whom a great quantity of yellow bile gathered in the stomach…64 After consideration on very many occasions of children, a large number of young men and youths – and of the same child both as infant and when grown to youth – I have not found any difference in heat between childhood and the prime of life…65

Yet most remarkable – and this is strikingly different from Aristotle’s practice (and from that of most Hippocratic writers) – is the frequency with which Galen uses the second person singular to address someone in his audience by means of the personal pronoun su, or soi, and by means of second person singular verbs and imperatives: In such an investigation it will be apparent to you that spring is in an exactly middle position with respect to each of the extremes.66

61 16,4–5 (1.533 Kühn): Ὥστε πᾶν τοὐναντίον ἡμεῖς ἀποφαινόμεθα τοῖς ὑγρὸν καὶ θερμὸν ὑπολαμβάνουσιν εἶναι τὸ ἔαρ. Cf. 31,3–5 (1.557 Kühn): “Here again we will state that if it is not necessary that a dry mixture automatically be hot, too…” (πάλιν γὰρ κἀνταῦθα φήσομεν, ὡς, εἴπερ οὐκ ἔστιν ἀναγκαῖον, εἴ τίς ἐστι ξηρὰ κρᾶσις, εὐθὺς ταύτην εἶναι καὶ θερμήν). 62 50,17–19 (1.588 Kühn): εἰ δ' ἄλλοθέν ποθεν ἔχουσιν ἔννοιάν τε καὶ διάγνωσιν θερμοῦ καὶ ψυχροῦ, λεγέτωσαν ἡμῖν. 63 60,12–13 (1.604 Kühn): πολλοὺς γὰρ καὶ τῶν φύσει λεπτῶν ἐθεασάμην παχυνθέντας καὶ τῶν παχέων λεπτυνθέντας. 64 76,11–13 (1.630 Kühn): οἶδα γὰρ ἐγώ τισιν ἱκανῶς φλεγματώδεσιν ἀνθρώποις ἀθροιζομένην ἐν τῇ γαστρὶ χολὴν παμπόλλην ξανθήν. 65 55,26–29 (1.597 Kühn): Οὕτως οὖν ἔμοιγε μυριάκις ἐπισκεψαμένῳ καὶ παῖδας καὶ νεανίσκους πολλοὺς καὶ μειράκια καὶ τὸν αὐτὸν παῖδα καὶ βρέφος καὶ μειράκιον γενόμενον, οὐδὲν μᾶλλον ἐφάνη θερμότερος οὔτε παιδὸς ἀκμάζων οὔτ' ἀκμάζοντος παῖς. 66 11,24–12,1 (1.526 Kühn): καὶ δὴ καὶ σκοπουμένῳ σοι κατὰ τάδε φανεῖται τὸ ἔαρ ἀκριβῶς μέσον ἁπασῶν τῶν ὑπερβολῶν.

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You will understand this from the quotation itself, if I transcribe it for you in its entirety.67 Throughout all of them I would ask you to pay very careful attention, and to consider…68

In cases like these, the impression is given of a teacher addressing and communicating with a student inviting him to think along with, or respond to what he has heard or to verify for himself what has been presented.69 The following passages, where the student is invited or instructed to persuade himself of what has been said by means of verbs of saying and understanding (“you will see”, “you will say”), give an impression of the density of such addresses: If, then, I were to ask you which is hotter, the well-mixed water or the well-mixed air, you would not be able to say either. Since both are equally pleasant and well-proportioned for the body, it makes no sense, I am convinced, to describe one as hotter and the other as colder. If, indeed, you consider the extreme cases, where the water in the receptacle reaches boilingpoint, and where the air is completely scorched, then it is obvious that you will be equally burnt by both. And, similarly, if you consider the cases where the water is so cold as to be nearly frozen, and where the air is completely cooled, as in the case of a snowstorm, then it is clear, here too, that in both these cases you will be cooled and will freeze to the same extent. You will thus understand that the extremes of heat and cold come about in exactly the same way in air as they do in water, and the midpoint between these two extremes, too, comes about in the same way in both. The spaces between all these extremes and the midpoint, therefore, will also involve the same distances, the same degrees of difference, in both water and air: you will say that the degree to which it may be hotter than the midpoint may be the same in both cases. So you will say also that water may be colder to the same degree as air, in spite of the fact that the specific nature of the tactile sensation is not the same in each case.70 And – as was demonstrated in the course of the previous argument – here too you may, if you wish, compare the spring, which is the most well-mixed of the seasons, with the nature of

67 14,10–12 (1.530 Kühn): εἴσῃ δ' ἐξ αὐτῆς τῆς ῥήσεως, εἰ πᾶσαν αὐτήν σοι παραγράψαιμι, τόνδε τὸν τρόπον ἔχουσαν. 68 14,24–25 (1.531 Kühn): ἐν ἅπασι δ' αὐτοῖς προσέχειν σε τὸν νοῦν ἀκριβῶς ἀξιῶ καὶ σκοπεῖσθαι. 69 Cf. Hine 2009, 23: “The reader is addressed qua learner of a skill or technique”. 70 54,17–55,10 (1.595 Kühn): εἰ τοίνυν ἐροίμηνσε, πότερόν ἐστι θερμότερον, ἆρά γε τὸ ὕδωρ τὸ εὔκρατον ἢ ὁ ἀὴρ ὁ εὔκρατος, οὐκ ἂν ἔχοις εἰπεῖν οὐδέτερον. ἀμφοῖν γὰρ ὄντων ὁμοίως ἡδέων τε καὶ συμμέτρων τῷ σώματι τὸ μὲν θερμότερον εἶναι λέγειν αὐτῶν, τὸ δὲ ψυχρότερον οὐδένα νοῦν ἔχειν ἡγοῦμαι. καὶ μὴν εἰ νοήσαις τὸ τῆς δεξαμενῆς ὕδωρ εἰς ἄκρον θερμότητος ἀφικνούμενον, ὡς ζεῖν, ἢ τὸν ἀέρα τελέως ἐκφλογούμενον, ὅτι πρὸς ἀμφοῖν ὡσαύτως καυθήσῃ, πρόδηλον. εἰ δὲ δὴ καὶ νοήσαις αὖθις ἢ τὸ ὕδωρ οὕτω ψυχρόν, ὡς ἐγγὺς ἤδη πήξεως ἥκειν, ἢ τὸν ἀέρα τελέως ἐψυγμένον, ὡς ἐν τοῖς νιφετοῖς γίγνεται, δῆλον, ὡς καὶ πρὸς τούτων ἑκατέρων ὁμοίως ψυχθήσῃ τε καὶ ῥιγώσεις. οὐκοῦν καὶ θερμότητα καὶ ψῦξιν ἄκραν ὡσαύτως μὲν ἀέρι νοήσεις ἐγγιγνομένην, ὡς δ' αὔτως ὕδατι, καὶ τῶν ἄκρων ἑκατέρων τὸ μέσον ὁμοίως ἀμφοῖν ἐγγιγνόμενον. ὥστε καὶ τὸ μεταξὺ πάντων τῶν ἄκρων τε καὶ τοῦ μέσου κατά τε τὸ ὕδωρ καὶ τὸν ἀέρα τὰς αὐτὰς ὑπεροχάς τε καὶ διαστάσεις ἕξει, καὶ τοσούτῳ ποτὲ φήσεις εἶναι τοῦ μετρίου θερμότερον θάτερον, ὅσῳ θάτερον. οὕτω δὲ καὶ ψυχρότερον τοῦ μετρίου τοσούτῳ φήσεις εἶναί ποτε τὸ ὕδωρ, ὅσῳ καὶ τὸν ἀέρα, καίτοι τό γε τῆς προσβολῆς ἴδιον οὐ ταὐτὸν ἑκατέροις ἦν.

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well-mixed skin, the comparison being particularly apt when taking the middle of the spring. For it is at this time that the earth, too, is at a midpoint between moisture and dryness. In that part of spring which borders on summer, the earth is already drier; and even more so at the beginning of summer itself. What I mean by hot and dry in the context of skin, you may gather from the condition of earth which arises at the end of spring or beginning of summer.71

Sometimes, more active participation is encouraged, and the student is invited to perform some kind of experiment: If, then, you take skin as the yardstick and, as it were, standard against which to examine all other parts of the animal, and compare these with it, you will find the eight different types of imbalance within those parts. I will in fact discuss all of them for you individually.72 If, furthermore, you put dry earth, ash, or some other such thing which is completely driedout, in water, using equal quantities of each, you will produce a body which is in the middle with regard to the opposition of dry and wet.73 Some people, certainly, are both thin and thin-veined; but if you cut any one of those veins there emerges fat, which has clearly grown underneath the skin in the membrane within.74 There is therefore nothing surprising in the fact that drugs, too, need first to be broken into small, fine parts, and secondly to be in contact with our bodies for at least a very small amount of time, in order to become hot. But you – if you expect them to appear hot already without having first broken them down or heated them – seem to me to have forgotten the sense of the term ‘hot in power’, you are applying a test to them relevant only to the ‘hot in activity.75 If you were to apply any of these drugs, having first made it extremely fine, to a body which has been cooled down, it is not heated at all; and for this reason we generally massage the

71 65,19–29 (1.613 Kühn): καί σοι πάρεστιν, εἰ βούλει, καὶ νῦν, ὥσπερ που κἀν τῷ πρὸ τούτου λόγῳ δέδεικται, τὸ μὲν ἔαρ, ὅτι τῶν ὡρῶν εὐκρατότατόν ἐστιν, εἰκάζειν εὐκράτου δέρματος φύσει καὶ μάλιστά γε τὰ μέσα τῆς ὥρας τῆσδε. τηνικαῦτα γὰρ οὖν καὶ ἡ γῆ μέση πως ὑγρότητός τε καὶ ξηρότητός ἐστιν. ὅσα δὲ τῷ θέρει συνάπτει τῆς ἠρινῆς ὥρας, ταῦτ' ἤδη ξηροτέραν ἔχει τοῦ συμμέτρου τὴν γῆν, ἔτι δὲ μᾶλλον ἀρχομένου θέρους. Ὃ τοίνυν λέγω δέρμα θερμὸν καὶ ξηρόν, εἰκάζοις ἂν μάλιστα τῇ τῆς γῆς διαθέσει τῇ γιγνομένῃ τελευτῶντος ἦρος ἢ ἀρχομένου θέρους. 72 37,21–25 (1.568 Kühn): εἰ δὴ τοῦτο κανόνα τε καὶ οἷον κριτήριον ἁπάντων τῶν τοῦ ζῴου μορίων προστησάμενος ἐξετάζοις τε καὶ παραβάλλοις αὐτῷ τἆλλα, τὰς ὀκτὼ διαφορὰς εὑρήσεις τῶν δυσκρασιῶν ἐν αὐτοῖς. Καὶ δὴ καὶ κατὰ μέρος δίειμί σοι περὶ πάντων ἐφεξῆς. 73 33,13–16 (1.561 Kühn): καὶ μὲν δὴ καὶ ξηρὰν γῆν ἢ τέφραν ἤ τι τοιοῦτον ἕτερον ἀκριβῶς αὐχμηρὸν ἀναδεύσας ὕδατι κατὰ τὸν ὄγκον ἴσῳ τὸ μέσον ἐργάσῃ σῶμα τῆς κατὰ τὸ ξηρόν τε καὶ ὑγρὸν ἀντιθέσεως. 74 62,6–8 (1.607 Kühn): εἰσὶ δή τινες ἰσχνοί θ' ἅμα καὶ φλέβας ἔχοντες μικράς, ἀλλ' εἰ τέμοις ἐξ αὐτῶν ἡντινοῦν, προπίπτει πιμελή, δῆλον ὡς ὑποπεφυκυῖα τῷ δέρματι κατὰ τὸν ἔνδον ὑμένα. 75 89,15–21 (1.651–652 Kühn): Οὐδὲν οὖν θαυμαστόν, εἰ καὶ τὰ φάρμακα πρῶτον μὲν εἰς λεπτὰ καὶ σμικρὰ καταθραυσθῆναι δεῖται, δεύτερον δὲ χρόνῳ τινὶ κἂν ἐλαχίστῳ τοῖς σώμασιν ἡμῶν ὁμιλῆσαι πρὸς τὸ γενέσθαι θερμά. σὺ δ', εἰ μήτε καταθραύσας αὐτὰ μήτε θερμήνας πρότερον ἀξιοῖς ἤδη φαίνεσθαι θερμά, τί ποτε σημαίνει τὸ δυνάμει θερμόν, ἐπιλελῆσθαί μοι δοκεῖς· ὡς ἐνεργείᾳ γοῦν θερμὰ βασανίζεις αὐτά.

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cooled parts with such drugs, raising heat in the process of the massage, and simultaneously also making spare what has until then been made dense by cooling, in order that the drug may sink in and, making contact with the animal’s innate hot, be changed and heated. For even if some very small part of it acquires heat in activity, it thus transmits this to the whole by virtue of its continuity – just as if you were to set the end of pine-torch alight from a tiny spark; there too the fire proceeds to take hold of the whole torch, and has no further need of the spark.76

Galen sometimes also addresses his audience by means of a second person singular imperative: What happens then is that such a substance is struck, and pushed outwards, by another similar substance from within, and this latter by another, and so on; and you must thus conceive of a large number of sooty vaporizations wedged up against each other, which over a period of time become intermingled and conjoined, forming a single body.77 Now, I want you to conceive these bodies as the elements of all things.78

In the following example, the impression is conveyed of Galen the schoolmaster addressing his student both in the second person singular indicative and in the imperative in order to warn him that he will ignore Galen’s advice at his own peril:

76 90,3–13 (1.652–653 Kühn): εἰ δὲ κατεψυγμένῳ σώματι περιπάττοις ὁτιοῦν αὐτῶν ἀκριβῶς λεπτὸν ἐργασάμενος, οὐδ' ὅλως θερμαίνεται καὶ διὰ τοῦτο τρίβομεν ἐπὶ πλεῖστον τὰ κατεψυγμένα μόρια τοῖς τοιούτοις φαρμάκοις, ἅμα μὲν ἀνάπτοντες τῇ τρίψει θερμασίαν, ἅμα δ' ἀραιὸν ἐργαζόμενοι τὸ τέως ὑπὸ τῆς ψύξεως πεπυκνωμένον, ἵν' εἴσω τε δύῃ τὸ φάρμακον ὁμιλοῦν τε τῷ συμφύτῳ τοῦ ζῴου θερμῷ μεταβάλληταί τε καὶ θερμαίνηται. καὶ γὰρ εἰ μόριον αὐτοῦ τι σμικρότατον ἐνεργείᾳ κτήσαιτο τὴν θερ-μασίαν, εἰς ἅπαν οὕτω διαδίδωσι κατὰ τὸ συνεχές, ὡς εἰ καὶ τῆς δᾳδὸς ἅψαις τὸ ἄκρον ἀπὸ σμικροῦ σπινθῆρος. For further examples see 107,18–19 (1.681 Kühn): “If, on the other hand, you were to compare it with a harder sort of iron, then, conversely, you will find that it is acted upon more than it acts.” (ἀλλ' εἰ σκληρότατον αὐτῷ παραβάλλοις σίδηρον, ἔμπαλίν σοι φανεῖται πάσχειν μᾶλλον ἢ δρᾶν.); 111,5–7 (1.686–687 Kühn): “And when you examine the power (of drugs), they should be administered, not to bodies in all conditions, but as far as possible to those in the simplest, most extreme conditions” (προσφερέσθω δὲ μὴ πάσῃ διαθέσει σώματος, ὅταν ἐξετάζῃς αὐτοῦ τὴν δύναμιν, ἀλλ' ἁπλουστάταις ὡς ἔνι μάλιστα καὶ ἄκραις); 41,17–19 (1.574 Kühn): “Moreover, if you were to examine them by reference to all that exists, they still do not cease to be dry and cold, even in that context.” (καὶ μὲν δὴ κἂν εἰ πρὸς τὴν ὅλην οὐσίαν ἀποβλέπων ἐξετάζοις, οὐδ' οὕτως ἐκπέπτωκε τοῦ ξηρά τ' εἶναι καὶ ψυχρά); 113,27–114,2 (1.691 Kühn): “For if you make this kind of conjecture the beginning of your enquiry, you can discover more quickly the proper power of each.” (εἰ γὰρ ἀπὸ τοῦ τοιούτου στοχασμοῦ τὴν ἀρχὴν τῆς ἐξετάσεως αὐτῶν ποιοῖο, θᾶττον ἂν ἐξευρίσκοις τὴν οἰκείαν ἑκάστου δύναμιν.); 44,11.12 (1.579 Kühn); 55,2.6.8 (1.596 Kühn); 58,11.16.17 (1.601 Kühn); 87,10.21 (1.648 Kühn). 77 66,27–67,5 (1.615 Kühn): ταύτην οὖν ἑτέρα τοιαύτη πάλιν ἐκ τοῦ βάθους ἀναφερομένη πλήττει τε καὶ ὠθεῖ πρόσω καὶ ταύτην αὖθις ἑτέρα κἀκείνην ἄλλη καὶ πολλὰς αἰθαλώδεις οὕτω μοι νόει σφηνουμένας ἐπ' ἀλλήλαις ἀναθυμιάσεις ἐν τῷ χρόνῳ περιπλέκεσθαί τε καὶ συνάπτεσθαι καί τι ποιεῖν ἓν σῶμα τοιοῦτον. 78 29,8–9 (1.555 Kühn): ταυτὶ μὲν οὖν μοι νόει τὰ τῶν γιγνομένων τε καὶ φθειρομένων ἁπάντων στοιχεῖα.

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If, on the other hand, you wish to compare many children with many people in their prime, then compare thin examples of both, or well-fleshed, or fat; and, similarly, make sure that they have the same colour, and all other characteristics, as far as is possible. In seeking to discover the difference due to different ages you will conduct your investigation more reliably on the basis, in brief, of natures which are as similar to each other as possible.79 (…) So too in the case where you make the comparison with one and the same child, obviously you must take care that all external conditions are precisely the same, in order to avoid the false attribution of some difference in heating and cooling arising from some of these to the change in age. You may perhaps think that the examination that I am recommending is a long one; but at least it is truthful, above all things, taken as it is from the very essence of the subject under enquiry, as discussed in my work on Logical demonstration. Now, you may rather choose the short version – and not care whether it is false. Know, however, that the path on which you intend to walk is not only false, but is a long one, too. You will not find the object under enquiry within three or four years, but will preserve your ignorance throughout your whole life (…) Let us then use sense perceptions to judge which body is hot and which cold – in activity, at least, and no longer just in capacity – putting aside all other indicators, to begin with at least. And indeed, I leave you to judge on the basis of your trials, but shall myself relate my own judgement.80

Thus the impression is conveyed of a speaker or teacher addressing an individual listener or reader or student. This need not be one specific individual, it can just be a generalized ‘you’ referring to members of the audience to whom Galen is speaking. This is in itself not so remarkable in a lively text, and it may well be a matter of variation only – for we find these expressions alongside third person singular or first person plural verbs,81 or impersonal instructions with modal verbs 79 Cf. the final words of Corp. Hipp., Aer. 24.9 (250,9–10 Jouanna, 2.92 Littré): “On the basis of these things you can infer and understand the others, and you will not go wrong” (ἀπὸ δὲ τούτων τεκμαιρόμενος τὰ λοιπὰ ἐνθυμεῖσθαι, καὶ οὐχ ἁμαρτήσῃ.) 80 52,12–53,18 (1.591–593 Kühn): εἰ δὲ καὶ πλείω παιδία πολλοῖς ἀκμάζουσιν ἐθέλοις παραβάλλειν, ἰσχνὰ μὲν ἰσχνοῖς, εὔσαρκα δ' εὐσάρκοις καὶ παχέα παχέσι παράβαλλε· οὕτω δὲ καὶ χρόας ὡσαύτως ἔχοντα καὶ τῶν ἄλλων ἁπάντων ὡς οἷόν τε. τὴν γὰρ ἐν ταῖς ἡλικίαις διαφορὰν ἐξευρεῖν ζητῶν ἐπὶ τῶν ὁμοίων ὡς ἔνι μάλιστα φύσεων ἀσφαλέστερον ἂν ἐπισκέπτοιο. … οὕτω δὲ δηλονότι καὶ αὐτὸν τὸν ἕνα παῖδα παραβάλλων ἑαυτῷ τὰς ἔξωθεν ἁπάσας αὐτοῦ περιστάσεις ἀκριβῶς ὁμοίας φυλάξεις, ἵνα μὴ τὸ διά τινα τούτων ἐν θάλψει τε καὶ ψύξει διάφορον εἰς τὴν τῆς ἡλικίας ἀναφέρηται μεταβολήν. μακρὰν ἴσως σοι δόξω λέγειν τὴν ἐξέτασιν ἀλλ' ἀληθῆ γε παντὸς μᾶλλον ἐξ αὐτῆς τε τοῦ ζητουμένου τῆς οὐσίας λαμβανομένην, ὡς ἐν τοῖς ὑπὲρ ἀποδείξεως ἐλέγετο. σὺ δ' ἴσως αἱρήσῃ τὴν ἐπίτομον οὐδὲν φροντίζων, εἰ ψευδὴς εἴη. ἴσθι τοίνυν οὐ μόνον ψευδῆ βαδίσων ἀλλὰ καὶ μακράν. οὐ γὰρ ἔτεσι τρισὶν ἢ τέτταρσιν ἐξευρήσεις τὸ ζητούμενον, ἀλλ' ἐν παντὶ τῷ βίῳ φυλάξεις τὴν ἄγνοιαν. … Κρίνωμεν οὖν αἰσθήσει τὸ θερμὸν καὶ ψυχρὸν σῶμα τό γε κατ' ἐνέργειαν ἤδη τοιοῦτον καὶ μηκέτι δυνάμει, παρέντες τήν γε πρώτην τὰ ἄλλα σύμπαντα γνωρίσματα. καὶ δὴ σὲ μὲν ὡς [εὖ] κρινοῦντα πρὸς τὴν πεῖραν ἀπολύω, τὴν δ' ἐμὴν αὐτὸς κρίσιν ἑρμηνεύσω. 81 E.g. in 87,17–29 (1.648–649 Kühn): “In all these cases, then, the word “capacity” (δύναμις) is used (λέγεται) in a more or less improper way. But the first usage represents the most proper sense of something’s being such-and-such in capacity (δυνάμει); next after that is that based on proper or specific materials, as if you were to say (λέγοις) that a vaporization is a smoky flame in capacity, or that breath is air in capacity (δυνάμει). The term “in capacity” is also sometimes used (λέγεται) in contradistinction to “incidental” (κατὰ συμβεβηκός): one might for instance say (τις φαίη) that a cold bath heated the body of a well-fleshed youth incidentally, rather than by virtue of the body’s

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like χρὴ or δεῖ, “one must”, “one should”.82 We are clearly led to think of a classroom situation, where the teacher addresses his students, in particular the chemistry lecture room where the teacher is guiding the student in performing a chemical experiment, as the examples from 37,23–25 (1.568 Kühn) and 107,18 (1.681 Kühn) cited above aptly illustrate. And as a real schoolmaster, Galen frequently says that one should “pay close attention” now – an expression he uses both in combination with an addressed ‘you’83 and in impersonal constructions.84 As said, this is quite different from Aristotle, who rarely uses the second person singular (and mostly only in examples) and who addresses his audience in the second person plural only once (in a famous passage in Sophistical Refutations).85 What is further striking apart from the high frequency of these second person addresses is that Galen on several occasions refers to the readers of the text (hoi anagignōskontes) in the third person plural: Even here, though, one must first make a distinction regarding the terms which are necessarily going to occur in the following discussion, and a simplification of a matter which has by

own capacity. The terms hot, cold, dry and wet in capacity, then, will be used (λεχθήσεται) in all these senses. And it will appropriately be asked (ζητηθήσεται), why on earth do we apply (λέγομεν) the term “hot” to castor, spurge, pellitory, soap-wort, nitrum or copper ore, or the term “cold” to lettuce, hemlock, mandragora, salamander or poppy?”; cf. also 32,8–10 (1.559 Kühn): “If someone wishes (εἰ τις βούλεται) to recognize mixtures, he should begin his training (ἄρχεσθαι τούτῳ προσήκει) with those natures which are well-mixed and middle within each genus. By comparing the others with these, he will easily find out (ἐξευρήσει) the predominant or deficient in each case”; 34,3–4 (1.562 Kühn): “If, however, a body which partakes equally of wet and dry is also at a midpoint between heat and cooling, such a body will not appear either hard or soft to the touch (ἁπτομένῳ)”. On similar variations in Latin texts, esp. Celsus, cf. Hine 2009, 25: “one is also aware of the long stretches of instructions expressed in gerundive constructions … and other impersonal forms.” 82 E.g. 99,13–16 (1.667 Kühn): “The point to which one must pay particular attention with all drugs which are described as hot or cold in power is whether they belong by nature to those able to nourish…” (μάλιστ' οὖν χρὴ προσέχειν τὸν νοῦν ἐν ἅπασι τοῖς δυνάμει θερμοῖς ἢ ψυχροῖς εἶναι λεγομένοις, εἴτε τῆς φύσεώς ἐστι τῶν τρέφειν δυναμένων); 75,12–13 (1.629 Kühn): “He who intends to recognize mixtures properly must make these distinctions properly” (ἅπαντ' οὖν ταῦτα διορίζεσθαι χρὴ τὸν μέλλοντα καλῶς διαγνώσεσθαι κρᾶσιν); 77,13 (1.632 Kühn): “How should one distinguish these cases?” (πῶς οὖν χρὴ διαγιγνώσκειν αὐτούς;); 108,24–109,1 (1.683 Kühn): “And therefore one should observe this principle consistently; and one should constantly bear in mind that each body possesses some specificity of mixture which is proper to one particular nature, but differs from another particular nature…” (διὸ καὶ φυλάττειν αὐτὴν ἀεὶ χρὴ καὶ μεμνῆσθαι διὰ παντός, ὡς ἕκαστον τῶν σωμάτων ἰδιότητά τινα κέκτηται κράσεως, οἰκείαν μὲν τῇδέ τινι τῇ φύσει, διαφερομένην δὲ τῇδέ τινι). 83 E.g. in 71,12–13 (1.622 Kühn): “You must pay particular attention to this matter when you consider the mixture of a body.” (δεῖ δὲ προσέχειν μάλιστα τούτῳ τὸν νοῦν, ἐπειδὰν ἐπισκέπτῃ σώματος κρᾶσιν). 84 E.g. 61,6–9 (1.606 Kühn): “The reasons for what has been said should already be clear enough, even without my mentioning them, at least to anyone who pays attention (τοῖς γε προσέχουσι τὸν νοῦν)”. 85 184b3–8; see van der Eijk 1997, 117–119.

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implication already been demonstrated in advance, but which cannot be understood clearly by all readers of this work. And so once we have dealt with terms, let us then proceed to the actual matter.86 This point, too, was made most beautifully by the ancients, namely that “habits are acquired natures.” And perhaps there is no need now to do more than state that, leaving it to the readers to distinguish, under each different heading, whether such-and-such a person is cold by nature or as a result of habituation, and myself proceed – in the interests of brevity – to an account of the conditions of the body proper to each different mixture.87

We could of course regard this combination of references to the readers in the third person plural with the addresses of the students in the second person singular88 as just another example of variation or alternation (similar to the variation, in cross references, between the use of first person singular and plural, or between personal and impersonal instructions); but we can also view the text as reflecting, and perhaps as intended to reflect, an oral presentation to students that at the same time is being prepared for later, written consumption by an audience of readers.89 It is almost as if Galen was dictating the text to a scribe and as if the scribe copied even those remarks – stage directions, so to say, or asides to himself – that Galen would presumably have left out in a revision of the text for written publication. Yet rather than regarding this as evidence of the possibly un-edited stage of the text as we have it, we could also see this as a deliberate posture: Galen explicitly tells both his immediate addressees – in the second person – and his future readers – in the third person – what he is doing and why he is doing it, how he is organizing and arranging his discussion and for what reasons.

Statements of intent, cross references This brings us to statements of intent, announcements and cross references backward and forward.90 These are, of course, common in scientific discourse, although 86 27,10–16 (1.552 Kühn): καίτοι κἀνταῦθα χρὴ πρότερον ὑπὲρ τῶν ὀνομάτων διελέσθαι τῶν ἐμπίπτειν μελλόντων ἐξ ἀνάγκης εἰς τὸν ἐφεξῆς λόγον ἐξαπλῶσαί τέ τι πρᾶγμα, δυνάμει μὲν ἤδη προαποδεδειγμένον, οὐ μὴν ἐναργῶς γε πᾶσι τοῖς ἀναγιγνώσκουσι τόδε τὸ γράμμα νοηθῆναι δυνάμενον. ὑπὲρ τῶν ὀνομάτων οὖν πρῶτον εἰπόντες οὕτως ἐπανίωμεν ἐπὶ τὸ πρᾶγμα. 87 61,27–62,5 (1.607 Kühn): εἴρηται γὰρ δὴ καὶ τοῦτο κάλλιστα πρὸς τῶν παλαιῶν, ὡς ἐπίκτητοι φύσεις εἰσὶ τὰ ἔθη, καὶ οὐδὲν ἴσως δεήσει τοῦθ' ἅπαξ εἰρηκότας νῦν μηκέτι διορίζεσθαι καθ' ἕκαστον κεφάλαιον, εἴτε φύσει ψυχρότερος εἴτ' ἐξ ἔθους ὅδε τις, ἀλλὰ τοῦτο μὲν ἀπολιπεῖν τοῖς ἀναγιγνώσκουσιν, αὐτὸν δὲ βραχυλογίας ἕνεκα τὰς οἰκείας ἑκάστῃ τῶν κράσεων ἕξεις τοῦ σώματος ἐπελθεῖν. 88 For a similar variation between second person address and third person reference to the audience in Galen’s treatise Diagnosis by Μeans of the Pulse see Asper 2005, 25. 89 A further example of the ‘oral’ style of the work is the expression καὶ νὴ Δία “by Zeus” in 106,13 (1.679 Kühn). 90 On cross references see n. 55 above.

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the degree to which an author makes use of them, and the specific manner in which he does so (through active or passive verbs, with or without indication of the person or persons involved) can be variable; and, just like the use of first person singular or plural, or second person singular or plural, this, too, is an area where stylistic preferences, fashions, conventions and authorial choices become noticeable.91 Just as in a contemporary student style-guide for dissertation writing one may find instructions about the use or avoidance of phrases such as “I am now going to discuss this” and, more generally, the use or avoidance of the first person expressions, e.g. in order to enhance a sense of objectivity, we can likewise assume that in the ancient world, opinions differred on the extent to which such personalized expressions were deemed desirable or not. In Aristotle, for example, we frequently find the use of passive perfect verb forms in references (“as has been said above”) or passive future verbs (“as will be discussed shortly”); and the Hippocratic treatise Generation – Nature of the Child – Diseases IV shows a similarly regular use of cross references and transitional formulae.92 Yet although we find such passive or impersonal constructions in Galen too,93 this does not prevent him from having, at the same time, a very strong personal presence in his own discourse. A further striking example, in addition to those already cited, presents itself early on in Book II, where Galen announces a change of plan: I had intended first to give an account of the causes of each of the above-mentioned indicators, but since the investigation of the different ages is more urgent for present purposes, as well as making us better equipped for the discovery of the causes, we shall embark on this first.94

Initially, he says, he had planned to discuss the topic in a particular way, but for various reasons he has changed his mind and is now inserting a discussion of a different topic. Again, we could read this as a genuine reflection of an actual classroom situation in which the teacher is improvising, or as a biographical account of Galen’s actual practice in writing the work; but we can also regard this selfcorrection as part of the authorial posture. A further passage is towards the end of book II, where Galen says that he is going to finish with a korōnis (“flourish”, “wreath”) and heading: “I have decided to add this point, too. Let it be as it were a flourish with which to round off the entire argument; and I will end the second book here.”95 The term translated 91 On authorial choices cf. Hine 2009, 23–30. 92 See Regenbogen 1930. 93 In addition to the examples of passive verbs given above, further expressions found in Mixtures are ὥρα δ’ ἂν εἴη λέγειν ἤδη (2,4, 1.510 Kühn) or ἤδη καιρός λέγεσθαι, “it is now time to say” (27,22, 1.552 Kühn). 94 43,12–16 (1.577 Kühn): ἐβουλόμην μὲν οὖν πρότερον ἑκάστου τῶν εἰρημένων γνωρισμάτων ἐπελθεῖν τὰς αἰτίας, ἀλλ' ἐπεὶ πρὸς τὰ παρόντα μᾶλλον ἡ περὶ τῶν ἡλικιῶν ἐπείγει σκέψις εὐπορωτέρους θ' ἡμᾶς πρὸς τὴν τῶν αἰτιῶν εὕρεσιν ἀπεργάζεται, πρώτην ταύτην ἐνστησόμεθα. 95 84,18–20 (1.643 Kühn): ἔγνωκα γὰρ ἔτι τοῦτο προσθεὶς οἷον κορωνίδα τε καὶ κεφαλήν τινα τῷ λόγῳ παντὶ καταπαύειν ἤδη τὸ δεύτερον γράμμα.

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“flourish” (korōnis) refers, literally, to a particular stroke of the pen used to indicate the end of a page, chapter or column in a Greek book. We thus have here a rare case where Galen is referring, not just to the structure and organisation of a work, but – albeit metaphorically – to the physical appearance of his work in written form.96 In the sequel to this passage, we also find an interesting remark by Galen on the organization of his work in three books, on the different stages of its presentation, and on the work’s relationship to other works: This, then, is how things really are. What has been said requires a demonstration, but I consider that this would be too long to add here, in the context of the present book. It would, furthermore, require an audience with an understanding of the capacities of drugs. I therefore put off this exposition, for now at least. When, however, I go lay out the entire third book on mixtures, and demonstrate the method that concerns things wet, dry, cold and hot in their capacity – then, I have decided, I will write a whole subsequent book on the uneven bad mixture. With that the whole account of mixtures will be complete – an account which will provide a substantial basis for the method of treatment.97

Thus we are given the impression that there is a pause at the end of book II: Galen postpones the necessary “demonstration” for a later occasion, i.e. book III, as it would take too long to provide it now and the audience does not possess the necessary prerequisites. He seems to imply that, by the time he starts with book III, this absence of familiarity with “the capacities of drugs” will no longer pose a problem, either because the audience will in the meantime have acquired this or, perhaps more likely, book III itself meets this demand in that it provides both the necessary prerequisites and the “demonstration” announced.

Rhetoric of confidence A final point I would like to consider in Mixtures is the difference, or alternation, between dogmatism and uncertainty, apodeictic and exploratory discourse, in the 96 See Singer & van der Eijk in press. 97 85,8–18 (1.644–645 Kühn): τὸ μὲν οὖν ἀληθὲς ὧδ' ἔχει. δεῖ δὲ τοῖς εἰρημένοις ἀποδείξεως, ἣν μακροτέραν τ' εἶναι νομίζων ἢ ὥστε προσγράφεσθαι κατὰ τόνδε τὸν λόγον ἔτι τ' ἀκροατοῦ δεομένην ἐπισταμένου περὶ φαρμάκων δυνάμεως, ἀναβάλλομαι τό γε νῦν διελθεῖν. ἀλλ' ἐπειδὰν τὸν τρίτον λόγον περὶ κράσεων ἅπαντα διέλθω καὶ δείξω περὶ τῶν κατὰ δύναμιν ὑγρῶν καὶ ξηρῶν καὶ ψυχρῶν καὶ θερμῶν ἅπασαν τὴν μέθοδον, ἐφεξῆς οὕτω βιβλίον ὅλον ὑπὲρ ἀνωμάλου δυσκρασίας ἔγνωκα γράψαι. τελειωθήσεται γὰρ ἅπας ἡμῖν ὁ περὶ κράσεων λόγος εἴς τε τὴν θεραπευτικὴν μέθοδον οὐ σμικρὰς ἀφορμὰς παρέξει. See also note 51 above. As Singer notes: “The language from here to the end is extremely interesting for Galen’s view of the status of his own works as well as being somewhat problematic in translation, because of the use of terms which have a dual reference to an argument in the abstract sense and a book in the concrete sense. Thus, ‘third part of the argument’ here also means, simply, ‘third book of the treatise’: the term is logos – which is also the term translated ‘account’ in the last sentence, below.” (Singer & van der Eijk in press).

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manner in which the ideas and arguments are presented. This is, again, a feature we already observed in relation to the Aristotelian pragmateia and which belongs to the standard repertoire of techniques that the author of a treatise has at his disposal. Depending on the circumstances, subject matter and rhetorical strategy, an author can choose to create an impression of openness and unpredictability of the outcome of the investigation; he may even emphasize the difficulty or complexity of what he is examining, e.g. by raising questions or stating that things are difficult or by otherwise sounding caution.98 In Aristotle, for example, this “raising of problems” (diaporein) is part of the dialectical stage of the discussion and has an important epistemic, heuristic purpose. Alternatively, it can be motivated by pedagogic considerations, trying to involve an audience of students into a collective intellectual challenge or to instil a sense of seriousness and devotion. Yet it can also arise from a desire, on the author’s part, to create a sense of suspense: as the investigation proceeds, the difficulties and complexities become bigger and bigger and the reader is led to wonder where it will all end – and then suddenly there is a breakthrough in the argument, everything falls into place and the solution to all the difficulties has been found. Such a technique of creating suspense followed by resolution can, of course, enhance the audience’s admiration for the masterly and seemingly magical skills of the lead-investigator; and if the investigation has been presented as a collective enterprise, the audience will share in the success and there will be a communal sense of achievement and satisfaction. Galen was certainly no stranger to these techniques: in his case studies of patients in Prognosis, for example, he likes playing the wizzard or the diviner, producing solutions in seemingly hopeless situations where other physicians are at a loss.99 In Mixtures, the situation is less dramatic, but there are elements of the same procedure. Throughout the work, especially at the beginning, Galen repeatedly uses words referring to the seeking, examining nature of his project (zētein, skepsis, skopein, epelthein);100 and as we have already seen, there is a ‘dialectical’ stage in Mixtures as well. Far from dictating his views in a dogmatic manner, Galen presents the argument as an investigation whose results are not yet known right at the beginning but gradually unfold as the inquiry proceeds. Yet as the work advances, a clear ‘rhetoric of confidence’ emerges, which gets stronger and stronger. This confidence is marked by the increasing use of expres98 Questions in Mixtures are frequent: see, e.g., 4,9 (1.514 Kühn); 7,25 (1.520 Kühn); 8,10 (1.521 Kühn); 14,7 (1.530 Kühn); 46,26 (1.582 Kühn); 77,13 (1.632 Kühn); 102,13 (1.672 Kühn). 99 See Lloyd 2009. 100 E.g. 1,7–10 (1.509–510 Kühn): “I shall do what follows on from that, namely go through in this work the discovery of all the different varieties of mixture, how many there are, and of what kind, as one distinguishes them by genus and species.” (νυνὶ δ', ὅπερ ἐστὶν ἐφεξῆς ἐκείνῳ, ἁπάσας ἐξευρεῖν τῶν κράσεων τὰς διαφοράς, ὁπόσαι τ' εἰσὶ καὶ ὁποῖαι κατ' εἴδη τε καὶ γένη διαιρουμένοις, ἐν τῷδε τῷ γράμματι δίειμι); 36,19 (1.566 Kühn): “The man we are now seeking (ζητοῦμεν)…”; 49,23 (1.587 Kühn): “Now, since, in the case of any discussion of mixture, the starting-point is an examination (ἐπίσκεψις) of the elements…”.

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sions such as “it is quite reasonable to suppose”, “it should cause no surprise”, “we can confidently assert”, “this presents no difficulty”, or “this is in full accordance with what we said at the beginning”. Galen reassures his audience that everything is under control, that what appear to be counter-examples present no difficulties to the argument and that everything makes perfect sense. Most examples are from book III, as the argument is drawing to a close (though the use of these expressions also occurs earlier on):101 It is therefore natural that in the course of time some experience baldness, namely those whose skin was originally quite dry. For we have already shown that all parts of the body become drier in the process of aging.102 There is nothing remarkable in the fact that some drugs from a very small initial influence undergo an enormous change from their original nature…103 There should then be no difficulty about these, nor about the fact that wine heats the body considerably when drunk, but not when placed on the skin.104

A very effective use of this technique is presented by the following passage, where Galen first raises what appears to be an insurmountable problem against the argument he has been developing, but then shows that it is actually in full accord: But this point may perhaps appear to be in conflict: that some things which are eaten with the function of nourishment, when placed in contact with the skin, eat through it and make a wound. Examples are mustard, pickles, garlic and onion. And yet this fact too is in accord with our original assumptions. The reasons that what causes injury externally does not do so when eaten are all the following…105

101 E.g. in 34,5–19: “A total mixture of one with the other – of hot, cold, dry and wet, that is – is not possible (ἀδύνατον) for a human being. When earth is kneaded together with something wet, it appears to one that a combination has taken place, certainly, and so also that the whole of the one substance is mixed with the whole of the other; but actually this process is a placing alongside each other of very small parts, not a total mixture; the total mixture of the two is the function of God, and of Nature, especially in the case of total mixture of hot and cold. But the creation of such a setting-alongside, whereby each of the simple bodies escapes perception, is not the function of Nature alone, nor of God, but is achievable by us (ἡμέτερον) too. For it is not at all difficult (οὐδὲ γὰρ χαλεπόν) by this kind of combination to produce mud which is midway between wet and dry and also between hot and cold; and such a body will appear to you (σοι φανεῖται) well-mixed in terms of heat, as well as midway between hardness and softness.” 102 70,5–7 (1.620 Kühn): Εὐλόγως οὖν ἔνιοι φαλακροῦνται τοῦ χρόνου προϊόντος, οἷς ἐξ ἀρχῆς ἦν ξηρότερον τὸ δέρμα. δέδεικται γὰρ ἔμπροσθεν, ὡς τῶν γηρασκόντων ἅπαντα ξηραίνεται τὰ μόρια. 103 93,3–4 (1.657 Kühn): Θαυμαστὸν δ' οὐδέν, εἰ βραχείας ἀφορμῆς ἔνια λαβόμενα μεγίστην ἐκτροπὴν ἴσχει τῆς ἀρχαίας φύσεως. 104 94,5–8 (1.658 Kühn): περὶ μὲν δὴ τούτων οὐδὲν ἄπορον, ἀλλ' οὐδὲ διὰ τί πινόμενος μὲν ὁ οἶνος ἱκανῶς θερμαίνει τὸ σῶμα, κατὰ δὲ τοῦ δέρματος ἐπιτιθέμενος οὐ θερμαίνει. 105 95,26–96,13 (1.661 Kühn): Ἐκεῖνο δ' ἂν ἴσως δόξειε διαφέρεσθαι τό τινα τῶν ἐσθιομένων ἐν τροφῆς χρείᾳ κατὰ τοῦ δέρματος ἐπιτιθέμενα διαβιβρώσκειν τε καὶ ἑλκοῦν αὐτό, καθάπερ νᾶπυ καὶ τάριχος σκόροδά τε καὶ κρόμυα. καίτοι καὶ τοῦτο συμφωνεῖ τοῖς ἐξ ἀρχῆς ὑποκειμένοις· ἅμα μὲν γὰρ ὅτι … διὰ ταῦτα πάντα τὸ ἔξωθεν ἑλκοῦν ἐσθιόμενον οὐχ ἑλκοῖ.

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A striking case of a sustained, almost conjuring use of reassuring formulae – with persistent use of negatives denying that there is a problem – is presented by the following example: There is nothing problematic in any of this, nor in the fact that some drugs that are innocuous when applied externally cause great harm if drunk. And there are others that frequently cause harm when taken internally, but also frequently do good; and others again that are harmful both externally and internally. To speak generally, though, no thing has naturally the same action inside and outside the body. Not even the saliva of a mad dog, or the poison of an asp or viper, which indeed have been believed to have done harm on contact even without the presence of a wound, have the same power if only in contact with the skin as they do when taken internally. And there is no cause for surprise, either, in the fact that the power of some drugs does not reach far within the body: there is no necessity for all to have the same strength. Nor should it be considered a problem for our argument that many drugs that are taken internally do good only at a certain time, in a certain quantity and in mixture with certain things, and are actually harmful if taken at the wrong time, in excess and unmixed. This, after all, is true of food too, as of fire; we might even say, of everything which encounters the body from without (…) What, then, is so remarkable in the fact that there exists a drug so hot in power that it will eat through and burn us if taken in large quantities and when the body is empty, but in very small quantities, and taken in conjunction with things which control its strength, will not only do no harm but also benefit us by its heating?106

Instead of saying that there is nothing problematic or surprising, we also find rhetorical questions: Why should one be surprised, then, about the fact that opium, a drug so opposed to our nature, is very swiftly cooled, even when drunk hot, and that the body is simultaneously cooled with it?107

106 97,14–98,12 (1.664–665 Kühn): οὔτ' οὖν τῶν τοιούτων οὐδὲν ἄπορον οὔτε διὰ τί τῶν φαρμάκων ἔνια μὲν οὐδὲν ἡμᾶς ἔξωθεν ἀδικοῦντα μέγα τι κακὸν ἐργάζεται καταποθέντα. τινὰ δὲ πολλάκις μὲν ἔβλαψεν εἴσω ληφθέντα, πολλάκις δ' ὠφέλησεν· ἔνια δ' οὐ μόνον ἔσωθεν ἀλλὰ καὶ ἔξωθεν ἀδικεῖ. συλλήβδην δ' εἰπεῖν οὐδὲν ὁμοίως ἔσωθέν τε καὶ ἔξωθεν ἐνεργεῖν πέφυκεν. οὔτε γὰρ ὁ τοῦ λυττῶντος κυνὸς ἀφρὸς οὔθ' ὁ τῆς ἀσπίδος οὔθ' ὁ τῆς ἐχίδνης ἰός, οἳ δὴ καὶ χωρὶς ἕλκους ἔξωθεν προσπεσόντες ἀδικεῖν πεπίστευνται, τὴν ἴσην ἔχουσι δύναμιν ἢ τῷ δέρματι μόνον ὁμιλήσαντες ἢ εἴσω μεταληφθέντες. οὐ μὴν οὐδ' ἐκεῖνο θαυμάζειν ἄξιον, εἴ τινων φαρμάκων οὐκ ἐξικνεῖται πρὸς τὸ βάθος ἡ δύναμις· οὐ γὰρ ἀναγκαῖον ἅπαντα τὴν αὐτὴν ἔχειν ἰσχύν. εἰ δὲ πολλὰ τῶν εἴσω λαμβανομένων ἐν μὲν τῷδε τῷ καιρῷ καὶ μετὰ τοσῆσδε ποσότητος καὶ τῆς πρὸς τάδε μίξεως ὠφέλησεν, ἀκαίρως δὲ καὶ πολλὰ καὶ ἄμικτα ληφθέντα βλάβην ἤνεγκεν, οὐδὲν οὐδ' ἐντεῦθεν ἀπόρημα τῷ λόγῳ. καὶ γὰρ καὶ τοῖς σιτίοις ὑπάρχει τοῦτό γε καὶ τῷ πυρὶ καὶ πᾶσιν ὡς οὕτω φάναι τοῖς προσπίπτουσι τῷ σώματι. … τί τοίνυν θαυμαστὸν εἶναί τι φάρμακον οὕτω δυνάμει θερμόν, ὡς, εἰ μὲν πολύ τε λαμβάνοιτο καὶ κενῷ τῷ σώματι προσφέροιτο, διαβιβρώσκειν τε καὶ κατακαίειν αὐτό, εἰ δὲ παντελῶς ὀλίγον εἴη ἢ καὶ σὺν τοῖς κολάζουσι τὴν ἰσχὺν αὐτοῦ, πρὸς τῷ βλάπτειν μηδὲν ἔτι καὶ θερμαῖνον ὠφελεῖν; 107 103,5–8 (1.674 Kühn): τί οὖν θαυμαστόν, εἰ καὶ τὸ μηκώνιον, οὕτως ἐναντίον ἡμῶν τῇ φύσει φάρμακον, ἀποψύχεται μὲν αὐτίκα μάλα, κἂν θερμὸν ποθῇ, συγκαταψύχει δ' ἑαυτῷ τὸ σῶμα;

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Why should one be surprised, then, about the fact that the body is being filled up with a cold quality as long as a naturally cold food such as purslane or lettuce is being digested…108 And why should one be surprised if it happens that lettuce both acts and is acted upon…109

Finally, the following passages present a combination of a denial of any problem and an assertion of coherence: And indeed, the fact that any of these naturally cold substances, if you heat it up to a high degree, departs from its own nature, not only does not present a problem, but actually confirms our previous statements.110 But if none of the above phenomena is impossible, or even surprising, then those who deny that one and the same food may provide the function of both nourishment and drug to an animal should cease their argument.111

In addition to these formulae indicating that in the light of Galen’s theory there is nothing that presents a surprise or problem, Galen also says on a number of occasions that he and his students can be confident in their statements: If this is the case – as we have shown that it is – we may now confidently state that there are nine different kinds of mixture…112 We therefore have the confidence to assert, in quite general terms regarding all foods, that their nature is not only to be affected by our body, but also to act upon it…113

Conclusion When we relate Galen’s Mixtures to the preconceived ideas about the ‘treatise’ or pragmateia that I outlined in the beginning, we find that the work meets these expectations only up to a point. Mixtures has a remarkable degree of liveliness,

108 106,22–24 (1.679 Kühn): τί δὴ οὖν θαυμαστόν, ἄχρι μὲν ἂν πέττηται τὸ ψυχρὸν τῇ φύσει σιτίον, οἷον ἀνδράχνη τε καὶ θριδακίνη, ψυχρᾶς ποιότητος ἀναπίμπλασθαι τὸ σῶμα. 109 107,13–14 (1.681 Kühn): καὶ τί θαυμαστόν, εἰ τῇ θριδακίνῃ καὶ δρᾶν καὶ πάσχειν συμβέβηκεν. 110 103,14–17 (1.674 Kühn): καὶ γὰρ δὴ καὶ ὅτι τούτων ἁπάντων τῶν φύσει ψυχρῶν ὅ τι ἂν ἐπὶ πλέον ἐκθερμήνῃς, ἐξίσταται τῆς ἰδίας φύσεως, πρὸς τῷ μηδὲν ἄπορον ἔχειν ἔτι καὶ μαρτυρεῖ τοῖς προειρημένοις. 111 106,27–30 (1.680 Kühn): καὶ μὴν εἰ μηδὲν τούτων μήτ' ἀδύνατόν ἐστι μήτε θαυμαστὸν ἔτι, παυσάσθωσαν οἱ μὴ συγχωροῦντες ἓν καὶ ταὐτὸν ἔδεσμα καὶ τὴν ὡς τροφῆς καὶ τὴν ὡς φαρμάκου χρείαν τῷ ζῴῳ παρέχειν. 112 31,27–29 (1.559 Kühn): καὶ εἴπερ ἔχει ταῦθ' οὕτως, ὥσπερ οὖν ἔχει, θαρρούντως ἤδη λέγομεν ἐννέα τὰς πάσας εἶναι τῶν κράσεων διαφοράς. 113 107,21–23 (1.681 Kühn): Θαρροῦντες οὖν ἐπὶ πάντων μὲν ἁπλῶς ἀποφαινόμεθα τῶν σιτίων, ὡς οὐ μόνον πάσχειν ὑπὸ τοῦ σώματος ἡμῶν ἀλλὰ καὶ δρᾶν εἰς αὐτὸ πέφυκεν.

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directness and audience-orientedness; Galen’s own persona, as the author, teacher, lead-investigator and orchestrator of debates and arguments, is prominently present throughout the work; and the audience, both the immediate students and the future readers, are explicitly referred to on a number of occasions. Of course, more work is needed, based also on statistical data, to assess the significance of these results concerning Mixtures in comparison with other works by Galen and by other authors.114 Yet on the face of it, the features we have seen do not belong to the standard pattern of ancient treatises, certainly not those of Aristotle – nor, for that matter, those of authors contemporaneous with Galen such as Alexander of Aphrodisias or Sextus Empiricus; nor does the frequency with which Galen addresses the reader accord with that of the Hippocratic writers or someone like Aretaeus of Cappadocia – to mention another author of medical treatises of the Early Imperial Period.116 Once again Galen is proving a highly original and peculiar author with a strong authorial persona, keen to establish ‘klare Verhältnisse’ with his students and future readers.

Bibliography Texts quoted Helmreich, G. 1914. Galenus. De temperamentis. Leipzig.

Works quoted Asper, M. 1996. “Zu Struktur und Funktion eisagogischer Texte”. In: W. Kullmann et al. (eds.), Gattungen Wissenschaftlicher Literatur in der Antike. Tübingen, 309–340. Asper, M. 2005. “Un personaggio in cerca di lettore: Galens Großer Puls und die ‘Erfindung’ des Lesers.” In: T. Fögen (ed.), Antike Fachtexte. Berlin, 21–40. Asper, M. 2007. Griechische Wissenschaftstexte. Stuttgart.

114 The occurrences of the second person singular in Mixtures are certainly much more frequent than in The Formation of the Foetus, as Curtis 2009 bears out. More similar to Mixtures in this respect is Affected Places, which has a substantial number of direct addresses of the student by means of the personal pronoun (for instances see 8.7, 9, 20, 39, 48, 63, 84, 131, 133, 141, 182, 190, 222, 223, 284, 295, 308, 356, 364, 365 Kühn), or the treatises on the pulse (see Asper 2007, 333–337 with instances listed on p. 335, n. 105). Some of the rhetorical and compositional features discussed (e.g. identifying ‘differences’, discussing terminology, stating omissions, criticism of others for failing to understand the works of the ancients properly) are familiar from other works by Galen, e.g. Differences between Pulses or Tremor, Palpitation, Spasm and Rigor. 116 On Aretaeus see Nutton 2009. A further medical author that could be included in the comparison is Soranus of Ephesus; yet his only surviving work, the Gynaecia, seems to have a more practical orientation and to suit the textual type of the treatise less well.

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Crombie, A. 1995. Styles of Scientific Thinking in the European Tradition: The History of Argument and Explanation, Especially in the Mathematical and Biomedical Sciences and Arts. London. Curtis, T. A. 2009. Rhetorical Strategies and Generic Conventions in the Galenic Corpus. PhD Thesis Newcastle University, Newcastle upon Tyne (manuscript). Dorandi, T. 2007. Nell’officina dei classici. Rome. van der Eijk, P. J. 1997. “Towards a Rhetoric of Ancient Scientific Discourse: Some Formal Characteristics of Greek Medical and Philosophical Texts (Hippocratic Corpus, Aristotle).” In: E. J. Bakker (ed.), Grammar as Interpretation. Greek Literature in Its Linguistic Contexts. Leiden, 77–129. van der Eijk, P. J. 2009. “Aristotle! What a Thing for You to Say! Galen’s Engagement with Aristotle and Aristotelians.” In: C. J. Gill et al. (eds.), Galen and the World of Knowledge. Cambridge, 261–281. van der Eijk, P. J. 2010. “Galens Auseinandersetzung mit Aristoteles’ Ansichten zum Gesichts- und Geruchssinn”. In: Antike Naturwissenschaft und ihre Rezeption 20, 81–107. van der Eijk, P. J. 2012. “Exegesis, Explanation and Epistemology in Galen’s Commentaries on Epidemics I–II.” In: P. E. Pormann (ed.), Epidemics in Context. Berlin, 25–47. Flemming, R. 2008. “Commentary.” In: R. J. Hankinson (ed.), The Cambridge Companion to Galen. Cambridge, 323–354. Flemming, R. 2009. “Demiurge and Emperor in Galen’s World of Knowledge.” In: C. J. Gill et al. (eds.), Galen and the World of Knowledge. Cambridge, 59–84. Hanson, A. E. 1998. “Galen: Author and Critic.” In: G. W. Most (ed.), Editing Texts – Texte Edieren. Göttingen, 22–53. Hine, H. 2009. “Subjectivity and Objectivity in Latin Scientific and Technical Literature.” In: L. Taub & A. Doody (eds.), Authorial Voices in Greco-Roman Technical Writing. Trier, 13–30. Jouanna, J. 1984. “Rhétorique et médecine dans la Collection Hippocratique.” In: Revue des Etudes Grecques 57, 26–44. Jouanna, J. 2003. “La notion de la nature chez Galien”. In: J. Barnes & J. Jouanna (eds.), Galien et la Philosophie. Entretiens sur l’antiquité classique XLIX. Vandœuvres – Genève, 229–268. Kinneavy, J. L. 1971. A Theory of Discourse. Englewood Cliffs. Lengen, R. 2002. Form und Funktion der aristotelischen Pragmatie. Stuttgart. Lloyd, G. E. R. 1987. “Dogmatism and Uncertainty in Early Greek Speculative Thought.” In: M. Détienne (ed.), Poikilia. Etudes offerts à J. P. Vernant. Paris, 297–312. Lloyd, G. E. R. 2009. “Galen’s un-Hippocratic Case-Histories.” In: C. J. Gill et al. (eds.), Galen and the World of Knowledge. Cambridge, 115–131. Nutton, V. 2009. “Galen’s Authorial Voice: a Preliminary Enquiry.” In: L. Taub & A. Doody (eds.), Authorial Voices in Greco-Roman Technical Writing. Trier, 53–62. Oser-Grote, C. 1998. “Einführung in das Studium der antiken Medizin. Eisagogische Schriften des Galen in ihrem Verhältnis zum Corpus Hippocraticum.” In: W. Kullmann et al. (eds.), Gattungen Wissenschaftlicher Literatur in der Antike. Tübingen, 95–177. Pera, M. 1994. The Discourses of Science. Chicago. Perelman, C. & L. Olbrechts-Tyteca 1970. Traité de l’argumentation. La nouvelle rhétorique, 2nd ed., Brussels. Regenbogen, O. 1930. “Eine Forschungsmethode antiker Naturwissenschaft.” In: Quellen und Studien zur Geschichte der Mathematik 1, 131–182 (reprinted in Kleine Schriften, ed. F. Dirlmeier, Munich 1961, 141–194). Roselli, A. 2006. “Strategie espositive nei trattati ippocratici: presenza autoriale e piano espositivo in Mal. IV e Fratture e Articoli.” In: M. M. Sassi (ed.), La costruzione del discorso filosofico nell’ età dei presocratici. Pisa, 259–286. Schenkeveld, D. 1997. “Philosophical Prose”. In: S. E. Porter (ed.), Handbook of Classical Rhetoric in the Hellenistic Period 330 BC–AD 400. Leiden, 195–264.

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Singer. P. N. & P. J. van der Eijk in press. “Mixtures.” In: Galen, Works on Human Nature. Cambridge. Sluiter, I. 1995. “The Embarrassment of Imperfection. Galen’s Assessment of Hippocrates’ Linguistic Merits.” In: P. J. van der Eijk et al. (eds.), Ancient Medicine in Its Socio-Cultural Context. Amsterdam, Vol. 2, 519–535. von Staden, H. 1994. “Author and Authority. Celsus on the Construction of a Scientific Self.” In: M. E. Vázquez Buján (ed.), Tradición e innovación de la medicina latina de la antigüedad y de la alta edad media. Santiago de Compostela, 103–117. von Staden, H. 1995. “Science as Text, Science as History. Galen on Metaphor.” In: P. J. van der Eijk et al. (eds.), Ancient Medicine in Its Socio-Cultural Context. Amsterdam, Vol. 2, 499–518. von Staden, H. 1998. “Gattung und Gedächtnis: Galen über Wahrheit und Lehrdichtung.” In: W. Kullmann et al. (eds.), Gattungen Wissenschaftlicher Literatur in der Antike. Tübingen, 65–94. von Staden, H. 2002. “‘A Woman Does Not Become Ambidextrous’. Galen and the Culture of the Scientific Commentary.” In: R. K. Gibson & C. S. Kraus (eds.), The Classical Commentary: Histories, Practices, Theory. Leiden, 109–140. von Staden, H. 2006. “Interpreting ‘Hippokrates’ in the 3rd and 2nd Centuries BC.” In: C. W. Müller et al. (eds.), Ärzte und Ihre Interpreten. Munich, 15–48. von Staden, H. 2009. “Staging the Past, Staging Oneself: Galen on Hellenistic Exegetical Traditions.” In: C. J. Gill et al. (eds.), Galen and the World of Knowledge. Cambridge, 132–156. Untersteiner, M. 1980. Problemi di filologia filosofica. Milan. Vogt, S. 2005. “‘…er schrieb in Versen, und er tat recht daran’: Lehrdichtung im Urteil Galens.” In: T. Fögen (ed.), Antike Fachtexte. Berlin, 51–78. Wittern, R. 1998. “Gattungen im Corpus Hippocraticum.” In: W. Kullmann et al. (eds.), Gattungen Wissenschaftlicher Literatur in der Antike. Tübingen, 17–36.

Ralph M. Rosen

Galen on Poetic Testimony Abstract: Galen had an abiding reverence for the classicized Greek poets of his day, in keeping with the prevailing cultural norms of the educated elite. He wrote monographic works on Attic comedy, and often peppered his medical treatises (particularly the psychological and propaedeutic works) with quotations from Homer, the Greek lyric poets and the tragedians. But while he regarded the study of poetry as essential for a complete education, however nebulously construed, he was conflicted about its utility for the scientific enterprise. Often in On the Opinions of Hippocrates and Plato (Plac. Hipp. Plat.), for example, Galen ridicules the Stoic Chrysippus for misusing the testimony of poets in the service of philosophical and scientific argument, while elsewhere in the treatise he freely cites classic poets as illustrative of his own arguments. In Protrepicus, too, he includes mousikē (encompassing for Galen something like our notion of ‘the literary’) as one of the ‘elevated arts’ (semnai tekhnai), the cultivation of which will help humans live according to truth and reason. This paper will examine Galen’s complicated, often inconsistent, attitude to the role of ‘literature’ in his work, focusing specifically on questions of poetic vs. logical/philosophical authority. In particular, I will discuss how Galen aligns his own practice of invoking poetic authors as evidence or exempla with Plato’s, and attempt to clarify what he believed literary testimony could contribute to his argument, both rhetorically and philosophically.

In his short treatise, Protrepticus (Exhortation to Medicine), Galen’s formulation of what constituted an educated, intelligent man was by and large consonant with prevailing norms of his day, and can be summed up well in the contrast he draws early in the work (ch. 3) between those who follow Fortune (tykhē) and those who follow Hermes. The followers of Fortune live random, unpredictable lives, largely devoid of reason, while the followers of Hermes are devoted especially to the literary and scientific tekhnai – the ‘high’ (semnai) and rational (logikai) arts, as Galen calls them (ch. 14), to distinguish them from the less desirable banausic arts, which exercise the body rather than the mind. Galen’s main criterion for defining an art was that it be useful and ‘beneficial to life’ (ch. 9), and he railed in Protrepticus against such frivolous and useless arts as acrobatics, or athletics, which he regarded as pernicious to both mental and physical health. It will come as no surprise that he ends the treatise, doubtless with a touch of humor, with the claim that medicine is the ‘best’ (aristē) of the arts (14.5). Although he defers discussion of the matter to another time, it is not difficult for anyone to consider medicine one of the ‘useful’ arts, and the same can be said for most of the other arts that Galen exhorts his readers to study (14.4), which are largely scientific (mathematics, astronomy) or rhetorical (grammar, law). But among these ‘high’ and ‘useful’ arts

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he also includes poetry and music.1 Galen is clearly working with a broad notion of ‘utility’ here (biōpheles) here, since however ‘useful’ we can claim poetry is for a good life, it seems to offer a far different sort of utility than that of medicine or mathematics. Galen was, as I will suggest in this chapter, conflicted in his attitudes towards poetry, and towards literary authors more generally, especially when it came to incorporating them into his own scientific enterprise. He had a scholarly, even philological interest, in some authors who had become classics by his time, as he notes in his autobiographical works,2 and he seemed to believe that there was genuine knowledge to be gained from studying poets and other literary authors – if not quite an intrinsically ‘scientific’ kind of knowledge, at least something ancillary to, and illustrative of it. Even by Galen’s time the tension between poetic and scientific or philosophical knowledge would have already been ancient: this is precisely the question at hand in Plato’s Ion, for example, and Galen would also have been familiar with Plato’s notion of an ‘ancient quarrel’ between poetry and philosophy.3 The Ion, for example, famously showed Plato’s skepticism about the epistemic claims that poets and rhapsodes might make about their subject matter, but even he would quote freely from the poets in philosophical discussion, and often invoked poetic testimony to corroborate or embellish an argument.4 Literary 1 For Galen, a true tekhnē must be ‘useful’; cf. Protr. 9.3 (p. 130.25–26 Barig.): ὁπόσοις τῶν ἐπιτηδευμάτων οὔκ ἐστι τὸ τέλος βιωφελές, ταῦτ' οὐκ εἰσὶ τέχναι. (…any practice whose goal is not useful for life is not a tekhnē.) Galen’s interest in the question of the utility/non-utility of knowledge taps into a philosophical debate that extended back to Plato and Aristotle. Galen’s endorsement of “useful” knowledge aligns his thinking with a Socratic-Platonic tradition rather than an Aristotelian one, which ranked “theoretical” knowledge higher than practical knowledge precisely because of its impracticality and “uselessness”. See, e.g., the opening of Aristotle, Metaph. A 1–2, 981b13– 982b27, and Nightingale 2004, 222–240, on Aristotelian theōria, and the privileging of “uselessness”. 2 See in general his treatise On my own books, and esp. ch. 20.1, where he mentions his 48 books on writers of Classical Athens, which include many commentaries on the poets of Old Comedy. Cf. Boudon-Millot 2007, 233–34, De Lacy 1966, 265. The recently discovered treatise, On Avoiding Distress, also discusses his works on Old Comedy, all of which, we learn here from Galen, were destroyed in the great fire in Rome of  192. See On Avoiding Distress (Περὶ ἀλυπίας) chs. 20–29, in Boudon-Millot and Jouanna, 2010, with commentary, pp. 83–92. 3 For the locus classicus, see Res publ. X, 607b–c; see Murray 1996, 14–19, and most recently, with bibliography, Most 2011, 1–20. 4 In general, see Murray 1996, 9–24. For one example of Plato’s engagement with poetic texts for philosophical purposes, cf. Nightingale’s discussion (1992 and 1995, 47–62) of his use of Euripides’ Antiope in Gorgias. At the same time, Plato was well aware of the pitfalls of poetic exegesis in the service of philosophical discourse, as his occasional parodies of poetic interpretation show; cf., e.g., the discussion of Simonides’ poem in Plato, Prot. 339a-347b. Part of the point of Socrates’ long analysis of Simonides’ poem is to show the inadequacies of literary intepretation, as his dismissive statement at 347c3 makes clear: “…for it seems to me that discussing poetry is most like vulgar and low-class drinking-parties” (καὶ γὰρ δοκεῖ μοι τὸ περὶ ποιήσεως διαλέγεσθαι ὁμοιότατον εἶναι τοῖς συμποσίοις τοῖς τῶν φαύλων καὶ ἀγοραίων ἀνθρώπων). Later in this passage, 347e5, Socrates complains that when men bring poets into a discussion, “many people say that the poet means one thing in his work, and others something else, and they keep on discussing an issue that they

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citation, then, in the service of philosophical and scientific writing was commonplace enough from an early period not only for rhetorical purposes, but also, no doubt, to mark a writer’s elite cultural background. But literary citation in the context of medical writing, specifically, might give us some pause, especially in a writer as devoted to logical thinking and empirical truth as Galen was.5 The Hippocratic Corpus, after all, which Galen admired and assimilated so deeply, was strikingly devoid of allusions to literary (and especially poetic) authors. In a paper entitled ‘Galen and the Greek Poets’, written in 1966 while he was working on his great CMG edition of Galen’s On the Opinions of Hippocrates and Plato (De Lacy 2005 = Plac. Hipp. Plat.), Philip De Lacy noted a prevailing ambivalence about, and occasional hostility towards, poetry during the second century , at least among philosophical writers such as Plutarch and Epictetus, and he points out various places in Galen where he specifically disparages the use of poetic testimony in scientific discussion.6 It seems all the more curious, therefore, that in a work presented as a ‘protrepticus’ to the study of medicine, Galen not only recommends the study of poetry (mousikē), along with the other higher arts, but also freely invokes poetic authors throughout the work, as if to demonstrate how one would put into practice the advice of the treatise. Galen, it seems, was pulled in two directions by different forces: on the one hand, he wanted to show off his broad, polymathic education as something genuinely useful to intellectual endeavors, not just as an ornament or empty symbol of social status. On the other, his commitment to rigorous syllogistic thinking often made the poets and their

can never actually confirm one way or another…”, and he concludes by urging that “we put the poets aside and hold our conversations just with each other, and put to the test the truth and our ourselves” (…ἐπαγόμενοί τε αὐτοὺς οἱ πολλοὶ ἐν τοῖς λόγοις οἱ μὲν ταῦτά φασιν τὸν ποιητὴν νοεῖν, οἱ δ’ ἕτερα, περὶ πράγματος διαλεγόμενοι ὃ ἀδυνατοῦσι ἐξελέγξαι·… καταθεμένους τοὺς ποιητὰς αὐτοὺς δι’ ἡμῶν αὐτῶν πρὸς ἀλλήλους τοὺς λόγους ποιεῖσθαι, τῆς ἀληθείας καὶ ἡμῶν αὐτῶν πεῖραν λαμβάνοντας·). 5 By ‘literary’ here I mean referring to literature that is not itself, in its original context and genre, medical or otherwise technical. Galen did cite some poetry we would refer to as ‘didactic’ or ‘scientific’, such as the pharmacological treatises of Andromachus the elder and Damocrates (both 1st cent. ), but both of them were physicians in their own right, and, as we would expect, Galen regarded such poetry differently from non-scientific ‘classics’ such as Homer or Euripides. On Galen’s use of didactic poetry, see von Staden 1998, Vogt 2005; see also Fabricius 1972, and Nutton 1997. 6 De Lacy (1966, 265) cites Plac. Hipp. Plat. V 7.42–43 as a passage that shows Galen’s respect for the ways in which poets portray human behavior, but even so, his repudiation of poetic testimony in the service of scientific argument here is unambiguous. In criticizing the views of “Chrysippus and many Stoics” on reason and the passions, he says: “Ignorance of a thing is pardonable…but it is not pardonable to handle the argument so ineptly as to cite as proof of so important a doctrine the words of comic and tragic poets – men who do not try to prove anything but only adorn with beauty of language the speeches they think appropriate to the character speaking in the play – and to fail to mention what Plato said in proof of it…”. Cf. also Plac. Hipp. Plat. II 2.5.

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ways of thinking seem distracting or frivolous at best, dangerous at worst.7 I propose here, then, to examine in detail Galen’s own ambivalence towards the use of poetic texts in his work, and to attempt to understand what might have drawn him, like a moth to a flame, to a literary practice so fraught with philosophical and logical peril. It has to be said at the outset that Protrepticus is hardly a work of science – its overall cast is, as its title suggests, hortatory and quasi-philosophical, and even though it ends by claiming that the best tekhnē is medicine, there is little explicitly medical about this treatise. Still, we might call it a para-medical, in that it ends up focusing on a topic that has a variety of medical consequences – namely, as it turns out, the evils of athleticism – and deploys poetic citation in the same ways that we find it in his more straightforwardly medical discussions. We may begin by examining closely a section of Protrepticus that shows just how conflicted Galen was about rhetorical strategies that relied heavily on the authority of poets. In ch. 9, Galen has introduced, not altogether smoothly, the subject of athletes, which will occupy him for the rest of the work (in fact, more than half of the whole). While he spent the first half of the work speaking in platitudinous generalities about the differences between high and low tekhnai, and about the need to avoid greed, vanity and other vices that ruin body and soul, he suddenly – and in keeping with Galen’s often free-associative writing habits – gets fixated on athletes. Everyone will know, he says, that such activities as acrobatics are hardly real ‘arts’ (9, Barig. 130.25–27), but, he continues: τὸ δὲ τῶν ἀθλητῶν ἐπιτήδευμα μόνον ὑποπτεύω, μή ποτ' ἄρα τοῦτο καὶ ῥώμην σώματος ἐπαγγελλόμενον καὶ τὴν παρὰ τοῖς πολλοῖς δόξαν ἐπαγόμενον, δημοσίᾳ παρὰ τοῖς πατράσι τετιμημένον ἡμερησίαις ἀργυρίου δόσεσι καὶ ὅλως ἴσα τοῖς ἀριστεῦσι τετι[μη]μένον, ἐξαπατήσῃ τινὰ τῶν νέων ὡς προκριθῆναί τινος τέχνης. (9, Barig. 132.2–6) But I’m suspicious only of the occupation of athletes, in that, because it promises them strength of body and offers popular fame, publicly remunerates them with daily gifts of silver in accordance with our ancestors, and honors them as if they were the full equivalent of heroes, it may deceive some young men into thinking that it’s preferable to a (real) art.

From this point Galen constructs an argument in ch. 9 along the following lines: – Humans should try to cultivate their kinship with the gods, not beasts. (9, Barig. 132.8–12) – The excellence of the gods stems from their logos (καθ' ὅσον λογικόν ἐστι), and by implication has nothing to do with bodies or materiality, in contrast to athletes.

7 See De Lacy 2005, 624, comm. ad p. 104.9, which lists the passages throughout Plac. Hipp. Plat., and elsewhere, where Galen discusses both illegitimate and legitimate uses of poetic testimony.

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Athletic training is an art that concerns only the body, which aligns the person with beasts; which is to say, it suggests a largely non-rational life.8 Athletes have nothing useful to contribute to society, and everyone knows, he says, that men are considered excellent not because of their prowess at throwing the discus or at wrestling, but for the “beneficence that derives from their art”. (ἀλλὰ διὰ τὴν ἀπὸ τῶν τεχνῶν εὐεργεσίαν, 9, 132.18 Barig.)

Galen ends this paragraph with a reference to two exemplary figures who straddle the human and divine realms, Asclepius and Dionysus, each of whom invented an art of enormous benefit to humankind, medicine and winemaking, respectively. This is hardly one of Galen’s more rigorous arguments, and most of his premises could be easily enough contested, if one wanted to do so. It seems that Galen sensed this as well, which is why he felt compelled to advert, towards the end of ch. 9, to poetic authority. “If you are not willing to believe me…” (εἰ δ' οὐκ ἐθέλεις ἐμοὶ πείθεσθαι…9, 132.22 Barig.), he says, the reader should at least have some respect for the utterances of the Pythian Apollo, since he has impeccable credentials. Apollo was the one, after all, as Galen points out, who addressed Socrates as ‘wisest’, and praised Lycurgus as god-like in four verses which he then proceeds to quote (9, 133 Barig.).9 The point of this quotation is, however, extremely opaque, and a second one that immediately follows, in which Galen notes that the Pythia referred to Archilochus as a “friend of the Muses”, hardly helps. The opening of ch. 10 finally makes it clear that these verses are supposed to show little more than that great men are referred to as divine by a very authoritative source. He challenges an imaginary adversary here to name any athletes who are given such epithets: λέγε δή μοι καὶ σὺ τὰς τῶν ἀθλητῶν προσαγορεύσεις. ἀλλ' οὐκ ἐρεῖς ὅτι μηδ' ἔχεις εἰπεῖν, εἰ μή τι τοῦ μάρτυρος ὡς οὐκ ἀξιόχρεω κατέγνωκας· (10, 134.7–8 Barig.) Tell me, then, what epithets you use for athletes. And don’t go saying that you have no reply to this – unless you reject as unworthy the evidence from this witness.

The logical bullying here is practically comical, and this may in fact be part of Galen’s intent here: Galen started out wanting to argue that athletes are more bestial than divine, but adduces as a “witness” (martys) oracular citations that say nothing more than that some people who are excellent are called divine. Obviously 8 σώματος δ' ἄσκησις ἀθλητικὴ ἀποτυγχανομένη μὲν αἰσχίστη, ἐπιτυγχανομένη δὲ τῶν ἀλόγων ζῴων οὐδέπω κρείττων (Protr. 9, Barig. 132.12–14). (Athletic training of the body, when it fails, is utterly shameful, and even when it succeeds makes one no better than irrational animals). 9 ἥκεις, ὦ Λυκόοργε, ἐμὸν ποτὶ πίονα νηὸν / Ζηνὶ φίλος καὶ πᾶσιν Ὀλύμπια δώματ' ἔχουσι. / δίζω ἤ σε θεὸν μαντεύσομαι ἢ ἄνθρωπον, / ἀλλ' ἔτι καὶ μᾶλλον θεὸν ἔλπομαι, ὦ Λυκόοργε. (You have come, Lycurgus, to my rich temple / dear to Zeus and to all who hold Olympus. / I’m not sure if I should call you god or man, / but I expect that you’re even more a god, Lycurgus). Herodotus also quoted these lines at I 65.3.

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such ‘evidence’ does nothing to ‘prove’ that athletes cannot also be excellent men, worthy of being called divine as well. Galen must realize this, and so cudgels any antagonist with the Pythia’s very authority. His train of thought runs like this: look at the kind of people that the Pythia calls divine – you will find no athletes in that group; therefore, no athletes can ever be divine. As if bad logic were not enough, Galen then makes the authority of his witnesses a matter of class and culture. For if, he says, this opponent here does reject the authority of the Pythia, (ὡς οὐκ ἀξιόχρεω), it would indicate that he has succumbed to the benighted opinions of “the many”: ἐμφαίνειν γὰρ ἔοικάς τι τοιοῦτον, ὅταν ἐπὶ τοὺς πολλοὺς τὸν λόγον ἄγῃς μάρτυρας καὶ τὸν παρὰ τούτων ἔπαινον προχειρίζῃ. (10, 134.9–10 Barig.) For you seem to imply something of this sort [i.e., that the testimony of the Pythian verses is worthless], when you appeal to the many as your witnesses, and offer your praise [of athletes] based on their opinions.

Galen’s reasoning here is again suspect, but rhetorically powerful: even his antagonist, he goes on to say, would consult only “a few” trained professionals – not “the many” – when he is sick, or needs a builder or shoemaker, so why would he trust the masses, who do not have the knowledge or expertise that his witnesses do? Showing that a doctor is wiser in matters of medicine than a layperson is straightforward enough; but the only claim Galen could make for the superiority of his poetic witnesses is one of tradition, and the cultural assumption that poets are wiser than the common person. There seems no other justification, in any case, for Galen’s next witness (10, 134.18–26 Barig.), nine verses from a now-lost play by Euripides, probably his Autolycus, which begins, “of the thousands of evils throughout Greece, there is none worse than the race of athletes…”, and proceeds to enumerate the familiar complaints against them – their unreflective life, their overeating, and their general cluelessness in life. Two other Euripidean quotations follow (10, 136.1–8 Barig.), one of which Galen even calls “more refined/subtle” (λεπτομερέστερον), each reflecting on the uselessness of athletic training for military service. What follows, however, is striking; it is almost as if Galen felt some guilt at browbeating his imaginary opponent with his poetic authorities, and a need to defend himself. The passage is worth quoting in full: πότερον οὖν Εὐριπίδου μὲν καὶ τῶν τοιούτων καταγνῶμεν, τοῖς δὲ φιλοσόφοις ἐπιτρέψωμεν τὴν κρίσιν; ἀλλὰ καὶ πρὸς τούτων ἁπάντων ὥσπερ ἐξ ἑνὸς στόματος ὡμολόγηται φαῦλον εἶναι τὸ ἐπιτήδευμα. οὐδὲ μὴν οὐδὲ τῶν ἰατρῶν τις ἐπῄνεσεν αὐτό· πρῶτον μὲν γὰρ Ἱπποκράτους ἀκούσῃ λέγοντος ‘διάθεσις ἀθλητικὴ οὐ φύσει, ἕξις ὑγιεινὴ κρείσσων’, ἔπειτα δὲ καὶ τῶν ἄλλων ἁπάντων τῶν μετ' αὐτὸν ἀρίστων ἰατρῶν. ὅλως μὲν οὖν ἐπὶ μάρτυρος οὐκ ἐβουλόμην κρίνεσθαι· ῥητορικοῦ γὰρ τὸ τοιοῦτον μᾶλλον ἢ τιμῶντος ἀλήθειαν ἀνδρός· ὅμως δ' ἐπειδή τινες ἐπὶ τὸν τῶν πολλῶν ἔπαινον καταφεύγουσι καὶ τὴν παρὰ τούτων κενὴν δόξαν, ἀφέντες αὐτὸ ἐπιτήδευμα γυμνὸν τῶν ἔξωθεν σκοπεῖν, ἠναγκάσθην κἀγὼ τούτους προχειρίσασθαι τοὺς μάρτυρας, ἵν' ὅτι μηδ' ἐνταῦθα πλέον ἔχουσί τι γιγνώσκωσιν. (10, 136.8–19 Barig.)

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Should we then condemn Euripides and the testimony of such people, and instead trust in the judgment of philosophers? But they too are absolutely unanimous in considering this practice [athletics] vulgar. Not even has any doctor ever approved of it. For, first off, you can hear Hippocrates saying, ‘The athletic condition is not natural; the healthy condition is better’, and then all the other doctors – the best ones – after him. And so, in the end, I would not want to form a judgment (or, ‘for the matter to be judged’) on the basis of a witness: that is the kind of thing a rhetorician does, rather than one who respects the truth (ῥητορικοῦ γὰρ τὸ τοιοῦτον μᾶλλον ἢ τιμῶντος ἀλήθειαν ἀνδρός). Nevertheless, because some take refuge in the praise other people give them, and in empty glory they get from them, and abandon an unbiased consideration of the practice itself, I am forced in this crowd to offer these kinds of witnesses, so that they will realize that they do not have the upper hand even on this subject.

So now, it seems, Galen is claiming – after having just adduced five poetic citations in the service of his rant against athletes – that he knew all along that this was not an especially legitimate strategy! He was driven to it, however, only because this is how the ignorant masses tend to argue – subjectively, emotionally and without applying objective standards of alētheia. It was a prophylactic move on his part, as he claims, an attempt to beat the enemy at their own rhetorical game, assuming already that true logical argument would get him nowhere with such a crowd. It is very difficult to assess how much of this is meant to be taken ironically, how much seriously. Indeed, it is certainly a familiar enough ploy from satirical genres for writers to offer ironic disclaimers about questionable rhetorical strategies they may adopt, and then turn them against their targets, and there is plenty in Galen that one can call satirical.10 The line between seriousness of purpose and playfulness in such cases is usually very blurry. In Galen’s case, the irony, if not outright contradiction, that arises from his dismissal of the validity of poetic citation, immediately after engaging in the very practice, is itself its own sort of rhetorical strategy, and helps make the larger case of the treatise for the importance of cultivating the literary arts. Literary authors, that is – or at least the ones selected for citation – offered dogmatic versions of the values that Galen wanted to argue for philosophically, and their authority as “enduring classics” afforded them an exemplary, rather than a syllogistic, function. A citation, in other words, could cut straight through an argument to the philosophical pay-off. This is what Galen means, it seems, when he claims that people who fall back on the authority of poets are “rhetoricians” (in the pejorative, sophistic sense): because they tend not to bother with any kind of formal argument, they cannot necessarily be trusted if one is trying to persuade on a given question with an appeal to reason and logic. But this only means that the testimony of poets is not rigorous, not that the conclusions they offer are not valid or even powerful in the way they are expressed. Galen calls popular thinking “empty opinion” (kenē doxa) and claims to be quoting authorities as “witnesses” because this is a strategy that “the many” would understand (since they engage in it themselves). Galen never states what kinds of author10 See Rosen 2008.

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ities the people are quoting for their “praise” (epainos) of athletes, but presumably they are as dogmatic in their own way as those adduced by Galen. Given Galen’s claim in ch. 10 that he was driven to quote authorities by his need to match popular strategies, but otherwise found the practice objectionable, it might give us pause to see that the rest of the treatise is full of similar quotations from poetic authors. At ch. 13 (144.4–5 Barig.), for example, asking what practical good an athlete’s strength is, he even recycles two lines from the quotation from Euripides he used in ch. 10 (about how useless an athlete is against the enemy if he is holding a discus), with this sarcastic introduction, “Again, you can cite Euripides, who will exalt them [athletes] (hymnēsei) by saying…” Another noteworthy poetic quotation occurs at the end of the same chapter (13), where Galen has just finished showing, “clearly” (saphes), as he says, that athletic training provides nothing useful for practical life. As if this is not enough, he then wants to show that there is simply nothing intrinsically worthy of athletics, i.e., that even among themselves their achievements are of no consequence (ὅτι δὲ καὶ ἐν αὐτοῖς, οἷς ἀσκοῦσιν, οὐδενός εἰσιν ἄξιοι λόγου, 14, 146.15–16 Barig.). He says we can “learn this” by recounting a mythos from a poem of one of the “great literary men” (τῶν οὐκ ἀμούσων ἀνδρῶν τις). The poet is unknown, but Galen tells the story, with likely roots in the fable tradition, of a contest pitting animals against humans, in which, of course, humans come off the worst in all areas of competition (14, 146.17–148.9 Barig.). After quoting a few verses, Galen concludes (14, 148.10 Barig.): “In a thoroughly delightful way (pany kharientōs) this story demonstrates that (epideiknusi) athletic strength is not a part of human activity”. Once again, it is difficult to gauge the tone of this passage: it is hard to believe that Galen actually thought that a fable-like story would ‘prove’ anything, especially since comparing human athletics to the physical prowess of animals is an obvious red herring, and the fact that he stresses the kharis of his exemplum may show what his real motivation was – namely, to let a pleasant bit of imaginative literature stand in (in this case, with questionable legitimacy) for an actual argument. The combination of the passage’s kharis and poetic authority with Galen’s own rhetoric, functions, in the end, as a captatio benevolentiae that aligns the sympathies of the reader with Galen, encouraging them to share in the author’s Schadenfreude against his targets and not to worry too much about the strength of the case. Protrepticus has a lighter, more sweeping, theme than most other Galenic treatises, so we can perhaps forgive him for what appears to be a rather cavalier, inconsistent use of literary citation in the work. But he cites poetic authors frequently in more rigorously scientific works as well, and it is worth considering his attitude towards that practice in these contexts. To this end, we may consider the use of poetic testimony in Galen’s major work, Plac. Hipp. Plat., which is full of citations from the classicized poets of his day, as well as plenty of criticism of

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those who misuse them in scientific discourse. We will find here the same ambivalence about the poets as we saw in Protrepticus, but a more consistent application of the device, and a more fully developed critique of its misuse. Plac. Hipp. Plat. is an expansive work ostensibly comparing the opinions of Hippocrates and Plato, but in fact with a special focus on the problem of the nature of the soul, from both behavioral and biological points of view.11 The work as a whole is noteworthy for the amount of poetic citation it contains, partly because his main target throughout, the Stoic Chrysippus, seems to have cited poets frequently in his own work on the soul (which Galen in turn will sometimes cite), and partly because Galen himself found them useful to bolster his own arguments.12 But it is clear that Galen is as fraught as ever about what the poets can offer, and on numerous occasions he even makes this explicit. One revealing example occurs at II 5.94–95, where Galen had actually just endorsed one of Chrysippus’ arguments. The details of the argument need not concern us here, but in general it involves the question of whether speech emanates from the brain or some other part of the body more continuous with its physical manifestation, such as the chest. At 95, Galen says: ταῦτα μὲν οὖν ὀρθῶς εἴρηται τῷ Χρυσίππῳ καὶ διὰ τουτ’ ἄν τις αὐτῷ καὶ μᾶλλον μέμψαιτο, διότι καὶ κατιδὼν τὸ ἀληθὲς ὅμως οὐ χρῆται· τὰ δὲ ἀπὸ τῆς θέσεως ἐπικεχειρημένα καὶ τούτων ὅσα μᾶλλον ποιηταὶ μαρτυροῦσιν ἢ οἱ πολλοὶ τῶν ἀνθρώπων ἢ ἐτυμολογία τις ἤ τι τοιοῦτον ἕτερον, οὐκ ὀρθῶς. κάλλιον γὰρ ἦν ἐπιμείναντα τοῖς κατὰ τὴν ἀποδεικτικὴν μέθοδον ὑποβαλλομένοις λήμμασιν ἐξετάσαι τε καὶ κρῖναι διὰ τῆς αἰσθήσεως. αὐτὸς δὲ ὥσπερ οὐ κατ' ἐπιστήμην, ἀλλὰ κατὰ τύχην εἰρηκὼς τὸ ἀληθὲς ἀπεχώρησέ τε τῆς ζητήσεως αὐτοῦ καὶ ποιητὰς ἐπάγεται μάρτυρας. Now Chrysippus was correct in saying this, and therefore one might blame him the more, because even though he sees the truth he does not use it; but what he said about arguments from position and about those among them that rest for the greater part on the evidence of poets, or the majority of mankind, or an etymology, or something else of that kind, was not correct. He would have done better to remain with the premises supplied by the scientific method, and to examine and judge them through sense perception. It is if he had spoken the truth not from knowledge, but by chance; of his own accord he abandoned the investigation of it and brings in poets as his witnesses (tr. De Lacy 2005).

This is part of a long, belabored theme that comes and goes throughout Plac. Hipp. Plat., as Galen works his way through Chrysippus’ arguments about how various bodily functions relate to the soul. Galen’s major complaint against Chrysippus’

11 See De Lacy 2005, 48–50, for an account of Galen’s organization of Plac. Hipp. Plat.. See also Hankinson 1991 and Donini 2008, 186–91. 12 Galen cites an impressive range of canonical Classical poets in the course of Plac. Hipp. Plat., although the bulk of the quotations are taken from either Homer, mentioned by name 17 times, or Euripides, 15 times (and these poets are also quoted many other times when their names happen not to be mentioned). See Tieleman 1996, 219–48, on Stoic (and specifically Chrysippus’) use of poetry for philosophical purposes.

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use of poetic testimony is that he adduces passages that are either irrelevant to his argument or actually work against it. His comment at Plac. Hipp. Plat. III 8.28, for example, at the end of a long discussion of Chrysippus’ analysis of the myth of Athena’s birth, is typical: ἐχρῆν γὰρ αὐτὸν ἢ μηδ' ὅλως ἧφθαι τοῦ μύθου μηδέν γ' ἀναγκαῖον ἔχοντος ἀνδρὶ φιλοσόφῳ πρὸς ἀπόδειξιν δόγματος, ἢ ἁπτόμενον, ὅπερ ἦν μάλιστα τὴν ἀντιλογίαν συνέχον, ἀκριβῶς ἅπαν διεξελθεῖν, εἰ καὶ πλειόνων ἔχρῃζε λόγων, οὐκ ὀκνήσαντα τοὺς πολλοὺς προσγράψαι. Either he should not have used the story at all, as it does not contain anything necessary to a philosopher for the proof of a doctrine; or in using it he should have dealt carefully and exhaustively with the point that was the crux of the contradiction, and even if it required a rather full discussion, he should not have hesitated to add it. (tr. De Lacy 2005)

The issue at hand here was the nature of psychic pneuma, whether it originates in the hearts and travels up to the brain, or vice versa. Chrysippus felt this could be illustrated – with a little finessing of the details – allegorically with the myth of Athena’s birth. Galen found Chrysippus’ analysis of the myth wanting, deems it irrelevant, as we can see from the passage just quoted, but then proceeds in sections 29–32 to show how one could (as Galen puts it) “bring the myth in line with the facts” if one wanted to:13 ὥστ' εἴ τις βούλοιτο τοῖς ἀληθέσι συνάπτειν τὸν μῦθον, ἐν τοῖς κάτω μέρεσι κυηθεῖσαν τὴν φρόνησιν, τουτέστι τὸ πνεῦμα τὸ ψυχικόν, ἐν τῇ κεφαλῇ φήσει τελειοῦσθαι καὶ μάλιστά γε κατὰ τὴν κορυφήν, ὅτι κατὰ ταύτην ἐστὶν ἡ μέση καὶ κυριωτάτη τῶν ἐγκεφάλου κοιλιῶν. Therefore, if a person wishes to fit the myth with the facts, he will say that wisdom, that is, psychic pneuma, after being conceived in the lower parts, reaches full development in the head, especially the top of the head, because that is the location of the brain’s middle and most important ventricle. (tr. De Lacy 2005)

Here we have another amusing – doubtless intentionally so – example of Galen’s competitive bravado in manipulating non-scientific literary discourse. He immedi13 Chapter 8 of Plac. Hipp. Plat. III is largely given over to Chrysippus’ allegorizing of a Hesiodic version of the birth of Athena (although the lines Galen quotes are only preserved here; cf. De Lacy 2005, 640 comm. ad p. 226.4–22). Chrysippus wanted to argue that when Zeus swallowed Metis, and Metis became pregnant with Athena, the fact that Athena is said to have been born from the head of Zeus was an allegorical façon de parler: wisdom comes out of one’s mouth, which is located in one’s head, but the ‘gestation’ and ‘birth’ of wisdom can be said to take place internally, in Zeus’ belly, where, according to the theogony that Galen quotes from Chrysippus’ text, Metis “lay in hiding” (Plac. Hipp. Plat. III 8.13, p. 226.12). This interpretation would allow Chrysippus somewhat more easily to maintain that the rational part of the soul is located in the heart. But Galen just finds this to be special pleading, presumably because the myth so clearly offers the image of Athena (‘wisdom’) coming forth from Zeus’ head (the brain as seat of reason). At sections 29–32, Galen then proceeds to interpret the myth (“to make the myth fit the facts”) as an allegorical reflection of “psychic pneuma”, engendered in the “lower parts” of the body, pumped up from the heart through the arteries to the ventricles of the brain, where it completes its development.

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ately catches himself, however, and makes it clear that such allegorizing, even if properly done, is more ornamental than essential to an argument. He makes this point by citing Socrates’ famous dismissal of the practice in Plato’s Phaedrus (229d3-e4), when Phaedrus had asked Socrates about the myth of Boreas and Orithyia. Quoting Socrates’ words in this passage, Galen says that he considers such interpretations of myth “as otherwise charming”, but the mark of an “excessively ingenious and laborious, and not entirely enviable man” (“τὰ τοιαῦτα” πάντα μυθολογήματα “ἄλλως μὲν χαρίεντα ἡγοῦμαι, λίαν δὲ δεινοῦ καὶ ἐπιπόνου καὶ οὐ πάνυ εὐτυχοῦς ἀνδρός”, Plac. Hipp. Plat. III 8.33), in the end, not worth the time and effort it would take to sort out all the details.14 Galen concludes: “Chrysippus should have read this passage and then abandoned myths, and he should not have wasted his time explaining his hidden meanings … It would be better,” he says, “for the man who really seeks the truth not to ask what the poets say; rather he should first learn the method of finding the scientific premises (τῶν ἐπιστημονικῶν λημμάτων)” that is, to be able to know when it is legitimate to use premises from sense-perception, experience, from life, from the arts, and from intellection (τίνα μὲν ἐξ αἰσθήσεως ἁπλῆς, τίνα δ' ἐξ ἐμπείριας ἤτοι τῆς κατὰ τὸν βίον ἢ τῆς κατὰ τὰς τέχνας, τίνα δὲ ἐκ τῶν πρὸς νόησιν ἐναργῶν χρὴ λαβόντα περαίνειν ἐξ αὐτῶν ἤδη τὸ προκείμενον, III 8.35.10). This training, Galen says, would have led Chrysippus to the truth, not the poets, myths and non-experts “whom he quoted as friendly witnesses in his first book on the soul” (οὓς ὡς ἑαυτῷ μαρτυροῦντας ἐν τῷ προτέρῳ περὶ ψυχῆς ἔγραψε, Plac. Hipp. Plat. III 8.38). This stance by now will feel familiar enough: a cocky, satirical Galen lording his methodological superiority over a long-dead, and so defenseless, author. Indeed, this attitude directed specifically against Chrysippus permeates Plac. Hipp. Plat. But it is worth emphasizing that what Galen really objects to is not so much Chryisppus’ integration of poetic testimony into his scientific arguments, as his misuse of them; what really irritates Galen is that Chrysippus wastes everyone’s time with poets and myths because he misunderstands their relevance to his arguments. Time and again in Plac. Hipp. Plat. we find Galen explaining what Chrysippus’ misunderstood poetic exempla do show, and this involves him in the same sort of poetic explication that he found misapplied in his predecessor. At Plac. Hipp. Plat. IV 6.18–38, for example, in a discussion of the difference between passions (pathē) and errors (hamartēmata) of the soul as the forces that account for a person’s bad behavior, Galen objects that Chrysippus misreads the cause of Medea’s crime in Euripides’ play. Galen is here quarreling with Chrysippus over whether “passions” are “judgments” (kriseis) (cf. esp. Plac. Hipp. Plat. IV 6.10), which is to say, whether they are rational elements that have somehow gone bad

14 Galen continues with Socrates’ complaint in the Phaedrus passage that myths involve so many fantastic and absurd creatures that one would need ‘a lot of leisure time’ to make allegorical sense out of all of them (…πολλῆς αὐτῷ σχολῆς δεήσει, Plac. Hipp. Plat. III 8.34).

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(as Chrysippus), or a distinct part of the soul entirely different from reason (as Galen). Galen notes at IV 6.19 that Chrysippus had quoted Euripides, Medea 1078– 1079 to make his point: “I understand the evils I am going to do / but anger prevails over my counsels” (καὶ μανθάνω μὲν οἷα δρᾶν μέλλω κακά, / θυμὸς δὲ κρείσσων τῶν ἐμῶν βουλευμάτων). Galen never says that a quotation from Euripides “proves nothing” (vel sim.) about human psychology, but instead he proceeds to offer (IV 6.20–27) his own analysis of the verses, designed to show that Medea’s crime must have been caused by something very different from a judgment, i.e., a pathos that works against one’s rational decisions. Galen would never regard the testimony of poets as a substitute for “doing science”, but there can be no question that he felt the poets important as a part of the rhetoric of science.15 At the same time, however, he never completely abandoned a hint of skepticism, even cynicism, at times, about how scientific writers adduced the poets. At Plac. Hipp. Plat. III 2.18, for example, again taking Chrysippus to task for his undiscriminating approach to poetic evidence, Galen says that anyone familiar with many poets will know that “sooner or later, in some verse or other, they are witnesses to all doctrines”.16 He makes this revealing statement after having quoted some of Chrysippus’ citations of Hesiod: ἐν οἷς ἐγὼ μὲν ἐκπλήττομαι τῆς μεγαλοψυχίας τὸν Χρύσιππον. δέον γὰρ ὡς ἄνθρωπον ἀνεγνωκότα τοσούτους ποιητὰς καὶ γιγνώσκοντα σαφῶς ἅπασι τοῖς δόγμασιν αὐτοὺς μαρτυροῦντας ἄλλοτε κατ' ἄλλα τῶν ἐπῶν, ὥσπερ καὶ Πλούταρχος ἐπέδειξεν ἐν τοῖς τῶν Ὁμηρικῶν μελετῶν, ἐκλέγειν μὲν ἐξ αὐτῶν ὅσα μαρτυρεῖ τῷ σπουδαζομένῳ πρὸς αὐτοῦ δόγματι, παραλείπειν δὲ τὰ μαχόμενα καὶ πᾶν ἐνίοτε κατασκευάζοντα τοὐναντίον· ὁ δ' ὁμοίως ἑξῆς ἁπάντων μέμνηται. In these citations I am amazed at Chrysippus’ loftiness of mind. Being a person familiar with the work of so many poets and knowing perfectly well that sooner or later, in some verse or other, they are witnesses to all doctrines, as Plutarch also showed in the Homeric Studies, Chrysippus should have selected from them whatever supports the doctrine he favors and omitted lines that disagree and at times prove the contrary view; but he quotes all alike, one after another.

And perhaps even more startling is when Galen as much as says (III 3.2) that, when a poet presents conflicting views on a given topic, the truer position will be the one that is represented by the greater number of passages! It has to be said, I think, as passages like this make clear, that Galen was not an especially sensitive or insightful reader of poetry, but he had internalized its cultural authority so thoroughly, as Protrepticus makes clear, that he could draw on it for its rhetorical power, even in the context of scientific argument, which privileged a very different form of authority, with different standards of inference and truth.

15 In this regard, Galen surely owed much to Stoic conceptions of to pithanon; see Tieleman 1996, 264–87. 16 See also Tieleman 1996, 244–45.

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Bibliography Texts quoted Barigazzi, A. 1991. Galeni, De optimi codendi genere; Exhortatio ad medicinam (Protrepticus). Berlin (= CMG V.1.1). Boudon-Millot, V. 2007. Galien, vol.1: Sur l’ordre de ses propres livres; Sur ses propres livres; Que l’ excellent médecin est aussi philosophe (Ord. Lib. Prop.; Lib. Prop.; Opt. Med.). Paris (ed. Budé). Boudon-Millot, V., & J. Jouanna 2010. Galien: Ne pas se chagriner. Paris. De Lacy, P. 2005. Galeni, De Placitis Hippocratis et Platonis [= Plac. Hipp. Plat.], ed., transl. and comm. 3 vols. (vol. 1 3rd ed., vols. 2 and 3 2nd ed.), Berlin: Akademie-Verlag (= CMG V.4.1.2).

Works quoted De Lacy, P. 1966. “Galen and the Greek Poets”. In: Greek, Roman and Byzantine Studies 7, 259– 266. Donini, P. 2008. “[Galen’s] Psychology”. In: Hankinson 2008, 104–209. Fabricius, C. 1972. Galens Excerpte aus älteren Pharmakologen. Berlin. Hankinson, R. J. 1991. “Galen’s Anatomy of the Soul”. In: Phronesis 36.2, 197–233. Hankinson, R. J. (ed.) 2008. The Cambridge Companion to Galen. Cambridge. Nightingale, A. W. 1992. “Plato’s Gorgias and Euripides. Antiope: A Study in Generic Transformation”. In: Classical Antiquity 11, 121–141. Nightingale, A. W. 1995. Genres in Dialogue: Plato and the Construct of Philosophy. Cambridge. Nightingale, A. W. 2004. Spectacles of Truth in Classical Greek Philosophy: Theoria in its Cultural Context. Cambridge. Nutton, V. 1997. “Galen on Theriac: Problems of Authenticity”. In: A. Debru (ed.), Galen on Pharmacology: Philosophy, History and Medicine. Leiden, 133–152. Rosen, R. M. 2010. “Galen, Satire and the Compulsion to Instruct”. In: M. Horstmanshoff (ed.), Medical Education: Selected Papers Read at the XIIth International Hippocrates Colloquium Universiteit Leiden 24–26 August 2005. Leiden, 325–342. Tielemann, T. L. 1996. Galen and Chrysippus on the Soul: Argument and Refutation in the De placitis Books II–III, Leiden. Vogt, S. 2005. “…“er schrieb in Versen, und er tat recht daran”: Lehrdichtung im Urteil Galens”. In: T. Fögen (ed.), Antike Fachtexte/Ancient Technical Texts. Berlin, 51–78. von Staden, H. 1998. “Gattung und Gedächtnis: Galen über Wahrheit und Lehrdichtung”. In: W. Kullmann et al. (eds.), Gattungen wissenschaftlicher Literatur in der Antike. Tübingen, 65–94.

Ineke Sluiter

The Violent Scholiast: Power Issues in Ancient Commentaries 1

Abstract: In this paper I will explore the power dynamics between commentator and source text. While the commentator will usually present his work as an effort to bring out the true meaning of the source text, in fact, the commentator clearly exerts considerable power in defining the meaning and importance of the source text, and in establishing just who the author of that source text ‘really’ was. It will turn out that commentators are aware of the possibility to conceptualize the relationship between commentator and source in terms not just of power, but even of violence. For obvious reasons, however, they shy away from using that terminology for their own work, reserving it to describe the efforts of their competitors. The ‘violent commentator’ thus becomes a foil against which the self-fashioning of the commentator takes place. Special attention will be paid to commentators’ strategies of appropriation that tend to focus on ‘first words’ and beginnings in general, the ideal locus to manifest the power and authority of the commentator. Since this paper will discuss a generic feature of widely divergent types of commentaries, my material will consist of a number of different ancient commentaries, specifically Homeric scholia and texts by Galen.

1 Introduction: who is in control? At first sight, undertaking to write a commentary is an act of supreme humility. The commentator puts his best efforts at the service of elucidating an admired author and claims to be no more than an instrument to do full justice to the source. To give just one example: Galen claims that the commentator of Hippocrates should aim to bring out Hippocrates’ intention (gnōmē). What the exegete says should both be consistent with the author’s text and it should be true. The tacit assumption is that the coincidence of these two elements is the ideal situation.2 1 A first version of this paper was presented to the Cambridge Laurence Seminar 2000 on ancient scholia. I would like to thank the participants, particularly organizers Pat Easterling and Franco Montanari, for their helpful and stimulating criticism. I am also grateful to the members of the Amsterdam Hellenist Club for their lively discussion of and useful comments on an earlier draft of this paper. This paper is part of my research project on ancient commentaries, on which I am preparing a monograph. 2 Cf. Sluiter 1998, 16f.; Galen, In Hipp. Epid. III Comm. I, 17A.507 Kühn. For the gnōmē of the author (even if false) as aim of the commentator, cf. Galen, In Hipp. Progn., 18B.17f. Kühn. For gnōmē and usefulness as the combined aim, cf. Galen, In Hipp. Epid. I Comm. I, 17A.6 Kühn. The ‘tacit assumption’ that what the author means will also be true is part of the ‘Principle of Charity’ (Sluiter 1998).

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In reality, however, the power dynamics between source and commentary is far more complex than this simple picture suggests. In this paper, I will focus on those power issues in ancient commentaries where it is clearly the commentator who has the upper hand. In particular, after a first exploration of the issues involved (section 2) and the role of commentaries in cultural survival (section 3), I will look at how commentaries deal with the beginnings of their source texts, and how they thus establish themselves as a (literally and figuratively) overwhelming presence from the very start (section 4). But I will not only be interested in such actual instances of power play on the part of the commentator, but also in the question of whether and how power and violence were connected to notions of interpretation in antiquity itself. This will be the topic of section 5. As my primary examples, I will look at the scholia and other forms of commentary on Homer and demonstrate how they appropriate the Homeric text to further their own goals, how they define what counts as an educated command of those texts, and how they betray an awareness of the possibility to conceptualize the relationship between commentator and source in terms of power and violence. For additional examples, I will look at some medical and philosophical commentaries. My claim is that the issue I am describing here is a general feature of the commentary genre.

2 The powerful commentator A priori there is no reason why we should accept the commentators’ rhetoric about their supportive and even submissive attitude towards their source. It is easy to see that the source is effectively powerless to defend itself against potential misrepresentation by the commentator (wilful or otherwise) of its aims, objectives, contents, and methods. This is a problem for any written text, as Plato’s Socrates eloquently points out in the Phaedrus (275e).3 Even given the best intentions of the commentator, the danger of such misrepresentation cannot be avoided. Secondly, the commentator will put his source in a one-down position as soon as he undertakes to write his commentary, by the very fact that such an activity seems necessary. Apparently, the source was not ‘good enough’ to convey unaided whatever it meant to convey. If the commentator needs to come to the rescue, that puts the source text in the position of the weaker party, in need of support and protection.4 This perspective is the negative corollary to the notion that a text is so good and important that it ‘deserves’ a commentary (the basis for canonization).

3 Plato, Phaedr. 275e: a written logos cannot select its audience with care; it will speak to everyone. πλημμελούμενος δὲ καὶ οὐκ ἐν δίκῃ λοιδορηθεὶς τοῦ πατρὸς ἀεὶ δεῖται βοηθοῦ· αὐτὸς γὰρ οὔτ’ ἀμύνασθαι οὔτε βοηθῆσαι δυνατὸς αὑτῷ. 4 Cf. Sluiter 1998; 2000, 187–189.

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A third way in which the power balance between commentator and source is tipped in favor of the commentator becomes visible when the commentator in fact clearly does have objectives of his own, and employs the source to further those goals. The value attached to tradition made the commentary a popular vehicle for scholarly discussion: the choice for the commentary genre meant that the commentator wanted to be seen as part of and heir to a tradition, and usually such a commentator would try to appropriate the authority of the source text for the views he himself wanted to espouse in a process of creative interpretation.5 Galen, for example, frequently claims that his own, most recent, medical insights can in fact already be found in Hippocrates, if only one knows how to read him correctly. Astronomers, mathematicians, scholars interested in harmonics, philosophers and doctors chose en masse for the genre of the commentary rather than that of an independent treatise to get their ideas across; frequently, they would use this as an opportunity to show that they were themselves backed by the greatest authorities in the field. A fourth and notable power issue has to do with the often overwhelming amount of annotation and secondary material provided by the commentator, which tends to physically overpower and obscure the source text. In papyri and codices with marginal commentary, this is manifest in the lay-out of the page, with often a rather small block of source text hemmed in on all sides by a plethora of scholiastic information and criticism.6 But stand-alone commentaries can be even worse. From the late Hellenistic period onwards, the commentators developed their own set of generic expectations. A commentary would have prolegomena, discussing a number of the issues (increasingly standardized) that a reader was supposed to familiarize himself with before engaging the original text – or the actual commentary on the original text.7 These often substantial introductions created a major physical obstacle between the reader and the source text. As we will see, once the patient reader made it to the beginning of the source text itself, he would be confronted by the densest and most intense amount of annotation anywhere in the whole commentary. Commentaries were (and are) not always designed to leave maximum space and breathing room to the original texts: instead, they can be heavily invested in making their own claim to fame fast and massively. Finally, there are the details of this process of appropriation and authoritative self-presentation, which also suggest that the commentators exert a form of power 5 Cf. Mansfeld 1994, 26; 155ff. et saep. for this notion. 6 Gumbrecht 1999; 2003, 44ff. discusses the ‘marginal’ physical presence of the commentary (suggesting support function), and the physical limitation of space on the page, but also the requirement of copia ‘fullness’. 7 Cf. for the topical nature of these introductions Plezia 1949; Mansfeld 1994; Copeland & Sluiter 2009, 49. These prolegomena are a form of what Genette 1997 would call ‘paratext’ within the ‘metatextual’ genre of the commentary: one has to get through these before even getting to the commentary itself. In this way different layers of text are interposed between the reader and the source text.

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over their source.8 It is the commentator who selects the parts of the source text that he deems worthy of commentary.9 Lemmatic commentaries fragment and atomize the texts into manageable bits and take them on in these small chunks at a time. The commentator determines what questions are worth discussing, and which ones will be passed over in silence. The emphasis and preferences of the commentary may misrepresent the primary thrust of the source text, a process observable in commentaries on literary texts just as much as in ‘scientific’ commentaries. To illustrate this, let us recall the mostly didactic purpose of commentaries: they are used as a study tool.10 In dealing with a poetic text like Homer’s, one of the goals of the commentator (but not necessarily of the poet) is to increase the students’ knowledge of grammar and rhetoric. Interestingly, what we see happen in these commentaries is not only that the commentators tend to identify strongly with the poet (as when they try to give voice to what they perceive as the poet’s ideas): they also tend to make the picture symmetrical. This means that they will provide a picture of Homer as a proto-teacher of grammar and rhetoric; they will create a poet in their own image and make him resemble themselves. This procedure then provides us with a Homer intent on teaching grammar and rhetoric. The commentators will not just point out features in the Homeric text that illustrate certain grammatical or rhetorical phenomena, but they explicitly ascribe the intention to teach rhetoric and the rest to Homer himself. The former activity would just be an instance of the commentary exploiting the source text for certain purposes that contemporary society may deem desirable, without making any claims about Homer’s own intentions. The latter strategy creates a colleague-teacher in the language disciplines. One example must suffice here:11 in the first book of the Iliad, Achilles tells his mother the story of his conflict with Agamemnon, part of which is a literal repetition of an earlier part of the book, where that same story was told in the voice of the Homeric narrator.12 Here is how one scholiast explains this phenomenon (Schol. Hom. A 366a bT): ῥητορικὸς ὢν ὁ ποιητὴς καὶ τρόπον ἀνακεφαλαιώσεως βουλόμενος διδάξαι ἡμᾶς ταὐτὰ πάλιν ἐξ ἀρχῆς διηγεῖται. Because the poet is interested in rhetoric and wants to teach us the figure of recapitulation, he tells us the same thing again from the beginning.

8 See also Most 1999, x-xi. 9 This choice is often dictated by what the commentator perceives as the needs of his audience. The ideal commentary after all bridges the gap separating new readerships from the original texts. 10 Cf. Sluiter 1999. 11 For this strategy and the example, cf. Sluiter 1999 (here at 179). 12 Homer, Il. I 366ff., cf. I 12ff.

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Homer is here credited with a didactic intention – instruction in the effective use of language – properly belonging to the grammarian/commentator only. The commentator has recreated Homer in his own image. In all the ways discussed above, the relation between source text and commentary is twisted to the advantage of the commentary: rather than being defended by the commentator who ignores his personal interests in the service of the source text, the source cannot in fact defend itself against its commentators, who turn the source into an instrument to demonstrate the indispensability of the commentary, the importance and legitimacy of the commentator’s project, or the validity and venerable old age of ideas offered by the commentator – whether or not such ideas truly correspond with the views of the source author.

3 Commentaries and cultural survival Commentaries are obviously linked to processes of canonization. In selecting a text as the object of a commentary, the commentator acknowledges the special status of that source text, thereby either initiating or confirming a process of canonization. Knowledge of the source apparently counts as a form of cultural capital and the commentary claims to facilitate the acquisition of that knowledge.13 At the same time, it also defines the nature of that knowledge by determining what it is, precisely, that counts as ‘knowing a text’. If one sees culture as an evolutionary process, what we are witnessing here is a special form of survival of cultural information. Whereas elements of popular culture may survive from one generation to the next by a simple process of imitation without much institutional support, the preservation of other bits of cultural information is strongly promoted by a welldeveloped educational system, which will help define what counts as cultural literacy in a given society.14 In the case of our canonical texts with commentaries, the transmission and continuing accessibility of the original text is being secured through the commentary in a process of selective retention of some of the various interpretations and uses that the source text offers.15 The commentary itself sur13 Cf. Bourdieu 1984, 11ff. and passim. 14 Hirsch 1987 gives a fascinating overview of the units of cultural information, often isolated from their original contexts, that are supposed to form the mental furniture of an adequately culturally literate American. He does not use Dawkins’ term ‘meme’, although his description strongly evokes it (see the next note). 15 We may compare Dawkins’ use of the term ‘meme’ for the ‘unit of cultural transmission’. His examples of memes include tunes, ideas, catch-phrases, clothes fashions (1976, 206). Dawkins 1982, 109 draws a clearer distinction between the postulated ‘meme’ itself (the replicator that is the cultural equivalent of the gene in natural evolution), with a definite structure ‘realized in whatever physical medium the brain uses for storing information’, and the ‘phenotypic effects’ or ‘meme products’ (the ways in which a meme expresses itself (words, music, visual images etc.)). However, in common usage the term ‘meme’ (however imprecise) has come to be used for these phenotypic effects.

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vives through its symbiosis with the source text or, as the case may be, as its parasite. Some commentary genres do not even require the independent survival of the original text: the commentary absorbs so much of the source text that it can be read independently and hence survive on its own.16 However, if one thinks in these terms of cultural survival, commentaries are not just passive co-survivors, but they play an interesting double role. On the one hand, they embody survival in an educational environment: a text, any text, will clearly need readers to remain fully alive in the bloodstream of a culture. Obsolete texts ‘die out’. A commentary testifies to its author having patiently worked his or her way through an original text (and a body of secondary literature), and having appropriated that text, having made it ‘his (or her) own’, while making the results of his or her reading available to other students. The text to which the commentator devotes himself is temporarily brought back to life: at least for as long as the commentator is alive, the source text is part of the cultural bloodstream of that generation. The commentary aids in the cultural transmission of its source, and tries to survive, either symbiotically or as a parasite, itself.17 A modern parallel is the novel Fahrenheit 451 by Ray Bradbury, who paints a dire picture of a society in which firefighters are employed to torch libraries and destroy books, and where a small group of brave volunteers try to ensure the survival of the texts by memorizing a book each. Every book needs a live ‘carrier’ to remain alive itself.18 So the commentary helps to guarantee the survival of the source text. But on the other hand, we are also dealing with a power issue here in that the commentary is not identical to the source text. It offers a specific reading of the original to prospective students, not necessarily the original itself. Insofar as commentaries are indicative of student use of a text, they both define units of cultural transmission (‘one ought to know this text’), and redefine and transform them (‘knowing this text means knowing x’). In that sense the commentary helps produce the adaptations (the adaptive readings) that guarantee optimal fitness for the source, while at the same time ensuring the contemporary relevance of the commentary itself.

16 The best example of this is the medieval summa, which can be used as a stand-alone textbook. It quotes or summarizes the argument of the source text in such a way that no separate reference to that source text is necessary. The earliest example is the Summa super Priscianum by Petrus Helias, the commentator on Priscian, around the middle of the 12th century. See Copeland & Sluiter 2009, 444–460. For an evolutionary vision on commentaries, see also Sluiter 1998. 17 Cf. Sluiter 2000, 188. 18 My regretted former teacher Simon Slings once remarked that if necessary under those conditions he would take it upon himself to represent the pseudo-Platonic Clitopho, on which he had written his doctoral dissertation.

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4 Transformation and appropriation: commentary on opening words One way to illustrate this transformation and the power issues involved in it is to wonder about the empirical fact that commentaries are always at their densest and fullest at the very beginning. Of course many factors play a role here: the same phenomena need not be discussed over and over again, and impatience and boredom may also play a role, but it seems fair to assume a great eagerness to fully occupy and claim the territory of the source text right from the start. That is the place to assert one’s own claims to authoritative expertise against those of scholars who may have rival claims to be the ultimate spokesperson for the source author. The famous opening words of the Iliad and the responses they provoked may serve as an example. There can be very little doubt that the opening lines of the Iliad were a powerful unit of cultural literacy. Anyone with even the most superficial acquaintance with Greek (popular or highbrow) culture would (or should) have been able to come up with μῆνιν ἄειδε, when challenged, or to recognize those verses or any allusion to them. Under those circumstances one might have thought that these words could almost be passed over in silence in a commentary or a series of scholia, if one assumes the purpose of the latter to be to bridge the gap between the original audience and the (later) reader of a text – and this is, after all, one of the ways to define the work of a philologist. However, when one checks the scholia and the epimerisms, one finds the very opposite. Not only are the scholia and epimerisms unusually numerous here, but in addition they seem to represent virtually every possible approach one could take to these verses, at least – and this is the crucial point to which I will return – if one took a scholarly interest in them. The scholia on the first verse of the Iliad fill four pages in Erbse’s edition, and the epimerisms on the same verse take up fourteen pages in Dyck’s edition.19 The very first scholion (AT) raises the following questions, initially presented in the form of a ζήτημα, the heuristic instrument of ancient philologists: why does the work start with a name of bad omen, μῆνις? Several explanations are suggested, the first of which hints at Aristotle’s theory of κάθαρσις and then proceeds in rhetorical terms: such a beginning, the scholiast claims, makes the audience more attentive (προσεκτικωτέρους), a standard function of the prooemium according to rhetorical theory. A second explanation is that saying something ‘bad’ about the Greeks in the beginning will make the later laudatory statements about the victori-

19 Of course I realize that Erbse and Dyck have brought together any scholia they could find on these verses: an ancient reader of the beginning of the Iliad, who was using an annotated text, would not have been confronted with the same overwhelming number as we are. However, it seems certain that any commentary he used would have commented on these verses at some (considerable) length, and that suffices for my argument.

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ous party all the more credible (πιθανώτερα) – again an explanation based on a rhetorical strategy, that of aiming for probability. Several other opinions are strung together after these first two: μῆνις is simply the main theme and subject-matter (ὑπόθεσις) of the poem;20 we witness Homer’s invention of the tragic proem, because (?) the narrative of misfortunes makes us (once again) attentive (προσεκτικούς); and Homer behaves like a great doctor in first provoking the afflictions of our souls only to heal them later (note how there is again a link with the genre of tragedy). A last note in the first compound scholion in Erbse’s edition refers to the various degrees of anger, apparently distinguished by how ‘old’, or inveterate, the emotion is, as expressed by the Greek words ὀργή, θυμός, χόλος, κότος, μῆνις. These different stages are compared to figs at different stages of cultivation, or maybe rather of ripeness. The scholiast notes, incidentally, that Homer does not always keep the different terms apart. In the following scholia several more questions are raised: why doesn’t Homer start at the beginning? Why isn’t the work called the Achilleia, like the Odysseia (Schol. Hom. A 1b, bT). What is the verbal origin of the word μῆνις? (The scholiast derives it from μένω, no doubt because it was supposed to indicate ‘lasting’ anger). What is the correct word accent? (Schol. Hom. A 1c, AbT). Schol. Hom. A 1d (AT) turns to the second word, ἄειδε, and notes the use of the imperative instead of the optative, which one would not expect in a prayer to a goddess.21 Apart from numerous parallels for this instance of poetic licence or usage, the scholiast also offers an alternative solution: in reality, the poet may not be addressing the Muse, but himself. Schol. Hom. A 1e (1 and 2, bT) identify a different problem in the same word: apparently, what the poet means is not ‘sing’, but (a causative) ‘make me sing’. The scholiast also makes the subtle suggestion that in the Iliad, ‘singing’ is apparently called for in the proem, because there will be a lot of misery, and singing brings pleasure; whereas in the Odyssey, with a superb story-teller for its main character, ἔννεπε ‘tell’ is the better choice. The next scholion explains that it is normal to call the Muse ‘goddess’ (Schol. Hom. A 1f, bT), and that, in spite of some critics’ view, an address of the Erinys would be uncalled for. And on and on it goes, word by word: Schol. Hom. A 1g-i (AT) are all concerned with the words Πηληιάδεω Ἀχιλῆος, about which we learn that ‘Peleiad’ is a derivative noun, and that the genitive of Achilleus should be spelled with one lambda here, both metri causa and because of various etymologies of the name: he brings misery (ἄχος) to the Trojans (Ἰλιεῦσιν), or he never ((privative) α-) touched mother’s milk with his lips (χείλεσι).22 All of these remarks concern just the first (and we might think fairly unproblematic) verse, parsed word for word. We see a constant pattern here: a problem 20 For the use of this term, cf. Meijering 1987, 122ff.; Nünlist 2009, 24 n. 5. 21 The point was apparently first made by Protagoras, on whom see below at n. 23. 22 οἱ δὲ παρὰ τὸ μὴ θιγεῖν χείλεσι †τροφῆς†. ὅλως γὰρ οὐ μετέσχε γάλακτος. The alpha of Achilles is to be deduced from μὴ θιγεῖν (which paraphrases the alpha privans).

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is formulated and solutions for it are offered, that is, the same text (the commentary) both sets the problem, and hence defines what it is that we should consider a problem, and gives the answer. The commentator thus determines what kind of knowledge it takes to (truly) grasp the text. I will not deal with everything the epimerisms have to say about the first verse, but just about the first two words (μῆνιν ἄειδε) there are eleven pages of notes, specifying the exact morphological classification of the two words, and everything there is to know about their derivation, spelling, accent, declination or conjugation, and meaning, with the same information about related or similar words thrown in for good measure, everything abundantly illustrated with examples. We also hear about words in different dialects. The information is highly technical and its density is intimidating. The very point of these exercises seems to be to redefine a piece of popular culture and transform it into the object of ‘higher cultural studies’. If the student looked at the first verse of the Iliad in happy recognition and confident that this part at least he knew, he was in for a surprise. As it turned out, he did not know the first thing about these verses. The scholiasts are not inventing this strategy here. On the contrary, they are in effect inserting themselves into a long tradition of making good use of the symbolic value of classical opening words. This symbolic value creates the opportunity for the shock effect at the very beginning of the commentators’ work, when they redefine something seemingly simple and familiar as something problematic and difficult. Protagoras had done the very same thing, turning to this very same verse (and in fact, becoming the source of the scholion discussed above), when he problematized the use of an imperative to address a goddess (thus inaugurating speech act theory), and when he questioned the legitimacy of the grammatical gender of μῆνις, apparently struck by the discrepancy with the (biologically) male characteristic denoted by the word.23 The first comment reveals something very significant: unless to someone who knows and uses the grammatical term ‘imperative’ (or in Greek ἐπίταξις (ἐπιτακτικός)), there would not have been a problem with ἄειδε.24 Before the invention of the grammatical category and term ‘imperative’, to a Greek this would simply have been the normal and in fact most frequent form to use in a prayer in Greek epic. It is the development of the study of language and hence of grammatical metalanguage itself that 23 For the distinction of speech acts by Protagoras, cf. Diogenes Laertius IX 53f.; for his criticism of the imperative, see Aristotle, Poet. 19.1456b15ff.: τί γὰρ ἄν τις ὑπολάβοι ἡμαρτῆσθαι ἃ Πρωταγόρας ἐπιτιμᾷ, ὅτι εὔχεσθαι οἰόμενος ἐπιτάττει εἰπὼν μῆνιν ἄειδε θεά; τὸ γὰρ κελεῦσαι, φησίν, ποιεῖν τι ἢ μὴ ἐπίταξις ἐστιν. For the gender of μῆνις (and πήληξ), see Aristotle, Soph. El. 14.173b17ff. (on soloecism): ἔστι δὲ τοῦτο καὶ ποιεῖν καὶ μὴ ποιοῦντα φαίνεσθαι καὶ ποιοῦντα μὴ δοκεῖν, καθάπερ ὁ Πρωταγόρας ἔλεγεν, εἰ ὁ μῆνις καὶ ὁ πήληξ ἄρρεν ἐστίν· ὁ μὲν γὰρ λέγων οὐλομένην σολοικίζει μὲν κατ’ ἐκεῖνον, οὐ φαίνεται δὲ τοῖς ἄλλοις, ὁ δὲ οὐλόμενον φαίνεται μέν, ἀλλ’ οὐ σολοικίζει. It is likely that Protagoras was also commenting here on the authority of Homer, and its relation to truth. Cf. De Jonge & Van Ophuijsen 2010, 489–490; Rademaker (forthcoming) discusses these Protagorean remarks in connection with Protagoras’ philosophical views. 24 This issue was first brought to my attention by the late Professor Kees Ruijgh.

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made Protagoras’ problem conceivable. The distinction of the very names of εὐκτική and προστακτική (for the optative and imperative mood respectively), or εὐχή and πρόσταξις for the types of speech ‘prayer’ and ‘command’ apparently created the concomitant expectation of a clear distribution in actual language use: the former (and no other) should always be used in prayers, and the latter (without alternative) in commands. The distinction of the grammatical terminology itself could thus create a perception of incongruity in cases where πρόσταξις, with its top-down implication, was seen to be used to address the gods. The critic defines the problem and establishes an answer. Incidentally, the very fact that someone like Protagoras had discussed and criticized the form of expression of this verse made it almost inevitable that there would be further scholarly accretions: the cumulative nature of commentaries is one of their most persistent traits. Once raised, a question is most unlikely to be dropped from the scholarly repertoire.25 The temptation to say something new and original about the very beginning of a popular work must have been hard to resist.26 Seneca reports (disdainfully) that the grammarian Apion (who in antiquity seems to have stood for the perversion of everything a scholar should be)27 interpreted the first two letters of μῆνιν, the opening word of the Iliad, as a secret code used by Homer to indicate that he had written 48 (μη') books – probably and hopefully a facetious argument in the debate over whether or not Iliad and Odyssey had been composed by the same author.28 The obsessive questions raised by the grammarians also lent themselves to parody and clever inversion: the narrator of Lucian’s True History reports that when he was visiting the Isles of the Blessed he availed himself of the opportunity to ask Homer in person why he had started the Iliad with the word μῆνιν. The startling answer was that it had simply occurred to Homer to do so: no special reason!29 In his eleventh oration, Dio Chrysostom supports his outrageous attempt to prove that Troy never fell to the Greeks with an appeal to the proem of the Iliad. Supposedly, Homer had not quite made up his mind as to how bold he could get in his lies when he started the poem, so at least in the first five verses he is straightforward about what really happened: the gist of the story, says Dio, is the misery and losses of the Greeks.30 The interest in first lines and first verses comes close to being a universal in commentary production: Servius’ commentary on Virgil’s Aeneid book I discusses 25 Cf. Sluiter 2000, 191. 26 On ancient ‘memoria incipitaria’ and the high recognition value and memorability of first lines as a factor in intertextual allusions, see Conte 1985; 45–64; 1986, 35; 70; 76–87. 27 Cf. Damon 2008. 28 Seneca, Ep. mor. 88.40. 29 Lucian, Var. Hist. II 20. I was reminded of this passage by Barbara Graziosi. 30 Dio Chrysostom, Or. 11.35f., esp. 36: ἐνταῦθά φησι περὶ μόνης ἐρεῖν τῆς τοῦ Ἀχιλλέως μήνιδος καὶ τὰς συμφορὰς καὶ τὸν ὄλεθρον τῶν Ἀχαιῶν, ὅτι πολλὰ καὶ δεινὰ ἔπαθον καὶ πολλοὶ ἀπώλοντο, καὶ ἄταφοι ἔμειναν, ὡς ταῦτα μέγιστα τῶν γενομένων καὶ ἄξια τῆς ποιήσεως, καὶ τὴν Διὸς βουλὴν ἐν τούτοις φησὶ τελεσθῆναι ὥσπερ οὖν καὶ συνέβη. This is a close paraphrasis of Iliad I 1–5.

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on average 3.5 verses per page of commentary; however, the first eleven verses are discussed in eleven pages of commentary (1:1). It is interesting that Servius borrows the question of why Virgil started with arma from Homeric scholarship – Servius has to reject the question as nonsensical, since arma was not originally the first word of the Aeneid (Servius accepts the story that Tucca and Varius, Virgil’s editors, threw out the original beginning).31 Examples of overwhelming density of commentaries at the very beginning of the source text can easily be multiplied.32 Homer remains a special case because his poetry is the primary object of the teaching of the grammatikoi, the language teachers. In fact, the occupation and appropriation by the grammarians of Homer’s text, right from its very first verses, was so complete and successful that the first words of the Iliad, and more in general, its first five lines, became emblematic of the work of the grammarian. This is a most remarkable thing and worth pondering: the very words μῆνιν ἄειδε can be used to evoke, not the Iliad as such, but the work and profession of the grammarian. It is no coincidence that in his attack on the grammarians, Sextus Empiricus uses the first line of the Iliad to demonstrate that the concept of ‘parts of speech’, one of the foundational notions of the art of grammar, is incoherent.33 This would have been the very first line any student had to parse (i.e. divide into ‘parts of speech’). In a number of mocking epigrams, grammarians are ridiculed for their pedantry, poverty, and hard-handed pedagogy (as well as for more general traits such as poor looks, general detestability, deviant sexual behavior and unhappy marriages): the vehicle for these sentiments is precisely a parodistic use of these verses.34 Here is one example of why it is impossible for a grammarian to be a good-natured or happy fellow (Anth. Gr. IX 173, Palladas):35

31 See Copeland & Sluiter 2009, 124ff., esp. 129. 32 In the corpus of commentaries on Aristotle, see e.g. Ammonius, In Arist. Cat., Comm. Arist. Gr. 4.4, who offers almost six pages of commentary on Aristotle, Cat. 1a1 (15.3–20.12), with a much lower density and skipping of lines in the rest of the commentary; Simplicius, In Arist. Cat., Comm. Arist. Gr. 8 offers 7.5 pages on the same line, with the same lower density and skipping of lines later on. In Galen’s Hippocrates-commentaries we see the same phenomenon: Galen, In Hipp. Epid. I Comm. I, has 28 pages for the first chapter (17A.15–37 Kühn), with 45 pages for the remaining 37 chapters. And he spends eleven pages, more than on almost any other aphorism, on the very first of Hippocrates’ Aphorisms I 1 (17B.345–356 Kühn); cf. Sluiter 1995, 196ff. Hippocrates’ Greek does not play a role in ancient literary criticism with the exception of that very first aphorism, which is mentioned by Ps.-Demetrius, De elocutione 4. 33 Sextus Empiricus, Adv. math. I 131–140 (Blank’s commentary at Adv. math. I 133 recognizes the use of the first verses of the Iliad as a standard example); cf. Adv. math. VIII 80–82, and especially IX 350–351, where Sextus argues that μῆνις is not a ‘part’ of the first verse. 34 Cf. Brecht 1930, 36f.; Sluiter 1988, 59–61. 35 Cf. Anth. Gr. IX 174 (Palladas): Ἐνθάδε παιδεύουσιν ὅσοις κεχόλωτο Σάραπις/τοῖσιν ἀπ’ οὐλομένης μήνιδος ἀρχομένοις. Other μῆνιν epigrams are, e.g. Anth. Gr. IX 168, 169; XI 279 (Palladas), 400 (Lucianus), 401 (Lucilius – where the target is not the grammarians themselves, but a doctor who refuses to have his son educated beyond verse three of the Iliad (πολλὰς δ’ ἰφθίμους ψυχὰς Ἄιδι προίαψεν) because he realizes that as a doctor he is perfectly capable of

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Ἀρχὴ γραμματικῆς πεντάστιχός ἐστι κατάρα· πρῶτος μῆνιν ἔχει, δεύτερος οὐλομένην, καὶ μετὰ δ’ οὐλομένην, Δαναῶν πάλιν ἄλγεα πολλά· ὁ τρίτατος ψυχὰς εἰς Ἀίδην κατάγει· τοῦ δὲ τεταρταίου τὰ ἑλώρια καὶ κύνες ἀργοί· πέμπτου δ’ οἰωνοί, καὶ χόλος ἐστὶ Διός· πῶς οὖν γραμματικὸς δύναται μετὰ πέντε κατάρας, καὶ πέντε πτώσεις, μὴ μέγα πένθος ἔχειν; The origin of grammar is a five-line curse: the first has ‘wrath’, the second ‘accursed’. After ‘accursed’ again ‘the Danaans’ many woes’. The third line takes ‘the souls to Hades’; ‘Prey’ and ‘swift dogs’ belong to the fourth, to line five ‘birds of prey’ and ‘the anger of Zeus’. How is it possible for a grammarian after five curses and five ‘cases’ not to have great sorrow?

Note how the appropriation is enunciated quite clearly right from the start: the five verses are no longer defined as the opening of Homer’s Iliad, but they are the beginning of grammar itself. One could counter that this transformation of what μῆνις evokes is what gives the epigram its rhetorical and humorous force, but it seems to me that, quite to the contrary, the associations of μῆνις with grammar are the presupposition shared by poet and audience. The rhetorical punch consists in the supposed effect of the ‘five curses’ on the character, attitudes, and, in fact, life of the grammarian. The poem is reminiscent of the scholiasts’ worry over the ominous beginning of the Iliad. The last two verses play on the sound-effect of πέντε, πέντε, πένθος. Πτῶσις is often used in these verses on grammarians: it is the technical term for ‘case’, of course,36 but its etymology lends itself to various kinds of wordplay: here, the association is probably ‘downfall’, elsewhere it may also have sexual overtones.37 To sum up: grammarians and other commentators (both in their work on Homer’s Iliad and other texts) systematically transform and redefine cultural capital such as ‘the Iliad’ to encompass knowledge as they and the tradition they are working in choose to define it. For Homer, for instance, this transformation entails

teaching his son how to send souls to Hades himself, cf. Sluiter 2010, 25); see further Sluiter 1988, 59. 36 All five cases of the noun do indeed occur in the first five verses of the Iliad (but the poet of the epigram makes no attempt to preserve them in his paraphrase). 37 Cf. Anth. Gr. XI 139 (Lucilius), which plays on several words that are both grammatical technical terms and allow a sexual interpretation.

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knowledge of grammar, especially prosody and morphology, meter, and rhetorical and literary criticism. The commentator thus stakes out a domain where the educated person’s knowledge of, for example, the opening line of the Iliad, is clearly marked off from that of the layman. As Teresa Morgan rightly explains,38 education has a vested interest in creating its own sets of standards, which are not readily attainable without having followed its curriculum. Political and institutional factors come into play here. The educated man’s μῆνιν ἄειδε encodes a body of knowledge that is a far cry from the ability of the man in the street simply to memorize, quote or recognize the verse. The power balance between source text and commentary is clearly tipped in favor of the latter.

5 Violent interpretation I have saved for this last part of my paper the most obvious category of exercising power: the use of violence. What I will be looking at in this section is the configuration of ancient discourse on ‘violent interpretation’.39 I will show that ‘violence’ is indeed a category used by ancient exegetes in thinking about possible relations between source text and commentary or interpretation. For obvious reasons, this category is invoked especially in criticizing competing interpretations of the source text, on which the critic claims particular and exclusive competence:40 it is a label used to dismiss readings of a text that one personally rejects. ‘Violent interpretation’ in the strong sense refers to the purposeful and wilful distortion of a text to suit the purposes of the interpreter; in a weaker sense, it means forcing an interpretation on the source text that is unwarranted by its internal rules or logic.41 In the latter case, it need not be attributed to any criminal intent on the part of the

38 Morgan 1998, e.g. 170, 175f., 188 (on how knowledge of ‘language’ is redefined as it gets turned into ‘grammar’; Morgan works within the theoretical framework of Bourdieu (e.g. 1984) in this book). 39 In our own time, the violence of (any) interpretation has been topic of discussion ever since Sontag 1967. 40 See Sluiter 1998, where a similar case of different types of rhetoric used for the source text and for the competition is illustrated. For the source text the interpreter uses the Principle of Charity; harsh criticism is mostly reserved for the interpreter’s competition. 41 In Plato’s Sophist 241d, exceptionally, the term βιάζεσθαι is self-attributed, not without irony: in order to defend his position, the Eleatic Stranger claims it will be necessary to apply some force (βιάζεσθαι) to ‘what is’ and ‘what is not’ so that ‘what is not’ is in some respect, while ‘what is’ is not in some way (βιάζεσθαι τό τε μὴ ὂν ὡς ἔστι κατά τι καὶ τὸ ὂν αὖ πάλιν ὡς οὐκ ἔστι πῃ). The force is here applied to what a concept (τὸ ὄν, τὸ μὴ ὄν) means, although obviously the text by Parmenides is in the background. βιάζεσθαι is deemed necessary in order to try and preserve the internal consistency of the argument. Creating a forced consistency (as a reproach) also appears in Plato, Crat. 436cd … εἰ γὰρ τὸ πρῶτον σφαλεὶς ὁ τιθέμενος τἆλλα ἤδη πρὸς τοῦτ’ ἐβιάζετο καὶ αὑτῷ συμφωνεῖν ἠνάγκασεν.

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exegete, but may be caused by ignorance and lack of understanding. I will give an overview of the relevant features of this discourse of ‘violence’ here, and add a series of illustrative texts in an appendix. Before turning to the notion of violence in engaging a text, it is worth reminding ourselves of the traditional relationship between bia and logos, which is often rather one of opposition than connection: Philoctetes is to be brought to Troy either through violence or by verbal persuasion.42 But from Gorgias onwards, the idea that words can be a form of violence also crops up regularly.43 In Plato’s Republic, Thrasymachus tells Socrates that he will not be able to get away unnoticed with ‘doing violence through words’, i.e. forcing Thrasymachus’ hand through dialectic.44 One can get carried away by words violently.45 And Aeschines accuses Demosthenes of using ‘verbal force’.46 In Aristotle, slander (κακηγορία) is considered a ‘violent’ (βίαια) form of private transaction.47 Βίαιος even becomes something of a technical term in rhetorical theory. It is used to designate an argument ‘which turns what appears to be a strong point in the opponent’s position to one’s own advantage’. And it also applies ‘more generally to tendentious or strongly assertive arguments’.48 Hermogenes uses the term βίαιος ὅρος ‘forcible definition’ for a ‘Head, in which facts used by one party to characterize an action in one way are used paradoxically by the other to give an opposite characterization’.49 In all of these cases, words can be a form of violence, but what we will be looking for specifically in the rest of this section is a form of violence that has a text as its object. The earliest texts that discuss doing violence to a text are not themselves commentaries: they form part of judicial rhetoric, but they do deal with the interpretation of laws and decrees. Attic orators may warn the jurors of the attempts of their adversaries to distort (διαστρέφειν) the laws to their own advantage. They apply their tricks (τέχνας) to the laws and attempt to annihilate them

42 Sophocles, Phil. 563: ἐκ βίας … ἢ λόγοις. The many examples include Euripides, Suppl. 347 λόγοισι πείθων, εἰ δὲ μή, βίαι δορός; Isocrates 4.40.2 μετὰ λόγου καὶ μὴ μετὰ βίας διαλύσασθαι τὰ πρὸς ἀλλήλους; Plutarch, Vita Num. 12.4.1 καὶ γὰρ εἰρήνην Ἕλληνες καλοῦσιν ὅταν λόγῳ, μὴ βίᾳ, πρὸς ἀλλήλους χρώμενοι λύσωσι τὰς διαφοράς. 43 In Gorgias’ Helen 6, various factors are investigated that would exculpate Helen. After an initial opposition between βία and λόγος (ἢ βίᾳ ἁρπασθεῖσα ἢ λόγῳ πεισθεῖσα), the λόγος part is worked out in 8–14. Logos is a great potentate (δυνάστης μέγας), and in 12 it turns out to exercise such an irresistible force that the difference with actual violence is elided. 44 Plato, Res publ. 341b οὔτε μὴ λαθὼν βιάσασθαι τῷ λόγῳ δύναιο. 45 Plato, Leg. 701c βίᾳ ὑπὸ τοῦ λόγου φερόμενον. 46 Aeschines 3.72 καὶ τέλος ταῦτ’ ἐνίκα, τῷ μὲν λόγῳ προσβιασαμένου Δημοσθένους, τὸ δὲ ψήφισμα γράψαντος Φιλοκράτους. 47 Aristotle, Eth. Nic. 1131a8–9. 48 Heath 1995, 254 (Glossary). Hermogenes, Peri Stas. 3.110 49 Heath 1995, 254 (Glossary). Cf. Hermogenes, Peri Stas. 73.16–74.4, esp. 74.1–4.

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through their words (ῥήμασι τοὺς νόμους ἀναιρήσειν), or to make justice disappear (ἀφανιεῖν).50 In the commentary tradition, the terms used most often in the context of ‘violent interpretation’ are βία and cognates (βίαιος, βιαίως, βιάζομαι etc.). As the examples in the Appendix show, an interpretation may be applied βιαίως, ‘in a forced way’, both to the wording of the text (lexis) and to its meaning. Commentators are accused of ‘using force or violence’ (βιάζεσθαι), the result of their work (e.g. the resulting prosody) may be called ‘forced’ (βίαιος), and they themselves may be styled ‘violent’ (βίαιος).51 But the semantic field of violent interpretation comprises more words: one scholion states that interpreters who ‘fight’ (μάχεσθαι) the obvious meaning of a text, are ridiculous.52 And in fact, when Plato had talked about ‘coming to the rescue’ (βοηθέω) of a written logos, and of its inability to ‘defend itself’ (ἀμύνεσθαι), a similar notion of violence seems to be in the air.53 The discourse of ‘violence’ also plays a role in the well-known agonistic tone which ancient scholars adopt throughout their work to disparage their rivals. Often such disparagement is phrased in other terms, as when opposing views are called ‘absurd’ (ἄτοπον), and the competitors themselves are γελοῖοι, as we just saw. Galen also frequently calls the views of the competition absurd (προφανῶς ἄτοπον) and nonsense (ληρώδης).54 But βία-words also occur: for an author like Apollonius Dyscolus, the phrase πῶς οὖν οὐ βίαιον … (‘how can it not be forced, then, [to say] …’), may be just another put-down for his adversaries.55 However, it is still worth paying attention to the semantic fields to which different terms of disparagement belong. Accusing other exegetes of the use of ‘violence’ indicates an awareness of the applicability of this category to the relationship between commentator and source. The opposite would be to make it the purpose of the commentary simply to bring

50 Cf. Isocrates 11.4 σὺ δ’ ἀνάβηθι δεῦρο, ἐπειδὴ δεινὸς εἶ διαβάλλειν καὶ τοὺς νόμους διαστρέφειν; Aeschines 3.35 his opponent ἐποίσει τέχνας τοῖς νόμοις; 3.16 judges, please show my adversary ὅτι οὐ προσδέχεσθε κακοῦργον σοφιστὴν οἰόμενον ῥήμασι τοὺς νόμους ἀναιρήσειν; Isocrates 8.1 his adversaries hope to τὰ ἐκ τῶν νόμων δίκαια τοῖς σφετέροις αὐτῶν λόγοις ἀφανιεῖν. Examples derived from Hillgruber 1988, 105–20 (Anhang: Gesetzesinterpretation bei den attischen Rednern). 51 βιάζεσθαι, e.g. Schol. Hom. T 94a (A); βιαίως, e.g. Schol. Hom. Ξ 221a (Α); βίαιος (prosody), e.g. Schol. Hom. E 329a (A); βίαιος (commentator), e.g. Schol. Hom. B 865 (A). 52 Schol. Hom. Ξ 437a (A) γελοῖοι δὲ οἱ τοῖς φαινομένοις μαχόμενοι. For fuller quotation, see Appendix. 53 Plato, Phaedr. 275e, see at n. 3. 54 E.g. Galen, In Hipp. Aph. 17B.870f. Kühn: the fact that the text is ‘nonsensical’ and its contents ‘obviously absurd’ are reasons for Galen to reject the authenticity of the aphorism discussed here. 55 Cf. e.g. Synt., Grammatici Graeci II.ii, 48.12; 327.11 Uhlig. Uhlig comments (on Synt. 365.4): de grammaticis qui contra sermonis leges et rationem aliquid contendunt βίαιον saepius legimus apud Apollonium … de opinionibus, quae contra rationem pugnant.

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out the γνώμη of the author, as we saw above (n. 2):56 the commentator who sticks to that principle makes his own interests subservient to those of his source, the commentator who uses violence exercises a destructive power over his source text. Galen adds even more colorful language to the discourse of ‘violent interpretation’. He uses the verbs λυμαίνομαι ‘to treat like dirt’, and λωβᾶσθαι ‘to abuse, to maltreat’, and he adds the idea that the violent commentator may corrupt the text itself (by simply changing it) rather than just distorting the interpretation.57 Galen offers a particularly good example of the idea that destroying, i.e. corrupting, a text ultimately equals corrupting or destroying the ideas conveyed by that text, and hence ruining the γνώμη of its author, the goal of a responsible commentator. The term for this kind of violence is διαφθείρειν:58 εἰ δ’ ἔξεστι προστιθέναι τοῖς καταφατικῶς εἰρημένοις ἀποφάσεις, ἅπαν οὕτω τις διαφθείρει δόγμα καὶ γνώμην οὐδεμίαν φυλάξει τῶν παλαιῶν βεβαίαν. If one can add negatives/negations to positive statements, one will destroy all teaching and will not preserve intact any opinion of the ancients.

However, for the idea that a misguided interpretation is a destructive force and ultimately a form of ‘killing’ the author, we can actually once again go back all the way to Plato, this time to his Protagoras. The setting also shows that interpretation in antiquity is a matter of competition. Protagoras and Socrates have had to be prodded to continue their discussion, and Protagoras opens what is now a testing of strength by introducing poetry as the new arena in which to debate virtue (Prot. 339a3ff.). When Socrates admits that he approves of a certain poem by Simonides, Protagoras demonstrates that the poet in fact contradicts himself. Socrates feels, he says, ‘as if I had been hit by a good boxer’ (ὡσπερεὶ ὑπὸ ἀγαθοῦ πύκτου πληγείς, 339e1f.), implying that he and Protagoras are at this point locked in an almost physical battle, and that the criticism of Simonides, with whom he had aligned himself, feels as a personal blow. Stalling for time, he turns to Simonides’ compatriot Prodicus, and implores him to come to Simonides’ rescue (βοηθεῖν τῷ ἀνδρί, 340a1): what Protagoras did is construed as an attack. Prodicus is called

56 A frequent term used to designate a ‘good’ interpretation is ὑγιής ‘sound’, obviously deriving from the semantic field of ‘health’. It is not a pure antonym to βίαιος, therefore, although the opposition could work through a middle term such as κατὰ φύσιν. 57 Galen, In Hipp. Epid. VI Comm. I (17A.793 Kühn): εἰς τὸ ἕκτον τῶν ἐπιδημιῶν Ἱπποκράτους συγγραμμάτων ἐλυμήναντο πολλοὶ τῶν ἐξηγητῶν, ἄλλος ἄλλως, ὡς ἕκαστος ἤλπισε πιθανῶς ἐξηγήσασθαι, τὴν κατὰ τοῦτον λέξιν ὑπαλλάττων. Galen, Adv. Lycum (18A.196f. Kühn): Λύκος τοίνυν ἔγραψε μὲν ἐξηγητικὰ τῶν Ἱπποκράτους ἀφορισμῶν ὑπομνήματα, λωβᾶται δὲ τοῖς δόγμασι τἀνδρὸς ἑκατέρωθεν οἷς τε ψέγειν καὶ οἷς ἐπαινεῖν τινα τῶν ἐπ’ αὐτοῦ λεγομένων οἴεται καὶ δι’ ὧν ἀντιλέγειν ἐπιχειρεῖ. 58 Galen, In Hipp. Epid. VI Comm. II (17A.993 Kühn). For γνώμη as the σκοπὸς τῆς ἐξηγήσεως, see Galen, In Hipp. Epid. III Comm. I, 17A.507 Kühn, and supra n. 2. This Galenic nexus between ruining a text and ‘destroying’ an author is investigated in Sluiter 2010, esp. 48–49.

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in to help (παρακαλεῖν) μὴ ἡμῖν τὸν Σιμωνίδη ἐκπέρσῃ ‘lest Protagoras completely destroy Simonides for us’ (a7). The verb ἐκπέρθω has strong associations with violence and is normally used of the destruction of an enemy city after a siege.59 The way to save Simonides is to show that he did not, in fact, contradict himself. Simonides and his poem are exchangeable here, and the implication is clear: interpretation can be utterly destructive, destructive interpretation is ascribed to someone else, and interpretation can be a matter of competitive performance, and hence a form of aggression (the blow of a boxer). In Socrates, the saving grace in his use of ἐκπέρσῃ is its patent and ironic hyperbole. Galen is in dead earnest.

6 Conclusion In this paper I have looked at the power dynamics between commentator and source. Although the rhetoric of most commentators puts the source in the dominant position, in fact the balance is tipped in favor of the commentator in a number of ways: the source is ‘defenseless’, it is supposed to need a commentary, the commentator is in a position to further his own goals through the commentary, and he can retroject his own interests into the text he is studying. The commentary may overwhelm the source, and choose what body of knowledge the source is supposed to represent. Although the presence of the commentary proves that the source text is being kept alive as a piece of cultural capital (in that sense the commentary can function as a survival machine for the ‘original’), the chances of survival for the commentary increase with the importance of the source text, so that the commentary is both survival machine and symbiotic ally of the source. The commentary does not just transmit cultural information, it also transforms and redefines it. What is transmitted in the scholia on Homer, for instance, is not so much (knowledge of) the Iliad, but a body of knowledge belonging to the intellectual domain of the grammarian, poetry as grammar. It is that specific knowledge as much as the poetry itself that is transmitted to later generations. Being an educated man may be defined on a rather modest level by having knowledge of the Iliad, but at a more advanced level one is expected to understand not just what μῆνιν ἄειδε means, but also why those words and not others open the poem, and one should be able to deal with a whole array of technical information. Only then can one be considered to ‘know’ the field of knowledge that is still called the Iliad, but that is in fact defined by its teachers, the grammarians/scholiasts/commentators. It is obviously important for a commentator to commit this ‘coup’ of transforming a poetic text into an archive of technical knowledge straightaway. It is also 59 Its use may have been provoked by the use of πολιορκούμενον that just precedes it, describing the situation in which Scamander found himself when he was beleaguered by Achilles (Plato, Prot. 340a).

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necessary for the author of a metatext (scholion, commentary) to stake out his own claims of expertise right at the beginning of his text, to disparage the competition, and to demonstrate surprising new insights. This explains why the beginning of any source (first word, first line, first chapter) attracts such heavy exegetical artillery. In the case of the grammarians, their successful appropriation of the (poetic) texts appears from the fact that the first five verses of the Iliad are often an effective allusion, not to the poem that they derive from, but to the art of grammar itself. Power relationships such as these turn out to be part of the ancient conceptualization of the work of the commentator. This is most obvious from the fact that they even use the discourse of ‘violence’ (the extreme form of power) in discussions of how the source text is handled in interpretation. Distortion and annihilation of the laws by one’s adversary in a court of law is a topos among the Attic orators. The notions of violence, force, maltreatment, or treating a text like dirt are used to disparage one’s intellectual opponents or competing interpreters. ‘Violent interpretation’ is deemed so socially and intellectually undesirable that it is not normally self-ascribed, but reserved for evaluations of the work of others. Only ironically does anyone use it to describe his own activities, and not surprisingly, we seem to find this ironic use only in Plato (n. 41). And while Socrates claims with ironic hyperbole that Protagoras will ‘completely destroy’ Simonides, unless he comes to the rescue, Galen cannot see the humor of this: destroying a text means destroying the author.

Appendix: some examples βιαίως Schol. Hom. Ξ 221a (Α): ἄπρηκτόν γε νέεσθαι· τούτεστι πορεύεσθαι· οὕτως Ἀρίσταρχος. Δημήτριος (fr. 15 St.) δὲ “γενέ〈ε〉σθαι” ἀντὶ τοῦ γενήσεσθαι, βιαίως πάνυ· οὐδὲ γὰρ τὸ πυθέεσθαι (B 119 al.) πυθέεσθαι γίνεται οὐδὲ τὸ λαβέσθαι λαβέεσθαι, ἵνα καὶ τὸ γενέσθαι (Γ 323 al.) γενέεσθαι γένηται. In this text, νέεσθαι is first paraphrased by πορεύεσθαι, which is Aristarchus’ solution. Demetrius suggests not reading word division between γε and νέεσθαι, and to regard the resulting γενέεσθαι as a future tense.60 The scholiast objects on the grounds that no other thematic aorist infinitive undergoes such ectasis to produce the form of a future infinitive. That is why he calls the reading ‘utterly forced’.

60 Cf. Schol. Hom. Ξ 221b (bT): … ἀντὶ τοῦ ὑποστρέψειν· οὕτως Ἀρίσταρχος· τινὲς δὲ τὸν γενέεσθαι μέσον μέλλοντα ἐξεδέξαντο διαλελυμένως (‘in uncontracted form’), ὡς τὸ κρανέεσθαι (I 626)· γείνω γὰρ γενῶ γενοῦμαι γενεῖσθαι, διαίρεσις γενέεσθαι. Note that the future of γίγνομαι (γενήσομαι) does not occur in Homer, who uses the subjunctive instead (οὐδὲ γένηται, e.g. Od. VI 201, XVI 437).

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The implication seems to be that the absence of a relevant analogy makes this reading wilful and not defensible by argument.

βιάζομαι Schol. Hom. T 94a (A): ἀθετεῖται ὡς περισσὸς καὶ κακοσύνθετος· τί γὰρ ἄλλο δύναται ποιεῖν ἡ Ἄτη ἢ βλάπτειν; οὐχ ὑγιῶς δὲ οὐδὲ τὸ ἕτερον τέτακται· ἔδει γὰρ ἄλλον. βιάζονται δέ τινες τὸν Ἀγαμέμνονα λέγειν ἐφ’ ἑαυτοῦ καὶ τοῦ Ἀχιλλέως· καθολικὸς δέ ἐστιν ὁ λόγος· κοινότερον γοῦν εἰπὼν ἐπὶ τὸν ἡγεμονικώτατον Δία ἀνῆλθεν. καὶ ὅλως παρῴδηται ἐκ τῶν Λιτῶν [sc. IX 507]: βλάπτουσ’ ἀνθρώπους· αἱ δ’ ἐξακέονται ὀπίσσω. In Iliad XIX 86ff., Agamemnon tries to argue that he is not to blame for the fight with Achilles, but that it was all the fault of Ate, who walks over the heads of men: (vs. 94) βλάπτουσ’ ἀνθρώπους· κατὰ δ’ οὖν ἕτερόν γ’ ἐπέδησε. The scholiast comments that the verse is being athetized because it is redundant and poorly composed. What else could Ate do but inflict damage? He also finds fault with the use of ἕτερον (one of two): one would have expected ἄλλον, since a transition is made here to the example of how even Zeus could not resist Ate (this interpretation may be borne out by the Homeric sequel: vs. 95 begins with καὶ γάρ). Apparently, some critics tried to save the verse and to defend ἕτερον, but the scholiast is critical of their efforts, stating that they ‘make the forced claim’ (βιάζονται) ‘that Agamemnon is talking about himself and Achilles’.61 In fact, however, the verse has a wider application, as appears from the transition to Zeus. In this instance, the critic would like to excise the verse, and he labels as ‘violent interpretation’ a competitor’s fanciful (‘forced’) attempt to defend the reading. There is one other use of βιάζομαι in the Homeric scholia which may refer to a ‘forced interpretation’. In Iliad XXI 328ff. Hera urges Hephaestus to set fire to the river Xanthos, who is threatening Achilles. The boiling of the river is compared in XXI 362f. to a pot in which a tender juicy hog is cooked (ὡς δὲ λέβης ζεῖ ἔνδον, ἐπειγόμενος πυρὶ πολλῷ / κνίσην μελδόμενος ἁπαλοτρεφέος σιάλοιο). The scholion Φ 363e (Gc) focuses on κνίσην μελδόμενος. If this is the correct reading, Comanus thinks μελδόμενος is used in an active sense as the equivalent of τήκων. Peisistratus and Hermogenes, however, argue that the text should read κνίσῃ μελδομένου … σιάλοιο (so that the hog cooks in its own fat). Reading μελδόμενος would mean that the pot was melting (οἱ δὲ πεποιήκασι τὸν λέβητα τηκόμενον)! Hermogenes explains the erroneous reading from the old spelling ΜΕΛΔΟΜΕΝΟ (without the υ). When the text was transliterated into new spelling, the copyist did not realize

61 In his commentary on Homer, Iliad XIX 94, Leaf also points out the possibility of ἕτερον referring to each of the parties in a conflict, but such a veiled allusion to Achilles’ part of the guilt does not seem to sit well with the sequel.

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that the omikron stood for ου, ended up with an incomprehensible text, and ‘emended’ to μελδόμενος. Hermogenes also addresses the claim that the mediopassive form would be equivalent to the active here. Although there are cases for which this is true (e.g. λοιδορούμενος instead of λοιδορῶν, or πεπληγυῖα instead of πλήσσουσα), there is an important dissimilarity between those cases and the present one: βιάσεται γὰρ λέγειν “ὡς δὲ λέβης πυρὶ πολλῷ τήκων”, κωλυούσης τῆς ἐπιφερομένης λέξεως· ἔσται γὰρ ἀσύνετον τὸ σιάλοιο. (The construction of σιάλοιο becomes a problem for Hermogenes in this interpretation of μελδόμενος because he reads κνίσῃ, not κνίσην.) In this sentence, βιάσεται is probably passive (equivalent to the more usual βιασθήσεται). It refers to the exegete whose hand is forced into reading something that cannot be construed, because the next word prevents it. It is that tension and the impasse that ensues that explain why the exegete ‘is forced’: nobody would willingly embrace an impossible solution. If the verb were active, the grammar would be odd indeed: we would then have to assume that the object of βιάσεται (and subject of λέγειν) (either ‘we’ or ‘Homer’) is irregularly left out. A remarkable instance of the verb βιάζομαι occurs in the scholia on Pindar, where it is pointed out that Pindar is willing to ‘do violence’ to the myth when it suits his purpose.62 Here the ‘violence’ is perpetrated by the poet under discussion rather than by a (competing) interpreter.

βίαιος In Schol. Hom. B 865 this word is used to designate ‘violent’ critics.63 It is also used to describe the ‘forced’ or ‘violent’ prosodic effects postulated by some critics, 62 Cf. Nünlist 2009, 179 n. 20 and 261 on Schol. Pind. I 1.15b (on the number of Geryon’s dogs: ἔθος τῷ Πινδάρῳ πρὸς τὸ ἑαυτοῦ συμφέρον καὶ τὰς ἱστορίας βιάζεσθαι). Nünlist suspects the use of βιάζεσθαι may sound harsher than is meant. On the other hand, the willingness of a poet to ‘force’ his material if it suits his purpose chimes in with the unwillingness to make a move in their texts that would have forced them to ‘destroy the story’ (λύειν τὴν ὑπόθεσιν, ἀναιρεῖν τὸν μῦθον). Cf. Meijering 1987, 118f.; Nünlist 2009, 66–68; Aristotle, Poet. 1460a33. 63 Schol. Hom. B 865 (A) {τῶι} Γυγαίη τέκε λίμνη· ἄνευ τοῦ ι, Γυγαίη τέκε λίμνη, ἡ κατὰ Ἀρίσταρχον εἶχε διόρθωσις. οἱ δὲ περὶ Χαῖριν (fr. 1 B.) καὶ Διόδωρον καί τινες τῶν καθ’ ἡμᾶς προστιθέασι τὸ ι, ἵν’ 〈ᾖ〉 λίμνῃ ἔπι Γυγαίη τέκε, †κακῶς†· μηδέποτε γὰρ Ὅμηρον λιμνῶν τέκνα ἱστορεῖν. βίαιοι δέ εἰσιν. The text in Homer discusses the mother of the two leaders of the Maeonians, τὼ Γυγαίη τέκε λίμνη ‘the two of whom were borne by the lake Gygaea’. The scholiast defends the reading λίμνη (nom.) as opposed to λίμνῃ (dat.), the latter being proposed by Chaeris and Diodorus c.s., and by some of the scholiast’s contemporaries. On the latter reading, Gygaea would have given birth ‘in’ or ‘on the border of’ a lake, rather than being a (nymph of a) lake herself. Their motivation is that Homer never records children of lakes. But these critics are called βίαιοι. Κακῶς is strange in its present position: the reading with ι is certainly being rejected (so in that sense κακῶς is appropriate), but it looks as if κακѿς is in the wrong place, since the μηδέποτεsentence explains the motivation of those who want to read the ι rather than motivating its

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for instance the synaloephe that becomes necessary if we accept the emendation of κρατερώνυχας ἵππους into κρατερωνύχεσ’ ἵπποις, proposed by Zenodotus.64 A ‘violent’ or ‘forced’ interpretation is flagged by πῶς γὰρ οὐδὲ βίαιόν ἐστιν οὕτως ἀκοῦσαι … in Galen’s commentary on The doctor’s office. Interestingly, Galen claims the critics are right in their understanding of the text, but they have to give a forced interpretation of its textual form.65

μάχεσθαι Critics who ‘put up a fight’ (μάχεσθαι) against the obvious reading are targeted in Schol. Hom. Ξ 437a.66 Hector is wounded by Ajax, brought into safety by his compatriots and brought to his senses. He sits on his heels (litt. ‘on his knees’) and vomits blood. Some critics are so alarmed at the idea that he should be ‘sitting on rejection. On the other hand, the infinitive construction may be a clear enough indicator that we are back to the point of view of the τινες. 64 Schol. Hom. E 329a (A) 〈αἶψα δὲ Τυδεΐδην μέθεπε κρατερώνυχας ἵππους·〉 ὅτι Ζηνόδοτος γράφει κρατερωνύχεσ’ 〈ἵπποις〉, βίαιος *δ’ ἔφη* συναλιφή (δ’ ἔφη Α, δ’ ἔφη ἡ Vill., δ’ ἡ Bk., fort. δέ ἐστιν ἡ vel δέ φασιν ἡ Erbse, fort. δ’ ἔσθ’ ἡ vel δ’ ἂν εἴη ἡ ego). It looks as if ἵπποις instead of ἵπποισι ought to be a bigger problem than the synaloephe. The T-scholion on O 299 is too unclear to be included in the discussion (δείσεσθαι· ἀντὶ τοῦ δείσειν, καὶ ἔστι βίαιον. ἢ μέσον ὄντα αὐτὸν ἐδιπλασίασεν). Several issues seem to be mixed up here: the word θυμῷ (cf. O 298–299) is positioned between [μέσον?] μεμαῶτα and δείσεσθαι and could be construed with either. Eustathius (1016.45) mentions the side-by-side use of longer and shorter forms (active and medium [μέσον]) (οἴομαι, οἴω etc.). Erbse tentatively suggests (dub. proposuerim) ἢ μέσου ὄντος τὸ σ ἔδει διπλασιάσαι, referring to the spelling of δείσεσθαι. It is not entirely clear who or what is targeted by βίαιος – as it stands it could even be Homer himself! For ‘forced’ prosodic results, see also Apollonius Dyscolus, Adv., Grammatici Graeci II.i, 140.6f. Schneider βιά〈ζονται〉 συγκοπὰς συνδέσμων παραδεχόμενοι, ὅπερ οὐκ ἂν ἔχοιεν ἐπιδεῖξαι. 65 Galen, In Hipp. Off. med. III, 18B.783 Kühn: ἕτεροι δὲ … ἀληθῆ μὲν εἶπον λόγον, ἐξηγήσαντο δὲ βιαίως τὴν λέξιν. πῶς γὰρ οὐδὲ βίαιόν ἐστιν οὕτως ἀκοῦσαι … The qualification of the ἐξήγησις as βιαίως is repeated at 18B.784 Kühn. 66 Schol. Hom. Ξ 437a (Α) ἑζόμενος δ’ ἐπὶ γοῦνα 〈κελαινεφὲς αἷμ’ ἀπέμασσεν〉· διὰ τοῦ ε αἱ Ἀριστάρχου καὶ αἱ πλείους, ἀπέμεσσεν. Ζηνοδότειος δέ ἐστιν ἡ διὰ τοῦ α, ἀπέμασσεν. βραχὺ δὲ διασταλτέον μετὰ τὸ γοῦνα, ἐπὶ τὰ γόνατα καθίσας ἤμει. γελοῖοι δὲ οἱ τοῖς ἑξῆς συνάπτοντες, ἐπὶ γοῦνα κελαινεφὲς αἷμ’ ἀπέμεσσεν, ἵνα μὴ ἐπὶ τὰ γόνατα κάθηται. γελοῖοι δὲ οἱ τοῖς φαινομένοις μαχόμενοι· σύνηθες γὰρ οὕτως λέγειν. (‘sitting on his heels [litt. ’knees’], he wiped off/he vomited dark blood: The editions of Aristarchus and the majority of editions read apemessen (he vomited) with an e; the reading with a is Zenodotean, apemassen (he wiped off). One should pause and punctuate briefly after gouna (knees), sitting down on his heels [litt. knees; i.e. with his knees on the ground], he vomited. The people who connect it with what follows are ridiculous: ‘he vomited dark blood on his knees’, so that he does not sit on his knees. People who fight the obvious reading are ridiculous: for it is normal usage to put it like this’). One may wonder whether there is also a reminiscence in τοῖς φαινομένοις μαχόμενοι of the fact that strictly speaking one’s knees are not the right part of one’s anatomy to do any ‘sitting’ on (English speakers recognize this strangeness; Dutch do not (cf. ‘op je knieën zitten’)).

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his knees’, that they prefer to connect ‘on his knees’ with what follows: he vomits blood over his knees. These critics are called ‘ridiculous’ (γελοῖοι) twice. There is no need for them to ‘fight the phainomena’, for ‘sitting on one’s knees’ is a normal expression in Greek for kneeling, crouching or sitting on one’s heels.67

Bibliography Texts quoted Blank, D. L. 1998. Sextus Empiricus. Against the Grammarians. Oxford. Hillgruber, M. 1988. Die zehnte Rede des Lysias. Berlin. Leaf, W. 1971 [1900–1902]. The Iliad/[Homer]. 2nd ed., Amsterdam [London].

Works quoted Bourdieu, P. 1984. Distinction. A Social Critique of the Judgement of Taste. Tr. by Richard Nice. Cambridge, MA. Bradbury, R. 1953. Fahrenheit 451. New York. Brecht, F. J. 1930. Motiv- und Typengeschichte des griechischen Spottepigramms. Leipzig. Conte, G. B. 1985. Memoria dei poeti e sistema letterario. 2nd ed., Torino. Conte, G. B. 1986. The Rhetoric of Imitation. Genre and Poetic Memory in Virgil and Other Latin Poets. Transl. ed. foreword, Charles Segal. Ithaca, NY/London. Copeland, R. & I. Sluiter (eds.) 2009. Medieval Grammar and Rhetoric. Language Arts and Literary Theory AD 300–1475. Oxford. Damon, C. 2008. “‘The Mind of an Ass and the Impudence of a Dog’: A Scholar Gone Bad.” In: I. Sluiter & R. M. Rosen (eds.), KAKOS. Badness and Anti-Value in Classical Antiquity. Leiden, 335–364. Dawkins, R. 1976. The Selfish Gene. Oxford. Dawkins, R. 1982. The Extended Phenotype. The Gene as the Unit of Selection. Oxford. Genette, G. 1997. Paratexts. Thresholds of Interpretation. Tr. by Jane E. Lewin. Cambridge. Gumbrecht, H. U. 1999. “Fill up Your Margins! About Commentary and Copia.” In: G. W. Most (ed.), Commentaries – Kommentare. Göttingen, 443–453. Gumbrecht, H. U. 2003. The Powers of Philology: Dynamics of Textual Scholarship. Urbana, IL. Heath, M. 1995. Hermogenes On Issues: Strategies of argument in later Greek rhetoric. Oxford. Hirsch, E. D. 1987. Cultural Literacy. What Every American Needs to Know. Boston. Jonge, C. C. de & J. M. van Ophuijsen 2010. “Greek Philosophers on Language.” In: E. J. Bakker (ed.), A Companion to the Ancient Greek language. Oxford, 485–498. Mansfeld, J. 1994. Prolegomena: questions to be settled before the study of an author, or a text. Leiden.

67 Cf. Il. IX 570 πρόχνυ καθεζομένη, where the T-Scholion a.l. refers to the Glossographers’ paraphrase ἐπὶ γόνυ.

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Meijering, R. 1987. Literary and Rhetorical Theories in Greek Scholia. Groningen. Morgan, T. 1998. Literate Education in the Hellenistic and Roman Worlds. Cambridge. Most, G. W. (ed.) 1999. Commentaries – Kommentare. Göttingen. Nünlist, R. 2009. The Ancient Critic at Work. Terms and Concepts of Literary Criticism in Greek Scholia. Cambridge. Plezia, M. 1949. De commentariis isagogicis. Kraków. Rademaker, A. M. forthcoming. “The Most Correct Account: Protagoras on Language Use.” In: J. M. van Ophuijsen & M. van Raalte (eds.), Protagoras of Abdera: The Man, His Measure. Leiden. Sluiter, I. 1988. “Perversa subtilitas. De kwade roep van de grammaticus.” In: Lampas 21, 41–65. Sluiter, I. 1995. “The Poetics of Medicine.” In: J. Abbenes et al., Literary Theory after Aristotle. Amsterdam, 193–213. Sluiter, I. 1998. “Metatexts and the Principle of Charity.” In: P. Schmitter & M. J. van der Wal (eds.), Metahistoriography. Theoretical and Methodological Aspects in the Historiography of Linguistics. Münster, 11–27. Sluiter, I. 1999. “Commentaries and the Didactic Tradition.” In: G. W. Most (ed.), Commentaries – Kommentare. Göttingen, 173–205. Sluiter, I. 2000. “The Dialectics of Genre: Some Aspects of Secondary Literature and Genre in Antiquity.” In: M. Depew & D. Obbink (eds.), Matrices of Genre. Cambridge, MA, 183–203. Sluiter, I. 2010. “Textual Therapy. On the Relationship between Medicine and Grammar in Galen.” In: H. F. J. Horstmanshoff (ed.), Hippocrates and Medical Education: Selected Papers Read at the xii th International Hippocratic Colloquium. Universiteit Leiden, 24–26 August 2005. Leiden, 25–52, Sontag, S. 1967. Against Interpretation and Other Essays. 3rd ed., New York.

C. Greek Mathematical Writing

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Authorial Presence in the Ancient Exact Sciences Abstract: A formal analysis of ancient mathematical texts reveals tight narrative structures which, to us, imply a strong authorial presence. Once this formal analysis is put in historical context, however, the evidence appears more complicated. Let us suggest, as a first approximation, that ancient authorship would be marked along two dimensions: (1) the Voice, and (2) the Competition. An ancient author would inhabit a space (imagined or real) of performance, his or her body and voice imagined as constitutive to the verbal artifact. (2) An ancient author would be understood to stand in competition with other past or present authors. Greek mathematics is a genre which completely disavows the voice. Its space is enclosed in the material textuality of the diagram; its script is in part unpronounceable. It is a genre that went through no Atticism: pronunciation was never constitutive to the text. And yet, it is as competitive as any other Greek genre, ultimately justifying the preliminary formal impression of authorial control. Is the silence of the mathematicians, then, an active silence- an attempt to create a genre to overcome all speech? If so, was it ever successful?

Here is the claim of this article. Greek writing emanates from an authorial center (section 1). Greek mathematics, in particular, emanates from authorial design (section 2). But this may not be the central form of authorial presence in Greek mainstream literature (section 3). Greek mathematics is not performative, mainstream Greek literature is: the consequences of this opposition are explored in sections 4– 5. There was, indeed, authorial presence in the ancient exact sciences. But the unique textuality of this authorial presence marks the exact sciences as a genre standing alone – the sui generis of the ancient system of genres.

1 The Importance of Being an Ancient Author Greek literature was written by authors – so that even what were, in effect, anonymous works, circulated under names such as “Homer” or “Hippocrates”. Indeed, it appears that a major reason for collecting a work in antiquity would be its authorial status. This is perhaps best considered with the aid of the following

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table 1, setting out the number of papyri fragments for each Greek author from whom more than five identified fragments were found:1 Homer Demosthenes Euripides Hesiod Isocrates Menander Thucydides Plato Callimachus Aristophanes Pindar Apollonius Aeschines Herodotus Xenophon

1668 186 170 158 118 117 96 90 83 57 57 52 50 47 42

Sophocles Aeschylus Alcaeus Hippocrates Theocritus Sappho Archilochus Alcman Aesop Aratus Bacchylides Aristotle Astrampsychus Lysias Euphorion

36 32 28 24 24 23 18 15 14 14 14 12 10 10 10

Plutarch Stesichorus Epicharmus Galen Hyperides Achilles Tatius Anthologia Graeca Anubion Aristides (Aelius) Euclid Eupolis Lycophron Ptolemy Simonides Theophrastus

9 9 7 7 7 6 6 6 6 6 6 6 6 6 6

These 45 authors are responsible, between them, for about 3,000 papyrus fragments or about three quarters of the identified fragments (or a little less than half of all literary papyri). The bulk of ancient libraries was dedicated to these authors at the center of the canon.2 Here, in chart form, are the frequencies for the non-Homer authors in the table (we ignore Homer for the sake of better resolution): The rapid decline in the curve (somewhat masked by ignoring Homer) means that ancient readers collected works in reference to popularity of authors: effectively, they collected names.3 The Anthologia Graeca is a very striking counter-

1 “More than five” is a handy cut-off point, as 5 happens to be a rare survival number, with only three authors (Anacreon, Antimachus, Hipponax), so that there is a fairly neat division between “more than five” and “less than five”. 2 The key to our argument however is not the very numbers of such identified authors but their sloping curve: it is obvious that “identified authors” would be authors (or in other words, all we do is to revisit the fact – in itself significant – that the manuscript tradition left us with few anonymous works). It is difficult to control for the way in which the manuscript tradition determines our identification of authors in papyri; I pursue this question in a monograph now in writing, based on evidence such authors’ names extant on colophons and titles, as well as general considerations on the identity of the papyrus adespota. My conclusion is that the adespota are by a great many very minor authors, and do not conceal a large number of moderately famous authors that swamps the apparent sharp slope of the curve among the identified authors. The curve has a longer tail: but it is a tailed curve. 3 Imagine, for instance, that ancient readers would be interested in having the various genres represented in their book-baskets, so that they made sure they had tragedy and comedy, elegy and prose, philosophy and medicine; but they couldn’t care less which authors they happened to own in the various genres. The resulting curve would have been much less steep in that case: we learn, therefore, that ancient readers did not collect genres but instead collected names.

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number of fragments

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author’s ranking Fig. 1.: Frequencies for non-Homer authors.

example – striking, that is, in its scarcity. Whereas the typical medieval codex is indeed an anthology in character – a collection organized typically by subject matter4 – the ancient papyrus roll would be typically organized around the name of its author (and would not the Anthology, too, be for the ancients the work of an editor-poet?). Several of these names are effectively mere labels: so, as mentioned above, Homer, Hippocrates, but also Aesop, Astrampsychus and, arguably, Euclid. But the ancients did not see things this way and considered even such authors to be real individuals possessing a biography – often in the literal sense. Several on Homer, Hippocrates and Aesop are extant. Let us consider this in more detail: biographies (or effective autobiographies) are extant, at least in fragmentary form, for about two thirds of the 45 authors above, with the exceptions of: Callimachus, Herodotus, Alcaeus, Theocritus, Archilochus, Alcman, Bacchylides, Astrampsychus, Euphorion, Plutarch, Stesichorus, Achilles Tatius, Anubion, Euclid, Eupolis, Ptolemy

4 I have made a survey of (i) a random selection of Paris codices in the ancient exact sciences in Greek, Latin and Arabic (by “random” I mean that I selected all the manuscripts whose inventory number is a multiple of 5), (ii) all the Laurentian and Vatican Greek codices in the ancient exact sciences. 98 codices include works on a single topic by various authors, while 19 include multiple works by the same author; 71, with a single treatise each, cannot be classified in the same way. We find that when codices in the exact sciences join together several works, relatively little effort is made to keep together works by the same author, but there is a common practice of bringing together works on a single topic.

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It appears that the two major determinants for the existence of a biography are: (1) absolute popularity, (2) association with classical Athens.5 I shall return to discuss the role of an association with classical Athens later on in this article. All I wish to point out right now is that the ancients not merely collected names: they collected names for which they had biographical details (or for which they concocted such). The most popular canon was organized around recognizably fleshand-blood individuals. I move now to another table, setting out all the papyrus fragments whose century of production as papyrus roll (as estimated by papyrologists) is the same as their century of composition as literary work (as estimated by literary scholars): 3rd −2nd centuries , 12 identified same-century literary papyri out of 473 total (23 per thousand): Callimachus*2, Aratus, Cercidas, Chares, Dionysius Scytobrachion, Philicus, Phoenix, Posidippus*2, Sosylus, Meleager. 1st century  to 1st century , 5 identified same-century literary papyri out of 1717 total (3 per thousand): Meleager, Dioscorides, Nicarchus II*3, 2nd-3rd centuries , 32 identified same-century literary papyri out of 3940 total (8 per thousand): Achilles Tatius*2, Antonius Diogenes*2, Aelius Aristides*2, Arrian, Chariton*3, Dictys Cretensis*3, Dionysius (Gigantias), Harpocration, Heraclides, Herodotus Med., Hierocles, Lollian*2, Menelaus, Pancrates*2, Phlegon, Plutarch*5, Ptolemy, Triphiodorus*2 Later Antiquity, 1 identified same-century literary papyrus out of 1538 total (less than 1 per thousand): Themistius

The majority of extant literary papyri are identified: roughly 4,000 out of 7,000. It is likely that same-century literary papyri would have a higher incidence among the unidentified (though a great chunk of the unidentified – e.g. practically all unidentified Attic drama, of which we have almost 200 fragments – is certain to be more than a century old6). The numbers we get are lower bounds, the real 5 Homer and Hesiod get their biographies because of their sheer popularity; Hyperides gets his biography because of his association with classical Athens. The most striking counter-example is Herodotus, both popular and related to classical Athens; I am sure there had to be biographies in circulation in antiquity itself. It is striking that what remains are archaic, or Alexandrian poets: but this is to a large extent a reflection of the structure of the ancient canon whose three major segments were: Archaic poetry; classical Athens; and Alexandrian poetry (see section 3 below). 6 But some of it is effectively anonymous and likely to be same-century: as pointed out in Cavallo 1996, quite a few papyri with ancient novels are extant from the 1st–2nd centuries , and most of those are likely to have been written at about the same time. To be more precise, however, there are 44 anonymous novels, likely to have been written in the 1st–2nd century , distributed as follows: 6 1st cent., 14.5 2nd cent., 16.5 3rd cent., 6 4th cent., .5 5th cent., .5 6th cent. (we get “half” papyri when a papyrus is attributed to a range of two centuries). This however should be measured against the total number of papyri fragments from the century, so that the actual incidence of anonymous novels is (numbers per thousand papyri fragments): 6.7 1st cent., 5.3 2nd cent., 8 3rd cent., 8 4th cent., 0.8 5th cent., 1 6th cent. It is therefore not quite correct to say that the novel had

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number being possibly even several times larger. Even so, it is minuscule. Two periods have a slightly more significant presence of the same-century papyrus: Ptolemaic (23 per thousand or perhaps even, with unidentified included, something like 10 percent or so); Second Sophistic (8 per thousand or perhaps, with unidentified included, a few percent or so). These are the two periods when the doors of the canon were slightly left ajar (as seen in table 1 above): even though most of the canon is archaic or from classical Athens, it did open itself somewhat to several authors of Ptolemaic Alexandria and, to a lesser extent, the Second Sophistic. An average working life of 25 years yields also a 75% chance that a samecentury papyrus is nevertheless posthumous. This roughly cancels out the effect of considering the possibility that many more same-century papyri lurk among the unidentified (which I took to mean that the incidence of same-century papyri among all papyri is several times the incidence among identified authors). The conclusion is that the incidence of contemporary papyri (those by a living author) was very small in Ptolemaic Alexandria (to be precise, very small up to 200  or so) and that it was, later than that, vanishingly small. The canon may have been composed of flesh-and-blood authors; but their presence had to be screened – or amplified? – by the veil of the past. It is a canon of dead white males – dead more than anything else. (Women were less discriminated against than the living: Sappho alone could have had roughly as many papyri in circulation as did all living authors combined). This is quite remarkable. Notice well: we do not find that a living author was less popular, on average, than the popular dead authors. We find that all living authors taken together were less popular than even the relatively minor dead authors. This seems to form some kind of paradox. Papyri cannot leap from beyond the grave. So where did papyri hide themselves as long as their authors were still alive? The answer must be that they did so (a) in small quantities and (b) away from the sands of Egypt. That is, we must assume that living authors, even the most successful ones, did not have anything approaching the same kind of circulation of Demosthenes, or even of Hyperides. And we must also assume that living authors did not circulate widely in a geographic sense, either, so that they were practically unknown outside of the very major urban centers where most literature was written.7 its most distribution in the era of its composition, that of the High Empire. Rather, it is correct to note that it has established its position fairly rapidly (though a distinctly minor one: about one percent of literary papyri, including papyri by known authors). Then, at the end of the fourth century, it rapidly fell out of fashion. 7 A separate question is that of the local authors of non-Alexandrian Egyptians. They are practically non-existent. (Tryphiodorus, two fragments; Pamprepius, one; and the cache of Dioscorus of Aphrodito’s autographs). Why would a non-Alexandrian Egyptian produce his work in non-Alexandrian Egypt? He would instead move to Alexandria.

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Starr 1987 remains the classical study of the distribution of works within an ancient author’s lifetime. The article concentrates on the Roman case (for which we have considerable evidence, especially in the many meta-literary observations in Cicero’s prose and in Augustan poetry), but there is no reason to doubt that its results hold for Greek literature of the Hellenistic and later periods as well. As Starr sums up, the ancients circulated texts (1987, 213) “in a series of widening concentric circles determined primarily by friendship”. To be an ancient author meant to belong to an elite network of friendship, within which one’s work could subsist. One sent one’s work to one’s friends, who might or might not send it onwards. Little wonder, then, that works by living authors did not penetrate non-alexandria Egypt – or, conversely, that residents of non-Alexandria Egypt did not aspire to become authors. Now, the elite networks of friendship were central social institutions in antiquity: a major study (contemporary with Starr), Herman 1987, posits a duality of the vertical (local relations between elite and its city) and the horizontal (long-range relations between elites in different cities), the horizontal constituted by networks of “ritualized friendship”. We have followed so far a contrast, or duality – very small scale exchange of contemporary works among elite networks of friends; very large scale reproduction of the very fixed canon established by ancient education. This is the contrast of the horizontal and the vertical, of elites and their cities: one of the basic dualities forming ancient civilization. And the launching of a new work into the canon should be conceived of as a two-stage launch within the terms of this duality: first, a work would circulate within an elite network and only then, through the long and continuous approval of such a circle, it could begin to form part of wider education and dissemination, joining the lasting canon. For both stages, the figure of the author would be crucial: a known person in the network of friends; a biographical presence for the wider, posthumous reception.

2 Authorial Design in the Greek Exact Sciences Consider Archimedes’ Spiral Lines. A long introduction spells out the project in terms referring to Archimedes’ previous communications (with Conon, to whom a set of results without proofs was conveyed; with Dositheus, who kept asking Archimedes for the proofs of those results). Archimedes explains that some of the results were in fact fabricated, false claims designed to embarrass those who would try to prove them. Having failed with his trap (no one did try) Archimedes now reveals the secret, and sends the proofs of some of those results. And so, we see the network of friends in action; not so friendly after all. Archimedes now tells Dositheus that he will, in this book, provide proofs for the set of results dealing with the measurement of the area of the spiral.

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A promise is made; and then Archimedes lurches on to the actual set of proofs. First, general proofs on motion and proportion – nothing to do directly with the spiral. Second, a set of results on tangents to the circle. Third, some otherworldly, abstract claims in the quantitative properties of series and the ratios they give rise to. Nothing to do with the spiral, nothing to do with each other: Archimedes swings wildly from one topic to the next, creating a surface of maximal rupture and tension. Only at this point does the spiral get defined and certain basic properties of it are found – and yet, no sign of how the spiral is to be measured. It is as if Archimedes has settled into a fourth line of inquiry altogether, the general study of the spiral. And then, suddenly, at about halfway through the treatise, the various threads of the argument are being brought together: it is understood that the spiral gives rise to a series with its ratios (one has to be aware, of course, of the spiral as an outcome of a certain motion in proportion); tangents to the circle enclosing the spiral have certain properties that, together with the quantitative results reached already, allow Archimedes to show the impossibility of the area of the spiral being greater or smaller a certain value; at the end, the spiral’s area is one third the circle enclosing it. This is then surprisingly extended to further rotations of the spiral beyond the first one. It all fits together, it turns out: no wild swings, no rupture, merely the appearance of one. In a major feat of retrospective surprise, we find how Archimedes was, within the treatise and without playing tricks – promising to send out provable results (and then sneaking in a couple of decoy propositions), promising to provide a proof (and then approaching it in a circle). The pragmatics of an agonistic, tournament-like communication within a small circle of mathematical friends is imported into the writings themselves. And so we end up with a text marked by mystification and surprise. The text has certain poetic properties, which can be accounted for in terms of the communication setting. Archimedes had the means and the motive and we conclude that this text displays a certain authorial design. Indeed, I would argue that this type of design is the most common in Archimedes’ writing, and the role of surprise and maximal tension in the work of Archimedes was a major concern of my book, Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic (Netz 2009). In that book, I also considered the question of the place of the author in a Greek mathematical text. Most familiar, perhaps, is the absent author of Euclid’s Elements, the Cheshire Cat’s Smile half-visible through dead formulas such as “I say, that” (introducing the particular definition of goal). The mathematical author, in such writings, is the most impersonal. And indeed the formulaic character of the Greek mathematical language is decidedly counter-authorial. Presumably, you cannot speak in your own voice when you speak through long-established forms

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alone.8 Homer did, for the Greeks: but there could have been only one such author, one for a given set of formulaic constraints. Well, in point of fact, Euclid assumes something of the role of the mathematical Homer: he is the only notable mathematical author to have no personal voice of his own (so would impersonality be, somehow, Euclid’s authorial mark?). Other mathematicians tend to speak much more, primarily through the vehicle of the introduction, where the specifically mathematical formulaic constraints are absent. But more than this: as pointed out in Netz 2009, chapter 2, there is often an interplay at place between introduction and main text, between discursive prose and formulaic proof. Archimedes tends to follow his introduction with a few more spare, introduction-like, less formulaic proofs. In some works later than Archimedes, we even seem to see a constant backand-forth between proof and its discussion: Hypsicles’ study of the regular solids (known as Elements XIV), is especially interesting, as the text keeps reverting to the discursive level of the introduction, talking about possible proofs as alternatives and as related to another set of proofs – which Hypsicles is keen to criticize – offered by Apollonius. Once again, we see the agonistic context seen already with the Spiral Lines; once again, the agon becomes explicit and with it – the figure of the author.9 This is not an isolated phenomenon of the Hellenistic author. Instead, it is Euclid – this must be emphasized again and again – who is isolated in our evidence. Later mathematical authors are all often discursive, sometimes pedantically so (say, in the schoolmasterly mathematics of Nicomachus of Gerasa), sometimes in very rich, interesting ways. As acerbic as a Hellenistic mathematician, endearing in his gruff combativeness, is the last major author of ancient mathematics, Pappus, as discussed by Cuomo 2000 and Bernard 2003. Bernard emphasizes the rhetorical tools used by Pappus – a creature of his civilization where rhetorical teaching was widespread. Cuomo looks in detail at certain episodes, especially of an agonistic character, where Pappus speaks, in the first person, building up his authority as against philosophers and rival mathematicians. In particular, he sets himself up as the representative of tradition. And so the shared mathematical culture is not impersonal at all: to the contrary, it is a term invoked by an individual, to assert his personal credit. To be the master of one’s tradition is a personal achievement. Archimedes writes in a surprising manner. Hypsicles’ personal voice keeps breaking through. Pappus is combative and gruff. In short, different mathematical

8 On the Greek formulaic mathematical language, see Netz 1999, chapters 3–4. As pointed out there, the phenomenon of a formulaic language is limited to the main text of proofs; introductions are written in standard, discursive prose. 9 In Arabic translation, we have Diocles’ Burning Mirrors (Toomer 1976), similarly turning from the formulaic to the discursive and back again – if we can trust, that is, the evidence of its late transmission. The conclusion suggests itself: in the age following Archimedes, a highly discursive mathematical text became more common.

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authors make different choices. This is the fundamental observation, which I have insisted upon in Netz 2005: even though mathematics is a study in necessity (so that the mathematician’s results cannot be otherwise), there is no necessity governing the mathematician’s creation: he chooses his goal as well as the way there. This provides ample room for the construction of a mathematical persona, and it is easy for us to see – by considering the mathematician’s context of communication – that such construction is indeed deliberate. Archimedes chooses to surprise us; Hypsicles – to address us, Pappus – to strike us as combative. A mathematician may choose to have his texts marked by authorial design; most ancient mathematicians clearly did. Not all did equally. We have noted several times already Euclid’s avoidance of more discursive introductions, with the result that his works are completely determined by a pre-established, formulaic language. Now, even so, the way the various proofs are structured can be striking in and of itself and in this way present us with the impression of authorial design. But this is not the usual impression in Euclid’s Elements. Many books contain a clear “capstone” theorem towards which the treatise builds (e.g. Pythagoras’ theorem, I 47, i.e. the capstone of Book I, or the construction of perfect numbers, IX 36, the capstone of the theory of numbers in book VII-IX). But the accumulation of results leading up to such capstone theorems has too many asides, too many results included for the sake of inclusion – so as to satisfy Euclid’s basic project of enumerating the fundamental tool-box of Greek mathematical known results.10 Euclid, in a sense, concedes authorial design for the sake of a pre-determined project. Having embarked on recording the results Greek mathematicians already know by heart – and arranging them in axiomatic order – Euclid simply has relatively room left for maneuver. This effect is most apparent in Euclid’s case, where the results are proved prior to him already, but it may equally hold in other cases, where mathematicians set out to prove new results. Indeed, a good example may come from Euclid’s Elements themselves. Book X may not have had any extended precedents: it might have been Euclid’s most extensive original contribution to the Elements.11 Its fundamental structure is as follows. Basic properties of the algebra of what we may call irrationals are established (X 1–20), following which a classification of kinds of irrationals is gradually constructed. Once elements of the classification are in place, most propositions from that point onwards are determined according to a classification-set: so for instance propositions X 42–47, (42) “The Binomial is divided into terms at one point only”; (43) “The first Bimedial is 10 For this function of the tool-box, see especially Saito 1997. 11 Or perhaps not: perhaps once again Euclid merely followed on previous results, say by Theaetetus (on whose contributions to the study of irrationals see, still, Knorr 1975, Burnyeat 1978: as is apparent from such sources, we cannot really tell). Even if Book X is essentially “by Theaeteteus”, its authorial structure remains the same – and needs simply to be ascribed to Theaetetus rather than to Euclid.

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divided at one point only”; (44) “The second Bimedial is divided at one point only”, (45) “The Major is divided at the same point only”; (46) “a straight line productive of a rational and a medial (area) is divided at one point only”; (47) “A straight line productive of two medial (areas) is divided at one point only”. Or even more simply, propositions 85–90: (85) “To find the first apotome”; (86) “To find the second apotome”; (87) “To find the third apotome”; (88) “To find the fourth apotome”; (89) “To find the fifth apotome”; (90) “to find the sixth apotome”. To concede your text to such pre-established sequences is to renounce, to a certain extent, authorial power.12 Such is the result whenever the sequence of results is more or less “combinatorial” as in Book X, i.e. going mechanically through a preestablished sequence of possible positions made available by a classification. Quite a few ancient mathematical works had such a character, particularly by Apollonius. His works, other than the Conics (in itself containing quite a few “classificatory” passages) “included works such as Cutting off of a Ratio, Cutting off of an Area, Determinate Sections, Tangencies, Inclinations, Plane Loci”, all of which are lost from the main Greek tradition but the first of which is extant in Arabic, while the next five are reported in great detail by Pappus. The Cutting off of a Ratio is typical. It deals effectively with one problem alone: “Given two straight lines … and a fixed point on each line, to draw through a given point a straight line which shall cut off segments from each line (measured from the fixed points) bearing a given ratio to one another”. Apollonius then proceeds to solve the problem for the various cases to which it gives rise, e.g. the two lines being parallel to each other or intersecting; or, if not parallel, the fixed points being on the intersection, or otherwise, etc.13 This is very far away from the spirit of surprise and mystification of Archimedes’ treatises and instead we see the same attitude of Elements X: a problem gives rise to a certain classification and the narrative structure merely follows upon this pre-established classification, goes through the pre-established set of options. Compositionally, this is rather like serialism (where a musical composition would be reduced to a fixed row of 12 tones). The author establishes a certain basic classification, but from that point onwards he effectively renounces authorial control, relinquishing it to the mechanism of the classification itself. Such, then, are Greek mathematical texts: different from each other. The author’s voice may be heard – or it may not. Authorial design might be maximalized; or it might be renounced. There is a choice in the writing of a mathematical text, it is not a product of necessity. And so some authors chose to project their authorial identity and others, in some works, chose not to.

12 I wonder if this may not be a Euclidean strategy: a somewhat similar phenomenon is the way in which book XI, setting out the basic principles of solid geometry, closely hews to the pattern established in Book I: it is a three-dimensional adaptation of Book I. Euclid, once again, constrains himself deliberately. 13 Heath 1921, 175–180.

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3 Ancient Authoriality But is this at all the right way to look for an author? We looked for authorial design: effectively, following a modern formalist fascination with the textual strategies through which an artifact might broadcast – or not – its implied author.14 There is something in Spiral Lines that broadcasts surprise and mystification; Hypsicles’ text constructs a persona of its author, as does Pappus’ collection. On the one hand, a text (that we encounter as a modern printed edition, that the ancients would have encountered as sets of papyrus rolls). On the other hand, impressions such a text gives rise to regarding the identity and intentions of a person engaged in its composition. And this dyad is where the question of the author, for us, is located. It is, above all, a matter of papyrus craftsmanship. (Barthes, reducing the author, called it a “scriptor”: the author reduced to its core book-making function.) But is this how the question of the author presented itself to an ancient reader? We have noted, in section 1 above, two parameters: ancient literary papyri were collected in reference to names; such names would possess a biography (real or fictional). And so, authors mattered. But through what function? We might perhaps have taken it for granted, so far, that this authorial function was book-making; if merely because the authors were ultimately collected in the form of books. But the consensus of literary scholarship is that the function that mattered, in antiquity, was different. Books implied not an author and a literary craft; they implied performance, body, space. An author no doubt: but not the authorial presence of, say, a Nabokov; rather, more like the authorial presence of a Nijinsky. We may cite an avalanche of authorities in the secondary literature – a few example suffice. Say, Gentili 1990, Nagy 1996 (a certain conclusion: the primarily performative character of archaic poetry), or Goldhill & Osborne 1999 (stressing the obvious: the performative character of Athenian drama and speech-making), or Cameron 1995 (for a debate, concerning not the existence but the centrality of performance in Hellenistic poetry), or Gleason 1995 (for yet another self-evident truth, that the Second Sophistic was a culture of performance); or, going beyond Greek literature (but as an important witness to the sophisticated, writerly literature of the Hellenistic and later periods), we note the way in which Roman poetry is best understood as a subtle statement within a culture where poetry evokes above all the act of performance (perhaps best seen through the most “modern” of poets, Horace: e.g. Barchiesi 2007). But there is hardly any point in quoting all that literature which merely shows that classical scholarship, through the last quarter-century, was largely dedicated to the discovery of ancient performance. Instead, let us go back to the 45 leading authors on papyri, now divided according to their original performance context: 14 The concept made famous by Booth 1961. Is it even possible to extract a single “implied author”? Is it desirable? – A post-structuralist debate made famous by Barthes 1977, and made possible through the central position that the dyad author/text takes in modern literary thought.

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A. Understood to be sung by a poet: Homer Hesiod Pindar Alcaeus Sappho Archilochus Alcman Bacchylides Stesichorus Simonides

           authors, total: 

A. Understood to be performed in a dramatic festival: Euripides Menander Aristophanes Sophocles Aeschylus Epicharmus Eupolis

        authors, total: 

A. Understood to be performed as public speech: Demosthenes Isocrates Aeschines Lysias Hyperides Aristides (Aelius)

       authors, total: 

Here are the rest, divided into four major categories: B. Witnesses to Classical Athens, whose unperformed prose nonetheless resonates with speech or drama: Thucydides Plato Herodotus Xenophon

     authors, total: 

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B. Effective Hellenistic responses to the earlier genres of performance: Callimachus Apollonius Theocritus Aratus Euphorion Anthologia Graeca Lycophron

        authors, total: 

B. Science and philosophy: Hippocrates Astrampsychus Plutarch Galen Anubion Euclid Ptolemy Theophrastus

         authors, total: 

B. Others: Aesop Achilles Tatius

   authors, total: 

I have pointed out in section 1 above that most Greek literary papyri were inscribed many years later than the composition of their literary content. We can put this in clearer terms. Most Greek literary papyri were inscribed in a civilization later than that of their literary content. Greek literary papyri of the A1–3 sequence above all commemorated a past civilization of the polis, aristocratic, non-Athenian and lyrical (many of the authors in A1); or democratic Athens (A2–3, B1). The rest were either Alexandria’s engagement (all in its first generation or so) with this literary canon, in a sense, as it was canonized (B2); or science (B3). (B4 clearly counts for little: it means that ancient literature also had a few counter-example; or that Aesop could be perhaps understood more performatively, as folktale; or that the novel, indeed, came closest to a modern conception of literature and its author – but then never became a dominant genre, and ultimately disappeared). We do find that the majority of the truly successful literature of antiquity was understood by its readers to have been composed, originally, for performance. A minority either directly served one in understanding such original performances (B1) or creatively reacted to them (B2). The one significant counter-example, such as it is, is category B3, that of science and philosophy. It would actually have been quite a bit bigger had we moved Plato and Xenophon there from B1; but then again,

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are Thucydides and to a lesser extent Herodotus not quasi-scientific authors? We find that writing in the scientific spirit had the best chance to become popular, to the extent that they could be seen to reflect on the Athenian culture of performance. Now let us consider the evidence presented here together with the conclusion of section 1. There, we envisaged a literary world of a two-stage launch, based first on gift-exchange within a network of elite friends, only gradually giving rise to wide reception of an established author. Now, we point out that the basic model for the literary work was that of performance. How can we square the two? How can we have a gift-exchange within a network of elite friends, dealing with performances? First of all, we can: that is concentrating on the lyrical form which is likely based on small-scale performances among elites (perhaps of a “sympotic” character). This is the context from which most of group A1 derives, from Archilochus onwards. In archaic civilization, where the use of writing was rare, such elite sympotic performances were simply the medium through which the elite cultural network was formed. Mutatis mutandis, the sociology of Sappho is indeed comparable, at some level, to that of Horace. But clearly categories A2 and A3 – drama and speech – represent a very distinct sociology. The breakthrough from composition to canonicity passes through a large public event, the drama festival or the speech. Aeschylus would become a household name directly through the event of his performance, just as Demosthenes would become a household name directly through his participation in the public life of Athens. Stage One, in such a case, would not be “horizontal”, inside the elite network, but “vertical”, an author-within-his-city event. There was essentially no such thing as the off-Dionysia success in antiquity – theatrical productions gradually gaining entry into the mainstream through a route other than the Athenian festivals.15 Now, the phenomenon of festival presenting a contest of original dramatic poetry was not unique to Athens of the 5th–4th centuries ;16 nor of 15 Plato is supposed, overwhelmed by Socratic speech, to have taken back his tragedies, already accepted for performance (Diogenes Laertius III 5. Can we believe any of that?). So did Plato’s drama ever had any life as a purely literary phenomenon? (Snell thought Aristotle could have been acquainted with Plato’s tragedies: Trag. Graec. Frag. 46 fr. 1–3, with justified question marks). Or consider Menander’s Imbrians: P. Oxy. 1235 tells us that the play was designed for production in the year 302/1 but was not produced then (apparently the entire festival did not take place), to be taken up in a later festival (see O’Sullivan 2009). So did it have a life, briefly, as a not-yet-produced play? But even so: this is not a show first performed in Delos, say, gradually taking over the main stages. It was first performed in the Dionysia, by a poet who regularly was first performed in the Dionysia. The one real geographic exception was Epicharmus, a Syracusean playwright who did obtain a foothold in the canon. (But this should not be exaggerated: the Epicharmus papyri appear to be learned documents, as indeed is the case with the papyri of other minor comic authors such as Eupolis and Cratinus: see Perrone 2009, 233). 16 For “contemporary” comedy, see Csapo & Slater 1994, 188. (The original Pleiad, of course, was seven Hellenistic dramatic authors, made canonical by fellow-scholars and yet leaving no more

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course was public speech. And yet Athens ruled. Gorgias did not survive in the papyri record: one had to have performed primarily in Athens so as to make a name. In short, throughout antiquity, ancient authors possessed more than just a biography. They possessed, in the mind of their readers, voice and body, a space and an occasion. The rule of Athens can well be understood in this sense as a self-perpetuating system. Since the occasion of literature was essential to its reception, there was a bias favoring works deriving from certain (favored) occasions. But since those occasions became better known, there was a stronger bias to collect them and not others: less frequently collected occasions were more dimly understood as occasions and for that reasons could not even function as literary works. Such a process could well proceed to the point that just one set of occasions survives – which is what has happened in antiquity. The ancients ended up collecting works emerging from a single set of occasions, clustering together in a single place and time – the one which started out with the most advantage – which happened to have been classical Athens. (And so, perhaps, a correlate: the rise of a world-literature would follow upon an erosion of the sense of occasion, of the literary work as performance?) Such speculations aside: what is clear is the fact that the major determinant of non-lyrical canonicity was a particular place and time, meant that the audience must have been actively aware of that particular place and time. Indeed, drama would never again become a candidate for canonicity: since it was impossible to write, in the Greek-speaking Roman world, a fifth-century Athenian tragedy, it essentially became impossible to write a tragedy tout court – that is, impossible to write a tragedy as a contribution to the literary mainstream (though it was still possible to produce new plays for local performance). There had to be some way, however, of allowing new speech – perhaps, other than epic, the most valued of all literary forms – into the literary mainstream. The solution was found by the Second Sophistic: partying as if it were the 340s. One simply pretended one’s space was Athens, one’s time was classical.17 It was Atticism: a literary movement arranged around a specific voice with its specific place. Such was the power of the ancient sense of occasion: entire genres were defined by their original occasions in space and time. Does all this mean that ancient authors had no use for Booth’s ironies, Shklovsky’s plots? Of course they had: Plato could be quite an ironic writer, and the Iliad has a rather interesting narrative structure. Ancient authors had their devices and knew how to use them. But this, apparently, was not fundamentally constitutive to their identity as “authors” – as names that serve as cultural signs warranting

than a tiny impression upon the evidence of papyri – and only if the Alexandra is indeed by Lycophron: see e.g. Gutzwiller 2007, 121.) 17 For the imaginary geo-chronography of the Second Sophistic, see in particular Bowie 2004.

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collectability. What was fundamentally constitutive, in this sense, was the imaginability, in detail, of physical occasion: a singing bard, performing actors, a speech delivered. Or more precisely: craftsmanship, cleverness in composition, in such authors who were not primarily performed, often took the form of assuming different voices (Plato, again), modulating intimated spaces (the Alexandrian poets). To be a non-performed author would involve playing with the poetic ideals of performance. In more basic terms, a constant focus of modern scholarship of ancient literature was its oral character. This once took the form of a cognitive claim: the ancients did not even know how to read silently and instead always read aloud (Balogh 1927). Debunked as a cognitive claim (Knox 1968, Gavrilov 1997), the thesis carries meaning as a sociological observation (Johnson 2000): the ancients could and did read silently, often enough, but a major context for reading was not solitary but social, the reading-together and discussion, among a group of friends, of a piece of literature (networks of friendship, again). But we can eschew reading practices altogether and focus on an observation which is neither cognitive nor sociological, instead being poetic: Greek literature, in both its production and reception, foregrounded the voice and space of an implied performance, even if the work was read silently; even if in solitude. It is against this background that authorial presence in the Greek exact sciences is to be measured. And so, if we found in the previous section that the Greek mathematicians were able authors, casting their personas in effective and varied ways, we still did not begin to tackle their position as ancient authors. For this purpose, a comparison is in order.

4 Visual Texts, Imagined Spaces I vividly recall (just what were my parents thinking?) watching an episode of I, Claudius, with a particular image etched onto my young brain: Caligula (or was it Tiberius?) thumbing a pornographic roll. Seven thousand literary papyri dug in Egypt – and not one to satisfy Caligula!18 And it is not as if Caligula could not have come by his pornographic images. 18 Or indeed pornographic contents, though Philaenis’ erotic guide (P. Oxy. 2891) would have come close to that. It is clear that papyrus rolls whose function was primarily sexual arousal were at least extremely rare. Daniel Boyarin once suggested to me (p.c.) that this absence may signal the ancient avoidance of solitary reading, but this assumes too much about the social use of the frankly sexual. What we moderns find most shocking is the (qualified) public context in which what we would term pornography was often displayed – whether on Greek vases or on Pompeian walls. Caligula, incidentally, would have enjoyed the fifteenth-century  Turin Papyrus 55001 with its combination of text and splendid (now fragmentary) pornographic images, very rare in Egyptian art as a whole. But obviously the visual was not shunned on Egyptian papyrus.

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Rather, he would have to turn to other media. The culture was awash with the nude – quite simply, it was awash with the visual, images in your face everywhere. And within all that, there was a certain decorum about the ancient papyrus. This decorum was very strict indeed and it seems to have encompassed the visual as a whole, which, on the literary papyrus roll (unlike most any other ancient surface) was typically shunned. The evidence is as follows. A few dozen ancient drawings survive on the physical support of a papyrus (Cedopal counts 23 “Pièces illustrées”, which however means such illustrated manuscripts that cannot be assigned to any other category; this then is a slight undercount).19 Most do not contain any text besides the drawing and the assumption has to be that, in most such cases, we find an artist’s sketchbook or perhaps a dedicated art book.20 A mere handful appear to be illustrated literary texts:21 P. Oxy. 2331 3rd cent. . The Heracles Papyrus, a sequence of poetic lines interspersed with drawings. Neither are canonical: the language is apparently Imperial Greek (Page 1957), the

19 Others survive on parchment, attested through the manuscript tradition, from Late antiquity onwards, beginning with two codices of Vergil – The Vatican Codex (4th cent.) and the Codex Romanus (5th cent.) – and one of Homer (Ambrosian Iliad, 5th–6th cent.). As will be noted below, it is clear that in the sphere of bookmaking dominated by the Christian parchment codex, illustrations do begin to be used, and would become commonplace at the latest by the Early Middle Ages (indeed, already the three illustrated manuscripts of Vergil and Homer form a substantial fraction of the codices surviving through normal transmission from Late Antiquity itself). It should be noted that the as yet unedited Bibl. Nat. Cod. supp. gr. 1294, a papyrus and a roll and an illustrated one to boot, nevertheless may be a third- or fourth-century Christian (or Jewish) martyrology (Stephens & Winkler 1995, 470), i.e. it hails from the sphere of bookmaking dominated by the Christian parchment codex – emerging, however, as our first extant evidence for this new development. 20 It is a reasonable assumption that such collections of drawings could occasionally serve as mobile repositories of iconographic tradition – say, you travel from Athens to a provincial town (Oxyrrhynchus?) and you wish to carry with you an aide-memoire for the execution of works of art; since the scenes depicted would normally be narrative scenes treated in canonical texts, such collections of drawings (which could also perhaps come with captions, quotations, etc.) would end up not completely unlike illustrated literary texts (Horsfall 1979, 43). Their function however would be very different – perhaps comparable to the function of musically notated drama (which, we often think, could have served as some kind of aide-memoire to the travelling musician: West 1992, 270). 21 P. Soc. Ital. 1368 has a tiny text fragment (perhaps referring to something as being “Chthonic”, probably in prose) above a figure which may well be Hermes Psychopompus. Circular but solid reasoning suggests this is a magical text (where the coupling of text and image would be commonplace, and where the Chthonic, as well as Hermes, are very common indeed); a religious context was conjectured by the original publication, Minto 1952. Weitzmann never says never (1959, 133): “It has been suggested that this fragment belonged to a religious, funerary text. Yet the figure could also be out of a mythological context. Hermes looking at Alcestis whom he leads into Hades would look no different… These are the uncertainties one will encounter in dealing with such disiecta membra as shreds of papyri”.

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drawings are obviously done in a rather offhand fashion. A recent study refers to this as a “graphic novel” (Nisbet 2011). The text is probably a parody of the epic form, probably ironic, humorously referring to its drawings as “grullos” which might mean a sketch somehow not intended in earnest (see below). This interpretation may seem to apply equally well to: P. Colon. 179 2nd cent. . The text and the figures are more difficult to interpret: I follow Hammerstaedt 2000 – a study of the term “grullos” – in seeing here, once again, an effort in humor, a parody of poetic forms. P. Oxy. 3001 2nd cent. . A Homeric cento (i.e., picking up lines from Homer and “mixing them up” in an original order so as to carry an original meaning). Intention cannot be established, certainly not with such a brief fragment, but the cento form may strike us as in some sense “ironic”. P. Oxy. 2652–3 2nd–3rd cent. . Two scraps with a mostly extant, as well as a mostly lost figure. The mostly extant figure carries the caption “Agnoia”, so it could well be a representation of the character of that name from Menander’s Perikeiromene and it appears likely that this is an illustrated text of Menander, especially in light of the following papyrus. (However, this could also be a stand-alone annotated set of drawings of figures from comedy). P. Soc. Ital. 847 1st–2nd cent. . This fragment of comedy consists of two main sections of text enclosing a small space intended for a figure; a leg seems to survive. Almost certainly then this is an illustrated text of New Comedy. (Which? See e.g. Dedoussi 1980. Very likely, this would be Menander).

What we completely fail to see – we have zero examples of – are mainstream illustrated texts, those from the “serious” canon. It is striking that the only illustrated Homer is from a cento. Two conclusions powerfully emerge. In antiquity, illustrated literary texts were rare – and they were undignified. In particular, illustration even appears to have been thought of as funny. Now, this is in stark opposition to the culture of the illustrated text best known to us, that of the Middle Ages, where illustrated literary texts are commonplace, and dignified. Indeed, in medieval bookmaking culture, lavishness of illustration is roughly speaking correlated with the status of both book content and book owner.22 It is important to emphasize this stark opposition of antiquity and the Middle Ages, since the most influential theory of ancient book illustration, that of Kurt Weitzmann – summed up in his Illustrations in Roll and Codex (1947) but presented in an entire, imposing series of magisterial studies that still dominate all of Byzantine art history – claimed that the Middle Ages, in that regard, were precisely continuous with antiquity itself. This essentially presupposes the existence of the ancient illustrated mainstream text (a presupposition for which, once again, there is zero positive evidence) because Weitzmann requires that the ancient book is a carrier (indeed, the main carrier) of iconographic continuity. What were Byzantine illuminations? They were, so Weitzmann, the more or less faithful copies made by subservient scribes who preserved generation by generation the very same icono-

22 A simplification but also a truism. Consider the centrality of the gospel to book illumination in general, as well as the obvious correlation between lavish illustration and royal patronage or, later on, other forms of elite patronage (for a tour of the evidence, see de Hamel 1994).

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graphic models going back all the way to the invention of the illustrated text in the Hellenistic world, henceforth to be copied and copied again and again. In short, the entire position of textual illustrations within books and within art as a whole never changed significantly from around 300  to around 1500 . We were always medieval. Scholarship today looks for agency and so – as can be imagined – quite apart from the problem of the lack of evidence, contemporary Byzantine scholars are sometimes critical of Weitzmann’s interpretation. Byzantine art surely is not to be reduced to any set of mechanical operations. As Lowden argues even for Weitzmann’s star exhibit, the Octateuch, “the illustrated Octateuch manuscripts are not a late-antique, even less a pre-Constantinian, product, but a middle and late Byzantine phenomenon” (Lowden 2010, 109). So book illustration is always original and reflective, never the mere copying by scribes. We were never medieval. To a large extent, this is sufficient to remove any plausibility from Weitzmann’s theory which ultimately relies on the assumption that the most likely account of a book illustration is a previous book illustration because, you see, scribes are like that.23 But someone after all had to be original along the way and the evidence makes abundantly clear that the locus of creativity – creating the broad outlines of the illustrated literary book we are familiar with – was that of Late Antiquity, the bookmaking culture dominated by the Christian parchment codex, the period of a radical transformation of the Western book, as radical as the invention of print or of digital media. Now, Weitzmann and his followers have a powerful argument to deploy against the evidence e silentio. So, for instance, Wright 1993, 101: “Very few excavated papyrus literary fragments have illustrations of any kind, and the ones actually found are generally from insignificant unidentifiable text; but since most of our papyrus finds come from mummy cartonnage and dump heaps, we should not expect normally to find fragments of fine collector’s editions.” This argument is not without merit. After all, illustrated books form such a substantial fraction of our Late Ancient codices transmitted through the textual tradition, precisely because within the textual tradition the chances of survival are

23 Weitzmann’s main positive arguments were those. First, that narrative art in other media can be explained in terms of a source in book illustration, especially since we sometimes find monumental iconographic cycles whose “pace”, in terms of the sequence of scenes, would make sense in the terms of book illustration (1947, 37–43). This seems to miss the precise ways in which such monumental iconographic cycles do indeed situate themselves vis a vis the text they narrate, quite regardless of their iconographic source (for the complexity of such relationships, see Horsfall 1979). Second, Weitzmann identified certain formal properties of early book illustration that make sense within the material constraints of the papyrus roll and its columns (1947, 69–77). This has a certain validity – but what Weitzmann mostly uses are the constraints of a space defined by several narrow columns, constraints that would have applied equally well in the early codex as on the roll.

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inverted: it is the most valuable which stands the best chance of being conserved.24 Zero is zero and having no positive evidence to bolster your claim is always a liability. At the very least, then, we should say the evidence rules that Weitzmann’s theory is speculative. But there are two more things to note which I think render it not merely speculative, but also deeply unlikely. First, the extant papyri are, indeed, often valuable. Perhaps past scholars tended to think of them as materially unimposing precisely because they are visually unimposing. But Johnson (2004) has shown the following fundamental fact: that among a considerable fraction of our papyri, one can trace a very strict adherence to rules of production that suggest a high level of professionalism. Those are high-end products of skilled artisans; nothing suggests these are second-tier products. Second, Weitzmann did not read his Wallace-Hadrill (I mean of course Wallace-Hadrill 199425). He did not consider the trickle-down effect. Had the most valuable books in antiquity possessed illustrations, we would have expected at least some effort of illustration to mark even second-tier products, so as to endow them with some of trappings of the elite. Clearly no such pressure to imitate the elite via the insertion of visual elements was felt in the production of the ancient literary roll. To the contrary: the highly polished and professional papyrus roll, so abundant in Oxyrrhynchus and elsewhere across Imperial Egypt, would most plausibly make sense as the local elites’ attempt to imitate what they saw as metropolitan practice. We are led to believe the evidence of our eyes: this is how elite papyri looked like. So let us make more precise what the evidence can or cannot support. The argument above makes it quite likely that there never was a perception that “the best people have their Homer with nice pictures”. Probably the perception always was that “the best people have their Homer unillustrated”. An illustrated Homer 24 One would still have to account for the special case of the Herculaneum papyri, which clearly formed a segment, at least, of the holdings of a book collector. In general, the argument needs to be qualified. Collector’s books, too, would eventually be rendered useless through old age or through falling into the wrong, unappreciative hands. (Wright would be surprised by what he could find in today’s dump heaps). It may be said that a more valuable book would be thrown away only when it has been substantially damaged already (hence less likely to withstand the rigors of time in the Egyptian desert), or that because of its lengthier period in circulation, would be likelier to perish in a disaster such as a fire. Both arguments are valid but their nature should be clarified: they are probabilistic, not absolute. They do imply that our extant papyri tend to downplay the frequency of the most valuable books, but they do not suggest that they should completely erase any evidence for them. Zero examples do remain a problem for a theory predicting the presence of such books. 25 So p. 183: “I have argued that this innovation and spread [fashions of wall paintings and “luxuries” documented in Vesuvian findings] was driven by emulation, not simply the internal competition within a closed elite but the aggressive competition from outside that elite…” – and the lesson for us is at once apparent: had the rolls owned by the best people in Alexandria been illuminated with entire cycles of illustration, then surely more modest efforts of illustration would have been apparent everywhere in the ancient literary roll. Here is the rule I suggest: an elite practice that could have been emulated, would have been.

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was always at the best extremely rare. Do I say it did not exist? Of course not. Most likely it did. Millions of Homer rolls were produced in antiquity, and it is absurd to believe not a single bookmaker did go for the experiment of illustration.26 Probably a number did. But the evidence suggests such experiments would have remained as such – isolated efforts that never took hold as a mainstream form possessing unquestioned elite status. Indeed, the evidence suggests powerfully that the inclusion of the visual always went together with an undertone of the unserious, of the ironic, perhaps the funny. Why should that be the case? Here is a thought. Suppose I would write briefly like this or like that. This would be strange, would it not? It would almost be read off as an attempt to raise a smile, to be ironic towards the very act of writing. And why is that? Because it would shout out I am a piece of writing. This would be an act of estrangement; because it would be incongruous. When the Heracles Papyrus refers explicitly to its drawings, it brings out just that estrangement, just that incongruity. The visual was funny, in antiquity, because it was wrong. We come back to the idea of a certain decorum. At the first instance of course this is a matter of markedness. In a context were the illustrated book is extremely rare, the inclusion of illustrations inside a book is highly marked and therefore carries the meaning of a difference, of an estrangement. But this simply pushes backwards the explanatory burden. We must identify a more fundamental reason why illustration would be functionally alien to the ancient literary text – and this jumps out of the evidence we have discussed in the previous section. For we noted how the ancient literary text was a vehicle of imaginary performances, evoking the imaginary space, the projected voice in its embodied speech. It is not about the physical papyrus. The literary text points elsewhere, to a non-papyrus reality. And thus the absence of the illustration is just one of many absences on the literary papyrus which form a pattern, together: the absence of punctuation, of wordboundaries27, the absence of any articulation of the roll in terms of letter size, letter color28, etc. – the avoidance of anything that marks the text as carrying anything other than the bare minimum required for the sake of a proposed performance. 26 While not an example of an illustrated work of the canon, Varro’s Hebdomades was indeed exactly such a one-off, isolated example (singled out by Pliny as worthy of notice precisely because of its status as a one-of-a-kind wonder: Pliny’s Natural History XXXV 2.11). This work – a collection of 700 portraits of illustrious people attached to brief notes on each (epigrams?) – clearly however belongs to the world of scholarship and science rather than to literature. It was a kind of a biographical herbal. (More on this below.) 27 The medieval invention of word division is discussed by Parkes 1993, Saenger 1997. Their accounts are vitiated by subscribing to an erroneous theory of the absence of silent reading in antiquity (debunked, as noted above, most effectively by Gavrilov 1997, but known to be wrong since Knox 1968). Word division was invented in the Middle Ages to facilitate not silent reading, but rather the liturgical use of a book that formed, in its physical presence, the ritual center of a community’s devotion. 28 While not as widely recognized as the absence of word boundaries and punctuation, the ancient papyrus stands in contrast to the medieval one in its overall avoidance of visual semiotics – i.e. in

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Analytically, there are two forces at play. First, images of course are evocative; they would inevitably bring a scene vividly to the mind.29 But which scene? Look at an illustration of the Iliad, and you are brought to the walls of Troy; a picture of Medea – and you are at Corinth. But is this the aim? This would be to rob the roll of its authorial power. To bring back to life the author, we are meant to reimagine an original act of performance: a bard in a Pan-Hellenic festival; actors on the Athenian stage. For this purpose, images of Troy and Corinth are if anything counter-productive, not bringing us face to face with the author but rather bracket him in the direct communion of reader and scene that bypasses the authorial voice. Second, what are we even trying to do with this roll? We are trying to use it for the purpose of a performance re-enacted, virtually or concretely, with perhaps a professional lector or through our own voice, whether silently or aloud (once again – Johnson 2000). And if so, it is immediately obvious why all interpretation is eschewed on the ancient papyrus. This is because interpretation, for the ancients, is understood to reside in the actual moment of performance and the roll for this reason provides no interpretation, not even punctuation and word boundaries (let alone contrasts in word size and color). This is a matter for the voice to provide and the roll merely provides the barest minimum of information required for the voice to do its part. And if so – if these are the mere abbreviated guidelines for virtual or concrete performance, a kind of ancient XML – it becomes even absurd to ask for the insertion of illustrations. It is a bit like asking that sheet music of Beethoven’s Sixth be accompanied with pictures from Disney’s Fantasia.30 The underlying point is that this is not about the papyrus. We are not using the piece of written document as a tool for thinking about Troy and Corinth, or as an object of pleasure on its own right. Rather, this is a tool meant to evoke a more central cultural phenomenon, that of the performance. It acts on the one hand to recall an originating, canonical moment of performance, the one constitutive of

not allowing of the visual properties of script (other than the discrete selection of alphabetic symbols) any semiotic significance. It does not matter how big a letter is (they are of the same fixed size, unlike the medieval manuscript with its use of initials and other effects based on letter size), which font it uses (there is no plurality of miniscule and majuscule as in the later medieval manuscript), what color it has (it is always dark brown, unlike the medieval manuscript which is typically at least bichromatic), how it is positioned in the space of the column (it is algorithmically positioned according to the requirements of the text and there is no meaningful degree of freedom in the positioning of letters, unlike the medieval manuscript with its careful use of marginalia, not to mention tabulation and other formats). 29 As the ancients of course pointed out: see e.g. Plutarch, Glor. Ath. (Mor. 346F) and discussion of this passage in Zanker 1981, 311. 30 The point needs emphasis: this claim does not mean that the ancients always read aloud. Professional musicians can after all ‘read’ notated music silently, and the ancients must often, perhaps more often than not, read their rolls silently. But such a reading would have a function comparable to that of the professional musician reading a score ‘silently’: as the mental evocation of an imaginary act of performance.

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the authorial presence of a Homer, a Euripides; it acts on the other hand as a tool for the re-enactment of such canonical moments of performance in the salons of the Greco-Roman elite. This is the opposite of the medieval book, where it was all about the parchment, a ritual tool of devotion or of erudition calling for the reader to relate to it – the actual physical presence of a written text – as the focus of one’s cultural identity. And, if it is all about the parchment, what’s more natural than making the surface of that parchment as splendid as possible? But – on the other hand – on the surface of the papyrus, an illustration would be all wrong because it would shout out I am a piece of writing whereas the audience would normally keep pretending, while reading, that this was a piece of performance. Let us separate evidence from interpretation. The evidence is that there are zero examples extant of canonical illustrated literary texts; illustration is rare and extra-canonical. This is the opposite of the medieval case. Now follows interpretation. First of all, I argue it is simply contrived to ignore the evidence by ascribing it to the bias of survival. The pattern is too stark; the logic of the trickle-down of elite cultural forms makes such an account unlikely. Instead, we should believe what we see: the ancients did not illustrate canonical literary texts, and the medievals did. Which – here comes mere interpretation – is to be expected given what we independently know about ancient and medieval attitudes to text and performance. In what follows, I shall heavily rely on this bit of interpretation – but the ensuing oppositions make its logic stand out more clearly and so serve to support this interpretation further. All of the above speaks to the canonical literary text, where illustration appears to have been perceived as incongruous. But not so all books. I mentioned above the incongruity of writing like this or like that. But there would be nothing incongruous in writing, say: Y=X12+X22. So incongruity does not reside in the superscript and subscript per se; it resides in the generic contexts of their use. The same seems to have held in the ancient book. Indeed – and here is the ultimate irony – Weitzmann’s theory essentially relied on the evidence from ancient scientific texts, where illustrations, indeed, were commonplace. So Weitzmann 1947, 47: “Several examples are from scientific fields, especially mathematics and applied mathematics. Such scientific texts are so in need of illustrations by diagrams that they could hardly have existed at any time without them. While previously we considered the beginning of the Hellenistic period as the start of book illumination, we must now make the restriction that this applied only to literary texts and not to scientific ones, which must already have had explanatory drawings considerably earlier.” Indeed. Weitzmann goes on to cite examples from geometry, astronomy and magic. In general, we can say as follows. The use of diagrams was generically constitutive to the exact sciences, with the text itself marked by reference to diagrammatic labels, and in fact the majority of our extant papyri in geometry (mostly elementary teaching) or in theoretical astronomy (of which they are only a handful)

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do carry diagrams.31 There is a substantial group of extant magical papyri (Betz 1992 translates a collection of over 130). They nearly always demand some inscriptional activity, often just calling for the inscription of letters or ad-hoc symbols in well defined configurations, but sometimes requiring entire images which are then conveyed by the papyrus itself. Further, while illustrated medical papyri are rare, at least two herbal illustrations are extant on papyrus (P. Tebt. 679, Johnson Papyrus – the latter, 5th cent. , is so late as to belong already to the world of the famous sixth-century Vienna Dioscurides, extant through normal manuscript tradition and on a par with the illustrated Vergils and Iliad). Illustration seems to have been generically required by the form of herbals but fairly uncommon otherwise in medicine. Still, the internal evidence of the text of both Apollonius of Citium’s Commentary to Hippocrates on Fractures as well as Soranus’ On Bandages implies that the illustrations extant in their medieval manuscripts are authorial; the same seems likely for a group of obstetric illustrations in Soranus’ Gynecology.32 We find a new set of oppositions, to extend our opposition of the ancient, and the medieval, literary texts. First, while the ancient literary text was, in the normal run of things, not illustrated, the ancient technical text often carried illustrations. Second, while such illustrations were essential in some fields – most strictly the exact sciences, but also magic and the herbal – they were merely an option, rather infrequently exercised, in most medical contexts other than the herbal. The herbal and the magical papyri share one thing in particular: they eschew any performative function. The ancient illustrated herbal is a stripped-down reference work, a sheer repository of information: it is not a discursive discussion of the powers of material medica (such discursive pharmacological treatises do not appear to have been illustrated). It also goes without saying that the magical papyri are non-discursive. Indeed, they very directly foreground the physical act of writing, so that, in the case of magic, it is indeed all about the papyrus.33

31 I discuss these papyri in Netz (forthcoming), arguing both for the educational context of most geometrical papyri as well as isolating the papyri of theoretical astronomy. Geographical papyri are extremely rare – they do not even register as a papyrological genre in Mertens-Pack – but the Artemidorus papyrus (Gallazzi et al. 2008) is of course organized around a map. 32 See the discussion in Stückelberger 1994, 88–94. While the internal evidence of the text of Aristotle suggests that, in their original context in the Peripatos, texts would often refer to images, it is unclear what form such images took and how, and if, they circulated in antiquity (for which see Stückelberger 1994, 74–78. Such Aristotelian diagrams follow the same pattern of distribution: they are almost always present when the exact sciences are discussed, and are optional in the life sciences.) 33 So as to bring out the contrast between the exact sciences and mainstream literature most forcefully, I concentrate in this discussion on the diagram (directly comparable to the illustration). Analogous observations can be made for the essential role tables play in ancient astronomical writing (for the primary evidence, see Jones 1999).

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What about the mathematical papyri, then? Are they rather like magic, in the sense that their drawings are the thing itself, that thing around which the discourse is arranged? I have argued since Netz 1999, 51–56, that this is indeed the case. The Greek mathematical diagram is not some kind of explanatory illustration, designed to help the reader find his way through a claim. Rather, it forms the very subject of the claim. What Greek mathematicians do is to enact operations on a diagram, virtually constructing it and then making claims surrounding it. The physical limitations of the diagram as a perfect instantiation of the object under discussion are well understood, but the subject matter is not some abstract object external to the diagram. Rather, it is the diagram taken in through a make-believe perception which takes it as if it did perfectly instantiate the object at hand: the diagram as imagined.34 And so the Greek mathematical diagram serves a very distinct function, firmly focused on the papyrus itself. It is not a pointer to some other reality – no Troy, no Corinth. To the contrary: the text itself points to the diagram (through its use of diagrammatic labels), organizes itself in relation to it. The Troy and the Corinth of a Greek mathematical text – the space where action takes place – is in fact the space of the points and the lines of the figure. All of Greek literature is evocative of a space, but if the space of literary works is that of imagined performances, that of Greek mathematics is that of geometrical space as executed on the surface of papyrus. All of Greek literature is performative, but if the performance of Greek literature is that of the voice and the body, that of Greek mathematics lies within the construction of lines drawn within a geometrical configuration. Here, for once, space and performance have both been folded into the papyrus roll itself. We have now covered a long way from the pornographic roll of I, Claudius, to the geometrical drawings of an author such as Euclid. What we see, throughout, is that the use of the visual is not a trivial matter, it is not an afterthought that may or may not be attached to works. Rather, the use of the visual is a powerful marker of book culture as a whole, of the spaces it evokes, of its relation to performance. The starkest opposition obtains, we find, between the use of the visual in Greek literary texts, and in Greek mathematics. In this respect, at least, Greek mathematics was the anti-literature. But the relationship between science on the one hand, and literature on the other, is more complicated than that: medicine, as it were, forms a middle ground. Apparently it more closely resembled wider literary practices, evoking a culture of performance. The same, I argue, does not appear to hold for mathematics. We need to address, then, this emerging opposition: the different roles of performance in ancient medicine and mathematics.

34 Netz 2009b extends the discussion of Netz 1999 in this regard.

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5 Performance in Ancient Science The performative character of (a significant part of) Greek medicine is by now a commonplace. Some Hippocratic treatises must have been delivered (perhaps in a form somewhat different from that of the written text we possess) as public speeches;35 Galen continuously refers to his public performances, that involved not merely speech but indeed the theater of the body in violent exercise: he cut up animals in public, you see.36 Each is directly related to wider cultural forms of public performance: the Hippocratic ‘rhetorical’ treatises belong to the birth of rhetoric in the classical polis, while Galen’s performances belong to the Second Sophistic. More precisely: in a sense, some Hippocratic authors were rhetors; in a sense, Galen was a sophist. Greek medicine participated, on equal footing, in its wider culture of performance. To some extent the connection between science and performance is straightforward: science involves teaching and normally teaching involves more than just reading and writing. Van der Eijk identifies a pedagogic side to the rhetoric of some Hippocratic texts and in general it is clear that ancient teaching sometimes involved what we would call “lectures”.37 Some philosophical schools attracted many students38 and we have reports of medical performances whose audiences seem to have been more “students” than “spectators”, most clearly in the evidence discussed by von Staden 1997, Gleason 2009.39 It would be wrong however to equate oral teaching, in general, with “performance”. Although of course a lot can be said about the performative character of the teacher-student encounter in the context of private teaching, there is still a clear difference between such encounters and the public displays of, say, Galen’s public dissections. So for instance, Theaetetus, recalling for Socrates’ sake his experience in learning from Theodorus: “ἀτὰρ κινδυνεύεις ἐρωτᾶν οἷον καὶ αὐτοῖς ἡμῖν ἔναγχος εἰσῆλθε διαλεγομένοις, ἐμοί τε καὶ τῷ σῷ ὁμωνύμῳ τούτῳ Σωκράτει.”–“τὸ ποῖον δή, ὦ Θεαίτητε;”–“περὶ δυνάμεών τι ἡμῖν Θεόδωρος ὅδε ἔγραφε […] ἡμῖν οὖν εἰσῆλθέ τι τοιοῦτον […]”

35 The locus classicus for this phenomenon remains Lloyd 1979, 88–98; van der Eijk 1997, 93–97, is a more recent statement of the basic evidence. 36 Von Staden 1997 presents the evidence for the rhetorical, or sophistic Galen; Gleason 2009 looks more closely at the theater of cruelty. 37 The Greek word, akroasis, is telling: an akroatēs could be a “student” or a “member of the audience of a public speech”. But perhaps not too much emphasis is to be put on such etymologies. 38 Theophrastus had two thousand students (so Diogenes Laertius V 2.36). The biographical tradition on philosophers sometimes provides such suspicious, but suggestive, bits of evidence. 39 The evidence for medical performance is very much about our two major corpora, the Hippocratic and the Galenic. Authors known through testimony alone do not allow us a similar glimpse of their rhetorical side, yet it should also be said that the biographical evidence for Herophilus, say, or Erasistratus does not mention public performance; the relatively few extant medical authors other than Hippocrates and Galen were selected by the medieval tradition for their value as compendia; they tend to be less discursive.

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“I believe you’re asking just the sort of question that occurred to your namesake Socrates here and myself, when we were having a discussion a little while ago.”–Socrates: “And what was that, Theatetus?”–“Theodorus here was proving to us a point about powers […] So the idea occurred to us […]”40

Are we to imagine a roomful of students? Theaetetus emphasizes the duality of “us” (which appears to mean him as well as the younger Socrates41) and “Theodorus”. The teacher is confronted with two students.42 The teaching of the theoretical exact sciences would have been rare through most of antiquity43 and there is nothing inherently surprising in the notion of such teaching being carried out in small groups. Quite likely this would most often take the form of a single student following a mentor – after all a central way in which the ancient conceived, at least, of education (and one which is of course very much still with us).44 And so we should think of the oral teaching of the ancient exact sciences (in any advanced form) as a private rather than a public practice. 40 Plato, Theaet. 147c7-d7, using (with a tiny revision) Levett’s translation from Burnyeat 1990. 41 The “us” could also conceivably be used to refer more vaguely to a wider group, out of which Theaetetus selects to emphasize himself and Socrates as the authors of the original classification; but in fact the original is so rich with deictic references (well brought out by Levett’s “Socrates here” (toutōi), “Theodorus here” (hode)), that it is likelier, as a matter of style, that had he meant a wider group of “we” to contrast with the narrower pair of Theaetetus/Socrates, this would have been visible in the language itself. 42 The pseudo-Platonic Amatores begins with a related scene (132a1-b3), with two boys debating (or so it appears) a point of astronomy. In this scene a teacher is not involved (this is the classroom of Dionysius the grammarian): the astronomy in question is extra-curricular. 43 I have discussed this in several places, most fully in Netz 2002, 201–208. My conclusion there was that there was on average perhaps (order of magnitude) one creative mathematician per year of antiquity. The clustering of creative mathematicians in a given time and place would normally be very low indeed: most typically isolated individuals, with perhaps a few dozen at most in Alexandria at the peak of its creativity. 44 Ancient advanced education was primarily a matter of teachers brokering canonical texts for their student-readers (Mansfeld 1994, Snyder 2000). This could have been done with a group or with individuals, but the general rule is that lecture is for the sake of text and not vice versa. Whether or not this suggests a more “individual” relation to study depends on how ‘individual’ reading was in general. At any rate, the cultural imagination was based on the idea of education as a mentoring relationship with its erotic overtones (familiar to the literature since Marrou 1948/ 1956, ch. 3, and of course even before). I find it striking that the depictions of education (Beck 1975) are often so intimate: a student reading alone, with a teacher, with a single peer. In short, advanced mathematical education with a single mentor guiding a prospective pupil through complicated texts would be within the norm of ancient culture and is to be expected. The question remains how elementary mathematics was taught. It is conceivable that the schoolmaster could have assembled a group of his students, and lecture them on the application of Pythagoras theorem or on Euclid’s definitions. This then would qualify as an example of “ancient mathematical lecture” or even, if you will, “ancient mathematical performance”. I exclude this (realistic) scenario from the following discussion. Hippocratic and Galenic performances have a direct interface with the writings in the Hippocratic and Galenic corpus; the schoolmaster’s elementary teaching does not appear to have such an interface with the writings of Archimedes.

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The question then emerges: was there a public face to the ancient exact sciences? The very question strikes us with the full effect of a shock.45 We are by now so conditioned to the public character of ancient culture that it is inconceivable to us to imagine such a central ancient genre as that of the exact science surviving without a public face. But in fact it is not easy to find evidence for such a public face. Less than 150 persons (including “anonymi”) can be associated with the ancient exact sciences with any certainty; for about 30 of these, something can be said about their involvement in teaching and education (for the rest, we have merely the works or, more often, mere testimonies for such works, without any indication of the author’s life and practices). We can note several types of such involvement: – Father / child pairs. Archimedes / Phidias, Hypsicles / his father, Galen / Nicon, Hypatia / Theo. In all four pairs, father and child share interests in the exact science and it is at least likely that the father guided the child’s scientific education, directly or indirectly (Galen’s autobiographical notes suggest an indirect guidance).46 – The biographies of two philosophers report that they were taught mathematics by two teachers each: Arcesilaus studied with Autolycus and Hipponicus47; Philonides studied with Eudemus and Dionysodorus;48 a chain of teaching is attested in Cyzicus (though the evidence is late and less certain): Eudoxus teaching Helicon as well as Polemarchus, the latter teaching Callipus49 (fur45 Indeed, I am not familiar with its being raised. It is even hard to come by passages arguing for the opposite – that Greek mathematicians did perform in public – though this presupposition does creep in through over-translations (see e.g. n. 47 below). Sidoli 2009 makes the claim explicitly, apparently without a sense that it is in any way controversial. The article is very well argued and I therefore have to confess my surprise at the argument proposed by Sidoli, that the fact that there are typically two diagrams in the manuscript tradition of analysis-and-synthesis pairs, one for both analysis and synthesis, is a marker of an oral origin for such presentations. How would that practice be transmitted into the textual form we actually possess? Sidoli 2009, 139, seems to suggest the duality is there to inspire a manner of using the text in public teaching, but clearly at this point the argument is extremely weak. What we see is a choice made by ancient authors or their copiers to treat both analysis as well as synthesis as a full proposition – as indeed they are, formally, each possessing their own construction and proof. This is all worth bringing out in some detail, as an a fortiori argument, if you will: ‘If a scholar as precise and well read as Sidoli cannot come up with a better argument for Greek mathematical orality…’ 46 I discuss this phenomenon, with references there, in my discussion in Netz (forthcoming), where I argue that Philonides’ father could have been a mathematician. 47 Diogenes Laertius IV 29–32. As I check the reference, I come across Hicks’ translation of Diogenes Laertius IV 32: “He also attended the lectures of the geometer Hipponicus”. This is the kind of over-translation one often finds in the literature, the Greek being in this case διήκουσε δὲ καὶ Ἱππονίκου τοῦ γεωμέτρου, “he also learned from Hipponicus the geometer”. 48 P. Herc. 1044 col. 25 lines 4–8, Gallo 1980, 82; I discuss this in Netz (forthcoming). 49 For the evidence see Sedley 1976, 27. The evidence for Helicon is especially problematic: Plato’s 13th letter (as well as Plutarch, who may well rely on the same letter).

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ther, we are also told, as we mentioned above, that Theaetetus studied with Theodorus). Such reports do not settle the kind of group within which the studies took place. When mathematicians reveal something of their practice of intellectual exchange, what we see is a network of peers sometimes involved in a communal study of sorts, with two or three individuals meeting together or forming a correspondence between them: so Archimedes, writing to Dositheus (in the preserved treatises The Quadrature of the Parabola, On the Sphere and the Cylinder I, II, On Spirals, On Conoids and Spheroids), to Eratosthenes (in the preserved treatise Method), to Conon (implied most clearly by introduction to On Spirals), and referring to an intended meeting between Dositheus and Heraclides, perhaps himself a mathematician (introduction to On Spirals); Apollonius writing to Eudemus and meeting with both him and Philonides (introductions to Conics I, II); Pythion writing to Conon; Zenodorus meeting with Diocles (for the last two, see Diocles’ On Burning Mirrors, Introduction, Toomer 1976, 34); Basilides meeting with Hypsicles’ father as well Hypsicles writing to Protarchus (‘Euclid’s Elements XIV’, Introduction).50 We have at least four moments of a mathematician addressing a royal: Archimedes addressing the Sand-Reckoner to Gelon; Eratosthenes addressing his mini-treatise of the finding of two mean proportionals to Ptolemy; Conon’s identification of the Lock of Berenice; and a tale according to which Ptolemy once asked Euclid for a shorter way to study whereupon he was told there was no royal road to geometry (the latter clearly belongs to the genre of invented bon mot; but it is perhaps significant that this kind of exchange is part of the cultural imagination). All four are from the same context of the early Hellenistic kingdom. Maybe relevant as well is Thrasyllus, serving Tiberius, or maybe consider even Vitruvius, addressing Augustus. While only indirectly related to the subject of “public performance”, it is important to note a certain practice that may have been complementary to the public speech, namely the public monument. Euctemon (together with Meton?) set up a parapegma;51 an astronomical model was set up by fourth-century  mathematicians at Cyzicus (for which see more below); Eratosthenes set up a monument with his mesolabion; Archimedes built a sphere; this may or may not be reflected by the Antikythera Mechanism; A monument of some kind called “astronomy of Eudoxus” was dedicated at Delos in the second century  (An inscription? A diagram? An instrument?);52 Ptolemy set up public astro-

50 I avoid here references to the many addressees of mathematical texts whose identity as mathematicians cannot be established. 51 Hannah 2002, who also briefly discusses the archeological evidence for parapegmata; a full reference is to be found in Lehoux 2007. 52 Inscr. Del. 1442 B.42, 1443 B II.109.

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nomical instruments.53 (It is interesting that the content of such mathematical monuments is mostly – but not uniquely – astronomical.) Ancient philosophers sometimes engaged with mathematical contents in their teaching. Plato, we are told, gave a lecture on the Good whose contents were frustratingly mathematical.54 Aristotle’s treatment of the rainbow is explicitly mathematical55 while many other passages in his writings use a mathematical approach that would have demanded a mathematical-like presentation, most obviously in the Prior Analytics and some passages in the Physics; the latter is explicitly an akroasis, whatever that means precisely, and in general Aristotle’s corpus belongs to the classroom (whether in the form of lectures or of more intimate “seminars”).56 From late Hellenistic times on, some works whose nature is more of a compilation or a commentary seem to belong to a philosophical education: the earliest maybe Geminus, a Stoic, and he is followed by diverse authors such as Theo of Smyrna, Apuleius, Nicomachus and Porphyry (Platonists), Sosigenes (Aristotelian) and Cleomedes (a Stoic again). All such authors seem to wish to incorporate mathematical contents into philosophical teaching. Such works could be intended simply for reading, or they could be incorporated into a mentor-pupil study, or finally they could form the basis of public lectures. It is very likely, finally, that Proclus’ commentary to Euclid’s Elements was indeed used as part of his teaching, and overall the impression is that, in the Neo-Platonist schools of Late Antiquity, public teaching of (theoretical, though elementary) mathematics would have become standard. All of this, however, involves the teaching of mathematical contents, within the philosophical curriculum and by the hands of teachers whose professional identity was “philosopher”. Such teaching took place in the context of such ancient philosophy that took interest in science, i.e. early, or late Platonism, and the forms of Aristotelianism or Stoicism that fell under its influence. A few cases stand out. (i) In Aristophanes’ Birds, Meton has to speak out in public: he is put, after all, on stage (lines 992–1019). I have to say, my impression is Meton does not know what to do there. The entire point seems to be that while the priest, the poet and the oracle-monger all wish to take over comedic speech through their overflowing performance of resonant Greek, Meton bungles his presence on the stage, getting all lost in his instrumentation.57 (ii) It is definitely appropriate to speak of a “mathematical school” in fourth-century  Cyzicus – but in which sense? Several mathematicians, in a few cases perhaps known to be in contact with each other (see n. 49 above),

53 Taub 2002. 54 A famous passage: Aristoxenus’ Harmonics, Introduction to Book II. 55 Vitrac 2002. 56 I have discussed this in Netz 2001. 57 “Breathless explication… exaggerated gestures” is how Amati 2010, 219, imagines the performance. This is not the stentorian presence of the preceding unwelcome guests.

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were active there; Epicurus speaks against “Cyzicians”, wishing to lump at least some of these together, in the context of a polemic against mathematical astronomy. In the most explicit passage (the fragment of On Nature XI surviving through P. Herc. 154, 1042), the focus of the discussion is on the astronomers’ reliance on astronomical instruments or models.58 It is impossible to tell from this context whether Epicurus speaks against a practice of public teaching where astronomy is explicated via an appeal to an instrument; the same kind of practice in a private mentor-pupil relation; or merely to published texts that refer to the use of instruments. This interpretative difficulty is probably not due to the fragmentary survival of this text, but to its strict epistemological character. Epicurus does not write so as to tell us about practices in Cyzicus; he writes so as to convince us that astronomical devices are not reliable. In short, tantalizing as the evidence is, it does not tell us anything concrete about the practices of astronomical education in Cyzicus. (iii) In another lively and tantalizing passage59, Pappus responds to the pupils of his peer Pandrosion (remarkably, a female mathematician). How they were taught we do not know. What we do see is that Pappus’ knowledge of the work of such budding mathematicians is through written correspondence where unproved claims are circulated, Archimedes-style (III, p. 34.1–2 Hultsch). We normally tend to think that Pandrosion and her students were all Alexandrians, just like Pappus. The centrality of the written mode of communication is therefore striking (and the similarity to Archimedes could not be a coincidence: they were emulating canonical models – the key issue for Pappus’ mathematical culture, as shown by Cuomo 2000). The sociological building block of ancient mathematics was the person-to-person relation: father-to-child, mentor-to-pupil, author-to-patron, above all peer-to-peer. This relation could be face-to-face but its written form was no less important. This is why so many of our extant mathematics survives in the form of letters.60 There

58 The extant text stands as two unequal segments (using the divisions of Sedley 1976): Col. I a, 21 lines, discussing optical illusions and their epistemological significance for astronomy; a lacuna of 170 letters or roughly a colon; and then seven colons mostly extant, all engaged with the use of instruments by certain astronomers. 59 Pappus, Coll. III, introd., esp. p. 30.17–22, p. 34.1–8 Hultsch. See discussion in Cuomo 2000, Bernard 2003. 60 I discuss the letter format in Netz 2009, 92–107. In general, it is important to note that mainstream Greek mathematical style does not show traces of a mentor-pupil relationship. It is therefore unlike Babylonian as well as the Heronian-style geometry prevalent in Greek educational mathematical papyri, where one constantly uses second person singular imperatives, with the implication of a teacher directing the student (see e.g. Robson 2008, especially chapter 4, for some examples as well as for the educational context, brought out very powerfully by Robson throughout her work). The “I say, that” / impersonal imperatives combination implies instead the peer-to-peer correspondence characteristic of mainstream Greek mathematics.

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was no taboo on the public display of mathematical knowledge, but we do not see any evidence of mathematicians displaying their knowledge through the form of public speech; instead, we do have some evidence for mathematicians displaying their knowledge through the form of public monument, as well as philosophers (of a particular kind) displaying their knowledge of mathematics in their public lectures. Such exercises are inherently unfair, but let me consider how, counterfactually, our evidence for mathematical lectures could have looked like. This would serve to bring into relief the qualitative difference between our evidence for mathematics and for other ancient forms of knowledge. And so, for instance, Plutarch does not relate this legend about Archimedes: “When Archimedes visited Alexandria together with his father, and attended Euclid’s lectures, he was so overwhelmed that he burst out crying. Noticing this, Euclid said: ‘Phidias, your child will achieve great things.’”61 Diogenes Laertius does not quite say this: “Demetrius, as we have mentioned, is our authority that Chrysippus was the first to give lectures in the open air; however, others say that Eudoxus, in his lectures on astronomy, was the first to do so.”62 And nowhere do we have Ptolemy write to the effect that: “They claim that through their methods the eclipse can be predicted more accurately, but, unlike me, would never agree to make such a prediction in public.”63 Apocryphal or not, the ancient testimonies often bring out in lively detail the public performance underlying so much of the ancient practices of knowledge. This is simply never the case with the exact sciences. Of course, it can be that we have lost such references. Perhaps they were written down and then lost; perhaps no one bothered to write them down in the first place. This is all possible. And yet the fact remains that the one ancient author in the exact sciences who does come through as possessing a public persona – Archimedes – is never presented as a lecturer. He is lost in thought; or indirectly present, his hand merely pulling at the rope guiding an instrument, whether in the launching of the Syracusia or with the war-machines.64 There is no sense that it would be appropriate for an author such as Archimedes to suggest to Gelon, say, that it is time to present in public the results of On Floating Bodies. He just does not seem to have engaged in outreach. Once again, we should define more precisely what the evidence can or cannot support. We cannot say that authors in the ancient exact sciences did not perform

61 Modeled on Marcellinus, Vita Thuc. 54, told of Herodotus and Thucydides. 62 Instead, Diogenes Laertius, Vita Chrys. 185, provides the first part alone – that Demetrius claimed Chrysippus to be the first open-air lecturer (or the first one at a particular location? – this hardly matters for our purposes). 63 Compare to Galen and, say, the pneuma in the goat (Galen’s Anatomical Procedures VII 16, Kühn 2.644–646). 64 Jaeger 2008 analyzes well the key feature of the Archimedes’ legend: loss. He could not be understood; he died.

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in public. (Nor can we say they did.) We can say this: in the eyes of ancient audiences – and of the scientists themselves – such public performance was not seen as a defining form of exact scientific practice. Instead, the defining form of exact scientific practice was that of peer-to-peer communication. This perception would have marked the exact sciences as distinct from other forms of knowledge or culture in general, where public performance was at least one of the more central forms, perhaps the central, defining form par excellence.

6 Conclusion The preceding two sections were broadly similar in structure. A certain practice is assumed by much of the literature to be universal; I suggest that we take seriously the fact that it is attested in one context, but not in another, and find a meaning in this pattern. Illustrations are attested for ancient scientific (and especially mathematical), not literary texts; performance is attested in most Greek cultural forms, but not in the exact sciences. This, I argue, should indicate what was established as the defining form. So, even if practiced as an isolated experiment, the illustrated literary text never took hold in antiquity as a mainstream form; even if ancient exact scientists did lecture on their topic, such performances did not form a significant part of their professional identity. The two claims are not merely similar, but complementary: here, illustration is established as a mainstream form, but performance is not; there, performance is established as a mainstream form, but illustration is not. The evidence is negative or more precisely, contrastive: I argue for the absence of illustrations here, performances there, by contrasting them with their profusion in other contexts. In some sense, the negative evidence is more compelling for the case of illustrations. There are many hundreds of fragments of canonical, ancient literary texts, with a high degree of professional execution – all of them without illustrations. The equivalent would have to be hundreds of passages of ancient testimonies to the ancient mathematical practice, where reference could have been made to performance and yet it is not mentioned. To some extent this is the difference between documenting illustrations, a material practice, and performances, a flesh-and-blood practice. Illustrations are artifacts and so may or may not survive; performances are only indirectly attested. But there is a more general point at play here. We are just not told all that much about the Greek mathematical practice. We merely have the mathematical texts. Which, after all, is in and of itself relevant to our argument. The Greek exact sciences left a substantial trace in the form of extant writings.65 But they do not register as a visible cultural form attested 65 In Netz (forthcoming), I count 29 authors in the exact sciences, broadly defined, extant from antiquity; a large part of this must represent a Byzantine bias for preserving mathematical contents, but this is indeed part of a larger trend of preserving more “technical” and less performative works.

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through its contemporary observers. Even for the ancients themselves, the exact sciences were primarily a set of texts. A single biographical image – that of Archimedes; but otherwise mathematicians are rarely if ever invoked as concrete persons. In other words, the very dearth of evidence for or against mathematical performance underscores the textual character of Greek mathematical practice. The complementarity of the two preceding sections is that of text and performance. I note the centrality of a certain textual procedure (the visual) in the Greek exact sciences; I also note the marginality of performance there; while noting the marginality of text-centered practices (such as illustrations) in mainstream Greek literature, as well as the centrality of performance there. This complementarity echoes that of the two sections 2 and 3. In section 2 I surveyed the practices of authorial design in Greek mathematics, emphasizing their textual character (reminiscent of more textual traditions in literature and perhaps directly related to the more textual approach of Hellenistic poetry). In section 3 I noted the essentially performative character of authorial presence in mainstream Greek literature. Surely, then, Greek mathematics is a textual practice and so its authorial presence is textual; while mainstream Greek literature is performative and so its authorial presence is performative. No surprise there. We can add a bit more to this truism. In the first section, while noticing the central role of authorial identity to ancient canonical reception, I emphasized the two layers of reception: within a circle of elite peers, and within larger audiences. The two layers, I emphasized, carry a deep sociological meaning: they signify the two vectors of ancient culture, the horizontal (bringing together elite members of different cities) and the vertical (bringing together the public of a city). We did notice, along the way, that the sociological building block of the Greek mathematical practice was the person-to-person relation. We can reformulate this now to say that Greek mathematics existed entirely within the horizontal vector: it was a cultural practice that brought together elite members of the ancient Mediterranean, but did not engage the audience of the city at all. As I said, there was no outreach there. Once again, this is not inherently surprising. The fundamental observation, however, once again, is contrastive. Ancient cultural practices, generally speaking, did aim to reach the vertical vector. Even intellectual disciplines such as philosophy or medicine would often engage in the culture of performance. The choice to remain within the horizontal vector was a choice unique to the Greek exact sciences, marking their authorial presence as a strictly textual practice implying the recognition by peers and not by wider audiences. In short, mathematics was the opposite of literature, but not by renouncing the authorial, but by staking out an opposite model of what the authorial meant. Mathematicians stood apart; which is apparently where they wanted to stand. Such was the structure of genres, authoriality and performativity, in antiquity itself. In the early modern era the literary authorial voice itself was reconfigured to encompass strategies of a more textual

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character. This would have consequences for the place of science within the system of genres, and for the nature of the scientific authorial voice.

Bibliography Texts quoted Betz, H. D. 1992. The Greek Magical Papyri in Translation. Chicago. Mertens-Pack = Pack, R. A., & P. Mertens. The Greek and Latin Literary Texts from Greco-Roman Egypt. (http://promethee.philo.ulg.ac.be/cedopal/index.htm) Stephens, S., & J. Winkler 1995. Ancient Greek Novels: the Fragments. Princeton, NJ. Artemidorus: Gallazzi, C., B. Kramer & S. Settis 2008 (eds.). Il Papiro di Artemidoro. Milan. Diocles: Toomer, G. J. 1976. Diocles on Burning Mirrors. New York. Pappus Alexandrinus: Hultsch, F., 1875–1878 (ed.), Pappi Alexandrini collectionis quae supersunt. Berlin. Plato: Burnyeat, M. F. 1990 (ed.), The Theaetetus of Plato. Indianapolis.

Works quoted Amati, M. 2010. “Meton’s Star-city: Geometry and Utopia in Aristophanes’ Birds.” In: Classical Journal 105, 213–227. Barchiesi, A. 2007. “Carmina: Odes and Carmen Saeculare.” In: S. J. Harrison (ed.), Cambridge Companion to Horace. Cambridge, 144–160. Barthes, R. 1977. “The Death of the Author.” In: R. Barthes & S. Heath (ed., transl.), Image – Music – Text. New York, 142–148. Beck, A. G. 1975. Album of Greek Education. Sydney. Balogh, J. 1927. “Voces Paginarum, Beiträge zur Geschichte des lauten Lesens und Schreibens.” In: Philologus 82, 84–109, 202–240. Bernard, A. 2003. “Sophistic Aspects of Pappus’ Collection.” In: Archive for History of Exact Sciences 57, 93–150. Booth, W. 1961. The Rhetoric of Fiction. Chicago. Bowie, E. 2004. “The Geography of the Second Sophistic: Cultural Variations.” In: B. Borg (ed.), Paideia: The World of the Second Sophistic. New York, 65–86. Burnyeat, M. f. 1978. “The Philosophical Sense of Theaetetus’ Mathematics.” In: Isis 69, 489–513. Cameron, A. 1995. Callimachus and his Critics. Princeton, NJ. Cavallo, G. 1996. “Veicoli materiali della letteratura di consumo. Maniere di scrivere e maniere di leggere.” In: O. Pecere & A. Stramaglia (eds.), La letteratura di consumo nel mondo greco e latino. Cassino, 11–46. Csapo, E., & W. J. Slater 1994. The Context of Ancient Drama. Ann Arbor, MI. Cuomo, S. 2000. Pappus of Alexandria and the Mathematics of Late Antiquity. Cambridge. Dedoussi, C. 1980. “Fr. 246 (PSI 847): An Illustrated Fragment of Menander’s EϒNOϒXOΣ.” In: Bulletin of the Institute of Classical Studies 27, 97–102.

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van der Eijk, P. 1997. “Towards a Rhetoric of Ancient Scientific Discourse.” In: E. J. Bakker (ed.), Grammar as Interpretation: Greek Literature in its Linguistic Contexts. Leiden, 77–129. Gallo, I. 1980. Frammenti Biografici da Papiri. Rom. Gavrilov, A. K. 1997. “Techniques of Reading in Classical Antiquity.” Transl. M. f. Burnyeat. In: Classical Quarterly 47, 56–76. Gentili, B. 1990. Poetry and its Public in Ancient Greece: from Homer to the Fifth Century. Baltimore. Gleason, M. 1995. Making Men. Princeton, NJ. Gleason, M. 2009. “Shock and Awe: the Performance Dimension of Galen’s Anatomy Demonstrations.” In: T. Whitmarsh & J. Wilkins (eds.), Greek Culture in the Roman World. Cambridge, 85–114. Goldhill, S., & R. Osborne 1999. Performance Culture and Athenian Democracy. Cambridge. Gutzwiller, K. J. 2007. A Guide to Hellenistic Literature. Oxford. de Hamel, C. 1994. A History of Illuminated Manuscripts. London. Hammerstaedt, J. 2000. “Gryllos. Die antike Bedeutung eines modernen archäologischen Begriffs.” In: Zeitschrift für Papyrologie und Epigraphik 129, 29–46. Hannah, R. 2002. “Euctemon’s Parapēgma.” In: C. J. Tuplin & T. E. Rihll (eds.), Science and Mathematics in Ancient Greek Culture. Oxford, 112–132. Heath, T. L. 1921. A History of Greek Mathematics. Oxford. Herman, G. 1987. Ritualized Friendship. Cambridge. Horsfall, N. 1979. “Stesichorus at Bovillae?” In: Journal of Hellenic Studies 99, 26–48. Jaeger, M. 2008. Archimedes and the Roman Imagination. Ann Arbor, MI. Johnson, W. A. 2000. “Towards a Sociology of Reading in Classical Antiquity.” In: American Journal of Philology 121, 593–627. Johnson, W. A. 2004. Bookrolls and Scribes in Oxyrrhynchus. Toronto. Jones, A. 1999. Astronomical Papyri from Oxyrrhynchus. Philadelphia. Knorr, W. R. 1975. The Evolution of the Euclidean Elements. Dordrecht. Knox, B. M. W. 1968. “Silent Reading in Antiquity.” In: Greek, Roman and Byzantine Studies 9, 421–435. Lehoux, D. 2007. Astronomy, Weather, and Calendars in the Ancient World. Cambridge. Lloyd, G. E. R. 1979. Magic, Reason and Experience. Cambridge. Lowden, J. 2010. “Illustrated Octateuch Manuscripts: a Byzantine Phenomenon.” In: R. Nelson & P. Magdalino (eds.), The Old Testament in Byzantium. Washington, DC, 107–152. Mansfeld, J. 1994. Prolegomena: Questions to be Settled Before the Study of an Author, or a Text. Leiden. Marrou, H. I. 1948/1956. A History of Education in Antiquity (orig. Paris 1948). Transl. G. Lamb. London 1956. Minto, A. 1952. “Frustulum Papyraceum con Resti di Figurazione Dipinta: Hermes Psychopompos (?).” In: Aegyptum 32, 324–332. Nagy, G. 1996. Poetry and Performance: Homer and Beyond. Cambridge. Netz, R. 1999. The Shaping of Deduction in Greek Mathematics: a Study in Cognitive History. Cambridge. Netz, R. 2001. “On the Aristotelian Paragraph.” In: Proceedings of the Cambridge Philological Society 47, 211–31. Netz, R. 2002. “Greek Mathematicians: a Group Picture.” In: C.J. Tuplin & T. E. Rihll (eds.), Science and Mathematics in Ancient Greek Culture. Oxford, 196–216. Netz, R. 2005. “The Aesthetics of Mathematics: a Study.” In: P. Mancosu et al. (eds.), Visualization, Explanation and Reasoning Styles in Mathematics. New York, 251–293. Netz, R. 2009a. Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic. Cambridge. Netz, R. 2009b. “Imagination and Layered Ontology in Greek Mathematics.” In: Configurations 17, 19–50.

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Nisbet, G. 2011. “An Ancient Greek Graphic Novel.” In: G. Kovacs & C. W. Marshall, Classics and Comics. Oxford, 27–41. O’Sullivan, L. 2009. “History from Comic Hypotheses: Stratocles, Lachares, and P.Oxy. 1235.” In: Greek Roman and Byzantine Studies 49, 53–79. Page, D. 1957. “P.Oxy. 2331 and Others.” In: Classical Review 7, 189–192. Parkes, M. B. 1993. Pause and Effect: an Introduction to the History of Punctuation in the West. Berkeley, CA. Perrone, S. 2009. “Lost in Tradition. Papyrus Commentaries on Comedies and Tragedies of Unknown Authorship.” In: Trends in Classics 1, 203–240. Robson, E. 2008. Mathematics in Ancient Iraq: a Social History. Princeton, NJ. Saenger, P. 1997. Spaces Between Words: the Origins of Silent Reading. Stanford, CA. Saito, K. 1997. “Index of Propositions Used in Book 7 of Pappus’ Collection.” In: Jinbun Kenkyu: The Journal of Humanities (Faculty of Letters, Chiba University) 26, 155–188. Sedley, D. N. 1976. “Epicurus and the Mathematicians of Cyzicus.” In: Cronache Ercolanesi 6, 23–54. Sidoli, N. 2009. “Drawing Diagrams and Making Arguments in Greek Geometry.” In: Reports of the Tsuda College Institute for Mathematical and Computer Science: Proceedings of the 19th Symposium in the History of Mathematics 30, 133–150. Snyder, H. G. 2000. Teachers and Texts in the Ancient World. London. von Staden, H. 1997. “Galen and the ‘Second Sophistic’.” In: Bulletin of the Institute of Classical Studies 41, 33–54. Starr, R. J. 1987. “The Circulation of Literary Texts in the Roman World.” In: Classical Quarterly 37, 213–223. Stückelberger, A. 1994. Bild und Wort. Mainz. Taub, L. 2002. “Instruments of Alexandrian Astronomy: the Uses of the Equinoctial Rings.” In: C. J. Tuplin & T. E. Rihll (eds.), Science and Mathematics in Ancient Greek Culture. Oxford, 133–149. Vitrac, B. 2002. “Note Textuelle sur un (Problème de) Lieu Géométrique dans les Météorologiques d’Aristote (III. 5, 375 b 16–376 b 22).” In: Archive for History of Exact Sciences 56, 239–283. Wallace-Hadrill, A. 1994. Houses and Society in Pompeii and Herculaneum. Princeton, NJ. Weitzmann, K. 1947. Illustrations in Roll and Codex. Princeton, NJ. Weitzmann, K. 1959. Ancient Book Illumination. Cambridge, MA. West, M. L. 1992. Ancient Greek Music. Oxford. Wright, D. H. 1993. The Vatican Vergil: a Masterpiece of Late Antique Art. Berkeley, CA. Zanker, G. 1981. “Enargeia in the Ancient Criticism of Poetry.” In: Rheinisches Museum 124, 297–311.

Serafina Cuomo

Accounts, Numeracy and Democracy in Classical Athens Abstract: This paper explores the possibilities of account inscriptions as evidence for ancient numeracy. Keeping a focus on fifth-century Athens, we ask: who did the math for the many account inscriptions that survive? And who was meant to read those accounts on stone? We pay particular attention to issues of accountability and political participation, and explore the question of formatting. The paper distinguishes account inscriptions into two main types according to format, and suggests a link between format and reading circumstances. Ultimately, the paper argues, numeracy was inextricably linked to questions not just of democracy, but also of empire, both facets of Athenian life at that time.

The Athenians were a calculating people. The volumes of Inscriptiones Graecae relative to fifth-century Athens contain almost two hundred items (out of about one-and-a-half thousand), which can be categorized as accounts.1 The inscriptions deal with different subject-matters: the most famous are perhaps those relative to the tribute of the members of the Delian League, both assessments,2 and lists of the one-sixtieth portions given to Athena.3 Many are building inscriptions recording expenditure on the Erechtheion, for instance, or the Parthenon.4 We have a few auction lists,5 as well as a relatively large number of documents relative to the finances of institutional bodies, such as the treasuries of temples.6 All with one feature in common: numbers, sometimes written out in letters, sometimes in acrophonic mathematical notation, are a significant part of the content of the inscription.7

1 I will concentrate here on the fifth century  only. I plan to consider fourth-century material in future research. 2 Inscr. Graec. I3 71 (425/4 ), 77 (422/1 ), 100 (410/9 ). Henceforth all dates are  unless otherwise indicated. 3 Inscr. Graec. I3 259–290. On tribute lists, the main work is still Meritt, Wade-Gery & McGregor. 4 Inscr. Graec. I3 397–400, 433, 435, 436–451 (Parthenon, 447/6 or 433/2), 455–458, 460–470, 472, 474–478 (Erechtheion, 409/8 to 406). A recent analysis of the information from building inscriptions in Feyel 2006; still very useful, and focussed on the building inscriptions of Epidaurus, is Burford 1969. 5 Inscr. Graec. I3 421–430 (all from 414). 6 E.g. Inscr. Graec. I3 296–9 (treasury of Athena Polias, 430/29 to 427/6). 7 E.g. Inscr. Graec. I3 52, 73, 130 (letters); Inscr. Graec. I3 64, 101 (mathematical notation). For the acrophonic notation from an epigraphic point of view, see Tod 1911/12; Guarducci 1968 I 417–428: the alphabetical notation was already in use in certain contexts in the fifth and fourth centuries.

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There are many ways in which we can look at these objects (they are, of course, objects, not ‘just’ texts). One of the most common approaches to account inscriptions has been to focus on their contents, and the historical information they can provide about, for instance, the Athenian Empire, or the Athenian economy. Benjamin Meritt’s work would be a case in point: his seminal studies of the tribute lists and other financial documents focussed on chronology, the ins and outs of financial policy, and exactly how many and what numerals might fit within a lacuna.8 Conversely, historians have reflected on the context of inscriptions – for instance, the fact that the accounts were publicly displayed. Many of these documents were produced in pairs, one to be deposited with the assembly, one to be displayed in the agora, often as a self-standing stele.9 Diane Harris has commented that, although the Athenian accounting system may have been derived from the Persian one, the inscription of selected accounts on stone and in public is not something we find in other, non-democratic, ancient cultures.10 Whether and to what extent Athenian epigraphic habits can be related to the political character of the polis is, of course, a much-disputed question: after all, epigraphic habits exist in societies, such as the Roman Empire, which are not traditionally considered democratic.11 On the other hand, and this is a point which Charles Hedrick derives from Plato, orality allows for discussion and modification of views, and could thus implicitly be seen as more democratic than writing, whose stability also results in the inability to engage in discussion and to change.12 Issues of reading and orality beg the question of literacy. Were the Athenians able to read inscriptions – does the proliferation of public texts indicate that the rate of literacy was high? Or, if many Athenians were unable to read, was the function of inscriptions ritual and symbolic, rather than straightforwardly informative? Rhodes and Osborne comment in the introduction to their selection of Greek historical inscriptions: We have deliberately used the verb ‘see’ rather than ‘read’. Though in theory the purpose of a published text is that it should be available to be read, some texts were published in such a way that they were not easy to read […]. Nevertheless, some other texts were laid out in ways designed to aid intelligibility […]13; and we think it would be a mistake to make too much of the symbolic aspect of inscription and too little of the notion that texts were published so that they could be read.14

8 See e.g. Meritt 1932, 1937. 9 Meritt & West 1934; Rhodes 2001a. 10 Harris 1994, 223. See also Lewis 1986 for a link between democracy and inventories inscriptions. 11 See e.g. Thomas 1992; Hedrick 1999. 12 Hedrick 1994, 162–169; cf. e.g. Plato, Phaedrus 274c–275e. 13 The example given is no. 45 in Rhodes & Osborne 2003 = SIG3 239, from Delphi, listing paid amounts in words. As I shall suggest later, the formatting Rhodes and Osborne refer to does not particularly aid intelligibility of the numerical information contained in the inscription. 14 Rhodes & Osborne 2003, xiii. Cf. also e.g. Thomas 1989; Osborne 1994, 15.

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In other words, the two aspects that we could call, respectively, the ‘symbolic’ and the ‘informative’ function of inscriptions, are compatible; and yet, according to Rhodes and Osborne and others,15 we can still identify inscriptions which were more obviously not meant to be read. We can use literacy as a springboard to approach inscriptions (in particular, account inscriptions) with a different question in mind: what can these documents tell us about the ability to count, calculate, and measure–in other words, about numeracy? While the study of literacy in ancient Greece and Rome is a thriving field, very little exists about numeracy.16 The few studies that have discussed the topic with relation to classical Athens have emphasized how pervasive operations of counting and calculating were in the working of assemblies and law-courts. Attention has also been paid to the significant number of counting boards that have survived.17 The relevance of account inscriptions to issues of numeracy, however, has largely remained unexplored. There are important differences between literacy and numeracy in ancient Greek and Roman society. For instance, literacy appears prima facie to have been socially more valued than numeracy. This asymmetry is far from being selfexplanatory – there were ancient societies (the Assyrian Empire, for instance) where numeracy was very highly valued indeed. On the other hand, one significant similarity is the fact that there are degrees of numeracy, just as there are degrees of literacy. Some people might have been able to write their name and little else; analogously, people might have been able to add and subtract, but not divide. Some people were able to write poems that scanned, or to prove theorems: they were what we could call the upper end of the spectrum in their respective areas of knowledge. It is probably the case that in antiquity fewer people were able to do theorems than poetry: a simple look at the evidence, even allowing for accidents of survival, indicates that the top level of numeracy was probably more thinly populated than its literacy equivalent.18 Interestingly, however, the opposite may have held true for the lower end of the spectrum. The rate of basic numeracy in ancient Greece and Rome may well have been higher than the rate of basic literacy. On the whole, at least before the advent of credit cards and computerized tills, numbers have a tendency to be used more extensively than letters in daily life, including the daily life of a society whose economy is not completely monetized. Even barter tends to require some degree of counting or measuring. It could even be said that, unlike other forms of numerical notation, the acrophonic notation, used in inscriptions until the end of the first century  and 15 Davies 1994, 211; also Linders 1992; Hedrick 1999, 393. 16 A notable exception, and a seminal influence on this paper, is Netz 2002b; see also Asper 2003. More work exists on numeracy in other ancient cultures, e.g. Imhausen 2003, Robson 2008, Rossi 2009. 17 See Schärlig 2001, who lists some thirty counting boards, Netz 2002b. 18 For an estimate of the upper end of the numerate spectrum, see Netz 2002a.

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found on most of those of our extant counting boards that are inscribed,19 has a rationale. The written note for a number, at least some times, was the initial of the name of that number: Δ for δέκα, Γ (which here is actually a graphic variant for Π) for πέντε, and so on. It is possible that this facilitated number recognition.20 More importantly, the range of media and forms of expression for numeracy was wider than their literacy equivalents, and the skills required or indeed sufficient to support numeracy were, in principle, accessible to a wider group of people. Letters by definition only exist as written signs, but numbers–especially ‘ancient’ numbers, which were arguably more ‘concrete’ than our abstract, modern ones– could be anything. They could be objects counted, they could be written, could be made up with fingers or moved around, in the concrete form of counters, on a counting board. As Netz pithily puts it, “we imagine numbers as an entity seen on the page; the Greeks imagined them as an entity grasped between the thumb and the finger.”21 In sum, one can plausibly speculate that the rate of ancient numeracy may have exceeded that of literacy.22 Having laid out some preparatory ground, in this paper I will raise two related questions: who were the authors of the fifth-century Athenian account inscriptions? I do not mean who cut the stone, but who did the calculations – who counted and produced the figures that were then engraved on stone? The second question is one of audience: who was meant to read the account inscriptions? Indeed, in the light of my previous remarks about symbolic and informative functions of inscriptions, were account inscriptions meant to be read at all? I will not attempt to give a definitive answer to either question. Instead, in the next sections I will offer reflections and explore possible directions for research on the themes of authorship and readership, respectively.

1 Who were the authors of the account inscriptions? Who did the calculations in the first place? Given what we know about fifth-century Athens, there appear to be a limited number of possibilities: public slaves, privately-owned slaves, citizens with specific expertise who were selected to do calculations precisely because they were

19 Schärlig 2001. 20 Errietta Bissa remarked (personal communication) that knowing the acrophonic notation necessitated knowledge of some letters of the alphabet and therefore some literacy. Which is a fair point, although learning some alphabet letters was arguably not too difficult: see Immerwahr 1992, 97. Thus, learning enough letters to be able to recognize acrophonic notation would have made you barely literate, but moderately numerate. 21 Netz 2002b, 9. 22 Netz 2002b, 3.

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experts, and citizens with no specific expertise.23 Let us consider those possibilities in turn. While we know that public slaves acted in several capacities in the fourth century,24 we simply have no evidence of them being employed for this particular task during the fifth century. A useful parallel could be drawn with the late Roman Republic, where we do know that slaves and ex-slaves could be used to maintain public accounts, because the sources tell us so.25 On the other hand, there seems to have been an expectation in Athens (as we shall see later) that anyone could count on their fingers or follow a calculation on the abacus. The question is then, is the silence of the fifth-century sources on this point evidence of the absence of public slave accountants? Conversely, if public slave accountants did exist in the fifth century, why are our sources silent about them? Some scholars would even explain the generally lower status of numeracy (compared to literacy) in ancient Greek and Roman society, on the basis of vast contingents of slave accountants. But if that was the case, and if slave accountants were a constant across Greek and Roman society, why do we find different representations of them, and of public numeracy, in the late Roman Republic, or indeed, subject to further historical scrutiny, in fourth-century Athens? Ultimately, whoever did the calculations in reality (and we may never be able to know), what matters for the present purposes is that public slaves were in no sense represented as the authors of the account inscriptions. We have to look for authorship elsewhere. What about slaves belonging to private citizens? Again, there is no mention of them in our sources, and it would seem implicitly unacceptable in a supposedly democratic process, where any citizen might be eligible for office, to expect people to provide their own administrative staff. Thus, even if private slaves were employed, we could fall back on our previous remarks about public slaves, and add the consideration that the way in which the Athenians represented what happened, was further complicated by the need to uphold values such as equality and participation in a society which, like all others, was stratified in terms of wealth and social status. We are left with perhaps the most obvious solution, i.e. that citizens, in their capacity as officers, did the calculations themselves. But which officers? Many of

23 Rhodes 2001b, 144, on the office of grammateus: “Some of the actual writing may have been done by salaried clerks, or even by slaves, but until a change in the 360’s which allowed for more professionalism it was assumed that every tribal contingent of fifty in the council would contain a man who was competent to act as the state’s principal secretary for a tenth of the year.” 24 E.g. Aristotle, Ath. pol. 50.2: public slaves for burials of unclaimed bodies, 54.1: workmen for roads; Inscr. Graec. II2 120 (362, translation Hamilton 2000, 347): “Eukles the public scribe”, in charge of recording the objects of a sacred treasury; Inscr. Graec. II2 212 (346): rowers; Harding 1985, 45 (375/4 ): certifier of silver coinage. 25 Cuomo 2009.

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the posts in the governance of the polis involved some financial administration. Generals were apparently expected to reckon their own campaign expenditure.26 The pōlētai, who were in charge of public contracts and taxes, also had to produce yearly accounts on whitened tablets,27 and there were officers whose concerns were more specifically maintaining (rather than producing) the whitened tablets themselves.28 Above all, however, we have mentions of two posts: treasurer and accountant. The fourth-century Constitution of the Athenians states that the treasurers of Athena (the main contingent of treasurers, later to absorb those of the other gods) were chosen specifically from the higher income group: πρῶτον μὲν γὰρ εἰσὶ μὲν δέκα, κλη[ροῦτα]ι δ' εἷς ἐκ τῆς φυλῆς, ἐκ πεντακοσιομεδίμνων κατὰ τὸν Σόλωνος νόμ[ον (ἔτι γὰρ ὁ] νόμος κύριός ἐστιν), ἄρχει δ' ὁ λαχὼν κἂν πάνυ πένης ᾖ. First there are the ten treasurers of Athena, elected one from a tribe by lot, from the Fivehundred-bushel class, according to the law of Solon (which is still in force), and the one on whom the lot falls holds office even though he is quite a poor man.29

This appears confirmed in a text sometime identified as a fragment of Theophrastus, where various qualifications for office (virtue, experience, wealth) are discussed: “for instance, in the post of treasurer, as has been said, they retain the property qualifications.” (ἐν μὲν γὰρ τῇ ταμιείᾳ, καθάπερ εἴρηται, τὰς οὐσίας τηροῦσιν.)30 The selection procedure may have not been limited to the treasurers of Athena alone, because, according to a fifth-century inscription, the treasurers of the other gods “shall be selected by lot […] just as are the [treasurers] of the sacred monies of Athena.” (ταμίας δὲ ἀροκυαμεύεν τοῦτον τῶν χρεμάτον ὁταμπερ τὰς ἄλλας ἀρχάς, καθάπερ τὸ τῶν ἱερῶν τῶν τῆς Ἀθεναίας.)31 If we take this evidence as unproblematic, then the people in charge of one of the most important (and prestigious) financial administration tasks in Athens, were not just anybody. They were indeed selected, but not in terms of their expertise – rather on the basis of their wealth. More than an assumption that rich people would be numerate because they needed to manage their estates (the possibility of slaves employed for this task rears its head with greater force here than it did earlier), we have the idea, also current in the Roman Republic, that rich people will be better at administering the state’s finances because they have fewer incen26 See e.g. Inscr. Graec. I3 71, lines 45–50 (425/4). 27 Aristotle, Ath. pol. 47.2–3 (there is a lacuna). The accounts in question are simple lists with names and figures. 28 Aristotle, Ath. pol. 47.5, 48.1. 29 Aristotle, Ath. pol. 47.1 (Loeb tr.), cf. 7.3, 8.1. 30 Oliver 1977, 327. 31 Inscr. Graec. I3 52 lines 13–15 (tr. Fornara 1977). Cf. Ferguson 1932, chapters 2 and 14, for the secretaries’ rota; Linders 1975, 44f.; Sinclair 1988, 80; Hansen 1979/1991, 233; Harris 1995, 11–19.

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tives to embezzle public monies, and are in a better position to pay the fines involved for transgression of procedure. But the evidence presented above is not unproblematic. The fifth-century inscription is slightly at odds with the lengthier evidence from Constitution of the Athenians. The text mentions selection by lot only, and has no word about property qualifications. This could be either because the criterion of membership of the pentekosiomedimnoi was not in use at the time, or because it was so obvious that it needed no mention. The evidence from the Constitution of the Athenians is itself not internally consistent. The second part of the passage quoted above clashes with the first. If the treasurers are by definition drawn from the richest families in Athens, then how can one of them be a poor man? Again, it is possible that the regulations about income qualification had been informally, if not officially, discarded with time, because the income bracket distinctions had themselves become obsolete with the gradual erosion of privileges limited to the rich, towards a more ‘radical’ democracy.32 The inscriptions also mention accountants (logistai), sometimes referred to as organized in a board of thirty. The so-called decree of Kallias, about repaying loans to sacred treasuries, says: λογισάσθον δέ; οἱ λογισταὶ οἱ τριάκοντα οἵπερ νῦν τά; ὀφελόμενα τοῖς θεοῖς ἀκρ-; ιβῶς συναγωγῆς δέ τῶν λογισττῶν ἡ βουλή; αὐτοκράτωρ ἔστω. Calculation shall be made by the thirty Logistai now in office of that which is owed to the gods precisely, and the Boulē shall be solely competent to determine when the Logistai are to meet together.33

It would seem that the accountants carried out calculations, including calculations of interests on loans, in a more ‘specialized’ way than other officers involved in Athenian finances. In an inventory dated to between 409/8 and 407/6, the logistai are charged with responsibilities more often associated with the treasurers.34 The Constitution of the Athenians has this to say on the matter: [κ]ληροῦσι δὲ καὶ ἐξ αὑτῶν οἱ βουλευταὶ δέκα, τοὺς λογιουμένους τ[αῖς ἀ]ρχαῖς κατὰ τὴν πρυτανείαν ἑκάστην. κληροῦσι δὲ καὶ ἕνα τῆς φυλῆς ἑκάστης, καὶ παρέδρους βʹ ἑκάστῳ τῶν εὐθύνων […] κἄν τις βούλ[ηταί] τινι τῶν τὰς εὐθύνας ἐν τῷ δικαστηρίῳ δεδωκότων […] γράψας εἰς πινάκιον λελευκωμένον τοὔνομα τό [θ' αὑ]τ[ο]ῦ καὶ τὸ τοῦ φεύγον-

32 Cf. Aristotle, Ath. pol. 26.2 for an example relative to the archons, 30.2 for changes under the Five Thousand. Cf. Davies 1971, xvii; Hansen 1979/1991, 106–109; Rhodes 1993, 146, 551. 33 Inscr. Graec. I3 52 (second half of the fifth century ), tr. Fornara 1977, 130–132 (no. 119). See also Inscr. Grace. I3 32 (discussion in Samons 2000, 133–136), 259 line 2, 260 line 1, 261 line 1 (tribute quota lists, referring to 30 something – perhaps logistai?); Rhodes 1985, 111; Harris 1995, 16. 34 Inscr. Graec. I3 377; Ferguson 1932, 31n2: “The rôle played here by the Accountants remains as yet unintelligible. That they should receive sacred moneys is surprising; that they should give them, bewildering”; cf. also Samons 2000, 280.

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τος […]δίδωσιν τῷ εὐθύνῳ […] Κληροῦσι δὲ καὶ τάσδε τὰς ἀρχάς· πέντε, οἷς προστέτακται δημοσίους ἐργάτας ἔχουσι τὰς ὁδοὺς ἐπισκευάζειν· καὶ δέκα καὶ τούτοις δέκα, πρὸς οὓς ἅπαντας ἀνάγκη τοὺς τὰς ἀρχὰς ἄρξ[αντ]ας λόγον ἀπενεγκεῖν. οὗτοι γάρ εἰσι μόνοι τοῖς ὑπευθύνοις λογιζόμενοι καὶ τὰς εὐθύνας εἰς τὸ δικαστήριον εἰσάγοντες. The Council also elect by lot ten of their own body as accountants, to keep the accounts of the officials for each presidency. Also they elect by lot auditors, one for each tribe, and two assessors for each auditor […] and if anyone wishes to prefer a charge […] against any magistrate who has rendered his accounts before the jury-court […] he writes on a tablet his own name and that of the defendant […] and gives it to the auditor […]. They also elect by lot the following officials: five highway-constructors, whose duty it is to repair the roads, with workmen who are public slaves; and ten auditors and ten assessors with them, to whom all retiring officials have to render account. For these are the only magistrates who audit the returns of officials liable to account and bring the audits before the jury-court.35

Again, the evidence presents problems of interpretation. Above all, it is not clear how much of this applies to the fourth century only, and whether the author is talking about different groups of logistai, or about one group who did accounts and audited everybody who held office. In his commentary on the Constitution of the Athenians, P.J. Rhodes indicated both that there were different groups of logistai, some drawn from the boulē, some not (and the possibility is open that those latter were not citizens), and that the information about accountants provided by fourth-century sources, including some inscriptions, may not be transferred back onto our picture of the fifth century.36 If in order to become a treasurer in the fifth century you had to be categorized as rich, it was politically poignant that their actions should be specifically scrutinized by the accountants, who were ordinary citizens, drawn from the boulē by lot, and not subject to special requirements.37 And if the treasurers were not drawn from the wealthy citizens, then it would seem that your average Athenian, in the second half of the fifth century  at least, was expected to be more than basically numerate. Beyond the ambiguities of the evidence and the minutiae of procedure, it is time to ask: why does it matter? What are the wider implications of knowing who did the maths in the account inscriptions? In my view, the question of authorship provides insight into two wider issues: one is accountability, the other is political participation. As is well known, Athenian officers had to render accounts at the end of their period of service, a ceremony known as euthunai, and sometimes viewed as a

35 Aristotle, Ath. pol. 48.3–4, 54.1–2 (Loeb tr.); cf. Sinclair 1988, 79; Hansen 1979/1991, 220–224. 36 Rhodes 1993, 597f. (citing e.g. Inscr. Graec. II2 847). 37 Antiphon 5.69–71 mentions that a board of Hellenotamiai were accused of embezzlement and sentenced to death (and later found innocent). Cf. Samons 2000, 280: “the Logistai’s actions arguably reflect a financial system in which officials were always subject to any orders of the dēmos, whatever their ‘regular’ functions.”

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hallmark of the transparent processes of democratic governance.38 If the calculations were carried out by officers rather than slaves – if the accounts were put together and maintained by the citizens themselves, then the link between accounts and accountability is reinforced. They are both part of what it means for Athens to be democratic. At the same time, we detect, in the Constitution of the Athenians but also in inscriptions such as the so-called decrees of Kleinias and Kleonymos, an attempt to tighten up mechanisms of control, via for instance the creation of extra layers of auditing and checking. The decree of Kleinias stipulates a system of identification seals and sealed account books, “so that it will be impossible that fraud be committed by those bringing the tribute payments”, whereas the document associated with Kleonymos regulates the appointment of tribute collectors.39 Our sources testify to the difficulty of both making every officer (in principle, every Athenian citizen) accountable and responsible for producing his own accounts, and of producing viable accounts at a time when, thanks to the expansion of the Athenian sphere of influence, the scale and complexity of financial administration were growing. To put it bluntly, the Athenian polis had become the Athenian Empire. Financial administration in empires (even rather inefficient and short-lived empires) is a problem. Generalizing wildly, the solutions available in antiquity included what we could call ‘the Mesopotamian solution’, where public financial administration is in the hands of a selected and highly specialized group, the ‘scribes’, with relatively high social status. Teaching is in the form of intensive training, often running in families, and different accounting techniques are tried out and developed over time.40 On the other hand, we have what we could call ‘the Roman solution’, where many of the accountants are slaves and ex-slaves, with relatively low social status but personal links and vicinity to the state officers, including the emperor. Because of their standing, what we know about them tends to be filtered through the eyes of other, often hostile, observers. At the same time, the elite-produced evidence about Roman clerks, accountants and secretaries betrays a diffused anxiety about the importance of their role, and its dissonance with respect to other indicators of social prestige and respectability.41 The problem with articulating an ‘Athenian solution’ to the problem of imperial financial administration, is precisely the link between accounts and accountability: if all citizens are to participate in the governance of the polis, all citizens must also be accountable, i.e. responsible for producing their accounts, i.e. increasingly

38 Cf. Aristotle, Ath. pol. 4.2 mentions euthunai at Draco’s time, cf. 8.4, 27.1, 48.4; Aeschylus, Persae 213; Tolbert Roberts 1982. 39 Klenias: Inscr. Graec. I3 34 (448/7 ), tr. Fornara 1977, 104–106 (no. 98). An earlier date is possible. Cf. Meritt, Wade-Gery, McGregor, ATL III 13–18. Kleonymos: Inscr. Graec. I3 68 (426 ), tr. Fornara 1977, no. 133. Cf. Constantakopoulou 2009. 40 All thoroughly explored in Robson 2008. 41 See e.g. Muñiz Coello 1982, Purcell 2001, Cuomo 2009.

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highly numerate. The alternative is delegating, but, if we are talking about a direct rather than a representative democracy, and if accountability is a political function which (like all political functions) ought not to be delegated, then it would appear inevitable that every citizen, in order to be a good citizen, ought also to possess some specialized knowledge. A good embodiment of this contrast is the earlier figure of Aristeides, widely credited with the first assessment, in 477, of how much tribute the participants in the Delian League should pay. According to a later source: ταχθεὶς δὲ ἐπὶ τὴν διάταξιν τῶν φόρων, οὕτως ἀκριβῶς καὶ δικαίως τὸν διαμερισμὸν ἐποίησεν ὥστε πάσας τὰς πόλεις εὐδοκῆσαι. διὸ καὶ δοκῶν ἕν τι τῶν ἀδυνάτων ἔργων συντελεκέναι, μεγίστην ἐπὶ δικαιοσύνῃ δόξαν ἐκτήσατο καὶ διὰ τὴν ὑπερβολὴν τῆς δικαιοσύνης δίκαιος ἐπωνομάσθη. He (Aristeides) was put in charge of the tribute assessment, and he shared out the amount so precisely and fairly that all the cities were well pleased. Since he seemed to have accomplished something impossible, Aristeides got the greatest reputation for justice, and because he was so excessively just he was known as ‘Aristeides the Just’.42

Precision is a skill, to do with one’s knowledge, whereas fairness or justice are virtues, to do with one’s character. And yet, precision and fairness go hand in hand in Aristeides’ assessment–without precision there could have been no justice; without justice the precision could have been twisted towards self-gain. Notice, however, which of the two has greater social cachet: the Athenian statesman’s moniker is not ‘Aristeides the precise’! Plutarch, who ran his life of Aristeides in parallel with that of the Roman Cato the Elder, wrote of the same episode: μέγα δὴ οὖν ὄνομα τοῦ Ἀριστείδου καὶ θαυμαστὸν ἔχοντος ἐπὶ τῇ διατάξει τῶν φόρων ὁ Θεμιστοκλῆς λέγεται καταγελᾶν, ὡς οὐκ ἀνδρὸς ὄντα τὸν ἔπαινον, ἀλλὰ θυλάκου χρυσοφύλακος. […] τοῦτο μέν, εἰπεῖν, […] καλὸν καὶ στρατηγικὸν ἀληθῶς ἡ περὶ τὰς χεῖρας ἐγκράτεια. So then Aristeides had a great and admirable name for putting order in the tribute. But Themistocles is said to have ridiculed him, claiming that the praise he got […] was not fit for a man, but rather for a mere money-guardian. […] However […] Aristeides […] remarked […]: ‘[…] the honourable thing, and that which makes the real general, is his control over his hands.’43

While redolent of attitudes which we find elsewhere in Plutarch, and thus evidence for later views, the exchange between the two statesmen is also exemplary of the tensions we have been exploring here: excessive numeracy could be frowned upon. At the same time, the task of ‘money-guardian’ is explicitly designated as one of enormous power (24.2). Aristeides’ final barb can be read in at least two ways:

42 Diodorus Siculus, Bibl. XI 47.2, in Osborne 2000, 17, together with reports in Thucydides, V 18.5 and Aristotle, Ath. pol. 23.4–5. 43 Plutarch, Vita Arist. 24.4 (Loeb tr. with modifications). Cf. Vita Arist. 4.2–5, where Themistocles has Aristeides indicted for theft at the latter’s euthunai.

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control over one’s hands means the ability to remain honest when exposed to huge amounts of wealth, but it also evokes the image of a skilled calculator, deft with his fingers or manipulating counters on an abacus. With his ideal combination of knowledge and virtue, the Athenian democracy would require everybody to be an Aristeides. The dilemma is in essence not unlike that much discussed by Plato: whether it is in fact a good idea that everybody should be able to participate in the governance of the polis, or whether Athens should be run by ‘the best’. The question then becomes, what counts as ‘best’, whether it is a matter of virtue or skill, whether virtue is a skill that can be taught (a tekhnē), and so on.44 These are questions whose discussion in our extant sources again betrays a diffused anxiety about the perils of democracy–questions that Plato, for one, does not seem to have definitely settled. In conclusion, it can be argued that the question of authorship for the account inscriptions is, at heart, also a question about political participation.

2 Who was the audience for the account inscriptions? Who was meant to read these texts–were these texts meant to be read at all? Were the account inscriptions actually informative, or did they have a ritual meaning? As we said in the introduction, these questions have been debated for some time now, and discussion has flared up in particular with the case of inventory inscriptions. It seems legitimate to transfer the terms of that debate over to account inscriptions, both because in some cases (specifically the material from Delos), accounts and inventories were on the same stele, as part of the same inscription, and because in essence the issue is the function and character of lists, a category to which both accounts and inventories belong. The majority of scholars has cast doubt on the actual informative value of list inscriptions. In the case of inventories (lists of goods belonging to a god which were handed over, year to year, to the next group of caretakers), Tullia Linders, John Davies, Diane Harris, all point out that what mattered were the identities (and consequently, responsibility) of the officers involved in the transaction, rather than the amount or use of the funds or objects transacted.45 In Linders’ words, the inscriptions […] record not so much book-keeping as the way administration worked, which was by means of personal encounters and oral communication. […] every official was in all

44 Cf. e.g. Plato, Euthyd. 305c–307c, Meno 70a, 86c–d, 89c–90b, 91b, 93a–94e, 96d, 99e–100b, Gorg. 520d9–11, Prot. 319e–320b, also Isocrates 13.21; Xenophon, Apol. 29–31. Secondary literature includes Cambiano 1991; Roochnik 1996, 62f.; Euben 1997, 244; Cuomo 2007, chapter 1. 45 Linders 1988, 1992; Davies 1994, 207f., cf. 211.

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his doings under the surveillance of other officials, [so] mutual control was the consequence. […] [The inscriptions] are therefore, to my mind, monuments of actions performed, not records to be consulted.46

Or, to cite Harris, the accountability factor is only a small part of the publication of these special documents on stone: the papyri or whitened boards in the city archive serve that function, while the stelai serve as insurance of the gods’ favour upon the action described in the text.47

A smaller group of scholars, primarily Sara Aleshire and Richard Hamilton, are more sanguine about the actual value of the inventories as records, especially since entries reporting items missing, and other details about changes in the material recorded, point to an actual use of the information that goes beyond a purely symbolic value.48 If we portray the two positions in an extreme way, for the purpose of discussion, we could say that a strong reading of the symbolic value of list inscriptions makes sense of the fact that very many of extant documents of this kind originate within a religious context. Even the so-called tribute lists, after all, are one specific portion of the actual tribute lists, namely the money given to Athena. A strong symbolic reading does not have to commit to high rates of literacy or numeracy. Moreover, it is eminently compatible with the idea that classical Athenian politics can usefully be read as performance, and that social hierarchies were negotiated or questioned within that framework.49 On the other hand, a strong reading of the informative value of the inventory (and, by extension, account) inscriptions makes sense of the fact that money and time were spent on carving those stones in all their minute details. As Samons remarks, the gods would presumably have been satisfied with a descriptive relief where the personified dēmos handed over goods and coins to them50–after all, unlike the Babylonians, the Greeks did not have an accountant god demanding exacting precision. It also seems to me that what few sources we have about actual reading of the inscriptions (e.g. the so-called ‘formulae of disclosure’), plus references to counting in Aristophanes and, in the fourth century, the orators,51 rather indicates that the numbers in inscriptions at least sometimes were for counting 46 Linders 1992, 36. She also thinks that the main intended ‘readership’ for the inscriptions was the gods. 47 Harris 1994, 216; already in Giovannini 1990, 133, echoed in Osborne 2000, 97: “if whitened boards were often sufficient to ensure accountability to men, accountability before the gods demanded inscription on stone.” 48 Aleshire 1989; Hamilton 2000, 25–29, 258, 273. 49 See e.g. Ober 1989, 1998; Goldhill & Osborne 1999. 50 Samons 2000, 315. 51 Hedrick 1999; Aristophanes, Vesp. 655–718 (first staged in 422); Demosthenes 18.229; Aeschines 3.59 (discussion in Cuomo 2001, 20–24).

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and not just for seeing. The political scenario emerging from this interpretation is that the records were verifiable by everybody (even those who could not decipher the written signs, if only they could follow the operations on their fingers), so that the account inscriptions truly were accountability embodied. If, again, a numerate person could go through the steps of calculation in some of the inscriptions, they could have replicated the experience of checking the possessions of the goddess Athena, or the tributes of the allies, or the properties of disgraced citizens put up for auction, and in that replication acquire authorship not just of the account, but of the wider context within which the account had significance. On this reading, then, potentially replicable accounts provide means of extending participation in a truly democratic fashion. Is there a third way? P. J. Rhodes concedes that “in their published form these documents were valuable for what they symbolized as well as for the detailed information that they contained”, but he also wonders who would read the Athenian tribute lists? Who would read a long and elaborate text concerning the treasury of Athena or the dockyards, which recorded not what should be there now but what the officials of ten years ago had received from the officials of eleven years ago and had in their turn passed on to the officials of nine years ago?52

Rhodes’s puzzlement has an intuitive appeal for us today. And yet, how can we know whether an ancient Athenian would have shared it? For us lists, accounts and inventories are the quintessential ‘browsing’ material, not something one actually reads. At the same time, in the ancient world lists were common not only on inscriptions, and not only in the form of accounts: think of the ship catalogue in the Iliad or the funerary inscriptions for the public burial of the Athenian war dead.53 What if ancient reading practices, or cognitive approaches to lists, accounts and inventories, were completely different from ours? One element that needs to be considered in greater depth is formatting. The formatting of accounts has received some attention from scholars in neighbouring fields: Eleanor Robson, for instance, has analyzed tabulation in Mesopotamian accounts on clay tablets.54 In the Greek world, on the other hand, while accounts have not been thoroughly analyzed from this point of view, scholars have discussed the formatting of inventory inscriptions, mostly because of the information they can provide about the material culture of religion and the layout of temples. Factors at play include the order in which items are listed, as well as the taxonomic categories used to arrange the information (for instance, weight, type of object, material). Attention has also been paid to how new items are incorporated into the list,

52 Rhodes 2001b, 140f. A balanced view in Cleland 2005, 8f. 53 Homer, Iliad II 494–759; Inscr. Graec. I3 1144, 1146, 1147, 1149, 1150, 1162, 1180, 1184, 1186, 1190, ranging in date from 464 to 411 . 54 Robson 2003, 2004.

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whether an appendix is added at the end, or new acquisitions are integrated into the inventory. For a parallel, you can think of an old-style library catalogue, but one where the alphabetical order is not established as the main arranging criterion, and where it is impossible to insert new record cards in between the ones from previous years, without writing all the record cards again from scratch. Generally speaking, formatting changes across the time-span of inventories from the same treasury, and across inventories from different places. Sometimes there appears to be a discernible order in the way in which the information has been put on stone: for instance, the sequence of rooms being inventoried.55 In exploring the reasons why inventories of the so-called Independence period of Delos (314–166 ) are rather ostentatiously different from those extant from the period of the island’s subordination to Athens, Richard Hamilton suggested: One might conclude […] that politics determined the form of the inventories. Athenians demanded accountability; the Delians, left to their own devices, let anarchy reign and changed their format at will. Although this may not tell us as much as we wish to know, it certainly carries us beyond the ‘symbolic’ interpretation.56

Other times the arranging criteria remain obscure, and the actual informativeness of the inventory is put in question, because it appears that not all items are included, without any access to the possible reasons for selection.57 Obviously, we are faced with the same problem again: how can we understand how ancient inventories were put together and used (or not used, as the case may be)? Is there a rationality in the taxonomy of information that is independent of historical circumstances? Or is it rather the case that, in Liza Cleland’s words, “the manner in which a catalogue describes and identifies its objects must be conditioned by the social and cultural existence of these objects”?58 That question will have to be left open for the time being – let us shift our focus onto accounts. Given that the type of information conveyed is simpler, we can identify two basic formats in account inscriptions from the fifth century: one where numbers are interspersed in the text (whether written out in figures or in letters, see fig. 1), and one where numbers are clearly marked out and content is arranged in columns, usually a list of numbers on one side and a list of nouns on the other side (numbers are always in figures – I will refer to this format as ‘tabular’, see fig. 2). Even within similar formatting, information can be presented in slightly different ways. Meritt noticed that some accounts were arranged chronologically (say, money loaned every year, year after year) and some thematically (say, expenses on the 55 See e.g. Harris 1995. 56 Hamilton 2000, 2. He also notes that there were frequent changes in format in the Athenian inventories (chapter 4), with perhaps an (unsuccessful) attempt to “organize all dedications into a coherent system” (272). 57 See e.g. Linders 1988, with references to previous work. Contra Aleshire 1989, 107 f. 58 Cleland 2005, 4 f., 47–49.

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Fig. 1.: From Inscr. Graec. I3 248, an example of ‘interspersed’ formatting, from Petrakos 1999, 148.

fleet, expenses on the infantry, and so on).59 When totals are stated, they again are sometimes thematic (sum total of a certain type of object), sometimes chronological (sum total after a year). Sum totals can be marked out in the formatting by being engraved in a single line bridging the gap between two columns of text. Practice is not consistent: for instance, the assessment of 425 is arranged by geographical region, and it contains sum totals after some of the regions, and a grand total at the very end. On the other hand, many of the tribute quota lists (only some of which contain district headings) do not state sum totals, and there is debate as to what criterion, if any, informs their arrangement, which tends to be in columns.60 One of the factors affecting formatting must have been how much room was available for figures on the designated slab of stone,61 and (if different formatting commanded slightly different prices) how much money the commissioners were prepared to spend. Jean Bousquet suggested that the fourth-century account inscriptions from Delphi are in interspersed format so as “to avoid mistakes and confusion”, especially given that stone cutters and readers of those accounts would have included people from all parts of Greece, brought up with different numerical notation systems.62 Overall, however, it seems very likely that at least some of the times formatting was deliberately tabular or deliberately interspersed on grounds that cannot be limited to ‘practical reasons’. Thus, the record of the treasurers of other gods for 429/8, although lacunose, would appear to have followed the procedure laid out in the decree of Kallias, according to which totals had to be calculated 59 Meritt 1932, 58–60. 60 The assessment is Inscr. Graec. I3 71; a tribute quota list with totals at Inscr. Graec. I3 259 (454/ 3); quota lists without totals at e.g. Inscr. Graec. I3 260, 263, 264. Cf. Paarmann 2004; discussion of the division into district headings, which starts in 443/2 and ends in 430/29: 84. 61 Paarmann 2004, 92–95, has a good example from the tribute quota lists. 62 Bousquet 1988, 146, 189 f., 276. He thinks, however, that the actual calculations preliminary to the inscribed accounts were in acrophonic notation, which assumes cultural uniformity or capacity for translation at least among the accountants.

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Fig. 2.: From Inscr. Graec. I3 261, fr. 7–8, an example of ‘tabular’ formatting (ATL I, fig. 8).

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separately for gold and silver, and the totals listed.63 Also, it is probably significant, and it warrants further research, that tribute quota lists and the auction lists tend to be formatted in columns, while temple treasury inventories and building accounts veer between tabular and interspersed formats. I would take as a general premise that number recognition and understanding of numerical information are aided when numbers are written in figures rather than spelled out in letters, when there are columns rather than continuous text, and when there are sum totals. Keeping in mind that possibly more people would have recognized the numbers than were able to read all the words, those same people may have been able, especially under favorable formatting conditions, to single out and identify the numbers as being the core information provided by the inscription. In other words, formatting in columns may have been deliberately chosen to aid visibility and suggest replicability. The more indistinct formatting of interspersed inscriptions, on the other hand, may have been chosen in order to emphasize accumulation, where the purpose of an inventory, for instance, may have been to display the amassing of resources, to dazzle with a map of Athenian treasure. An instance of this could be the accounts of the Athenian amphiktiones of Delos from 377 to 373, where different types of information are listed together (income from interest paid on loans by cities, individuals, rent, expenditure, cities and individuals falling into arrears, and real estate belonging to the god Apollo) and totals taken, but both figures (in numbers) and totals are embedded in a continuous flow of text.64 With regard to our initial questions, then, and without falling into either extreme reading of the function of list inscriptions, it could be said that tabular formatting may facilitate reading, and thus foster an informative function for the document, whereas interspersed formatting meshes more manifestly with a symbolic interpretation of what lists and inventories were for. In conclusion, I would like to argue that, to the extent to which formatting was significant, a certain choice of format for account inscriptions was also a deliberate manipulation of the conditions for readership of those inscriptions.

Conclusion My two main claims in this paper have been first, that the question of authorship of account inscriptions is also a question about political participation, and second, that the formatting of an account inscription may be significant in that it may have deliberately determined the condition of its being read or being seen, indicating 63 Inscr. Graec. I3 383, also mentioned in Samons 1996, 94. 64 The formatting not always reflected in the translation: I. Délos 98*, no. 28 in Rhodes & Osborne 2003.

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that the readership of account inscriptions was (at least sometimes) deliberately shaped one way or the other, and ultimately for political purposes. But perhaps when it comes to politics we have been looking at the wrong context all along. I have asked earlier, how would the Athenians themselves have read the account inscriptions? There are at least two literary works that can provide an answer to that. The first, Aristophanes’ Wasps, is about an Athenian man’s efforts to drive his father away from obsessive jury-service. Having tried several strategies, he exhorts the old man to read the tribute list (655–663): 655

660

ἀκρόασαί νυν, ὦ παπίδιον, χαλάσας ὀλίγον τὸ μέτωπον. καὶ πρῶτον μὲν λόγισαι φαύλως, μὴ ψήφοις ἀλλ' ἀπὸ χειρός, τὸν φόρον ἡμῖν ἀπὸ τῶν πόλεων συλλήβδην τὸν προσιόντα, κἄξω τούτου τὰ τέλη χωρὶς καὶ τὰς πολλὰς ἑκατοστάς, πρυτανεῖα, μέταλλ', ἀγοράς, λιμένας, μισθώσεις, δημιόπρατα· τούτων πλήρωμα τάλαντ' ἐγγὺς δισχίλια γίγνεται ἡμῖν. ἀπὸ τούτου νυν κατάθες μισθὸν τοῖσι δικασταῖς ἐνιαυτοῦ, ἓξ χιλιάσιν – ”κοὔπω πλείους ἐν τῇ χώρᾳ κατένασθεν”. γίγνεται ἡμῖν ἑκατὸν δήπου καὶ πεντήκοντα τάλαντα.

Then listen, pop, and relax your frown a bit. First of all, calculate roughly, not with your counters but on your fingers, how much tribute we receive altogether from the allied cities. Then make a separate count of the taxes and the many one percents, court dues, mines, markets, harbors, rents, proceeds from confiscations. Our total income from all this is nearly two thousand talents. Now set aside the annual payment to the jurors, all six thousand of them, ‘for never yet have more dwelt in this land.’ We get, I reckon, a sum of one hundred and fifty talents.

Further calculations expose many ugly truths about Athens, her officers and her empire: 665

669 670 698 700 703 705

710

{Φι.} καὶ ποῖ τρέπεται δὴ 'πειτα τὰ χρήματα τἄλλα; {Βδ.} ἐς τούτους τοὺς “οὐχὶ προδώσω τὸν Ἀθηναίων κολοσυρτόν, ἀλλὰ μαχοῦμαι περὶ τοῦ πλήθους ἀεί”. […] κᾆθ' οὗτοι μὲν δωροδοκοῦσιν κατὰ πεντήκοντα τάλαντα ἀπὸ τῶν πόλεων ἐπαπειλοῦντες τοιαυτὶ κἀναφοβοῦντες· “δώσετε τὸν φόρον, ἢ βροντήσας τὴν πόλιν ὑμῶν ἀνατρέψω.” […] σκέψαι τοίνυν ὡς ἐξόν σοι πλουτεῖν καὶ τοῖσιν ἅπασιν ὑπὸ τῶν ἀεὶ δημιζόντων οὐκ οἶδ' ὅπῃ ἐγκεκύκλησαι, ὅστις πόλεων ἄρχων πλείστων ἀπὸ τοῦ Πόντου μέχρι Σαρδοῦς οὐκ ἀπολαύεις πλὴν τοῦθ' ὃ φέρεις ἀκαρῆ· […] βούλονται γάρ σε πένητ' εἶναι, καὶ τοῦθ' ὧν εἵνεκ' ἐρῶ σοι· ἵνα γιγνώσκῃς τὸν τιθασευτήν, κᾆθ' ὅταν οὗτός γ' ἐπισίξῃ ἐπὶ τῶν ἐχθρῶν τιν' ἐπιρρύξας, ἀγρίως αὐτοῖς ἐπιπηδᾷς. εἰ γὰρ ἐβούλοντο βίον πορίσαι τῷ δήμῳ, ῥᾴδιον ἦν ἄν. εἰσίν γε πόλεις χίλιαι αἳ νῦν τὸν φόρον ἡμῖν ἀπάγουσιν· τούτων εἴκοσιν ἄνδρας βόσκειν εἴ τις προσέταξεν ἑκάστῃ, δύο μυριάδ' ἂν τῶν δημοτικῶν ἔζων ἐν πᾶσι λαγῴοις καὶ στεφάνοισιν παντοδαποῖσιν καὶ πυῷ καὶ πυριάτῃ, ἄξια τῆς γῆς ἀπολαύοντες καὶ τοῦ 'ν Μαραθῶνι τροπαίου. νῦν δ' ὥσπερ ἐλαολόγοι χωρεῖθ' ἅμα τῷ τὸν μισθὸν ἔχοντι.

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[Father] In that case, where is the rest of the money routed? [Son] To the ‘I won’t betray the Athenian rabble and I’ll fight for the masses’ bunch! […] And then they extort fifty talent bribes from the allied cities by terrifying them with threats like this: ‘You’ll hand over the tribute, or I’ll upend your city with my thundering!’ […] Then consider this: you could be rich, and everyone else too, but somehow or other these populists have got you boxed in. You, master of a multitude of cities from the Black Sea to Sardinia, enjoy absolutely no reward, except for this jury pay […] Because they want to keep you poor, and I’ll tell you the reason: so you’ll recognize your trainer, and whenever he whistles at you to attack one of his enemies, you’ll leap on that man like a savage. If they wanted to provide a living for the people, it would be easy. A thousand cities there are that now pay us tribute. If someone ordered each one to support twenty men, then twenty thousand loyal proles would be rolling in hare meat, every kind of garland, beestings and eggnog, living it up as befits their country and their trophy at Marathon. As it is, you traipse around for your employer like olive pickers!65

Not only is the old Athenian able to go through the sums, verifying that the calculations are correct, but also his growing numerical awareness parallels a political learning process, and allows him (and Aristophanes’ audience) to expose what lies behind the rhetoric of tribute-paying, or indeed, even of democratic governance and equality. Doing the maths here amounts to finding out that, politically, things do not really add up, even though the sums themselves may be verified. The second text is The Peloponnesian War. A key passage in Thucydides describes Pericles giving an account to the dēmos that is not too far from the information we find in our account inscriptions. You can imagine a few old men quickly reckoning on their fingers as the statesman speaks: παρῄνει δὲ καὶ περὶ τῶν παρόντων ἅπερ καὶ πρότερον […] τά τε τῶν ξυμμάχων διὰ χειρὸς ἔχειν, λέγων τὴν ἰσχὺν αὐτοῖς ἀπὸ τούτων εἶναι τῶν χρημάτων τῆς προσόδου, τὰ δὲ πολλὰ τοῦ πολέμου γνώμῃ καὶ χρημάτων περιουσίᾳ κρατεῖσθαι. θαρσεῖν τε ἐκέλευε προσιόντων μὲν ἑξακοσίων ταλάντων ὡς ἐπὶ τὸ πολὺ φόρου κατ' ἐνιαυτὸν ἀπὸ τῶν ξυμμάχων τῇ πόλει ἄνευ τῆς ἄλλης προσόδου, ὑπαρχόντων δὲ ἐν τῇ ἀκροπόλει ἔτι τότε ἀργυρίου ἐπισήμου ἑξακισχιλίων ταλάντων (τὰ γὰρ πλεῖστα τριακοσίων ἀποδέοντα μύρια ἐγένετο […]), χωρὶς δὲ χρυσίου ἀσήμου καὶ ἀργυρίου […] χρήμασι μὲν οὖν οὕτως ἐθάρσυνεν αὐτούς, ὁπλίτας δὲ τρισχιλίους καὶ μυρίους εἶναι ἄνευ τῶν ἐν τοῖς φρουρίοις καὶ τῶν παρ' ἔπαλξιν ἑξακισχιλίων καὶ μυρίων. […] τοῦ τε γὰρ Φαληρικοῦ τείχους στάδιοι ἦσαν πέντε καὶ τριάκοντα […] τὰ δὲ μακρὰ τείχη πρὸς τὸν Πειραιᾶ τεσσαράκοντα σταδίων […] ἔλεγε δὲ καὶ ἄλλα οἷάπερ εἰώθει Περικλῆς ἐς ἀπόδειξιν τοῦ περιέσεσθαι τῷ πολέμῳ. [Pericles] gave them the same advice as before […]: that they should […] keep a firm hand upon their allies, explaining that the Athenian power depended on revenue of money received from the allies, and that, as a general rule, victories in war were won by abundance of money as well as by wise policy. And he bade them be of good courage, as on average six hundred talents of tribute were coming in yearly from the allies to the city, not counting the other sources of revenue, and there were at this time still on hand in the Acropolis six thousand talents of coined silver (the maximum amount had been nine thousand seven hundred talents […]). Besides, there was uncoined gold and silver […]. As to heavy-armed infantry, he told them that there were thirteen thousand, not counting the sixteen thousand men who garrisoned the

65 The whole passage at Aristophanes, Vesp. 655–712, tr. J. Henderson 1998 (Loeb edition).

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forts […]. [T]he length of the Phalerian wall was thirty-five stadia […] and the Long Walls to the Peiraeus were forty stadia […]. And Pericles used still other arguments, as was his wont, to prove that they would be victorious in the war.66

Pericles’ account, which immediately precedes Thucydides’ so-called pre-history of Athens (II 15), can be considered a state-of-the-union speech regarding Athens on the verge of the Peloponnesian War. For our purposes, not only does it show accounting in action–it also reveals the ambiguity inherent in an apparently cogent demonstrative process. Pericles’ speech seems persuasive and reliable precisely because it sounds like an account: so many monies, so much wealth, so many soldiers, so many metres of wall. See and count for yourselves, he appears to be saying, just like some inscriptions did, in perfectly democratic fashion. At the same time, how many people in the audience actually checked Pericles’ account against, say, the information deposited in the archive by means of whitened tables? And how many found the speech persuasive, and the information contained in it credible, primarily because of the speaker–because of the trustworthiness of Pericles’ testimony about the state of finances, the military and defence infrastructures? The account here is at the same time transparent in principle, and potentially opaque to further inquiry, let alone challenge. Like the sums in Aristophanes’ play, it is revealing, but at the same time it conceals all sorts of machinery.67 Perhaps the real framework for account inscriptions has also been obscure all along: we have tried to read these documents in the key of democracy, when the real political context for Athenian numeracy is empire–an empire actively intent on perpetuating its identity as a democracy.68 The figures we find carved in stone are in fact the end-result of an accounting process which has taken place elsewhere, including somewhere else than Athens. They are the abridgement of an original, extended version, and the gap between the two versions creates what we could call a centre and a periphery of information: the centre being not simply Athens, but the archive with the whitened tablets within Athens, accessible in principle to any citizen but in actuality probably hardly ever revisited with an eye 66 Thucydides II 13 (Loeb tr.). 67 Some interesting reflections on performance and what the performance conceals, or leaves obscure, in Jameson 1999; Osborne 1999. 68 Samons 2000, 313–316, similarly writes: “it seems impossible to attribute Athenian publication practice in the area of finance to some kind of ‘democratic principle of freedom of information’ or to an attempt ‘to provide accountability’ for Athens’ officials. The important financial records of Athens […] were all ‘free’ and stored in the public archives. […] But why, then, did the Athenians decide to inscribe certain financial records on stone and not others? […] Such publication may reasonably be associated with the oncoming Peloponnesian War and the desire to publicize Athens’ abundant sacral wealth and the scrupulous management of these resources. […] the increased publication of sacral records such as the Parthenon inventories in no way implies that such documents acted as ‘talismans’ or dedications to the gods themselves […]. But it arguably does emphasize the close connection in Athenian society between the military operations of the polis and the city’s gods.” See also Hedrick 1999, 399f.

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to enforcing everybody’s potential control.69 What we have in actuality is the inscribed reference to repeated actions of calculating and counting, which can themselves no longer be checked, and may have been subject, as Aristophanes’ passage implies, to very undemocratic pressures to begin with. The mode of public numeracy in Athens reflected, and shaped, its ambiguous identity as a democracy/ empire, constrained both by the need to control and the demand for accountability. More generally, an exploration of numeracy in the ancient world can indeed be revealing, precisely because numbers, far from being straightforward, invite ambiguity. They may seem simple, but they are not – they are held as the most obvious model of objectivity, and yet are open to manipulation. The paradoxical nature of simple numbers was indeed recognized in ancient literature: Prometheus in Aeschylus’ play calls them ‘the greatest sophisma’, a word which has an undertone of ‘ruse’ or ‘stratagem’, and the Pythagoreans, Plato and Aristotle philosophized endlessly about the mysterious behaviour of odd and even numbers, or even simply of the (non) number one. Transferring this onto a more explicit political level (which is of course arguably present in all the authors just mentioned), numbers allow a sort of transparent opaqueness, or accessible impenetrability, which can be, and has been, and inevitably still is, deployed extensively in social, economical and political contexts. Giving in to the inevitable easy pun, we can conclude that the question of who counted in ancient Athens does count – our task as historians is now to write a better story of exactly how much.

Bibliography Texts quoted ATL = Meritt, B. D., H. T. Wade-Gery, & M. F. McGregor 1939–1953. The Athenian Tribute Lists. Cambridge, MA, 4 vols. Inscr. Graec. = Berlin-Brandenburgische Akademie der Wissenschaften 1873-2003. Inscriptiones Graecae. Berlin. (SIG = Supplementum) Rhodes, P. J., & R. Osborne (eds.) 2003. Greek Historical Inscriptions 404–323 BC. Oxford.

69 The notion of inscription device, and the discussion of centre and periphery in empires, as articulated in Latour & Woolgar 1986 and Latour 1987, fit the Athenian case almost ridiculously well.

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Works quoted Aleshire, S. B. 1989. The Athenian Asklepieion. The People, Their Dedications, and the Inventories. Amsterdam. Asper, M. 2003. “Mathematik, Milieu, Text. Die frühgriechische(n) Mathematik(en) und ihr Umfeld.” In: Sudhoffs Archiv 87, 1–31. Bousquet, J. 1988. Études sur les comptes de Delphes. Paris. Burford, A. 1969. The Greek Temple Builders at Epidauros: A Social and Economic Study of Building in the Asklepian Sanctuary. Liverpool. Cambiano, G. 1991. Platone e le tecniche. 2nd ed., Rom. Cleland, L. 2005. The Brauron Clothing Catalogues. Oxford. Constantakopoulou, C. 2009. “Tribute, the Athenian Empire and small states and communities in the Aegean”, in A. Slawisch (ed.), Trade and finance in the fifth century BC Aegean world (Istanbul), forthcoming 2013. Cuomo, S. 2001. Ancient Mathematics. London. Cuomo, S. 2007. Technology and Culture in Greek and Roman Antiquity. Cambridge. Cuomo, S. 2009. “All the Proconsul’s Men: Cicero, Verres and Account-keeping.”, AION Quaderni 15, Naples 2011, 165–185. Davies, J. K. 1994. “Accounts and Accountability in Classical Athens.” In: R. Osborne & S. Hornblower (eds.), Ritual, Finance, Politics. Athenian Democratic Accounts Presented to David Lewis. Oxford, 201–212. Euben, J. P. 1997. Corrupting Youth: Political Education, Democratic Culture, and Political Theory. Princeton. Ferguson, W. S. 1932. The Treasurers of Athena. Cambridge, MA. Feyel, C. 2006. Les artisans dans les sanctuaires grecs. Athens. Fornara, C. W. (ed.) 1977. Translated Documents of Greece and Rome. Vol. 1: Archaic Times to the End of the Peloponnesian War. Baltimore. Giovannini, A. 1990. “Le Parthénon, le trésor d’Athéna et le tribut des allies.” In: Historia 39, 129–148. Goldhill, S. & R. Osborne (eds.) 1999. Performance Culture and Athenian Democracy. Cambridge. Guarducci, M. 1968. Epigrafia greca I. Roma. Hamilton, R. 2000. Treasure Map. A Guide to the Delian Inventories. Ann Arbor. Hansen, M. H. 1979/1991. The Athenian Democracy in the Age of Demosthenes (orig. Kopenhagen 1979). Transl. J. A. Crook. Oxford 1991. Harding, P. 1985. From the End of the Peloponnesian War to the Battle of Ipsus. Cambridge. Harris, D. 1994. “Freedom of Information and Accountability: the Inventory Lists of the Parthenon.” In: R. Osborne & S. Hornblower (eds.), Ritual, Finance, Politics. Athenian Democratic Accounts Presented to David Lewis. Oxford, 213–225. Harris, D. 1995. The Treasures of the Parthenon and Erechtheion. Oxford. Hedrick, C. W. 1994. “Writing, Reading, and Democracy.” In: R. Osborne & S. Hornblower (eds.), Ritual, Finance, Politics. Athenian Democratic Accounts Presented to David Lewis. Oxford, 157–174. Hedrick, C. W. 1999. “Democracy and the Athenian Epigraphical Habit.” In: Hesperia 68, 387–439. Imhausen, A. 2003. Ägyptische Algorithmen. Eine Untersuchung zu den mittelägyptischen mathematischen Aufgabentexten. Wiesbaden. Immerwahr, H. R. 1992. Review of Thomas 1992. In: American Journal of Philology 113, 96–99. Jameson, M. H. 1999. “The Spectacular and the Obscure in Athenian Religion.” In: Goldhill & Osborne 1999, 321–340.

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Latour, B. 1987. Science in Action: How to Follow Scientists and Engineers Through Society. Milton Keynes. Latour, B. & S. Woolgar 1986. Laboratory Life: The Construction of Scientific Facts. Princeton. Lewis, D. M. 1986. “Temple Inventories in Ancient Greece.” In: M. Vickers (ed.), Pots & Pans. A Colloquium on Precious Metals and Ceramics in the Muslim, Chinese and Graeco-Roman Worlds, Oxford 1985. Oxford, 71–81. Lewis, D. M. 1988. “The Last Inventories of the Treasurers of Athena.” In: D. Knoepfler (ed.), Comptes et inventaires dans la cité grecque, actes du colloque de Neuchâtel en l’honneur de Jacques Tréheux. Neuchâtel, 297–308. Linders, T. 1975. The Treasurers of the Other Gods in Athens and Their Functions. Meisenheim am Glan. Linders, T. 1988. “The Purpose of Inventories: a Close Reading of the Delian Inventories of the Independence.” In: D. Knoepfler (ed.), Comptes et inventaires dans la cité grecque, actes du colloque de Neuchâtel en l’honneur de Jacques Tréheux. Neuchâtel, 37–47. Linders, T. 1992. “Inscriptions and Orality.” In: Symbolae Osloenses 67, 27–40. Meritt, B. D. 1932. Athenian Financial Documents of the Fifth Century. Ann Arbor. Meritt, B. D. 1937. Documents on Athenian Tribute. Cambridge, MA. Meritt, B. D. & A. Brown West 1934. The Athenian Assessment of 425 B.C. Ann Arbor. Muñiz Coello, J. 1982. Empleados y subalternos de la administración romana. I. Los ‘scribae’. Huelva. Netz, R. 2002a. “Greek Mathematicians: a Group Picture.” In: C.J. Tuplin & T.E. Rihll (eds.), Science and Mathematics in Ancient Greek Culture. Oxford, 196–216. Netz, R. 2002b. “Counter Culture: Towards a History of Greek Numeracy.” In: History of Science 40, 321–352. Ober, J. 1989. Mass and Elite in Democratic Athens: Rhetoric, Ideology, and the Power of the People. Princeton. Ober, J. 1998. Political Dissent in Democratic Athens: Intellectual Critics of Popular Rule. Princeton. Oliver, J. H. 1977. “The Vatican Fragments of Greek Political Theory.” In: Greek, Roman, and Byzantine Studies 18, 321–339. Osborne, R. 1994. “Introduction. Ritual, Finance, Politics: an Account of Athenian Democracy.” In: R. Osborne & S. Hornblower (eds.), Ritual, Finance, Politics. Athenian Democratic Accounts Presented to David Lewis. Oxford, 1–21. Osborne, R. 1999. “Inscribing Performance.” In: Goldhill & Osborne 1999, 341–358. Osborne, R. 2000 (ed.). The Athenian Empire. 4th ed., London. Paarmann, B. 2004. “Geographically Grouped Ethnics in the Athenian Tribute Lists.” In: T. H. Nielsen (ed.), Once Again: Studies in the Ancient Greek Polis, Stuttgart, 77–109. Petrakos, B. 1999. Ο ΔΗΜΟΣ ΤΟΥ ΡΑΜΝΟΥΝΤΟΣ II: Ω ΕΠΙΓΡΑΦΕΣ. Athens. Purcell, N. 2001. “The ordo scribarum: a Study in the Loss of Memory.” In: Mélanges de l’École française de Rome 113, 633–674. Rhodes, P. J. 1985. The Athenian Boule. 2nd ed., Oxford. Rhodes, P. J. 1993. A Commentary on the Aristotelian Athenaion Politeia. 2nd ed., Oxford. Rhodes, P. J. 2001a. “Public Documents in the Greek States: Archives and Inscriptions, Part I.” In: Greece & Rome 48, 33–44. Rhodes, P. J. 2001b. “Public Documents in the Greek States: Archives and Inscriptions, Part II.” In: Greece & Rome 48, 136–153. Robson, E. 2003. “Tables and Tabular Formatting in Sumer, Babylonia, and Assyria, 2500–50 BCE.” In: M. Campbell-Kelly et al. (eds.), The History of Mathematical Tables from Sumer to Spreadsheets, Oxford, 18–47. Robson, E. 2004. “Accounting for Change: the Development of Tabular Book-keeping in Early Mesopotamia.” In: M. Hudson & C. Wunsch (eds.), Creating Economic Order: Record-keeping,

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Standardization, and the Development of Accounting in the Ancient Near East. Bethesda, 107–144. Robson, E. 2008. Mathematics in Ancient Iraq. A Social History. Princeton. Roochnik, D. 1996. Of Art and Wisdom: Plato’s Understanding of Techne. University Park, PA. Rossi, C. 2009. “Mixing, Building, and Feeding: Mathematics and Technology in Ancient Egypt.” In: E. Robson & J. Stedall (eds.), The Oxford Handbook of The History of Mathematics. Oxford, 407–428. Samons II, L. J. 1996. “The ‘Kallias Decrees’ (IG I3 52) and the Inventories of Athena’s Treasure in the Parthenon.” In: Classical Quarterly 46, 91–102. Samons II, L. J. 2000. Empire of the Owl. Athenian Imperial Finance. Stuttgart. Schärlig, A. 2001. Compter avec des cailloux: le calcul élementaire sur l’abaque chez les anciens Grecs. Lausanne. Sinclair, R. K. 1988. Democracy and Participation in Athens. Cambridge. Thomas, R. 1989. Oral Tradition and Written Record in Classical Athens. Cambridge. Thomas, R. 1992. Literacy and Orality in Ancient Greece. Cambridge. Tod, M. N. 1911/12. “The Greek Numeral Notation.” In: The Annual of the British School at Athens 18, 98–132. Tolbert Roberts, J. 1982. Accountability in Athenian Government. Madison.

Steffen Bogen

Diagrammatic Reasoning: the Foundations of Mechanics 1

Abstract: Diagrams are an essential part of science writing, and they have become central to the philosophy of science, too (e.g., Stjernfelt, Krämer). At the beginning of the 20th century, Charles S. Peirce developed his influential concept of ‘diagrammatic reasoning’ that includes questions of epistemology and even metaphysics. How diagrams challenge the history of science will be discussed with reference to cases, chosen from the mechanical works of Pseudo-Aristotle, Archimedes and Hero of Alexandria. The paper will show how operating with diagrams was fundamental to the new profession of engineers trained in mathematics. Special attention will be paid to the interaction of imagination and graphical materiality in diagrammatic reasoning. Thereby, an alternative to logo-centric positions emerges that tend to distinguish strictly between subjects and objects of language.

In many cases to write science also means to draw science.2 A highly specialized form of drawing emerged with the diagrams of ancient mathematics. It is an open question how such graphical practice could transfer to other branches of ancient philosophy and science, which happened especially in the case of Aristotle and his followers. In this transfer the meaning of the figures changes, even if the graphical acts as such may be similar. This article focuses on figures in the fields of mechanics, pneumatics and writings describing the construction of siege engines and catapults. Even those examples are, however, heterogeneous.3 Some of them explain simple mechanical principles, others refer to the function of complex machines or automata. Is it legitimate to compare these figures with geometrical diagrams? What are their functions in technical writings? What constitutes ‘authorship’ in these cases and what is the complementary role of the reader? These are the questions that I will address in the following.

Diagrammatic reasoning Right away, it is important to avoid a common misunderstanding: one should not confuse the figures in the technical writings with contingent pictures or mere illustrations. It is already the use of letters within the figure that speaks against the 1 Thanks to Markus Asper for his helping hand in many questions, especially those of language. 2 Latour 1990 pointed to the essential role of drawings in the practice of the sciences. 3 Lefèvre 2002, 111–113.

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assumption of embellishing illuminations. Reviel Netz has studied the norms that govern the relation of text, letters and figures in Greek mathematics4: standardized phrases refer to single steps of geometrical constructions. Letters are the crucial link between the propositions of the text and positions within the figure. The combination of text and lettered diagram is completely different from any other genre of book illustration. The explanation of a lettered diagram does not intend to evoke pictorial effects in the reader’s imagination but to analyze the relations of graphical components. In mathematical contexts the diagram even provides the actual object of the argument: The diagram is not a representation of something else, it is the thing itself. It is not like a representation of a building, it is like a building, acted upon and constructed. Greek geometry is the study of spatial action, not of visual representation.5

Netz analyzed how ‘necessity’ and ‘generality’ is shaped within this context.6 A typical method is to introduce rules of how to draw a specific diagram. Its identity depends on these rules, which concern relations between graphical connections, distances and orientations. Figures may look different to the naïve viewer and still be identical by mathematical definition. By transforming the diagram, mathematicians draw conclusions. They assume, for example, that a certain relation, which the rules do not describe explicitly, is not implied by the diagram. Subsequently, this assumption is refuted. It is thus shown that the quality or relation in question is part of the identity of the figure, which means that it is part of the rules applied. Such deduction is based on the graphical realization of the diagram. Only because the drawing surface saves the traces, one can reflect on different rules of construction, even if the relevant relations are not known at the moment of drawing itself. It is a main concern of my article to point out that figures in mechanical and pneumatic treatises can be subject to similar forms of reasoning. Already at the beginning of the 20th century Charles Sanders Peirce argued that “all necessary reasoning without exception is diagrammatic”.7 He developed a concept of rationality that is closer to the transformation of diagrams rather than to words and speech alone.8 I will try to use Peirce’s philosophical insight in order to take a fresh look at the origins of technical sciences. I would like to argue that diagrams played an essential role in the development of crucial concepts in the field of mechanics – perhaps even as its foundation or first principle is concerned, namely the belief that there are certain and determined relations between enforced movements in space. 4 Netz 1999. 5 Netz 1999, 60. 6 Netz 1999, 168 and 240, see also Netz & Noel 2008, 87–116 and Netz 2009, 71–80. 7 Peirce 1932–1958, 7.161–162 (“On the Logic of Drawing History from Ancient Documents especially from Testimonies”). 8 Current approaches in the philosophy of science: Stjernfelt 2007, Krämer 2009.

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Transmission of figures My approach has to cope with the long-standing disdain with which editors neglected the actual manuscripts and the transmitted figures. Wilhelm Schmidt, for example, who edited Hero’s writing at the beginning of the 20th century, did not trust the drawings of his sources (fig. 1). He judged them to be drawn “ohne Perspektive in ziemlich primitiver Weise.”9 Such attitude, however, is inappropriate for a genre of drawings that stand in the tradition of the lettered diagram. Schmidt follows the judgment of the early prints, the text of which he, being a philologist and a textual critic, actually wants to correct. Bernardino Baldi, for example, who translates Hero’s Automata for the first time into Latin for publication in print in 1589, informs his addressee, the Conte Giulio Tieni, student of ingenious things (“studioso delle cose d’ingegno”10), that he decided to ‘modernize’ the figures passed down in the Byzantine manuscripts. In his opinion they became barbaric by the ignorance of the copyists (“per l’ignoranza de copiatori […] imbarbarite”).11 The editio princeps of Federico Commandino (Urbino 1575) had already shifted the paradigm (fig. 2). Pictures drawn in perspective replaced the simple diagrammatic drawings. Instead of constructive patterns that defied differences between inside and outside, more or less pretty vessels are shown, as known to the reader from collections of antiques. The figures of Commandino are still the model of Schmidt’s modern edition who, without a hint at the tradition, redraws them (fig. 3). Schmidt decides, however, not to reproduce purely ornamental details and pictorial effects. Cast shadows disappeared and the mannered handle of the amphora has been simplified. The figures of the oldest manuscripts, however, have almost completely changed. Therefore, the critical edition of the text has led, paradoxically, to an arbitrary redrawing of the figures.12 What concerns the authenticity of drawings in ancient treatises on mechanics, Wolfgang Lefèvre’s recent survey is quite cautious too: To become convinced of the authenticity of drawings, one needs both: a close and fitting interconnection between text and image, on the one hand, and on the other the actual occurrence of the images in the oldest and most reliable manuscripts we have. Due to the nature of the transmission process […] even then one has to be prepared to meet with a broad variety of versions of one and the same drawing which can all claim authenticity to these criteria.13

9 Hero: Schmidt 1899, 5: “without perspective, in a quite primitive manner”. 10 Hero: Baldi 1589, fol. 2r. 11 Hero: Baldi 1589, fol. 2v/3r: “Le figure che già per l’antichità, e per l’gnoranza de copiatori erano affatto imbarbarite, come è noto à lei, e puo essere à tutti quelli che si sono abbattuti ne gli essemplari Greci, sono da me state rimodernate e ridotte nel termine ch’ella vede.” 12 Already Drachmann 1963, 20 critizes the editorial disdain of figures. The new standard is: Archimedes: Netz 2004. 13 Lefèvre 2002, 111.

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Fig. 1: Hero Alexandrinus, A Vessel for Discharging Different Liquids, Byzantine manuscript (13th cent.)

Ancient authors were completely aware of the problems that the manual copying of the figures presented. A commentary on the astronomical poet Aratus states that

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Fig. 2: Hero Alexandrinus, A Vessel for Discharging Different Liquids, ed. Commandino 1575

while Homer is corrupted only by one sort of scribe, the scribe of letters, Aratus is corrupted by the writer and the drawer (zōgraphoi). Only the ignorants would accuse the author Aratus himself of their mistakes.14 Modern philologists considered the figures to be victims of the scribal tradition and its corruptions. But the design of new figures was an intervention much harsher than everything that happened in Byzantine and Arabic manuscript tradition. 14 Anonymus, Isagoga in Aratum bis excerpta ed. E. Maass 1898, 329, 19 and Stückelberger 1994, 127 with further examples.

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Fig. 3: Hero Alexandrinus, A Vessel for Discharging Different Liquids, ed. Schmidt 1899

Art historians who classified the figures more correctly then some philologists as diagrams refrained from a more detailed analysis, too. Kurt Weitzmann wrote in his Studies of Ancient Book Illumination: The simplest form of illustration is, of course, the diagram, and there are certain scientific texts, especially in the field of mathematics, which need them so much that they cannot exist without them. […] It would not, of course, have been worth while to deal with such simple diagrams from the artistic point of view were it not for the fact that in other texts the diagrams are elaborated beyond the point of scientific necessity.15

Weitzmann’s classification of diagrams as “scientific illustration” constructs a neat division of labor between the history of sciences and the history of art: the art historian does not claim to be qualified to answer the question of why the diagram is “scientifically necessary” and of how this necessity differs from artistic elaboration. The distinction is thus taken for granted without further reflections. The reservation and disdain, which modern scientists expressed towards the figures, are in striking contrast with their antique appreciation. Diagrams are seen as integral parts of the text and thereby authorized. Philon of Byzantium wrote in his Mēkhanikē syntaxis:

15 Weitzmann 1959, 5.

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τούτων δὲ ὧν δεδηλώκαμεν πασῶν τῶν πυργοποιιῶν ἐν αὐτῷ σοι τῷ βιβλίῳ τὰ σχήματα γέγραπται, σαφέστερον ἵνα καταμάθῃς.16 For all fortifications that we have explained, we prepared schemata for you in this same book, in order that you may better understand them.

The remark becomes topical and thus the existence of schemata or diagrams is not specific to single authors anymore, but forms part of the scientific genre. Often the usefulness of the figures is motivated by limitations of a purely verbal description. Athenaeus ‘the Mechanic’ uses such an argument at the end of his treatise on mechanics.17 Similarly, Aelianus ‘the Tactician’ writes in his introduction: ὁσάκις δ’ ἄν μοι ὁ λόγος ἐξασθενήσῃ ἐναργῶς παραστῆσαί τι τῶν θεωρημάτων, ἐπίκουρον παραλήψομαι ἐπὶ καταγραφῆς τὴν τῶν σχημάτων διατύπωσιν, ἵνα τὴν ὄψιν τῇ νοήσει συλλήπτορα παράσχω.18 Whenever words are not sufficient to represent any of my statements clearly, I will resort to schematic drawings (skhēmatōn diatupōsis), so that I can provide vision (opsis) as assisting comprehension (noēsis).

But what does the interplay of imagination and comprehension in this context actually mean?

A diagram as technical argument Lefèvre classifies the drawings in ancient treatises on mechanics as “diagrammatic” or “schematic”: I use the term ‘schematic’ the way engineers do as a label for a type of plan which ignores, in contrast to architectural plans, the exact spatial form and spatial relations of a device and of its parts in favor of a rendering of the interconnections of the parts. Schematics do not aim at representing the exact appearance of an object. Electrical schematics, schematics for a complex heating system of a building, or underground plans are good instances of modern schematics in this sense.19

A diagram that refers to a technical device, signifies something different from a diagram in a purely mathematical context. The big difference is that the figure refers to an actual object at all, instead of being an autonomous object of reflection that simply embodies rules of graphical construction. It remains, however, key to a deeper understanding of these figures that the reference is still based on con-

16 17 18 19

Philo of Byzantium, Pneum. 18–21. Athenaeus mechanicus 39, 7. Aelianus tacticus, Tact. 1, 5. Lefèvre 2002, 115.

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structive rules and principles. The graphical construction may refer to some aspects of the technical construction. The rules of transformation, which govern the reception of the figure, may refer to the interconnections of the parts and the intended operations of the technical device. A simple but revealing example can illustrate these analogies.

Fig. 4: Ps.-Aristotle, Adjacent Wheels, ed. Hett 1955

This is the first figure of the pseudo-Aristotelian Problemata mēkhanika (fig. 4).20 There are no figures in manuscripts, but the explanation of the lettered diagram is so simple, that the figure can be reconstructed easily. The text develops the argument as follows: three circles are placed on a straight line in contact to each other. The text refers to the figure with the notion of “circle” (kuklos). So the whole diagram could be drawn in a geometrical context, too. But the explanation intends also to evoke the imagination of rotating wheels. By the imagination of wheels the figure gets a pictorial meaning, which is foreign to pure geometrical forms. Note, however, that the principle of the circle is implied in this reference: a wheel is round and its construction is hardly possible without the notion of how to draw a circle. The constructive analogy supplements the imagination. What we see on the paper remains a generalized form: it is not a single wheel with concrete 20 From Hett 1955, 335.

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dimensions and determined materiality but its principle, subject to further reflections. The circles become wheels mainly by imagining movements. The first chapter of the Problemata mēkhanika seems almost to intend to give a practical introduction to such an active form of reception that is essential for understanding the text. It starts with the notion that the circle has to be imagined as a “combination of opposites”.21 Imagine that the wheel rotates: then you may apply the “opposite of the moving and of the stationary” to the relation of border and centre. Further the imagined rotation leads to the notion that every position on the circle, “from whatever point it begins, returns again to the same point.”22 These practical exercises culminate in the statement that different sides of the circle move into different directions: “one extremity of the diameter moves forward while the other moves backwards.”23 What may sound strange at first, then leads to a more complex statement: circles or wheels in contact move into opposite directions. This statement is not new and independent, but one can deduce it from the principles already established. The correlation becomes evident through the transformation of the diagram (fig. 5). The arrows added in the diagram indicate how changing imaginations of movements can be assigned to the figure. Therefore, the column of diagrams in figure 5 should be read as imaginative transformation of one and the same figure. The argument begins from imagining a rotating wheel. The text suggests the breaking up of the image into two opposites: the two ends of the diameter move into different directions. These two related imaginations are then assigned to the points Γ and Δ. When the wheel rotates clockwise, Γ moves upwards and Δ downwards. This assertion also extends to the two points Β and Ε that are adjacent to Γ and Δ. The reader of the treatise thus gets a starting point that helps him to determine in which direction the other wheels rotate. By the rule that extremities of the diameter move in opposite directions, the arrows appointed to Α and Ζ can be deduced. Α is the reversal of Β and Ζ the reversal of Ε. The arrows that refer to one and the same wheel, Α and Β on the one side and Ζ and Ε on the other side, can be merged into circular forms which both move counter-clockwise. One can, thus, concentrate on the relation already postulated in the cited law: wheels that are in contact move into opposite directions. It turns out that no new rules of imagination had to be introduced. It was sufficient to repeatedly apply the idea of the wheel as combining of opposites, as the text states: “But owing to the fact that a circle has two opposite movements at the same time […] many circles move simultaneously in contrary directions.”24 21 22 23 24

Ps.-Aristotle, Probl. mech. 847b18 f. Ps.-Aristotle, Probl. mech. 848a6–8. Ps.-Aristotle, Probl. mech. 848a20–22. Ps.-Aristotle, Probl. mech. 848a20–22.

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Fig. 5: Ps.-Aristotle, Imagination of Movement (arrows added)

The example illustrates that the text’s claim to give general laws of mechanical movements is bound to the drawing and imaginative transformation of diagrams.

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Consequences that result from the adoption of rules can be drawn within the graphical form. The diagram remains in some sense the object that the author talks about. Nevertheless, the graphical figure refers to material objects and furthermore to principles that should be valid beyond graphical construction. These are not restricted to the transformation of the diagram, but should apply to the experience of actual wheels and their movements, too. The figure intends not only to support a complete understanding of the text, but also an appropriate understanding and perception of mechanical devices. The question of why one can experience the rules of transformations not only in diagrams, but also in technical constructions, remains an epistemological problem, which the engineer may leave to the philosopher as long as his constructions work. To summarize: the analyzed diagram is not a contingent expression of specific thoughts developed in the text – it is the medium in which the idea of mechanically determined movements can develop. The lettered diagram, a metonym of mathematical reasoning, is still an attempt to draw conclusions. The graphical traces unite both sides of the technical process in one and the same figure: they refer to rules of constructions and rules of mechanically determined movements. The merging of the two informations keeps the promise that there is a necessary link between the construction of the device and the (intended) movements within it. Thus, in these somehow unimpressive figures the idea emerged that there is something as novel as a world that can be disposed by technology at all.

Authoring and reading diagrams The figure of the Problemata mēkhanika that I have discussed above, explains a basic mechanical principle, which can be employed in different constructions. Such abstract examples are rather rare in those ancient writings that are still extant. Figures, however, that refer to the combination of such mechanisms in specific constructions, for example siege engines and automata, are numerous. In the manuscript tradition some devices may even become associated as ‘inventions’ with the author’s name, like the Ctesibius’ catapult or Hero’s fountain. Even the complex figures should not be regarded exclusively as construction manuals but as a set of tools or mechanisms that one could recombine in different ways and adapt to specific contexts. Usually, neither figure nor text gives any information about dimensions, and there is no advice concerning any detail of construction. Whoever wanted to attempt to actually build such devices would have needed further competences. Often the texts hint to that by indicating that some expert may carry out the construction according to the information in the figure.25 Again,

25 Stückelberger 1994, 130–133 provides a sample of quotations.

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and most importantly, the diagram argues for a pre-determined relation between the construction and its intended effects. It remains important that this relation can be established and controlled to some degree on paper with a specifically trained imagination. By choosing text and figure as media of argumentation, the author already claims a sort of knowledge that differs from the skills of craftsmen26: the trial and error of technical know-how is replaced by graphical arguments. One can reproduce, ascertain, and even prove this knowledge to some extent without heavy materials, just by lines drawn on paper. The competence to anticipate movements within the drawing can be taught simply by words – in lecture rooms without exhausting and expensive labor. On the other side the author is not a pure philosopher who treats movements and their principles on a purely verbal and thus abstract level of concepts. I will illustrate the difference between the two by the example of philosophical discourse which enables us to distinguish between tekhnē (e.g., applied mechanics) and epistēmē (physics). Among ancient philosophers who reflected on the nature of elements, there was ample discussion on the question of whether or not a natural vacuum should be possible. Authors, however, who wrote about pneumatics shifted the focus of discussion. The reason for why no vacuum occurs, is not of vital importance, but it is the question how this principle can be translated into a rule of imagination that concerns the diagram. If a vacuum has to be avoided, one has to imagine some element in every part of the drawing surface. Even the white paper does not mean an absence of any element but air in general. Accordingly, one has to consider air to be not void, but a body. It can be pressed against water and enforce other movements. In a siphon the outflow of water will be replaced by other water, and so on. The text may explain the reasons of why such things are the way they are, very briefly with reference to different philosophers. It is more important to teach the reader the rules of imagination. Therefore, it is the use of diagrams that distinguishes the author of mechanics or pneumatics from both philosophers that use pure words, and craftsmen who build material and not only graphical constructions. Complementing the part of the author, we have to consider the role of recipients, inscribed into text and diagram. In order to sketch these roles, some preliminary remarks on the state of technical knowledge as secret knowledge seem to be appropriate. To have technical knowledge means to have natural forces at one’s disposal, and the powerful took care with whom they shared such knowledge. This seems to be evident if one considers siege engines, although, as Pamela O. Long argued, technology was not regarded as crucial per se to military victory in antiquity and seems openly purveyed.27 If we assume that technological devices (autom-

26 Schürmann 1991, 31f., Meißner 1999, 139–141, Long 2001, 20–24, Asper 2007, 27–35. 27 Long 2001, 21.

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ata) in temples or palaces should amaze and astonish the naive observer, we are lead to the same assumption. Accordingly, to write down technical knowledge is a delicate task. On the other hand the text may create a new community of insiders and thus enables a dialogue between craftsmen and political elites, that had no place in the daily routines of the work-shop.28 Perhaps, therefore, it is astonishing that ancient technological authors wrote quite openly without too much fear of revealing any secret. They feel apparently certain that the diffusion of the texts itself could be controlled by members of their own class and by political leaders. The ancient authors, however, were completely aware of the fact that their writings dealt not only with moving things but also with differences of visual understanding. Hero of Alexandria writes, introducing his book on The Construction of Automatons (Περὶ αὐτοματοποιητικῆς): Τῆς αὐτοματοποιητικῆς πραγματείας ὑπὸ τῶν πρότερον ἀποδοχῆς ἠξιωμένης διά τε τὸ ποικίλον τῆς ἐν αὐτῇ δημιουργίας καὶ διὰ τὸ ἔκπληκτον τῆς θεωρίας.29 The knowledge of how to construct automatons was held in high regard by former technicians, both because of the wide range of technological artistry and because of the astonishing effects on audiences.

Colleagues may estimate the “technological artistry”, while the broader audience may bear testimony to the effects only. In this context one may recall that Aristotle quotes automata as example for an astonishment that may lead to philosophical insight. Thus he hints at the same split of receptional degrees. ἄρχονται […] ἀπὸ τοῦ θαυμάζειν πάντες εἰ οὕτως ἔχει, καθάπερ τῶν θαυμάτων ταὐτόματα τοῖς μήπω τεθεωρηκόσι τὴν αἰτίαν.30 Everybody starts […] from wondering whether something is so (that is, as it seems), for example in the case of wonders the automatons, for those who have not yet contemplated the reason.

It is important to understand that the construction of an automaton and the explanation of such a device by text and figure aim at very different goals. The automaton aims at the astonishment of an audience by certain effects; the texts, however, addresses recipients to whom the secret of the automaton’s internal workings is disclosed. In such a process the technical author plays a double role: his machines pose riddles that his writings resolve.

28 Meißner 1999, 143–146. 29 Hero, Autom. 1.1, p. 338.3–6 Schmidt. The Greek text here consists, oddly, of nothing but an absolute genitive (see Schmidt’s apparatus). 30 Aristotle, Metaph. Α 2, 983a12–16. I am following Jaeger’s text here who, however, wishes to move τοῖς μήπω τεθεωρηκόσι τὴν αἰτίαν further down in the text.

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Explaining an automaton I would like to stress this point by a close reading of an automaton, explained by Hero.31 According to Lefèvre “many of the drawings in the still extant manuscripts [of Hero] can be regarded as authentic”.32 My example is taken from chapter I, 16 of the Pneumatics. Its topic is an automaton with singing birds. The oldest manuscript, which Schmidt already used for his critical edition, is a thirteenth-century Byzantine codex, now kept in the Biblioteca Marciana in Venice (fig. 6). It includes wonderful figures that can be analyzed in its interrelations with the accompanying text. We will see that the feature, in which the technical writing differs radically from the automaton, is its visuality. The performance of the machine and the explanation of the diagram involve the public’s capacity of imagination in a completely contrary manner. As is usual at the beginning of the chapter the author explains how the automaton should impress the public: κατασκευάζεται οὖν ἦτοι ἐν κρήνηι ἢ ἐν ἄντρωι ἢ καθόλου ὅπου ἐπίρρυτον ὕδωρ ἐστίν, ὄρνεα πλείονα διακείμενα καὶ τούτοις παρακειμένη γλαῦξ, ἥτις ἐπιστρέφεται αὐτομάτως παρὰ τὰ ὅρνεα καὶ πάλιν ἀποστρέφεται. καὶ ἀποστραφείσης μὲν φθέγγονται τὰ ὄρνεα, ἐπιστραφείσης δὲ πρὸς αὐτὰ οὐκέτι φθέγγονται. καὶ τοῦτο πλεονάκις γίνεται. κατασκευάζεται δὲ τὸν τρόπον τοῦτον. (The figures of) several birds are arranged near a fountain, or in a cave, or in any place where there is running water. Near them sits an owl, which, apparently of her own accord, turns at one time to the birds and then again away from them. And when it turns away from them, the birds sing. When it turns back to them, they are mute. This is repeated several times. It is constructed in the following way.33

The text describes the visual effect that is performed by the mechanical device. The automaton is constructed in such a way as if the represented animals would move according to their own nature. The owl, the predatory bird, turns with a threatening glance to the little singing birds. They do not want to attract further attention and thus instantly fall silent. The observer is encouraged to imagine the scene in the categories of chase and flight. In such a way, a naïve observer perceives movements that ancient philosophers would classify as movements according to the nature of animals. At the same time, however, this is a problematic perception, because a technical device performs by definition movements against nature.34 The parts of the mechanical apparatus do not act intentionally according to their being, but because the movements are the necessary consequence of other

31 32 33 34

See also Bogen 2005b. Lefèvre 2002, 113. Hero, Pneum. I 16, 90. My translation follows Woodcroft 1851, 30 (with changes). Krafft 1967, 12–15.

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Fig. 6: Hero Alexandrinus, Automaton with Singing Birds, Byzantine manuscript (13th cent.)

movements within the construction. The surface of the automaton, however, covers the mechanism. Unlike the observed automaton, the diagram and the explanations it provokes reveal a chain of mechanical and pneumatic movements that replace the scheme of chase and flight.

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Ἔστω κρουνισμάτιον ἀεὶ ῥέον τὸ Α· τούτωι δὲ ὑποκείσθω στεγνὸν ἀγγεῖον τὸ ΒΓΔΕ ἕχον πνικτὸν διαϐήτην ἢ καμπύλον σίφωνα τὸν ΖΗ καὶ καθιεμένην χώνην τὴν ΘΚ, ἧς ὁ καυλὸς ἀπεχέτω ἀπὸ τοῦ πυθμένος τοῦ ἀγγείου ὅσον ὕδατι διάρρυσιν. ἐχέτω δὲ καὶ πλείονα συριγγίδια, οἷα εἴρηται, ὄντα τὰ Λ. συμϐήσεται οὖν πληρουμένου μὲν τοῦ ΒΓΔΕ ἀγγείου τὸν ἀέρα τὸν ἐν αὐτῶι ἐκθλιϐόμενον καὶ τὰς τῶν ὀρνέων ποιεῖν φωνάς, κενουμένου δὲ μετὰ τὴν πλήρωσιν διὰ τοῦ ΗΖ διαϐήτου μηκέτι φθέγγεσθαι. Let A be a stream perpetually running. Underneath let there be placed a small air-tight vessel, BCDE, provided with an inclosed diabetes or bent siphon, ZH. In that siphon let there be inserted a funnel, ΘΚ, between the extremity of which and the bootom of the vessel a passage is left for the water. Let the vessel be provided with several smaller pipes, as described above, Λ. When BCDE is being filled with water, it will happen that the air that is driven out will produce the notes of birds. And as the water is being drawn off through the siphon HZ, after the vessel is filled, the birds will be mute.35

The comprehension of the text depends on an active transformation of the diagram. The reader has to break down the figure into parts that represent technical components. There is no established code, which would repeatedly connect a letter to a specific element of the construction. The letters are used in an alphabetical order. The first mention in the text is crucial. Within the drawing the letter is an index to an adjacent line or graphical mark. It thus instructs the reader to decompose the figure and recombine single drawing acts. For example, the air-tight vessel is always named by four letters at its vertices, although only its overall function as vessel is concerned. By means of the letters names of technical components are associated with particular elements of the drawing. The graphic construction refers to a technical construction. The letters, however, are also important to transfer movements that the text describes, to the drawing. Therefore, the reader has to understand how a movement of a component induces another element of the construction to change its position, too. The surface of the paper represents a space where things move according to mechanical and pneumatic principles. Such rules can be defined more or less explicitly. According to these rules, for example, the elements will always move to their ancestral places, water downwards and fire upwards; there is no natural vacuum; the elements oust each other, and so on. These characteristics of the diagram contrast with the pictures of owl and birds that are drawn at the top of the figure. There, one does not need to decipher any letters in order to recognize animal patterns, which appear spontaneously, by evocation of images that last in the memory. By seeing the configuration of lines as bird, owl, etc., one sees them already in an oriented way: one recognizes in which direction the animal looks or if it turns around and many other specifics, which can be diversified within the pattern.

35 Hero, Pneum. I 16, 90–92. My translation follows Woodcroft 1851, 31 (with minor changes).

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In some sense the drawing demonstrates the shift of imagination from a naïve view to an informed one: the pictures at the top provoke the application of preestablished patterns, just as the performance of the automaton is meant to evoke the pattern of pursuit and flight. Unlike these pictures, the lines with lettered vertices lead to another kind of imagination. When one has found the way through the technical maze, the images at the top look different, too: one suddenly understands, that one does not have to see two owls but one owl and that this owls turns around at a specific moment within the performance. The confrontation of the figures is not achieved by pictorial means, but by the information related to the diagram. Therefore, the second part of the verbal explanation addresses the question of how one can coordinate the rotation of the column with the owl at the top with the singing and falling silent of the birds. ἵνα οὖν ἡ γλαῦξ ἐπιστρέφηται καὶ ἀποστρέφηται, ὡς προείρηται, προκατασκευάζεται τὰ μέλλοντα λέγεσθαι· ἔστω γὰρ ἐπί τινος βάσεως τῆς Μ ἄξων βεϐηκὼς ὁ ΝΞ ἀπὸ τόρνου εἰργασμένος, περὶ ὃν περικείσθω ἁρμοστὴ σύριγξ ἡ ΟΠ εὐκλύτως δυναμένη περὶ αὐτὸν στρέφεσθαι· ταύτῃ δὲ συμφυὲς ἔστω τυμπάνιον τὸ ΡΣ, ἐφ’ ᾧ ἐπιϐήσεται ἡ γλαῦξ συμφυὴς αὐτῷ ὑπάρχουσα· περὶ δὲ τὴν ΟΠ σύρριγγα δύο ἁλύσεις ἐπὶ τἀναντία ἐπιληθεῖσαι αἱ ΤΥ, ΦΧ διὰ τροχίων δύο ἀποδεδέσθωσαν ἡ μὲν ΤΥ εἰς βάρος ἐκκρεμάμενον τὸ Ψμ ἡ δὲ ΦΧ εἰς κοῖλον ἀγγεῖον τὸ Ω ὑποκείμενον τῷ ΖΗ σίφωνι ἢ πνικτῷ διαϐήτῃ. συμϐήσεται οὖν κενουμένου τοῦ ΒΓΔΕ ἀγγείου τὸ ὑγρὸν φέρεσθαι εἰς τὸ Ω ἀγγεῖον καὶ ἐπιστρέφεσθαι τήν τε ΟΠ σύριγγα καὶ γλαῦκα, ὥστε βλέπειν πρὸς τὰ ὀρνιθάρια, κενωθέντος δὲ τοῦ ΒΓΔΕ ἀγγείου κενοῦσθαι καὶ τὸ Ω διά τινος ἐν αὐτῷ πνικτοῦ διαϐήτου ἢ καμπύλου σίφωνος, ὥστε πάλιν καταϐαρῆσαν τὸ Ψ βάρος ἀποστρέψαι τὴν γλαῦκα κατὰ τὸν καιρὸν ἐκεῖνον, ὅτε πληροῦται τὸ ΒΓΔΕ ἀγγεῖον καὶ πάλιν αἱ τῶν ὀρνέων γίνονται φωναί. In order that the owl turns herself towards, or away from, the birds, as we have said above, one should prepare the following contrivance. Let a rod (ΝΞ) turned in a lathe rest on any support Μ: round this rod let a tube ΟΠ be fitted, that must be able to move freely about it, and having attached to it the little drum ΡΣ, on which the owl is to be securely fixed. Round the tube ΟΠ let a chain pass, the two extremities of which, ΤΥ and ΦΧ, wind off in opposite directions, and are attached, by means of two pullies, the one, ΤΥ, to a weight suspended at Ψ, and ΦΧ to an empty vessel Ω, which lies beneath the siphon or enclosed diabetes ΖΗ. When the vessel ΒΓΔΕ is being emptied, consequently the liquid is carried into the vessel Ω and thus causes the tube OΠ and the owl to revolve, so that it faces the birds. But when ΒΓΔΕ is emptied, Ω becomes empty likewise by means of an enclosed or bent siphon contained within it; Therefore, the weight Ψ, again weighing down, causes the owl to turn away exactly when the vessel ΒΓΔΕ fills up and the birds commence singing again.36

Who is able to relate to the given explanation, leaves behind the illusionary image of chase and hunt and imagines intertwining flows of water and air, weights and forces pushing and pulling. A diagrammatic representation of serial movements has broken up the overall imagination of a pictorial scene. 36 Hero, Pneum. I 16, 92–96. The translation follows, again, Woodcroft 1851, 31–32 (with changes, thanks to M.A.).

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The explanation of the automaton and the destruction of illusion seem to be completely successful. The diagram, however, may evoke another kind of illusion: on paper, everything in the graphical construction works smoothly. The challenges of how to implement the technical processes in reality, are not even mentioned. Thus, the figures may develop into fantasies of power, which pretend that natural forces can be manipulated completely according to human interests and ideas. The pictorial embellishment of the diagram is part of such an illusionism of second order. The figure is part of a precious Byzantine manuscript written on parchment. The figures are composed of brightly colored double lines that go far beyond what the strictly technical perspective requires. To some extent, the manuscript and its figures can be regarded as an embodiment of technical thoughts, parallel to the fabrication of machines, but not necessarily subordinated to that purpose. What appears as a supplement of technical construction, becomes a construction of its own right that stages the limited access to technical knowledge. At the center a force of imagination stands, shared by author and reader, that other parts of society lack. The thirteenth-century manuscript includes not only writings of Hero but also an early copy of Ptolemy, furnished with beautifully colored maps. This was, perhaps, one of the most wanted manuscripts of the Renaissance. In 1491 a copy was ordered for the Biblioteca Laurenziana (cod. 86, 28). Another manuscript was in the library of Matthias Corvinus, king of Hungary. Still in 1540 a legate of Francois I. in Venice ordered a copy of Marcianus 516 for the royal library.37 The list could be continued. These examples show that at least in the 15th and 16th centuries the books refer not only to the enforced movements of things but, as demonstrations of technical knowledge, also to the power and prestige of its owners. Perhaps one can transfer this impression to the situation of its emergence in the 3rd to 1st centuries .

Summary This article focused on diagrams in technical writings. I have argued that these figures were not contingent illustrations of the text, but the proper and actual medium of technical reasoning, even if many of them were changed or completely lost in manuscript tradition. They were intended to be diagrammatic or schematic drawings that explain some aspects of the interconnections of technical parts as well as their intended movements. This relationship is in the center of all technical reasoning. It starts from the assumption of a world, where movements can enforce other movements and where similar material conditions yield similar results. Thus,

37 Compare the survey of Hero: Schmidt (1899), Supplementum, 3–56 (19).

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the diagrams are crucial for the whole genre of mechanics: their authors argue on a par with mathematicians, from which they borrow the graphical forms. They claim a sort of knowledge that differs from skills of craftsmen, on the one side, and the purely verbal language of philosophers on the other side. The actual act of drawing, however, participates in both: governed by verbalized principles and reproducible on a material surface as graphical trace. It is a crucial task of the text to teach the rules of how to anticipate the intended movements on the basis of the graphical form alone. Within these features of genre the authors may compete. How are these rules explained and established, then? Are the mechanical principles combined to yield new machines and how are the astonishing effects described? These are the questions from which a specific notion of mechanical authorship may arise. But the manuscripts also represent the capacity of the reader to relate to the technical process. The recipient is dissociated from other social groups that are simply impressed by technical effects. With the choice of expensive parchment for example or the embellishment of the figures, the owner of the manuscript may represent his own social rank and power. The figures may refer, therefore, not only to a mere and pure knowledge, but to the social significance of this knowledge and the reputation of the author and his readers.

Bibliography Texts quoted Aratus: Maass, E. 1898. Commentariorum in Aratum reliquiae. Collegit, recensuit prolegomenis indicibusque instruxit. Berlin. Aristoteles: Hett, W. S. 1955. Minor Works. On Colours; On Things Heard; Physiognomics; On Plants; On Marvellous Things Heard; Mechanical Problems; On Indivisible Nines; Situations and Names of Winds; On Melissus, Xenophanes, and Gorgias Apollodor. London. Aelianus Tacticus: Köchly, H., & W. Rüstow 1853–1855. Griechische Kriegsschriftsteller, 2 vol. Leipzig. Archimedes: Netz, R. 2004. The Works. Translation and Commentary. Cambridge. Athenaeus Mechanicus: Whiteheard, D., & P. H. Blyth 2004. On Machines (Peri mēchanēmatōn). Stuttgart. Hero Alexandrinus: Schmidt, W., & H. Schöne 1899. Opera quae supersunt omnia. Vol. 1: Pneumatica et automata. Leipzig. Hero Alexandrinus: Commandino, F. 1575. Spiritalivm Liber. Urbino. Hero Alexandrinus: Baldi, B. 1589. De gli automati, overo machine se moventi. Urbino. Hero Alexandrinus: Woodcroft, B. 1851. The Pneumatics of Hero of Alexandria. Translated and Edited. London. Philo of Byzantium: Schöne, R. 1893. Mechanicae syntaxis [libri] quartus et quintus. Berlin.

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Works quoted Asper, M. 2007. Griechische Wissenschaftstexte. Formen, Funktionen, Differenzierungsgeschichten. Stuttgart. Bogen, S. 2005a. “Schattenriss und Sonnenuhr. Überlegungen zu einer kunsthistorischen Diagrammatik. ” In: Zeitschrift für Kunstgeschichte 68.2, 153–176. Bogen, S. 2005b. “Gezeichnete Automaten. Anleitung zur List oder Analyse des Lebendigen?” In: U. Pfisterer & A. Zimmermann (eds.), Animationen / Transgressionen. Das Kunstwerk als Lebewesen. Berlin, 115–146. Drachmann, A. G. 1963. The Mechanical Technology of Greek and Roman Antiquity. Copenhagen. Krafft, F. 1967. “Die Anfänge einer theoretischen Mechanik und die Wandlung ihrer Stellung zur Wissenschaft von der Natur.” In: Beiträge zur Geschichte der Wissenschaft und Technik 9, 12–34. Krämer, S. 2009. “Operative Bildlichkeit. Von der ‚Grammatologie‘ zu einer ‚Diagrammatologie‘?” In: M. Hessler & D. Mersch (eds.), Logik des Bildlichen. Zur Kritik der ikonischen Vernunft. Bielefeld, 94–123. Latour, B. 1990. “Drawing Things Together.” In: M. Lynch & S. Woolgar (eds.), Representation in Scientific Practice. Cambridge, 19–68. Lefèvre, W. 2002. “Drawings in Ancient Treatises on Mechanics.” In: J. Renn & G. Castagnetti (eds.), Homo Faber. Studies on Nature, Technology, and Science at the Time of Pompeii. Rom, 109–120. Long, P. O. 2001. Openness, Secrecy, Autorship. Technical Arts and the Culture of Knowledge from Antiquity to the Renaissance. Baltimore. Meißner, B. 1999. Die technologische Fachliteratur der Antike. Struktur, Überlieferung und Wirkung technischen Wissens in der Antike (ca. 400 v.Chr. – ca. 500 n.Chr.). Berlin. Netz, R. 1999. The Shaping of Deduction in Greek Mathematics. A Study in CognitiveHistory. Cambridge. Netz, R., & W. Noel 2008. The Archimedes Codex. Revealing the Secrets of the World’s Greatest Palimpsest. Cambridge. Netz, R. 2009. Ludic Proof. Greek Mathematics and the Alexandrian Aesthetic. Cambridge. Peirce, C. S. 1932–1958. Collected Papers. Cambridge. Schürmann, A. 1991. Griechische Mechanik und antike Gesellschaft. Studien zur staatlichen Förderung einer technischen Wissenschaft. Stuttgart. Stjernfelt, F. 2007. Diagrammatology. An Investigation on the Borderlines of Phenomenology, Ontology, and Semiotics. Dordrecht. Stückelberger, A. 1994. Bild und Wort. Das illustrierte Fachbuch in der antiken Naturwissenschaft, Medizin und Technik. Mainz. Weitzmann, K. 1959. Ancient Book Illumination. Cambridge.

Alan C. Bowen

Three Introductions to Celestial Science in the First Century  Abstract: In the Hellenistic era, diverse authors undertook self-consciously to introduce their readers to the science of astronomy. Curiously enough, the science which they presented and effectively defined was not the same in each case; and the techniques and strategies which each writer employed to establish himself as an authority and his account as authoritative differed as well. This is especially true of writers in the first century , when this kind of project was apparently born. In this paper, I shall focus on: Diodorus Siculus’ accounts of Babylonian, Greek, and Egyptian astronomy in his Bibliotheca historica; book 9 of Vitruvius’ De architectura; and Geminus’ Introductio astronomiae. My aim will be to answer three questions: 1. How does each writer present himself and his account of astronomy to the intended reader? 2. How does the rhetorical stance taken by each writer bear on what he actually says about astronomy, its fundamental projects, and its goals? 3. What are the underlying conceptions of what the astronomer knows, his practice, and his place in the broader intellectual culture? The broader aim is to clarify how each writer contributes to the intellectual context in which Greco−Latin astronomy of the first century  was transformed.

Introduction In the Hellenistic era, diverse authors undertook to introduce their readers to what was called ἀστρολογία in Greek or astrologia in Latin, terms which I will render uniformly by “science of the heavens” or “celestial science”.1 Curiously enough, the science which they presented and effectively defined was not the same in each case; and the techniques and strategies which each writer employed to establish himself

1 Throughout their history, the Greeks used several terms to designate the science of the heavens (ἀστρονομία, ἀστρολογία, μαθηματική) and its practitioners (ἀστρονόμος, ἀστρολόγος, μαθηματικός); and Latin usage was equally varied. The problem is that these terms were not in either language mere synonyms: indeed, the choice of a given term was often significant – consider, e.g., Hipparchus’ valorization of the μαθηματικοί rather than the ἀστρολόγοι as the true experts and authorities in the science of the heavens (cf. Mastorakou 2007). This situation is even more complicated when Greek and Latin writers turned to the related science of alien cultures. In view of this, I have thought it prudent on the present occasion to avoid adding yet more confusion by using the English term “astronomy”; and, thus, I have opted for a generic, less loaded translation of ἀστρολογία and astrologia, fully realizing that I am side-stepping for now the important question of why the writers to be discussed chose those particular terms in the first place.

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as an authority and his account as authoritative differed as well. This is especially true of writers in the first century , when this particular topos was apparently born. To explicate this phenomenon, I should make it clear that I am defining “introduction” as “the presentation of a particular subject matter, in this case, celestial science, by a writer who stands before the reader as a reliable, if not authoritative, guide”. Such an introduction need not be the beginning (προοίμιον, exordium, principium, prooemium) of a treatise nor must it be a treatise (εἰσαγωγή, introductio) in its own right: as we will see, introductions of this sort may occur in the course of a treatise that is of quite a different nature as well as in a transcribed series of lectures. Moreover, it should also be clear that what such an introduction presents need not be the very first thing that one learns of a subject;2 nor in fact need it be something that would even appear in a treatise expounding such preliminary information.3 In other words, what I propose to define as an introduction is the occasion, that literary moment, in which a writer presents an entire field of discourse, celestial science, to a reader much in the way as he would introduce another person. When we consider the literary remains of celestial science in Greek and Latin, it is striking that there are no such introductions to this science until the first century  when there are several. Why this should be so is a good question and well worth pursuing. After all, given that the existence of several introductions of this sort suggests a lack of consensus at the least, if the distribution of extant introductions is not a mere accident of history, it is yet further evidence of deficiency in the standard narrative found in most accounts today of the history of western astronomy.4 Be that as it may, my aim on this occasion is to move beyond this narrative by arguing that the first introductions of this sort do indeed belong to first century , and then by examining the instances found in the Bibliotheca historica by Diodorus Siculus,5 book 9 of Vitruvius’ De architectura,6 and Geminus’ Introductio astronomiae7 in order to identify:

2 Thus, it is beside the point to object that this definition is too broad because it includes in its denotation Ptolemy’s Almagest, a work not typically described as “introductory” because of its tacit requirement of substantial prior knowledge of the subject. 3 If we hope to avoid anachronism and reading ourselves into the past, it would be prudent not to call introductions those treatises which were not demonstrably written or used to initiate readers into a given subject. 4 On the standard narrative and its failings, see Bowen 2001, 2002, and 2009a. 5 Diodorus was active from ca 80 to ca 20 . See Sacks 1990, 160–203 for a reconstruction of his life and times. 6 Vitruvius’ dates are uncertain, though there is very good reason to think that his De arch. was written in the interval 30–20 . On his name, dates, and life, see Rowland, Howe, & Dewar 1999, 2–7. 7 On Geminus’ date, see Bowen 2006, 199 n. 4 or, for a different line of argument, Evans & Berggren 2006, 15–22.

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how these writers present themselves to the reader, how the rhetorical stance taken in each case bears on what each says about the science of the heavens, and what this entails about their views and expectations of what this science really is and who its practitioners are.

My broader purpose is to understand the intellectual context of the great change in Greco-Latin celestial science that is evident in the first century , I mean, the emergence of horoscopic astrology and its related world-view. My sources in this study are not new. Indeed, they are known but largely dismissed by adherents of the standard narrative because they are deemed technically weak and either wrong or confused. Yet, if we are to understand the impact of Babylonian celestial science on the Greco-Roman world and how the native science was transformed to accommodate it, then it is important to see how Greek and Latin writers at the time presented celestial science to their readers. And so, in this project, the technical and factual blemishes and obscurities are important only as minor matters to be noted and explained, if possible. What is of primary importance now is how these writers establish themselves and their accounts as authoritative, and what they tell their readers about the science of the heavens, its fundamental projects, and its goals. For, by means of their accounts, these writers shaped the intellectual context in which Greco-Latin celestial science reinvented itself.

The first Hellenistic introductions to celestial science We should start by considering a few texts earlier than the first century  that have been or might be viewed as introductions, if only to sharpen the point of this paper. There is, for example, P. Parisinus graecus 1, a second century text commonly known as the Ars Eudoxi.8 Plainly, our definition rules out taking this text as an introduction because the author is completely invisible. This is actually a good outcome in that this definition puts the burden of proof on those disposed on the basis of some tenuous inferences concerning its provenance and use to viewing this work as introductory. Specifically, it requires them to provide compelling argument against the less speculative and better founded view that it is a compilation (see Neugebauer 1975, 600) for purposes unknown.9

8 On this papyrus, see Bowen 2008b. 9 For the bald assertion that this work is an introductory survey, see, e.g., Evans & Berggren 2006, 10–12. Their confidence that it is by Leptines and entitled “Introductio caelestis” is unwarranted: cf. Bowen 2008c.

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P. Hibeh 1.27, however, may seem more problematic. In this papyrus, which dates to the third century , the author tells the reader that he will present a calendar of the major festivals in the Egyptian wandering year of 365 days. The text is regrettably fragmentary and there is a troubling change in hand from the earlier columns in which the author talks of his project and the later columns which simply record the calendar. Still, it is worth considering: [Column 1] (insufficient text remains) [Column 2] [1] [xxxxx] … a very wise man in Saïs who was also of service to us, for we lived in the Saïte nome for five years. [2] So, he set out the whole truth (ἀληθεί[αν]) for us and demonstrated it on the stone device (ἔργου) xxxxOLMOU which is called a gnomon in Greek. [3] He said that the courses of the Sun were two: one which defines nighttime and daytime and one which defines winter and summer. [4] Then, as I was able to make a summary most accurately in the fewest words [Column 3] so that the variety of the fractions (μορίων) not seem a lengthy and strange thing to you to understand, we will focus on the obligatory (ἀναγκαίας) days. [5] In reference to the risings and settings of the star[s], the ἀστρολό[γοι] and the sacred scribes use the days of the month (κατὰ σελήνη[ν]). [6] Thus, they conduct the greatest number of festivals on the same date (ἡμέρᾳ) year by year (κατ᾽ ἐνιαυτ[όν]) without making changes in the case of either a setting or a rising star; but some festivals they conduct. … (at least 6 or 7 columns missing; Grenfell & Hunt 1906, 145)

Even if the change in hands is not significant – and to concede this is perhaps overly generous – the presentation in the early columns differs from the first-century introductions that I have in mind in two ways. In the first place, though the author of this papyrus and the authors of the later introductions take a position between the reader and the subject matter, the author of this papyrus does not presume to do this on his own authority, but on that of another, some anonymous wise man – perhaps, an Egyptian – in Saïs.10 To judge from what survives of the papyrus, the author’s only intervention lies in omitting all but the “days of obligation” from the calendar: otherwise, like the wise man from Saïs, he is invisible. Second, there is a critical difference in what is presented: the papyrus focuses on a ritual calendar, whereas our first-century texts look to celestial science as a whole. Accordingly, though P. Hibeh 1.27 may appear initially to fit our definition of “introduction”, what has survived of it does not warrant the claim that this topos in the exposition of celestial science is attested before the first century . Finally, there is Polybius and his digression concerning what makes for success in military operations (IX 12.1–20.10). Since, as Polybius says, the issue of military success and failure lies largely with the commander himself, this digression focuses on what a commander should and should not do, a matter ultimately of what he

10 Regardless of whether this claim is true or a literary device, its effectiveness is far from clear.

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knows or has learned be it from practice (τριβή), inquiry (ἱστορία), or systematic experience (ἐμπειρία μεθοδική). It is under the last rubric that Polybius includes an admittedly superficial exposure to celestial science and geometry: Some of [the commander’s] experience needs [formal] learning (μάθησις) and scientific principles (θεωρήματα) in addition, and especially principles from celestial science (ἀστρολογία) and geometry – his work on these is not great for this purpose at least, though the matter is important and can contribute importantly to the operations just mentioned. (IX 14.5)

As one might expect, what commanders presumably ought to know of celestial science is limited to matters of timekeeping: Polybius (IX 14.6–19.4) mentions the need to understand the pattern of variation in the lengths of daytime and nighttime throughout the year, the division of the year into seasons and of the day into hours, the determination of nocturnal hours by the risings and settings of the zodiacal signs throughout the year, and the phases of the Moon. The upshot, then, is that while Polybius does indeed present himself and his history to the reader, and that while what he says of celestial science (IX 14.6–19.4) is interesting in its own right, he does not really introduce his reader to celestial science as such; instead, he identifies what the reader should expect a proper military commander to know. So, absent any real contenders to status as an introduction to celestial science in the period before the first century , let us now turn to Diodorus.11

Diodorus Siculus and his Bibliotheca historica It is in the proem to book I that Diodorus defines himself in relation to the reader.12 He does this in three steps. The first (I 1.1–2.8) is a general encomium of historical 11 Evans & Berggren (2006, 2, 8–12) are hardly alone in assuming that all that one needs to warrant talk of an introduction is a text that covers the elementary stages of a subject. For them, the Introductio astronomiae is a popularizing text belonging to the genre of astronomical surveys, and ought to be understood in relation to P. Parisinus graecus 1 and Cleomedes, Caelestia (but see Bowen & Todd 2004, 1–17; Bowen 2008d). Now, apart from their undefended claim that this treatise was in fact elementary in its time, their unquestioning faith that it must be the sort of text that Strabo has in mind at Geogr. I 1.21, and their presumption that Cleomedes’ text, a text written some 250 years later, is a sound basis for understanding Geminus’ treatise, the real historiographical problem is that they uncritically perpetuate a form of “interpretation” that makes understanding celestial science in its (immediate) cultural and intellectual contexts unreasonable, if not impossible. A more carefully thought out notion of what an introduction is will surely afford a better vantage point for a coherent study of contemporary discussions of celestial science by authors who do not necessarily fall within the modern “canon” of writers in the history of Greco-Latin astronomy. 12 Each of the numerous complete books of Diodorus’ Bibl. (except books II, III, and XI) comes with a proem as do many of the books that are incomplete. See Sacks 1990, 9–22, for defense of the view that these proems are substantially Diodorus’ and not taken from other writers.

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writing and historians; the second is effectively an argument that he is the first historian to undertake writing a proper history (I 3.1–8); and the third is a statement of his special qualifications for this task (I 4.1–5). The opening contention of the proem is that, since we learn from experience (ἐμπειρία), it is right that we all be grateful to writers of universal histories (κοιναὶ ἱστορίαι) because, in offering us instruction without the attendant danger, they enrich our common (way of) life (κοινὸς βίος) and extend our experience by showing us things that will be of use in our own lives. The experience derived from history consists mainly in our understanding (σύνεσις) of the failures and successes of others (I 1.1–2). To elaborate why such gratitude is indeed owing and thus to enhance further the standing of these historians, Diodorus likens them to servants (ὑπουργοί) of divine Providence (I 1.3).13 This comparison emphasizes that the historian’s global unification of the human past, a unification rooted in the kinship (συγγένεια) of all mankind, is a basis for making decisions about the future.14 To conclude his commendation of history and historians, Diodorus cites further considerations (I 1.4–2.8), the basic force of which is that “one must, therefore, acknowledge that the acquisition of this [subject] is in fact most useful for all the circumstances of life” (I 1.4). Once he has established the great importance of historical writing, Diodorus demonstrates that he is the first to undertake this task properly (I 3.1–4.5). As he says, previous writers have failed to convey the full benefit of their task by limiting themselves to single, self-contained wars fought by a single people or polis. Indeed, he continues, few have attempted to write a history that ranges from the earliest times to their own day; and, of those that have, some have done so without dating the events, others have ignored mythic times or the barbarians, some again have not been able to complete their work, and none has carried his account beyond Macedonian times. In short, though a universal history would be of the highest benefit to mankind, no one before Diodorus has tried to encompass all events and times in a single systematic treatise (σύνταξις, I 3.2–3). Then, after reiterating the shortcomings of current historical writing and emphasizing both the great difficulty of writing a universal history and the promise of its supreme utility (τὸ χρήσιμον, I 3.4–8), Diodorus asserts his qualifications. 13 Diodorus, Bibl. I 1.3: “Indeed, [Providence] has brought together the order of the visible heavenly bodies and our natures into a common relation (κοινὴν ἀναλογίαν), and moves every age continuously on its cycle, apportioning what befalls each from its appointed destiny; and [these historians], by recording the common affairs of the inhabited world just as the affairs of a single polis, have delivered their works as a single account of the past and a place of judgment (χρηματιστήριον)”. 14 I 1.3 χρηματιστήριον (place of judgment): as Diodorus says, historical accounts allow us to use the mistakes of others as examples for correction and to address events in our own lives not by investigating what is being done now but by imitating what succeeded in the past (I 1.4). His underlying point is that those who must act now typically lack the luxury and means of discovering what others are doing concurrently in similar circumstances.

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Chief among them is that he has been working at it for 30 years, much of it spent traveling throughout Asia and Europe (at no small risk to himself, as he says) in order to familiarize himself with the important sites and thus to avoid error.15 Next is his great passion for this project and the fact that he has had access to documentary materials assembled from around the world in Rome; and last is that he has a good working-knowledge of Latin (I 4.1–5). Thus ends Diodorus’ argument that he is the leading authority and guide to a subject of vital importance to the reader. As he would have it, his readers may rest supremely confident in the truth and benefit of what he has to say.16

The Egyptian science of the heavens The rest of book I concerns the Egyptians. In its second part, Diodorus turns from his account of the Egyptian rulers prior to the Trojan War to a summary review of Egyptian customs, in particular, those that are most incredible and those that will prove especially useful to the reader, since many of these practices were still in effect in his time and admired by the Greeks (I 69.1–2). Indeed, so Diodorus claims, many Greek intellectuals – he mentions Homer, Pythagoras, and Solon – came to Egypt to gain knowledge of Egyptian laws and ways, on the ground that they were worthy of note (I 69.3–4). After repeating the Egyptian argument that writing, the observation of the stars, the theorems of geometry, most of the arts (τέχναι), and the best laws were discovered by Egyptians (I 69.5–7), Diodorus describes numerous interesting features of Egyptian life (I 70.1–80.6) and so comes to the matter of priestly education and celestial science. As he tells the story, the sons of priests were trained in the techniques of landmeasurement (γεωμετρία) and arithmetic reckoning (ἀριθμητική, I 81.1–4). The latter, Diodorus adds, is very helpful to those who work on matters of celestial science (τὰ περὶ τὴν ἀστρολογίαν), given that the Egyptians had carefully observed and recorded the arrangements and motions of the heavenly bodies from ancient times (I 81.4). He amplifies this by saying that they have observed most avidly the motions of the wandering stars, that is, their circuits and stations, and, further, the powers of each relative to the births of animals, of which good effects and which bad effects they are productive. And while they are often successful in predicting to men what is going to befall them in life, frequently they announce upcoming destructions of crops or the opposite, bumper crops, and further, plagues for men and cattle; and from observation over a long time they have foreknowledge of earthquakes, floods, the risings of comets, and all the things which to the many seem impossible to know. (I 81.4–5)

15 As Kenneth Sacks points out (1990, 161 and nn. 1–2), while Diodorus does mention travels to Egypt and Rome, there is no evidence other than this claim that he did in fact travel to Europe and Asia. 16 On the issue of truth, see Polybius I 5.5.

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After this brief account of Egyptian celestial science comes more discussion of Egyptian customs, and then book 1 concludes by listing famous Greek intellectuals who came to Egypt to gain knowledge (I 96.1–98.10: cf. I 69.3–4). Diodorus again mentions Pythagoras and others, and includes the proof tendered that such visits did actually occur (I 96.1–3). But this time he adds new details: They opine (ὐπολαμβάνουσι) that Democritus too spent five years with them and learned many things in ἀστρολογία; and that Oenopides likewise spent time with the priest-ἀστρολόγοι (τοῖς ἱερεῦσι καὶ ἀστρολόγοις) to learn different things and especially the solar circuit, namely, that [the Sun] has its course at an inclination and makes its motion in the direction opposite to the other stars.17 In the same vein, they opine that even Eudoxus studied celestial science (ἀστρολογήσαντα) with them and gained a reputation worthy of note when he passed on many useful things to the Greeks. (I 98.3–4)

Thus far Diodorus has established three claims. First is that the Egyptians, a barbarian people, have a long history of studying the heavens.18 Second, that their celestial science was essentially astrological in that it involved making predictions of harm and benefit on the basis of the positions of the heavenly bodies. And third, that certain well-known Greeks enhanced or even secured their reputations by transmitting the Egyptian science of the heavens to their fellow countrymen.19 Notice, however, that the science purportedly disseminated by the Greeks did not include astrology – at least, Diodorus makes no mention of it. Let us now consider what he says about the Chaldaeans and their celestial science.

The Chaldaean science of the heavens In book II, after recounting the history of the Assyrian kings and the destruction of the their empire (ἡγεμονία) by the Medes (II 1.3–28.8), Diodorus writes: But it seems not inappropriate for us to say a few words about the Chaldaeans in Babylon and their antiquity, so that we omit nothing worthy of record. (II 29.1)

In characterizing the Chaldaeans,20 Diodorus likens them to Egyptian priests in their devotion to the study of the gods and their expertise in celestial science,

17 τοῖς ἄλλοις ἄστροις: scil. the fixed stars. 18 Indeed, the longest if one accepts their argument that the Chaldaeans were colonists from Egypt and learned their astronomy from Egyptian priests (I 81.6: cf. I 28.1). 19 Diodorus’ language gently suggests some reservations about this claim. Moreover, he is not entirely clear about wherein the fame of the Greek notables is supposed to lie. At I 69.3 and II 1.2– 3, he suggests that they were famous before coming to Egypt; yet I 98.4 indicates that Eudoxus acquired his reputation by disseminating Egyptian astronomy. 20 On the Chaldaeans and what Greek writers understood by “Chaldaean”, see Eck 2003, 153 n. 3.

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adding that the Chaldaeans practised all the mantic arts as well as the various rituals for warding off evils and securing good outcomes (II 29.2–3). He next distinguishes the education of Chaldaean children from that common among the Greeks, and makes plain his much higher regard for the former. He contends that Chaldaean education in celestial science produces skilled practitioners with a true mastery of the details in a field which remains coherent over time. In contrast, he says, the outcome of Greek education is incoherence and confusion because the field is defined by the quest for profit and an attendant imperative for doctrinal innovation, an imperative evidenced by the constant founding of new schools and the radical criticism of others on fundamental points (II 29.4–6).21 Diodorus’ tantalizing comparison of Chaldaean and Greek education offers the Chaldaean “home-schooling” in celestial science as a model of success and Greek schooling as the paradigm of failure. But what exactly is being compared? One possibility is that in II 29.5 he means Greek education in philosophy, since he writes of the term φιλοσοφία: παρὰ δὲ τοῖς Ἕλλησιν ὁ πολὺς ἀπαράσκευος προσίων ὀψέ ποτε τῆς φιλοσοφίας ἅπτεται. But among the Greeks, ordinary people approach and engage in philosophia unprepared at some point late (in life).22

Yet, he also uses φιλοσοφία in II 29.2.4 for what is passed down from father to son in Chaldaean education: παρὰ μὲν τοῖς Χαλδαίοις ἐκ γένους ἡ τούτων φιλοσοφία παραδέδοται. Among the Chaldaeans, the philosophia of these matters is handed down from the family.

So, perhaps he is instead comparing modes of education in celestial science, as one might expect. Regrettably, the little that we know of ‘Greek’ astrology dating from the third quarter of the second century  does not help to sort this out. Though there is slight evidence in the Hellenistic world of astrological activity in this period,23 and though astrology was undoubtedly a feature of life in Diodorus’ time,24 we have no contemporary evidence bearing on the question of education 21 See Strabo, Geogr. XVI 1.6 for an account of Chaldaean celestial science that indicates doctrinal differences among its practitioners. 22 On the text, see Eck 2003, 155 n. 3. 23 There are, for example, several citations found in writers of the fifth and sixth centuries  of a manual, Astrologoumena, pseudepigraphically ascribed to Petosiris and Nechepso that is thought to derive from this time (see Fuentes Gonzélez 2005). These fragments were collected by Riess (1892), though more are known now. As Pingree (2008, 547) observes, however, these citations entail “radical reworking of the original texts” and so it is extremely difficult to say just what these original texts maintained. Still, there are useful parallels in some cases with Demotic texts suggesting an origin in Babylonian astral omen texts of the Achaemenid period. 24 In addition to literary sources such as Cicero, Diodorus, Vitruvius, and Geminus, there are remnants of a few horoscopes: see p. 308 nn. 25–26.

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in “Greek” astrology and likewise no evidence of competition among astrologers in this period25 as there is in later centuries.26 In short, the imprecision and lack of detail in his remarks on education make it impossible to determine what Diodorus is actually telling his readers here. Diodorus then relates some details of the Chaldaean outlook. Their conviction that the cosmos is by nature both uncreated and indestructible, and that its order is governed by Providence, underwrites their long-term interest in observing the motions and powers of the heavenly bodies, and in predicting the future (II 30.1– 2). He next outlines their doctrines regarding the planets or Interpreters (ἑρμηνεῖς, II 30.3–5), the 30 zodiacal stars or Counseling Gods (βουλαῖοι θεοί, II 30.6–7), how the planets are ominous (II 31.1–3), the 24 non-zodiacal stars (II 30.4), the Moon (II 30.5–6), eclipses (II 30.6), and the Earth (II 31.7).27 As he indicates (II 31.7–9), there is much more to tell; but since it would be alien to his history (τῆς ὑποκειμένης ἱστορίας ἀλλότριον) – I take this to mean that he does not deem it useful to the reader – he concludes by noting that the Chaldaeans have the highest standing in celestial science of all men and have pursued it most diligently, though he finds their claim to have observed the heavens for 473,000 years prior to Alexander’s crossing into Asia (334 ) hard to believe.

Diodorus and his Greek readers Diodorus takes pains to secure his history as the record of all human affairs to his own times, an authoritative record which he asserts will be supremely useful to his readers. The utility here is primarily political – many of Diodorus’ exempla address the reader’s hopes for effectiveness in matters concerning the maintenance and preservation of the polis. But Diodorus also includes what we may call cultural matters presumed to be of interest and use to the reader as well. Among these are his accounts of Egyptian celestial science and its Chaldaean counterpart. Diodorus’ presentation of the Egyptian and Chaldaean sciences of the heavens assimilates them to Greek celestial science by using the same name, ἀστρολογία.

25 Cf. Neugebauer & Van Hoesen 1987, 16–17, 76–78. 26 See Jones 1999, 5–7, 249–250. 27 Diodorus’ preference for the properly demonstrative character of Greek scientific thought is evident here when he offers a rare criticism of a barbarian celestial science: “They (the Chaldaeans) offer very weak demonstrations concerning the eclipse of the Sun and do not dare to make predictions or to circumscribe (περιγράφειν) the times for this precisely. Concerning the Earth, they make very strange (ἰδιωτάτας) remarks, saying that it is like a boat and hollow”. (II 31.6–7) I take the claim about weak demonstrations to mean that their remarks were not really appropriate to proper causal explanations. Note that Diodorus seems to have been aware that the Babylonians aimed only to determine when eclipses were possible.

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This is remarkable. After all, given that he effectively defines these barbarian celestial sciences by their predictive power and their role in human life, he might just as easily have assimilated them to the Greek mantic arts. It is also remarkable that in limiting himself to what is useful, he focuses on astrology. But that said, the question then is: How are these accounts actually to be useful? It is regrettable that Diodorus’ discussion of the Greeks in later books does not describe their celestial science. What we have on this score comes only in books I and II. Still, given Diodorus’ emphasis on the utility of his history, what, we may ask, is the specific point of his accounts of Egyptian and Chaldaean celestial science? To answer this, we must take cognizance of the likelihood that Diodorus’ Greek readers were aware of astrological activity in their midst (and perhaps even of how it differed by positing astral influence and supplying a rationale in physical theory). Next, we should notice that Diodorus limits Greek celestial science to its classical or traditional domain;28 and that astrology is, for him, a demonstrably credible means of predicting the future and thus for securing benefits and avoiding harms.29 Given all this, it would seem that Diodorus is in fact urging an appropriation of barbarian celestial science within the context of the concerns of classical Greek celestial science. Diodorus does not, however, indicate how this appropriation would work or how it should be construed. Thus, for example, he does not tell his reader whether this barbarian science is simply a new subject to be taken up with others in the Greek science of the heavens or whether classical Greek celestial science is now to provide what is needed (models, parameters, and computational techniques, and tables) for making astrological predictions.30 Instead, he seems content to leave his reader with the general thesis that Greek celestial science ought somehow to include its barbarian counterpart, because, as he holds, this will be a great benefit in human affairs. At the same time, Diodorus does point out a great opportunity for renown: not only has he remarked that it is with an eye to a place in history’s favor that men have been zealous to discover new sciences and arts for the service of mankind (I 2.1), he has emphasized that Greeks in the past have secured or enhanced their reputations by disseminating barbarian celestial science.

28 To judge from what Diodorus writes, this domain was established in the fifth and fourth centuries  and was defined primarily by an interest in the celestial sphere – the Eudoxus known in the first century  was likely the Eudoxus who inspired Aratus’ Phaenomena, not the Eudoxus of Aristotle, Metaph. Λ 8 (1073b17–1074a14) – that is, by an interest in timekeeping and geography. 29 Cf. I 1.3, I 81.5, II 31.1–3. See also Diodorus’ accounts of the Chaldaean predictions concerning Alexander (XVII 112) and Seleucus (XIX 55): note esp. XIX 55.9, which reflects poorly on Greek philosophical arguments against the Chaldaean art (cf. XVII 112.4–5). 30 Whether Diodorus aims to support Greek astrological activity in his time or to redirect it is unclear, since this question depends on the nature of the appropriation that he envisages. Note that Greeks did use Babylonian computational schemes in preparing horoscopes and almanacs (see Jones 1999, 15–18).

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Vitruvius and De architectura 9 Within a decade of the publication of Diodorus’ Bibliotheca in 30 , Vitruvius wrote a treatise on architecture which also has occasion to introduce the science of the heavens.31 But this time, the rhetorical setup is different. Whereas Diodorus sought to convince his readers that his subject was of critical importance, that he was the first to undertake it properly, and that he was well qualified for the task, Vitruvius sets out to convince one person, Augustus, to receive his book kindly. Vitruvius’ argument to Augustus is short and neat (I praef. 1–3). After flattering Augustus for his great accomplishments and effectively commending himself to Augustus because he has the good sense to present his book at the right time, Vitruvius points to his historical connection to Augustus. He was, he says, originally recognized by his father, Julius Caesar; and when the latter died, he transferred his support to Augustus himself. For this reason, he adds, he was employed by Augustus32 who awarded him a stipend (commoda) and continued it at the urging of his sister Octavia. Thus, having reminded Augustus of his past service, and seeing that Augustus is embarking on an extended program of building commensurate with his accomplishments, Vitruvius now offers in payment of his debt to Augustus a book explaining the technical terms and principles of architecture in a way that will allow Augustus to teach himself how to evaluate the works built for him. Thus far Vitruvius has attempted to convert Augustus from a casual recipient to a patron in receipt of a work by a loyal and esteemed client-advisor. There are plainly advantages to be gained by this, not least of which would be admission to the circle of famous writers that had formed about Augustus.33 Or, if this seems over-reaching, it would at least put him in the company of those distinguished architects whom Augustus employed to build his monuments. Yet, this would not exhaust Vitruvius’ aims so far as his readership is concerned. For he plainly expects other readers as well (see I praef. 18); and it is equally clear that they are to include other architects.34 31 See Sacks 1990, 161; 300 n. 6, above. 32 Vitruvius (I praef. 2) does not say that he was employed as an architect (architectus) but asserts only that he was put in charge of the design and construction (apparatio) of catapults (ballistae) and artillery devices for firing arrows at short range (scorpiones). Yet he does include such work in Arch. X 10–11, thus indicating that, in his view, it is a branch of the architect’s disciplina: cf. I 1.8. This view of the architect’s ambit is also found in Philo’s Belopoeica (Diels & Schramm, 51.11–22, 59.34–45) and Strabo’s Geogr. XII 8.11, XIV 2.5. 33 See Fantham 1996, 67–84 for a very useful discussion of patronage and patrons in late Republican and early Imperial times, albeit one that focuses mainly on poetry. 34 On the rare occasion in which he does address readers other than Augustus, Vitruvius does so obliquely, a fact which introduces some curious dynamics as, for example, when he explains to Augustus that plagiarists and others who abuse writers should be dealt with as criminals and severely, noting that he has neither plagiarized other writers nor failed to offer unbounded thanks to those whose works he has used (see VII praef.: cf. I 1.18).

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But how do Vitruvius’ efforts to establish his book as a work that Augustus should read and be guided by make it authoritative or even important to other readers? Certainly, what Vitruvius writes about architecture to the great employer of architects will merit the attention of other architects and may even empower them in that they will know what Augustus knows. That, however, does not go far enough to qualify Vitruvius as an authority or expert for these readers. Of course, one might argue that Vitruvius’ authority for these other readers derives from his fiction that he is a literary client-advisor of Augustus. But my own sense is that, while true, this too does not go far enough. As I see it, Vitruvius did not really aim for the sort of authority claimed emphatically by Diodorus, but sets his sights on something different – status as an author, who by prescribing to the authority the details of what an architect should know, how he should be educated, as well as the profession’s best practices, compels his fellow professionals to take what he writes very seriously and to deal with it in a way that must ultimately be subject to Augustus’ approval too. We should note that Vitruvius has also delimited the scope of what he has written. To put it prosaically, while he may tell Augustus all manner of details about walls and their construction, his aim is not to have Augustus build a wall or even to know how to build a wall: his aim is to equip Augustus to judge that a wall has been well built. But what does this emphasis on aesthetic judgment entail? Vitruvius’ answer comes in the next chapter, where he casts this question in terms of what should go into the education of the architect, and incidentally forestalls the querulous objection that Augustus already knows enough to judge what is built for him. Vitruvius first maintains that the architect’s expertise (scentia) arises from practice (fabrica) or “hands-on-experience” and reasoning (ratiocinatio) which demonstrates or explains works completed with due measure of skill and theory.35 What is unusual is his view that this expertise is enhanced by many disciplines (disciplinae) and diverse branches of learning (eruditiones), and his contention that would-be architects who pursue both theory and practice to the fullest will attain their goal more quickly and with authority (auctoritate, I 1.1–2). For Vitruvius, an architect should have a natural talent (ingenium) and be amenable to learning. As he says, to be educated (ut litteratus sit), [the architect] must be skilled in drawing and learned in geometry; he should know many histories, pay careful attention to the philosophers, understand [the science of] music, and not be ignorant of medicine; he should know the responses of legal experts and comprehend celestial science and the recognized principles of the heavens (astrologiam caelique rationes cognitas). (I 1.3)

35 res fabricatas sollertiae ac rationis pro portione. For the text, see Krohn 1912, 2.17–18: cf. Fleury 1990, 69 n. 10; Granger 1931–1934, 1.6 n. 1.

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In I 1.4–10, Vitruvius explains why all these subjects and others are necessary.36 He concludes by remarking that from celestial science are ascertained east, west, south and north, and, further, the theory of the heavens (the equinox, solstice, and the courses of the stars). If one is not acquainted with these matters, he will not in any way be able to understand the theory of sundials (horologiorum rationem, I 1.10)

and by insisting that since this (scil. architectura) is such a great discipline adorned and abounding in diverse and numerous branches of learning, I think that only those can rightly declare themselves without qualification37 to be architects who have been nourished in the knowledge of a great many literary works and arts from childhood by making their ascent by way of the steps of these disciplines, and who have arrived at the very lofty temple of architecture.38 (I 1.11)

But Vitruvius must now deal with the objection (ascribed diplomatically to the inexperienced and not to Augustus himself) that he includes more than is humanly feasible in his account of the architect’s education (I 1.12). He responds by noting that all the disciplines mentioned have a connection to one another and a common ground, and that a general education (encyclios disciplina) such as he is urging is put together like a single body from these members (I 1.12). He then points out that this does not mean that the architect must be more skilled in each of these disciplines than those who devote themselves to them alone or that he should even try to acquire such skill. For, as he says, the individual arts (artes) consist of the work and its theory (ex opere et eius ratiocinatione), and that only the latter is shared with every learned man and is, therefore, relevant to the architect (I 1.12–16). In his view, [the architect] who from the individual disciplines has a moderate understanding of their wellknown parts and theories, I mean, those which are necessary for architecture, will seem to have done enough and much more, so that, if there should be any need to make judgments or recommendations about these matters and the arts, he will not fall short. (I 1.16)

36 He lists and gives reasons for his including letters (so that the architect can read), draughtsmanship, geometry, optics, arithmetic, history, philosophy (for character formation), physical theory (praeterea de rerum natura, quae graece φυσιολογία dicitur, I 1.7), music, medicine, and law. 37 repente: lit. “suddenly”, “all at once”. I take Vitruvius to mean those who can say that they are architects without having to explain in what way this is true. 38 It may be opportune to note here Vitruvius’ request at I 1.18 of both Augustus and any other readers – this is one of the few times in which Vitruvius acknowledges readers other than Augustus, albeit he does so obliquely – that he be forgiven if anything which he writes is inadequate in regard to the rules of literary art.

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Celestial science for architects Vitruvius has commended celestial science as part of the critical apparatus needed to judge architecture and architects by presenting it as a component of the architect’s education: his stated rationale is that this science is needed for the design and construction of sundials (I 1.10). This brings us to book IX and its numerous puzzles. Before presenting celestial science, Vitruvius opens book IX by enjoining what appears to be an act of piety. As he says, rather than honoring and supporting victorious athletes, it would be far better to honor writers who benefit all mankind with the everlasting utility (utilitas) of their works. After all, athletes and their accomplishments do no good for anyone other than themselves, but writers and thinkers like Pythagoras, Democritus, Plato, and Aristotle foster all those things without which no state can be safe (IX praef. 1–2). Accordingly, Vitruvius reasons that writers should be accorded the highest honors and offers examples to make his case (IX praef. 3–4).39 He does not, however, mention any noteworthy astrologi, so the precise aim and relevance of this opening is unclear at this point. (I will return to this.) Still, after valorizing such writers further (IX praef. 15–17), he concludes: Thus, Caesar, I have written these books relying on these authors and applying their ideas and suggestions; and [having given accounts] of buildings in the first seven and of water in the eighth, I will in this [book] give an account of the principles of sundials (de gnomonicis rationibus), that is, of how [these principles] are found in the world from the Sun’s rays through the shadows of a gnomon, and for what reasons [these shadows] are lengthened and contracted. (IX praef. 18)

Thus, in IX 1.1, Vitruvius begins by remarking that the divine intelligence (divina mens) has arranged the behavior of shadows in such a way that the equinoctial shadows cast by gnomons vary in length depending on the terrestrial location of the gnomon, and that the lengths of these equinoctial shadows indicate40 the shapes of the analemmata on the basis of which the hour lines are constructed (taking due account of the locations and the shadow of the gnomons). He then explains that the ἀνάλημμα is the configuration (ratio) searched out in the course of the Sun and discovered by observation of its shadow as [this shadow] lengthens towards winter solstice (ad bru-

39 He adduces Plato and his explanation of how to double a square (IX praef. 5), Pythagoras and his discovery and demonstration of the properties of the set square (norma, IX praef. 6–8), Archimedes and his discovery of how to assess the purity of metals in terms of their relative buoyancy (IX praef. 9–12), and the mathematici Archytas and Eratosthenes for their methods of duplicating the cube (IX praef. 13–14). 40 The verb, a form of designo, suggests that the length of the equinoctial shadow is a key factor in marking out or defining the shape of the analemma.

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mam).41 By means of this configuration, through architectural principles and drawings by compass, [the Sun’s] work in the world is discovered.42 (IX 1.1)

This mention of the world (in mundo) opens the way to his description of the continuously rotating celestial sphere with its axis and pivots (IX 1.2), and its zodiacal belt made up of 12 zodiacal constellations which are equal in size (IX 1.3). He then adds that, while exactly which of these constellations are visible will vary with the season, at any point in time there will be six above the horizon and six below (IX 1.3). So far so good. At this point, however, Vitruvius shifts from the celestial sphere and what is tolerably relevant to the theory of sundials to what is substantially less so, the seven planets which move in increasing longitude (per graduum ascensionem), each on its own circuit (circumitio), through the zodiacal constellations in the direction opposite to the daily rotation (IX 1.5). He states some basic facts about the motions of these planets (IX 1.5–10),43 and includes a discussion aimed at convincing his reader that Venus and Mercury do in fact make stations and retrogradations (IX 1.6–7).44 He even attempts to explain this behavior for the planets above the Sun (Mars, Jupiter, and Saturn, XIX 1.11–13). The chapter ends by stating the order of the planets (IX 1.14–15) and explaining how this ordering accounts for their differences in temperature (IX 1.16). There follow four chapters which give two accounts of the Moon’s phases (IX 2), correlate the Sun’s position in the zodiacal constellations with the seasons and the length of daytime (IX 3), and describe the non-zodiacal constellations to the north (IX 4) and to the south (IX 5). Chapter 6 opens by trying to pull the preceding together. As Vitruvius says, I have given instruction so that there is an overview (ut sit perspectus) concerning the revolution of the world about the Earth and the arrangement of the 12 zodiacal constellations and of the stars in the northern and in the southern part. For the tracings (descriptiones) of the analemmata are found from this turning of the world, the contrary course of the Sun through the zodiacal constellations, and the equinoctial shadows of gnomons. (IX 6.1)

But once more he veers from this (ceterum ex astrologia. …) to the effects (effectus) that the 12 constellations, the five planets, the Sun, and the Moon have on human life. He concedes to the Chaldaeans their prowess in casting nativities (genethlialogiae ratio), a discipline which, he says, Berosus first brought to Cos and taught to Antipater and Achinapolus (who reportedly cast nativities based on the moment of conception and not on the moment of birth (IX 6.2)). 41 scil. ad brevimam (= brevissimam) diem: lit. “towards the shortest daytime [of the year]” (cf. 3.3). 42 effectus in mundo: see Soubiran 1969, 73 n. 5. 43 E.g., their sidereal periods and the time they take to traverse one constellation. 44 The proof fails because Vitruvius does not realize that the planet’s motion on its epicycle leads to retrogradation only if there comes a point when this motion is greater than the planet’s motion due to the deferent. See Figure 1, p. 45.

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Figure 1: A test for retrogradation Planet P will exhibit retrogradation to an observer at E only if (R−r)·v1 < r·v2.

Then, in contrast (autem), he observes de naturalibus rebus, a phrase meant to recall Greco-Latin physical theory,45 that Thales, Anaxagoras, Xenophanes, and Democritus have left well thought-out theories (rationes excogitatae) which explain “on the basis of what things the nature of things is governed and how [this nature] has its effects (effectus)” (IX 6.3). And he adds that, of those who followed their findings (quorum inventa secuti), Eudoxus, Euctemon, Callippus, Meton, Philippus, Hipparchus, Aratus, and others have discovered the risings and settings of the stars, and the signs of changes in the weather, on the basis of celestial science through their teachings of the parapegma (ex astrologia parapegmatorum disciplinis, IX 6.3). Such men, Vitruvius says, merit our admiration and deference because they were of such great dedication (cura) that they seem with divine intelligence to declare in advance (ante pronuntiare) the upcoming signs46 of changes in the weather. (IX 6.3)

Next (IX 7) follows an account of the analemma. But, surprisingly, after indicating some fundamental lines and pointing out the complexity of using the analemma to mark off the hour lines throughout the year, Vitruvius breaks off his account saying: Thus, I have passed over [these matters] not because I am deterred out of laziness; but lest I give offense by writing at length, I shall lay out by whom the kinds of sundial and their

45 See 312 n. 36. Vitruvius’ especially admires Democritus: see IX praef. 14. 46 significatus post futuros: lit. “signs that are going to occur later”.

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tracings have been invented. Since I am not able at this time to invent new kinds, and since those of others should not seem to be commended as my own, I shall, accordingly, speak of [sundials] that have been handed down to us and by whom they were invented. (IX 7.7)

And so chapter 8 begins by listing various species of sundial and their inventors, and by observing that there is a literature which the reader may usefully consult, “provided that he understands the tracings of the analemma” (IX 8.1). The remainder of book IX concerns waterclocks, including anaphoric clocks which are also designed with the aid of the analemma (IX 8.8–15).

Vitruvius on celestial science Book IX is easily faulted for its lack of organization and because it says both too little and too much – too little because it does not clarify the construction of the sundial, and too much because extended passages are irrelevant to this. Though I have no good excuse for the organization of this book, I do think that its range of topics is largely intelligible if one allows that the focus on sundials is part of a broader agenda. To begin, Vitruvius apparently recognizes two species of celestial science, both concerned with divination or the interpretation of signs in the heavens for purposes of prediction (cf. IX 6.2, 6.3). The first is Chaldaean genethlialogical astrology associated with Berosus and his pupils; the second is Greek celestial science rooted in Greek physical theory (which is causal in nature) and centered on the parapegma and sundial.47 Indeed, the lack of any remark to the effect that the connection between sign and signified in the parapegma is actually a correlation, and the claim that the various ‘parapegmatists’ followed the discoveries of those luminaries who offered causal explanations of natural things suggest that Vitruvius should in fact be included among those who think that the risings or settings of the constellations are causes of changes in the weather.48 As for his presentations of the analemma, sundial, and waterclock, they cohere with the second, Greek celestial science, as do his descriptions of the gnomon and its shadows, the rotating celestial sphere, and the Sun’s progress through the zodiacal belt.49 Vitruvius’ excursion into Chaldaean celestial science is unexpected but rests, I think, on several considerations. First is a general presumption that, as an important part of celestial science, it belongs in the education of the architect. More to

47 It is Greek celestial science in the sense that Vitruvius does not name any astrologus who wrote in Latin. 48 See below Geminus, Introd. astron. ch. 17. 49 This is also the sort of celestial science which underlies the medical theory that Vitruvius espouses: cf. I 1.10, I 6.1.

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the point perhaps is that Vitruvius sees a way to connect this Chaldaean form of divination with the parapegma, sundial, and Greek physical theory by his ‘naturalistic’ or causal account of the role of the Sun in producing the stations and retrogradations of the superior planets (cf. IX 6.11–13) and the thesis (unelaborated) that the celestial bodies have effects on human lives (IX 6.2). Also to the point, I suspect, is that by elevating Greek celestial science centered on the parapegma and sundial to the standing of Chaldaean astrology, a discipline that did interest Augustus,50 Vitruvius is enhancing the importance of this Greek science as well as his own contribution. (This might explain why he postpones naming noteworthy celestial theorists until IX 6.3 – as well as indicate that the preface to book IX does not enjoin and perform an act of piety so much as suggest how Vitruvius expects his own work to be received.) Be that as it may, Vitruvius’ account of the planetary motions, his explanation of the planetary stations and retrogradations, his description of the Moon’s phases51 cohere with his mention of Chaldaean astrology.52 That book IX says too little is readily explained in part by the purpose of the De architectura as stated in book I. Still, it is odd that Vitruvius tries to explicate the construction of the sundial without defining the key units of time (the hour, day, and year) or indicating how it does indeed depend on the rotating celestial sphere and the annual motion of the Sun. But perhaps there is a clue when Vitruvius excuses himself for not going into the details of how to use the analemma to draw hour lines (IX 7.7). The rule would seem to be that, when presuming to instruct Augustus, one should not tell him things that he might already know.

Preliminary summation Diodorus and Vitruvius adopt different strategies in presenting themselves to their readers. Whereas Diodorus stands before his Greek readers as the best qualified exponent of a subject, universal history, said to be of vital interest to all, Vitruvius offers advice to Augustus and, so far as his other (Latin) readers, his fellow architects, are concerned, he makes himself a necessary part of any conversation among them about architecture and the education of architects. In both instances, the reader is drawn in by the claim of the utility of what the author writes. According to Diodorus, when classical Greek celestial science becomes astrology, it will benefit humankind by allowing anyone to make decisions about what he should and should not do, and by making events in his life intelligible. But on the questions of what this science actually looks like and how it works as a whole Diodorus is silent. Vitruvius, for his part, likewise sees the great utility of the Chaldaean art 50 See Barton 1994a, 40–43; Barton 1994b, 40–47. 51 Note the comparison of how Berosus and Aristarchus explained them. 52 I am not sure what to make of the explanation of the planets’ temperatures.

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and proposes its inclusion in classical Greek celestial science. But, unlike Diodorus, he characterizes the union of these sciences by putting it under the rubric of divination and by emphasizing the role of causal theory or explanation in each. That is, in recasting classical Greek celestial science as a science of divination with a product, the sundial and the parapegma, he indicates that the union of the Greek and Chaldaean sciences of the heavens will enable ordinary people to know time itself and to take advantage as they are best able of all its key moments. This recasting is remarkable for its denying a view that goes back to Plato at least. That is, not only does each writer omit to suggest that the utility of this science consist in its value for a privileged few bent on attaining wisdom, he actually construes celestial science as a rival to (moral) philosophy rather than as a subject ultimately propaideutic to it. For both Diodorus and Vitruvius, this transformation of native Greek celestial science will also have an impact on practice. For, by envisaging a class of scientists who can actually make a living by casting horoscopes, developing parapegmata for given locales, and designing (if not making) sundials, both writers conceptualize a profession of celestial science as opposed to a mere intellectual discipline to which individuals may contribute in other ways and contexts.

Geminus and his Introductio astronomiae At first glance, Geminus’ treatise might seem an unlikely candidate for the present study because the author does not explicitly address the reader in presenting his subject. There is after all, no preliminary explanation of who he is, what he proposes to do, and why the reader should pay him attention, such as we find in the treatises by Diodorus and Vitruvius. Such concerns, however, are mistaken in supposing that Diodorus and Vitruvius exhaust the variety of rhetorical strategies that may serve in making what I have called an introduction. As I see it, Geminus has achieved the same effect by adopting a rhetorical strategy in which the authority claimed is that of a teacher whose pronouncements are, for the most part, cast impersonally and (presumably) meant to be construed as objective and true by his student-reader. To begin, we should note that Geminus does in fact address his reader; and that when he does, it is in the first person plural.53 This plural is, of course, on occasion an obvious fiction: in 1.22, for example, when he writes:

53 See, e.g., 1.22 (bis), 1.40, 6.5, 8.4, 8.29 (bis), 8.30, 8.38, 8.39 (bis), 8.47, 16.19, 16.20, 17.5, 17.18, 18.7 (bis).

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Concerning the remaining [wandering] stars, we will give the explanation (τὴν αἰτίαν) [of how their phenomena can be rendered through smooth, circular motions] in other [books].54 But right now we will indicate the reason why (δι᾽ ἣν αἰτίαν), in the case of the Sun, though it moves at the same speed, it traverses equal arcs in unequal times.

Τhe “we” is a useful courtesy, typical of Greek urbanity, that means “I” (cf. 17.5, 17.17). In other instances, Geminus’ “we” authorizes him to report (and characterize) customary usage (6.5, 16.19–20). In still others, it serves to mark points where he “assists” the reader in the course of an arithmetic (8.29–30, 8.38–39, 8.47, 18.7) or a geometrical argument (1.40). Geminus’ standing as teacher and authority is further enhanced when he distinguishes what belongs in more advanced studies and what belongs in a first introduction (πρώτη εἰσαγωγή) such as the current treatise evidently is (5.14–15, 5.17). This is sufficient, I think, to warrant the working hypothesis that Geminus’ Introductio astronomiae instantiates the same topos in presenting celestial science as do the texts from Diodorus and Vitruvius: the primary difference is that, whereas Diodorus and Vitruvius explicitly undertake to establish their authority, Geminus chooses to let the style of his text do the bulk of this work.55 But, when we adopt this hypothesis, we must also admit that Geminus’ strategy leaves unanswered two key questions: – –

What exactly is he teaching? and Who are his intended readers?

Plainly, the intended readers of this treatise are a select group; and if the principles of their selection are not wholly arbitrary or extrinsic, then it is fair to suppose that they are self-selected on the basis of criteria or considerations evident in the treatise itself. So, our two key questions are, in fact, closely interconnected.

Geminus and his readers But what are these criteria or considerations indicating just who the intended reader is? Evans and Berggren (2006, 9) suppose that Geminus’ target is either the ancient general reader seeking a smattering of astronomical lore as part of some interest in the liberal arts or the tyro astronomer with aspirations for further study 54 ἐν ἑτέροις scil. βιβλίοις (“books”, cf. 16.32, 17.48). Geminus’ use of λόγος militates against understanding ἐν ἑτέροις λόγοις (cf. Aujac 1975, 191 s. v.). Whether these books were to be sections of the current treatise (πραγματεία, cf. 5.24, 17.46) or of another is unclear. The fact is that they have not survived, if they were ever written. 55 That Geminus’ treatise is entitled an Introductio in some medieval manuscripts carries no weight. Indeed, the various titles assigned to the work illuminate the predilections of medieval copyists: it is unlikely that any goes back to antiquity.

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in the subject. This is unhelpful because it limits the treatise to a subset of its positive assertions, anachronistic so far as it appears to suppose that the ancient ‘liberal arts’ were not part of a larger program of education or agenda, and misleading in that there is no evidence of a program of education intended to produce ἀστρολόγοι simpliciter in the first century .56 Still, I agree, what matters largely in Geminus’ presentation of celestial science are the technical details (definitions, statements of observational fact, parameters, models, and historical remarks). But this hardly settles the matter of readership: it only raises the related question of the point of Geminus’ marshaling these details as he does. Now, one of the striking features of Geminus’ exposition is its emphasis on causation and causal explanation. Such emphasis is, by Geminus’ own lights, characteristic not of the celestial theorist but of the philosopher: to judge from Simplicius’ report, Geminus held that: it is for physical theory to inquire into the substance of the heavens and of the celestial bodies, into their power and quality, and into their coming into existence and destruction. Through these [investigations],57 it can certainly offer demonstrations concerning size, shape, and ordering. Celestial science, on the other hand, does not attempt to speak about anything of that sort. Instead, it demonstrates the order of the celestial bodies after declaring that the heavens really are a cosmos, and speaks about the shapes, sizes, and distances of the Earth, the Sun, and the Moon, about the eclipses and conjunctions of celestial bodies, and about quality and quantity in their movements. It follows that since celestial science deals with the theory of quantity, duration, and type of shape, it is reasonable for it to need arithmetic and geometry for this. And concerning these matters, which are the only ones about which it undertakes to supply an account, it has the authority to make inferences through arithmetic and geometry. Now celestial and physical theorists will in many cases propose to demonstrate essentially the same [thesis] (e.g., that the Sun is large, that the Earth is spherical), yet they will not follow the same procedures (ὁδοί). For whereas [physical theorists] will make each of their demonstrations on the basis of substance, or power, or “that it is better that it be thus”, or [the processes] of coming into existence and change, celestial theorists [will do so] on the basis of the [properties] incidental to shapes or to sizes, or on the basis of the quantity of motion and of the time interval appropriate to it. And physical theorists will in many cases deal with the cause by focusing on the causative power (ποιητικὴ δύναμις); whereas celestial theorists, since they make their demonstrations on the basis of extrinsic properties,58 are not adequate observers of the cause in explaining (ἀποδίδωσιν) that the Earth or the celestial bodies are spherical, for example. Sometimes they do not even aim to comprehend the cause, as when they discourse on an eclipse. At other times [celestial theorists] make determinations in accordance with a hypothesis (ὑπόθεσις) by setting out some modes (τρόποι) [of accounting for the phenomena]; and, if these are the case, the phenomena will be saved. (Kidd 1988–1999, F18.5–32)59

56 To demonstrate that there was such education, Evans and Berggren would have to address numerous questions concerning what these advanced studies actually were, who was undertaking them and from whom, when they took them, where, and why. 57 Kidd 1988–1999, F18.7: reading νὴ διὰ τούτων. 58 Kidd 1988–1999, F18.27 ἀπὸ τῶν ἔξωθεν συμβεβηκότων: cf. F18.23–24. 59 See Bowen 2007 for discussion of this passage and for demonstration of its consistency with the Introductio.

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So, by addressing issues of causation as he does, say, in chapters 2 (the Chaldaean theory of aspects) and 17 (the parapegma), Geminus plainly injects philosophical considerations into his account of celestial science and so includes philosophers among his readers.60 This, incidentally, increases the likelihood that Geminus’ criticisms of the views held by philosophers that – – –

the planetary eastward motion in longitude is apparent, not real (12.14–19), Oceanus covers the torrid zone between the tropics (16.21–23), and that Sirius causes the intensification of summer heat (17.32–35)

are directed to readers who actually have a philosophical interest or background. At the same time, it accounts for the facts that there is no mention of utility such as one finds in the introductions by Diodorus and Vitruvius; and that, while Geminus mentions numerous instruments (see Evans & Berggren 2006, 27–43), there is no hint that celestial science includes, or even aims at, their construction. In the same vein, it also suggests that Geminus’ reference to the celestial bodies and their material constitution as either fiery or aetherial (17.15, 17.33) – a point of dispute in his time both among Peripatetics and between Stoics and Peripatetics – acknowledges philosophical partisans of either stripe and need not indicate indifference to the question as Evans and Berggren (2006, 26) maintain.61 But, given even this much, there is still no sound basis for positive claims about the philosophical affiliations of Geminus and these readers. Such allegiance was not a simple matter of doctrinal agreement in the first century : without an explicit statement from Geminus himself, one should leave open the question of whether he was a Stoic, say, or a Peripatetic, and whether he was writing for those of like mind or for his opponents.62 60 When Evans and Berggren opine that Geminus’ treatise is free of philosophical interest or concern (2006, 10, 25–26), it is evident that they have failed to understand Simplicius’ report, a text which they include in their study of Geminus (2006, 250–255). Part of the problem may be their lack of clarity on the question of what in this report (Diels 1882, 291.21–292.31) – why they use Diels’ text rather than Kidd’s (1988–1999, F18) is not explained – should actually be attributed to Geminus. In their introductory discussion of the Introductio, they make the non-committal remark that Geminus’ epitome of Posidonius’ Meteorologica “does seem to imply, at the least, an interest in Stoic physics”; but later, in an appendix, they seem to allow that Geminus may have in fact endorsed the substance of the report (2006, 250–252). On this question, see Bowen 2007, 330–331. 61 Though Geminus writes in 16.29 of the Sun’s rising from the aether and its setting into the aether, this does not make him a Peripatetic. This passage comes in the course of a discussion of a cosmology found in Homer and the ancient poets, a cosmology which apparently entails the view that the Ethiopians, since they are near the Sun’s rising and setting, are burned (black, καταιθομένου) by the Sun. In this context, αἰθήρ is the sky (“the blazer”) and it should not be distinguished from the (upper) air (ἀήρ, cf. Aujac 1975, 82): Evans and Berggren (2006, 215 n. 16) are mistaken in supposing it to be Aristotle’s fifth element. 62 When Evans and Berggren argue that – the Introductio is plainly not a Stoic treatise, given what Diogenes Laertius (Vitae VII 144–146, 155–156) says of such treatises some 300 years later, and

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Geminus and celestial science Given that Geminus’ treatise is addressed to readers with some philosophical interests or background, what conception of celestial science does it communicate to them? There is plainly much to say on this score: the treatise is vastly more detailed than the introductions offered by Diodorus and Vitruvius. On this occasion, however, I will focus on issues that are common to all three writers. First, let us note that while Geminus does mention the Chaldaeans twice (2.5, 18.9), only the first passage is explicitly astrological. After defining the aspect of opposition, Signs in opposition (κατὰ διάμετρον) are the ones positioned along the same diameter (2.1),

Geminus elaborates by writing: For Libra sets while Ares rises and Scorpio sets while Taurus rises; and the same definition (λόγος) [holds] in the case of the remaining zodiacal signs in opposition. Zodiacal signs in opposition are considered by the Chaldaeans for their sympatheiai in nativities as well. The reason is that (γὰρ) those born in opposition seem to be affected in common with one another (συμπάσχειν) and, as one might say, to be positioned opposite to one another. In addition (καὶ), the positioning of a stars (scil. planets) at the same time in zodiacal signs in opposition both helps and harms nativities in accordance with the traditionally recognized powers (παραδεδομένας δυνάμεις) of the stars. (2.4–6)

It is remarkable that Geminus, unlike Diodorus and Vitruvius, neither speaks of Chaldaean astrology nor acknowledges Chaldaean expertise. He simply describes the aspect of opposition, states that the Chaldaeans allowed its significance in casting nativities, and supplies a reason that has authority apparently not because it derives from the Chaldaeans but because it is a tenet of celestial science. In effect, Geminus makes it clear that there is but one ἀστρολογία and its authority derives from its standing as a science. Yet, Geminus plainly includes astrology in celestial science. So how does this science, which also includes concerns attested in earlier Greek scientific literature, – though Geminus may have had an interest in Stoic physical theory, he was neither a follower of Posidonius nor a “dedicated Stoic” since he held a number of non-Stoic views (2006, 23–27), they place undue confidence in Diogenes and overlook the ample evidence of radical intra-school dissent during Geminus’ time. For example, Strabo, himself a Stoic, not only reports that he studied Aristotelian philosophy with Peripatetics (Geogr. XVI 2.24), he also acknowledges dissent within his own school about Posidonius’/Geminus’ assertion of the need for a physical theory that validates one and only one account of the celestial motions (Geogr. II 3.8: cf. Seneca, Ep. mor. 88 with Bowen 2009b). Again, the Stoic philosophers, Boethus of Sidon (first century ) and Panaetius (late second century ) apparently denied the Stoic doctrine of conflagration (ἐκπύρωσις, Philo, De aet. mundi 76.1–84.5). It was no different among the Peripatetics: Xenarchus, for instance, famously repudiated Aristotle’s arguments for the existence of a fifth elemental body (aether) and argued that the heavens were composed instead of fire (see Falcon 2012).

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incorporate astrology? On this question, Geminus is silent. He does not give any hint that, like Vitruvius, he sees ἀστρολογία as a science of divination. Indeed, though he does, of course, recognize that configurations of the heavens affect nativities, at no point does he even write of astrological predictions concerning them. Strangely enough, the only astrological predictions that he indicates are meteorological: thus, in introducing the trine aspect, he writes: For if the North Wind blows when the Moon is in some one of the three zodiacal signs (scil. of the first trigon), the same condition will persist for many days. Wherefore, the ἀστρολόγοι, starting from this observation, predict northerly conditions. (2.8: cf. 2.9–11)

Moreover, what he emphasizes instead is the causal mechanism by which the planets in the various aspects affect nativities: Sympatheiai arise in three ways: by the diagonal, by the triangle, by the square. No sympatheia arises in accordance with another separation (scil. between zodiacal signs). And yet it would be reasonable that sympatheia arises from zodiacal signs positioned very close together, since the effluvium or efflux (ἀποφορὰ καὶ ἀπόρροια) which moves from the characteristic property (ἀπὸ τῆς ἰδίας δυνάμεως) of each of the [planetary] stars ought above all to be colored by or mixed up with the zodiacal signs that are nearby. (2.13–14)

Likewise, when Geminus discusses the parapegma in chapter 17, though he allows that stellar risings and settings may serve in making predictions about the weather (17.6, 17.23), he frames his remarks about this device in terms of causation. To see this, it helps to understand that this chapter does not concern “weather signs”63 but significations, where a signification (usually ἑπισημασία, but once σημείωσις (17.21)) is the connection of a sign (σημεῖον, cf. 17.9), say, the rising of a constellation, to its significatum, a change in the weather (cf. 17.2).64 Thus, each entry in a parapegma records at least one signification (17.6). Next, the bulk of the chapter is an attack on a peculiar apprehension (ἄλλοια διάληψις) among the uninformed (οἱ ἰδίωται) of the significations in a parapegma, an apprehension in which the risings and setting of the various fixed stars are

63 So Evans & Berggren 2006, 216 et passim. Aujac’s “pronostics météorologiques” (1975, 83 et passim) is only slightly better. 64 The sense of relation is clear in 17.6: “The predictions arising from ἐπισημασίαι in parapegmata do not arise from some determinate set of rules (παραγγέλματα) nor are they treated systematically in some science by virtue of their having a result (ἀποτέλεσμα) that is necessary. Rather, [people] have recorded them in their parapegmata by taking what is consistent (σύμφωνον) from what happens for the most part through daily observation”. Strictly speaking, signs have significata, not “results”. The decisive consideration, however, is that predictions do not arise from signs per se, but from the recorded connections of signs and their significata. That is to say, Geminus is writing, e.g., about the prediction, “When Aquila sets in the morning, there will be a storm at sea”, where the underlying connection (ἐπισημασία) appears in his parapegma as “On [day] 28 [when the Sun is in Cancer], for Euctemon, Aquila sets in the morning; a storm at sea occurs afterwards”. (Manitius 1898, 212.9–10)

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construed as causes (παραίτια) of changes in the weather. For Geminus, the correct view (δόξα), which is held by the physical theorist,65 is that these significations are not causal rules established systematically by some science (τέχνη) and with necessary conclusions, but generalizations of observations taken over a period of time. In other words, they are, as he sees it, rules of thumb. Thus, for Geminus, the significations in the parapegma properly understood constitute “a pretty unscientific part of celestial science”.66 But Geminus goes further. After using his attack on a popular understanding of the entries in a parapegma as a means of challenging the scientific standing of 65 17.1 ὁ μαθηματικὸς καὶ ὁ φυσικός (the scientist, that is, physical theorist). The difficulty with “the mathematician and the physical theorist” is that there is next to nothing in Introd. astron. ch. 17 that draws significantly or especially on mathematics (i.e., arithmetic, and geometry) in laying out the correct view of significations (cf. 17.16, 17.18–23). Granted, there is ample reference to globes marked out with stars in the Introductio; but this still does not bear on the question of the significations of their risings and settings, even if this question concerned those who typically analyzed celestial phenomena using such globes. And even if these latter theorists were called μαθηματικοί, it would be misleading to call them mathematicians. Admittedly, by Geminus’ time, μαθηματικός served to designate the practitioner of celestial science; yet Geminus typically uses ἀστρολόγος instead. Notably, it was also common to treat arithmetic, geometry, and celestial science as μαθήματα (things learned, bodies of knowledge, sciences, mathematical sciences): the related verb is μανθάνω (perceive, learn). In light of this, I translate ὁ μαθηματικός by “the scientist” (cf., e.g., Plato, Tim. 88c1, Soph. 219c2–7: Vitrac 2005, 272). This works at 6.11–12, when Geminus explains why sunrise follows quickly after sunset at northern latitudes where the horizon cuts off a small arc of the zodiacal circle, and distinguishes the μαθηματικὴ αἰτία (scientific explanation) and the σφαιρικὸς λόγος (spherical account, i.e., explanation using a marked sphere or globe). It also works at 7.8, when he affirms that Aratus, Phaen. 537–540 is in accord with τὰ μαθηματικά (scientific considerations) and τὸ φαινόμενον (what is apparent). The only difficulty comes when Geminus discusses whether there is an ocean between the tropic circles (16.21–24). For, after introducing Crates’ affirmation of one – an affirmation which Crates claims to be ἀκολούθως τοῖς μαθηματικοῖς (in accordance with scientific considerations or with scientists, 16.22), Geminus objects: ἡ δὲ τοιαύτη διάταξις ἀλλοτρία ἐστὶ καὶ τοῦ μαθηματικοῦ καὶ τοῦ φυσικοῦ λόγου (16.23). This is similar to the conjunction that we have at 17.1. Now, one could construe καὶ τοῦ μαθηματικοῦ καὶ τοῦ φυσικοῦ λόγου by taking the καὶ … καὶ as coordinate, which would entail that there are two coordinate forms of theory (one that is μαθηματικός and the other, φυσικός) and, thus, that μαθηματικός does not mean “scientific” here. But one may just as easily read 16.23 and 17.1 in the same way by taking the first καὶ in 16.23 as adverbial and the second as epexegetical (“But this sort of arrangement belongs in fact to something other than scientific, that is, physical, theory”). Both Manitius (1898, 181, 360) and Aujac (1975, 83) understand ὁ μαθηματικὸς καὶ ὁ φυσικὸς λόγος at 17.1 (cf. 16.23). This is possible. But rather than supposing that Geminus means to say that scientific or physical λόγος has a δόξα (view), it is better to construe the contrast in ch. 17.1 not as one between interpretations (διάληψις, δόξα) of the entries in a parapegma but as one between those who hold these interpretations. 66 17.25 ἄτεχνον γάρ τι μέρος τῆς ἀστρολογίας. Evans and Berggren (2006, 222) have “For this particular part of astronomy is not scientific”, which misconstrues the Greek – ἄτεχνόν τι μέρος τῆς ἀστρολογίας is the predicate, and the adjectival enclitic τι qualifies the complex ἄτεχνον μέρος (cf. Kühner & Gerth 1890–1904, 2.1.663 § 470.3.3) – and overstates Geminus’ criticism in a way that makes his composing a parapegma odd, if not irrational (see 2006, 275–276).

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the parapegma itself, he then focuses on the even more prevalent assumption that Sirius’ rising at the same time with the Sun is the cause (παραίτιος) of the intensification of summer heat (17.26–45). His argument proceeds by showing that – – –

–

the Sun is the cause of this intensification (17.27–29, 17.36), Sirius was taken as a sign correlated with the intensification (17.30–31), the poets and philosophers who suppose that Sirius causes this intensification have strayed far from the truth and physical theory (φυσικὸς λόγος) (17.32–35), and that apart from physical theory, it is evident that Sirius cannot be the cause of the intensification of summer heat (17.37–44).

Geminus (17.46–49) concludes by proposing that it would be better to use signs (σημεῖα) given by Nature. Thus, by focusing on changes in the air that occur in the course of nature and with a particular cause,67 one should make forecasts (προγνώσεις) from the solar and lunar risings and settings, from the halo that appears about the Moon, and so forth, since forecasts on this basis will have necessary conclusions. As he notes, such signs were used in this way by Boethus, Aristotle, Eudoxus, and many other ἀστρολόγοι. The upshot is that, though Geminus does affirm the inclusion in celestial science of astrology and the parapegma, his focus on causation leads him to ascribe higher epistemic value to astrology and to suggest that the parapegma might better be replaced by a study of the natural causes of the changes in the weather, a study not limited to the cyclical changes that may occur during a year.68 In other words, where Vitruvius proposes to unify astrology and the parapegma by construing celestial science as a form of divination rooted in causal theory and emphasizes the productive utility of this science, Geminus not only undermines the status of the parapegma, he also downplays genethlialogical prediction and treats meteorological prediction as an incidental feature of what is clearly more important epistemically, traditional (Greek) causal theory. It is hardly surprising, then, that he says nothing of the utility of celestial science and of who is to produce its instruments. In sum, what he offers his reader is an account of celestial science circumscribed by philosophical considerations.69 Of course, Geminus might have taken his reader in entirely new directions in the work(s) that he promises. The analysis offered here is predicated strictly on what

67 17.46 τὰς δὲ φυσικῶς γινομένας καὶ μετά τινος αἰτίας. 68 Geminus does not comment on whether the meteorological predictions based on the positions of the planets in the heavens (2.8–11) will be licensed by this causal theory. 69 Geminus’ philosophical interest in explanation or aetiology is evident in other chapters too: cf. ch. 1 (explanation of the planetary motions in longitude and the case of the Sun), ch. 8 (the genetic interpretation of the calendar), chs. 9–11 (the phases of the Moon, solar and lunar eclipses), ch. 18 (the genetic interpretation of a Babylonian lunar scheme).

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we have in the Introductio. As for the promised works, the most one is entitled to expect, given the Introductio, is a causal account of why the planets (other than the Sun) appear to have an unsmooth motion in longitude, given that their real motions are all circular and smooth – an account which, one hopes, would explain how to understand ch. 18, since it uses a Babylonian linear zigzag scheme to characterize the motion of the Moon (see Bowen & Goldstein 1996) – and more detailed information about the celestial sphere and how a celestial globe should be marked out.

Conclusion The main obstacle to understanding Greco-Latin celestial science in its intellectual context during the first century  is that of finding a vantage point from which analysis may usefully begin. Typically, efforts to contextualize the history of this science during this period fail precisely because of a longstanding and debilitating preference for anachronistic suppositions concerning what must have been available over the documentary evidence that is actually in hand. There is, I submit, a remedy for this, though it is surely not the only remedy: it begins by noticing that several writers in this time avail themselves of a particular literary topos, the introduction, in presenting their views of celestial science to their readers. The mere existence of these introductions suggests that the idea of celestial science itself was contested in the first century ; and the details of their accounts confirm this. At least, it does if one resists any tendency to privilege certain authors, focuses on what writers at that time were saying in the course of presenting their readers with their overviews of contemporary celestial science, keeps steady in the face of distracting claims that the overviews offered are factually wrong, and declines to read one’s expectations into the past by simply supposing that none of them really conveys the full extent of what was known as celestial science in that period.70 Next, from this literary vantage point, it is evident that the causa disputationis was astrology and the two-fold challenge of integrating the genethlialogical art with the traditional Greek science of the heavens, all the while maintaining the contribution of astrology to the conduct of human life. The disputes themselves prove to be significant and well worth further study, since they concern not only what celestial science should be but also who are its practitioners, how they are trained, and why one should undertake this science in the first place. Moreover, it is also evident that the choice of rhetorical strategy in introducing celestial science is very much a question of what this science is taken to be. For 70 The point is not to deny that these overviews involved selection and omission. The point is that any claim that something was omitted should not be a matter of supposition or mere inference but of hard argument.

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Diodorus and Vitruvius, celestial science is useful and so they present it in the course of a broader exposition that is itself useful. But claims of utility immediately raise the twin questions, ‘Useful for whom?’ and ‘Who says so?’ Thus, Diodorus and Vitruvius are obliged to identify this utility and to secure their authority, an obligation that they both address albeit in different ways. Geminus, however, presents celestial science not as something useful but as a corpus of empirical truths that are to be explained and understood. And so he adopts the role of the expositor, a role that largely precludes any need to establish his authority because the authority of his account largely derives not from him but from its combination of empirical truth and philosophical/historical analysis. Still, the Introductio astronomiae is not like Euclid’s Phaenomena or Elementa, for example, texts in which the author vanishes: at various points Geminus does appear to the reader, not to claim or justify his authority, but to display it in the act of teaching.

Acknowledgments This paper was completed during a very pleasant and productive stay at the Institute for Advanced Study in Princeton (2009–2010). I am grateful to Tracey Rihll and Michael Lurie for their patience and kindness in answering questions that arose during the writing of this paper, and to Francesca Rochberg for her very helpful comments on an earlier draft.

Bibliography Texts quoted Astrologoumena: Riess, E. 1892. “Nechepsonis et Petosiridis fragmenta magica”. In: Philologus, Supplementary Volume 6, 327–394. Diodorus Siculus, Bib. hist.: Bertrac, P., & Y. Vernière (ed. and transl.) 2003. Diodore de Sicile. Bibliothèque historique 1. Paris; Eck, B. (ed. and transl.) 2003. Diodore de Sicile. Bibliothèque historique 2. Paris. Geminus, Calendarium: Manitius, C. (ed. and transl.) 1898. Gemini elementa astronomiae. Pp. 212–233. Repr. 1974. Stuttgart. Geminus, Introd. astron.: Aujac, G. (ed. and transl.) 1975. Géminos. Introduction aux phénomènes. Paris; Manitius, C. (ed. and transl.) 1898. Gemini elementa astronomiae. Repr. 1974. Stuttgart. P. Hibeh 27: Grenfell, B. P., & A. S. Hunt (eds. ) 1906. The Hibeh Papyri: Part 1, Edited with Translations and Notes. London. P. Parisinus graecus 1 [= P. Louvre 2388 Ro + Paris, Louvre 2329 Ro]: Blass, F. W. (ed.) 1877. Eudoxi ars astronomica. Kiel; Letronne, M. 1865. “Traité d’astronomie d’après Eudoxe”. In: Notices et extraits des manuscrits de la Bibliothèque Impériale 18.2, 25–76.

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Philo Byzantinus, Bel.: Diels, H., & E. Schramm (eds.) 1919. Philons Belopoiika. Abhandlungen der preussischen Akademie der Wissenschaften, Philosoph.-hist. Kl. 16. Berlin, 7–68. Philo Judaeus, De aet. mundi: Cohn, L., & S. Ritter (eds. ) 1915. Philonis Alexandrini opera quae supersunt. Vol. 6. Berlin. Polybius, Hist.: Büttner-Wobst, T. (ed.) 1889–1905. Polybii historiae. Leipzig. Seneca, Ep.: Reynolds, L. D. (ed.) 1965. L. Annaei Senecae. Ad Lucilium epistulae morales. Oxford. Simplicius, In Phys. 1–4: Diels, H. 1882. Simplicii in Aristotelis physicorum libros quattuor priores commentaria. Commentaria in Aristotelem Graeca 9. Berlin. Strabo, Geogr.: Radt, S. (ed. ) 2002–2009. Strabons Geographika. 8 vols. Göttingen. Vitruvius, De arch.: Fleury, P. (ed. and transl.) 1990. Vitruve. De l’architecture 1. Paris; Krohn, F. (ed.) 1912. Vitruvii de architectura libri decem. Leipzig; Soubiran, J. (ed. and transl.) 1969. Vitruve. De l’architecture 9. Paris.

Works quoted Barton, T. S. 1994a. Ancient Astrology. London. Barton, T. S. 1994b. Power and Knowledge: Astrology, Physiognomics, and Medicine under the Roman Empire. Ann Arbor, MI. Bowen, A. C. 2001. “La scienza del cielo nel periodo pretolemaico”. In: S. Petruccioli (ed.), Storia della scienza: I. La scienza antica. Rome, 806–839. Bowen, A. C. 2002. “Simplicius and the Early History of Greek Planetary Theory”. In: Perspectives on Science 10.2, 155–167. Bowen, A. C. 2006. “Geminus and the Length of the Month: The Authenticity of Intro. ast. 8.43–45”. In: Journal for the History of Astronomy 37, 193–202. Bowen, A. C. 2007. “The Demarcation of Physical Theory and Astronomy by Geminus and Ptolemy”. In: Perspectives on Science 15, 327–358. Bowen, A. C. 2008a. “P. Hibeh 1.27”. In: P. Keyser & G. Irby-Massie (eds.), The Encyclopedia of Ancient Natural Scientists. London, 615–616. Bowen, A. C. 2008b. “P. Parisinus graecus 1”. In: P. Keyser & G. Irby-Massie (eds.), The Encyclopedia of Ancient Natural Scientists. London, 622. Bowen, A. C. 2008c. “Leptines (II)”. In: P. Keyser & G. Irby-Massie (eds.), The Encyclopedia of Ancient Natural Scientists. London, 505. Bowen, A. C. 2008d. “Cleomedes and the Measurement of the Earth: A Question of Procedures”. In: Centaurus 50, 195–204. Bowen, A. C. 2009a. “From Description to Prediction: An Unexamined Transition in Hellenistic Astronomy”. In: Centaurus 51, 299–304. Bowen, A. C. 2009b. ‘Seneca e la delimitazione degli ambiti di studio di musica e filosofia’. In: D. Castaldo, D. Restani, & C. Tassi (eds.), Il sapere musicale come cultura: da Teofrasto a Plutarco. Ravenna, 11–20. Bowen, A. C., & B. R. Goldstein 1996. “Geminus and the Concept of Mean Motion in Greco-Latin Astronomy”. In: Archive for History of Exact Sciences 50, 157–185. Bowen, A. C., & R. B. Todd 2004. Cleomedes’ Lectures on Astronomy: A Translation of The Heavens. Berkeley. Evans, J., & J. L. Berggren 2006. Geminos’s “Introduction to the Phaenomena”: A Translation and Study of a Hellenistic Survey of Astronomy. Princeton. Falcon, A. 2012. Aristotelianism in the First Century BCE: Xenarchus of Seleucia. Cambridge. Fantham, E. 1996. Roman Literary Culture: From Cicero to Apuleius. Baltimore.

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Fuentes González, P. P. 2005. “Néchepso-Pétosiris”. In: R. Goulet (ed.), Dictionnaire des philosophes antiques. Vol. 4. 601–615. Paris. Granger, F. (transl.) 1931. Vitruvius: On Architecture. 2 vols. Cambridge, MA. Jones, A. (ed.) 1999. Astronomical Papyri from Oxyrhynchus (P. Oxy. 4133–4300a). 2 vols. Philadelphia. Kidd, I. G. (ed. and transl.) 1988–1999. Posidonius. 3 vols. / 4 tomes. Cambridge. (Volume 1 was edited with L. Edelstein). Kühner, R., & B. Gerth. 1890–1904. Kühners ausführliche Grammatik der griechischen Sprache. 2 vols. (each in 2 parts). Hannover. Mastorakou, S. 2007. Hellenistic Popular Astronomy: Aratus’ Phaenomena. PhD Thesis, Imperial College, University of London. Neugebauer, O. 1975. A History of Ancient Mathematical Astronomy. Berlin. Neugebauer, O., & H. B. Van Hoesen (eds.) 1987. Greek Horoscopes. Philadelphia. Pingree, D. E. 2008. “Petosiris, Pseudo-”. In: C. C. Gillipsie, F. L. Holmes, & N. Koertge (eds.), Complete Dictionary of Scientific Bibliography. Vol. 10. 547–549. New York. Rowland, I., T. N. Howe, & M. J. Dewar. 1999. Vitruvius: Ten Books on Architecture. Cambridge. Sacks, K. S. 1990. Diodorus Siculus and the First Century. Princeton. Vitrac, B. 2005. “Les classifications des sciences mathématiques en Grèce ancienne”. In: Archives de philosophie 68, 269–301.

D. Science Writing as/and Literature

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On the Variety of ‘Genres’ of Greek Mathematical Writing: Thinking about Mathematical Texts and Modes of Mathematical Discourse Abstract: Scientists working today have a number of avenues open for the promulgation of their work. While electronic publishing of articles is now standard, new media, including podcasts and press conferences, are also used to publicize scientific research. Greco-Roman authors writing on scientific, mathematical and medical subjects also had a range of choices available to them as they selected the type of text to convey their ideas and information. Their choices included – but were not limited to – poetry, dialogue, lecture, question-and-answer text, letter, biography, recipe, epitome, encyclopedia, handbook, introduction and commentary. The consideration of the authorial choice of genre offers insights into how these writers regarded their own work, for example, in relation to the work of others. Furthermore, by choosing to write in a specific format, authors may have hoped to reach certain audiences; some texts are presumably more appropriate to students, others to specialists, still others to patrons or potential clients. And some types of texts have elements shaped by broader cultural convention rather than by the individual author. Given the range of options available to ancient writers on scientific, mathematical and medical topics, their choices of genre reflect authorial intention, including, for example, a desire to project a particular identity or image and/or to reach a special readership.

0 Introduction Mathematicians and scientists working today have a number of avenues open for the promulgation of their work. While electronic publishing of articles is now standard, new media, including podcasts, are also used to publicize scientific research. These technologies enable the emergence of innovative forms of communication (for example, the ‘sound-bite’), however the existence of a diverse range of options available for presenting scientific and mathematical material is not new. Surviving ancient Greco-Roman scientific, medical and mathematical texts display a surprising variety of forms, or genres, including, but not limited to, poetry, dialogue, lecture, question-and-answer text, letter, biography, recipe, epitome, encyclopedia and commentary. This empirically-derived short list suggests that ancient authors writing on scientific, mathematical and medical subjects had a number of options available to them as they sought to convey their ideas and information. To

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modern readers this is one of the most puzzling aspects of ancient scientific thought: the textual formats utilized for the exposition and dissemination of ideas. Furthermore, this area has not been the subject of much study. In my research I have examined the choice of medium used to convey the message, considering the implications, such as the effect of literary conventions associated with particular genres on the presentation of material by authors and subsequent reception by audiences. Here, I will concentrate on texts associated with mathematics. A particular style of presentation, in a systematic format, is often seen by modern readers as the hallmark of Greek mathematics. As M. R. Cohen and I. E. Drabkin described it on the very first page of their Source Book in Greek Science, the characteristic mathematical text is the ideal “rigorously deductive proof, the method of developing a subject by a chain of theorems based on definitions, axioms, and postulates, and the constant striving for complete generality and abstraction”.1 Yet, upon further examination we see that the ideas and practices of ancient Greek mathematics were presented in a wide variety of types of texts, for the most part in prose formats, but occasionally in poems. Some of these texts were written by mathēmatikoi, men who presented themselves and were recognized by others as ‘mathematicians’. But some of the texts that we would identify as ‘mathematical’ were written by non-specialists.2 There are many issues involved in the identification and description of different textual formats, types or genres, and there are also issues encountered in identifying and describing texts as ‘mathematical’. In both cases, these are larger topics which cannot be dealt with fully, or resolved, here. Nevertheless, it is important to recognize that the categories being invoked are not entirely clear-cut and unproblematic. I will first consider some of the issues involved in the use of the term ‘mathematical’, and then turn to the challenges of defining genres of mathematical (and, more broadly, ‘scientific’) texts. While, increasingly, historians are considering the various forms and authorial intentions reflected in mathematical writings, such writings have not previously been discussed from the point of view of genre. I will consider first the Euclidean Elements, and then turn to a number of types of texts used by ancient authors to communicate about mathematics: the proposition, question-and-answer text, commentary, letter, and poem. While this is not an exhaustive list of the genres used by ancient Greek writers for mathematical discourse, here I can only touch briefly on some others – including pragmateia (‘treatise’), skholion (lecture), eisagōgē (introduction) and bios (life) – simply to give a sense of the range of texts which should be considered.

1 Cohen & Drabkin 1958, 1. 2 See, for example, Cuomo 2001, 73–79 on this point.

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1 The problem with ‘mathematics’ When we look at an ancient Greek text, how do we know if it should be described as mathematics? What does it mean to use the terms ‘mathematics’ and ‘mathematical’ when reading and understanding ancient Greek texts? Is it the subject matter? The language? The vocabulary? The format or structure of the text? A style of argument? Is it through references made to the works of mathematicians? Is it through the use of certain techniques and tools, such as lettered diagrams? Historians of mathematics have not always agreed about the features that define a mathematical text. Several passages in Plato’s dialogues, notably the Meno and the Theaetetus, are regarded as important in the history of mathematics. David Fowler highlighted the significance of certain passages in the dialogues, particularly the Meno (82a-85d), which he regarded as “our first direct, explicit, extended piece of evidence about Greek mathematics”,3 yet the Platonic dialogues are more usually treated primarily as philosophical texts. Some ancient authors – primarily those identified as philosophers – wrote about the classification of different types of knowledge. Aristotle, in the Metaphysics, referred to the different types of knowledge (epistēmē), pointing to mathēmatikē as a distinct type of theoretical knowledge. Elsewhere Aristotle discussed the role of mathematics in its relation to other types of knowledge, including physics. Aristotle considered mathematics to be a type of theoretical knowledge, along with physics and metaphysics; he also outlined a system that classified some types of knowledge – including fields of mathematics, such as astronomy and optics – as subordinate to others.4 Amongst those authors who wrote on such topics, not all agreed as to the classification and relationship of theoretical knowledge; so, for example, Ptolemy (2nd cent. ) did not agree with Aristotle regarding the primacy of metaphysics, instead pointing to mathematics as the premier branch of philosophy.5 In addition to the ancient authors’ classifications of knowledge (epistēmē), there are other distinctions that are evident in works written by, for example, practitioners, teachers and researchers. Pragmatically, such texts convey a sense of the field of endeavour in which they were produced and intended to be read by others. However, boundaries between specialisms of mathematical practice were not always as clear-cut as our modern descriptions of relevant texts and practices suggest. We must be mindful that any systematic and formal classification of knowledge and practice very likely only reflected in a limited way the more informal actors’ categories of ancient authors and practitioners, and consumers (including

3 Fowler 1999, 7. 4 See, for example, Aristotle, Anal. post. 75b14–17; Phys. 194a7–8. See also McKirahan 1978; Lennox 1986. 5 Ptolemy, Alm. I 1. See also Taub 1993, 19–37. See also Sidoli 2004, 5–8.

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readers, patrons, teachers and other users of texts). With our heightened awareness that the meaning of the descriptor ‘mathematical’ may not always be entirely clear, the difficulty of identifying different types or genres of mathematical texts becomes even more apparent.

2 The problem with ‘genre’ Ancient authors did not explicitly problematize their authorial choices as decisions about genre. There are few theoretical discussions of specific literary genres; in fact, Gian Biagio Conte and Glenn Most have noted that there was no theory of genre, as such, in antiquity. Most of the ancient authors are “more interested in classifying existing works than in understanding the mechanisms of literary production and reception and are directed to the needs of the school and the library, not to the [literary] critic’s”.6 Those ancient Greek authors who did write on theoretical or taxonomical issues related to genre were not particularly concerned with prose, used for most scientific and mathematical texts. Poetry, drama and rhetoric were more gripping topics, and prose may have only been discussed under the rubric of rhetoric, encompassing speeches as well as historiography. Therefore, we cannot often turn to ancient discussions of scientific and mathematical texts to help us understand the significance of different forms of communication. When the ancient term for a particular type of text is known, we have an idea of the ‘actors’ categories’ used to describe such formats and texts. Philip van der Eijk has pointed to the range of generic labels given to a number of stylistic formats found within the Hippocratic corpus.7 However, in many cases we don’t have the author’s own label for the text (for example, either a title or a reference to the type of text), yet the form nevertheless seems clear; fortunately, in some cases we can see how ancient readers regarded the form of the text, through their references to it. Modern scholars have sought to define ‘genre’, but the definitions are often hotly debated.8 In 1974 Tzvetan Todorov, in a landmark article on “Literary Genres”, argued that a genre is always part of a system, “a certain horizon of expectation, i.e. a set of pre-existing rules which orient the reader’s understanding and allow him to receive and to appreciate the text”. Furthermore, genres “can only be 6 Conte & Most 1996, 631. 7 Van der Eijk 1997. 8 Today, the term ‘genre’ is increasingly used to classify non-literary and non-written forms of communication, including a type of painting, different types of music, and film, as well as speech acts. See Duff 2000, xiii. The term ‘genre fiction’ is used to refer to modern works of popular fiction that are regarded as highly standardized, for example historical romances, science fiction, and detective stories. Art historians use the term ‘genre painting’ to refer to a type of painting depicting ordinary activities, rather than historical or mythological subjects.

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defined by their mutual relations” within the genre system. Todorov was particularly sensitive to historical issues, and emphasized that a genre must be redefined in each historical period, “in accordance with the other contemporary literary genres”.9 Focusing on ancient Greco-Roman texts, Conte and Most have also considered genre from the readers’ point-of-view, emphasizing that genre is “not only a descriptive grid devised by philological research, but also a system of literary projection inscribed within the texts, serving to communicate certain expectations to readers and to guide their understanding.”10 They define ‘genre’ as referring to “a grouping of texts related within the system of literature by their sharing recognizably functionalized features of form and content”. Here I am largely concerned with written texts; in my treatment of mathematical writings I will use the following, suggested by David Duff, as my working definition of ‘genre’: “a recurring type or category of text, as defined by structural, thematic and/or functional criteria”.11 Following Duff’s suggestions regarding structure, theme and function, and Conte and Most’s emphasis on the functionalized features of form and content, it seems reasonable to begin a consideration of the genres of ancient scientific and mathematical texts by looking at form, content and function to help distinguish between different types of texts, or genres. Having said that, it is worth remembering that literary specialists are themselves often wary of classifying texts. Wai Chee Dimock, in a special journal issue of the Publications of the Modern Language Association of America dedicated to “Remapping Genre”, opened her introduction by asking “What exactly are genres? Are they a classifying system matching the phenomenal world of objects, a sorting principle . . . ? Or are they less than that, a taxonomy that never fully taxonomizes, labels that never quite keep things straight?”. She answered by arguing that no genre “is a closed book, none an exhaustive blueprint. . . . Far from being a neat catalog of what exists and what is to come, genres are a vexed attempt to deal with material that might or might not fit into that catalog. They are empirical rather than logical”.12 Dimock’s cautions regarding tidy categorization are apt; in considering genres of ancient Greek mathematical written texts, I have purposely adopted a non-theoretized methodology, choosing to pursue what may be regarded as a ‘from the ground up’, largely empirical, approach which proceeds from the texts themselves. My treatment begins with a close reading of the text, and I intend description of texts to support my argument. When possible, I aim to be mindful of actors’ categories, as well as the broader contexts in which the texts were produced, circulated and read. Genres reflect expectations, as well as conventions. 9 Todorov 1974, 958. There is a vast and voluminous scholarship on the question of genre, too extensive to be referred to in any comprehensive way here. 10 Conte & Most 1996, 631. See also Conte 1994, 105–128. Depew & Obbink 2000, 1–14, provides a useful overview of some of the issues surrounding genres of Greek and Roman literature. 11 Duff 2000, xiii. 12 Dimock 2007, 1377–1378.

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The categorization of genres is not always clear-cut; some texts also combine features of multiple genres, forming a sort of hybrid text. This evidence of ‘hybrid’ texts suggests that ancient authors and their readers may have had a relatively high tolerance for variation.13 Questions of normativity, regarding the features of a specific genre, are an historical problem, as Todorov suggested. Ancient authors and readers had different expectations than ours, and likely had a different degree of adaptability and flexibility in composing and encountering mathematical texts than do their modern counterparts. The taxonomy I offer has been arrived at by empirical means, attempting to consider, particularly, form and function. But even these distinctions are not always clear-cut: a particular text may have sections which reflect a number of genres. Similarly, as we have seen with Plato’s dialogues, an individual text may have had more than one function, for example a teaching text may have been used to attract students, not simply as a pedagogical tool. Here I concentrate on texts whose content is, broadly speaking, ‘mathematical’; in many cases I am guided by the ancient authors themselves indicating that they are writing about mathematics, or about the work of a particular mathematician.

3 Authorial choices As already noted, ancient Greek authors had a wide range of options in the type of text they used for communicating their ideas and information; some of these were borrowed from existing forms, others they created for themselves. To some extent, textual formats represent choices which reflected authorial intention, but the extent to which the use of a particular format reflects an intentional choice made by an author (or editor) is open to debate, and not always clear to us. Nevertheless, in some instances there are clear indications that the author deliberately exercised choice; for instance, the “Letter to King Ptolemy”, one of the texts discussed in some detail below, incorporates a number of types of text (including the proof and the epigram) into the epistolary format. Some choices made by ancient authors – for example, the decision to write in hexameter verse – could immediately place the text within the broader traditions of epic and didactic poetry.14 In other instances, the relative cultural weight of the decision to employ a particular type of text is not immediately clear to us. For other, less obviously literary, formats, it is not always clear what these choices implied to their authors and intended readers. For example, as Todd Curtis has

13 Netz 2009, 129–136 discusses ‘hybrid’ treatises, from a different perspective. 14 The extent to which authors have a ‘choice’ or make a ‘decision’ to write in, say, hexameter, cannot be addressed here; I do recognize that broader cultural norms and constraints may operate, limiting ‘choice’.

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shown, Galen’s decision to present some of his ideas on the medical study of the pulse in the style of an introductory text, offered to beginning students, involved a complex interplay with his other treatments of the same topic intended for more advanced readers/practitioners.15 A focus on ideas alone occludes other important information conveyed by authors through their adoption of particular voices and genres. Classicists have traditionally made a strong break between literary and non-literary texts. A certain number of important technical and scientific texts have received a great deal of attention as literature, particularly the works of Lucretius, Vergil and Aratus. Furthermore, the rhetoric of scientific and technical texts has been recently addressed within the context of a wider move to explore the centrality of rhetoric to ancient Greco-Roman literature and culture. However, when classicists and historians of science, mathematics and medicine consider such texts, the tendency has been – generally – to ignore the genre of communication, concentrating instead on the content and ideas. There has been little work done to improve our understanding of the dynamics of authorial choice and reader expectations established by a scientific text’s genre. Ancient Greek mathematical texts have often been regarded as being characterized by their impersonal style. Professional scientific writing in the contemporary world generally avoids the use of the first person and adopts an impersonal or depersonalized style. Yet, in antiquity, the creation of a distinctive voice or persona was often central to the process of establishing one’s authority as a scientific or medical author. The question of authorial voice is in some cases key to understanding these texts, even when the author is unidentified or unknown to us. Strategies of self-presentation have been considered by a number of scholars working on technical texts, not only in the ancient period.16 Thorsten Fögen has considered the Elder Pliny’s strategies of self-presentation through which he aims to come across as scholarly and authoritative, in some cases supporting the views of his predecessors, whilst in other instances distancing himself from them.17 In certain mathematical texts, the creation of an impersonal, disembodied voice distinguished those texts. In contrast, as Vivian Nutton has noted, Galen frequently adopts self-referential personal forms, compared with other writers (including Rufus of Ephesus (ca 70–100 ) and Aretaeus of Cappadocia (150–190 ?) who tend to use more neutral language.18 Genre may also be used to target certain audiences; some texts are more appropriate to students, others to specialists, still others to patrons, clients, etc. Remembering that genres were sometimes developed and used for specific areas of or

15 16 17 18

Curtis 2009. See, for example, the contributions in Biagioli & Galison 2003, on scientific authorship. Fögen, in this volume. Nutton 2009, 59.

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approaches to knowledge (for example, the encyclopedia, developed by Pliny the Elder to display a breadth of knowledge),19 my focus here is on formats and genres used to communicate about mathematics, noting that others have written about the diversity of genres of medical writings, for example, in the Hippocratic Corpus itself.20

4 Genres of mathematical writing Using the term ‘mathematical’ as a label might suggest that there is unanimity in understanding this descriptor.21 In some cases, it is not clear whether a text should be labeled as ‘mathematical’, or what, precisely, that label might entail. There is also the danger of applying such terms ahistorically, by suggesting that the modern usages map onto those of ancient authors and practitioners. Modern readers do not always agree as to what characterizes a mathematical text; in fact, ancient authors who wrote about mathematics did not always agree in its definition either. Furthermore, there is no precise agreement as to what distinguishes a mathematical text from one that is not mathematical. (For example, Nathan Sidoli, in his treatment of Ptolemy’s mathematical discourse, “omits passages which may be about mathematics but do not form part of the mathematical argument”; he refers to such material, which may include introductory material such as definitions and first principles, as “discussion”.)22 Reviel Netz has emphasized the use of technical language and lettered diagrams as key features of Greek mathematical texts;23 Sidoli has argued that “the basic elements of Greek mathematical exposition are words, numbers and diagrams”.24 As work by Serafina Cuomo and others has shown us, in this volume and elsewhere, ancient mathematical practices can be seen as a spectrum. The texts associated with these different practices are, likewise, somewhat different in form, with sophisticated treatises such as Archimedes’ Method at one end, and texts such as multiplication tables and account inscriptions at the other.25 Perhaps

19 See, for example, Doody 2010; Murphy 2004. 20 Van der Eijk 1997. 21 I am grateful to Bernard Vitrac for corresponding with me about these issues. 22 Sidoli 2004, 9 restricted his discussion of mathematical prose to include only those portions of texts that “do” math, rather than speak about math. 23 See Netz 1999a, 12–67. 24 Sidoli 2004, 8. 25 See Cuomo, in this volume. Recently, there has been a shift in attention to texts and sources which reflects wider mathematical practices. Questions such as the way in which a history of numeracy may differ from a history of mathematics have been posed. On such questions in the Greek context, see Cuomo 2001; in the Babylonian context, Robson 2009; in the Egyptian, Imhausen 2003.

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unsurprisingly, scholarship has often concentrated on authors at the high end of the spectrum. Markus Asper has suggested that there were two cultures of people engaged in two rather distinctive types of mathematics in Greek antiquity: practitioners, on the one hand, and a more elite group of theoreticians, on the other.26 But there were individuals, notably, for example, Archimedes (third cent. ) and Hero (first cent. ), who crossed whatever boundaries might have existed between these two groups. Cuomo has noted that mathematics was associated “not only with a certain subject-matter (numbers, geometrical figures), but also with a certain style”.27 Aristotle had earlier recognized this, noting that for some styles of argument and presentation audiences have clear expectations: “Some people do not listen to a speaker unless he speaks mathematically, others unless he gives instances, while others expect him to cite a poet as witness”.28 Whether there was a distinct genre of ‘mathematical text’ in antiquity is a question to be considered. Those authors writing about mathematical topics used a variety of formats, including some that look similar to question-and-answer texts; other texts are deliberately cast as letters, in some cases addressed to specific individuals, including patrons.29 To give an idea of the sort of variety that exists, we might include the following as types of texts relevant for ancient Greek mathematics: proposition, letter, problem text, dialogue, poem, commentary, treatise, lecture, introductory text, narrative, and biography. However, this is not intended as a complete list of all genres or formats used for communicating mathematical ideas and methods by ancient Greek authors; others might include the handbook. Certainly, some of those listed have particular relevance for mathematical texts.30 It must be emphasized that these labels cannot be taken to always represent strict divisions between formats, or a hard and fast taxonomy; some dialogues, for example, Plato’s Timaeus, which has sections which are usually regarded as mathematically-informed, reads almost like a monologue, or lecture. Furthermore, some texts may contain elements of a number of genres and there are some overlapping categories. So, for example, some ‘teaching texts’ are written as poems; in considering prose writings, there seem to be various types of texts, but it is sometimes difficult to know how to distinguish them. Even within a particular genre of text, such as the commentary, there may be a number of other genres of writing contained within that larger text. There are some types of texts which are particularly associated with the writings of ancient Greek mathematicians. Many examples of letters written by mathe26 Asper 2009. 27 Cuomo 2001, 32. 28 Aristotle, Metaph. 995a5–7 (1572). 29 On Eratosthenes’ “Letter to King Ptolemy”, see Taub 2008b. 30 Netz 1999b, 282 has noted that there has not been a great deal of interest in stylistic features of ancient Greek mathematics, with a preference generally for concentrating on contents and logical forms.

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maticians, including Archimedes, survive; sometimes these serve as an introduction to a mathematical text which is itself presented in a different format (such as a proposition). Introductions, even those in the form of a letter, have been regarded as somewhat ancillary to the main text; the literary theorist Gérard Genette described introductions (and other ‘boundary’ objects used in published work) as “paratexts”. He did, however, recognize that paratexts convey important messages, and even serve to mediate and shape the reading of the main text; they may well adhere to certain conventions (for example, of address) and rhetorical forms. Genette was concerned with modern printed works, but the concept of “paratext” has also been applied, by Asper, to the letter-as-introduction used by ancient Greek mathematicians.31 As an example of such a paratext and text, Archimedes begins a letter to Dositheus: “Greetings. Earlier, I have sent you some of what we had already investigated then, writing it with a proof”. This serves as an introduction to the text On the Sphere and the Cylinder, most of which is presented in the form of propositions and proofs.32

5 The archetypal mathematical text: The Elements For many readers, the term ‘mathematics’ brings to mind a distinctive type of text, one that exhibits a particular linguistic style and form of presentation. Many ancient Greek mathematical texts have their own character, which will be familiar particularly to students of geometry. So, for example, as has already been noted, the use of technical, formulaic language and lettered diagrams are sometimes regarded as key features of Greek mathematical texts. The Elements of Euclid, which relies on such features in abundance, often serves as the archetypal ancient Greek mathematical text. Historically, the Elements has loomed large, and shaped expectations of what mathematical texts, and indeed, particularly in later periods, what scientific texts should look like. (Interest in the formal qualities of mathematical texts is still important to mathematicians today; with this in mind, in October 2004 the Royal Society held a special two-day discussion in London about mathematical proof.33) It is almost a truism that many of the ‘high-end’ mathematical texts, such as the Elements, are associated with what may be regarded as the distinctive voice of a particular author, a particular individual, such as Archimedes or Ptolemy.34 Having said that, the Elements is now thought to be the work of compilation, rather

31 Asper 2009, 118; see also Genette 1997, 1–15 et passim. 32 See Netz 2004, 31, et passim. 33 Netz (in this volume) explores the idea of genre in mathematical texts from a different perspective, i.e., that of authorial presence. 34 See Netz 2002 and 2009 on Archimedes’ style.

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than that of a single author; how that might be reflected in ‘authorial’ voice is a not entirely clear.35 Historians of mathematics believe that the Elements was, in part, synthesized and systematically presented by Euclid in ca 300 ; the thirteen ‘books’ cover a variety of topics in a range of mathematical and literary styles.36 David Fowler has emphasized that Euclid should be understood as “the compiler, not the author, of the work: he is believed to have taken source works by other mathematicians and edited them, adapting and rearranging the material, perhaps even inserting new material of his own, to make the complete treatises”.37 While the style of presentation within the Elements is not completely uniform, a particular format is characteristic: that of the proposition and proof. Sidoli has described the proposition as the “basic unit of mathematical prose”.38 In addition to multiple examples of propositions (and proofs or solutions), the Elements has certain other important features, in particular the statement at the very beginning of the text, of what may be regarded as ‘the essential preliminary matter’, classified under the headings Definitions (horoi), Postulates (aitēmata) and Common Notions (koinai ennoiai).39 The format of the proposition is often seen as not only characteristic of but, indeed, definitive of mathematical discourse.

6 Proposition Modern terminology to describe and distinguish various elements of formal mathematical texts is not universally agreed; we have evidence too that in antiquity

35 Diogenes Laertius and Pliny the Elder are also sometimes described as ‘compilers’; they each make reference to their numerous sources. 36 Books 1–4 are concerned with plane geometry, book 5 treats the theory of proportions, and book 6 deals with the similarity of plane figures. Books 7–9 are concerned with number theory, book 10 with commensurability and incommensurability, books 11–12 treat three-dimensional geometric objects, and book 13 the construction of the five regular solids. Later non-Euclidian additions include book 14, which may be due to Hypsicles of Alexandria (ca 200 ), and book 15, which may be at least partly the work of a sixth-century pupil of Isidorus of Miletus. See also Mueller 2008. On the history of early modern editions and translations of the texts, see the Brown University Library online exhibition From Euclid to Newton: An Exhibition in Honor of the 1999 Conference of the Mathematical Association of America. 37 Fowler 1999, 205. On Euclid’s work as a compiler and editor, see Knorr 1975, 303–312. On the editions of Euclid, including the recension by Theon of Alexandria, see Heath 1921a, 360 f. Cf. to Eutocius’ role as a commentator on and compiler of an anthology of solutions to the Delian problem, Heath 1921b, 540 f. 38 Sidoli 2004, 8. 39 Not all of the definitions are used in the Elements; Heath believed that some may have been included out of a respect for tradition. Certainly, the influence of Aristotle, and possibly Plato too, is evident in the setting out of the preliminary terminology. Heath 1921a, 373. As noted above, Sidoli regards definitions, etc., as non-mathematical “discussion”. Sidoli 2004, 9.

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there was felt the need to discuss difficulties encountered in the naming of parts of such texts. A mathematical proposition is a formal statement of a theorem (which is to be demonstrated) or a problem (which is to be solved).40 In his Commentary on Euclid’s Elements, Proclus (412–485 ) discusses the distinctions made by different authorities between theorems and problems, making it clear that not every author used these terms in the same way.41 The terminology of propositions was considered important enough that several ancient authors wrote extensively on the subject.42 Pappus, a fourth-century mathematical author, also discussed these terms, in the preface to book 3 of his Mathematical Collection, but it is not entirely clear when particular items of terminology were first adopted.43 Other technical terms, such as “lemma” (something assumed), “porism” (some result incidentally revealed in the course of the demonstration of the main proposition under discussion), “analysis” and “synthesis” are also discussed by Proclus (In Eucl. 211–213; 255–266); Pappus discusses analysis and synthesis in the Mathematical Collection, book 7.44 The structure and varieties of propositions, as well as their relationship to mathematics more generally, have been the subject of study since antiquity, as well as the technical terminology used in mathematical texts. The crucial form of presentation within the Elements is the proposition. Keeping in mind the definition of ‘genre’, as a recurring type or category of text, as defined by structural, thematic and/or functional criteria, ancient authors, such as Proclus and Pappus, as well as modern scholars, including Heath (in his work on Archimedes and Apollonius, as well as on Euclid) and Netz, have addressed the characteristics of the proposition in a way which suggests that it might be regarded as a genre in itself.45 Technical terminology was clearly a subject of discussion itself in antiquity. As part of his rather lengthy discussion of the first proposition, Proclus briefly lists and explains the formal divisions, and their functions, contained therein:46 40 Cf. Sidoli 2004, 8. 41 Proclus, In Eucl. 77.7–81.2. See also Mueller 1981, 11; Knorr 1986, 348–360; Netz 1999b, 288; Sidoli 2004, 8–9. 42 Cf. Heath 1921b, 533f. 43 See Netz 1999b on this latter point. 44 Cf. Heath 1921b, 533. On definitions of lemma, porism, etc., see Heath 1921a, 372 f. All references to Proclus are to the Friedlein edition of the commentary of the first book of Euclid, unless otherwise noted. For a translation of the passage from Pappus (book 7) on the Definition of Analysis and Synthesis, see Heath 1921b, 400f. On Pappus, see Jones 1986, particularly 1–3, 66–74; Cuomo 2000. 45 Heath included separate sections on terminology in his translations of Archimedes (1912, clv– clxxxvi) and Apollonius (1896, clvii–clxx). In his translation of Euclid, Heath (1925/1956) included sections dealing with terminology in his first chapter, treating “Theorems and Problems”, “The Formal Divisions of a Proposition”, and “Other Technical Terms”. See also Netz 1999b. 46 Proclus, In Eucl. 203.1–15, Morrow transl. 1970/1992, 159, which I have adopted, with a few emendations; the fuller discussion of the parts of the proposition occupies 203.1–210.6. Proclus’

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The enunciation (protasis) “states what is given and what is being sought from it, for a perfect enunciation consists of both these parts”. The claim of the proposition is stated in general terms; the protasis is equivalent to a conditional statement that if x, then y.47 The specification (or setting-out; ekthesis) “takes separately what is given and prepares it in advance for use in the investigation”. As Heath notes, the ekthesis “states the particular data”, for example, “a given straight line AB, two given triangles ABC, DEF, and the like, generally shown in a figure and constituting that upon which the proposition is to operate”.48 The definition or specification (diorismos) takes “the thing that is sought and makes clear precisely what it is”. It restates what is required to be done or to prove in terms of the particular data already stated; a statement of the conditions of possibility may also be contained in the diorismos.49 The construction (kataskeuē) “adds what is lacking in the given for finding what is sought”, including any additions to a figure by way of construction that are necessary to enable the proof to proceed. The proof (apodeixis) itself “draws the proposed inference by reasoning knowledgeably (or, in a manner capable of knowledge, or scientifically, epistēmonikōs) from the propositions that have been admitted”, to prove the particular claim.50 The conclusion (sumperasma) “reverts to the enunciation, confirming what has been proved” or accomplished. As Heath points out, “the conclusion can . . . be stated in as general terms as the enunciation, since it does not depend on the particular figure drawn; that figure is only an illustration, a type of the class of figure, and it is legitimate therefore, in stating the conclusion, to pass from the particular to the general”.51

The first proposition presented in the Elements serves as an example, for Proclus himself takes his audience through it in detail, examining the formal structure: “Let us view the things that have been said by applying them to this our first problem. Clearly it is a problem, for it bids us devise a way of constructing an equilateral triangle”.52 formal division of the proposition is discussed by Heath 1921a, 370 f., Heath 1925/1956, 129–131, and Netz 1999b. 47 Netz 2004, 6; Netz 1999b. There is no reference to a diagram in the enunciation. 48 Heath 1921a, 370; cf. Netz 2004, 6. 49 Netz 2004, 6, regards the diorismos as an “exhortation by the author to himself”. Cf. Heath 1921a, 371. See also Thomas 1939, 394–397 and his discussion of the diorismos in the Meno, and Knorr 1986, 73–74. 50 Proclus, In Eucl. 203.12–13: ἡ δὲ ἀπόδειξις ἐπιστημονικῶς ἀπὸ τῶν ὁμολογηθέντων συνάγει τὸ προκείμενον. 51 Heath 1921a, 370. 52 Proclus, In Eucl. 208–210, Morrow 1970/1992, 162–164. Netz 1999b, 284 noted that it is not the ideal example.

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Its format is explicated by Proclus as follows (I have placed the corresponding passage from the Elements in brackets following):53 – The protasis (enunciation, which in this case he explains consists of both “what is given and what is being sought”): “If there is a finite straight line, it is possible to construct an equilateral triangle on it”. (On a given finite straight line to construct an equilateral triangle.) – The ekthesis (the exposition, or setting-out): “Let this be the given finite straight line”. (Let AB be the given finite straight line.) – The diorismos (definition or specification): “It is required to construct an equilateral triangle on the designated finite straight line”. (Thus it is required to construct an equilateral triangle on the straight line AB.) – The construction (kataskeuē), which includes any additions to the original figure by way of construction that are necessary to enable the proof to proceed: “Let a circle be described with center at one extremity of the line and the remainder of the line as distance; again let a circle be described with the other extremity as centre and the same distance as before; and then from the point of intersection of the circles let straight lines be joined to the two extremities of the given straight line”.54 (With centre A and distance AB let the circle BCD be described; again, with centre B and distance BA let the circle ACE be described; and from the point C, in which the circles cut one another, to the points A,B let the straight lines CA, CB be joined.) – Next comes the proof itself, in which the particular claim is proven: “Since one of the two points on the given straight line is the center of the circle enclosing it, the line drawn to the point of intersection is equal to the given straight line. For the same reason, since the other point on the given straight line is itself the center of the circle enclosing it, the line drawn from it to the point of intersection is equal to the given straight line . . . Each of these lines is therefore equal to the same line; and things equal to the same thing are equal to each other . . . The three lines therefore are equal, and an equilateral triangle [ABC] has been constructed on this given straight line”. (The elisions here represent the omission of Proclus’ comments on the proof.) (Now, since the point A is the center of the circle CDB, AC is equal to AB. Again, since the point B is the center of the circle CAE, BC is equal to BA. But CA was also proved equal to AB; therefore each of the straight lines CA, CB is equal to AB. And things which are equal to the same thing are also equal to one another; therefore CA is also equal to CB. There the three straight lines CA, AB, BC are equal to one another. Therefore the triangle ABC is equilateral; and it has been constructed on the given finite straight line AB.) 53 Euclid, Elem., transl. Heath (1925/1956), I 241–242. 54 Friedlein presents the text in a corrupt state; Morrow’s transl. follows Francisco Barocius’ 1560 text here (Procli Diadochi Lycii in Primum Euclidis Elementorum Commentariorum Libri IV a Francisco Barocio Patritio Veneto Editi, Padua, 1560).

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Proclus then states the general conclusion, the sumperasma: “An equilateral triangle has therefore been constructed upon the given straight line”. In the Elements, there is no formal conclusion (sumperasma) for the first proposition, restating in general terms what was to be proved or done, but simply an assertion that what was required to be done was accomplished: “[Being] what it was required to do”. Proclus notes that Euclid adds: “This is what it was required to do”, thus showing that this is the conclusion of a problem; Proclus explains that in the case of a theorem, Euclid states: “This is what was to be demonstrated” (the equivalent of our Q.E.D.).55

In actual fact, according to Proclus, not all propositions have all of the formal divisions listed above, even though the enunciation, proof and conclusion are (once again, according to Proclus) always found.56 So in many propositions no construction is needed, as the figure given is itself sufficient for the proof; Proclus noted that in the problem “to construct an isosceles triangle with each of the base angles double the other angle” there is neither a setting-out nor a definition.57 (In addition to the lack of uniformity with regard to the form of propositions within the Elements, and subsequent mathematical texts, there are also different styles of proof; while this is important from the standpoint of the mathematical argument being made, it is perhaps less important in defining a genre.58) It is clear even from Proclus’ Commentary on the Elements that the formal character of the geometrical proposition was an object of study in itself; certain formal features could be considered as characteristic, and expected, serving specific functions.59 Other writers also concerned themselves with explaining features of mathematical texts. As was mentioned earlier, the fourth-century  mathematical author and commentator, Pappus of Alexandria, is credited with a Mathematical Collection in eight books, in Gerald Toomer’s view a compilation probably made after his death of originally separate works on different mathematical topics; not all of the Collection survives.60 As was Proclus, it is clear from Pappus’ discussion at a number of places in this work that he was concerned with the form of mathematical texts; so, for example, in the preface to book 3, he discussed the character 55 Proclus, In Eucl. 210, Morrow 1970/1992, 164. 56 Proclus, In Eucl. 203, Morrow 1970/1992, 159. See also Heath 1921a, 371. 57 This problem is found in Elements IV 10; cf. Proclus, In Eucl. 204, Morrow 1970/1992, 159; Cf. Heath 1921a, 371. 58 For example, on the proof by analysis, see Heath 1921a, 371 f. Heath 1925/1956, 136–137 discusses the use terms by Aristotle, Pappus and Proclus. The Elements has many examples of reductio ad absurdum; the first being in book 1, Proposition 6. See Heath 1925/1956, 255–256. 59 Netz (1999b) has argued that Proclus has developed his own terminology and exegesis in his Commentary; from my standpoint, whether or not the terminology and breakdown of the proposition pre-date Proclus is immaterial to my argument. 60 Toomer 1996b, 1109.

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of problems and theorems.61 Proclus himself had provided information about the (in some cases, contrasting) views of some of his predecessors, including Carpus and Geminus.62 While the formal structures of the proposition were adopted by other mathematical authors – including Archimedes in various of his writings, Apollonius (in the Conics), and Eratosthenes, in his report of the duplication of the cube – in some cases they deviated from the exact, idealized, format of the proposition as described by Proclus. (It is important to recognize that the invention of this schematic format for the proposition may have been due to Proclus himself.) While, to some extent, the Elements served as an exemplar text, as Netz has noted, Archimedes “had many variations on the Euclidean structure. General conclusions are avoided, and construction, setting-out, and proof are often intermingled”.63 Within the expected formal structure of the geometrical proposition, there was a degree of variability, even license, as to what specific features might or might not be included by individual authors and editors. The proposition can be considered to be a genre of mathematical text, but it is not only used in mathematical texts; logical texts also employ propositions and proofs, though the specific characteristics of these vary. Generality is one of the key features of the geometrical proposition, a feature also shared with logical propositions, as Aristotle explained in the Prior Analytics.64 Further, the proof is not a format confined to mathematics; indeed, the question of the relationship between logical and geometrical proofs has been investigated by historians, and there is a considerable literature on this topic.65 Aristotle discussed the structure of geometrical proofs in his Prior Analytics I 24.66 The ambition to provide a generalized explanation in the form of a proposition and proof is emphasized by the choice made by many Greek authors to communicate via a text employing general terms; this characteristic generality helps to explain why this type of text – the proposition and proof – has been regarded by some as the ideal format for mathematical and scientific explanation. However, Greek mathematics does not require (in a logical sense) this explicit generality; Euclid without protaseis and conclusions would still be mathematics.67 61 In addition to his interest in mathematical texts, Pappus was also concerned with questions relating to the practice of mathematics more generally. For example, Pappus (Coll. V, preface 1–3) contrasts the mathematical “practice” of bees to the mathematics accomplished by humans; see also Cuomo 2000, 57–90. 62 Proclus, In Eucl. 241–244 (Morrow 1970/1992, 188–191). See also Knorr 1986, 348–360. 63 Netz 2004, 120. 64 Aristotle, Anal. pr. 41b6–26. 65 See, for example, Frede 1974; Mueller 1981, 11–15. See also, e.g., Smith 1989, 111–112; Fowler 1999, 388–390. 66 See also Smith 1989, 144. 67 I thank Ian Mueller for this suggestion (personal communication); it might even be argued that Euclid would be clearer without protaseis and conclusions.

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7 Question-and-answer (problem) texts The focus of attention on a proposition to be demonstrated (if a theorem) or solved (as a problem) is a feature shared by many texts concerned with mathematics.68 As was hinted above, the terminology used was not always precisely delineated, and we find problems (problēmata) presented in a number of types of texts, in some cases, with solutions, in others not. Recalling Fowler’s suggestion that the Meno may represent “our first direct, explicit, extended piece of evidence about Greek mathematics”,69 the genre of dialogue, particularly in the form of the Socratic model devised by Plato, can be understood more generally as being extremely well suited to the presentation of problems. However, very few of the ‘problems’ presented in the Socratic dialogues are concerned with mathematics; rather, Plato was concerned with philosophical issues. Plutarch, one of the few ancient authors to compose a dialogue concerned with scientific issues, also presented some mathematics in his dialogue On the face on the moon. But of all the interlocutors named in the dialogue, it is only the one described as a mathematician, Theon, who never himself speaks; Plutarch presents the mathematician as a silent participant in the discussion of the problems posed.70 Aristotle, while he was at Plato’s Academy, is understood to have compiled notes on various “difficulties” that intrigued him; this collection of problems was available to members of his own school, the Lyceum.71 Over time, a number of Peripatetic philosophers added to the collection. While the text known as the Problems in the Aristotelian corpus has the stamp of his school, the work was apparently compiled over a period of time and may not have reached its present form before the fifth century ; in other words, it may not be the work of one individual, but many.72 Other authors and/or compilers also produced collections of ‘problems’ as texts; some problēmata texts deal with nature, some with literature. Question-and-

68 Knorr 1986, 349 has pointed out that “from the purely formal viewpoint the distinction between problems and theorems is largely artificial. One can easily recast any problem as a theorem, merely by incorporating into the protasis of the theorem all the details of the construction of the problem”. 69 Fowler 1999, 7. 70 The intriguing nature of Theon’s silence cannot be addressed here. But, see Netz (in this volume) on the silence of mathematicians. 71 Louis 1991, xxiii–xxxv; cf. Inwood 1992. The compiling of a collection of difficulties and problems resonates with other aspects of Aristotle’s activities, including the forming of a collection of constitutions, as well as his suggestions for taking reading notes and making lists of opinions. 72 Scholars tend to agree that the author of the so-called Pseudo-Aristotelian Problems (Problēmata) is not Aristotle, although Aristotle is known to have written a book of problems. Some of the material included in the Pseudo-Aristotelian Problems seems actually to have its source in the work of Aristotle; several ancient authors (including Plutarch and Cicero) described portions of the Problems as Aristotelian. See Hett 1936, vii. Cf. also Louis 1991.

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answer texts follow a basic pattern in which a question is posed and an answer is provided. The answers may range from rather brief (a few lines) to somewhat lengthy (the equivalent of several pages). Questions are not necessarily related to one another, although in some cases questions on similar topics are grouped together.73 There is an argument for suggesting that certain logical and mathematical texts (particularly propositions) can be understood as related to these problēmata or question-and-answer texts; in certain geometrical texts, for example Euclid’s Elements, problems are presented and solved; Hellmut Flashar has noted that geometrical problems imply a task to be completed.74 The pseudo-Aristotelian Problems is composed of thirty-eight books, covering a wide range of subjects, from problems connected with medicine (book 1) to problems concerned with mathematical theory (book 15), and questions about shrubs and plants (book 20).75 The following (question 10) is an example of the sort of ‘problem’ presented in book 15, as one of the questions concerning mathematics:76 Why are the shadows thrown by the moon longer than those thrown by the sun, though both are thrown by the same perpendicular object? Is it because the sun is higher than the moon, and so the ray from the higher point must fall within that from the lower point? Let AD be the gnomon, B the moon, and C the sun. The ray from the moon is BF, so that the shadow will be DF; but the ray from the sun is CE, and its shadow therefore will necessarily be less, viz. DE.77

Here, a question arising from observation – the length of shadows – is answered by means of a geometrical demonstration. However, it is not clear that this problem is about mathematical theory; rather, the question concerns the shadows cast by the sun and moon. Here, a geometrical demonstration is used to present an argument about phenomena. Another problem text, the pseudo-Aristotelian Mechanical Problems (or Mechanica) is thought to be the earliest surviving text on the mechanics, and

73 Hine 1981, 27–29. See also Cherniss 1976/2000, 2–5, in which he discusses the zētēmata literature, which posed questions concerned with the meaning of a passage in a text (traditionally in Homer, but also applied to other texts as well). Collections of questions focusing on nature include the pseudo-Aristotelian Problems and Plutarch’s Natural Questions. 74 Flashar 1975, 298. 75 On the Problems see Flashar 1975 and Sharples 2006, as well as the other articles in de Leemans & Goyens 2006. 76 One of the reasons I chose this question as an example is because it refers to another piece of writing – in this case a drawing or diagram. I have decided against providing a diagram here as, to my knowledge, no ancient version survives. While the text suggests that it was accompanied by a diagram, it may have been left for readers or students to construct themselves. However, there are similar references to such visual aids in works by Aristotle, for example the Meteorology; such diagrams may have been included in a text, or displayed to an audience during a lecture. Taub 2003, 103–115; Netz 1999a, 37. See also Sider 2005, 15–19 on diagrams in ancient texts. 77 Ps.-Aristotle, Probl. 912b4–10, transl. Forster in Barnes’ ed., 2.1419, question 10.

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includes thirty-five problems. Like the pseudo-Aristotelian Problems, the problems posed in the Mechanical Problems (MP) are presented as questions to which answers are (usually) given; for the most part, a geometrical proof is offered. Sylvia Berryman describes the MP as a “treatise”; W.S. Hett has suggested that the Problems originally may have been a series of lecture notebooks organized by subject area, to which new problems and answers were continually being added.78 The problems contained in the MP may have also had a pedagogical function. Certainly, the posing of problems for solution was a well-tried didactic technique.

8 Commentary Proclus presented his ideas on the Elements in a commentary, signaling the canonical status of the work. Proclus’ commentary may have been based on lectures. As Thomas Heath noted, Proclus refers to “hearers”,79 and there is evidence that other commentaries were read out to students by teachers.80 Proclus does indicate that he intends his audience to be students.81 This is particularly interesting, because some modern authors have described the Elements as a ‘textbook’.82 As part of the developing literary culture of the ‘book’, the didactic and scholarly traditions produced a variety of handbooks, epitomes, and commentaries; the works of Aristotle and mathematical texts (such as Nicomachus of Gerasa’s) were often the topic of such treatments. Detailed scholarly exegesis of the Homeric poems was underway by the third century , and eventually philosophical and mathematical texts (as well as medical works) were also the focus of some very careful attention. While commentaries on various types of texts were important from the third century , the commentary was a particularly significant genre for scientific and mathematical writing in the later period. Theon of Alexandria (fl. 364 ), apparently working with several collaborators, including his daughter Hypatia (d. 415 ), prepared commentaries on a number of works, including Ptolemy’s Almagest.83

78 Berryman 2009, 106; Hett 1936, viii; see also Coxhead 2012. 79 Proclus, In Eucl. 210.19, cf. 375.9; Heath 1921b, 532. However, because the vocabulary for ‘listening to’ and being a ‘student’, ‘disciple’, or ‘follower’ is related, it is not clear whether or not Proclus meant ‘hearers’ or, more generally, ‘students’; see Taub 2008a, 14. 80 See Taub 2008a, 29. 81 See, for example, Proclus, In Eucl. 81–84; 210. See also Morrow 1970/1992, xxiv. 82 For example, Boyer 1968, 111. 83 Bernard 2008a, 423 f. Bernard 2008b, 793–795, includes a review of the attributions of commentaries and editions to Hypatia and Theon. Bernard 2008b, 794 (citing Theon’s commentary on the Almagest 319.6–10, Rome edition) notes that Theon saw his own “interpretative stance [as a commentator] as the continuation of Ptolemy’s own work as a commentator of the ancients, and urged the most able of his companions to go the same way”.

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Typically, a passage from the ancient source is quoted, and then a comment appended, which may be of any length, from one sentence to the equivalent of a number of pages. Additionally, the commentator may refer to other works, by the author of the target text, or other writers. Some of the commentators offer insights into issues concerning the understanding of the nature of mathematics and the work of mathematicians, issues alluded to at the beginning of the discussion here. In his commentary on Aristotle’s Physics (193b23), Simplicius (sixth century ) comments on the following passage (only briefly quoted here): “We must next consider in what way the mathematician differs from the physicist”. Simplicius notes that Aristotle “quite justifiably wants to show the difference between the physicists and the mathematicians, since they appear to concern themselves with the same subjects”.84 Even as commentaries encouraged a close engagement with particular texts, they often served as vehicles for the presentation of the commentator’s own ideas. This is the case in Proclus’ Commentary on the Elements, in which, as head of the school of philosophy of Athens, the ‘Academy’,85 he is concerned to a great extent with philosophical issues. Commentaries often functioned within teaching contexts, in which lectures and discussion took place; in his biography of his teacher Plotinus, Porphyry reports that “in our gatherings he would have the commentaries read out to him”.86 With his students in mind,87 Proclus saw part of his task as being to explicate the text of the Elements; to some extent, his treatment coincides with what we might expect from a literary or textual critic; his commentary may itself be a compilation.88 In addition to considering the structures of the proposition (as detailed above), Proclus considers Euclid’s mathematical writings, and his work specifically in composing the Elements.89 Ian Mueller, in a 1992 foreword to Morrow’s translation of Proclus’ commentary, helpfully contextualized Proclus’ work as a Neoplatonist, as a teacher of philosophy and as a philosopher interpreting a mathematical text.90 Netz, in a 1999 84 Simplicius, In Arist. Phys. II 290.1–5 (Fleet 1997, 45), slightly amended. Instead of ‘physicist’, Fleet translates “natural scientist”, Hardie & Gaye in their translation of Aristotle’s Physics, 193b23, use the phrase “student of nature”. In the passage quoted, Simplicius discusses the passage at length, making references to both Aristotle’s On the Heavens and Plato’s Timaeus. 85 But as Mueller 1992, x–xi, notes, not the Academy of Plato. 86 Quoted by Grafton & Williams 2006, 34, citing Porphyry, Vita Plot. 14.10–14; see also Sluiter 2000, 191, on commentaries and oral teaching. On commentaries more generally see Most 1999 and Gibson & Kraus 2002. 87 Mueller 1992, ix and xxx–xxxi. 88 Heath 1921b, 534. 89 Proclus, In Eucl. 68–70. 90 Mueller 1992. But it is important to remember that many of the authors considered here were not, and should not be, considered to be simply ‘mathematicians’ or ‘philosophers’. Although they may have had primary areas of interest in mathematics or philosophy, they often had views on a range of intellectual areas; See, for example, Tybjerg 2005 on Hero’s philosophical views. Differences in the classification of knowledge (discussed briefly above) are also relevant here.

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study of Proclus’ description of the proposition, suggested that Proclus had himself devised the scheme and (possibly) the terminology to describe Euclidean propositions, and that he had done so as part of his project to produce a commentary on the Elements;91 he has suggested that even if it was not devised by Proclus himself, it was probably not done by a mathematician, but by a philosopher producing a commentary on Euclid, and developing his own terminology (based to some extent on terms used by earlier philosophers).92 Netz points out that “the scheme serves as the springboard for an extensive discussion of the philosophy of mathematics, in the commentary to the first proposition of the Elements”, suggesting that “for Proclus himself, the scheme functions as a way of identifying the philosophical issues arising from mathematics”.93 Proclus composed his commentary within the context of his Neoplatonist Academy, as part of his teaching program. As a teacher of philosophy, Proclus used philosophical terminology and approaches to illuminate his reading of the Elements; Netz has argued that the scheme described by Proclus is particularly illuminating from a philosophical, rather than a mathematical perspective. In fact, some readers of Proclus’ Commentary have regarded it primarily as a work of philosophy, even though the target text of his commentary was the most canonical of Greek mathematical works.94

9 Letter (Greek ἐπιστολή, epistolē) Letters were important for communication generally in the Greco-Roman world and, as a genre, have particular import for certain communities (for example, the early Christians). Ancient Greek mathematicians also communicated via letters, and a number survive (although the genuineness of some has been questioned). Eratosthenes lived in Alexandria, where he was Librarian and royal tutor to Ptolemy’s son Philopator, and was the recipient of letters from Archimedes, living in Syracuse. Archimedes corresponded with a number of individuals interested in mathematics; he apparently often sent out enunciations without proofs, that is, puzzles in advance of the works themselves.95 A very rich and, from the standpoint of genres, intriguing text is the Letter to Ptolemy III (Euergetes), attributed to Eratosthenes (ca 285–194 ) and preserved

91 Netz 1999b, 302. 92 Netz 1999b, 302–303. 93 Netz 1999b, 302–303. 94 See, for example, Mueller 1992. 95 Netz 2004, 13. Interestingly, the Oxford English Dictionary lists as the first (but now obsolete) definition of “proposition”: “Something proposed for discussion or solution; a problem, a riddle; a parable”.

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in Eutocius’ (480–540 ) Commentary on Archimedes’ Sphere and Cylinder.96 Here, within a commentary, we find a letter, which contains a proof, as well as poetry (a quotation near the beginning of the text and also an epigram, ascribed to Eratosthenes, which closes it). The geometrical proof in this letter has the same basic format as we might expect, with some variation. The author described two different methods of finding mean proportionals, one by geometrical demonstration, the other using an instrument whose construction he describes. The author then goes on to explain that both the geometrical demonstration and the instrumental solution have been placed on a votive monument, as an offering from Eratosthenes of Cyrene, together with an epigram, extolling his solutions to the problem.97

10 Poem Poetry was among the genres in which mathematical problems were presented. In the Letter to Ptolemy, mentioned above, the author first offers the problem to be solved by quoting an unnamed tragedian: μικρόν γ’ ἔλεξας βασιλικοῦ σηκὸν τάφου διπλάσιος ἔστω, τοῦ καλοῦ δὲ μὴ σφαλεὶς δίπλαζ’ ἕκαστον κῶλον ἐν τάχει τάφου. You have mentioned a small precinct of the royal tomb; Let it be double, and, not losing this beauty, Quickly double each side of the tomb.98

The letter is also concluded or signed with a poem, an epigram, which serves as a poetic seal or sphragis. The solution to the problem is presented, and celebrated

96 For the text of the Letter, see Eratosthenes, “Letter to King Ptolemy”, in: Eutocius, ed. J. L. Heiberg Archimedis Opera (2nd ed., 1915) 3.88–96; see also the translation by I. E. Drabkin (1948) in A Source Book in Greek Science, eds. M. R. Cohen & I. E. Drabkin (New York) 62–66; portions of the Letter are edited and translated by Ivor Thomas (1939) in Selections Illustrating the History of Greek Mathematical Works (Cambridge, MA) 1.257–261 and 291–297, but the text from Eutocius is not completely reproduced there. Wilamowitz 1894/1971 thought that the letter was a forgery, but Thomas 1939, 256, note a, suggested that “there is no reason to doubt the story it relates”. 97 I have discussed this letter in detail in Taub 2008a. Historians generally agree that the quotation which purports to be from the monument is genuinely the work of Eratosthenes. 98 Transl. Netz 2002, 214, slightly amended (Eutocius 88. 8–10, ed. Heiberg = 64. 10–12, ed. Mugler). Wilamowitz 1894/1971, 53–54, argued that these lines could not be from any play by the great Athenian tragedians, and must have been the product of a minor poet; cf. Thomas 1939, 258, note a. The fragment is Trag. Graec. Frag. 2.166.

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in the epigram,99 which even those who doubt the authenticity of the entire text attribute with confidence to Eratosthenes, because of its elegance and beauty: If you plan, of a small cube, its double to fashion, Or—good sir—any solid to change to another In nature: it’s yours. You can measure, as well: Be it byre, or corn-pit, or the space of a deep, Hollow well. As they run to converge, in between The two rulers—seize the means by their boundary-ends. Do not seek the impractical works of Archytas’ Cylinders; nor the three conic-cutting Menaechmics; And not even that shape which is curved in the lines That Divine Eudoxus constructed. By these tablets, indeed, you may easily fashion— With a small base to start with—even thousands of means. O Ptolemy, happy! Father, as youthful as son: You have bestowed all that is dear to the Muses And to kings. In the future—O Zeus!—may you give him, From your hand, this, as well: a sceptre. May it all come to pass. And may he, who looks, say: “Eratosthenes, of Cyrene, set up this dedication.”100

The quotation from the tragic poet and the epigram confer a degree of literary interest and distinction on the Letter, while presenting a story-problem and its solution, which is worked out in detail in the central portion of the text. Erastothenes’ nickname in antiquity was ‘Beta’, acknowledging his accomplishments in a number of fields, while suggesting that he was not the highest achiever in any. However, a mathematician of the greatest renown in antiquity, Archimedes, also chose poetry as a way to present a mathematical problem. His Cattle Problem was offered as a poem. The text of the Cattle Problem was discovered and edited in 1773 by G. E. Lessing, who, as Eratosthenes had been, was employed as a librarian; while his predecessor had been in Alexandria, Lessing was at the Herzog August Library in Wolfenbüttel. The text opens in the following way: “A Problem [problēma] which Archimedes devised in epigrams, and which he communicated to students of such matters at Alexandria in a letter to Eratosthenes of Cyrene”.101 (This is not the only letter 99 Within the Letter as a whole, it is made clear that the solution exists in a number of different formats, including the written proof, as well as the instrument which is described by the author as his innovation. 100 Transl. Netz 2002, 214 (Eutocius, In Archim. Sphaer. cyl. 96. 10–27 Heiberg = 68. 17–69. II Mugler). Knorr 1989, 144f. has suggested that the Letter was dedicated to the fourth King Ptolemy (Philopator), Eratosthenes’ tutee, perhaps on the occasion of the endowment of royal honors on the infant heir apparent, the fifth Ptolemy (Epiphanes); on this reading, the Letter would have been written late in Eratosthenes’ career. See also Wilamowitz 1894/1971, 65–66 on ambiguities in the epigram. 101 Transl. Thomas 1941, 202, with slight emendation.

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from Archimedes addressed to Eratosthenes that we have.102) The problem itself is presented as a poem in epigrammatic form, forty-four lines in the modern edition. While some scholars have questioned whether Archimedes was responsible for the poem, most assume that he was familiar with the problem.103 Unlike Eratosthenes’ epigram, which provides the sphragis as a supplement to the prose letter addressed to Ptolemy, in the Cattle Problem the mathematical problem is itself tightly woven into the poetic format. Interestingly, no ancient prose setting of the mathematical contents of the problem is known.104 Here is a portion of the English prose translation by Ivor Thomas:105 If thou art diligent and wise, O stranger, compute the number of cattle of the Sun, who once upon a time grazed on the fields of the Thrinacian isle of Sicily, divided into four herds of different colours, one milk white, another a glossy black, the third yellow and the last dappled. In each herd were bulls, mighty in number according to these proportions . . . .

Following the listing of the relevant proportions for each herd, both bulls and cows, the reader is then promised: If thou canst accurately tell, O stranger, the number of cattle of the Sun, giving separately the number of well-fed bulls and again the number of females according to each colour, thou wouldst not be called unskilled or ignorant of numbers, but not yet shalt thou be numbered among the wise. But come, understand also all these conditions regarding the cows of the Sun. When the white bulls mingled their number with the black, they stood firm, equal in depth and breadth, and the plains of Thrinacia, stretching far in all ways, were filled with their multitude. Again, when the yellow and the dappled bulls were gathered into one herd they stood in such a manner that their number, beginning from one, grew slowly greater till it completed a triangular figure, there being no bulls of other colours in their midst nor none of them lacking. If thou art able, O stranger, to find out all these things and gather them together in your mind, giving all the relations, thou shalt depart crowned with glory and knowing that thou hast been adjudged perfect in this species of wisdom.106

The solution requires finding the number of bulls and cows of each of four colors, or to find 8 unknown quantities. The seemingly simple question belies the surprisingly difficult character of the problem. Lessing published an incorrect solution; an ambiguity in the text contributed to J. F. Wurm’s solution of a simpler form. In 1880 A. Amthor discussed the complete problem, and partly solved it. Amthor did

102 See also “The Method of Archimedes’ Treating of Mechanical Problems – to Eratosthenes” in Heath 1912, 1–51, discovered by Heiberg in 1906 and recently the subject of study by Netz & Noel 2007. 103 Cf. Heath 1921b, 23. 104 Netz 2009, 167 f. See also Krumbiegel & Amthor 1880 on the problem. 105 To my knowledge, there is no English verse translation (though several German versions exist). 106 Thomas 1941, 202–205.

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not write out the solution, but provided the first four significant figures; many accounts of the solution are based on his paper.107 Why was this intriguing problem presented as a poem? Wilbur Knorr suggested that Eratosthenes composed the first part of the problem, and that the second part is Archimedes’ response.108 There are a number of features of the Cattle Problem which reinforce links between Archimedes and Eratosthenes. First of all, there is the allusion to Homer’s Odyssey and the cattle of the Sun. In the very opening lines of the Odyssey (I 6–10), there is a reference to the cattle of Helios, foreshadowing the forbidden slaughter of these livestock by Odysseus’ companions in book 12. The number of animals (seven herds of cattle, and of sheep, with fifty in each), and the place where they pasture, the island of Thrinacia, is specified in book 12 (lines 127 ff.), when the goddess Scylla speaks to Odysseus: “… you will reach the island Thrinacia, where are pastured the cattle and the fat sheep of the sun god, Helios, seven herds of oxen, and as many beautiful sheep flocks, and fifty to each herd”. Eratosthenes’ interest in Homer was well attested, as is his interest in number theory (through the use of his sieve (koskinon) for finding successive prime numbers.109 The Cattle Problem locates Thrinacia in Sicily, the home of Archimedes.110 By triangulating himself between Eratosthenes (arguably one of the greatest intellectuals of his age) and Homer (revered as one of the greatest Greek poets), Archimedes (if he was the author of the Cattle Problem) has highlighted intellectual bonds amongst the three, via numbers and poetry. But Eratosthenes and Archimedes, or whoever the authors of these mathematical poems might have been, were not alone in their interest in composing mathematical problems in poetry. The Greek Anthology has forty-odd poems which are mathematical problems presented as epigrams; many of these were collected by Metrodorus (ca 500 ) but would have been written much earlier.111 The number of mathematical poems that survive suggest that such poetry was not simply the reserve of these two correspondents, sending each other challenging problems. The relationship of problem-poems to story-problems suggests that there might be other generic issues involved.

107 Amthor 1880, 156 ff. See Vardi 1998 for a history of modern solutions. Sadly, I was unable to locate a copy of D. H. Fowler, “Archimedes’ Cattle Problem and the Pocket Calculating Machine” (1980 with additions in 1980, 1981, and a postscript 1986), Warwick. 108 Knorr 1986, 295. 109 See Nicomachus, Ar. I 13 for a description of the “sieve”. 110 See also Strabo, Geogr. VI 2.1 and Thucydides VI 2.2 on Thrinacia. Netz 2009, 34 and 167 f., apparently assumes that Archimedes is the sole author of the Cattle Problem. 111 See Paton 1918, 25–107.

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11 Other genres of discourse about mathematics In addition to those already discussed, there are other genres which were used by ancient Greek authors writing about mathematics. While a detailed consideration of any of these is not possible here, it nevertheless is important to emphasize the range and diversity of genres in which mathematics was presented and discussed. Proclus refers to the Elements as a pragmateia (at 83.1), a word which the Greek-English Lexicon of Liddell-Scott-Jones (LSJ) suggests might be translated as “treatise”.112 The word ‘treatise’ is a modern term; the English word ‘treatise’ refers to a written work dealing formally and systematically with a subject. (The word’s origin is Middle English tretis, from Old French traiter, and the Latin tractare meaning ‘handle’ or ‘treat’.) Van der Eijk has pointed out that the “treatise” is a “less well defined species of text” sometimes referred to by this modern term; its style is usually considered to be less elaborate and its formal structure does not fit in with categories of prose recognized in antiquity such as dialogue, letter, commentary, handbook (tekhnē) and introduction (eisagōgē).113 Other ancient works dealing with scientific subjects, similarly described as treatises, appear to have begun as lectures;114 as was mentioned earlier, it has been suggested that Proclus’ Commentary on the Elements was a series of lectures and, indeed, the format of the work is somewhat different from what we encounter in some other commentaries, particularly with the two prologues which precede the work. It is worth noting too that Theon of Alexandria’s recension of the Elements has as its title in some manuscripts “Lectures”.115 The boundaries between certain genres may well have been blurred because lectures, written down as notes, were edited for publication. Another example of a written work which may have first been a series of lectures is Cleomedes’ (ca 200 ) text known as The Heavens. Cleomedes appears to have been a professional teacher; that The Heavens served a pedagogical purpose is indicated by the use of elementary argumentation and the frequent explication of terminology. At several points Cleomedes’ language – which refers to ‘lecture courses’ (skholai) – suggests that the work probably had its origin as a series of lectures.116

112 Indeed, Morrow 1970, 68, translates pragmateia here as “treatise”. See Liddell-Scott-Jones 1968, 1457. 113 Van der Eijk 1997, 89. The Greek term pragmateiai may also describe what we regard as ‘treatises’; see Dirlmeier 1962, 9–11. 114 On the possible relationship between lectures and treatises, particularly relating to work of Aristotle, see Taub 2008a, 18–22. 115 On the editions of Euclid by Theon of Alexandria, see Heath 1921a, 360. I have discussed the oral character of certain genres, particularly lectures and poetry, in Taub 2008a, particularly 13– 18. 116 Cf. Cleomedes, Cael. II 2.7 and II 7.12; see the translation by Todd & Bowen 2004, 127 and 165.

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The publication of lectures as written works, in various forms including commentaries, is only one indication that there was an active market for pedagogical works in the Greco-Roman world. Certain works were intended to serve as introductions (eisagōgai) or teaching texts; several of these survive, including Nicomachus of Gerasa’s (between  50 and 150) Introduction to Arithmetic, an elementary text on mathematics, and Geminus’ (ca 50 ) Introduction to the Phenomena),117 concerned with astronomy. Both works begin with definitions, and it is relatively easy to imagine that they would have supplemented lectures; students may well have appreciated a written text to consult before and after the oral presentation. Along with this work on arithmetic, Nicomachus produced an Introduction to Harmonics, an Introduction to Geometry (which has not survived), and possibly an Introduction to Astronomy. His Introduction to Arithmetic was used as a teaching text throughout later antiquity and into the Middle Ages (in a Latin paraphrase produced by Boethius (ca 480–ca 525 ); a number of commentators, including Iamblichus (ca 245–ca 325 ), Asclepius of Tralles (died ca 560/570 ) and Philoponus (ca 490–570s ), wrote about the work, indicating that it was the focus of further study itself.118 Iamblichus’ On the Pythagorean Life was intended to serve as an introduction to a series of mathematical works. In this text, Iamblichus presents mathematics as a way of life and offers a narrative of the life of Pythagoras. Other lives (bioi) of Pythagoras were presented in the third century, notably by Diogenes Laertius and Porphyry, for whom the life (bios) of Pythagoras was only one amongst several accounts of lives of important figures they offered, within a larger work. Asper has considered the importance of narrative accounts given by Greek mathematical and medical writers; the account of a life is a particular type of narrative which may be the proto-genre of the scientific biography.119 Certainly, like the proposition, it is a genre which often has a particularly mathematical stamp, and which was farreaching in its impact, well beyond the boundaries of the ancient Greek world.

12 Then, and now My aim in thinking about genres of discourse on mathematics is, in part, to try to understand the place of these texts in wider Greek (and Roman) culture. However, an interest in the genres of mathematical discourse is not restricted to the ancient period. In fact, there has in recent years been a surge of attention amongst mathe-

117 The dates for Geminus are not agreed; see Jones 1999, Bowen & Todd 2008, Taub 2003, 25. 118 See Toomer 1996a for publication details for these commentaries on Nicomachus. More generally, see Mansfeld 1998, 1–5. 119 See Asper, in this volume 421; see also Taub 2007.

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matics teachers and pedagogical theorists to issues related to genre, authorial voice and other stylistic features in mathematical teaching texts.120 Two specialists in mathematics education, David Pimm and David Wagner, asked the following questions in 2003: “What kinds of mathematics are there? And what are possible bases for distinction or grouping, what are some salient features that could be stressed or ignored?” They suggested that there are several possible ways to address such questions: “One way, important both to libraries and to Mathematical Reviews, is by means of the traditional yet still-evolving categories such as “geometry”, “algebra”, “calculus”, “analysis”, and “number theory” – though these can generate turbulence at the boundaries, as well as increasingly requiring hybrids: algebraic geometry, topological algebra, analytic number theory, geometric topology, and so on”. Another possible way of “cutting up mathematics”, they suggested, “is to agree it is primarily written and then try to find bases (whether of form or function) for distinguishing and grouping types of writing into different kinds”. Pimm and Wagner then noted that “the question subsequently arises as to whether any observable differences are purely superficial or are in some way necessary, produced in response to demands of the situation: does form always have to follow function?”. They proposed that “an initial list might include the textbook, the published journal article, the written expository lecture, the letter (or increasingly e-mail message), the popular account or the encyclopedia entry, where each is also influenced by other non-mathematical examples of the ‘same’ form”.121 I began my consideration of the variety of genres of Greek mathematical writing by noting that, in common with modern mathematicians, ancient authors had many textual formats and modes of discourse available for communication. Then, as now, the genres used to communicate about mathematics mattered, and provide windows through which we see the interaction between technical literature, its authors and readers, and broader culture.

120 See, for example, Gerofsky 1999; Morgan 1998; Pimm & Wagner 2003. 121 Pimm & Wagner 2003, 159 f. I thank Markus Asper and Gerd Graβhoff for encouraging me to write this chapter, and the late Ian Mueller, Laurence Totelin, Lauren Kassell, Niall Caldwell, Aude Doody, Frances Willmoth and Michael Coxhead for their helpful comments and suggestions on an earlier draft.

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Bibliography Texts quoted Archimedes, Bov.: “Problema Bovinum”. In: Lloyd-Jones, H., & P. Parsons (eds.) 1983. Supplementum Hellenisticum. Berlin, 77–79; “Problema Bovinum”. In: J. L. Heiberg (ed.) 1893. Archimedis Opera Omnia cum Commentariis Eutocii. Volumen II. Leipzig, 527.1–532.9; “Indeterminate Analysis: The Cattle Problem. Archimedes (?), Cattle Problem, Archim. Ed. Heiberg ii. 528.1–532.9”. In: Thomas, I. (ed.) 1941. Selections Illustrating the History of Greek Mathematics, II: from Aristarchus to Pappus. Cambridge, MA, 202–205. Aristotle, Phys.: Hardie, R. P., & R. K. Gaye (transl.) 1984. “Physics”. In: J. Barnes (ed.), The Complete Works of Aristotle, The Revised Oxford Translation. Volume One. Princeton, 315–446. Aristotle, An. pr.: Jenkinson, A. J. (transl.) 1984. “Prior Analytics”. In: J. Barnes (ed.), The Complete Works of Aristotle, The Revised Oxford Translation. Volume One. Princeton, 39–113. Aristotle, Metaph.: Ross, W. D. (transl.) 1984. “Metaphysics”. In: J. Barnes (ed.), The Complete Works of Aristotle, The Revised Oxford Translation. Volume Two. Princeton, 1552–1729. Aristotle, Probl.: Forster, E. S. (transl.) 1984. “Problems”. In: J. Barnes (ed.), The Complete Works of Aristotle, The Revised Oxford Translation. Volume Two. Princeton, 1319–1527. Cleomedes, Cael.: “The Heavens”. In: R. B. Todd & A. C. Bowen (transl.) 2004. Cleomedes’ Lectures on Astronomy: a translation of The Heavens. Los Angeles. Eratosthenes: “Eutocii Commentarii in Librum II, De Sphaera et Cylindro. Ut Eratosthenes”. In: J. L. Heiberg (ed.) 1893. Archimedis Opera Omnia cum Commentariis Eutocii. Volumen III. Leipzig, 88–97; “The Solution of Eratosthenes. Eutocius, Commentary on Archimedes’ Sphere and Cylinder ii., Archim. ed. Heiberg iii: 88.4–90.13 and 88.3–96.27”. In: Thomas, I. (ed.) 1939. Selections Illustrating the History of Greek Mathematics, I: from Thales to Euclid. Cambridge, MA, 257–261 and 290–297. Eratosthenes: “Letter to Ptolemy Euergetes, in Eutocius, Commentary on Archimedes’ Sphere and Cylinder, pp. 88–96 [Heiberg]”. In: M. R. Cohen & I. E. Drabkin (eds.) 1958. A Source Book in Greek Science. Cambridge, MA, 62–66. Euclid, Elem.: “Elements”. In: T. L. Heath (transl.) 1925/1956. The Thirteen Books of Euclid’s Elements. Translated from the text of Heiberg, with an introduction and commentary by Sir Thomas L. Second edtion revised with additions. 3 vols. New York. Eutocius, In Sphaer. cyl.: “Eutocii Commentarii in Libros, De Sphaera et Cylindro”. In: J. L. Heiberg (ed.) 1893. Archimedis Opera Omnia cum Commentariis Eutocii. Volumen III. Leipzig, 1–225. Nicomachus, Ar.: Nicomachi Geraseni Pythagorei introductionis arithmeticae libri II rec. R. Hoche. Leipzig 1866. Pappus: “Collection”. In: F. Hultsch (ed.) 1876/1965 Pappi Alexandrini Collectionis. Volumen I. Berlin/Amsterdam; 1877/1965 Pappi Alexandrini Collectionis. Volumen II. Berlin/Amsterdam. In: A. Jones (ed.) 1986. Pappus of Alexandria. Book 7 of the Collection. Edited, with translation and commentary by Alexander Jones. New York. Proclus, In Eucl.: Procli Diadochi Lycii in Primum Euclidis Elementorum Commentariorum Libri IV a Francisco Barocio Patritio Veneto Editi. Padua, 1560; Proclii Diadochi in Primu Euclidis Elementorum Librum Commentarii ex Recognitione Godofredi Friedlein. Leipzig, 1873; “Commentary on Euclid’s Elements [In Eucl.]”. In: G. R. Morrow (transl.) 1970/1992. Proclus: A commentary on the first Book of Euclid’s Elements. Princeton. Simplicius, In Arist. Phys.: “Simplicii in Physicorum II”. In: Diels, H. (ed.) 1882. Simplicii in Aristotelis Physicorum: libros quattuor priores commentaria. Berlin, 259–393; On Aristotle’s Physics 2. In: B. Fleet (transl.) 1997. Simplicius. On Aristotle’s Physics 2. London. Stoici veteres: Von Arnim, H. F. A. (ed.) 1903–1924. Stoicorum Veterum Fragmenta. 4 vols. Leipzig.

362

Liba Taub

Works quoted Amthor, A. 1880. “Das Problema bovinum des Archimedes”. In: Zeitschrift fiir Math. u. Physik (Hist. litt. Abtheilung) 25, 153–171. Asper, M. 2009. “The Two Cultures of Mathematics in Ancient Greece”. In: E. Robson & J. Stedall (eds.), The Oxford Handbook of the History of Mathematics. Oxford, 107–132. Bernard, A. 2008a. “Hupatia of Alexandria (ca 380–415 CE)”. In: P. T. Keyser & G. L. Irby-Massie (eds.), The Encyclopedia of Ancient Natural Scientists: the Greek tradition and its many heirs. London, 423–424. Bernard, A. 2008b. “Theōn of Alexandria (Astr.) (ca 360–385 CE)”. In: P. T. Keyser & G. L. IrbyMassie (eds.), The Encyclopedia of Ancient Natural Scientists: the Greek tradition and its many heirs. London, 793–795. Berryman, S. 2009. The Mechanical Hypothesis in Ancient Greek Natural Philosophy. Cambridge, UK. Biagioli, M., & P. Galison (eds.) 2003. Scientific Authorship: credit and intellectual property in science. New York. Boyer, C. B. 1968. A History of Mathematics. New York. [Brown University Library] n.d. From Euclid to Newton: An Exhibition in Honor of the 1999 Conference of the Mathematical Association of America (online). Providence, RI. Available at: http://www.brown.edu/Facilities/University_Library/exhibits/math/nofr.html (accessed 3rd May 2010). Cherniss, H. 1976/2000. Plutarch’s Moralia in Seventeen Volumes. XIII, part I, 999c–1032f. Cambridge, MA. Cohen, M. R., & I. E. Drabkin 1958. A Source Book in Greek Science. Cambridge, MA. Conte, G. B. 1994. Genres and Readers: Lucretius, Love Elegy, Pliny’s Encyclopedia. Translated by Glenn W. Most, with a foreword by Charles Segal. Baltimore. Conte, G. B., & G. W. Most 1996. “Genre”. In: S. Hornblower & A. Spawforth (eds.), The Oxford Classical Dictionary. Third Edition. Oxford, 630–631. Coxhead, M. 2012 “A Close Examination of the Pseudo-Aristotelian Mechanical Problems: Poetry and Mechanics”. In: Studies in History and Philosophy of Science, 43(2), 300–306. Cuomo, S. 2000. Pappus of Alexandria and the Mathematics of Late Antiquity. Cambridge, UK. Cuomo, S. 2001. Ancient Mathematics. London. Curtis, T. 2009. “Didactic and Rhetorical Strategies in Galen’s De pulsibus ad tirones”. In: L. Taub & A. Doody (eds.), Authorial Voices in Greco-Roman Technical Writing. Trier, 63–79. De Leemans, P., & M. Goyens (eds.) 2006. Aristotle’s Problemata in Different Times and Tongues. Leuven. Depew, M., & D. Obbink (eds.) 2000. Matrices of Genre: authors, canons, and society. Cambridge, MA. Dimock, W. C. 2007. “Introduction: Genre as Fields of Knowledge”. In: Publications of the Modern Language Association of America 122(5), 1377–1388. Dirlmeier, F. 1962. Aristoteles Eudemische Ethik, übersetzt von Franz Dirlmeier. Berlin. Doody, A. 2010. Pliny’s Encyclopedia. Cambridge. Duff, D. (ed.) 2000. Modern Genre Theory. Harlow. Van der Eijk, P. J. 1997. “Towards a Rhetoric of Ancient Scientific Discourses: some formal characteristics of Greek medical and philosophical texts (Hippocratic corpus, Aristotle”. In: E. J. Bakker (ed.), Grammar as Interpretation: Greek literature in its linguistic contexts. Leiden, 77–129. Flashar, H. 1975. Aristoteles: Problemata physica, übersetzt von H. Flashar. Zweite durchgesehene Auflage. Berlin.

On the Variety of ‘Genres’ of Greek Mathematical Writing

363

Fowler, D. H. 1999. The Mathematics of Plato’s Academy: a new reconstruction. Second Edition. Oxford. Frede, M. 1974. “Stoic vs. Aristotelian Syllogistic”. In: Archiv für Geschichte der Philosophie 56(1), 1–32. Genette, G. 1997. Paratexts: thresholds of interpretation. Cambridge, UK. Gerofsky, S. 1999. “Genre Analysis as a Way of Understanding Pedagogy in Mathematics Education”. In: For the Learning of Mathematics 19(3), 36–46. Gibson, R. K., & C. S. Kraus 2002. The Classical Commentary: histories, practices, theory. Leiden. Grafton, A., & M. Williams 2006. Christianity and the Transformation of the Book: Origen, Eusebius, and the library of Caesarea. Cambridge, MA. Heath, T. L. 1896. Apollonius of Perga Treatise on Conic Sections. Cambridge, UK. Heath, T. L. 1912. The Method of Archimedes, recently discovered by Heiberg. A supplement to The Works of Archimedes 1897. Edited by Sir Thomas L. Heath. Cambridge, UK. Heath, T. L. 1921a. A History of Greek Mathematics. Volume 1: From Thales to Euclid. Oxford. Heath, T. L. 1921b. A History of Greek Mathematics. Volume 2: From Aristarchus to Diophantus. Oxford. Heath, T. L. 1925/1956. The Thirteen Books of Euclid’s Elements. Translated from the text of Heiberg, with an introduction and commentary by Sir Thomas L. Heath. Second edtion revised with additions. Volume I: Introduction and Book I, II. Cambridge. Hett, W. S. 1936. Aristotle: Problems. Volume 1. Cambridge, MA. Hine, H. M. 1981. An Edition with Commentary of Seneca, Natural Questions, Book Two. New York. Imhausen, A. 2003. “Egyptian Mathematical Texts and their Contexts”. In: Science in Context 16(3), 367–389. Inwood, M. J. 1992. “Problematic Problems”. In: The Classical Review (New Series) 42(2), 285– 286. Jones, A. (ed.) 1986. Pappus of Alexandria. Book 7 of the Collection. Edited, with translation and commentary by Alexander Jones. Part 1. Introduction, Text, and Translation. New York. Jones, A. 1999. “Geminus and the Isia”. Harvard Studies in Classical Philology 99, 255–267. Keyser, P. T. & G. L. Irby-Massie (eds.) 2008. The Encyclopedia of Ancient Natural Scientists. The Greek tradition and its many heirs. London. Knorr, W. R. 1975. The Evolution of the Euclidean Elements: a study of the theory of incommensurable magnitudes and its significance for early Greek geometry. Dordrecht. Knorr, W. R. 1986. The Ancient Tradition of Geometric Problems. Boston. Knorr, W. R. 1989. Textual Studies in Ancient and Medieval Geometry. Boston. Krumbiegel, B. and A. Amthor. 1880. “Das Problema Bovinum des Archimedes”, Historischliterarische Abteilung der Zeitschrift Für Mathematik und Physik 25, 121–136 and 153–171. Lennox, J. G. 1986. “Aristotle, Galileo, and ‘mixed sciences’”. In: W. A. Wallace (ed.) Reinterpreting Galileo. Washington, DC, 29–51. Louis, P. 1991. Aristote: Problèmes, I, Sections I a X. Paris. Mansfeld, J. 1998. Prolegomena Mathematica: From Apollonius of Perga to late Neoplatonism. With an appendix on Pappus and the history of Platonism. Leiden. McKirahan, R. D. Jr. 1978. “Aristotle’s Subordinate Sciences”. In: The British Journal for the History of Science 11(3), 197–220. Morrow, G. R. 1970. Proclus: A commentary on the first Book of Euclid’s Elements. Princeton. Morgan, C. 1998. Writing Mathematically: the discourse of investigation. London. Most, G. W. (ed.) 1999. Commentaries – Kommentare. Göttingen. Mueller, I. 1981. Philosophy of Mathematics and Deductive Structure in Euclid’s Elements. Cambridge. Mueller, I. 1992. “Foreword to the 1992 edition”. In: G. R. Morrow, Proclus: A commentary on the first Book of Euclid’s Elements. Princeton, ix–xxxi.

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Mueller, I. 2008. “Euclid of Alexandria (300–260 )”. In: P. T. Keyser & G. L. Irby-Massie (eds.), The Encyclopedia of Ancient Natural Scientists: the Greek tradition and its many heirs. London, 304–306. Murphy, T. 2004. Pliny the Elder’s Natural History. Oxford. Netz, R. 1999a. The Shaping of Deduction in Greek Mathematics: a study in cognitive history. Cambridge. Netz, R. 1999b. “Proclus’ Division of the Mathematical Proposition into Parts: how and why was it formulated?” In: The Classical Quarterly (New Series) 49(1), 282–303. Netz, R. 2002. “Greek Mathematicians: a Group Picture”. In: C. J. Tuplin & T. E. Rihll (eds.), Science and Mathematics in Ancient Greek Culture. Oxford, 196–216. Netz, R. 2004. The Works of Archimedes. Volume I: The Two Books On the Sphere and the Cylinder. Translated into English, together with Eutocius’ commentaries, with commentary, and critical edition of the diagrams. Cambridge. Netz, R. 2009. Ludic Proof: Greek mathematics and the Alexandrian aesthetic. Cambridge. Netz, R., & W. Noel 2007. The Archimedes Codex: Revealing the Secrets of the World’s Greatest Palimpsest. London. Nutton, V. 2009. “Galen’s Authorial Voice: a Preliminary Enquiry”. In: L. Taub & A. Doody (eds.), Authorial Voices in Greco-Roman Technical Writing. Trier, 53–62. Paton, W. R. 1918. The Greek Anthology. Volume V. Cambridge, MA. Pimm, D., & D. Wagner 2003. “Investigation, Mathematics Education and Genre: an essay review of Candia Morgan’s Writing Mathematically: the discourse of investigation”. In: Educational Studies in Mathematics 53(2), 159–178. Robson, E. 2009. “Mathematics Education in an Old Babylonian Scribal School”. In: E. Robson & J. Stedall (eds.), The Oxford Handbook of the History of Mathematics. Oxford, 199–227. Sharples, R. W. 2006. “Pseudo-Alexander or Pseudo-Aristotle, Medical Puzzles and Physical Problems”. In: P. de Leemans & M. Goyens (eds.), Aristotle’s Problemata in Different Times and Tongues. Leuven, 21–32. Sider, D. 2005. The Fragments of Anaxagoras. Second Edition. Sankt Augustin. Sidoli, N. 2004. Ptolemy’s Mathematical Approach: Applied Mathematics in the Second Century. Ph. D. thesis, University of Toronto. Simpson, J. A., & E. S. C. Weiner (eds.) 1989. The Oxford English Dictionary. Second edition. Volume XII: Poise–Quelt. Oxford. Sluiter, I. 2000. “The Dialectics of Genre: some aspects of secondary literature and genre in antiquity”. In: M. Depew & D. Obbink (eds.), Matrices of Genre: authors, canons, and society. Cambridge, MA, 183–204. Smith, R. 1989. Prior Analytics. Translated, with introduction, notes, and commentary, by Robin Smith. Indianapolis. Taub, L. 1993. Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of Ptolemy’s Astronomy. Chicago. Taub, L. 2003. Ancient Meteorology. London. Taub, L. 2007. “Presenting a ‘Life’ as a Guide to Living: Ancient accounts of the life of Pythagoras”. In: T. Söderqvist (ed.), The History and Poetics of Scientific Biography. Ashgate, 17–36. Taub, L. 2008a. Aetna and the Moon: explaining nature in ancient Greece and Rome. Corvallis. Taub, L. 2008b. “‘Eratosthenes Sends Greetings to King Ptolemy’: Reading the contents of a ‘mathematical’ letter”. In: J. W. Dauben et al. (eds.), Mathematics Celestial and Terrestial. Festschrift für Menso Folkerts zum 65. Geburtstag. Deutsche Akademie der Naturforscher Leopoldina, Acta Historica Leopoldina 54. Halle (Saale), 285–302. Taub, L., & A. Doody (eds.) 2009. Authorial Voices in Greco-Roman Technical Writing. Trier. Thomas, I. (ed.) 1939. Selections Illustrating the History of Greek Mathematics, I: from Thales to Euclid. Cambridge, MA.

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Thomas, I. (ed.) 1941. Selections Illustrating the History of Greek Mathematics, II: from Aristarchus to Pappus. Cambridge, MA. Todd, R. B., & A. C. Bowen 2004. Cleomedes’ Lectures on Astronomy: a translation of The Heavens. With an introduction and commentary by Alan C. Bowen and Robert B. Todd. Los Angeles. Todorov, T. 1974. “Literary Genres”. In: T. A. Sebeok (ed.), Current Trends in Linguistics. Volume 12: linguistics and adjacent arts and sciences, part 3. The Hague, 957–962. Toomer, G. J. 1996a. “Nicomachus (3)”. In: S. Hornblower & A. Spawforth (eds.), The Oxford Classical Dictionary. Third Edition. Oxford, 1042. Toomer, G. J. 1996b. “Pappus”. In: S. Hornblower & A. Spawforth (eds.), The Oxford Classical Dictionary. Third Edition. Oxford, 1109. Tybjerg, K. 2005. “Hero of Alexandria’s Mechanical Treatises: Between Theory and Practice”. In: A. Schürmann (ed.), Geschichte der Mathematik und der Naturwissenschaften in der Antike (GMN) 3: Physik/Mechanik. Stuttgart, 204–226. Vardi, I. 1998. “Archimedes’ Cattle Problem”. In: The American Mathematical Monthly 105(4), 305–319. Wilamowitz-Moellendorff, U. v. 1894. “Ein Weihgeschenk des Eratosthenes”. In: Nachrichten der K. Gesellschaft der Wissenschaften zu Göttingen, Phil.-hist.Klasse, 15–35. Reprinted in: Kleine Schriften. Berlin 1971. Vol. 2, 48–70.

Apostolos Doxiadis and Michalis Sialaros

Sing, Muse, of the Hypotenuse: Influences of Poetry and Rhetoric on the Formation of Greek Mathematics Abstract: In recent years, the multidisciplinary study of ancient Greek mathematics has started to look at unusual connections and influences. Perhaps the most unexpected of all is literature, either in its older, archaic forms, or in its shaping influence on the fifth-century development of rhetoric. Setting a cognitively oriented framework, in which the investigation of the birth of logico-deductive proof in Classical Greece becomes more sensitive to the revelation of extra-mathematical influences, we investigate how aspects of narrativity, as well as literary or rhetorical methods, could have entered into early Greek mathematical thinking.

1 Introduction 1

1.1 Overview

“Two plus two equals four” is often stated as a prototype of objective knowledge: the result is the same no matter who derives it. In this sense, all mathematical writing is inspired by an ideal of anonymity. Yet, all works produced by human beings are affected to some degree by the aims, capabilities and weaknesses of their creators. So, whether they are presenting original discoveries, writing expositional treatises, or putting together compendiums of previously existing knowledge, mathematical authors cannot help but inject aspects of themselves into their texts. Thus, the investigation of the mindset of mathematical authors – a mindset that is partly shaped by the non-mathematical cultural influences that they are exposed to – becomes significant to a study of the history of mathematics. In this paper we investigate the intellectual makeup of the early Greek mathematicians, in an effort to identify the cultural influences that may have played a crucial part in the creation of the kind of mathematics we find in the works of Euclid (300 ),2 what we shall call Greek-style. 1 We are grateful to Markus Asper, Serafina Cuomo, Michael Gagarin, Katerina Ierodiakonou, Pavlos Kalligas, Vassilis Karasmanis, G. E. R. Lloyd, Barry Mazur, Reviel Netz, Christopher Pelling, Dimos Spatharas and Yoryis Yatromanolakis, who read and commented on an earlier version of this paper. We are also indebted to Theodora Hadjimichael for editorial comments and to Margarita Metzger for her assistance. 2 For the dating, we draw on Keyser & Irby-Massie 2008, Hornblower & Spawforth 2003, and Netz 1997, 6–9. For the latest discussion of Euclid’s dating, see Sialaros 2012, 42–9.

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The introduction offers an overview of early Greek mathematics and discusses its distinctive characteristics. Emphasis is given to the fact that the first Greek practitioners were not what we would call today ‘professional mathematicians’, but well-educated individuals, and, as such, proficient in the arts of logos, which include rhetoric. In the last part of the introduction, we discuss pre- and nonGreek ancient rhetoric and compare it with Greek rhetorical practices. In section 2, we present the internal scheme of the Greek mathematical proposition, and argue in favour of the traditional view that it is at least as old as Euclid. Following this, we present the standard form of the Greek forensic speech and compare the two patterns, identifying some marked similarities. In section 3, we analyze the microstructure of speeches and show how certain poetic figures were applied by Greek orators for the formation of arguments and the achievement of persuasion; finally, we show that the same figures were similarly used in Greek-style mathematical propositions. We support the view that this use of narrative-poetic tools to mathematical practice reveals the importance of non-mathematical cultural influences in the formulation of the Greek mathematical style.

1.2 ‘Greek style’: a new kind of mathematics Discussing the mathematics of ancient cultures, Lloyd writes: “There is nothing inevitable about the way in which [mathematics] developed, and [its] international modern character should not mask [its] very divergent early manifestations”.3 This statement is supported by the fact that we find varied mathematical traditions in the ancient world. What we call Greek-style mathematics is characterized by the existence of general propositions,4 axiomatic-deductive methodology, impersonality5 and the use of diagrams.6 This style differs not just from ancient, non-Hellenic mathematics, but also from a kind of mathematics that existed in the Greek world in tandem to it, i.e. the practical, computational techniques used by accountants, land-measurers, or architects.7 The Greeks praised highly the mathematical abilities of the Egyptians and believed that their ancestors had learned the art from them.8 Extant Greek texts from Hellenistic Egypt contain the same type of practical mathematics as that of texts in the demotic Egyptian language written at about the same era.9 However,

3 Lloyd 1996, 225. 4 See Karasmanis 2000, 15–21; Netz 1999a, 240-70. 5 See Asper 2009, 118f. 6 See Huffman 2005, 342–68; Netz 1999a, 12-67; Fowler 1999, 201. Although no diagrams have been preserved, the original texts obviously rely on several diagrams. 7 See Cuomo 2001, 6–16. 8 Herodotus II 109; Aristotle, Μetaph. A 1, 981b23; Ps.-Democritus fr. 299; Proclus, In Eucl. 64.18. 9 See Friberg 2005, 268.

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Greek-style mathematics is markedly different; so much so, that its differences from what preceded it cannot be explained by a simple time-evolvement, of the earlier into the later.10 In order to illustrate this point, we look at examples of the two kinds of mathematics. In the most advanced Egyptian mathematical treatise we possess, contained in the “Rhind” papyrus (2000–1800 ),11 the author, Ahmes, promises to provide “knowledge of all things and insight into all that exist,” a statement that we can assume to mean, among other things, that it presents state-of-the-art mathematical knowledge. The papyrus contains a long list of problems, such as the distribution of wages among a number of labourers. Here is a typical one, Problem 26: A quantity and a fourth part of it give together 15. Calculate with 4; of this you must take the fourth part, namely 1; together 5. Then the division 15:5 = 3 is carried out, finally a multiplication, 4×3= 12. The required “quantity” is therefore 12, the fourth part is 3, together 15.12

There is no doubt that the arithmetic abilities expressed in this type of problems allowed the Egyptians to perform complex calculations for use in accounting, architecture, land-measurement, etc. The extant evidence shows that Egyptian mathematics was purely of this variety, and far removed from the kind we find in Euclid. Compare Ahmes’ problem with Proposition I 7 of the Elements: Ἐπὶ τῆς αὐτῆς εὐθείας δύο ταῖς αὐταῖς εὐθείαις ἄλλαι δύο εὐθεῖαι ἴσαιἑκατέρα ἑκατέρᾳ οὐ συσταθήσονται πρὸς ἄλλῳ καὶ ἄλλῳ σημείῳ ἐπὶ τὰ αὐτὰ μέρη τὰ αὐτὰ πέρατα ἔχουσαι ταῖς ἐξ ἀρχῆς εὐθείαις. Εἰ γὰρ δυνατόν, ἐπὶ τῆς αὐτῆς εὐθείας τῆς ΑΒ δύο ταῖς αὐταῖς εὐθείαις ταῖς ΑΓ, ΓΒ ἄλλαι δύο εὐθεῖαι αἱ ΑΔ, ΔΒ ἴσαι ἑκατέρα ἑκατέρᾳ συνεστάτωσαν πρὸς ἄλλῳ καὶ ἄλλῳ σημείῳ τῷ τε Γ καὶ Δ ἐπὶ τὰ αὐτὰ μέρη τὰ αὐτὰ πέρατα ἔχουσαι, ὥστε ἴσην εἶναι τὴν μὲν ΓΑ τῇ ΔΑ τὸ αὐτὸ πέρας ἔχουσαν αὐτῇ τὸ Α, τὴν δὲ ΓΒ τῇ ΔΒ τὸ αὐτὸ πέρας ἔχουσαν αὐτῇ τὸ Β, καὶ ἐπεζεύχθω ἡ ΓΔ. Ἐπεὶ οὖν ἴση ἐστὶν ἡ ΑΓ τῇ ΑΔ, ἴση ἐστὶ καὶ γωνία ἡ ὑπὸ ΑΓΔ τῇ ὑπὸ ΑΔΓ· μείζων ἄρα ἡ ὑπὸ ΑΔΓ τῆς ὑπὸ ΔΓΒ· πολλῷ ἄρα ἡ ὑπὸ ΓΔΒ μείζων ἐστὶ τῆς ὑπὸ ΔΓΒ. πάλιν ἐπεὶ ἴση ἐστὶν ἡ ΓΒ τῇ ΔΒ, ἴση ἐστὶ καὶ γωνία ἡ ὑπὸ ΓΔΒ γωνίᾳ τῇ ὑπὸ ΔΓΒ. ἐδείχθη δὲ αὐτῆς καὶ πολλῷ μείζων· ὅπερ ἐστὶν ἀδύνατον. Οὐκ ἄρα ἐπὶ τῆς αὐτῆς εὐθείας δύο ταῖς αὐταῖς εὐθείαις ἄλλαι δύο εὐθεῖαι ἴσαι ἑκατέρα ἑκατέρᾳ συσταθήσονται πρὸς ἄλλῳ καὶ ἄλλῳ σημείῳ ἐπὶ τὰ αὐτὰ μέρη τὰ αὐτὰ πέρατα ἔχουσαι ταῖς ἐξ ἀρχῆς εὐθείαις· ὅπερ ἔδει δεῖξαι. Given two straight lines constructed on a straight line and meeting in a point, there cannot be constructed on the same straight line, and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that which has the same extremities with it.

10 In a much-discussed article, Unguru (1975) questioned the universality of mathematics. For a discussion on the links between Egyptian and Greek mathematics, see Cuomo 2001, 5; Fowler 1999, 9, 265, 372; Bernal 1992, 602–7, and Kahn 1991, 1–4. Numerous other elements of Greek culture appear in pre-Hellenic societies; see Burkert 1992; 2004, and West 1997. 11 Most of our knowledge of Egyptian mathematics relies on sources dating to the Middle Kingdom (2055–1650 ); see Rossi 2009, 407; Imhausen 2009, 782; Robins & Shute 1987. 12 Translation by van der Waerden 1950/1954, 16.

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Fig. 1: Τhe diagram, accompanying the proof of Proposition I 7 of Euclid’s Elements, of the construction of a hypothetical second triangle, ADB, on AB, with the same side lengths as the given, ACB. For, if possible, given two straight lines ΑC, CΒ constructed on the straight line AB and meeting at the point C, let two other straight lines ΑD, DΒ be constructed on the same straight line AB, on the same side of it, meeting in another point D, and equal to the former two respectively, namely each to that which has the same extremity with it, so, that CΑ is equal to DΑ which has the same extremity A with it, and CΒ to DΒ which has the same extremity Β with it; and let CD be joined. Then, since AC is equal to AD, the angle ACD is also equal to the angle ADC; therefore the angle ADC is greater than the angle DCB; therefore the angle CDB is much greater than the angle DCB. Again since CB is equal to DB, the angle CDB is also equal to the angle DCB. But it was also proved much greater than it: which is impossible. Therefore, given two straight lines constructed on a straight line and meeting in a point, there cannot be constructed on the same straight line, and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that which has the same extremities with it; what it was required to prove.13

The most marked difference between the Egyptian and the Greek examples is that the former seems to arise directly out of a specific, practical need, to which it caters, whereas the latter is a statement made in general terms, far removed from everyday reality.14 The Egyptian mathematician tackles an arithmetical problem and gives its solution, without any derivations; the result is presented in the form of a recipe, with no general methodology mentioned. The Greek, on the contrary, presents an extended deductive proof of a general, abstract proposition that, furthermore, relies on results established in earlier propositions. Although the corpus of Greek mathematical texts is large and heterogeneous,15 and the style of presentation varies from author to author16 and, on occasion, even 13 For Euclid’s Elements, here and henceforth, we adopt Heath’s (1956) translation with minor changes. As no original diagrams have been preserved, the diagrams we provide are modern reconstructions as presented in Heath 1956 and Mogenet 1950. For a discussion on the extant material, see Fowler 1999, 209–217. 14 Egyptian geometry is no exception to this rule; see Taton 1957/1963, 30–32. 15 Introductions to Greek mathematics are provided by Heath 1921, van der Waerden 1950/1954, and Cuomo 2001. 16 For example, Hero’s Metrics focuses on measurement problems using methodologies similar to those present in the traditions of Egypt and Babylon; see Lloyd 1992, 596.

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within the work of a single author, Greek-style mathematics is essentially different from Egyptian. However, many of the characteristics of Egyptian mathematics are also to be found in other ancient cultures, like Babylonian and Chinese, as the following two examples show: a. Most of the available information on Babylonian mathematics belongs to the period from 1800 to 1600 , and comes from cuneiform texts preserved on clay tablets.17 The texts can be classified into two major groups, tables and problems. Here is problem A.O. 6770: Length and width as much as area; let them be equal. You in your procedure, the product you take twice. From this subtract 1. You form the reciprocal. With the product that you have taken you multiply and The width it gives you.18

b. The most important aspects of ancient Chinese mathematical thinking are reflected in the Zhoubi Suanjing (“Arithmetic Classic of the Zhou Gnomon”) and the Jiuzhang Suanshu (“Nine Chapters on the Mathematical Art”), dated between 100  and 100 .19 These texts take the form of dialogues, where an anonymous questioner sets the problem. This is the first problem from the latter work: Now given a field 15 bu broad and 16 bu long. Tell: how much field? Answer: 1mu.20

Like the Egyptian, Babylonian and Chinese mathematics is in the form of concrete arithmetical problems from agriculture, architecture, or taxation. We could assume that the surviving mathematics of these cultures indicates a more general, underlying method; however, nowhere in the extant texts do we find a hint of its existence.21

1.3 Professing the art: the first mathematicians in the Greek style Proclus (450 ), probably based on Eudemus (350 ), attributes to Thales (600 ) the introduction of geometry from Egypt to the Greek world.22 However, since 17 Introductions to Babylonian mathematics are provided by Neugebauer 1951, van der Waerden 1950/1954 and Robson 2008. Although some geometric investigation is present in Babylonian mathematics, geometric concepts played a secondary role; see Neugebauer 1951, 14 f. For a comparative study between Babylonian and Egyptian mathematics, see Friberg 2005. 18 Translation by van der Waerden 1950/1954, 73 f. 19 See Lloyd 2009, 18, and Cullen 2009, 606. Lloyd’s comparative studies of ancient Greek and Chinese science have contributed greatly to the understanding of both; see Lloyd 1996; 2002; 2003; 2006; 2009. 20 Kangshen et al. 1999, 61. 21 See Lloyd 2009, 24. 22 Proclus, In Eucl. 65.7, 352; Diogenes Laertius, Vita Phil. I 24.10.

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we have no extant text of Thales, this testimony cannot be verified.23 The first complete Greek mathematical texts we possess are the treatises On the Moving Sphere and On Risings and Settings, attributed to Autolycus of Pitane (ca 330 ). Euclid’s Elements are dated around thirty years later.

Fig. 2: A timeline of the sources for Greek mathematics. We have no textual evidence for mathematical activity before 600 , and only second-hand reports of theoretical mathematics until 330 , written centuries after the discoveries they refer to.

Greek mathematical texts have come down to us in three forms: a) as full treatises, as the works of Autolycus or Euclid; b) as fragments of earlier texts included in the works of later authors, such as the squaring of the lunes by Hippocrates of Chios (ca 430 ) and the solution on the problem of the doubling of the cube by Archytas’ (400 ), which we find in Simplicius (500 ) and Eutocius (500 ) respectively;24 and c) in references to earlier works that are now lost, such as in Proclus’ account of Thales’ mathematics. Thus, though there are no extant complete texts before Autolycus, we have some evidence of earlier Greek mathematics in which some elements of the Greek style can already be detected. Taking these earlier Greek mathematical texts into account, the shaded part of Fig. 2 can be further broken down into two parts:

Fig. 3: From 600  until the middle of the fifth century , our only evidence of Greek theoretical mathematical activity is through reports in other authors’ works. From about 430  onwards, we have more indirect information.

23 Neugebauer, Heath, and Dicks doubt that Thales made any geometrical discoveries (Neugebauer 1951, 190; Heath 1956, 131; Dicks 1959, 294–309), whereas van der Waerden and O’Grady argue for the opposite (van der Waerden 1950/1954, 89f.; O’Grady 2002, 219). 24 Both rely on the authority of Eudemus.

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Greek-style mathematics was created some time in the period indicated by the shaded area. Besides the names mentioned above, ancient sources – some of which are more credible than others – praise the contributions to mathematics of Pythagoras (550),25 Anaxagoras (450), Democritus (450), Oenopides (450), Theodorus (430), Bryso and Antiphon (400), Hippasus (400), Hippias (400), Leodamas (400), Leo (400), Plato (400), Theaetetus (380), Aristaeus (350), Menaechmus (350), and Eudoxus (350).26 To give a rough and very fragmentary outline of their achievements, Pythagoras allegedly proved the theorem that bears his name and the construction of the cosmic solids;27 Anaxagoras, Bryso and Antiphon attacked the problem of squaring the circle;28 Oenopides, Leodamas and Theaetetus discovered theorems and problems in plane geometry;29 Democritus and Eudoxus worked with solid geometry;30 Menaechmus and Aristaeus studied the conic sections,31 Hippasus developed the theory of the harmonic means;32 Hippias discovered the curve afterwards known as the ‘quadratrix;’33 Theodorus studied incommensurability,34 and Plato discovered the method of analysis.35 Although some of these thinkers are known primarily for their mathematical work, most were active in other fields as well. Some sources describe them as ‘philosophers’ (e.g. Pythagoras, Eudoxus, Hippasus, Democritus and Plato),36 ‘sophists’ (e.g. Hippias, Bryso and Antiphon),37 ‘astronomers’ (e.g. Oenopides and Menaechmus),38 with Hippocrates of Chios being the sole given the mundane voca25 All dates are . 26 For more information on this period, see Allman 1976, Heath 1921, vol. i, 65–353, van der Waerden 1950/1954, 82–200, and Cuomo 2001, 4–61. For a more detailed catalogue, see Netz 1997, 6–9. 27 Proclus, In Eucl. 426.6–10, 65.15–21. For the life of Pythagoras, see Diogenes Laertius, Vita Phil. VIII. 28 Proclus, In Eucl. 65.21; Aristotle, Phys. 185a17, Soph. el. 172a2; Themistius, In Arist. An. post. 5.1, 19.11; Philoponus, In Arist. An. post. 13.3, 112.8; 149.10; Eutocius, In Archim. Dim. cir. III 228.15. 29 Hero, Def. 138.11.1; Proclus, In Eucl. 66.2–67.1, 283.7. 30 Archimedes, Meth. III 84.8, Sphaer. cyl. I 9.3; Proclus, In Eucl. 67.2; for Democritus, see also Heath 1921, vol. i, 176–181. 31 Pappus, Coll. VII 672.12–674.19; Proclus, In Eucl. 72.24, 78.9; Eutocius, In Archim. Sphaer. cyl. 78.13–84.11. 32 Iamblichus, In Nicom. 100.23. 33 Proclus, In Eucl. 272.7, 356.11; for applications, see Pappus, Coll. IV 250.33. 34 Plato, Theaet. 147d2. 35 Proclus, In Eucl. 211.21; Diogenes Laertius, Vita Phil. III 24.8. 36 Diogenes Laertius includes them in his Lives of the Philosophers. It is worth mentioning that Eudoxus is described as “astrologer, geometer, doctor, and lawgiver”; Diogenes Laertius, Vita Phil. I 14.1–16, VIII 86.1, VIII 84, IX 34, III. Iamblichus, Vita Pyth.; Aristotle, Metaph. 984a8, Eth. Nic. 1101b27; Proclus, In Eucl. 65.15–67.2, 426. 37 Suda, sub vocibus; Athenaeus, Deipnosophistae XIII 89.5; Anaximenes (hist.), Test. (fr. 10); Aristotle, Hist. anim. 563a7, Soph. el. 171b16; Plutarch, Vita dec. orat. 832b-852e. Notice that Bryso is included by Diogenes Laertius in his Lives of the Philosophers I 16.6. 38 Hero, Def. 138.11.3; Proclus, In Eucl. 72.24, 78.9, 283.7; Theo, Math. Plat. 201.25.

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tion of ‘merchant’.39 This lack of specialization in mathematics should not be surprising. The word mathēma, from which comes the adjective mathēmatikos, originally had the literal meaning of “that which is learned” or a “subject of instruction”,40 and came to refer specifically to geometry and arithmetic only later.41 Thus, in the fifth century, and possibly even in the first part of the fourth, a mathematician was, strictly speaking, “a person who is fond of learning”.42 Asper writes on the occupation of mathematicians in the classical age: Perhaps it would be adequate to think of theoretical [i.e. Greek-style] mathematics as some form of game rather than something pertaining to the professional occupation which it has become today, and which practical mathematics has always been.43

In this sense, the founders of Greek mathematics were, by modern standards, amateurs. Motivated by a sort of reductio ad absurdum, our paper seeks some of the formative influences on the creation of Greek-style mathematics within the special characteristics of the cultural context in which it developed, especially as this context affected the intellectual habits of the first mathematicians. For, if the technical challenges posed in Mesopotamia and Egypt, combined with the cultural tools available in those cultures, were enough for the invention of Greek-style mathematics – as they were definitely enough for the invention of advanced practical mathematics – it is highly probable that the people occupied with mathematics in those cultures would have invented it, rather than the Greeks. But they did not. Thus, since the Greeks were not more sophisticated than their predecessors in practical mathematics, the influences for the creation of the Greek style must be looked for outside mathematics itself. A corollary of this position is that the history of early Greek mathematics cannot be told without viewing its early practitioners as men of their particular culture. Here, history becomes intricately related to questions of authorship: Greek mathematical style is indeed ‘impersonal’; but, even disregarding the differences between the styles of individual authors inherent in this statement, we can say that it has general characteristics which reflect, if not the personalities of particular persons, then definitely their culturally-determined common ground.

39 Aristotle, Eth. Eud. IV 14, 1247a17; Philoponus, In Arist. Phys. 16, 31.3. 40 Croesus (Herodotus I 207) refers to his mathēmata; viz. the bitter experiences in his life. 41 LSJ, sub vocibus. See also Lloyd 1992, 570. 42 It is so used by Plato, Timaeus 88c, and Aristotle, Metaph. A 1, 981b23. 43 Asper 2009, 123; our emphasis.

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1.4 A parallel story: a new kind of rhetoric It has been noted that Greek-style mathematical thinking, was influenced by political and legal rhetoric and procedure.44 Cuomo sees this as the crucial factor which separates Greek-style and non-Greek mathematics: “The public life and political circumstances of Athens and other contemporary Greek states [was] a fundamental factor in creating this difference.”45 In the spirit of these observations, we will temporarily shift our emphasis from mathematics to rhetoric, i.e. the medium in which the citizens of a Greek city-state expressed the need, when involved in debate, to “secure a demonstration that would silence the opposition once and for all.”46 It is this field, and more particularly in its forms related to judicial practice, that we find some of the first elements of the systematic thinking that was later called ‘logical’.47 The Greeks themselves were aware of the importance of rhetoric in the formation of their world, considering it their own invention. Isocrates wrote: ἐγγενομένου δ᾽ ἡμῖν τοῦ πείθειν ἀλλήλους καὶ δηλοῦν πρὸς ἡμᾶς αὐτοὺς περὶ ὧν ἂν βουληθῶμεν, οὐ μόνον τοῦ θηριωδῶς ζῆν ἀπηλλάγημεν, ἀλλὰ καὶ συνελθόντες πόλεις ᾠκίσαμεν καὶ νόμους ἐθέμεθα καὶ τέχνας εὕρομεν. Because we developed the possibility of persuading each other about what we want, not only have we got rid of a savage manner of life but, coming to live together, we have created cities, established laws and discovered arts and crafts.48

However, advanced forms of rhetoric existed in several other ancient cultures. Their differences from Greek rhetoric are worth examining. Mesopotamian scribes write persuasive texts to their sovereign “individually, massively and often,"49 in ways that demonstrate advanced rhetorical skills. Their arguments are mostly composed of exemplary or cautionary narratives, or direct appeals to older wisdom. This type of rhetoric, as that found in oral cultures, gains authority through constant appeal to established values, and thus fulfils a fundamentally conservative function.50 In Mesopotamia, we also find adversarial rhetoric, often in the form of the precedence poem, a verse composition in dialogi-

44 Lloyd 1990, 142. Burkert notes that the “Greek success” in intellectual matters “had to do with freedom – of enterprise, of speech, of imagination, even of religion … The polycentricity of the Greek world must have played its role, the rise of the polis, the political system without a dominating and suffocating central power, the openness for agonistic competition.”; Burkert 2004, 14 f. 45 Cuomo 2001, 4 f. 46 Lloyd 2002, 66. 47 See Asper 2004, 73–77, 88–91. 48 Isocrates, Antid. 15.254. 49 Sasson 1998, 458. 50 See Kennedy 1998, 78.

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cal form in which “the explicit issue is the precedence of one of the speakers over the other.”51 There exist three genres of adversarial literature in Sumerian: a) the dialogues, which are usually between master and student, mostly consisting of narrative material; b) the diatribes which are discourses in inventive invectives, threats and boasts, usually between women; and c) the disputations, the most artful of the three, in which one natural object or tool debates with another on their relative merits. These disputations are set in a purely ritualistic setting; if there is a judgment between the two sides, it is up to a “wise ruler”.52 However, these forms of rhetoric are literary artefacts: there is no forensic rhetoric in Mesopotamia. Trials are judged by a closed circle of powerful men, whose views are shaped by the evidence of oaths and ritual tests.53 Egyptian rhetoric is mostly aimed at the preservation of Ma’at (“Order” or “divine justice”). It is guided by a fivefold canon: the value of silence; the art of knowing when to speak; the art of restraint and self-control; the canon of fluency; and the canon of truthfulness.54 Instruction in this kind of rhetoric teaches the speaker to speak in the service of the truth and to be aware of the temperament and ethos, i.e. character, likes and dislikes, of the person whom he seeks to persuade. This pair of central values is also present in Hebrew rhetoric, as expressed most clearly in the Biblical Proverbs. When the art of speaking is discussed in these, it is as a rule to warn against its misuses, i.e. lying or flattery.55 In the Hebraic view, the emphasis is on the rhetorical act of the listener, who must beware to distinguish true from false words. Indicative of this attitude is the fact that in Hebrew there is no transitive verb with the meaning “to persuade someone,” and persuasion always has a negative sense, as in trickery, or extortion.56 In all theses cases of ancient rhetoric, the most crucial aspect of the rhetorical art is the knowledge of the ethos of the person to whom it is addressed. The same is largely true in the case of Chinese rhetoric. In the Hanfeizi, the closest we have to a rhetorical treatise in ancient China, Han Fei writes: “As a whole, the difficulties in the way of persuasion lie in my knowing the heart of the persuaded in order thereby to fit my wording into it.”57 Arguably, Greek orators are also concerned with the attitudes of their audience; but as this is a collective entity, a jury or the whole dēmos rather than an individual, the appeal is essentially to collective attitudes, which are really functioning as principles, and thus play the role of major premises, often expressed in maxims or gnōmai.58 51 Alster 1990, 2. 52 See Hallo 2004, 29 f. 53 See Kennedy 1998, 120. 54 See Kennedy 1998, 59; Fox 1983, 13–16. 55 See Kennedy 1998, 134. 56 The only related verb patâ, which is not intransitive, has the negative sense of persuasion as deception; see Zulick 1992, 367–377. 57 Liao 1959, 106. 58 Aristotle, Rhet. 1394a26–27.

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Chinese rhetoric is also dissimilar from Greek, in not putting much emphasis on logical argument. Hall and Ames describe this clearly: “Throughout their history the Chinese have been more apt to argue along pathos- and ethos-based lines than to employ objective logos-style arguments.”59 Furthermore, when the latter are used they are mostly based on analogy, rather than deductive syllogisms. In fact, “the safest generalization concerning the rhetorical uses of language found in classical Chinese texts is that they involve ‘analogical reasoning’.”60 The ancient practice that comes closer to Greek rhetoric, both in its adversarial nature and the use of logos-type arguments, is the Chinese ming bian, from ming (naming), bian (distinction, argumentation).61 In this, we find a concern with logical methodology,62 as well as use of the enthymeme, Aristotle’s “rhetorical syllogism.”63 However, the logical arguments in ming bian are not as prevalent as in Greek rhetoric. The most sophisticated samples of these are in dialogues, in which a ruler and a scholar, or two scholars, are trying to establish the best interpretation of certain general principles, according to the rules and narratives of tradition.64 This kind of rhetorical opposition is less reminiscent of the verbal combats we find in Greek rhetoric and more of theoretical philosophical debate. The generality and abstractness of the issues argued about, as well as the immovable bounds of an encasing, traditional cosmology in which the discussion occurs, make this kind of confrontation seem either like a rarefied intellectual game of high wits or, more usually, a collaborative effort of two intellectuals for a common understanding, through appeal to the authority of tradition. Or, as Lloyd puts it, in the Chinese case we have “not logos, but the Dao.”65 Working from the Daoist principle of non-contention, Chinese ming bian “seems to offer a spirit of cooperation and compromise, while Greek rhetoric appears relatively confrontational and antagonistic.”66 Seen thus, the most characteristic aspect of Greek adversarial rhetoric is that, while non-Greek forms consist of relative evaluations of abstract entities, the Greek speeches are battles of conflicting narrative interpretations of reality, in which

59 Hall & Ames 1998, 135. The reference is to Aristotle’s three types of argument, i.e. pathos (emotions), ethos (character), and logos; Aristotle, Rhet. 1355b35–1356a23. 60 Hall & Ames 1998, 137. This reflects a prevailing underlying doctrine of analogies. The answer of Dong Zhongshu (197–107 ) to Emperor Wu’s inquiries on ruling the empire, are based on the premise that “the Way of Heaven (the universe) does not change; therefore, the Way of the ancients can be studied and restored in the present human society.” This principle largely shapes the Chinese view of rhetoric (quoted in You & Liu 2009, 47). 61 Xing Lu 1998, 40. 62 The philosopher Xunzi was interested in, and applied, the logical methodology, including coherence and proofs; see Xing Lu 1998, 296. 63 You & Liu 2009, 47. 64 For example, see You & Liu 2009, 44. 65 Lloyd 1996, 227. 66 Lu 1998, 300.

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“sentence clashed against sentence.”67 Greek adversarial rhetoric is a zero-sum game, where winner takes all,68 a view also supported by Kennedy, who concludes his comparative study of ancient rhetorical traditions by saying that “it was the needs of the democratic law courts in Greece that created the discipline of rhetoric as taught and practiced in the West.”69 The fact that the participants in these verbal combats are fighting – often quite literally – for their lives, and not in defence of some abstract intellectual principle, is crucial:70 this was not an art to be taken lightly, to be left to chance, or the inspiration of the moment. It was not a job for well-meaning amateurs, but trained experts in public speaking.71 In fact, from the first appearance of rhetoric as a distinct discipline, early in the fifth century , there appear manuals (tekhnai), either as theoretical treatises, the most famous of which is Aristotle’s Rhetoric, or collections of model speeches.72 Our brief examination agrees with the conclusion of Zulick: The Greek elevation and rationalization of rhetoric cannot be considered a universal norm … Instead, it is a particular development in a small society at a certain point in history; a development that needs to be heard again with newly estranged ears.73

This estrangement leads us to identify the following distinctive characteristics of the Greek forensic speech:74 a) it puts forth a particular narrative as a depiction of a sequence of allegedly real events, as a rule narrated in the form that best suits the speaker’s aims; 75 b) because it is delivered in a zero-sum agonistic environment, it has to take into account, at every point, possible serious objections76; c) the effec-

67 Burkert 2004, 15. 68 “[The Greek]‘contest-system’ in its purest forms (e.g., war or athletics), is a ‘zero-sum’ game, in which one person can only win if another, or several others, lose.” (Griffith 1990, 188.) 69 Kennedy 1998, 208–230. 70 In most Greek courtrooms – usually the reference is to Attic trials – a defendant had to present his case against that of a prosecutor, fighting for his material well-being, right of citizenship, or, often, life. But even in the case of the political assembly, one of the most often-debated issues was whether the polis should go to war or not. The fact that most of the persons who took this decision would also, in the event they decided to go, be doing the actual fighting – and thus often the dying – themselves, made these discussions anything but “mere rhetoric”. 71 Though a defendant would actually speak his own speech, this was as a rule written by a logographos, an expert speechwriter: Kennedy 1963, 127–129. 72 Cole 1991, 22–27; 81 f. Chinese rhetoric, on the contrary, was “not as well established and systematized”, Lu 1998, 302. 73 Zulick 1992, 379. 74 Apart from the forensic, there are also two other genres of Greek rhetoric, the epideictic and the deliberative or political; Aristotle, Rhet. 1358a36 75 This also applies to political rhetoric, whose speeches concern what we can call “narratives of the future”, i.e. scenarios for future events that may result from the application of particular plans or policies, expressed in a language with a strong narrative element. 76 See Gagarin 2001, 283.

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tiveness of a speech is determined by the vote of a large number of citizens;77 thus, there is no consideration of the particular whims or preferences of any one person, and so less of a reliance on what the individual listener thinks – though the speaker definitely acknowledges and plays up to his audience’s collective prejudices; d) speakers work on the assumption that words have specific, fixed meanings, which they refer to – though of course opposed speakers often disagree on what these meanings are;78 e) the speaker considers certain general principles as given, either in written (laws) or unwritten (gnōmai) form ; f) because of the civic needs that produce them, there are great numbers of speeches produced, making standardization necessary; though in a forensic trial the defence speeches are spoken by the defendant, these are as a rule written beforehand by people of some expertise and training, working inside a developing, self-reflexive practice, which is taught, discussed, and thus in constant development.79

2 The form of geometric and rhetorical demonstration 2.1 Geometric deduction: the internal scheme Euclid’s phrase, “ what it was required to prove” – more famous in its Latin form, quod erat demonstrandum – is present in every proved proposition in the Elements, marking the end of the deductive process. It is also a strong indicator of a fixed internal structure of the Euclidean propositions. According to Proclus’ well-known account, every complete geometrical proposition contains the following six elements:80

77 It is a distinctive characteristic of Greek culture, that already from the early Archaic Age, and possibly as early as the Bronze Age, the right to public speaking and civic decision-making processes was often not restricted to members of ruling elites but extended to common citizens. On the basis of written evidence from Dreros and elsewhere, Gagarin argues that–already from the 7th century , and maybe earlier–it was the people of a city-state, and not a god or despot, who were the formative power in the creation of laws (Gagarin 2008, 88–90.) Also, in a personal communication, Gagarin makes the important point that it is precisely this collective participation in civic decision-making – a more general condition that the existence in a polis of the political system of democracy, in the form it took in 5th century  Athens – that marks the crucial distinction of the Greek world, from earlier cultures. 78 This fixed sense of words does not exist in Chinese rhetoric, or culture; on the contrary, classical commentators “focus their interest on how a living item discloses its meaning within its various contexts, rather than assuming that terms have some univocal, essential meaning independent of how they are used.” (Hall & Ames 1998, 142.) 79 For some of these characteristics, see Asper 2004, 73–94. 80 Proclus, In Eucl. 203–204.23.

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1) The enunciation (protasis) states what is given and what is sought from it. 2) The setting-out (ekthesis) repeats and specifies what is given. 3) The specification (dihorismos) repeats the particular thing which is sought in a form consistent with the setting-out. 4) The construction (kataskeuē) adds new data, which shall be used in the process of finding what is sought. 5) The proof (apodeixis) draws the required inference by reasoning from acknowledged facts. 6) Finally, the conclusion (sumperasma) reverts to the enunciation, confirming what has been demonstrated.

Applying the scheme to proposition I 7 of Euclid’s Elements, we get: Enunciation: Given two straight lines constructed on a straight line and meeting in a point, there cannot be constructed on the same straight line, and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that which has the same extremities with it. Setting-out: For, if possible, given two straight lines ΑC, CΒ constructed on the straight line AB and meeting at the point C, let two other straight lines ΑD, DΒ be constructed on the same straight line AB, on the same side of it, meeting in another point D, and equal to the former two respectively, namely each to that which has the same extremity with it, so, that CΑ is equal to DΑ which has the same extremity A with it, and CΒ to DΒ which has the same extremity Β with it; Specification: [In this case, the specification is already mentioned in the setting-out. Via the reduction to the absurd, Euclid will show that the previous statement is not possible] Construction:

Fig. 4: Τhe diagram, accompanying the proof of Proposition I.7 of Euclid’s Elements, of the construction of a hypothetical second triangle, ADB, on AB, with the same side lengths as the given, ACB.

[A]nd let CD be joined. Proof: Then, since AC is equal to AD, the angle ACD is also equal to the angle ADC; therefore the angle ADC is greater than the angle DCB; therefore the angle CDB is much greater than the

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angle DCB. Again since CB is equal to DB, the angle CDB is also equal to the angle DCB. But it was also proved much greater than it: which is impossible. Conclusion: Therefore, given two straight lines constructed on a straight line and meeting in a point, there cannot be constructed on the same straight line, and on the same side of it, two other straight lines meeting in another point and equal to the former two respectively, namely each to that which has the same extremities with it.

Up to the 1990’s, Proclus’ description was thought to adequately describe Euclid’s mathematical practice in the Elements.81 However, this idea has been recently challenged by Reviel Netz, who argues that the internal scheme was a later formalisation, perhaps even by Proclus himself.82 This conclusion is mostly based on the view that Proclus’ account is the only one describing the internal scheme, as well as on the observation that, especially in the case of problems, the scheme fails to fit Euclid’s practice.83 This is partly right; arguably, Proclus was an influential systemiser and we owe a part of our contemporary image of the Elements to his own work.84 Nevertheless, Proclus’ account of the scheme is not unique; in fact, there are three additional ancient sources on the subject, which offer support to the view that the scheme is Euclidean.85 The oldest of these testimonies is that of Hero, written approximately four centuries before Proclus, and thus much closer to Euclid’s time. His description gives a better fit to Euclid’s practice: while Proclus assures the reader that the scheme he describes characterizes all geometrical propositions,86 Hero claims it is only applicable to theorems and not problems.87 The following table, which is based on Book II of the Elements, substantiates Hero’s 81 For the traditional point of view, see Heath 1956, 29–131. 82 See especially Netz 1998; 1999a; 1999b. 83 See Netz 1999b, 289–95. 84 For the possible influence of later scholars on early Greek mathematical texts see Netz 1998. 85 Hero, Def. 137.1.1. Knorr 1993 argued that Definitiones was written by Diophantus; see also Heath 1921, 314–318. Besides Proclus’ and Hero’s testimonies, we have two references concerning the internal structure of the geometrical proposition, both dating from the 10th century , as scholia to the Elements by unknown authors (see Euclid: Heiberg & Stamatis 1977, vii–xiii, 74.) For a detailed discussion, see Sialaros 2012, 204–25. 86 Proclus, In Eucl. 77.7. 87 Hero Def. 137.1.1. Problems deal with the generation, division, subtraction or addition of figures, and generally the changes which are brought about in them. Their aim is to construct something which, in a way, did not previously exist, as for example: “To inscribe an equilateral triangle in a circle”. Theorems aim at establishing the truth of a proposition about a given figure; for example: “In an isosceles triangle the angles at the base are equal”; see Proclus, In Eucl. 79.20–26, and Pappus, Coll. 650.14–20. Arguably, Euclid was aware of this distinction. This is supported by the way in which he chooses to end his proofs. In theorems, he writes “ what it was required to prove”, while in problems, “ what it was required to do”; see also Proclus, In Eucl. 81.5, 210.616, 233.112. There is no doubt that Hero’s omission of problems in Def. 137.3 (Hero: Heiberg, 156) was intentional: a few lines after the presentation of the scheme, he writes: “… in geometry, on the other side, the proposition is conceived either as a problem or as a theorem.” (…ἐν δὲ τῇ γεωμετρίᾳ ἡ πρότασις ἢ ὡς πρόβλημα ἢ ὡς θεώρημα λαμβάνεται.)

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claim: Euclid caps all theorems with general conclusions, while problems end with the proof part, and the specific conclusion internal to it, stated only with reference to the required construction:88

Fig. 5: A table showing the existence, or not, of the six constituents of Proclus’ formalization of the internal scheme of a theorem, in each proposition of Book II of Euclid’s Elements.

The comparison of Hero’s and Proclus’ descriptions shows that Hero describes Euclid’s practice more accurately, providing a strong argument that the scheme was there at least as early as Hero’s time, i.e. the first century . But even the earliest complete Greek mathematical text we possess, Autolycus’ On the Moving Sphere, has marked similarities with the Euclidean pattern. Though the enunciation is not repeated at the end of his propositions, as in the theorems of the Elements, their structure presents great similarities to the Euclidean problems: they contain an enunciation, a setting-out, a specification, a construction accompanied by the relevant diagram, and a proof, which ends in a sentence with a specific conclusion. Moreover, the same linguistic formulae that are used in Euclid to denote the internal division are present in Autolycus, as for example the words estō (“let there be”) to denote the beginning of the setting-out, and legō (“I say”) for the specification. This is the third proposition of Autolycus’ treatise: Enunciation: If a sphere, by rotating uniformly around her own axis, makes some points go through the circumferences of the parallel circle as it moves in equal times, those are similar.

88 Space does not allow us to present here an analysis for all propositions in the Elements. Some small variations do appear in other books; these however, are to such a small extent that the existence of a general scheme cannot be questioned; for a similar point of view, see Netz 1999b, 302.

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Setting-out: Let there be a sphere with AB as axis, and points A, B the poles. And let there be taken some points on the surface of the sphere, C D, and let CE, DF be parallel circles, along which the points C D move; and in equal time the point C travels along the circumference CE, and the point D the circumference DF. Specification: I say that the circumference CE is similar to the circumference DF. Construction:

Fig. 6: The diagram of the proposed construction in the proof of Proposition 3 of Autolycus’ On the Moving Sphere.

Proof: Because, if the circumference CE is not similar to DF, let the CE be similar to the DG. Therefore, in equal times, the point C travels along the circumference CE and the point D DG; but also in equal time the C travels along CE, and the D DF. Therefore, in equal times, the D travels along DF and D DG; and they belong to same circle. Therefore DG is equal to DF, the smaller to the larger, which is impossible. Therefore, CE is not similar to DG. Similarly, we may prove that no other is, except DF. Therefore, the circumference CE is similar to DF.89

Simplicius writes90 that he copies Hippocrates’ squaring of the lunes (ca 430 ) from Eudemus’ History of Geometry (ca 330 ), whose text was extant in his days, but is no longer.91 Simplicius remarks that Eudemus wrote in the “archaic style” (archaïkon ēthos), which he describes as hypomnēmatikon, i.e. “sketchy” or in the “way of an aide-memoire”. Nevertheless, he adds that he has amended this proof with comments from Euclid, to make it more amenable to his (contemporary) reader. From this we may infer that there was a significant difference in the way Euclid and Eudemus used to present their results. Therefore, the style of proposi-

89 Autolycus, Sphaer. 3.1; translation and italicized headings are the authors’. 90 Simplicius, In Arist. Phys. 53.28–69.34. 91 Hippocrates is considered to be the first author who wrote Elements (Proclus, In Eucl. 66.8).

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tional exposition that is considered as characteristic of the Elements is at least as old as Euclid, and possibly even older than the work of Autolycus.92

2.2 The standard form of the forensic speech Being as central as it was to various aspects of the life of the classical Greek polis, rhetoric can be – and has been – examined from many different points of view, without any one of them being necessarily more privileged than another; rather, each one adds a new dimension to our understanding. Our own discussion of the Greek forensic speech shall adopt a new viewpoint, the rationale of which is contained in the conclusions of section 1.4, on what we identify as perhaps its most important characteristic: it is a technique of supporting the validity of a particular narrative as an accurate representation of reality, and defending it against another, contesting one. Already by the middle of the fifth century , we find in the works of Gorgias, Antiphon and Lysias (450–400 ) strong structural similarities, that suggest an underlying generic template for the forensic speech.93 However, especially at this early age, this template must be thought of as an all-purpose, adaptable set of general guidelines, rather than a rigid structure. The establishment of a clear, standard form for the forensic speech does not come until later, in Aristotle’s Rhetoric.94 The attempt to find this exact form in earlier speeches yields only partial results: some speeches conform more and some less to various parts of it.95 Yet, as our main purpose for studying rhetoric in this essay is the investigation of its influence on mathematical thinking, and as the crystallization of a standard form, or internal scheme, for mathematical theorems does not come until after Aristotle, his formalization of the standard form of the forensic speech in the Rhetoric is particularly germane to our argument: this standard form was available to mathematicians at the time of the appearance of the internal scheme of the mathematical theorems. We propose that many of the elements employed in the forensic speech – for clarity, we use the description of its part as they appear in the Aristotelian formalization – can be best explained as adaptation of patterns and figures that

92 Cuomo points to the existence of a community of mathematicians who shared a specialized language, discursive conventions and criteria of validity and rigor; see Cuomo 2001, 136. Netz supports that by around 360 , much of Greek mathematics was articulated in the Euclidean style; see Netz 1999a, 275. Karasmanis maintains that plane geometry had already acquired an axiomatic form in Plato’s times; see Karasmanis 1990, 122. 93 Such templates are first discussed in Plato, Phaedrus 266c, 366d. 94 Aristotle, Rhet. 1414b. 95 We are grateful to Michael Gagarin for stressing the importance of this point (private communication) and guiding us to the work of Carey 1996, 33–46.

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had already been in use, for centuries, in Greek poetry. We shall discuss these for each of the speech’s four parts, as follows: a. Apart from appeals to the jurors’ feelings, the introduction (prooimion) puts forth the gist of the case, both in terms of what actually happened and its legal meaning – in the sense of identifying the laws according to which the action should be judged. For example, in the introduction to Lysias’ On the Murder of Eratosthenes, the defendant first outlines his story: he killed Eratosthenes catching him in flagrante delicto with his wife. He then states the legal meaning of his action: the punishment for adultery being, by Athenian law, death, he actually did the state a favor by killing Eratosthenes.96 This double function of the introduction is in direct accordance with common poetic practice in archaic poetry: in its most famous examples, the Iliad and the Odyssey, the opening verses outline both the story and its meaning.97 b. In the narration (dihēgēsis or prothesis), the speaker states his version of the story, and prompts witnesses to support it with their statements. Thus, the narration is the most crucial part of the process of persuasion.98 The plain style of its prose creates an illusion of total artlessness and, thus, truthfulness. In Isocrates’ words: “Orators … must use with precision only words in current use and only such ideas as bear upon the actual facts”.99 c. The pistis part of the speech consists of the nonartistic (atekhnoi) and the artistic (entekhnoi) pisteis.100 The nonartistic owe their name to the fact that they are not created by the speaker, but imported from the outside world. They include witnesses’ statements – under oath for free citizens, or torture, for slaves – contracts, or even the relevant laws. In a classical trial, all of these

96 Lysias, Caed. Erat. 92.4. In a personal communication, Spatharas notes that the more usual punishment for adultery, by Athenian law, was incarceration; the speaker in this case opts for the more extreme option however, turning in effect from defendant to prosecutor. 97 Homer, Il. I 1–5; Od. I 1–10. This device, already recognized by Hellenistic scholars and termed proanaphōnēsis, appears extensively in epic (Duckworth 1931, 320) but also in archaic lyric poetry (Griffith 1993, 64 f.). 98 Quintilian argued that narration is essentially another form of proof (Inst. IV 2.31); for an extensive discussion of his view see O’Banion 1992, 76–103. On the importance of storytelling as a tool for demonstration in Athenian courts, see also Gagarin 2003, 206f. For a more extended discussions of narrative in modern legal practice, see Amsterdam & Bruner 2001; Brooks & Gewirtz 1996; White 1985. 99 Isocrates, Evagoras 10: τοῖς δὲ περὶ τοὺς λόγους … ἀποτόμως καὶ τῶν ὀνομάτων τοῖς πολιτικοῖς μόνον καὶ τῶν ἐνθυμημάτων τοῖς περὶ αὐτὰς τὰς πράξεις ἀναγκαῖόν ἐστι χρῆσθαι. Translation by La Rue Van Hook 1945. 100 In Rhet. 1355b35–1356a23, Aristotle identifies three types of pisteis, ethos (character),pathos (emotions), and logos. We follow the practice of Kennedy 2007, 31, and Gagarin 1990, 24, in using the word pistis in its original form, rather than translating it as “proof”. To avoid confusion, it is good to remember that pistis means both the whole part of the speech, and parts of it; thus one can refer to “the” pistis, but also “a” pistis inside it. For a discussion of meaning of the notion of pistis, see Kennedy 1980, 68 f.

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were encased in a litigant’s speech, presented at various points at which he would interrupt, to put forth the appropriate pistis. The artistic pisteis, on the other hand, are arguments invented by the speaker, usually in the generic form “the reason why X and not Y happened is.”101 These can be either: a) counternarratives, i.e. alternative versions of the events in question which an orator discredits, to defend his own,102 or b) sub-narratives, i.e. variations on the main story generated by delving into motive.103 The distinction between arguments aiming at the events themselves, and those aiming at their motives, are known to orators already at the time of Antiphon, and marked in Greek rhetorical theory as staseis.104 It is in this way that the trial can be understood as a contest of narratives: each litigant is proposing his narration as true, and then creating counter- and subnarratives to it, to defend it against his opponent’s possible attacks, or the jurors’ possible doubts, derived from an intuitive application of narrative probability. In this sense, the purpose of the pistis is to identify the contestable parts of a speaker’s narrative and invalidate possible objections. The identification is performed in a procedure called the division (diairesis).105 There is a strong poetic antecedent for diairesis, going all the way back to Homer, in the poetic figure of the priamel.106 Fraenkel defines this as “a series of detached statements which through contrast or comparison lead up to the idea with which the speaker is primarily concerned”,107 and Bundy calls it “perhaps the most important structural 101 In this case, X is either the whole or a part of the speaker’s narrative, and the various Ys are variations of it. 102 For example, in Antiphon’s First Tetralogy 115.4, the prosecutor puts forth the case that the accused murdered the victim because the former owed some money. The murder occurred in a secluded spot, late at night, with no witnesses. As part of his argument, the prosecutor suggests that an alternative counter-narrative, i.e. the murder could have been committed by robbers, does not stand to reason, as the dead man had not been robbed. 103 In the form “you say that A did this for X reason, but I say that it was for Y reason.” For example, in Lysias’ Caed. Erat. 95.37–42, the defendant says that it could be suggested that he did not kill Eratosthenes catching him accidentally in flagrante delicto with his wife, but that he had planned the crime because of a previously existing grudge, arranging for a servant girl to call the victim to his house, so that he could stage this “surprise” discovery. The defendant then attacks this version of the story. 104 Gagarin 2002, 108. 105 Aristotle (Rhet. 1398a) mentions division as a standard form of rhetorical procedure. The various counter- and sub-narratives could either be listed in sequence and then dealt with one by one (as in Gorgias’ Enc. 11.6), or be presented, and then refuted, separately (as in Antiphon’s First Tetralogy 115.4). 106 For a detailed analysis of the priamel in Greek literature see Race 1982, 31–111, and Johansen 1959, 16–49. Diairesis appears also in philosophical arguments. In the Phaedrus 266b, Socrates declares that he is “a lover of these divisions (dihaireseis) and collections (sunagōgai)”, in fact calling those who are proficient in this process “experts in dialectic”; translation by Rowe 1986. 107 Fraenkel 1950, 407 f.

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principle known to choral poetry”.108 There are numerous variations of priamel in classical Greek literature. One of these is particularly interesting: an ordered set of items is presented, “in which the final term’s superiority is assumed from the beginning and a series of negative comparisons leads up to it.”109 In fact, the varieties of priamel cover both of the more characteristic forms of dihairesis: those in which an eventuality is broken down in its alternatives – of which only one is shown to be true – and those in which all possible alternatives – more than one of which can be true – are examined separately.110 d. According to Aristotle, the epilogue (epilogos) is aimed at four things: “[D]isposing the hearer favorably towards the speaker and unfavorably towards the opponent; amplifying and minimizing; moving the hearer towards emotional reactions (pathē); and to remind”.111 The first and the third are addressed to the emotions. But the second and fourth are related to the events and arguments in the speech, and thus refer back to the narration and the pistis. The speech will often end with a gnōmē, i.e. a maxim that expresses a general principle, either an actual proverb, or a proverb-like invention of the speaker. This is also in direct accordance with poetic practice.112

2.3 A comparison of the internal scheme and the standard form Taking into account the fact that the content of mathematics facilitates clearer form, less uncertainty and more rigorous arguments, there are strong similarities, in both form and function, in the internal structure of a mathematical proposition and the standard form of a forensic speech. In a sense, the former is a purer, more distilled form of the latter. Comparing by part: The introduction (of a forensic speech) sets out what is to be proved, both in concrete form (what happened) and general principle (what law applies); in this

108 Bundy 1962, 5. For a similar point of view, see Race 1982, 54–73. 109 See Race 1982, 33, and Bergmann 1868, 7. Notice the priamel structure in Antiphon’s First Tetralogy: the speaker details the versions of event which could not have happened (115.4) and concludes: “As all grounds for suspecting that the crime was unpremeditated are removed, it is clear from the circumstances of death themselves that the victim was deliberately murdered.” (115.5: “ἀπολυομένης δὲ τῆς ὑποψίας ἁπάσης αὐτὸς ὁ θάνατος ἐξ ἐπιβουλῆς ἀποθανόντα μηνύει αὐτόν.”) 110 The second case is analogous to those uses of priamel which are not antithetical. For example, see Gorgias’ discussion of Helen’s motives in his Encomium of Helen, where various motives are considered as possibilities, and each one is separately dealt with. A longer discussion of the priamel as a model for division can be found in Doxiadis 2012. 111 Aristotle, Rhet. III 19.1419b10–13: “ἐκ τε τοῦ πρὸς ἑαυτὸν κατασκευάσαι εὖ τὸν ἀκροατὴν καὶ τὸν ἐναντίον φαύλως, καὶ ἐκ τοῦ ἀυξῆσαι καὶ ταπεινῶσαι, καὶ ἐκ τοῦ εἰς τὰ πάθη τὸν ἀκροατὴν καταστῆσαι, καὶ ἐξ ἀναμνήσεως.” 112 For this device in Pindar, see Griffith 1993, 615.

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sense, it has a similar function to the first three parts of the mathematical internal scheme, enunciation, setting-out and specification: the first expounds the general proposition, the second defines the particular case under investigation, and the third repeats what is sought in a form consistent with the second. So, in both cases, the general law (rhetoric) or proposition (geometry) is applied to the particular case under investigation. The narration is analogous to the construction: the main task of the former is to provide the ground for the pistis, i.e. the concrete terms on which the deductive arguments will operate; the construction functions in a similar way, providing the material for the proof.113 It is true that some mathematical propositions may not require construction if the necessary material is already provided by the setting-out and the specification; in a similar way, however, forensic speeches that deal with famous cases, viz. those whose facts are considered already known, do not contain a narration: for example, there is no need for Gorgias to repeat the story of the Trojan War in his Encomium of Helen.114 Perhaps the most significant similarity between the standard form of a forensic speech and the internal scheme of a mathematical proposition is that between the pistis (speech) and the proof (proposition). We have already mentioned that division organizes the pistis; the proof is constructed on the same principle. As there are sub- and counter-narratives in the former, so there are counter- and sub-propositions in the latter: the proof either breaks down a proposition into various subcases, which are then proved one by one, or offers possible counter-truths, which are then disproved, establishing the truth of the proposition. For example, see how Archimedes tried to measure the circle: in order to prove that the area of a circle is equal to a right-angled triangle, one of the sides subtending the right angle of which is equal to the radius, and the other to the circumference of the circle, he proved that the area cannot be either greater, or smaller.115 This is a similar process to the one offered in Antiphon’s First Tetralogy.116 Another similarity lies in the equivalence of the relationship of the nonartistic pisteis to the artistic, in the proof

113 Proclus, In Eucl. 203.17. 114 Both narration and construction are modes of speech that in their basic form consist of action and state-of-affairs phrases, the latter referring to the same world of primary objects in which the action which the former describe occurs. This is in contrast to the theoretical mode, in which general principles or maxims play a bigger part – though such phrases may also appear, albeit in small doses, in narratives. This observation may also go some way towards explaining the fact that the same form of analysis can be applied to both forensic speeches and geometric propositions: the processes, which define their objects, i.e. narrative, and construction, respectively, are so similar, both consisting of action and state-of-affairs sentences, with a small dose of general principles. For a more detailed discussion of phrase types and phrase connections in narrative, see Doxiadis 2010; for their use in geometric propositions, see Doxiadis 2011. 115 Archimedes, Dim. circ. 1.138.5–1.139.4. 116 Antiphon, First Tetralogy 115.4. All other possible scenarios (counter-narratives) are stated, and then discarded one by one.

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of a mathematical proposition: like the rhetor, the mathematician both imports arguments such as definitions, common notions, postulates or previously proven propositions, into his proof, and invents his own. Finally, the conclusion of a theorem repeats the enunciation, in exact analogy of the way in which the epilogue of a forensic speech repeats the premises set out in the introduction. The repetition of the beginning at the ending is an elementary form of ring-composition, also an old trick of epic and lyric poetry. Referring to Greek literature, Fowler writes: In a narrative composition, where the structure of the tale often makes the end apparent, repetition [of beginning at the end] is not always found; but in two circumstances it is virtually unavoidable. The first occurs when some thesis is to be argued. The speaker states what will be proved (the heading), then presents arguments and naturally ends by repeating the opening statement as the conclusion (“QED”). The second is found when the discourse forms a digression within a larger whole.117

This is precisely the way in which this technique operates in both the standard form of the forensic speech and the internal scheme of the proposition: as a mechanism for arguing a thesis, by repeating the beginning at the end.118 However, if we are right to believe that construction (in geometry) functions similarly to narration (in rhetoric), then a repetition of the initial statement at the end is not required in the cases of problems – i.e. the types of propositions in which the aim is a construction – being analogous to the cases which Fowler describes, for poetry, in which “the structure of the tale often makes the end apparent”. This is exactly the same as we find in Greek-style proofs: unlike theorems, problems in Euclid do not repeat the enunciation at the end.119 In conclusion, we have shown that the internal scheme of the mathematical proposition and the standard form of the forensic speech present strong structural similarities. Though the emergence of both within a span of a few decades, in the fifth century , is an indication of possible influence, of either one on the other, the lack of texts from the earlier period of Greek-style mathematics makes it difficult to probe seriously into the issue of its extent or direction – from rhetoric to mathematics or the other way round. Nevertheless, as both forensic speeches and – to the extent that they are similar – mathematical propositions also share structural characteristics with a much older art, i.e. poetry, we think that conscious or unconscious influence on rhetoric and/or mathematics from that direction is very probable. Although we do not claim that the birth of Greek forensic rhetoric or Greek-style mathematics can be explained away by the influence of poetry, we do feel that the similarities indicate that poetry provided cognitive material which 117 Fowler 1987, 62. Ring-composition can also be much more complex, as discussed below. 118 That the repetition of the enunciation in the conclusion is a simple form of ring-composition has also been stated by Netz 2009, 124. 119 See Figure 5 and the related discussion.

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both made use of. This becomes more apparent when we look the microstructure of the forensic speech and the mathematical proposition, where more similarities with poetic technique become apparent. These we examine in the next section.

3 Poetic form as a way of thought 3.1 Chiasmus and ring-composition Bassett observes that poetic style was in many ways a model for rhetoric,120 and we have already seen elements of this in the use of priamel and proanaphōnēsis. We shall argue that Greek rhetors made extensive use of chiasmus (Χ) and ringcomposition (RC), two techniques widely used in archaic poetry.121 Before we proceed to our analysis we need to briefly introduce the basic concepts. Chiasmus (X) and ring-composition (RC)122 are symmetrical structures of phrases in the form ABB*A* (X) and ABCB*A* (RC), where B* and A* are similar to B and A.123 The similarity may be in the exact repetition, of words, phrases or thematic keys of A and B, either in the original form or the exact opposite, e.g. “night” in N* for “day” in N. We shall use the term pivot for the repeated element determining the similarity in a N-N* pair of X/RC.124 X/RC’s can be of arbitrary length, i.e. A1 A2 … AN A*N … A*2 A*1 (X), and A1 A2… AN …A*2 A*1 (RC). Moreover, RC’s can also be manytiered, with an element of Ai breaking down into further RCs, as Ai1 Ai2 Ai3… AiN … A*i3 A*i2 A*i1. The prevalence of X/RC in the Homeric epics is sometimes attributed to its power as mnemonic device.125 As memory – and thus also mnemotechnics –

120 Bassett 1920, 59. 121 It is quite possible that these figures were imported into the Greek world from elsewhere as X/ RC exists in many other traditions (Douglas 2007, 1–16). X/RC is something of a cognitive universal, and various cultures “could not have all learned it from one another” (p. 12). However, the universality of a form does not explain any particular use of it. (Metaphor is also universal, but its particular form in Homeric similes has been given extensive attention by scholars.) Mere suspicion, or even proof, of “universality” does not give us any particular reason for why a form is used or not used, more or less so, by any particular author, in any particular context. This must be studied, and revealed, wherever and to whatever degree and form – X/RC’s have many – it exists. A great contemporary researcher of X/RC remarks: “Not all Classical [Greek] compositions use chiasmus to the same extent, and frequently it appears to be more a poetical device … than an independent structural principle of form.” (Welch 1981, 250.) 122 The term “chiasmus” is also used by some authors, especially older ones, to describe forms of RC. 123 This typographical convention for presenting the various elements of X/RC is quite standard, as are the graphic conventions we use in the diagrams below. 124 We use the notation X/RC when we are referring to arguments or facts which apply to both X and RC. 125 See van Groningen 1958, 85.

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is often structured on an inner, underlying spatial form, the existence of a goingthere-and-back model, as encapsulated in the ancient “art of memory” (tekhnē mnēmonikē)126 could be at the root of the cognitive logic of X/RC. (It is worth noting that recent evidence from the neurosciences points at the grounding of the ars memoria on the structure of the brain, and in particular a collaboration of the hippocampus and the entorhinal cortex.127 This could also be the basis for understanding the mnemotechnic power of X/RC.) This kind of spatially-based process would account for, among many other things, the common pattern in the epics, of a series of questions being answered in an exact reverse order, as Odysseus’ questions to his mother Anticleia in Hades:128

Fig. 7: A diagrammatic depiction of a long chiastic (X) structure from the Odyssey, in which Odysseus’ questions to his mother are answered in reverse order. Summarized in Reece 1995, 213; numbers refer to lines.

126 See Yates 1999, 18f. We think that an important piece of evidence on the conscious use of X/ RC is given in the discussion of the action- and place-determined form of memory in Aristotle’s Mem. 451b10–452a30. The last part of this (452a17–30) describes the form of the operation of memory in X/RC. The fact that Yates calls his example a “baffling series of letters” (p. 377) and refers the reader to Ross’s note (Ross 1931, footnotes 4–6 to 452a20–27), which attempts to give order to what baffles Yates. In fact, Ross’s explanations are equally baffling, and depend merely on his unwarranted assumption that this sequence refers to numbers: neither Yates nor Ross see the centre-focused structure of RC as an underlying principle in this. The bafflement of these two important scholars is an example of what Douglas 2007, x, observes: “Apparently, when Western scholars perceive the texts to be muddled … it is because they do not recognize the unfamiliar method of construction. [i.e. ring-composition].” 127 See Becchetti 2010, 104, as well as the research referred to, in Moser et al. 2008, 69–89. 128 Homer, Od. XI 171–203; the summary adapted from Reece 1995, 213.

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RC is more than mnemotechnics, however. Reece calls it “perhaps the most important structuring device of oral narrative, building bridges between the many components of the larger poem … weaving the digressionary material into the larger fabric of the narrative.” Though it may have begun as an unconscious mechanism and “survived for its mnemonic and tectonic value [it soon became] an aesthetic principle as well, becoming a desirable and expected pattern of oral narrative”.129 Bassett was the first to see in X/RC more than aesthetic value: “We … may ask how far the chiastic order was determined by … [the] arrangement of ideas … [along with] poetic economy and possibly the element of surprise which sharpens the attention of the listener … [Potentially relevant, too, is] the psychological factor, the advantage of using one idea to suggest another, and thus to make the thought continuous”.130 Friedrich proposes that X was an element of what he calls lyric epiphany and supports that it creates “an illusion … of a synchronic, monocular vision of an absolute aesthetic truth – usually with a radical closure”.131 Like a joke’s, the effect of an X is not reducible to the sum of its parts: when you try to explain it, you gain in clarity only what you lose in impact. In this way, though X/RC was possibly invented and survived for mnemotechnic use or its pleasing rhythm of symmetry, it was later used for its capacity to unite phrases that could not be directly connected with the rationale of putting sentences together with the aim of representing action. The way of employment of X/RC in the process of persuasion in rhetoric is governed by some recurring patterns, the most basic of which we propose to examine.

3.2 Ring composition as cognitive tool In epic poetry, a standard use for RC is the framing of a general rule, used as a guide to present action.132 The general rule is provided by a paradeigma, i.e. an exemplary narrative of past events – as a rule mythological. Here is an example: in the last book of the Iliad, Achilles addresses Priam, proposing that, though both are in mourning, they eat before they proceed with their discussion. He uses the mythological precedent of Niobe as model, placing it at the center of an RC.133 Because of its symmetry and emphasis on the centre, RC gives added importance to the mythological story, blending it with the present in a continuous and aesthetically pleasing way.

129 Reece 1995, 220. 130 Bassett 1920, 5. 131 Friedrich 2001, 218. 132 For an extended analysis see Willcock 1964, 141–154, Austin 1966, 295–312. 133 Homer, Il. XXIV 601–612. Condensed in Willcock 1964, 142.

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Fig. 8: A diagrammatic depiction of an RC structure in Book XXIV of the Iliad, centering on a paradeigma. The description of the structure is in Willcock 1964, 142; numbers denote lines.

Fifth-century rhetors used this and other forms of RC,134 both to support an injunction (expressed as an action-phrase) and to demonstrate the truth of an observation (expressed as a state-of-affairs phrase). The central element of the RC can still be a mini story, but it is often a general principle, law or gnōmē, as in the following example from Lysias’ On the Murder of Eratosthenes. Here, the defendant is using the fact that the punishment for adultery by Athenian law is death as an excuse for his act, implying that he has really done nothing more than give Eratosthenes his just reward:135

Fig. 9: An RC structure centering on a general maxim-like assertion, from Lysias’ On the Murder of Eratosthenes.

Here, the pair (1–1*) pivots on the importance of the laws for the defendant’s position: in (1) he states that he sees this, and in (1*) he asks them, the jurors, to

134 To our knowledge, Worthington is the only scholar who has stressed the possible importance of X/RC in the study of his ring-composition: “the implications of ring composition in oratory cannot be underrated” (1994, 116). His own study of RC in Deinarchus stresses one particular aspect of this importance, in its use as a sort of editing device, to give structure to a speech when it is written ‘for publication’, as it were, after its oral delivery. 135 Lysias, Caed. Erat. 95.34. Our bold-italics and underlining of the pivots. Bracketed phrases are added for clarity. Pelling (2000, pp. 220–223) rightly points out that the repetition of the laws by Lysias aids the sleight-of-hand whereby he moves from an argument along the lines of ‘the laws allow’ to one ‘of the laws instruct’. For an extended discussion, see also Herman 1993.

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also see it. In terms of information given, (2*) is mere repetition, and thus unnecessary in either a simple logical, or even narrative, sense: its presence is patterdetermined, i.e. has the aim to complete the RC, creating a continuous link from the defendant’s action to the court’s decision. In this way, it is not just the undeniable truth of (3) that makes the appeal (1*) much stronger than a mere “please acquit me”: persuasion is achieved also by the effect of the total pattern, through a form tried in poetry for its effectiveness in analogous cases.

3.3 Chiasmus as cognitive tool The RC pattern we just described is based on analogy, whereas the two basic structures for X-type arguments that follow depend on polarities.136 Of these, the first has a direct X structure, while the second builds on an underlying X, which is only partly expressed. For the former, we can take as an example how Gorgias, in the Encomium of Helen, disposes of the first possibility brought up in his division, i.e. that Helen’s abduction was decided by the gods.137 This passage seems ponderous and repetitious when read in its prose form, a typical example of the excessive style often called “Gorgianism”;138 however, it

Fig. 10: The X structure of an argument in Gorgias’ Encomium of Helen, centering on a central chiastic maxim-like statement (3–3*).

136 Lloyd 1966, 1–6ff. discusses analogy and polarity as two major conceptual categories of archaic thought, both having roots in mythology. 137 Gorgias, Hel. 11.6. Pelling (private communication) makes the additional point, that the emphasis on superior strength in the central pair (3–3*), also prepares for the stress on bia in the next phase of the argument, thus conveying more continuity and cohesion in the overall run of the argument. 138 Kennedy 1989, 184.

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becomes razor-sharp if we see it as the extended X it is. The first outer parallelism pivots on the contrasting elements, “responsible/not-responsible” in (1–1*), while the second on the repetition of “god” in (2–2*). At the centre of the X (3–3*) is a gnōmē that the audience can naturally accept as true, which is in itself in basic chiastic form (ABB*A*). This construction contains both action and state-of-affairs sentences. Sentences (2) and (3) begin with “for”, a conjunction connecting them to the previous phrases, (1) and (2), respectively. In this sense, one might see in (1–2-3) a series of rather abrupt deductions. But the argument does not end there: (2*) and (1*) follow, which are without such direct links, from (3) and (2*). Their presence can only be explained as pattern-dictated in order to complete the X. The importance of formal pattern over the underlying narrative is seen especially in (2*), which though redundant in the logical sense, provides the missing link in the formal pattern, giving us a strong argument that such seemingly ‘deductive’ constructs are in fact originally driven by the patterns of a poetic form. The second X-type construction in early rhetoric is guided by another form of polarity, i.e. contradiction, which was already, in the fifth century , an acknowledged indicator of falsity.139 The central quadruple of this X is formed by a pair of action phrases, the first two of which together form a hypothesis: “if a happens” completed by “then b happens.” The third element of the X is the negation of the second, a negation whose truth is substantiated either from the narration (“b did not happen”), or derived from narrative possibility (“b could not have happened”). The fourth element repeats the first, completing the X pattern symmetrically. In the following passage from Antiphon’s First Tetralogy,140 the prosecutor is trying to rule out one of the counter-narratives set out in the division, i.e. that malefactors (robbers) could have murdered the victim. The way this appears in the text is: Οὔτε γὰρ κακούργους εἰκὸς ἀποκτεῖναι τὸν ἄνθρωπον· οὐδεὶς γὰρ ἂν τὸν ἔσχατον κίνδυνον περὶ τῆς ψυχῆς κινδυνεύων ἑτοίμην καὶ κατειργασμένην τὴν ὠφέλειαν ἀφῆκεν· ἔχοντες γὰρ τὰ ἱμάτια ηὑρέθησαν. Malefactors are not likely to have murdered him, as nobody who was exposing his life to a very grave risk would forgo the prize when it was securely within his grasp; and the victims were found still wearing their cloaks.141

There is something unusual in this pattern: what would naturally be (1*), in a standard-form X, has been moved to the top, in the position of (1). But this does not change the underlying X pattern which is:

139 In Gorgias’ Pal. 11a25 the speaker states that Odysseus says enantiōtata (“totally opposed things”) about the defender; he presents this as tantamount to a proof that he is lying; see Spatharas 2001, 398 f. 140 115.4. 141 Translation by Lamb 1941, 55.

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Fig. 11: The underlying X structure of the argument in the previous quote from Antiphon’s First Tetralogy.

Yet the arrangement, as it occurs in the speech, takes the form (1*-1–2-2*), with (1*), the conclusion, at the top. To understand why this happens, let us write this argument as we would write it today in logical form, the arrows marking the links from one phrase to the next:

Fig. 12: The statements in the X structure in fig. 11 in their linear sequence.

Notice that links i and ii make linear sense, i.e. each one bringing the next, the first as the completion of a state-of-affairs sentence, with (2) completing (1), and the second as a formal transformation: (2*) can be seen as an anadiplōsis of (2), i.e. the rhetorical form in which the last element of a sentence is repeated at the start of the next.142 But link iii is not justified from the content of the previous phrase: there is no linear deduction from (2*) to (1*). On the contrary, this linking can be explained only if we map the implicational connections (in dotted arrows in fig. 13) in two dimensions, the reason being that we need more than one of the previous statements in order to arrive at (1*) as a conclusion. In other words, for the implication to hold we need links iv and v operating together.143 Though Gorgias’ actual text only states the four phrases in a certain sequential order, the diagram reveals the power of an X structure: it encodes information in a way that implies the non-linear connections with maximum economy. This also 142 This is also derived from poetry. For a discussion of its use in Attic tragedy, containing many references to earlier uses, see Hutchinson 2001, 427–438. 143 Aristotle explicitly points out the effectiveness of placing opposite things next one to the other, to point out their antithesis; Aristotle, Rhet. 1410a20–25.

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Fig. 13: A diagrammatic depiction of the non-linear relationships of the statements in the X structure in fig. 11.

shows the characteristic effect of the X, that it “tightens and closes; there is an element of inevitability as exit replays introitus”.144 This kind of X-based pattern becomes clearer in its longer versions. In Gorgias’ Defense of Palamedes, the mythological hero defends himself against Odysseus’ false accusation, viz. that he betrayed the Greeks to the Trojans, accepting a bribe from Priam. The speaker uses a sub-narrative, created with details culled from knowledge of the underlying myth, which he considers common knowledge. The argument, as it appears in the speech, is (1*-2–3-4–4*-5a-5b-5c). The last three negative action-phrases operate in parallel, each one giving added corroboration for (4*), the main negative statement:145

Fig. 14: The full X form of the argument discussed, from Gorgias’ Defense of Palamedes. Bracketed phrases do not appear in the text.

144 Friedrich 2001, 241. 145 Gorgias, Pal. 11a6.

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Similarly to the previous example, the X here starts with (1*), i.e. the negation of (1): “If I committed treason”. The X-type argument in the speech has the exact same form as the one referred-to in Fig. 11, only longer: (1*-2–3-4–4*). Here (1) and (3*-2*-1*) are omitted, while (5a–5c) in this case are outside the X structure, offering additional evidence for (4*). As mentioned earlier in relation to its use as mnemotechnics (see n. 125 and n. 126), chiastic thinking was pervasive in Greek culture. As Friedrich writes: “Chiasmus was sufficiently pervasive in Archaic Greece to warrant our speaking of a chiasmic mind, or mental set, or even worldview” (2001, 240).146 Greek thinkers were trained “to read from the center outward and from the extremities towards the center” (Breck 1994, 29).147 Even as students learning the alphabet, they were taught to recite it in serial order, from alpha to omega, and then “backwards, from omega to alpha, and then both ways at once, alpha-omega, beta-psi … (to) mu-nu (in the middle),” the latter being obviously an extended chiasmus (Marrou 1956, 151). A mind as trained in X/RC as the mind of an educated Greek in classical times was – can easily supply (3*-2*-1*) in Fig. 14 and effect closure, as (1–2-3–4) is a cascading pattern, each one an anadiplōsis: (1) “How could I commit treason?”; (2) “Treason begins with discussion;” (3) “Discussion presupposes a meeting.” The inner sequence (3–4-4*) gives a trained mind the clear hint of the standard-form ABB*A* chiasmus (3–4-4*-3*), somewhat a brief form of the longer Homeric one already presented.148 Once the X-structure of the argument has been established, the listener can easily fill it in for himself. We can give the second X-type argument the generic form (1*-2–3- … -N-N*), where (1) as well as the rest of the sequence (…-3*-2*-1*) is omitted. The lacunae existing in this pattern should not surprise us, nor do they go against the existence of an underlying structure: on the contrary, it is precisely the structure that makes room for them, without the listener getting lost. These omissions are in full accordance with the practice used in logos-type pisteis in rhetoric: obvious things are often left unsaid. Aristotle writes that in rhetoric “the conclusion must neither be drawn from too far back nor should it include all the steps of the argument”, for the first situation would “cause obscurity,” while the second “is simply a waste of words because it states much that is obvious”.149 This is in accordance with the enthymeme, and not the syllogism, being the prime means of logical persuasion in rhetoric:150 to be persuasive, a concatenation of phrases need only be complete enough to lead a listener to fill its inevitably many gaps on his own.

146 147 148 149 150

For an extensive discussion of this view, see McCoy 2003, 22–25. See also our earlier comments on Aristotle’s argument in Mem. 452a17–30. Homer, Od. XI 171–203; summarized in Reece 1995, 213. Aristotle, Rhet. 1395b. Aristotle, Rhet. 1354a-b.

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3.4 Chiasmus and ring-composition in Euclid In this section, we aim to show how Euclidean propositions, both theorems and problems, follow X/RC patterns.151 This is the first proposition of book I of the Elements, with its underlying form marked:

Fig. 15: The full RC form of Proposition I 1 of Euclid’s Elements.

Fig. 16: The diagram of the construction in Proposition I 1 of Euclid’s Elements.

151 For a longer discussion, with a more complete typology and examples, see Doxiadis 2012.

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The problem appears to be in a continuous, extended RC form: the outer coupling (1–1*) consists of the enunciation and the conclusion,152 the second couple (2– 2*) of the setting out-specification and the last statement of the proof, and the third couple (3–3*) functions inside the proof itself. The central sequence (4–5-4*) presents strong similarities with the use of paradeigma in rhetoric: a known truth is used or implied. This crucial link, upon which the deduction depends upon, is lodged in the middle of the RC. In the next example (Elem. I 2), we have a cascading argument that leads to a non-trivial deduction, which is placed at the centre. This proposition includes two pairs of outer RC’s (1–2-2*-1*), and then breaks down in various internal X’s and RC’s (3–4-5–4*-3* and 6–7-6*). The latter is similar to (4–5-4*) of Elements I 1 (Fig. 15):153

Fig. 17: The RC structure of Proposition I 2 of Euclid’s Elements. The two outer pairs (1–2-2*-1*-1) enclose two separate, inner RCS, 3–4-5–4*-3* and 6–7-6*.

152 Netz 2009, 124, uses the term ring-composition for this outer pair of theorems. 153 Ancient Greek mathematical propositions were inextricably bound to the accompanying diagram (see Netz 1999b, 282, and Huffman 2005, 342–368); the logic of some parallelisms, such as (4–4*) is not immediately obvious from the letters: we must look at the diagram, as in this case, where a statement referring to a line (DL, in (4)), is then applied to its part (AL, in (4*)).

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Fig. 18: The diagram of the construction of Proposition I 2 of Euclid’s Elements.

Our third example is the fifth proposition of the Data154:

Fig. 19: The full RC form of Proposition 5 of Euclid’s Data.

154 In this example, note that since the propositions in the Data do not close with the “being what was required to prove,” the enunciation stays outside the RC structure.

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Fig. 20: The diagram of the construction of Proposition 5 of Euclid’s Data.

Finally we shall look at one example of an X-type structure (Elements I 19). In fashion typical of theorems – but not problems – the enunciation-conclusion pair marks the outer RC (1–1*); the next pair consists of the setting out and specification with the last sentence of proof (2–2*); the third (3–3*) couples the equivalent of the priamel-type rhetorical division (3) with the completion of the proof of its combined claims (3*). The core of the proof consists of two parallel inner X arguments:

Fig. 21: The full X form of Proposition I 19 of Euclid’s Elements. The outer three pairs (1–2-3–3*2*-1*) enclose two separate Xs, 4–5-5*-4* and 6–7-7*-6*.

Fig. 22: The diagram of the construction Proposition I 19 of Euclid’s Elements.

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In both we have: a) a statement (4 and 6); b) an implication (5 and 7) following from it and the application of a previously proven theorem, viz. I 5 and I 18, respectively; c) the negation of the implication (5* and 7*); and d) a repetition of the first statements, as a conclusion (4* and 6*).155 This inner pair is the exact structural parallel of the first kind of X-type shown in rhetoric, as for example in Fig. 10, where N* negates N at the centre of the chiastic argument.

4 Conclusion We have outlined a history of early Greek-style mathematics, arguing that many of its distinctive characteristics were established by the end of the fourth century  or even earlier. In addition, we maintained that these characteristics make it radically different to the problem-oriented, known mathematics of other cultures. In order to explain this difference, we looked for possible influences in various areas of the Greek culture. The first Greek-style mathematicians were also trained in other arts; moreover, they were citizens of states in which political decision-making and the dispensation of justice were conducted through debate and voting. Arguably, these processes heavily depended on rhetoric. We have shown how Greek rhetors made use of pre-existing toolboxes of logos developed mostly in the archaic age, in both quotidian narrative and artistic storytelling; but the same toolboxes were adopted by the early Greek mathematical authors: our analysis of early rhetorical speeches, and the brief examples from Euclid’s propositions, show that several characteristic structures of Greek mathematics are also present in rhetoric, both in the standard form of the speeches, and in the chiastic and ring-compositional patterns in the logos-type pisteis.156 In both rhetoric and mathematics, the patterns are too strong to be ascribed to mere chance. Rather, we believe that this is a strong indication that Greek forensic rhetoric and Greek-style mathematics were partly shaped by the influences we indicated in the cultural background of their creators. In this sense, Greek mathe-

155 To describe this X-type in the generic form we can say that an argument boils down to an inner pair X (N-N*), where (N*) is either a negation of (N), or a conclusion of (N) and (N-1), leading to a further conclusion (N-1*), which extends (N-1). Such an example is given by the central sequence in Elem. I 3, where (N-1): And since point A is the centre of circle DEF, AE is equal to AD. (N): But, C is also equal to AD. (N*): Thus, AE and C are each equal to AD. (N*): So AE is also equal to C. 156 Since the writing of this paper, it has come to our attention that, in the year when some of the ideas discussed here were first presented in an earlier form (Doxiadis 2010), Major, Timmerman and Major (2010) independently arrived at some conclusions related to ours on the cognitive role of ring-composition in rhetoric. Also, Sansone (2012), presents ample evidence supporting what is also a part of our thesis; namely, that many forms of logical argumentation seen in Attic rhetoric appear earlier in poetry and more specifically – in Sansone's – argument, in drama.

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matics is both personal and impersonal: personal, since everything that is written must have had an author and, what’s more, not all Greek mathematical authors write the same way; and impersonal, not just because of its aim of total objectivity, but because the ways of thought and expression of human beings are to a large extent determined by their culture, and people living in the same culture, at about the same time, receive the same kind of influences. This susceptibility to influence may be less true for the sophisticated, cosmopolitan intellectuals of the classical Greek polis, adventurous and innovative as they were, than the members of an isolated traditional society. But it is, nevertheless, true.

Bibliography Texts quoted Anaximenes: Fuhrmann, M. 1966. Testimonia, Ars rhetorica vulgo Rhetorica ad Alexandrum. Leipzig. Antiphon: Pendrick, G. 2002. Antiphon the Sophist: The Fragments. Cambridge. Archimedes: Mugler, C. 1970. De Sphaera et Cylindro, Archimède, vol. 1. Paris. Archimedes: Mugler, C. 1970. Dimensio Circuli, vol. 1. Paris. Archimedes: Mugler, C. 1971. Ad Eratosthenem Methodus, Archimède, vol. 3. Paris. Aristotle: Bywater, I. 1894. Ethica Nicomachea. Oxford (repr. 1962). Aristotle: Louis, P. 1964–1969. Historia animalium. Paris. Aristotle: Ross, W. D. 1924. Metaphysica. Oxford (repr. 1970). Aristotle: Ross, W. D. 1950. Physica. Oxford (repr. 1966). Aristotle: Ross, W. D. 1959. Rhetorica. Oxford (repr. 1964). Aristotle: Ross, W. D. 1958. Sophistici Elenchi, Aristotelis Topica et Sophistici Elenchi. 1st ed. corr., Oxford (repr. 1970). Aristotle: Ross, W. D. 1964. Analytica Priora et Posteriora. Oxford (repr. 1968). Aristotle: Susemihl, F. 1884. Ethica Eudemia. Leipzig (repr. 1967). Athenaeus (Naucratis): Kaibel, G. 1877–1890. Athenaei Naucratitae Deipnosophistarum Libri XV. Leipzig. Autolycus: Mogenet, J. 1950. De Sphaera Quae Movetur. Louvain. Democritus: Diels, H. & W. Kranz 1952. Die Fragmente der Vorsokratiker, vol. 2. 6th ed., Berlin (repr. Dublin/Zürich 1966). Diogenes Laertius: Long, H. S. 1964. Vitae Philosophorum. Oxford (repr. 1966). Euclid: Heiberg, J. & E. Stamatis 1969. Elementa, Euclidis opera omnia, vols. 1–4. 2nd ed., Leipzig. Eutocius: Heiberg, J. & E. Stamatis 1915. Commentarii in Libros de Sphaera et Cylindro, Archimedis opera omnia cum commentariis Eutocii, vol. 3. Leipzig (repr. Stuttgart 1972). Eutocius: Heiberg, J. & E. Stamatis 1915. Commentarius in Dimensionem Circuli, Archimedis opera omnia cum commentariis Eutocii, vol. 3. Leipzig (repr. Stuttgart 1972). Gorgias: Diels, H. & W. Kranz 1952. Die Fragmente der Vorsokratiker, vol. 2. 6th ed., Berlin (repr. Dublin/Zurich 1966). Herodotus: Legrand, Ph. E. 1932. Historiae. Paris. Hero: Heiberg, J. 1903. Definitiones, Opera quae supersunt omnia, vol. 4. Leipzig. Hesiod: Solmsen, F. 1970. Opera et dies, Hesiodi opera. Oxford.

Sing, Muse, of the Hypotenuse

405

Homer: Allen, T. 1931. Ilias. Oxford. Homer: Von der Mühll, P. 1962. Odyssea. Basel. Iamblichus: Klein, U. 1894. In Nicomachi Arithmeticam Introductionem. Leipzig (repr. Stuttgart 1975). Iamblichus: Klein, U. 1937. De vita Pythagorica. Leipzig (repr. Stuttgart 1975). Isocrates: Mathieu, G. & É. Brémond 1938. Evagoras, Isocrate. Discours. 1st ed. rev. et corr., Paris (repr. 1967). Lysias: Albini, U. 1955. De caede Eratosthenis. I discorsi. Florence. Lysias: Lamb, W. R. M. 1930. Lysias. Cambridge, Mass. (repr. 2006). Pappus: Hultsch, F. 1876. Pappi Alexandrini Collectionis quae supersunt. Berlin. Philoponus: Vitelli, H. 1887. In Aristotelis Physicorum Libros Commentaria, Berlin. Philoponus: Wallies, M. 1909. In Aristotelis Analytica Posteriora Commentaria. Berlin. Plato: Burnet, J. 1900. Apologia Socratis, Platonis Opera, vol. 1. Oxford (repr. 1967). Plato: Burnet, J. 1903. Charmides, Platonis Opera, vol. 3. Oxford (repr. 1968). Plato: Burnet, J. 1901. Phaedrus, Platonis Opera, vol. 2. Oxford (repr. 1967). Plato: Burnet, J. 1903. Protagoras, Platonis Opera, vol. 3. Oxford (repr. 1968). Plato: Burnet, J. 1902. Respublica, Platonis Opera, vol. 4. Oxford (repr. 1968). Plato: Burnet, J. 1901. Symposium, Platonis Opera, vol. 2. Oxford (repr. 1967). Plato: Burnet, J. 1900. Theaetetus, Platonis Opera, vol. 1. Oxford (repr. 1967). Plato: Burnet, J. 1902. Timaeus Platonis, Opera, vol. 4. Oxford (repr. 1968). Plato: Rowe, C. J. 1986. Plato: Phaedrus. Warminster, Wiltshire. Plutarch: Mau, J. 1971. Vitae decem oratorum, Plutarchi moralia, vol. 5. Leipzig. Proclus: Friedlein, G. 1873. Commentarii in Primum Euclidis Elementorum Librum. Leipzig. Simplicius: Diels, H. 1882. In Aristotelis Physicorum Libros Commentaria. Berlin. Themistius: Wallies, M. 1900. Analyticorum Posteriorum Paraphrasis. Berlin. Theo: Hiller, E. 1878. De Utilitate Mathematicae, Theonis Smyrnaei Philosophi Platonici Expositio Rerum Mathematicarum ad Legendum Platonem Utilium. Leipzig. Lamb, W. R. M. 1941. Minor Attic Orators: Antiphon; Andocides. Cambridge, Mass. (repr. 1982). Lamb, W. R. M. 1977. Laches; Protagoras; Meno; Euthydemus. Cambridge, Mass.

Works quoted Allman, G. 1976. Greek Geometry from Thales to Euclid. New York. Alster, B. 1990. “Sumerian Literary Dialogues and Debates and their Place in Ancient Eastern Literature.” In: E. Keck et al. (eds.), Living Waters: Scandinavian Orientalistic Studies. Copenhagen, 1–16. Amsterdam, A., & J. Bruner 2001. Minding the Law. Cambridge, Mass. Asper, M. 2004. “Law and Logic: Towards an Archaeology of Greek Abstract Reason.” In: AION. Annali dell’università degli studi di Napoli ‘L’Orientale’ 26, 73–94. Asper, M. 2009. “The Two Cultures of Mathematics in Ancient Greece.” In: E. Robson & J. Stedall (eds.), The Oxford Handbook of the History of Mathematics. Oxford, 107–132. Austin, N. 1966. “The Function of Digressions in the Iliad.” In: Greek, Roman and Byzantine Studies 7, 295–312. Bassett, S. 1920. “Hysteron Proteron Homerikos.” In: Harvard Studies in Classical Philology 31, 39–62. Becchetti, A. 2010. “Hippocampal Formation and the Classical Art of Memory.” In: Proceedings of the National Academy of Sciences 107. Bekkeri, I. (ed.) 1854. Suidae Lexicon. Berlin.

406

Apostolos Doxiadis and Michalis Sialaros

Bergmann, F. G. 1868. La Priamèle dans les Différentes Littératures Anciennes et Modernes. Strasbourg. Bernal, M. 1992. “Animadversions on the Origins of Western Science.” In: Isis 83, 596–607. Breck, J. 1994. The Shape of Biblical Language: Chiasmus in the Scriptures and Beyond. Crestwood, NY. Brooks, P., & P. D. Gewirtz 1996. Law’s Stories: Narrative and Rhetoric in the Law. New Haven. Bundy, E. 1962. Studia Pindarica. Berkeley. Burkert, W. 1992. The Orientalizing Revolution: Near Eastern Influence on Greek Culture in the Early Archaic Age. Cambridge. Burkert, W. 2004. Babylon, Memphis, Persepolis: Eastern Contexts of Greek Culture. Cambridge, Mass. Carey, C. 1996. ”Nomos in Rhetoric and Oratory.” In: Journal of Hellenic Studies 116, 33–46. Cole, T. 1991. The Origins of Rhetoric in Ancient Greece. Baltimore. Cullen, C. 2009. “People and Numbers in Early Imperial China.” In: E. Robson & J. Stedall (eds.), The Oxford Handbook of the History of Mathematics. Oxford, 591–618. Cuomo, S. 2001. Ancient Mathematics. London. Detienne, M. 1967/1996. The Masters of Truth in Archaic Greece (orig. Paris 1967). Transl. J. Lloyd. New York 1996. Dicks, D. R. 1959. “Thales.” In: Classical Quarterly 9, 294–309. Douglas, M. 2007. Thinking in Circles. New Haven. Doxiadis, A. 2010. “Narrative, Rhetoric, and the Origins of Logic.” In: Storyworlds 2, 77–99. Doxiadis, A. 2012. “A Streetcar Named Demonstration.” In: A. Doxiadis & B. Mazur (eds.), Circles Disturbed: The Interplay of Mathematics and Narrative. Princeton. Duckworth, G. E. 1931. “Proanaphonesis in the Scholia to Homer.” In: The American Journal of Philology 52, 4, 320–338. Fowler, D. H. 1999. The Mathematics of Plato’s Academy: A New Reconstruction. 2nd ed., Oxford. Fowler, R. L. 1987. The Nature of Early Greek Lyric: Three Preliminary Studies. Toronto. Fox, M. V. 1983. “Ancient Egyptian Rhetoric.” In: Rhetorica 1, 9–22. Fraenkel, E. (ed.) 1950. Aeschylus: Agamemnon. Oxford. Friberg, J. 2005. Unexpected Links between Egyptian and Babylonian Mathematics. Hackensack, New Jersey. Friedrich, P. 2001. “Lyric Epiphany.” In: Language in Society 30, 217–247. Gagarin, M. 1990. “The Nature of Proofs in Antiphon.” In: Classical Philology 85, 22–32. Gagarin, M. 2001. “Did the Sophists Aim to Persuade?” In: Rhetorica 29, 275–291. Gagarin, M. 2002. Antiphon the Athenian: Oratory, Law and Justice in the Age of the Sophists. Austin. Gagarin, M. 2003. “Telling Stories in Athenian Law.” In: Transactions of the American Philological Association 133, 197–207. Gagarin, M. 2008. Writing Greek Law. Cambridge. Goldhill, S. 2002. Invention of Prose. Oxford. Griffith, R. D. 1993. “In the Dark Backward: Time in Pindaric Narrative.” In: Poetics Today 14, 4, 607–623. Griffith, M. 1990. “Contest and Contradiction in Early Greek Poetry.” In: M. Griffith & D. J. Mastronarde (eds.), Cabinet of the Muses. Atlanta, 185–207. Grimaldi, W. M. A. 1957. “A Note on the Pisteis in Aristotle’s Rhetoric”. In: The American Journal of Philology 78, 2, 188–192. Hall, D. L., & R. T. Ames 1998. Thinking from the Han: Self, Truth and Transcendence in Chinese and Western Culture. Albany. Hallo, W. W. 2004. “The Birth of Rhetoric.” In: Lipson & Binkley 2004, 25–46. Heath, T. L. 1921. A History of Greek Mathematics. Oxford.

Sing, Muse, of the Hypotenuse

407

Heath, T. L. (ed.) 1956. The Thirteen Books of Euclid’s Elements. 2nd ed., New York. Herman, G. 1993. “Tribal and Civic Codes of Behaviour in Lysias I” In: The Classical Quarterly 43, 406–19. Hornblower, S., & A. Spawforth (eds.) 2003. The Oxford Classical Dictionary, 3rd rev. ed., Oxford. Huffman, C. 2005. Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King. Cambridge. Hutchinson, G. O. 2001. Greek Lyric Poetry: A Commentary on Selected Larger Pieces. Oxford. Imhausen, A. 2009. “Traditions and Myths in the Historiography of Egyptian Mathematics.” In: E. Robson & J. Stedall (eds.), The Oxford Handbook of the History of Mathematics. Oxford, 781–800. Johansen, F. H. 1959. General Reflection in Tragic Rhesis. Copenhagen. Kahn, C. 1991. “Some Remarks on the Origins of Greek Science and Philosophy.” In: A. Bowen (ed.), Science and Philosophy in Classical Greece. New York, 1–10. Kangshen et al. (eds.) 1999. The Nine Chapters of the Mathematical Art: Companion and Commentary. Oxford. Karasmanis, V. 1990. “The Hypotheses of Mathematics in Plato’s Republic and His Contribution to the Axiomatization of Geometry.” In: P. Nicolacopoulos (ed.), Greek Studies in the Philosophy and History of Science. Boston, 121–36. Karasmanis, V. 2000. “On the First Greek Mathematical Proof.” In: Hermathena 169, 7–21. Kennedy, G. A. 1963. The Art of Persuasion in Greece. Princeton. Kennedy, G. A. 1980. Classical Rhetoric and Its Christian and Secular Tradition from Ancient to Modern Times. Chapel Hill. Kennedy, G. A. (ed.) 1989. The Cambridge History of Literary Criticism: Volume 1. Cambridge. Kennedy, G. A. 1994. A New History of Classical Rhetoric. Princeton. Kennedy, G. A. 1998. Comparative Rhetoric. Oxford. Kennedy, G. A. (ed.) 2007. On Rhetoric: A Theory of Civic Discourse. Oxford. Keyser, P., & G. Irby-Massie (eds.) 2008, Encyclopedia of Ancient Natural Scientists: The Greek Tradition and its Many Heirs. London. Knorr, W. R. 1993. “Arithmetike stoicheiosis: on Diophantus and Hero of Alexandria.” In: Historia Mathematica 20, 2, 180–192. Liao, W. K. 1959. The Complete Works of Han Fei Tzu. London. Liddell, H. G., & R. Scott 1843. A Greek-English Lexicon. Oxford. (= LSJ) Lipson, C. S., & R. A. Binkley (eds.) 2004. Rhetoric Before and Beyond the Greeks. Albany. Lloyd, G. E. R. 1966. Polarity and Analogy: Two Types of Argumentation in Early Greek Thought. Bristol. Lloyd, G. E. R. 1990. Demystifying Mentalities. Cambridge. Lloyd, G. E. R. 1992. “Methods and Problems in the History of Ancient Science: The Greek Case.” In: Isis 83, 564–77. Lloyd, G. E. R. 1996. Adversaries and Authorities: Investigations into Ancient Greek and Chinese Science. Cambridge. Lloyd, G. E. R. 2002. The Ambitions of Curiosity: Understanding the World in Ancient Greece and China. Cambridge. Lloyd, G. E. R. 2003. “Literacy in Greek and Chinese Science: Some Comparative Issues.” In: H. Yunis (ed.), Written Texts and the Rise of Literate Culture in Ancient Greece. Cambridge, 122–40. Lloyd, G. E. R. 2006. Principles and Practices in Ancient Greek and Chinese Science. Aldershot. Lloyd, G. E. R. 2009. “What was Mathematics in the Ancient World? Greek and Chinese Perspectives.” In: E. Robson & J. Stedall (eds.), The Oxford Handbook of the History of Mathematics. Oxford, 7–26. Lu, X. 1998. Rhetoric in Ancient China, Fifth to Third Century BCE. Columbia, South Carolina.

408

Apostolos Doxiadis and Michalis Sialaros

Marrou, H. I. 1956. A History of Education in Antiquity. New York. McCoy, B. 2003. “Chiasmus: An Important Structural Device Commonly Found in Biblical Literature.” In: Chafer Theological Journal 9, 2, 18–34. Moser, E. I., E. Kropff & M.-B. Moser 2008. “Place Cells, Grid Cells and the Brain’s Spatial Representation System.” In: Annual Review of Neuroscience 31, 69–89. Netz, R. 1997. “Classical Mathematics in the Classical Mediterranean.” In: Mediterranean Historical Review 12, 2, 1–24. Netz, R. 1998. “Notes and Debats – Deuteronomic Texts: Late Antiquity and the History of Mathematics.” In: Revue d’Histoire des mathématiques 4, 261–288. Netz, R. 1999a. The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge. Netz, R. 1999b. “Proclus’ Division of the Mathematical Proposition into Parts: How and why was it Formulated?” In: Classical Quarterly 49, 282–303. Netz, R. 2004. The Transformation of Mathematics in the Early Mediterranean World: From Problems to Equations. Cambridge. Netz, R. 2009. Ludic Proof. Cambridge. Neugebauer, O. 1951. The Exact Sciences in Antiquity. London. O’Banion, J. D. 1992. Reorienting Rhetoric: The Dialectic of List and Story. University Park, Pennsylvania. O’Grady, P. f. 2002. Thales of Miletus the Beginnings of Western Science and Philosophy. Sydney. Pelling, C. 2000. Literary texts and the Greek historian. London. Race, W. H. 1982. The Classical Priamel from Homer to Boethius. Leiden. Reece, S. 1995. “The Three Circuits of the Suitors: A Ring Composition in Odyssey 17–22.” In: Oral Tradition 10, 1, 207–229. Robins, G., & C. Shute 1987. The Rhind Mathematical Papyrus: An Ancient Egyptian Text. London. Robson, E. 2008. Mathematics in Ancient Iraq: A Social History. Princeton. Ross, W. D. 1931. The Works of Aristotle, Vol. III. Oxford. Rossi, C. 2009. “Mixing, Building, and Feeding: Mathematics and Technology in Ancient Egypt.” In: E. Robson & J. Stedall (eds.), The Oxford Handbook of the History of Mathematics. Oxford, 407–428. Sansone, David, 2012. Greek Drama and the Invention of Rhetoric. Malden and Oxford. Sasson, J. M. 1998. “The King and I: A Mari King in Changing Perceptions.” In: Journal of the American Oriental Society 111, 453–470. Segal, C. 1962. “Gorgias and the Psychology of the Logos.” In: Harvard Studies in Classical Philology 66, 99–155. Sialaros, M. (2012). Revisiting Euclid: a Contextual Study of Greek Mathematical Authorship. London. Spatharas, D. G. 2001. “Patterns of Argumentation in Gorgias.” In: Mnemosyne 54, 393–408. Taton, R. 1957/1963. “Ancient and Medieval Science: From Prehistory to  1450.” In: R. Taton (ed.), A General History of the Sciences, vol. 1 (orig. Paris 1957). Transl. A. J. Pomerans. London 1963. Unguru, S. 1975. “On the Need to Rewrite the History of Greek Mathematics.” In: The Archive for the History of Exact Sciences 15, 1, 67–114. Van Groningen, B. A. 1958. La composition littéraire archaïque grecque. Amsterdam. Van der Waerden, B. L. 1950/1954. Science Awakening (orig. Groningen 1950). Transl. A. Dresden. Groningen 1954. Van Hook, L. 1945. Isocrates. Cambridge (repr. 1998). Vidal-Naquet, P. 1967. “La raison grecque et la cité.” In: Raison Présente 2, 51–61. Welch, J. W. 1981. Chiasmus in Antiquity: Structures, Analyses, Exegesis. Provo, Utah. West, M. L. 1997. The East Face of Helicon: West Asiatic Elements in Greek Poetry and Myth. Oxford.

Sing, Muse, of the Hypotenuse

409

Wilfred, E. M., Timmerman, D. M., and Schiappa, E. 2010. “Terms of Art and Inferring Theory: When Did the Parts of a Speech Become Formalized?”. In: Timmerman, D. M. and Schiappa, E. Classical Greek Rhetorical Theory and the Disciplining of Discourse. Cambridge. Willcock, M. M. 1964. “Mythological Paradeigma in the Iliad.” In: Classical Quarterly 14, 141–154. White, J. B. 1985. Heracles’ Bow: Essays on the Rhetoric and Poetics of the Law. Madison. Worthington, I. 1994. “History and Oratorical Exploitation.” In: I. Worthington (ed.) Persuasion: Greek Rhetoric in Action. London, 109–129. Xu, G. Q. “The Use of Eloquence: The Confucian Perspective.” In: Lipson & Binkley 2004, 115–130. Yates, F. A. 1999. The Art of Memory. London. You, X. & Y. Liu. 2009. “Confucians Love to Argue: Policy Essays in Ancient China.” Xiaoye You’s Web Page (Penn State Server). (Last Accessed 10 Feb., 2010). Zulick, M. D. 1992. “The Active Force of Hearing: The Ancient Hebrew Language of Persuasion.” In: Rhetorica 10, 367–380.

Markus Asper

Making up Progress – in Ancient Greek Science Writing *

Abstract: Concepts of progress construct narratives. This paper examines ancient Greek medical and mathematical writers for the different forms that the story of progress can assume, and for the different ways that writers utilize it. Among the mathematical authors discussed are, e.g., Archimedes, Hero, and Proclus; among the medical, e.g., the Hippocratic treatise On Ancient Medicine and Galen. The paper describes the forms that these narratives take as rhetorical strategies and makes tentative inferences about their ideological background.

Among the means of human communication in words, the most versatile may be narrative, the object of the so-called ‘narrativist turn’, seemingly the latest broad trend in criticism. Narratological approaches have been tested not only in literary scholarship, but also in disciplines like sociology, political studies, medicine and even mathematics.1 In all of these fields, narratives either pervade practice, or the study of narratives (narratology) appears as a tool to understand these practices. Among the narratives that are especially powerful in scholarship, science, and their respective public recognition, is the narrative of progress.2 Accounts of progress, just as with any other accounts of series of facts in time, usually adopt the form of narrative. Such narratives of progress share the following essential structure: a narrator states that in the past, first a and then b happened, which now turn out to have become c, where it is taken for granted that b is more or better than a, and c is more or better than b.3 Since the story is often of direct * I would like to thank my colleagues Aloys Winterling and Philip van der Eijk for their helpful remarks. 1 Kreiswirth 2000, 295. See for instance Gross 1990, 123 on Newton. As for mathematics, see especially Doxiadis & Mazur 2012. 2 See Asper 2011, esp. 106–111 for ‘progress’ as a ‘frame-tale’, that is, a certain kind of narrative, among others in science writing. 3 See, e.g., the account of Lewis 1999, 159 on how the catapult ‘evolved’: “Artillery was invented at Syracuse in 399 B.C. in the form of the gastraphetes, a mechanised version of the hand-bow, which followed the same basic lines as the later crossbow. Although at first a hand arm, it soon evolved into two larger and static versions, one shooting heavy bolts and the other throwing stones. By about 370 it had reached Greece proper where, around 350 and probably in Macedon under the aegis of Philip II, the fundamentally new principle of torsion was devised, whereby the bow was replaced by a pair of arms inserted into vertical springs formed of twisted skeins of hair or sinew and held in a frame. After the death of Alexander torsion arrow-shooters and stone-throwers were in widespread use throughout the Greek world in field warfare and especially in siege work, both in attack and defence. A programme of intensive research and development around 270 came up with refined proportions and complex formulae for calibration, which brought the torsion catapult

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concern to the position of the narrator with respect to this series of events, which usually means that the reputation and authority of the narrator in his field and towards his audience is at stake, it does not come as a surprise that stories of progress are deeply formed by the narrator’s concerns and ideologies.4 In science, however, the narrative of progress has always had (and still has) special importance both to the construction of the scientists’ self and to the representation of science to the public. The privileged position of this narrative in science makes it the natural object of my interest in science writing. This paper places its focus on ancient Greek ‘scientific’ authors. I am, however, convinced that one could adopt the same approach with respect to contemporary science writing. Since concepts of progress have often, and almost naturally, been used in order to distinguish modern from ancient perspectives on life and the world, some general remarks on the ‘notion’ (I would prefer ‘narrative’) of progress in ancient Greece might seem appropriate. On the one hand, technical progress in antiquity was, from a modern perspective, quite slow. Ted Lendon, in his great and thought-provoking book Soldiers and Ghosts, maintains that in each century of antiquity fewer technological innovations occurred than in every single year of each of the two world-wars.5 Among historians of technology, therefore, the prevailing approach throughout the twentieth century has been to explain what is usually termed the ‘blocage’ of progress in antiquity.6 Accordingly, among scholars of the history of ideas, there has been a tendency to deny that ‘the ancient Greeks’ even had a broadly shared notion of progress. In order to explain and ascertain this hypothesis, scholars have quoted descendent views of history, such as the one in Hesiod’s myth of the ages that deteriorate from gold to iron,7 or cyclical ones such as the models of history favored among the to a state of comparative perfection and high performance. Thereafter the Greeks added only relatively minor refinements.” For a similar story, see Keyser (in this volume, 46–48). According to the minimal definition of Rimmon-Kenan, which I adopt, this is clearly a narrative: “[…] a ‘discursive formation’ […] is a narrative when double temporality and a transmitting (or mediating) agency are dominant in it.” (Rimmon-Kenan 2006, 16). See also Kreiswirth 2000, 294: “[…] someone telling someone else that something happened.” For a new approach towards defining ‘narrative’ compare Ryan 2006, 6–12 (“a toolkit for do-it-yourself definitions”, p. 9). 4 An implication of the fact that the notion of ‘scientific progress’ is in itself a normative concept (see Niiniluoto 2009, 2.2 “progress vs. development”). 5 Lendon 2005, 9. Naturally, the mathematics of this comparison are a little dubious. The comparison itself, however, is quite impressive. 6 See, e.g., Schneider 1989, 1–6; influenced by Finley 1963, 127 f.: “The list of Greek inventions | is a very short one indeed. Apparently the society as a whole lacked the mentality and the motivation to strive systematically for greater efficiency and greater productivity. Not even so practical a man as Vitruvius, not a philosopher but a working engineer and architect, shows the slightest awareness of the possibilities of technological progress.” See description and criticism of this stance in Cuomo 2007, 3 f.; for progress in ancient science see Keyser in this volume (48–58). 7 Schneider 1989, 41–45. – Interesting is the case of the Peripatetic Dicaearchus of Messana (Schütrumpf 2001, 260–270) who, according to the paraphrases in Varro and, especially, in Porphyry’s treatise on abstinence, in his Βίος ῾Ελλάδος, tried to rationalize traditional views of

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Stoics. The wide-spread concept of the mythical ‘first inventor’ (prōtos heuretēs) who has essentially found everything in a given field of knowledge and then handed it down to posterity as a closed body of knowledge, implicitly denies progress (and is, incidentally, quite close to Near Eastern concepts of the origins of knowledge).8 All of this seemed to sit well with the ideas of Wilhelm Dilthey and, especially, Karl Löwith who, in his influential Meaning in History (first published in 1949), derived essentially all modern and secular notions of progress from Christian eschatology.9 Therefore, it appeared only logical not to expect notions of progress in ancient Greek thought. At the end of the 60s, however, two works thoroughly revised the picture: Edelstein’s The Idea of Progress in Classical Antiquity and Dodds’s famous paper The Ancient Concept of Progress showed beyond doubt that ‘the Greeks’ had various concepts of progress, especially in fields concerned with knowledge, e.g. the sophists. Due to these circumstances, both Edelstein and Dodds intended to demonstrate that such concepts of progress existed, in forms that are similar to the typical modern ones. One, perhaps unavoidable, weakness of such reactive and, therefore, overly generalizing, approaches is, however, that the individual author’s intentions and thus the functions of his peculiar construction of progress remains invisible. These functions, however, are the focus of my paper. ‘Progress’, just as in Kuhn’s influential book on ‘revolutions’ in science,10 appears in these modern treatments as a general concept geared towards understanding factual history as such. Individual texts only serve to provide the material for constructing the general concept, that is, they do not come into view as motivated by individual concerns. Although this history-of-ideas approach is problematic, because the relation of an author’s ‘material’ to general ‘concept’ remains history as descendent by constructing a narrative of original happiness that is gradually destroyed by technical progress. Dicaearchus, however, focuses on the gradual deterioration of social relationships (see esp. fr. 56A.39–44 Mirhady). 8 Early instances in, e.g., Aeschylus, Prom. 442–506; Plato, Leg. III 677 C-D: Daedalus, Orpheus, Palamedes, Marsyas, Epimenides. Kleingünther 1933, v.a. 26–39 has collected the evidence. See also Zhmud 2006, 23–29. – As for Near Eastern parallels, I will mention only two: In the Gilgamesh epic, Uta-napishti brings onto his ark experts of all sorts of knowledge (XI 86, p. 143 transl. Maul), which is how knowledge survived the flood. Second, Berossus, a Hellenistic priest of Marduk in Babylon and author of the Babyloniaka, relates how Oannes, a fish-shaped being, immediately after creation taught mankind all branches of knowledge, including, e.g., language, writing, citybuilding, law-making, and geometry, “and since then, nothing was ever invented by anyone any more” (FGrHist 680 F 1 (4) f., vol. III C (1958), p. 369f. Jacoby: ἀπὸ δὲ τοῦ χρόνου ἐκείνου οὐδὲν ἄλλο περισσὸν εὑρεθῆναι). See Burstein 1978, 13 f. I should like to thank Stefan Maul for pointing out these two passages to me. 9 As for Dilthey, see Edelstein 1967, xix–xx with n. 27; Löwith 1953, 62 f., 182 f. Bury 1932, however, is less theory-driven. 10 Cf. Kuhn 1996, 160–166, on the interdependence of the notions of ‘science’ and ‘progress’. On Kuhn and further theoretical work on progress in his wake see Hess 1997, 22–30.

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unclear at best, I will introduce my argument with a couple of passages that can provide the background of what follows. Anyone who comes to the study of classical Greece from having read classical modern thinkers on progress like Pascal or Saint Pierre,11 will discover already in, e.g., Xenophanes, Thucydides, Plato, Aristotle, or, especially, Lucretius hints at similar concepts of progress.12 Besides some oddly cyclical overtones in, e.g., Aristotle,13 they all either describe or imply progress as a typically human way of gaining knowledge that depends on time and costs a great deal of effort, but is, on the other hand, successful and without limits. Two elements are especially remarkable: first, the historical growth of technical knowledge provides the paradigm of progress in all fields.14 Second, progress is presented as a success-story that is typically human15 – which means at the same time that it is anonymous. From a strictly literary point of view, that is, when looking at these scattered remarks as hinting at an underlying narrative of progress, we can describe the plot of such a narrative as continuous, almost as linear, and without end. Moreover, the narrative has an anonymous subject and is defined, to a certain extent, by the reluctance of its narrators to explicitly include their own personae into it. They prefer to leave open their own involvement with the sketched-out history of continuously increasing knowledge. How then does such a narrative of progress look in scientific writers?

(Α) Progress as a Story of Growth The structure of such a narrative of progress exhibits an infinite, cumulative plot. As I pointed out, this structure was probably already in the background of the passages from ancient Greece mentioned above. In mathematical and technological texts, however, one can find the narrative in a fully formed shape, well visible in,

11 For Pascal and Saint Pierre see Ritter 1972, 1041 n. 15 (Saint Pierre) and n. 47 (Pascal), resp. Cf. the figure of “bloße Kontinuität” in Löwith 1953, 176, and the definition of progress in Mittelstraß 1995, 665, all precisely the opposite of Kuhn. Occasionally, scholars have tried to harmonize both views of progress, e.g. Kullmann 1998, 29–34, for biology. 12 Xenophanes, fr. 21 B 18 Diels-Kranz; Thucydides I 71.3; Plato, Hipp. mai. 281d3–7; Aristotle, Eth. Nic. I 7, 1098a22–25; Pol. II 8, 1268b34–40. The ‘link’ to 17th- and 18th-century notions of progress is probably Lucretius’ De rerum natura, e.g. V 332–337, 1107, 1457, on which see Dodds 1973, 19. Helpful is the short bibliographical note on “ancient progress” in Lendon 2005, 394 f. 13 Aristotle, Metaph. Λ 8, 1074b8–14; Cael. I 3, 270b19 f.; Mete. I 3, 339b27–30; Pol. VII 10, 1329b25– 30. See Dodds 1973, 14. 14 Schneider 1989, 80. 15 Especially the context of Xenophanes seems to point at a contrast of human and divine knowledge, see Schneider 1989, 61 f. Compare Chaeremon, fr. 21 Trag. Graec. Frag. (quoted by Edelstein 1967, 66 n. 19).

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e.g., Archimedes’ prefaces and in Hero’s introductions. To illustrate, I concentrate on three passages taken from Philo of Byzantium, from Proclus, and from Pappus, in that order. Introducing his treatise on artillery, the Belopoiïka, Philo states that not all engineers have followed the same method:16 πολλοὶ γοῦν ἐνστησάμενοι κατασκευὴν ὀργάνων ἰσομεγεθῶν καὶ χρησάμενοι τῇ τε αὐτῇ συντάξει καὶ ξύλοις | ὁμοίοις καὶ σιδήρῳ τῷ ἴσῳ οὐδὲ τὸν σταθμὸν αὐτοῦ μεταϐάλλοντες, τὰ μὲν μακροϐολοῦντα καὶ εὔτονα ταῖς πληγαῖς ἐποίησαν, τὰ δὲ καθυστεροῦντα τῶν εἰρημένων· καὶ ἐρωτηθέντες, διὰ τί τοῦτο συνέϐη, τὴν αἰτίαν οὐκ εἶχον εἰπεῖν· ὥστε τὴν ὑπὸ Πολυκλείτου τοῦ ἀνδριαντοποιοῦ ῥηθεῖσαν φωνὴν οἰκείαν εἶναι τῷ μέλλοντι λέγεσθαι· τὸ γὰρ εὖ παρὰ μικρὸν διὰ πολλῶν ἀριθμῶν ἔφη γίγνεσθαι. Many have attempted the construction of machines that had the same size, used the same kind of construction, similar woods, and the same metal. And while they did not even change the weight (of the machine), they produced some (machines) that reached far and had great impact, but also some that fell short of mentioned. When they were asked why this was the case, they could not identify the reason. Thus, the saying of the sculptor Polyclitus applies to what will follow: he said that perfection (lit. ‘the good’) comes in small steps by way of many numbers.

Philo divides the history of catapult-making in two phases, an older one and a more recent one that includes his own time. The older was aporetic, success came only in his own time. Philo seems to see the transition from old to new not as a sudden break-through, but as a gradual accumulation of knowledge: progress came not through the revelatory invention of a single moment, but by the patient repetition of mathematical methods.17 This appears to be the gist of the quote from Polyclitus. Philo identifies the sponsorship of the Ptolemaic court as the reason for technical progress in this field.18 Obviously, Philo presents himself to the reader as the closure of a narrative, the plot of which is unending accumulation. Separated from Philo by many centuries, Proclus, the fifth-century Neoplatonist and philosopher of mathematics, among many other subjects, provides in his commentary upon the first book of Euclid’s Elements several instances of this plot of accumulating knowledge. In his long introduction one finds the so-called catalogue of geometers, a sort of history of theoretical mathematics from the beginnings down to Euclid, stripped down to names, chronological relations, and very basic accounts of what these mathematicians achieved. The substance of the catalogue is commonly understood to go back to the fourth-century ‘historian of science’ Eudemus of Rhodes, a Peripatetic.19 The catalogue lists 21 names, starting

16 17 18 19

Belop. p. 49.13–50.6 Thévenot (p. 106 Marsden). I am following Cuomo’s reading of this passage (2007, 51). Belop. p. 50.24–26 Thévenot (p. 108 Marsden). On the catalogue and Eudemus see Zhmud 2006, 166–213.

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with one Mamerkos.20 A typical passage from this text looks as follows (In Eucl. p. 67.20–23 Friedlein): Ἑρμότιμος δὲ ὁ Κολοφώνιος τὰ ὑπ’ Εὐδόξου προηυπορημένα καὶ Θεαιτήτου προήγαγεν ἐπὶ πλέον καὶ τῶν στοιχείων πολλὰ ἀνεῦρε […]. Hermotimus from Colophon carried further what Eudoxus and Theaetetus had already solved in outline,21 and found many of the principal propositions […].

Hermotimus is otherwise unknown. Here and throughout the whole catalogue, Proclus demonstrates a concept of mathematical progress that sets both big and small names on equal footing. Mathematical progress and thus mathematics as a discipline is the result of generations of men, patiently working together at a onedimensional series of improvements and accumulations. In the catalogue’s view, there are no revolutions, detours, or dead-ends in mathematics, nor periods of stagnation. Since the information contained by the catalogue goes back to Eudemus and since Eudemus was a contemporary of many of the mentioned names, one might assume that this view on mathematics was the one of the mathematicians themselves. Obviously, this is a group-centered narrative of progress: on the one hand, the plot of this narrative consists of individual discovery; on the other, however, these discoveries are connected and move in the same direction; essentially by virtue of being part of the same group. Another late-antique mathematician, Pappus of Alexandria (4th cent. ) confirms the impression gained from Proclus. All of Pappus’ works are lost, except his huge Collectio mathematica, which attempts to collect and arrange all mathematical knowledge, i.e., tries to provide a mathematical canon for posterity. Obviously, Euclid plays a significant role in this canon, which turns out not only to provide a certain canon of knowledge but also the canonized mind-set that goes with it (Coll. VII 32 (vol. 2, p. 676.25 ff. Hultsch): ὁ δὲ Εὐκλείδης […] ἐπιεικέστατος ὢν καὶ πρὸς ἅπαντας εὐμενὴς τοὺς καὶ κατὰ ποσὸν δυναμένους τὰ μαθήματα, ὡς δεῖ, […] Euclid, however, was extraordinarily fair and nice with everyone who could add on (συναύξειν) to mathematics even a little, as one should […]

The remark comes at the end of a harsh criticism directed at Apollonius of Perge, whose crime, as it seems, was not being an incompetent mathematician – which he obviously was not –, but being a mathematician who cared much more for his own reputation than for cohesion among the group of mathematicians, by, e.g., denying proper credit to his predecessors. Unlike Apollonius of Perge, Euclid was

20 P. 65.11–68.7 ed. Friedlein. 21 The verb must have the meaning of ‘providing the first proof, but using the ideas of others’. Compare LSJ s. v. προ-ευπορέω: ‘solve an ἀπορία, overcome a difficulty beforehand’.

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a nice man, at least, nice towards everybody who shared his (Pappus’ and presumably Euclid’s) idea of mathematics as an accumulating group-effort. This passage is remarkable because it connects the plot of continuous growth that seems to be typical for mathematical narratives of progress, with an explicit ‘ideology’ that is again group-centered. It downplays the differences in intellectual power and mathematical impact that obviously exist among the group (Hermotimus is not Euclid) and declares a unifying desire to further mathematics, no matter how much or how little, as the group’s common denominator. As we would expect, Pappus himself and his Collectio fit that bill perfectly. The ‘story of accumulation’ that presents progress as a narrative of how successful a group-centered effort was, is, and will be, clearly derives from this collective-focused group-ideology. There are more texts like these that show how the narrator’s ‘I’ becomes part of a narrative that constructs progress as a story of accumulation. Progress develops in many small steps, in a linear fashion, without sudden changes or unexpected ends. For the narrator who is usually involved in the practices that the story of progress intends to present and legitimize, such a plot has distinct advantages. The narrator enhances his authority by claiming discovery; nonetheless his activities always appear as part of a group-culture that comes with a certain collective authority and social standing. The subject is an important part of progress, but nonetheless just one among many. The ‘scientific I’ remains clearly subordinate to the group that defines the frame in which progress takes place. Thus, convention and tradition are vital parts of such a narrative of progress, which is why it is especially attractive for authors in ‘deuteronomic’ disciplines,22 namely writers of commentary. Much of this ideology translates directly into how Kuhn describes the mind-set of ‘normal science’.23 As I have indicated, such narratives exhibit a simple plot, which is strictly additive and cumulative and thus not very exciting. I have provisionally called it ‘the plot of accumulation’. It bears some resemblance to additive plots that we find in chronicles, which do not seem to follow any other logical structure but that of time passing.24 In the case of progress, these changes add on to one another, but

22 The term ‘deuteronomic’ has been coined by Netz and means a cultural preference for communicating the new by commenting upon the traditional; see Netz 1998, 261–288. 23 Kuhn 1996, 23–42; Feyerabend 1984, 102–106; in general McIntyre 1990, 65: “To share in the rationality of a craft requires sharing in the contingencies of its history, understanding its story as one’s own, and finding a place for oneself as a character in the enacted dramatic narrative which is that story so far.” 24 See, e.g., the Annales Sangallenses breves (cod. 9. Jh., Mon. Germ. Hist. Script. I, p. 64; I give only an excerpt): “703. 704. 705. 706. 707. 708 hiems durus, et Cotafridus dux moritur. 709. 710 Pippinus Alamanniam ingreditur. 711. 712. 713. 714 mors Pippini maiorumdomus. 715 mors Tagoberti regis iunioris. 716 pugna Karoli cum Ratpoto. 717. 718. 719. 720. 721. 722. 723. 724. 725 Sarraceni primitus ingrediuntur. 726. 727. 728. 729. 730 Lantfrid moritur. 731 Beda presbiter obiit Angulorum. 732. 733. 734 Carolus Frisiam vastat. 735 Carolus Wasconiam invadit. 736 Otwinus episcopus obiit.” This is the example often quoted by White, e.g., 1981, 7 f.

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aimlessly. Constant, yet never radical change leads to significant progress in a linear way. The single steps are ascribable to individuals, but essentially, one step is as important as any other. Within this structure, closure is not possible. Although not very appealing from an aesthetic point of view, the ‘message’ or ‘ideology’ of the plot is powerful.25 It has a great deal of attraction concerning the readers’ self-awareness as members of a group:26 since the story is open-ended, its contributions are basically equal, the community of contributors is non-hierarchic, and the constructed continuity is one-dimensional, a strong feeling of being part of the story is inspired in the addressee.27 Such narratives construct their narratees as legitimate successors to their narrators.28 The message’s focus is legitimate succession. Thus, a rather unadorned narrative of progress may nonetheless turn out to be a useful tool in order to seduce addressees who will find the narrative’s openendedness and inclusiveness per se appealing enough to understand themselves as its most recent continuation.29 Progress, however, can also appear as a story that has a certain end, often told after this end has actually been reached, which then adds a teleological touch to the whole narrative.

(Β) Progress as a Story with an Ending The construction of progress as a story with closure comes in handy in fields that, on the one hand, look back on canonized traditions, but do not, on the other, exclude competition. Hero of Alexandria, the aforementioned writer of mechanics in Nero’s time, occasionally stakes his claims to authority in such form. Hero sees himself as part of a tradition of mechanical writings, of which many have originated in Alexandria, perhaps in the same social context in which he himself 25 Perhaps this explains why to many this narrative of progress is the only one. See e.g. the criticisms of Feyerabend 1984, 102–106. 26 See Thurston 1994, 172 and Jaffe & Quinn 1994, 211: “[…] theoretical mathematicians in particular must recognize they are part of a team […] and must be willing to share credit.” 27 Compare the remark in Jaffe & Quinn 1993, 9 on mathematical primary literature that follows certain ideals of rigor in order to “permit steady and efficient advance”. The whole paragraph, even the whole paper, transmits an ideology of in- versus exclusion. 28 Clark 1995, 63: “What we get from such [histories of science] is an implicit audience as the ‘historical profession’ and, while often couched in terms of a metanarrative, such as the ‘progress of research’ or ‘cultural understanding’, the end of such histories seems simply self-legitimation and reproduction of the profession as end-in-itself.” 29 Chambers 1984, passim. Why is ‘progress’ such a great story? Taking up Phelan’s notion of ‘narrative progression’ (2002, 211–212), that is, of a movement towards resolving instabilities both within stories and between authors and audiences, the answer might be: progress as a story line is an instantiation of the principle of narrative progression and thus appears to give meaning to time itself. (Cf. Kreiswirth 2000).

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worked and taught (probably a form of arsenale). The more established this mechanical canon that comprises mostly Hellenistic writers, such as Philo and Ctesibius, the more important it is for Hero to hold his own as a worthy and equal contributor. As Philo did, Hero uses the introduction to his account of catapultmaking in order to construct one main difference between his predecessors and himself:30 Ἐπεὶ οὖν οἱ πρὸ ἡμῶν πλείστας μὲν ἀναγραφὰς περὶ βελοποιϊκῶν ἐποιήσαντο, μέτρα καὶ διαθέσεις ἀναγραψάμενοι, οὐδὲ εἷς δὲ αὐτῶν οὔτε τὰς κατασκευὰς τῶν ὀργάνων ἐκτίθεται κατὰ τρόπον οὔτε τὰς τούτων χρήσεις, ἀλλ’ ὥσπερ γινώσκουσι πᾶσι τὴν ἀναγραφὴν ἐποιήσαντο, καλῶς ἔχειν ὑπολαμϐάνομεν ἐξ αὐτῶν τε ἀναλαϐεῖν καὶ ἐμφανίσαι περὶ τῶν ὀργάνων τῶν ἐν τῇ βελοποιίᾳ, ὡς μηδὲ ἴσως ὑπαρχόντων, ὅπως πᾶσιν εὐπαρακολούθητος γένηται ἡ παράδοσις. My predecessors have composed a great number of detailed treatises on artillery including measurements and designs, but not one of them sets out the construction of machines in order nor do they set out their uses, but it is as if they have written down the details for all the readers who already know (about artillery). Therefore I think it appropriate to take over from them and give a clear description of machines in artillery, perhaps even of those that do not exist any more, in such a way that my account may be easy for everyone to follow.31

Hero proudly announces something no one, he claims, has ever done in technical writing on artillery, namely a description so accurate that even the non-expert will (presumably) be able to build and use these machines. One is left to wonder, however, who these non-experts might possibly be. Thus, Hero’s introductory move is perhaps meant to serve, rather, as an advertising self-description for expertreaders, too. Nonetheless, Hero clearly constructs a deficient past and announces his treatise as the end of an unsatisfactory history of catapult-literature. Later readers will not have to peruse any book on that topic other than Hero’s Belopoeica. In a strictly limited field, therefore, Hero claims to have ended progress. At the beginning of doxography, one finds, paradoxically, one of the boldest claims to have ended history, especially with respect to an illustrious one: preceding Hero by about 450 years, the sophist Hippias of Elis introduces one of his writings in the following manner:32 τούτων ἴσως εἴρηται τὰ μὲν Ὀρφεῖ, τὰ δὲ Μουσαίῳ κατὰ βραχὺ ἄλλῳ ἀλλαχοῦ, τὰ δὲ Ἡσιόδῳ τὰ δὲ Ὁμήρῳ, τὰ δὲ τοῖς ἄλλοις τῶν ποιητῶν, τὰ δὲ ἐν συγγραφαῖς τὰ μὲν Ἕλλησι τὰ δὲ βαρϐάροις· ἐγὼ δὲ ἐκ πάντων τούτων τὰ μέγιστα καὶ ὁμόφυλα συνθεὶς τοῦτον καινὸν καὶ πολυειδῆ τὸν λόγον ποιήσομαι. Of these, some (sayings) perhaps are uttered in Orpheus, some in Musaeus, in a few words, some here, some there; others, again, in Hesiod or Homer, others yet in the other poets, some in prose-writings, too, either Greek or Barbarian. But I have from all of these (collected) the

30 Hero, Belop. p. 73.6–11 Wescher (p. 18 Marsden). 31 Translation inspired by Marsden 1971, 19. 32 Hippias fr. 86 B 6 Diels-Kranz (from Clemens, Stromateis).

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most important and arranged them in groups according to topic (ὁμόφυλα), and now will begin this new and multi-faceted logos.

This fragment was probably part of the introduction of Hippias’ Synagōgē, which might have been a collection of doxai or perhaps remarkable ‘sayings’ (in that case, rather gnōmai) arranged according to topics.33 With this work Hippias, as is due for the true sophist, appears to have anticipated (rather than inaugurated) the genre of the ‘collection’ which became tremendously successful in imperial times. He even ‘invents’, at least for us, the category of prose-writing (sungraphai).34 What I find especially impressive, is the effortless shift of focus from the great authorities of the past to a single person, namely Hippias himself. Hippias constructs a succession of authority: ‘Orpheus, Musaeus, Homer, and all the others … and, now, I, Hippias of Elis’. At the same time, authority comes with a historical, and a geographical, dimension, which both focus on and end with Hippias. This rudimentary narrative of progress ends with the text the reader has in front of him. Authority has been transferred, history has come to an end with and in Hippias’ synthesis. These two texts adequately characterize the teleological form of the narrative of progress. As an aside, I would like to point at how heavily it depends upon texts as material basis of a tradition, from which the narrator can emerge as an individual. The curious possibility of wide-ranging and radical competition has often been discussed as a defining feature of early Greek medicine and philosophy, e.g. by G. E. R. Lloyd. Writing and certain social circumstances of Greek intellectual pursuit apparently created a situation which I have called the ‘extension of the combat zone’.35 For writing and textual tradition create the possibility, and even the need, of competing not only with one’s contemporaries in regions far away, but even with the most remote predecessors. Galen, for example, relates how he staged epideixeis – public lectures intended to establish the speaker in a competitive field or situation –, directed explicitly against medical ‘classics’ like Erasistratus, that is competitors that were long gone as persons,36 but still present as textual authorities. In the same spirit, Galen, again, observes with obvious satisfaction how long his claims had been accepted without serious criticism.37 All these statements operate within a narrative frame of progress that is not the collegial enterprise of continuous collaboration and ant-like accumulation, as it was in the case of mathemat33 The Synagōgē is mentioned by Athenaeus (Hippias 86 fr. B 4 Diels-Kranz) and amply discussed by Patzer 1986, who, however, does not believe in a mainly doxographical character of the Synagōgē, but sees a general argument, namely that which seems intellectually new is actually old and has already been said long ago, by authorities of the past (e.g., 110–112). 34 See Patzer 1986, 19. 35 Asper 2007, 352 with n. 199. The phrase is a translation of the novel Extension du domaine de la lutte by Michel Houellebecq (Paris 1994), which has, however, disappointingly been translated into English as ‘Whatever’. 36 Some material collected in Asper 2007, 351 f. 37 Praecogn. 5.21, p. 100.2 ff. Nutton.

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ics (even if some of the ants involved turned out to be famous later on). Rather, it is a struggle with, sometimes, war-like aspects: the winner is the one who manages to stay authoritative for the longest time. The prize of the struggle is, as it were, the conquest of time and thus the end of progress. In the end, there is but one authority who has the answer or the solution, and this is why the narrative exists, that is, the reason of why there is someone who constructs and tells it, in the first place.38 For these reasons, the teleological narrative of progress is much more satisfying from an aesthetic point of view: there is a certain amount of suspense, and there is closure. On the other hand, it cannot ever be useful for constructing group cohesion (other than, perhaps, belonging to the group of followers of a certain authority). The form of such narratives reminds one of the plot of novels, that is, narrative fictions that develop over time the story of an individual’s success against a background of seemingly insurmountable obstacles. Such obstacles might include the difficulty of the problem or certain handicaps of the hero, like being provincial, lacking powerful friends, having the wrong nationality, the number and power of competitors, etc. The narrative provides a happy ending which retrospectively has informed, structured, and even constructed the narrative itself. As one can imagine, the teleological plot of progress comes naturally as part of autobiography which one might understand as the seduction of the biography-constructing self by narrative.39 In such perspectives, any present becomes immaterial when compared with the present that closes the narrative.

(C) Progress as a Story of Return Progress as stories of continuous accumulation and teleological advancement to a given end are two forms of the narrative that are familiar to us. In Greece, a third one is quite prominent that, unlike the two already discussed, will surprise a modern reader:40 for in this one, the privileged regression to a paradigmatic past 38 To a certain extent, the same is true in the case of retrospectively constructed stories of anonymous progress that do not end with an individual’s triumphant success but with an absolute present. Cf., e.g., the account in Pliny, Nat. hist. XVIII 317 on how olive presses worked in ancient times, how in the century preceding his, a new technology was found and how this technology was improved within the preceding 22 years. 39 Compare Chambers 1984, 11–15, and Linde 1993. What she says about stories in institutions is also true for individuals: “Maintaining a usable past takes work.” (Linde 2009, 224). 40 Compare the practice of modern science as described by Kuhn 1996, 167: “When it repudiates a past paradigm, a scientific community simultaneously renounces, as a fit subject for professional scrutiny, most of the books and articles in which that paradigm had been embodied. Scientific education makes use of no equivalent for the art museum or the library of classics […].” To a certain extent, the history of science has become the “equivalent of the art museum”, e.g. with respect to past errors: see, e.g., Allchin 2001, 40; Darden 1987, 38 f.

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becomes the center-piece of the plot. Again, this shape of the story is intricately interwoven with fierce competition, especially in medicine. One of the best known and most often read treatises among the polemical treatises of the Hippocratic Corpus is On Ancient Medicine. In this treatise, the author attacks his competitors for doing something that, we thought, was the hallmark of scientific medicine and is practiced throughout the Corpus, namely deducing diagnoses and therapies from certain axiomatic principles, e.g., the four humors or the four elements. One of the core passages reads thus:41 Ἰητρικῇ δὲ πάντα πάλαι ὑπάρχει, καὶ ἀρχὴ καὶ ὁδὸς εὑρημένη, καθ’ ἣν καὶ τὰ εὑρημένα πολλά τε καὶ καλῶς ἔχοντα εὕρηται ἐν πολλῷ χρόνῳ, καὶ τὰ λοιπὰ εὑρεθήσεται, ἤν τις ἱκανός τε ἐὼν καὶ τὰ εὑρημένα εἰδὼς, ἐκ τουτέων ὁρμώμενος ζητέῃ. Ὅστις δὲ ταῦτα ἀποϐαλὼν καὶ ἀποδοκιμάσας πάντα, ἑτέρῃ ὁδῷ καὶ ἑτέρῳ σχήματι ἐπιχειρέει ζητέειν, καὶ φήσει τι εὑρηκέναι, ἐξηπάτηται καὶ ἐξαπατᾶται· ἀδύνατον γάρ. For a long time, medicine has had access to everything (it needed). Both a starting-point and a method have been found, according to which much useful (knowledge) has already been discovered over a long period of time – and the remainder will be found, if one is competent and, by knowing what has been discovered, if one proceeds in his research from these points. Anyone, however, who holds these things in contempt, attaching little value to them, and tries to proceed with a different method and in a different mode and claims to have found something, is caught up in deception and still deceives himself. For it is impossible.

In medicine, the anonymous author argues, new methods are unnecessary. The success of ‘ancient’ medicine demonstrates that both method and starting-points are already found.42 The only legitimate progress is to search along those predetermined lines, i.e., based on the ruling paradigm, for that which has not yet been discovered. Anyone who chooses a radically new beginning must be either a fraud or an idiot. Whoever the group may be that the medical theorists are attacking here (Empedocles is mentioned, and, as I have said, the method attacked is fundamental in many Hippocratic treatises), what is of interest for my current project is the dialectical way in which two competing concepts and narratives of progress are played off against each other. The author sees himself as part of an ongoing, accumulating enterprise that has discovered many things and will continue to discover whatever remains unknown, in due course. True progress, he maintains, means to continue the longestablished way of doing things, not to indulge in radical innovation.43 In terms of how to construct authorial authority and legitimate succession, the author has managed to secure the perfect stance: at the same time, he can exploit the legitimacy-bestowing authority of the past and the professional credit that comes with

41 Corp. Hipp., Vet. med. 2 (Jouanna p. 119.12–19 = vol. 1, p. 572.9–14 Littré). 42 See Edelstein 1967, 38–40. 43 The whole text reads as if an exponent of Kuhn’s “normal science” were talking to us about the advocates of a new paradigm (see above n. 23).

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the promise of new knowledge. This narrative of progress creates, surprisingly for us, authority through a privileged access to the past. As was the case with Hippias vis-à-vis Hero, the author of On Ancient Medicine has anticipated a way of using the past for the present that becomes increasingly wide-spread. This is especially evident with authors of the so-called Second Sophistic movement, which provides the frame for many intellectuals, among whom one should also place the physician Galen, probably the most-underrated writer of the Second Sophistic. Half a millennium later, the context of On Ancient Medicine has become the aurea aetas of the classics for Galen and his readers. Some things, however, did not change, for example the merciless competition among both medical practitioners and theorists. Thus, Galen offers a whole range of strategic applications of narratives of progress, among which are several instances of what I have called the plot of peripety and regression. In the Methodus medendi, a 1000-page long handbook on medical therapy, the reader often comes across passages in which Galen maintains that his superiority as a physician rests primarily on his faithfulness to the true doctrine of Hippocrates or, rather, realizing the full potential of what Hippocrates had intended. One quote will be sufficient (Meth. med. IX 8 (10.632.1–4 Kühn), addressing Eugenianus): Ταῦτ’ οὖν ἐπιδεικνύντι μοι πρόσεχε τὸν νοῦν, ἐκεῖνο διὰ μνήμης ἔχων ὡς οὔτ’ ἐν ἄλλοις τισὶ τὸ μεθόδῳ θεραπεύειν ἐστὶν οὔτ’ ἄλλος τις πρὸ ἡμῶν διωρίσατο πάνθ’ ἑξῆς αὐτὰ, καίτοι γε ὑφ’ Ἱπποκράτους εὑρημένης τῆς ὁδοῦ. Now pay attention to how I am going to demonstrate this! Keep in mind that no one else has discussed the method of therapy and that no one else before us has even defined all these things, although Hippocrates had already found the way.

In this context, Galen discusses his – non-Hippocratic – concept of certain ‘faculties’ (dunameis) of the human body that help along the healing process. We have the feeling that the rhetoric of succession and the construction of regression functions almost as camouflage for a fundamentally new concept. The same plot will be even more remarkable when Galen invokes as a second authority from the past not another physician, but Plato, which happens, e.g., in the great treatise On Anatomical Procedures (Anat. adm. VI 12 (2.581.1–6 Kühn), addressing Boethus): Ἀλλὰ σύ γε πειθόμενος ἐμοὶ καὶ Πλάτωνι τῶν μὲν ὀνομάτων καταφρονήσεις ἀεὶ, σπουδάσεις δὲ πρῶτον μὲν καὶ μάλιστα τὴν ἐπιστήμην τῶν πραγμάτων, εἶθ’ ἑξῆς, ὅταν ἕτερόν τινα διδάσκῃς, τὴν σαφήνειαν, ἧς καὶ τὸν Πλάτωνα καὶ ἡμᾶς […] φροντίζοντας ὁρᾷς. When you, however, follow me and Plato, you will always take little account of names, but you will, first and foremost, seek the knowledge of the subject, and then, whenever you teach someone, the clarity, concerning which you see Plato and me taking such great care.

Galen reduces the history of medicine to a diachronic point of unity (‘Hippocrates/ Plato and I’) and a field of competitors gone astray (‘no one else’). In order to

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make such an improbable argument convincing, one has to focus either on linguistic questions, as in these two examples that base the argument on definitions and clarity of language, or one has to interpret the classic. Galen has collected an impressive array of such arguments in his treatise De Placitis Hippocratis and Platonis, a fascinating source of ‘reading’ as a medical tool. In all cases, the gist of the argument leads to Galen’s self-positioning as a true follower, unlike his incompetent competitors. For Galen, the glorious past becomes an ally against the present. To simply claim novelty and truth or results that work, which to us seems so natural, especially in medicine, and which would even have corresponded to the facts, apparently did not seem viable to Galen. Thus, he disguises his contributions as exegeses of authorities hundreds of years past, by themselves far from clear, and medically clearly inferior to Galen himself. One is, of course, tempted to understand the whole construct as nothing but Galen’s personal ‘ideological patina’.44 There are, however, so many parallels in the ‘deuteronomic’ culture of the Second Sophistic and later antiquity that one at least cannot attribute this particular method of how to exploit the past to Galen’s individual character. Whatever one may think of that character,45 as a scientific writer Galen was imaginative and resourceful: he finds a remarkable image for his privileged access to the Hippocratic past and his concept of progress as a return, when he compares his readings and interpretations of Hippocrates with Trajan’s restoration of the Italian system of highroads that Augustus had inaugurated (Meth. med. IX 8).46 In both cases, modernity asserts itself as re-establishing a great feat of the past. Furthermore, both modes of re-instituting that past share the fact that the act of re-establishment itself has programmatic meaning: Trajan claims to be the new founder of Rome after the second Romulus, Galen claims to be Hippocrates alter. In both cases, progress is presented as a story of return. The narrator of the story of progress-as-return represents a sudden change, a peripeteia, to phrase it with Aristotelian plot-terms, towards progress. The message of such a plot clearly differs from those of the stories that I have discussed above: the story of return stages the reunion of two great individuals that meet each other across centuries. The anonymous mass of readers, or travelers in Trajan’s case, has no means of participation in this dialogue of heroes. In the story of progress as community-based growth, every reader was able to integrate himself into the narrative, which was why it was so popular in late-antique cultures of commentary. Here, however, progress has become the business not of communities, but of stars.

44 Smith 1979, 175; cf. Flemming 2008, 334 “legitimating cover”. 45 Most modern readers have actually disliked Galen. Famous is Wilamowitz’ assessment of Galen as “unerträglicher Seichbeutel” (Isyllos von Epidaurus, Berlin 1886, 112 with n. 12; see Asper 2005, 21; Schlange-Schöningen 2003, 23–24). Difficult to translate, this expression means something along the lines of ‘insufferable blatherskite’ (see Schwäbisches Handwörterbuch, 3. Aufl., erw. v. Hermann Fischer, Tübingen 1999, 390). 46 10.632.12–633.13 Kühn. Vgl. Swain 1996, 365 f.; v. Staden 1997, 51 f.

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Progress ends, paradoxically, by self-identification with the beginning. What could possibly top Trajan’s endeavor of road restoration? After Galen’s re-establishment of Hippocrates, what remains of medical progress? Nothing really remains, because progress has come to an end. The main point of such stratagems is, of course, to use the past to help contend against present competitors. As has often been observed, especially in the ‘deuteronomic’ cultures of imperial and late antique science writing, authors prefer to communicate progress and the discovery of the new as merely interpreting the old. Authors have to construct tales of progress on which they can base their authority as being modern, while at the same time leaving the revered past untouched. Moreover, they even employ the authority of the past in order to fashion their own. Occasionally, we can observe such complicated negotiations. In Proclus’ commentary on Euclid one comes across the interesting remark (In Eucl. 250.20–251.19 Friedlein) that we are obliged to Thales for his discoveries but to Geminus for generalizing them: Τῷ μὲν οὖν Θαλῇ τῷ παλαιῷ πολλῶν τε ἄλλων εὑρέσεως ἕνεκα καὶ τοῦδε τοῦ θεωρήματος χάρις. […] μειζόνως δὲ ἄν τις ἀγασθείη τῶν νεωτέρων τοὺς ἀποδείξαντας ἔτι καθωλικώτερον – ὧν ἐστι καὶ Γεμῖνος […] We are grateful to Thales of old for the discovery of many things and especially of this theorem. […] even more, however, one could feel joy about those of the more recent (mathematicians) who have demonstrated it even more generally, among whom is also Geminus.

This form of the story gives its author the freedom to revere the authoritative figures of the past, while at the same time clearly stressing the intellectual developments of the present: mathematical progress is depicted as generalizing theorems. Again, it is quite clear where in that story Proclus sees himself.

(D) Conclusions: Progress as Narrative In this paper, all I wanted to do was to present a case for looking at concepts of progress as narratives. I believe that the three ‘plots’ that I have identified and discussed above, are sufficient to prove my point. Nonetheless, there are more than just these three forms of narratives of progress, e.g., the science-fiction story in which the narrator claims that his knowledge is so advanced that he writes for readers of the future.47 There are also plots of reversal, e.g., Aristotle’s concept of philosophy’s past as its childhood: according to him, the philosophy of the Presocratics which is so much older than his own, babbles incomprehensibly, as a little child, while in his time philosophy has eventually grown up and is able to talk

47 Galen, Dig. puls. (see Asper 2005, 26 n. 23).

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sense.48 This concept of progress constructs authority as a reversal of the usual story-line, in which age comes with authority.49 In the same way, but about 2000 years later, Charles Perrault (1628–1703), one of the main players in the ‘Querelle des anciens et des modernes’, claims that we moderns are the true ancients of the world.50 Especially successful in terms of aesthetics is the plot of balancing history’s gains and losses that one finds in Dicaearchus’ Life of Greece: here, moral descent corresponds with and is triggered by technical progress. The almost tragic force of this story lies in its inevitability: man’s life and civilization depends on progress, but such a gain is necessarily balanced by losses of morality and social cohesion, leading eventually to war.51 In conclusion, I would like to offer two observations, a general and a more specific one. First, the more general: as soon as an author views himself in historical perspective vis-à-vis the knowledge in his field, he cannot help but construct a story that explains how history relates to his personal point of view. Such stories seem primarily to serve the author’s self-presentation. Instead of collecting such individual constructs in search of a general ‘concept of progress’ in a given time or field, one should, rather, face the fact that all these narratives are due primarily to the narrator’s constructions of identity, which may even shift from context to context.52 One could, for example, doubt that Galen had an abstract concept of progress, independent of his striving for distinction and self-positioning. As I have indicated above,53 (scientific) authors rely on authority which they conjure up, employing various strategies. One of these is telling a story of progress and assigning oneself a certain, prominent or less prominent, place in this story. Far from presenting objective histories of their fields, authors thus construct individual timelines of their fields that are geared towards the specific context of the argument. Very often, an important message of such narratives of progress is encoded in its plot-structure: for example, accumulative, teleological, or circular. The case of such narratives thus presents a strong example that supports Hayden White’s claim that form has content, too.54 The significant advantage of such stories is that they can 48 Aristotle, Metaph. A 10, 993a15–17: ψελλιζομένηι γὰρ ἔοικεν ἡ πρώτη φιλοσοφία περὶ πάντων […]. 49 Similarly, the famous story of Aristotle’s and Theophrastus’ manuscripts going amiss for centuries in a damp basement in Skepsis (as told by Strabo, Geogr. XIII 1.54 (608 f.)), turns out to be an explanation of reversal: later Peripatetics have an advantage over earlier ones. 50 “les veritables anciens du monde”, as quoted from Ritter 1972, 1041. Compare, as a strategy that just touches upon commonly shared narratives of progress, the title of Latour 1991/1993 “Nous n’avons jamais été moderns”. 51 On Dicaearchus see Schütrumpf 2001 and Saunders 2001, to whose classification of Dicaearchus as “ironic primitivist” (254) I do not subscribe. 52 There are certain parallels with Linde’s “life stories” (Linde 1993): stories of progress also create coherences, just as life stories do. In many cases, the latter participates in the former. 53 See introduction 3–4. 54 Perhaps a sub-story of ‘narrative identity’: see Kreiswirth 2000, 309. See White’s programmatic title The Content of the Form (1989).

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convey certain messages, simply by the means of narrative seduction, without even trying to argue for anything. Second, one might ask what determines, besides the individual context of a given passage, the concept of progress that appears in that passage. There might be an influence of the field, too: the ‘story of growth’, that is, a concept of progress as steady accumulation is clearly very popular in mathematics, but much less so in medicine. On the other hand the story-lines of progress as a ‘story with an end’ and as a ‘story of return’ appear frequently in medical writing. At least between these two fields of knowledge the structural differences between stories of progress point towards a fundamental difference in the social structure of the corresponding fields: mathematics appears as more group-centered and thus favors a group ideology that downplays individual competition (although Archimedes clearly has an interest in competition and mathematical showmanship).55 In medicine, however, competition among individuals and competing groups is ubiquitous, from the beginnings until at least the time of Galen. Therefore, medical writers employ the story of progress as one among many weapons to wield against their multiple competitors, and they shape the story according to their strategic needs. Mathematicians, on the other hand, favor stories of progress that allow them to understand themselves as part of a diachronic group-effort. At least to a certain extent, the range of stories of progress from which an individual author can choose, differs from field to field. Insofar as it is close to story-telling, making up progress in Greek antiquity shares most elements with its modern equivalents, which is why I could draw on theorists such as Löwith and Kuhn. There is, however, one major difference that points to the perspective of how the story-telling individual perceives time, namely the strange fact that ancient constructions of progress hardly ever concern the future. Rather, such narratives are geared towards giving a perspective to the present as a result of past developments. Only rarely, e.g., in the text from On Ancient Medicine quoted above, is there an optimistic notion of progress as a perpetually ongoing story of success. In most cases, the story-telling individual looks back to the past and makes up a narrative of progress that assigns meaning to the present by understanding it as the result of the past. It is, however, the rhetorical status of these narratives as contributions to the individual author’s self-fashioning, that explains the lack of a future perspective, rather than a fundamentally different notion of how time passes. In my introduction to this volume56 I had claimed that as soon as scientists write down anything, they become writers and thus are of interest for literary scholars. When these scientists, however, write on progress – which every scientist

55 On the comparative lack of a spirit of competition in Greek theoretical mathematics see Asper 2007, 161–173 (on Archimedes as exception of that rule, see 162 with n. 463). 56 Above 1–3.

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does, still today, who undertakes to persuade his audiences that whatever she presents is new or better than that which has preceded her, they become doubly involved with literary studies: as writers and as story-tellers. Among many other things, thinking about progress also provides a perspective that effortlessly unites science studies and literary criticism.57

Bibliography Texts quoted Dicaearchus of Messana: Mirhady, D. C. 2001. “Dicaearchus of Messana: the Sources, Text and Translation”. In: Fortenbaugh & Schütrumpf 2001, 1–142. Galen, Praecogn.: Nutton, V. 1979. Galen On Prognosis (Corp. Med. Gr. 5.8.1). Berlin. Hero of Alexandria, Belopoeics: Wescher, C. 1867. La Poliorcétique des Grecs. Paris. Pappus: Hultsch, F. 1876–1878. Pappi Alexandrini collectionis quae supersunt. Berlin. Philo of Byzantium: Marsden, E. W. 1971. Greek and Roman Artillery. Technical Treatises. Oxford. Proclus: Friedlein, G. 1873. Procli Diadochi in primum euclidis elementorum librum. Leipzig. Corp. Hipp.: Littré, É. 1839–1861. Œuvres complètes d’Hippocrate. Paris. Corp. Hipp., De vetere medicina: Jouanna, J. 2003. Hippocrate. Œuvres complètes. Tome 2, première partie. Paris. Marsden, E. W. 1971. Greek and Roman Artillery. Technical Treatises. Oxford.

Works quoted Allchin, D. 2001. “Error Types”. In: Perspectives on Science 9, 38–59. Asper, M. 2005. “Un personaggio in cerca di lettore. Galens Großer Puls und die ‘Erfindung’ des Lesers.” In: Th. Fögen (ed.), Antike Fachtexte – Ancient Technical Texts. Berlin, 21-39. Asper, M. 2007. Griechische Wissenschaftstexte. Formen, Funktionen, Differenzierungsgeschichten. Stuttgart. Asper, M. 2011. “‘Frame Tales’ in Ancient Greek Science Writing.” In: K.-H. Pohl & G. Wöhrle (eds.), Form und Gehalt in Texten der griechischen und chinesischen Philosophie. Stuttgart, 91–112. Atiyah, M. et al. 1994. “Responses to ‘Theoretical Mathematics […], by A. Jaffe and F. Quinn’”. In: Bull. Amer. Math. Soc. 30.2, 178–211. Brooks, P. 2002. “Narrative Desire”. In: B. Richardson (ed.), Narrative Dynamics. Essays on Time, Plot, Closure, and Frames. Columbus, OH, 130–137. Burstein, S. M. 1978. The Babyloniaca of Berossus. Malibu. Bury, J. B. 1932. The Idea of Progress. An Inquiry into Its Origin and Growth. New York. Chambers, R. 1984. Story and Situation: Narrative Seduction and the Power of Fiction. Minneapolis.

57 Compare Clark 1995, 1.

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Clark, W. 1995. “Narratology and the History of Science”. In: Studies in the History and Philosophy of Science 26.1, 1–71. McIntyre, A. 1990. Three Rival Versions of Moral Enquiry: Encyclopaedia, Genealogy, and Tradition. Notre Dame. Cuomo, S. 2007. Technology and Culture in Greek and Roman Antiquity. Cambridge. Darden, L. 1987. “Viewing History of Science as Compiled Hindsight”. In: AI Magazine 8.2, 33–41. Dodds, E. R. 1973. “The Ancient Concept of Progress”. In: id., The Ancient Concept of Progress and other Essays on Greek Literature and Belief. Oxford, 1–25. Doxiadis, A. & B. Mazur (eds.) 2012. Circles Disturbed: The Interplay of Mathematics and Narrative. Princeton. Edelstein, L. 1967. The Idea of Progress in Classical Antiquity. Baltimore. Feyerabend, P. 1984. “Fortschritt in Kunst, Philosophie und Wissenschaft”. In: Wissenschaft als Kunst. Frankfurt, 85–106. Finley, M. I. 1963. The Ancient Greeks. London. Flemming, R. 2008. “Commentary”. In: R. J. Hankinson (ed.), The Cambridge Companion to Galen. Cambridge, 323–354. Fortenbaugh, W. W., & E. Schütrumpf (eds.) 2001. Dicaearchus of Messana. Text, Translation, and Discussion. New Brunswick, NJ. Gross, A. G. 1990. The Rhetoric of Science. Cambridge, MA. Hankinson, R. J. 1994. “Galen’s Concept of Scientific Progress”. In: W. Haase (ed.), Aufstieg und Niedergang der Römischen Welt II 37.2. Berlin, 1775–1789. Hess, D. J. 1997. Science Studies. An Advanced Introduction. New York. Jaffe, A., & F. Quinn 1993. “‘Theoretical Mathematics’: Toward a Cultural Synthesis of Mathematics and Theoretical Physics”. In: Bull. Amer. Math. Soc. 19.1, 1–13. Jaffe, A., & F. Quinn 1994. “Response to Comments on ‘Theoretical Mathematics’”. In: Bull. Amer. Math. Soc. 30.2, 208–211. Kleingünther, A. 1933. Πρῶτος εὑρετής. Untersuchungen zur Geschichte einer Fragestellung. Leipzig. Kreiswirth, M. 2000. “Merely Telling Stories? Narrative and Knowledge in the Human Sciences”. In: Poetics Today 21, 293–318. Kuhn, Th. S. 1996. The Structure of Scientific Revolutions. 3rd ed., Chicago. Kullmann, W. 1998. Aristoteles und die moderne Wissenschaft. Stuttgart. Latour, B. 1991/1993. We Have Never Been Modern (orig. Paris 1991). Transl. C. Porter. Cambridge, MA, 1993. Lendon, J. E. 2005. Soldiers and Ghosts. A History of Battle in Classical Antiquity. New Haven. Lewis, M. J. T. 1999. “When Was Biton?”. In: Mnemosyne 52, 159–168. Linde, Ch. 1993. Life Stories. The Creation of Coherence. Oxford. Linde, Ch. 2009. Working the Past. Narrative and Institutional Memory. Oxford. Lloyd, G. E. R. 1991. “Who Is Attacked in On Ancient Medicine?” (orig. 1963). In: Methods and Problems in Greek Science. Cambridge 1991, 49–69. Löwith, K. 1953. Weltgeschichte und Heilsgeschehen. Stuttgart. Lowrie, M. 2008. “Cornelia’s Exemplum. Form and Ideology in Propertius 4.11”. In: Liveley, G. & P. Salzman-Mitchell (eds.), Latin Elegy and Narratology: Fragments of Story. Columbus, 165– 179. Mittelstraß, J. 1995. Art. “Fortschritt”. In: J. Mittelstraß (ed.), Enzyklopädie Philosophie und Wissenschaftstheorie. Vol. 1, 664–666. Netz, R. 1998. “Deuteronomic Texts: Late Antiquity and the History of Mathematics”. In: Revue d’histoire des mathématiques 4, 261–288. Niiniluoto, I. 2009. “Scientific Progress”. In: Zalta, E. N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2009 Edition), forthcoming URL = .

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Patzer, A. 1986. Der Sophist Hippias als Philosophiehistoriker. Freiburg. Phelan, J. 2002. “Narrative Progression”. In: B. Richardson (ed.), Narrative Dynamics. Essays on Time, Plot, Closure, and Frames. Columbus, OH, 211–216. Rimmon-Kenan, Sh. 2006. “Concepts of Narrative”. In: M. Hyvärinen et.al. (eds.), The Travelling Concept of Narrative. Helsinki, 10–19. Ritter, J. 1972. “Fortschritt”. In: Historisches Wörterbuch der Philosophie. Bd. 2, Basel, 1032–1059. Ryan, M.-L. 2006. Avatars of Story. Minneapolis. Saunders, T. J. 2001. “Dicaearchus‘ Historical Anthropology”. In: Fortenbaugh & Schütrumpf, 237–254. Schlange-Schöningen, H. 2003. Die römische Gesellschaft bei Galen: Biographie und Sozialgeschichte. Berlin. Schneider, H. 1989. Das griechische Technikverständnis. Von den Epen Homers bis zu den Anfängen der technologischen Fachliteratur. Darmstadt. Schütrumpf, E. 2001. “Dikaiarchs Bios Hellados und die Philosophie des vierten Jahrhunderts”. In: Fortenbaugh & Schütrumpf, 255–277. Smith, W. D. 1979. The Hippocratic Tradition. Ithaca, NY. von Staden, H. 1997. “Anatomy as Rhetoric: Galen on Dissection and Persuasion”. In: Journal of the History of Medicine 50, 47–66. Swain, S. 1996. Hellenism and Empire: Language, Classicism, and Power in the Greek World AD 50–250. Oxford. Thurston, W. P. 1994. “On Proof and Progress in Mathematics”. In: Bull. Amer. Math. Soc. 30.2, 161–177. White, H. 1981. “The Value of Narrativity in the Representation of Reality”. In: W. J. T. Mitchell (ed.), On Narrative. Chicago, 1–23. White, H. 1989. The Content of the Form. Narrative Discourse and Historical Representation. Baltimore. Zhmud, L. 2006. The Origin of the History of Science in Classical Antiquity. Berlin.

Brooke Holmes

In Strange Lands: Disembodied Authority and the Role of the Physician in the Hippocratic Corpus and Beyond Abstract: The role of the physician is usually defined by its outward-looking focus: the physician examines the bodies of others, rather than his own body. But in a medical tradition where the body is a site of truth, why should the physician neglect his own body? In this paper, I explore how the physician comes to be defined in early Greek medical writing as “structurally disembodied,” that is, as a subject position from which the body is viewed objectively and which is immune to the perils of its own embodiment. I begin by mapping the Hippocratic physician in relationship to other figures of knowledge and power in early Greek literature, focusing, in particular, on Odysseus and the addressee of the treatise Airs, Waters, Places. I then consider the near-total invisibility of the physician’s own body (sōma) in the Hippocratics texts. I also address the relationship of the social role of the practicing physician in the deontological texts to the role of a medical expert being established through rhetorical performance and written communication. Finally, I reflect on why the body may have been seen to pose a threat to medical subjects of knowledge. I argue that in establishing a “cut” between the knower and the body as an object of knowledge, the Hippocratic writers offer an early version of what will come to be known as objectivity. At the same time, the divided subject is also taken up within the ethical tradition as means of enabling reflexive knowledge and the care of the self.

The plague that struck Athens in 430  left high casualties in its wake.1 If we are to believe its most famous witness, the physicians were among the hardest hit. καὶ ὄντων αὐτῶν οὐ πολλάς πω ἡμέρας ἐν τῇ Ἀττικῇ ἡ νόσος πρῶτον ἤρξατο γενέσθαι τοῖς Ἀθηναίοις, λεγόμενον μὲν καὶ πρότερον πολλαχόσε ἐγκατασκῆψαι καὶ περὶ Λῆμνον καὶ ἐν ἄλλοις χωρίοις, οὐ μέντοι τοσοῦτός γε λοιμὸς οὐδὲ φθορὰ οὕτως ἀνθρώπων οὐδαμοῦ ἐμνημονεύετο γενέσθαι. οὔτε γὰρ ἰατροὶ ἤρκουν τὸ πρῶτον θεραπεύοντες ἀγνοίᾳ, ἀλλ᾽ αὐτοὶ μάλιστα ἔθνῃσκον ὅσῳ καὶ μάλιστα προσῇσαν, οὔτε ἄλλη ἀνθρωπεία τέχνη οὐδεμία. (Thucydides II 47)

1 I am grateful to Joshua Katz, Jim Porter, and Heinrich von Staden for their detailed feedback on this essay. I would also like to thank Markus Asper for the invitation to present this material at the “Writing Science” conference at New York University in April 2009 and his gracious hospitality on that occasion. Finally, I have benefited much from the responses of audiences at the “Writing Science” conference; at the 2010 History of Science Society Annual Meeting in Montréal; in the Department of History and Philosophy of Science at Indiana University-Bloomington; and in the Department of Classics at Cornell University. I owe special thanks to Faith Wallis and Reviel Netz for their probing questions.

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And they had not been in Attica many days when the disease first arose among the Athenians. It was said to have earlier fallen upon many quarters both around Lemnos and elsewhere, but neither a plague of such magnitude nor such a destruction of human life could be remembered anywhere. Neither did the physicians provide sufficient defense at the beginning, because they were treating the disease in ignorance, but they themselves died in greatest numbers to the extent they came in closest contact with it, nor did any other human tekhnē suffice.

The physicians’ ignorance, in short, costs them their lives, creating a vacuum of authority that the historian steps in to fill.2 Thucydides stakes his own claim to knowledge on his experience of the disease – a rare instance of the first-person in the Histories – as well as his observations of others afflicted with it.3 ἐγὼ δὲ οἷόν τε ἐγίγνετο λέξω, καὶ ἀφ᾽ ὧν ἄν τις σκοπῶν, εἴ ποτε καὶ αὖθις ἐπιπέσοι, μάλιστ᾽ ἂν ἔχοι τι προειδὼς μὴ ἀγνοεῖν, ταῦτα δηλώσω αὐτός τε νοσήσας καὶ αὐτὸς ἰδὼν ἄλλους πάσχοντας. (Thucydides II 48) I will describe only how [the disease] was and I will make clear those things on the basis of which someone investigating, if it should ever strike again, would be least ignorant, knowing something in advance; for I myself was sick, and I saw others suffering.

For the historian, then, if not for the physician, suffering yields knowledge, at least under these circumstances. What the physicians do not know, most obviously, is how to treat the plague. Their ignorance, however, goes deeper. Thucydides correlates the disproportionate mortality rate among the physicians with their proximity to the sick – a tacit reference, it would seem, to the concept of contagion. He has long been praised, in fact, for taking notice of a phenomenon that the Greco-Roman medical writers, from the classical era to Galen, were largely unable or unwilling to recognize.4 But there is another blind spot in early Greek medical writing that Thucydides’ account reveals, one that, unlike contagion, has received little attention: the vulnerability of the physician. The idea that the physician himself suffers disease is almost entirely absent from fifth- and fourth-century  medical writing. So, too, is the related idea that the speaker has gained knowledge of a disease by falling prey to it. In this paper, I argue that the implicit immunity of the physician is part of a larger feature of early Greek medical writing, namely, the disembodiment of those who claim expert knowledge about the nature of the body and its diseases. What is missing from these texts, in other words, is the idea that the physician has a 2 For the motif of medicine’s impotence in the face of plague in later texts, see Lucretius VI 1179, Vergil, Georg. III 548–550, and Fausti 2003, 46. 3 On the relative infrequency of the first-person voice in Thucydides, see Dewald 1987, 149–150; Humphreys 1996, 10–11; Thomas 2000, 226–227, 238 n. 71, explaining the historian’s avoidance of the first-person as part of his rejection of the epideictic milieu; Goldhill 2002, 41–43. 4 See Nutton 1983; Hankinson 1995; Fausti 2003. Jouanna 2001 discusses the limited ways in which the Hippocratic writers employ the concept of miasma.

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body susceptible to the forces that he masters in others. Disembodiment defined in these terms appears to be one of the essential features of medical authority in the Hippocratic texts. In recent decades, historians of ancient medicine have grown increasingly interested in the rhetorical construction of authority in the Hippocratic texts and in Greco-Roman medical writing more generally as part of an ongoing inquiry into the formal “scientific” or “technical” features of these texts and the rise of prose.5 These investigations have demonstrated that in texts likely to have been performed before or circulated within a larger public, authority tends to be secured through assertive self-presentation rather than through a stance of impersonality, as we find in the post-Enlightenment scientific tradition.6 What G. E. R. Lloyd has called the “egotism” of the more rhetorical Hippocratic authors is undoubtedly a fundamental aspect of their personae.7 But if we wish to grasp the full contours of these personae, we need to consider not only their strident claims to knowledge and technical expertise but also the silences and occlusions around which they form. I am interested here, accordingly, in examining what the Hippocratic texts affirm about authority, what we might call the “noise” of the first-person presence, together with what they ignore or implicitly deny – namely, that the expert on the physical body has a body of his own. The first-person presence in these texts carves out a subject position vis-à-vis the physical body that I will refer to as the “physician role.” The physician role is determined, in part, by the very structure of the healing relationship, which sepa-

5 For taxonomies of such features, see, e.g., Thesleff 1966; Guillén 1992; van der Eijk 1997. For an overview of the rise of prose, see Goldhill 2002. 6 The impersonal stance is not absent from ancient medical and scientific writing. It is particularly pronounced in Aristotle (Thesleff 1966, 89; Guillén 1992, 328; von Staden 1994b, 104; van der Eijk 1997, 117) and early legal texts (Humphreys 1996, 5). The Epidemics, despite the occasional use of the first-person voice, are also usually deemed to have an “impersonal” feel. 7 Lloyd 1987, 56–70. Thomas speaks of these texts’ “egocentric style” (2000, 242) and “egocentrism” (2003, 183). See also Humphreys 1996, 11 (“the arrogant, anxious presence of the writer in his text”); Asper 2007, 43–45, relating the strong personal stance to agonal contexts. Note, however, that these voices are anonymous, “without strongly projected individual contours, and without a pronounced personality” (von Staden 1994b, 105). For this reason, I do not use the language of a “scientific self” in discussing the Hippocratic Corpus, focusing, rather, on the contributions that a number of these authors make collectively to a position of medical authority. On constructions of a “scientific self” in later Greco-Roman medical writing, see, on Celsus, von Staden 1994b; on Galen, Debru 1992; Barton 1994, 133–168; Asper 2007, 333–337; Mattern 2008; Boudon-Millot 2009; Curtis 2009; Nutton 2009; von Staden 2009. See also Hine 2009 on Latin scientific and technical texts. The personae of Herodotus and Thucydides offer interesting contemporary parallels to the Hippocratic personae, although with the historians we are dealing with single-author works and authors who name themselves. Thomas 2000 nevertheless sees similarities between Herodotus’ self-presentation and that of the more rhetorical medical writers; see also Lateiner 1986. On Herodotus’ authorial persona, see further Dewald 1987; Marincola 1987; Goldhill 2002, 28; Baragwanath 2008, 78–81. On Thucydides, see above, n. 3.

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rates the sick or wounded body from the person who acts on it. It is informed, too, by the traditional concept of the iatros as a figure defined by his exercise of craft knowledge.8 But in fifth- and fourth-century  Greece, the nature of medical authority is undergoing a significant change as the very conditions of producing and enacting medical knowledge are transformed. These changes unfold within a burgeoning field of interest in – and claims to knowledge about – the physical body (sōma), its diseases, and human nature. The emergence of the body as an object of expert knowledge expands the epistemological authority associated with the physician and the intellectual ambitions of medicine as a tekhnē, transforming the dynamics of the clinical relationship in the process.9 In such a context, the concept of having a body acquires new implications that can help us better understand what is at stake in organizing an identity around the absence of the body. These developments go hand in hand with a shift in the performance conditions of medical knowledge in the classical period. It is likely that the more overtly rhetorical texts in the Hippocratic Corpus have their origins in epideictic performances, whether in front of a general audience or before an audience of students or prospective students, before circulating as written texts:10 medicine, from what we can gather, is of great public interest in the later decades of the fifth century  and the beginning of the fourth.11 The growth of contexts and mediums for the display of medical authority results in the embedded social role of the physician as a healer and an expert craftsperson being adapted into a rhetorical, performative, and textual phenomenon.12 Once it is displaced from the clinical encounter,

8 On the iatros as a craftsperson, see Homer, Il. XI 515 and Od. XVII 382–385, with Temkin 1953; Horstmanshoff 1990. 9 On learned medicine and the educated physician, see Aristotle, Pol. III 3, 1282a3–5, distinguishing among the craftsman (ho dēmiourgos), the “master-physician” (ho arkhitektonikos), and the educated layperson (ho pepaideumenos peri tēn tekhnēn). For the educated physician as an influential ideal, see Jaeger 1944, esp. 7–15; Kudlien 1970a, 11. 10 For rhetorical analyses of specific texts, see Jouanna 1988, 10–24, 167–174; 2003, x–xiii. For a discussion of those treatises that are likely to have been first performed orally, see Jouanna 1984, esp. 32 for the distinction between didactic texts (cours) and epideictic ones (discours). Not everyone would agree with Jouanna’s categorization of the treatises, but most scholars accept the distinction between didactic and epideictic texts. The difference of addressee obviously matters. For my purposes, however, both types contribute to the discursive articulation of disembodied authority. On the fluidity of the barrier between oral performance and written texts in the later fifth century, see Demont 1993, 192–196; Thomas 2003, esp. 180–188; Asper 2007, 27–28; Bakker 2009, 118. 11 On the public profile on medicine in this period and the epideictic milieu, see Demont 1993; Thomas 1993; Jouanna 1999, 177–285; Thomas 2000; Laskaris 2002; Thomas 2003, 175–176; Schiefsky 2005, 38–46. 12 We should include as part of the embedded social role the function of the iatros as a teacher. In the archaic and early classical periods, the iatros seems to have traditionally trained others, usually family members, on an apprenticeship model. While our evidence is limited, there is a consensus among scholars that this model starts to change in the later classical period as medical

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that role may be recast as a position of knowledge and expertise vis-à-vis the body.13 The clinical context persists, of course. In fact, the authority of the practicing physician is deeply affected, at least in elite and urban social spheres, by the rise of naturalizing medicine and rhetorical performance. Yet the encounter between the physician and the patient is governed by its own norms, as we will see in the so-called “deontological” treatises, which advise the physician (or the medical student) as to how to conduct himself with his patients and in public. The specificity of those norms means that the construction of medical authority through rhetorical performance must be understood as a particular kind of discursive effect, capable of establishing a specific subject position vis-à-vis the physical body. The articulation of the physician role in these terms, I suggest, has a powerful influence not only in medicine but also beyond it. I begin my inquiry in an unexpected place: the Odyssey. My aim in doing so is to establish an archaic and classical context within which to situate the disembodied medical expert at the crossroads of authority, knowledge, and vulnerability. I read Odysseus’ encounter with Hermes in Book X alongside what may be one of our earliest Hippocratic texts, Airs, Waters, Places (ca 425 ), in order to lay the foundation for my examination of disembodied knowledge in other early medical texts. In undertaking that examination, I define what I mean by disembodied knowledge more precisely by plotting the expansion of the clinical relationship within a field of medical inquiry into the physical body. I then read the amplified physician role that emerges within this field against the more socially embedded role of authority that we see outlined in the deontological texts. In the final section, I examine the specific problems posed to medical authority by the physical body, closing with some brief reflections on the implications of what I will call a “structurally disembodied” position of expert knowledge about the body, both for laypersons invited to care for their own health and for the subject of care in early ethical philosophy.

1 In Strange Lands: Odyssey X and Airs, Waters, Places By the time Odysseus and his men end up on Circe’s island they should already be home. They had come so close to Ithaca that they saw men tending the fires. But education moves outside the family: see Kudlien 1970a; Kollesch 1979; Althoff 1993; Jouanna 1996b; Dean-Jones 2003; Leith 2007, 37. 13 The authorial personae in the Corpus generally lay claim to a position of medical authority. The author of On Fleshes, for example, despite an expansive cosmological framework, still declares that he is writing “about the medical tekhnē” (περὶ τῆς τέχνης τῆς ἰητρικῆς, Corp. Hipp., Carn. 1 [Littré 8.584=188,5–6 Joly]). Jouanna 1988, 179–183 persuasively argues that the author of On the Tekhnē,

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then Odysseus falls asleep, and his companions inadvertently release the winds entrusted to him by Aeolus. The winds propel them back into a state of wandering and, eventually, they end up on Aeaea. After they land, Odysseus, encouraged by a sign of rising smoke in the island’s interior, dispatches a reconnaissance mission, but only the leader, Eurylochus, returns. Armed with Eurylochus’ report of his companions’ disappearance, Odysseus sets off into the forest alone in the hope of rescuing them. He is nearing Circe’s house when Hermes, in the guise of a young man, stops him short.14 πῇ δὴ αὖτ᾽, ὦ δύστηνε, δι᾽ ἄκριας ἔρχεαι οἶος, χώρου ἄϊδρις ἐών; ἕταροι δέ τοι οἵδ᾽ ἐνὶ Κίρκης ἔρχαται ὥς τε σύες, πυκινοὺς κευθμῶνας ἔχοντες. ἦ τοὺς λυσόμενος δεῦρ᾽ ἔρχεαι; οὐδέ σέ φημι αὐτὸν νοστήσειν, μενέεις δὲ σύ γ᾽ ἔνθα περ ἄλλοι. ἀλλ᾽ ἄγε δή σε κακῶν ἐκλύσομαι ἠδὲ σαώσω. (Homer, Od. X 281–286) Where, unfortunate one, are you going through the hill country, all alone, knowing nothing of the land? But your companions in Circe’s palace are penned up just like pigs, dwelling in close-confined sties. Are you coming here to free them? I do not think you will have a homecoming yourself, but you will remain there with the others. But come, I will free you from evils and save you.

Hermes’ promise of protection materializes in the form of a pharmakon capable of warding off Circe’s magic. The gods call it molu, and they alone have the power to dig up its roots (X 305–306).15 Odysseus – for he is the internal narrator of the story, recounting his wanderings to the assembled Phaeacians – then relates that Hermes showed him the phusis, “nature,” of the plant (καί μοι φύσιν αὐτοῦ ἔδειξε, X 303). What it is, precisely, that Hermes gives Odysseus is unclear. Part of the problem is the word phusis, which appears here for the first time in extant Greek literature (and the only time in Homer). The fact that Odysseus describes the plant – black at the root, with a white flower – immediately after the mention of its nature has led some scholars to understand phusis as “form” or “appearance.”16 It is likely, however, given the – sis suffix, that phusis refers to something more dynamic, such as the plant’s “process of growing” or “the nature [of the thing] as it is realized, with all its properties.”17 Moreover, as Heubeck argues in his commentary, the often seen as a generic sophist, represents himself as a physician defending his tekhnē; see Jouanna 1988, 47–48 on the likely medical authorship of On Breaths. 14 Davies 2008, 30 notes that both the sudden nature of the encounter with Hermes and the fact that Odysseus is alone are consistent with the folktale motif of the helper; see also Homer, Il. XXIV 339–469 (Hermes meets Priam). 15 On the lack of a human name for the plant, see Clay 1972. 16 See, e.g., Heinimann 1945, 16–17. 17 “Process of growing”: Jones 1973, 16; “the nature [of the thing]…”: Naddaf 2005, 14, after Benveniste.

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verb deiknunai probably encompasses not just the sense of “to show” but also “to instruct.”18 Taking into account the plant’s divine name and its partial concealment from mortals, we might speculate that Hermes instructs his protégé in the plant’s hidden powers. Indeed, the image of its dark roots contrasting sharply with the milky blossom visible on the surface resonates with later figurations of a nature that “loves to hide.”19 The passage implies that it is not simply the plant that confers immunity but esoteric knowledge of its nature. That nature, fittingly, remains obscure to us. In the end, we have to infer the plant’s efficacy from Odysseus’ report that the goddess’s potion failed to enchant him, allowing him to gain the upper hand. But the report contains an intriguing detail. Circe herself credits her guest’s invulnerability to the fact that he has “a mind that cannot be enchanted” (ἀκήλητος νόος, X 329) and, in the next line, she names him with the epithet polutropos, “many-turning” or “resourceful” (ἦ σύ γ’ Ὀδυσσεύς ἐσσι πολύτροπος, X 330). The epithet is rare, but it is taut with significance here. The only other place it appears in the poem is in the very first line, where it qualifies Odysseus as the as yet unnamed subject (andra) of the epic. In other early hexameter poetry it is paired only with Hermes in the Homeric Hymn dedicated to him (XIII 439). In the very moment, then, that Odysseus secures his identity, he seems to become the double of the god who intervenes to protect him, sharing in his polytropy.20 If his salvation can be credited in part to privileged knowledge akin to Circe’s own, he gains access to that knowledge, it would seem, not only through the gods’ will but also by virtue of his own mind. The adventures on Circe’s island are often read, justifiably, through the lens of comparative folklore.21 But we can also approach Odyssey X as a point of departure for thinking about the relationship between expert or privileged knowledge, power – including the power to protect others – and one’s own susceptibility to harm. The Odysseus adrift in Books 9–12 is the paradigmatic traveler through strange and often hostile lands, subject to incalculable risk. He is also the hero of mētis, cunning intelligence. While he bears responsibility for his men, he is himself in need of protection, as Hermes’ ominous words make clear (“Are you coming here to free them? I do not think you will have a homecoming yourself…”). Odysseus cannot help others without first saving himself, and, of course, by the end of the wanderings, he will have saved only himself. The Hippocratic treatise Airs, Waters, Places is, like the Odyssey, a text about a traveler in strange lands, lands that, in their own way, harbor numerous forces (dunameis) that shape and misshape human nature. The author spends the first half of the treatise concentrating on geographical and environmental factors that 18 Heubeck & Hoekstra 1989, 60, followed by Naddaf 2005, 14. 19 Nature “loves to hide”: Heraclitus fr. 22 B123 Diels-Kranz. But the motif of plants with magical roots is widespread: see Page 1973, 66, 125 nn. 34–35. 20 On the shared polytropy of Hermes and Odysseus, see Pucci 1987, 23–25. 21 See Page 1973, 51–69; Alexander 1991; Davies 2008.

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affect health – usually adversely – such as the orientation of a city, the dominant winds, the water used by the inhabitants, and the seasons. It may seem like the threats posed by winds and waters and changes of season hardly approach the magnitude of the Cyclops’ quasi-cannibalism or Circe’s bestializing magic. But in reality, they have serious and concrete effects on the “cavities” (κοιλίαι) of humans.22 Consider, for example, the corrosive diseases (dysenteries, hydropsy, and so on) that proliferate during a rainy season or the tyranny of pleasure under certain climactic conditions.23 Someone who “wishes to pursue the science of medicine correctly (ἰητρικὴν ὅστις βούλεται ὀρθῶς ζητεῖν)” should be on guard against these conditions and others he is likely to encounter in foreign lands (Corp. Hipp., Aer. 1 [Littré 2.12=186,1 Jouanna]). It is just this someone whom the author intercepts in the first line of the treatise to tell him what he has to do (τάδε χρὴ ποιεῖν). The opening address is located at the text’s level of enunciation rather than the level of narration: it is addressed to a reader or a listener, not a character. Nevertheless, it stakes out a position for the authorial persona not unlike that of Hermes, casting the addressee, in turn, in the role of Odysseus. Much like the god, the author observes the world around him from a position of privileged knowledge and, again like Hermes, he invites his addressee to approach this position. While the “gift” does not involve a literal pharmakon, the author of Airs does offer his reader or listener instruction in the nature of things, emphasizing the dunameis of various environmental influences and the phuseis of cavities. The instruction that he provides is designed to enable the itinerant physician to master the situations that he is about to encounter. There is, however, one critical point at which the two texts diverge. In each case, the traveler is intercepted to keep him from running into trouble. We have already seen the danger faced by Odysseus – nothing less than the loss of human form. What about the traveling physician? First and foremost, he avoids being caught unawares when traveling in unfamiliar lands. καὶ ἀπὸ τούτων χρὴ ἐνθυμεῖσθαι ἕκαστα. εἰ γὰρ ταῦτα εἰδείη τις καλῶς, μάλιστα μὲν πάντα, εἰ δὲ μή, τά γε πλεῖστα, οὐκ ἂν αὐτὸν λανθάνοι ἐς πόλιν ἀφικνεόμενον ἧς ἂν ἄπειρος ᾖ οὔτε νοσήματα ἐπιχώρια οὔτε τῶν κοιλιῶν ἡ φύσις ὁκοίη τίς ἐστιν. (Corp. Hipp., Aer. 2 [Littré 2.14= 188,6–10 Jouanna]) And it is necessary to consider each case from these givens. For if someone knows these things well – best of all, all of them, but if not, the majority of them – he will not be unaware, when

22 See, e.g., Corp. Hipp., Aer. 2 (Littré 2.14=189,13–14 Jouanna): ἅμα γὰρ τῇσιν ὥρῃσι καὶ αἱ κοιλίαι μεταβάλλουσι τοῖσιν ἀνθρώποισιν (For, together with the seasons, the [state of the] cavities changes in human beings), 10 bis (Littré 2.42–44=212,9–213,3 Jouanna; Littré 2.48=216,4–9 Jouanna). 23 See Corp. Hipp., Aer. 10 (Littré 2.48=216,5–9 Jouanna), 12 (Littré 2.56=222,4–5 Jouanna). Note that in the last example, the phrase ἀλλὰ τὴν ἡδονὴν ἀνάγκη κρατεῖν is part of a sentence that either follows or precedes a major lacuna. But the sense is clear enough and consistent with the representation of Asiatic peoples as less warlike and gentler than Europeans (e.g., Corp. Hipp., Aer. 16 [Littré 2.62=227,11–13 Jouanna]).

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he enters a city where he has no experience, of either the local diseases or the nature of the cavities, what sort of nature it is.

Ignorance, however, turns out to run a very specific risk. The addressee who masters the material set forth in the text evades the danger of “being at a loss in his therapy and failing utterly (ὥστε μὴ ἀπορεῖσθαι ἐν τῇ θεραπείῃ τῶν νούσων μηδὲ διαμαρτάνειν, Corp. Hipp., Aer. 2 [Littré 2.14=188,10–11 Jouanna]).”24 Several lines later, the author trumpets the positive results achieved by the physician who follows his advice: οὕτως ἄν τις ἐρευνώμενος καὶ προγινώσκων τοὺς καιροὺς μάλιστ’ ἂν εἰδείη περὶ ἑκάστου καὶ τὰ πλεῖστα τυγχάνοι τῆς ὑγιείης καὶ κατ’ ὀρθὸν φέροιτο οὐκ ἐλάχιστα ἐν τῇ τέχνῃ. (Corp. Hipp., Aer. 2 [Littré 2.14=189,6–9 Jouanna]) By investigating in this way and anticipating the decisive moments, someone would know best about each thing and reach health in the majority of cases and achieve not inconsiderable success in exercising the tekhnē.

The author thus promises both health and professional success. But these goods map onto two different beneficiaries: health for those whom the physician sets out to save, professional success for the physician. The idea that the physician has to protect himself, as Odysseus must, is not raised, except insofar as he has to secure his reputation. In fact, the author of Airs never mentions, either in the proem or later in the treatise, the vulnerability of the physician to the forces he hopes to master in order to save others: winds, waters, seasons – nothing leaves a trace on him. It is as if, in Airs, the very act of traveling keeps the traveler from being located anywhere in particular (a particular climate or a particular culture).25 The physician seems to lack a cavity of his own, that is, a body that would implicate him in the world described by the text. The comparison of our two texts, then, founders. It is true that the speaker of Airs bears similarities to Hermes. But the tacit immunity of the physician-addressee is more difficult to reconcile with the vulnerability of Odysseus. Then again, the

24 Brain 1982, observing that the treatise offers little in the way of specific instruction, proposes a more literal interpretation of the two infinitives in the result clause: he takes ἀπορεῖσθαι to mean “to be without resources,” i.e., the proper drugs, and διαμαρτάνειν to mean “to fail utterly.” The reading is attractive, and Jouanna seems to accept it (2003, 188 n. 4). Nevertheless, it does not rule out the less concrete sense of the verbs (knowing what to expect leads the physician to ensure his knowledge of the likely diseases is thorough and up-to-date and it helps him make predictions). See also Corp. Hipp., Aer. 24 (Littré 2.92=250,9–10 Jouanna). 25 We might infer that the ideal addressee is the product of a European milieu, in view of the information that Europeans are sharpest and most intelligent with regard to the tekhnai, in contrast to the more sluggish inhabitants of Asia: see Corp. Hipp., Aer. 24 (Littré 2.92=249,6–7; 250,5–7 Jouanna). But these are only inferences: the author is not explicit. For allegations of a European bias in the treatise, see Isaac 2004, 55–109; Calame 2005, 135–156. Cf. Thomas 2000, 88–98, who draws a more complex picture of the author’s treatment of Europe and Asia.

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differences between the two figures may be just what one would expect, given the strong generic differences between the two texts. Odysseus is a character in a narrative poem, and not just any character but an epic hero, moving through a world thick with danger. The physician, by contrast, is defined solely through his professional status within the parameters of a practical manual, albeit a manual that seems to have had a broad public.26 Everything else is pruned away. Yet it is precisely the nature of this pruning that is so interesting. For what we are witnessing in Airs and other late fifth- and early fourth-century  Hippocratic texts is the development of a new position of medical authority. Airs presents us with a figure who remains apart from the field of forces that he commands through his expertise. His circumscribed position is why there is no question, as there is for Odysseus, of saving himself before he saves others. But in exploring what such a position of medical authority looks like and how it takes form, we may not want to set Odysseus aside so quickly. Odysseus is, after all, not simply a character in an epic narrative. He is also a storyteller himself, and never more so than when he narrates his adventures at the court of the Phaeacians. His narration, set off within the poem by its own style, rivals not only that of the court poet, Demodocus, but also, as Egbert Bakker has recently argued, that of the epic poet himself.27 The hero’s split persona exposes a structural division between the position of the poet, who, endowed with godlike vision, stands at a distance in time and space from the events he narrates, and the position of the quest hero, who navigates, half-blindly, various obstacles and threats. Of course, part of the complexity of Odysseus and the Odyssey itself comes from the mutual contamination of these two perspectives, especially in Books 9– 12. The point-of-view of Odysseus the storyteller, who speaks with the benefit of hindsight, is subtly interwoven with the more limited point-of-view of the embedded hero.28 We can see, too, a mutual contamination of roles. Odysseus the narrator speaks not just as a poet but as a survivor, someone who has flirted with death

26 The ethnographic half of the treatise suggests a broader audience, as Althoff notes (1993, 222). Jouanna observes stylistic markings reminiscent of oral performance (1996a, 11 n. 14) and notes that “le paradoxe et que cette œuvre destinée à des hommes de l’art est parfaitement lisible par des profanes” (ibid.). I find it likely that Airs was destined for a general audience. In any event, it is certainly a text that contributes to the rhetoric of medical authority. 27 Bakker 2009, comparing the affinity between Odysseus and the poet of the Odyssey to that between Achilles and the poet of the Iliad (on which, see Martin 1989). On the stylistic differences between the voice of the bard and the narrative voice of Odysseus, see de Jong 2001, 225–226. 28 On contaminated perspectives, see, e.g., Homer, Od. X 232–243, where Odysseus is recounting the fate of the first expedition of men. We are led to believe that the report Eurylochus makes to Odysseus is the source of Odysseus’ knowledge. But Eurylochus’ report lacks the events recounted at X 232–243 (the mixing of the potion, its effects, the actual metamorphosis, and the herding of the victims into a pen). The excess knowledge of the narrator – presumably Odysseus but perhaps, also, the bard – thus noiselessly enters the text, intercalating a more expansive perspective with a perspective caught up in the unfolding events.

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time and again and never failed to slip its grasp, while Odysseus the polytropos hero often seems to command a perspective not unlike that of the Muse-inspired poet – or a god – even when he is in the middle of things. Recall what Circe says to him: you have a mind that cannot be enchanted. And yet, the thrill of the poem comes from the possibility that Circe might be wrong, from the possibility of Odysseus’ seduction, deception, and death, from his subjection to what Pietro Pucci has called “the empire of necessity.”29 The epic’s narrative drive requires that Odysseus never simply be a disembodied knower, immune to mortal dangers. He always, one might say, has skin in the game. But what about the epic narrator himself? Does he shed light on the nature of authorial immunity being articulated in the rhetorically oriented Hippocratic texts? The position from which he speaks is indeed circumscribed in intriguing ways. It is determined by the display of a specific kind of expertise: Alcinous praises Odysseus, for example, for telling his story, muthos, with a skill suited to the professional singer, the aoidos (Homer, Od. XI 368). Moreover, whereas Odysseus’ authority as a speaker is grounded in autobiographical experience, that of the singer is established through his first-person relationship to the Muses as representatives of a “god’s-eye” view of the past, a bond that is invoked at programmatic moments.30 Finally, the narrative unfolds in a specific spatiotemporal context, where the poet is suspended as a conduit between the audience and the vivid reality of a past made present through the intervention of the Muses. It is precisely the conditions of the performance context that protect the speaker from the dangers of the narrated world. For however much he is plunged through inspiration into “a kind of ecstasis… leav[ing] his own self and lodg[ing] himself in another self that thinks and acts in another time and place,”31 however much he speaks just like one present at the events related (e.g., Od. VIII 491), the first-person voice of the narrator remains protected from the action of the poem, for the simple reason that he is not present, and never was present, at those events as an embodied actor.32 He may express emotional involvement in the events 29 See Pucci 1987, 17, 148–154. On the tension between survival and danger that defines Odysseus in the poem, see Pucci 1987, 14–16, 62. 30 E.g., Homer, Il. II 761–762, XI 218–220, XIV 508–510; Od. I 1. Griffith 1983, 46–47 relates the reticence of the first-person speaker in Homer to the near-absence of references to the performance conditions and context, emphasizing that the proems to the poems (now lost) would have provided an occasion for the persona of the poet to emerge more fully. On the use of the god’s-eye view and other perspectival points in Homeric narration, see de Jong & Nünlist 2004. 31 Bakker 2009, 120. On the poet’s “presence” at Troy, see also Graziosi & Haubold 2010, 4–6. 32 Homer, Il. IV 539–542 is a fascinating passage in this context. The poet is concluding a description of a fierce battle: ἔνθά κεν οὐκέτι ἔργον ἀνὴρ ὀνόσαιτο μετελθών, / ὅς τις ἔτ’ ἄβλητος καὶ ἀνούτατος ὀξέϊ χαλκῷ / δινεύοι κατὰ μέσσον, ἄγοι δέ ἑ Παλλὰς Ἀθήνη / χειρὸς ἑλοῦσ’, αὐτὰρ βελέων ἀπερύκοι ἐρωήν (There no more could a man who was in that work make light of it, / one who was still unhit and still unstabbed by the sharp bronze / spun in the midst of that fighting, with Pallas Athene’s hold on / his hand guiding him, driving back the volleying spears thrown, transl. R. Lattimore). Who is this man? Kirk (1985, 398) sees him as a “hypothetical warrior,” and,

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through direct apostrophe to the characters, as when he addresses Patroclus on the threshold of death (Il. XVI 787). Nevertheless, he sees without being seen. The dangers faced by the poet arise, rather, from his role as an expert singer who is responsible for mediating a vast trove of privileged knowledge in the agonal space of performance: the inability to communicate information (e.g., Il. II 484) and, implicitly, the competitive pressures of other poets and other variants. They are, in short, dangers of the profession. The persona of the epic poet comes into sharper relief if we look to other archaic genres. In Hesiod’s Works and Days, for example, the speaker is more deeply embedded in the described world. He is, to speak in general terms, a mortal, as susceptible to sun and cold and hunger as his addressee. More specifically, he adopts an autobiographical stance as one who is very much a victim of events, here the avarice and foolishness of his brother Perses.33 It is not important whether the persona incorporates biographical truths. What matters, rather, is that the barrier between the speaker and the described world is relaxed. Hesiod grounds his authority in the experience of that world, as well as through wisdom expressed through moral maxims that apply as much to himself as to his audience. If we turn to other genres of archaic poetry, we find that permeability also characterizes the variants of the much discussed lyric “I”. These poetic personae, especially in monody, are often shaped by the speaker’s susceptibility to suffering, as is well illustrated by Sappho’s fragment 31 (LP), with its exquisite deconstruction of the erotically traumatized speaker. Perhaps the most interesting examples in this context, if also the most difficult to classify, are the personae of early philosophical poems such as “Parmenides” and “Empedocles,” whose claims to wisdom are established in part through the narration of transformative experiences: Parmenides’ story of his journey beyond the gates of Night and Day and his instruction at the hands of a goddess in the ways of being and seeming and Empedocles’ claim to have passed through many incarnations en route to his present divinity.34 The speakers bear some similarity to the Homeric poet or the poet of the Theogony, both of whom claim knowledge of immortal and cosmic proportions. But they also embrace the possibility of occupying the position of divine knowledge themselves through practices of reasoning and, especially for Empedocles, purification.35 Most important, in these practices given that he can be wounded, Kirk, I believe, is right. Still, there is a sense here of the poet and the audience moving in the midst of battle, protected only by the benevolence of Athena. Yet however much these spectators flirt with danger, they remain “structurally” protected from the violence being described. I am grateful to Barbara Graziosi for bringing this passage to my attention. 33 On the nature of Hesiod’s persona and for a decisive refutation of the older view that his poems express a new strain of self-expression in early Greek poetry, see Griffith 1983. 34 See Empedocles fr. 31 B112 Diels-Kranz; see also B146; Parmenides fr. 28 B1 Diels-Kranz. 35 On these practices as constitutive of an immortal self, see Miller 2011, esp. 43–77 on Parmenides and Empedocles. On Empedocles and Parmenides, see also Kingsley 1995, trying to reconstruct the priestly and shamanistic tradition that seems crucial to understanding Empedocles’ claims of

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the integrity of the self of the speaker is at stake: reason is redemptive, salvific, transcendence-making. Empedocles comes to save others only after having saved himself.36 These figures of authority draw us away from the more austere first-person voice of the epic poet, determined by the immediate performance context, toward the messier entanglements of an Odysseus-like figure, whose “I” bleeds into the narrrative being performed. But it is just these entanglements that seem so foreign to the construction of authority in Airs, too. Like the epic poet, the medical author identifies fully with his position of specialized expertise, expressed in terms of tekhnē, as does the persona constructed as an addressee. These positions promise a transpersonal view not unlike that provided by the Muses to the poet. Finally, the dangers faced by both the physician and the speaker – the epideictic milieu offers pitfalls of its own – are attendant on the performance of a professional role: damage to reputation but also the specific danger of not knowing and being at a loss. Elsewhere in the Corpus, the presence of rivals who may undercut one’s authority is explicit.37 The contexts where medical authority is exercised – the represented world of the physician in Airs, as well as its own conditions of performance – appear to exempt those wielding that authority from the field of physical forces over which they claim control, much as the poet-narrator stands outside the world that he represents. At the same time, the speaker of Airs and his addressee are hardly isolated from the world described in the treatise, as we can see if we return to the respective scenes of instruction in that text and Odyssey X. Whereas in the epic, the meeting of Hermes and Odysseus is described as a past event, and tersely at that, the medical text enacts instruction in the nature of things. The addressee is encouraged to adopt the author’s position of epistemic mastery by performing “experiments” that allow him to “see” for himself, through inferential reasoning, the workings of things that exercise their dunameis on human nature.38 The world of authority and, perhaps, those of Parmenides. The context established by Kingsley offers tantalizing parallels to the “shamanistic” aspects of the narrative voice of Odysseus adduced by Bakker 2005, esp. 14–18; 2009, 134–135. 36 See Empedocles fr. 31 B112 Diels-Kranz, with Stehle 2005 on the speaker’s relationship to his audience. 37 See, e.g., Corp. Hipp., Vet. Med. 13 (Littré 1.600=134,11–12 Jouanna). On this passage and eristic challenges more generally, see Demont 1993, 202–205. 38 See, for example, Corp. Hipp., Aer. 8 (Littré 2.36=207,12–208,3 Jouanna): εἰ γὰρ βούλει, ὅταν ᾖ χειμών, ἐς ἀγγεῖον μέτρῳ ἐγχέας ὕδωρ θεῖναι ἐς τὴν αἰθρίην, ἵνα πήξεται μάλιστα, ἔπειτα τῇ ὑστεραίῃ ἐσενεγκὼν ἐς ἀλέην, ὅπου χαλάσει μάλιστα ὁ παγετός, ὁκόταν δὲ λυθῇ, ἀναμετρεῖν τὸ ὕδωρ, εὑρήσεις ἔλασσον συχνῷ (If you wish, when it is winter pour some water into a jar with a measure and put it outside, where it will harden best; then, the next day, bring it inside where the ice will melt best, and, when it is melted, measure the water: you will find that it is far less). On the use of εὑρήσεις in the treatise, see also Corp. Hipp., Aer. 13 (Littré 2.56–58=223,2–6 Jouanna), 16 (Littré 2.64–66=230,1–3 Jouanna), 20 (Littré 2.74–76=235,9–236,2 Jouanna), 24 (Littré 2.90=248,3– 6 Jouanna). See Jouanna 1996a, 20–21 n. 37 for first- and second-person verbs more generally in

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the text is continuous with that of the addressee instead of being sealed in the past, as in epic. The knowledge at stake is not dependent on a divine gatekeeper. It is, rather, right there, ready to be discovered with one’s own hands and mind. The author speaks not as one inspired by the Muses but as a subject defined by observation, active engagement with the physical world, and argument. It is for this reason that another comparative strategy would place the speaker of Airs and his protégé next to Empedocles, who, in other fragments, uses the everyday device of the clepsydra to explain how we breathe, and Parmenides, who uses logic to trace a deductive line to the truth.39 The author’s position in the medical treatise is hardly just that of a spectator, restricted to the rare expression of pity for a hero he sees running headlong to his death. He is an active participant in the world that he describes, as is the addressee who, far from being asked to accept the speaker’s vision of the world on faith, can recreate it and test it for himself. Yet what needs to be determined is on what terms the figure of medical authority participates in the physical world that he describes. What we have seen of Airs suggests that the role of the physician is premised on unidirectional engagement with the cavities of others, that is, engagement that does not open the physician’s own cavity up to disease, contrary to what we saw in Thucydides’ account of plague. The subject of medical authority thus occupies a position of assumed immunity, a position that I described earlier as “structurally disembodied.” What are the structures that support the disembodiment of medical authority in the classical period? How is this disembodiment affected by the contexts where such authority is deployed? And what are the larger implications of a physician role articulated around the absence of the vulnerable body?

2 The Structure of Knowledge in Naturalizing Medicine The physician in Airs, Waters, Places, as we have just seen, is represented as standing outside the physical forces that harm his patients. But does this mean he is disembodied? Indeed, the claim that the physician occupies a disembodied position of knowledge may seem, at first glance, counterintuitive. To the extent that ancient Greek physicians engage the body through the senses, rather than through, say, the machines so dominant in modern biomedicine, they are sometimes invoked as early witnesses to a lost tradition of embodied medicine. The medical writers themselves emphasize the epistemological value of the senses. “The task,” the author of Epidemics VI writes, “is to bring the body under investigation: vision, the treatise. I use the word “experiment” loosely, recognizing that the Hippocratic authors do not pursue experimentation in the modern sense of the word. See Lloyd 1979, 146–169. 39 Empedocles fr. 31 B100 Diels-Kranz; Parmenides fr. 28 B8 Diels-Kranz.

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hearing, nose, touch, tongue, reasoning arrive at knowledge (τὸ σῶμα ἔργον ἐς τὴν σκέψιν ἄγειν, ὄψις, ἀκοή, ῥίς, ἁφή, γλῶσσα, λογισμὸς καταμανθάνει, Corp. Hipp., Epid. VI 8.17 [Littré 5.350=180,3–4 Manetti-Roselli]).”40 The portrait he draws appears to be the paradigm of embodied knowledge. Yet if we look closer at the grammar of the passage, we can see that it is organized by a split between the senses and reason, on the one hand, and the body (sōma) represented as an object of inquiry, on the other. Rather than representing knowledge as originating in or mediated by the body, the author casts the body as an object of inquiry while aligning the senses with reasoned investigation (logismos). That is, the senses form a continuum with reason, rather than with the physical body, understood here and elsewhere in the Hippocratic Corpus primarily as a field for the play of impersonal and often volatile forces associated with stuffs like the hot and the cold or bile and phlegm.41 It is true that physiological accounts of sensing, such as the explanation of sight, smell, and hearing in On Fleshes or the analysis of the brain in On the Sacred Disease, do submerge the senses into the dynamics of the humoral body.42 In Hippocratic representations of medical practice, however, regardless of the text’s subgenre, the physician’s senses function independently of the physiological stratum in the service of reasoned inquiry.43 It is worth emphasizing, moreover, the related fact that the senses are on the side of the reality of the physical world outside the self in classical medical writing. Their claim on truth is particularly pronounced in appeals to autopsia, “seeing for 40 See also Corp. Hipp., Off. med. 1 (Littré 3.272=30,2–7 Kühlewein). 41 On the nature of this body, see Holmes 2010b, 121–147. 42 Corp. Hipp., Carn. 15–17 (Littré 8.602–606=197,17–199,23 Joly); Corp. Hipp., Morb. sacr. 14 (Littré 6.388=26,14–27,4 Jouanna). The physiology of sensing was a common topic in the inquiry into nature. For early views, see Theophrastus’ De sensibus, although his accounts must be understood in light of the principles of Peripatetic doxology: see Baltussen 2000. 43 The opening of On Breaths is interesting in this context: εἰσί τινες τῶν τεχνέων, αἳ τοῖσι μὲν κεκτημένοισίν εἰσιν ἐπίπονοι, τοῖσι δὲ χρεωμένοισιν ὀνήϊστοι, καὶ τοῖσι μὲν δημότῃσιν ξυνὸν ἀγαθόν, τοῖσι δὲ μεταχειριζομένοισί σφας λυπηραί. Τῶν δὲ δὴ τοιούτων ἐστὶν τεχνέων καὶ ἣν οἱ Ἕλληνες καλέουσιν ἰητρικήν· ὁ μὲν γὰρ ἰητρὸς ὁρεῖ τε δεινά, θιγγάνει τε ἀηδέων, ἐπ’ ἀλλοτρίῃσί τε συμφορῇσιν ἰδίας καρποῦται λύπας· οἱ δὲ νοσέοντες ἀποτρέπονται διὰ τὴν τέχνην τῶν μεγίστων κακῶν, νούσων, λύπης, πόνων, θανάτου (There are some tekhnai that are troublesome to those who possess them but beneficial for those who use them, a common good for laypersons, but distressing to those who practice them. To the tekhnai of this kind certainly belongs what the Greeks call medicine. For the physician sees terrible things, touches unpleasant things, and harvests sorrows that are all his own from others’ misfortunes. But the sick are freed from the greatest ills on account of the tekhnē: from pain, sufferings, and death, Corp. Hipp., Flat. 1 [Littré 6.90=102,1–103,4 Jouanna]). On the passage and later echoes of it, see Jouanna 1988, 9, 128–129. The passage continues to treat the physician as an observer (rather than grounding observation in the body), although it colors his task with a vivid evocation of the woes associated with it. The fact that the physician remains on the side of observation, associated with a specific role (notice that the woes that he harvests are uniquely his) is consistent with my argument, but it does lend a note of empathy and emotional investment lacking in other Hippocratic texts. I thank Faith Wallis for reminding me of the passage.

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oneself.” In a well-known example, the author of On Generation/On the Nature of the Child builds support for his arguments about the nature of the embryo – that it is enclosed by a membrane, that it breathes – by introducing evidence from his own experience:44 καὶ μὴν ἓξ ἡμέρας μείνασαν ἐν τῇ μήτρῃ γονὴν καὶ ἔξω πεσοῦσαν αὐτὸς εἶδον· καὶ ὁκοίη μοι ἐφαίνετο ἐν τῇ γνώμῃ τότε, ἀπ’ ἐκείνων τὰ λοιπὰ τεκμήρια ποιεῦμαι· ὡς δὲ εἶδον τὴν γονὴν ἑκταίην ἐοῦσαν ἐγὼ διηγήσομαι. (Corp. Hipp., Genit./Nat. puer. 13 [Littré 7.488–490=55,4–8 Joly]) And indeed I myself saw seed that had remained in the womb for six days before falling out. And on the basis of how it appeared to me judging at that time, I will create the following proofs. But now I will explain how it was that I saw the six-day-old seed.

The author’s observation of the seed, as we can see, plays a pivotal role in grounding the proofs that he intends to offer, as the repetition of the verb “I saw” (εἶδον) makes clear.45 But the emphasis does not just fall on the observation. The author also uses a powerful first-person voice, underscored by the use of the intensive pronoun (autos). The effect is not that of narrow subjectivity. Rather, both the assertive first-person stance and the reference to a specific act of seeing, together with the appeal to proofs, cue an intensified, self-conscious argumentative mode that we see elsewhere in the rhetorical medical texts, as well as in Herodotus.46 The passage thus throws into relief an important facet of a common Hippocratic persona – namely, that of the expert observer who is adept at reasoning about what he sees. The act of vision is neither sensuous nor contingent but the handmaiden to medical knowledge. The concept of disembodied knowledge that I am working with here, in short, does not exclude sensory knowledge, but cooperates with it. But why not turn that critical gaze on one’s own body? If it is clear enough why such self-reflexivity is of little use to the (male) author of On Generation/On

44 For other cases of autopsia, see, e.g., Corp. Hipp., Carn. 18 (Littré 8.608=200,17–20 Joly), 19 bis (Littré 8.610=200,28–201,1 Joly; Littré 8.614=202,24–25 Joly), where the witnessing scenario is remarkably similar to that above; Corp. Hipp., Epid. V 46 (Littré 5.234=22,8 Jouanna). 45 The author repeats εἶδον again in conclusion (Corp. Hipp., Genit./Nat. puer. 13 [Littré 7.492= 56,6–7 Joly]). He also promises to offer another piece of evidence (ἱστόριον) that will make clear “to anyone wanting to know” that what he says is true (Corp. Hipp., Genit./Nat. puer. 13 [Littré 7.492=56,7–10 Joly]). 46 On the use of the language of proof at self-conscious moments of argumentative intensity in the medical writers, see Thomas 2000, 195–198, 235–247 on the polemical first person (esp. 242– 247 on its possible epideictic context); see also Debru 1992, 85–89, discussing later medical writing. On Herodotus, see Dewald 1987, 158; Marincola 1987, 131; Thomas 2000, 193. The use of the firstperson voice in the medical writers is often associated with claims to originality or innovation (Lloyd 1987, 61–69), although it can also be appropriated for a conservative stance (von Staden 1994b, 104). Van der Eijk observes that the first-person voice is common in archaic poetry when the speaker is invoking general truths (1997, 116).

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the Nature of the Child in the passage above, there are other situations where the speaker could take his own body as an object of observation and even experimentation. Far from being purely subjective, the speaker’s own corporeal experience, we might imagine, could facilitate the observation of general truths, as it does for Thucydides, who, in describing the symptoms of the plague, uses his own body as a portal onto the nature of all bodies while investing those observations with the full weight of autopsy. Plato, in fact, represents the physician’s susceptibility to disease as a natural asset in medical education in Book 3 of the Republic: ἰατροὶ μέν, εἶπον, δεινότατοι ἂν γένοιντο, εἰ ἐκ παίδων ἀρξάμενοι πρὸς τῷ μανθάνειν τὴν τέχνην ὡς πλείστοις τε καὶ πονηροτάτοις σώμασιν ὁμιλήσειαν καὶ αὐτοὶ πάσας νόσους κάμοιεν καὶ εἶεν μὴ πάνυ ὑγιεινοὶ φύσει. (Plato, Res publ. III, 408d10-e2) Physicians (I said) would be most clever if beginning from childhood they became familiar with the greatest number of the most diseased bodies, besides learning the tekhnē, and suffered every disease and were not in the least bit healthy by nature.

Socrates, who is speaking here, suggests that the physician’s own experience of disease can contribute to his general knowledge of the nature of the body and its pathologies. Some centuries later, Galen will introduce evidence from his own sufferings into his medical writings, turning his trained eye on his own body, and stories of self-experimentation are scattered through the annals of Western medicine and science.47 The Hippocratic writers, however, do not exploit this route to knowledge or authority, even when they are making general arguments about human nature. The physician’s powers of observation are turned on the bodies of other people: his gaze moves outward, not reflexively. Not only, then, is the physician immune to disease, at least in his role as a medical authority: he is also excluded as an object of medical inquiry. Before trying to better understand these two aspects of the physician role, I would like to consider a class of possible exceptions to my claim that the physician’s body is absent from the field of inquiry. These are cases in treatises addressed to a more general audience where we find the author appealing to embodied experiences that he assumes are shared by all of his listeners, such as having your leg fall asleep or getting a headache, in order to support his arguments about hidden causes and entities.48 These rhetorical strategies imply that the speaker himself belongs to a broader embodied community. 47 See Galen, Loc. aff. II 5 (Kühn 8.81). On self-experimentation in Western medicine, see Altman 1972; Schaffer 1992; Forcht Dagi 1995; Schaffer 1998; Strickland 1998; Schiebinger 2004, 388–392. 48 Corp. Hipp., Virg. 2 (Littré 8.466–468=22,17–20 Lami); Corp. Hipp., Morb. sacr. 3 (Littré 6.366= 11,9–13 Jouanna). See also, e.g., Corp. Hipp., Carn. 18 (Littré 8.608=200,7–8 Joly), where the author offers a similar example with the indefinite pronoun τις; Corp. Hipp., Nat. hom. 2 (Littré 6.34= 168,4–5 Jouanna). At Corp. Hipp., Flat. 14 (Littré 6.110=121,14–15 Jouanna), sleep, insofar as it is “common to all” (ἅπασι τοῖσι ζῴοισι κοινόν ἐστιν), can serve as a uniquely persuasive “witness” to what an author is saying (μαρτυρεῖ τοῖσιν εἰρημένοισιν). See also Corp. Hipp., Flat. 7 (Littré 6.100= 111,10–12 Jouanna): the belching most people experience is adduced to support an argument about

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The premise of the speaker’s participation in this community is made explicit in the few cases where we see the use of the first-person plural. The construction is especially striking in the treatise On Ancient Medicine, whose speaker moves between a first-person plural primarily allied with human beings as a species and a first-person singular aligned with the physician.49 It is as a member of the species that he appeals to “the most manifest of cases in which we are all experienced and which we will keep experiencing (τὰ φανερώτατα ὧν πάντες ἔμπειροι πολλάκις ἐσμέν τε καὶ ἐσόμεθα)” to support his argument about the causes of disease (Corp. Hipp., Vet. med. 18 [Littré 1.612–614=142,6–8 Jouanna]). The first of these cases is a flux from the head and nose, the symptoms of which, he assumes, are familiar to “those of us” who have suffered from it.50 By using the first-person plural here, he implicitly identifies with others who have suffered the affection, perhaps laying claim to a kind of muted autopsy. Yet, on closer examination, the force of the author’s rhetorical strategy lies not in his own experience but, rather, in the experience of the addressee, who is invited to verify the argument being put forth with the evidence produced by his own body. It is the addressee’s body, in other words, not the speaker’s first-person authority, that is being called upon to bear witness to the claims being made. The speaker withdraws into the crowd, trading his specialized knowledge for the collective knowledge of his audience – or at least a collective experience that is the proper basis for knowledge, as the speaker establishes in his polemical remarks on method in the opening chapters of the treatise.51 In so doing, he tacitly acknowledges that, like his addressees, he has a physical body. Nevertheless, the acknowledgement is not given rhetorical weight. One reason the speaker does not emphasize his own corporeal experience here may be because he is not primarily defined in the treatise by his participation in a community of sufferers. Except for his quiet implication in the first-person plural here and on a couple other occasions, he emphatically positions himself as a physician whose knowledge is acquired from observing the bodies of other people.52 The

bad regimen. On appeals to general experience in medical writing, see also the remarks of Diller 1932, 40; van der Eijk 1997, 117; Laskaris 2002, 129–132. 49 The complex authorial persona has suggested to some scholars an audience of experts and laypersons: see Jouanna 1990, 14–17; cf. Schiefsky 2005, 36–46, positing an audience of laypersons. On hybrid and lay audiences more generally, see Kollesch 1991, 179–181; Althoff 1993, 222–223; Demont 1993, esp. 192–201; Wittern 1998, 30–33; Dean-Jones 2003, 112–121; Cañizares 2010. 50 Corp. Hipp., Vet. med. 18 (Littré 1.614=142,8–15 Jouanna). 51 In the first chapter, the speaker argues that the audience should be able to test any statement put forth for themselves, rather than trusting in the “hypotheses” of the speaker: see Corp. Hipp., Vet. med. 1 (Littré 1.572=119,4–11 Jouanna) and the remarks at Corp. Hipp., Vet. med. 20 (Littré 1.620– 622=145,18–146,15 Jouanna). 52 For the first-person plural elsewhere in the treatise, see Corp. Hipp., Vet. med. 7 (Littré 1.584= 126,7 Jouanna), 15 (Littré 1.604=137,19 Jouanna): both examples refer to the use of cooked foods by both the author and his audience. See also, e.g., Corp. Hipp., Flat. 14 (Littré 6.112=122,14–16

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speaker’s claim to medical authority is particularly pronounced in a programmatic statement early in the treatise, where he declares that someone discussing the tekhnē must discuss things known to laypersons if he is to remain in touch with reality, “for it is a question of researching and describing nothing other than the affections that afflict these very people and on account of which they suffer (οὐ γὰρ περὶ ἄλλων τινῶν οὔτε ζητεῖν οὔτε λέγειν προσήκει ἢ περὶ τῶν παθημάτων ὧν αὐτοὶ οὗτοι νοσέουσί τε καὶ πονέουσιν, Corp. Hipp., Vet. med. 2 [Littré 1.572= 120,3–7 Jouanna]).” Sufferers, from the perspective of the physician, are other people. At this most methodologically significant moment, then, the author positions the physician – and, indeed, himself – formally on the side of disembodied experience, isolated from the broader embodied community. He stands outside the body looking in. The split between physicians and those who suffer is also evident in the speaker’s treatment of the history of medical inquiry. The first phase of discovery is better described as the origin of dietetics. At some time in a distant past, some particularly insightful people observe the corrosive effects of raw foods on their own natures. Driven by pain, they discover a means of avoiding it: they learn to cook. The second phase is still empirical in the sense that knowledge is gained through observation and testing, according to the method that was used to develop dietetics. But it is dominated by physicians, who, in developing medicine beyond dietetics, move away from research on their own bodies towards a rough-and-ready experimentation with the bodies of others as they work to find types of food suitable for the sick.53 The earlier phase of research on human nature persists insofar as each person develops knowledge for himself about the foods best suited to his nature. But a practice where “no one is a layperson but everyone is knowledgeable through use and necessity (ἧς γὰρ μηδείς ἐστιν ἰδιώτης ἀλλὰ πάντες ἐπιστήμονες διὰ τὴν χρῆσίν τε καὶ ἀνάγκην)” cannot be considered a tekhnē (Corp. Hipp., Vet. med. 4 [Littré 1.578=123,9–12 Jouanna]). Medicine, in contrast, is a proper tekhnē. One of the aspects that make it a tekhnē is the asymmetrical relationship between the observing physician and the embodied patient.54 The asymmetry of the clinical encounter offers us a way of beginning to answer the question of why the place of the physician does not coincide with that of the suffering body. For, quite simply, the clinical encounter structures a relationship that opposes the physician to the body. It is admittedly no great revelation to say that the physician is defined through his position in a relationship with the ailing

Jouanna): ὅταν οὖν ἐκ τοῦ εἰωθότος ἔθεος μεταστέωμεν, ἀπόλλυται ἡμῖν ἡ φρόνησις. For the firstperson plural in a later writer, see von Staden 1994b, 108–109, on Celsus. 53 Corp. Hipp., Vet. med. 6 (Littré 1.582–584=125,5–126,2 Jouanna). 54 The clinical relationship could also be expressed in terms of a triangle involving the doctor, the patient, and the disease: see Corp. Hipp., Epid. I 11 (Littré 2.636, ch. 5=190,3–6 Kühlewein). But this triangle often collapses in the medical treatises into an opposition between the physician and the body.

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patient. Such a relationship, after all, is visible not only in our earliest Greek texts but in older Egyptian and Babylonian medical writings. The very notion of a healing professional, summed up in the word iatros, assumes that the healer treats others on the basis of specialized knowledge. Otherwise, we have a situation like Herodotus describes in Babylon, where they have no need of physicians and the sick lie in the marketplace awaiting advice from passersby with experience of the ailment from which they are suffering (I 197). But, as I observed earlier, the role of the physician is changing as medicine itself changes in the classical period. The claim that I am making about disembodiment makes sense only in a context where the physical body has emerged as what I have elsewhere called a “conceptual object” – namely, within the context of naturalizing medicine and, more broadly, the inquiry into nature.55 The body emerges as an object with a nature (phusis) that is not immediately transparent but that can be studied and managed by those with proper technical knowledge and expertise. The rise of medical interest in the nature of the body, I suggest, expands the structure of the clinical relationship, transforming the roles of healer and patient. If we turn back to On Ancient Medicine, one reason suggests itself for the author’s relative lack of interest in his own body as a source of knowledge. For, despite the significance of human nature in the treatise and, hence, the potential for acquiring general knowledge through one’s own body, what comes to be most important are particularities, that is, the idiosyncrasies of individual natures, especially in their interactions with food and drink. The complexity of human nature is compounded in the case of disease. It is just this complexity, together with the need for greater study and precision that it entails, that, on the author’s view, differentiates medicine from dietetics. The greater complexity of human nature in disease presumably leads to the development of specialized knowledge acquired outside the limited experience of one’s own body.56 The physician following the proper method, at least in On Ancient Medicine, has two primary ways to gain such knowledge. On the one hand, the physician establishes his epistemic advantage vis-à-vis the general public by engaging with and closely observing a wide range of bodies and natures.57 Like the traveler not bound to a particular climate or a particular 55 Holmes 2010b. 56 See esp. Corp. Hipp., Vet. med. 7 (Littré 1.584–586=126,14–16 Jouanna): τί δὴ τοῦτ’ ἐκείνου διαφέρει ἀλλ’ ἢ πλέον τό γε εἶδος καὶ ὅτι ποικιλώτερον καὶ πλείονος πρηγματείης. See also Corp. Hipp., Vet. med. 9 (Littré 1.588=128,9–10 Jouanna), where medicine requires a greater degree of precision, akribeiē. On the specificity of medicine here, see further Diller 1975, 89; Schiefsky 2005, 176. For the differentiation between expert and lay knowledge, see also Corp. Hipp., Vet. med. 21 (Littré 1.624–626=148,4–19 Jouanna). 57 Such experience, together with knowledge of general principles (see above), allows him to aim at the proper measure in treatment (see Corp. Hipp., Vet. med. 9 [Littré 1.588–590=128,10–15 Jouanna]). See also Corp. Hipp., Vict. I 2 (Littré 6.470=124,17–24 Joly-Byl). On Vet. med. 9, see Schiefsky 2005, 185–207. For the meaning of aisthēsis in that passage, see Holmes 2010b, 167–169.

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land in Airs, he surveys bodies from a synoptic point-of-view that stands outside any body in particular.58 Such a point-of-view is built up from the physician’s own therapeutic and investigative experience. But his expansive field of vision, together with the authoritative perspective that it guarantees, ultimately transcends not just the limits of a single body but also the limits of a single lifetime insofar as it develops from his participation in a larger professional community, often expressed impersonally as the tekhnē.59 Many – although not all – of our extant Hippocratic texts stake their claims to authority on what they contribute to or communicate of the tekhnē, as we saw in the opening lines of Airs.60 On the other hand, the complexity involved in understanding the natures of bodies in medicine is often seen to require a grasp of the hidden causes and powers that determine health and disease, as is the case in On Ancient Medicine. Although such knowledge is built up from personal and collective experience, it is also established in the present tense of performance through self-conscious argument and references to observations, especially observations vouched for by the first-person speaker. Repeatedly in the Hippocratic Corpus, and especially in the rhetorical treatises, we find observations being translated into truth claims by being incorporated into conceptual frameworks and arguments about hidden forces and causes. The claim to be able to offer accounts of what is happening inside the cavity, below the threshold of what we feel of our bodies, is precisely what generates so much of the rhetorical “noise” that we find in some texts: the strong first-person voice, signs, and proofs.61 The stridency of this language and the insistent presence of an “I” can be chalked up to the difficulty of establishing transpersonal authority about the unseen world in a climate where claims to truth, never unchallenged among the poets, have become radically unstable. The result of these conditions is a first-person voice articulated through arguments designed to secure authority about what is hidden in the absence of Muse-like figures. The prehistory reconstructed by the author of On Ancient Medicine implies that technical knowledge arises when self-experimentation gives way, within the realm

58 The synoptic point-of-view is even more pronounced – and, in some cases, detached from experience altogether – in treatises more inclined towards the “philosophical” approach to human nature deplored by the author of On Ancient Medicine. The author of On Fleshes starts by going back to the beginning of the cosmos: see Corp. Hipp., Carn. 1 (Littré 8.584=188,14–17 Joly). The author of On Regimen believes someone wishing to treat human regimen must know not only the nature of man but also the dunameis of foods and drinks and exercises, the risings and settings of the stars, and so on: see Corp. Hipp., Vict. I 2 (Littré 6.468–470=122,22–124,17 Joly-Byl). 59 See von Staden 1996, 412 (writing about the Hippocratic Oath): “As a results-oriented, professional expertise, téchnê is learned, practised, and transmitted by individuals, yet it transcends them and their private lives, representing a transpersonal continuity and producing a transgenerational community.” 60 On the function of prologues for establishing the text’s importance to the tekhnē or general usefulness, see Lara Nava 1992, 348. 61 On this language, see Lloyd 1979, 59–102; Thomas 2000, 168–269, esp. 190–200.

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of medicine, to the pas-de-deux of the clinical encounter. We do not have to endorse this particular account of medical history to find it useful for understanding how the clinical relationship was being imagined once medicine had acquired an interest in the physical body and human nature as objects of specialized knowledge. For the very structure of the clinical relationship, in dividing the knowing agent from the helpless sufferer, divides the observer from the observed. Recall, for a moment, the passage from Epidemics VI. On closer inspection, we can see here that the fissure between the senses and reason, on the one hand, and the body, on the other, maps neatly onto the clinical relationship. The epistemological ambitions of naturalizing medicine, I suggest, expand the roles within this relationship. The role of the physician is elaborated into a position of expert knowledge about the physical body and human nature more generally, as well as a position of technical agency. The patient, for his part, is still a patient. But his role, too, develops to include serving as the object of investigation, rather than simply the target of healing. The two positions within the clinical relationship are thus rethought according to a structural opposition between, on the one hand, a “disembodied” position of observation and reasoned judgment, a position that often complements a synoptic point-of-view; and, on the other hand, the position assigned to the body as an object of inquiry and manipulation, frequently associated with ignorance. If a speaker interested in securing medical authority lays claim to the former position, we will hardly be surprised. Consider, for example, the opening chapters of On the Nature of a Human Being. The author, aiming to prove that there are four basic stuffs that constitute a human being, proposes an experiment of sorts that involves eliciting these stuffs from the body or, more specifically, from the bodies of other people: “if you were to give a man a medicine that draws out phlegm, he vomits phlegm for you…if you injure a man’s body so as to cause a wound, blood will flow from him (εἰ γὰρ διδοίης ἀνθρώπῳ φάρμακον ὅ τι φλέγμα ἄγει, ἐμεῖταί σοι φλέγμα… καὶ ἢν τρώσῃς αὐτοῦ τοῦ σώματός τι ὥστε ἕλκος γενέσθαι, ῥυήσεται αὐτῷ αἷμα, Corp. Hipp., Nat. hom. 5 [Littré 6.42=176,11–12; 178,1–2 Jouanna]).”62 The dynamics of the clinical encounter are adapted here to the inquiry into human nature, creating an eviden62 That the effects are produced through the bodies of other people is clear from the author’s discussion of how his opponents arrived at their conclusions: ὁρῶντες πίνοντας τοὺς ἀνθρώπους τὰ φάρμακα καὶ ἀπολλυμένους ἐν τῇσιν ὑπερκαθάρσεσιν… ὁρῶντες ἀποσφαζομένους τοὺς ἀνθρώπους καὶ τὸ αἷμα ῥέον ἐκ τοῦ σώματος… (They see those who drink drugs and die through excessive purgings… They see men who are cut and the blood flowing from the body …, Corp. Hipp., Nat. hom. 6 [Littré 6.44=178,11–12; 15–16 Jouanna]). The context suggests that those observing are other physicians. See also Corp. Hipp., Carn. 9 (Littré 8.596=194,15–23 Joly). The object body is not only that of the patient. We also find examples of proofs produced from the bodies of animals, e.g., Corp. Hipp., Artic. 8 (Littré 4.94–98=121,12–123,10 Kühlewein); Corp. Hipp., Carn. 8 (Littré 8.594=193,20–23 Joly); Corp. Hipp., Morb. sacr. 11 (Littré 6.382=21,15–22,4 Jouanna); Corp. Hipp., Mul. I 6 (Littré 8.30=100,10–11 Grensemann).

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tial scene organized by two positions: that of the anonymous persons whose bodies serve as sites of proof, and that of the observer, who manipulates the bodies of other people to generate proof. If we go back to the example of autopsia from On Generation/On the Nature of the Child, we find a similar scenario of the clinical encounter being repurposed for medical investigation. The author’s observations are embedded in a quasi-narrative frame: a kinswoman brings to him a courtesan who had recently conceived a child and asks him to induce an abortion. He orders (ἐκελευσάμην) the courtesan to jump, touching her feet to her buttocks; the seed falls out, apparently with a thud, on the seventh kick, and he makes the observations that he goes on to relate to his audience.63 The insertion of a narrative scene at this moment supports the construction of the first-person voice as a voice of observation and inquiry defined against the female patient who performs in accordance with the physician’s commands. We can see here, too, how the split between the role of the observing, manipulating subject and the role of the passive object of inquiry is underwritten by the implicitly hierarchical structure of the clinical relationship. The asymmetry of power implicit in that relationship is, if anything, exaggerated when it enlarges to encompass the investigation of the physical body. If the body is not forthcoming with signs, one must force nature to yield information, one author writes, using legal language reminiscent of the torture of slaves to produce evidence in court.64 The expansion of the clinical relationship beyond the healing event puts particular emphasis on the concept of a role. I have been fairly imprecise until now when talking about physicians, focusing on the authorial personae of the most rhetorical Hippocratic texts without excluding practicing physicians. Although these two groups are not the same, we have seen how they are implicated in each other: the clinical encounter is an important structural component of the construction of authority concerning the physical body in medical texts from the classical period, especially those oriented towards a general audience; the development of the physician role as a position of disembodied observation owes much to the rhetoric of medical authority in these treatises. Nevertheless, we must remain attentive to the ways in which the clinical encounter remains distinct from the contexts of oral performance and textual production in the classical period, especially in the sphere of the physician’s self-presentation. If we turn to the deontological texts of the Hippocratic Corpus, we do find interest not only in the question of how a physician should conduct himself but also in the question of what sort of a person the physician should be, where the concept of “person” is socially embedded and, to some degree, embodied. The main difficulty here is that virtually all the extant deontological texts have been

63 Corp. Hipp., Genit./Nat. Puer. 13 (Littré 7.490=55,8–19 Joly). 64 Corp. Hipp., Ars 12 (Littré 6.24=240,10–17 Jouanna). On the legal language, see von Staden 2007, 28–32.

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dated to the end of the fourth century  or later, making it hard to know whether the concerns that they express about the character and self-identity of the physician are a post-classical development.65 Still, given that the classical-era physician operated in a context where trust was crucial and in a culture where self-presentation was of the utmost importance in securing trust, what these later texts show us about the cultivation of a professional identity and the physician as a social and ethical actor can shed light on the authority of the physician role as it is being developed in epideictic performances and written texts.

3 The Practicing Physician The Hippocratic texts, as I have observed, do not represent either the authoritative speaker or the practicing physician as figures who have bodies that are vulnerable to disease or open to investigation. But we do find a few intriguing references in the Corpus to the kind of nature that is best suited to medical learning and inquiry, as well as to medical practice. In one of the rare such references outside the deontological texts, the author of On the Tekhnē claims that the ability to make medical discoveries rests not only on one’s training but also on the industriousness of one’s phusis.66 The idea that the physician should have a particular type of nature is elaborated in the treatise Law, whose author compares the natural ability of the physician, which must be adequate to the understanding of the medical tekhnē

65 For the argument that these concerns are due to the development of philosophy, see Edelstein 1967, 319–348; cf. Kudlien 1970b. Most scholars see Precepts and Decorum as Hellenistic or later, citing stylistic grounds and features that appear Stoic (or, less commonly, Epicurean): see Fleischer 1939, esp. 24, 59–60, 104–105 (dating Precepts and Decorum to the first or second century ); Moisan 1993, 10–26, arguing on stylistic grounds for a second-century  date for Precepts. Jouanna 1999, 380, 405–406 follows the first- or second-century  date suggested by Fleischer for Decorum but does not rule out a Hellenistic date for Precepts. Physician is usually dated earlier. Bensel (1922, 101–102) dates it to the second half of the fourth century ; his dating is followed by Jones (1923, 306) and Potter (1995, 298). Dean-Jones 2010, 71–72 seems to locate the text in the agonistic settings of the late fifth and early fourth centuries , but this is probably too early. Fleischer 1939, 56–57 places Physician in the third century  on stylistic and linguistic grounds; Edelstein 1967, 329 n. 19 concurs, adducing late Peripatetic ideals of the “gentleman” as a model; Moisan 1993, 169 sees the third century  as the earliest possible date (and allows that it may be as late as the first century ); Jouanna 1999, 404 dates the treatise to the Hellenistic period or even later. I would favor a late fourth-century  date, but it is difficult to be certain. Law is more difficult still: Edelstein 1967, 333 places it in the later fourth century . No doubt the most controversial text to date is the Oath: see below, n. 76. 66 Corp. Hipp., Ars 9 (Littré 6.16=235,7–8 Jouanna): δύνανται δὲ οἷσι τά τε τῆς παιδείης μὴ ἐκποδών, τά τε τῆς φύσιος μὴ ἀταλαίπωρα. See also Corp. Hipp., Off. med. 4 (Littré 4.284–288=32,17–33,10 Kühlewein), on natural formations of the fingers that are unsuited to surgical agility.

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(ἰητρικῆς σύνεσιν), to the soil in which the “seed” of medical learning takes root.67 The author of Decorum declares that for those engaged in the tekhnai, one’s nature is the most important thing, with wisdom following only what has been established by nature itself.68 Each of these texts recognizes the physician as someone endowed with a nature that determines his capacity to practice medicine. But nature is, in each case, a fixed state, and it is not defined in specific physiological terms. Are there aspects of the physician that have to be cultivated or managed? The physician is certainly advised in the deontological texts to take care of his appearance and his behavior in his interactions with the public and his patients. Texts like Physician, Decorum, and Precepts offer a host of suggestions as to how the addressee should present himself: he should dress modestly; he should avoid elaborate headgear; he should bear in mind how he appears at the bedside in terms of posture, dress, and demeanor.69 He should have a ready wit and eschew fussiness and show; he should give orders with calmness and good cheer, but he should be strict and sharp when necessary with the patient.70 He must be solemn and generous towards his fellow human beings while avoiding expressions of vulgarity.71 He must be moderate (σώφρων) in his lifestyle and in control of his desires.72 These last precepts shade into concerns about the physician’s character. Nevertheless, they keep the idea of cultivation in the foreground while rooting the self presented by the physician to his patients in his appearance and comportment. The most interesting evidence for the physician’s self-presentation in his professional practice is found in the opening lines of Physician, where the author recommends that the physician be of good complexion (εὔχρως) and “as fleshed out as nature intended him to be (εὔσαρκος…πρὸς τὴν ὑπάρχουσαν αὐτῷ φύσιν, Corp. Hipp., Medic. 1 [Littré 9.204=20,4–5 Heiberg]).”73 He goes on to explain the reasoning behind the advice: “For the common crowd considers those who are not in excellent condition with respect to the body to be unable to care for others (ἀξιοῦνται γὰρ ὑπὸ τῶν πολλῶν οἱ μὴ εὖ διακείμενοι τὸ σῶμα [οὕτως] οὐδ’ ἂν ἑτέρων ἐπιμεληθῆναι καλῶς, Corp. Hipp., Medic. 1 [Littré 9.204=20,5–7 Heiberg]).”74 Here, at last, we seem to have arrived at the idea that the physician has

67 Corp. Hipp., Lex 3 (Littré 4.640=8,1–7 Heiberg=272,1–6 Jouanna). Galen stresses natural ability as well: see Boudon-Millot 2009. 68 Corp. Hipp., Dec. 4 (Littré 9.230=26,7–15 Heiberg). 69 On dress: Corp. Hipp., Dec. 2 (Littré 9.228=25,17–19 Heiberg), 3 (Littré 9.228=25,21–24 Heiberg). On entering the room: Corp. Hipp., Dec. 11–12 (Littré 9.238–240=28,17–29 Heiberg). On headgear and perfumes: Corp. Hipp., Praec. 10 (Littré 9.266=33,22–34,2 Heiberg). 70 Corp. Hipp., Dec. 7 (Littré 9.236=27,24–26 Heiberg), 16 (Littré 9.242=29,13–19 Heiberg). 71 Corp. Hipp., Medic. 1 (Littré 9.206=20,15–18 Heiberg). 72 Corp. Hipp., Medic. 1 (Littré 9.204=20,9–13 Heiberg). 73 On the representation of the physician and his body in the early modern period and later (when the physician was portrayed as lean), see Lawrence 1998. 74 Ermerins’ emendation at Corp. Hipp., Praec. 6 (Littré 9.258=32,12 Heiberg), ἑαυτῶν for the ὑγιαινόντων of the manuscripts, produced the sense that the physician should care for himself,

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a physical body of his own that figures into the construction of his authority. Indeed, the masses appear to concur with Hermes that someone who fails to take care of himself cannot be trusted to take care of others. What is interesting, however, is that this idea is pointedly attributed to the many, implying that the care of the body, here as elsewhere in the deontological treatises, matters only for professional self-presentation. The construction of authority, of course, always takes place in dynamic interaction with a public and its expectations. Nevertheless, in attributing concerns about the care of the body to the masses, the author suggests that these concerns are not internal to the physician’s sense of identity.75 If we want a sense of how practicing physicians themselves may have understood their professional identity, our best source is undoubtedly what has been called “the most personal of Hippocratic texts of the classical epoch,” namely the Hippocratic Oath.76 The oath, after all, is a genre where the first-person speaker presents himself as an actor embedded in a network of social and ethical relationships with other people, as well as with the gods, and, through his performative utterance, binds himself to this community.77 The Oath not only conforms to these generic expectations but, in fact, exceeds them insofar as it insistently draws attention to the first-person speaker. The oathtaker assumes an obligation to “guard my bios” – “life” or “way of life” – “and my tekhnē in a pure and holy way (ἁγνῶς δὲ καὶ ὁσίως διατηρήσω βίον ἐμὸν καὶ τέχνην ἐμήν, Corp. Hipp., Iusi. 4 [Littré 4.630= 4,18 Heiberg=269,16 Jouanna]).”78 The phrasing here recognizes the physician’s but the reading is not accepted by most editors. For other examples of the “Physician, heal thyself” maxim, see Cicero, Fam. IV 5.5 and Amundsen 1977, 648. 75 Dean-Jones 2010 has recently reconsidered to whom this advice is directed, arguing that the addressee of Physician is not the beginning student but the teacher. The teacher, she argues, is being advised only to accept students who look healthy, presumably seeing the student through the eyes of a potential patient. 76 Von Staden 1996, 418 (emphasis in original), noting the high prevalence (vis-à-vis other Hippocratic texts) of possessive pronouns in the Oath. See also von Staden 2008, 437 (citing the “intensely personal nature of the performative enunciation of this oath”). The Oath is usually dated to the later fifth or fourth century . Some have argued, however, for a later date: see Ducatillon 2001; von Staden 2008 draws attention to linguistic features of the Oath that are more consistent with Hellenistic texts than with the classical-era Hippocratic texts. 77 On the Oath’s relationship to the oath genre, see von Staden 2008. 78 I print Jouanna’s text here and in n. 80. For the sense of bios as “manner of living,” see von Staden 1996, 419–422; 1997, 175–178; Boudon-Millot 2009. For the expression “in a pure and holy way” (ἁγνῶς…καὶ ὁσίως), see von Staden 1997, who concludes that it must be read in terms of an “internalisation and intellectualisation of purity … internalised as a condition characterized by a certain kind of mental life over which one has some control and for which one consequently is responsible” (188). For the combination of ἁγνῶς and ὁσίως, which is unusual in the classical period, scholars have often pointed to the elegiac inscription that appeared on the temple of Asclepius at Epidaurus (where ἁγνεία is found with ὅσια), conventionally dated to the fourth century . Bremmer 2002 challenges this dating and, accordingly, suggests that these adverbs entered the Oath at a later (Hellenistic) date. Cf. Chaniotis & Mylonopoulos 2005, 437, reaffirming

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mode of life and his tekhnē as discrete spheres.79 Yet by making both these goods objects to be guarded “in a pure and holy way,” the oathtaker conjoins the two spheres of action into a single field where he pledges to exercise moral vigilance. It is to this field that both the benefits that accrue to the physician who fulfills the oath and the punishments entailed by its violation apply.80 The Oath defines the physician, then, not only in terms of competence but also through his ethical character. The demands on the physician’s character are expressed explicitly through the various prohibitions: the physician swears, for example, not to violate the patient’s trust within the intimate space of the house by entering into sexual relations with the women and men, free or unfree, he meets there or by betraying what he sees or hears in the private domain.81 These demands are signaled implicitly through the reference to acting “in a pure and holy way.” The consequences of failing to uphold both aspects of one’s professional identity, moreover, are overseen by figures who do not exercise the power to harm elsewhere in the Hippocratic Corpus – namely, the traditional gods. The Oath thus positions the physician in a space unlike any other in the Corpus. The care of the self matters here. Indeed, the Oath stresses the idea of vigilant attention to one’s life and tekhnē as possessions of the self. Yet such care is organized not by the physician’s relationship to his own body and the impersonal forces that determine its well-being. It is defined, rather, by his social and moral obligations to his patients, his teachers, his fellow physicians, and the gods. The deontological texts and the Oath, in particular, are valuable insofar as they enrich our understanding of the professional role and self-identity of the physician in the classical period. They remind us that he is firmly located within the public milieu as a practitioner of medicine, while also suggesting something of the the earlier dating of the Epidaurian inscription on the basis of epigraphic evidence not considered by Bremmer (and thus supporting the earlier date of ἁγνῶς…καὶ ὁσίως). At the same time, the fluidity of the Oath’s phrasing in antiquity is suggested by our oldest ancient source, a third-century  papyrus from Oxyrhynchus (P. Oxy. 31.2547), which, in addition to diverging from the textus receptus in other ways, gives a variant reading for ἁγνῶς καὶ ὁσίως: ]ως κα[ὶ εὐ]σεβῶς. For recent discussions of the papyrus, see Ihm 2002 and Leith 2007. 79 Excellence in these two spheres continues to inform positive representations of the physician in the Hellenistic and Roman periods, as we can see, for example, in funerary inscriptions for physicians: see von Staden 1997, 159–172. 80 Corp. Hipp., Iusi. 8 (Littré 4.632=5,8–10 Heiberg=270,8–10 Jouanna): ὅρκον μὲν οὖν μοι τόνδε ἐπιτελέα ποιέοντι καὶ μὴ ξυγχέοντι εἴη ἐπαύρασθαι καὶ βίου καὶ τέχνης δοξαζομένῳ παρὰ πᾶσιν ἀνθρώποις ἐς τὸν αἰεὶ χρόνον, παραβαίνοντι δὲ καὶ ἐπιορκοῦντι τἀναντία τούτων (If I render this oath fulfilled, and if I do not blur and confound it, making it to no effect, may it be granted to me to enjoy the benefits both of life and of tekhnē, being held in good repute among all human beings, for time eternal. If, however, I transgress and perjure myself, the opposite of these. Transl. von Staden). 81 For the need to not violate the patient’s trust within the intimate space of the household, see also Corp. Hipp., Medic. 1 (Littré 9.206=20,19–23 Heiberg). Popular abuse of the physician at times represents him as violating this trust: see Amundsen 1977, 645–646.

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ideals of character and behavior that physicians might have imagined for themselves as both professionals and members of their communities. The relationship of these texts to those considered earlier, moreover, is instructive. On the one hand, the deontological texts conform to the expectations that we have developed from our study of the epideictic treatises. The Oath’s focus on the physician’s life (bios) in a social and professional rather than a biological sense, in particular, complements the portrait of the physician as disembodied. On the other hand, by expanding that portrait to include self-presentation and ethical obligations, both the Oath and deontological texts like Physician remind us of the differences between the negotiation of authority in the clinical encounter and the construction of medical authority in the rhetorical texts. The reference in Physician to the masses’ expectations about what a physician should look like makes it all the more interesting that our fifth- and early fourth-century  texts do not use the speaker’s care of his own body as a strategy for claiming authority, any more than they use the speaker’s body as a privileged site of evidence. The very specificity of the position of medical authority developed in the rhetorically inclined Hippocratic texts reminds us that although that position is indebted to the structure of the clinical relationship and the longstanding understanding of medicine as a craft, it emerges under unique discursive, performative, and conceptual conditions. In the clinical encounter, the physician meets his “audience” – the patient, as well as family members and onlookers – in a field defined socially, ethically, and pragmatically. The physician’s authority may still rely on rhetorical skill – as Gorgias immodestly stresses in Plato’s dialogue of the same name (456b1–5) – but it is constructed in relationship to immediate concerns about competence.82 By contrast, in the realm of the epideictic (or textual) “I,” authority, displaced from the clinical encounter, is negotiated vis-à-vis broader claims about human nature, disease, and the body and a more abstract concept of expertise.83 It is not that the epideictic “I” lacks a body. No doubt self-presentation mattered deeply in such contexts. But the performance context undeniably magnifies a speaking “I” – all the more pronounced in the written text – who, freed from the social conditions of the clinical encounter, comes more sharply into focus as a 82 The bedside could be a rhetorically contentious place, often populated by rival physicians. The beginning of On Diseases I, for example, seems addressed to a practicing physician who may have to defend his views before the patient or other physicians present at the bedside (Corp. Hipp., Morb. I 1 [Littré 6.140=2,3–6,4 Wittern]). On the physician’s everyday use of rhetoric, see Edelstein 1967, 65–85, 99–105; Lloyd 1979, 86–98; 1987, 56–70; Kollesch 1991, 182–183. On the practicing physician’s rhetorical use of learned medicine, see also Plato, Leg. IX, 857d2–4, where the idealized physician addresses his patient “almost like a philosopher, grasping the disease from its origin and going over every nature of bodies (ἐξ ἀρχῆς τε ἁπτόμενον τοῦ νοσήματος, περὶ φύσεως πάσης ἐπανιόντα τῆς τῶν σωμάτων)”; see also Leg. IV, 720d1-e2. 83 In some performance scenarios, the speaking “I” does engage in displays of expertise. In the second century , for example, Galen combines rhetorical performance with spectacular demonstrations of anatomical knowledge: see von Staden 1994a; Debru 1995; Gleason 2009.

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subject defined by claims to a specialized form of knowledge about the body and human nature. The “I” of treatises like On Generation/On the Nature of the Child and On Ancient Medicine is the subject of verbs of inquiry, demonstration, and argument, as a number of studies have shown. What we can now note is that these first-person claims to medical authority go together with an implicit cut between the knowing, observing subject and the object of knowledge, between the expert speaker and the physical body. Like the epic bard, the subject of knowledge is not implicated in the force-field he describes. He remains, like Homer, out of the fray even when he enters into the midst of violence and suffering. The role of the physician as a skilled social actor is thus transformed in the classical period in response to the rise of new contexts for the performance of medical authority. That role is abstracted, as it were, from the clinical encounter and developed through the first-person voices of the medical speeches and writings that proliferated in the later fifth and early fourth centuries . It is defined by a cut between the observing, reasoning subject of knowledge about the physical body and the body itself as an object of knowledge. In the final section, I take up the physical body more directly in order to revisit the question of vulnerability with which we began. For, by inquiring more closely into the body displaced, we can begin to explore the larger implications of disembodied medical authority in classical Greece and beyond.

4 Disembodied Authority and the Physician Role Let us begin by returning for a moment to Book 3 of the Republic, where, we can recall, Socrates proposed that physicians acquire their training, at least in part, through the experience of disease. He goes on to add a premise required for the feasibility of his plan: οὐ γὰρ, οἶμαι, σώματι σῶμα θεραπεύουσιν· οὐ γὰρ ἂν αὐτὰ ἐνεχώρει κακὰ εἶναί ποτε καὶ γενέσθαι· ἀλλὰ ψυχῇ σῶμα. (Plato, Res publ. III, 408e2–4) For [physicians] do not, I think, treat a body with a body. For then it would not be permitted that their bodies ever be or become bad. But they treat the body with the soul.

If, that is, the physician’s capacity for judgment were compromised by his diseases – as is true, Socrates says, for those who suffer diseases of the soul – they could not legitimately form part of his training.84 But, at least in the Republic,

84 Galen, reflecting on Socrates’ suggestion, also requires the physician to retain his mental faculties if his suffering is to be educational: Loc. aff. II 7 (Kühn 8.88–89).

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Plato insists that the soul cannot be corrupted by the ills that befall the body, opening up the education of the physician to self-experimentation.85 It seems likely that the Hippocratic writers would agree with Socrates that a body is not treated by a body. But they do not take it for granted that the capacity for judgment – the language of the soul is not consistently used in this sense in the Corpus – is insulated from the physical body. Indeed, the operating assumption in virtually all the extant Hippocratic texts is that corporeal disturbances can and often do have an impact on cognitive faculties, whether a writer is simply observing the failure of those faculties among a number of other symptoms or he is giving a self-consciously physicalist account of a disease such as epilepsy.86 Even in On Regimen, the treatise where the soul-body pair is most prevalent, the soul (understood in physicalist terms) is not exempted from the travails of the body.87 In short, the body for the Hippocratic writers is not just an object of knowledge. It is also a great source of disruption and vulnerability in human nature. The dangers that the turmoil of the body poses to the faculties on which the physician relies, especially in the event of disease, suggest why the Hippocratic writers might be uncomfortable with Socrates’ proposal. The author of On the Tekhnē acknowledges as much when he contrasts the physician, who “sets to work with a healthy mind in a healthy body (ὑγιαινούσῃ γνώμῃ μεθ’ ὑγιαίνοντος σώματος),” with ignorant, fearful, and suffering patients who are “full of disease (πλήρεις…τῆς νούσου, Corp. Hipp., Ars 7 [Littré 6.10–12=231,8–232,5 Jouanna]).” Here, the author recognizes the embodiment of the physician – an unusual case – only to contrast it with the state of the patient. For many medical writers, however, it seems to have been safer to exclude any consideration of the physician’s body, as if the very recognition of the body could put his authority at risk. Their reticence may give us another piece of the puzzle as to why medical authority in the Hippocratic texts is disembodied. For such disembodiment creates a buffer between the volatility of the physical body and the subject position from which medical knowledge and expertise is exercised. The disembodied position of authority in the medical texts, in other words, may be due as much to a suppression of the physician’s physicality as to the adaptation of the dynamics of the clinical relationship to inquiries into the body, disease, and human nature conducted in new arenas for the display of medical expertise. In the end, however, we have to remember that we are trying to explain a silence. It is impossible to know whether the Hippocratic authors were consciously motivated by concerns about the threat posed by physicality to medical authority when they represented themselves as immune to the symptoms that afflict their 85 The argument that the soul is unaffected by the corruption of the body is developed at length in Book 10 of the Republic. But in other Platonic dialogues (e.g., Phaedo, Timaeus, Philebus, Laws), the body can indeed be a source of danger for the soul, usually through its pleasures. 86 For examples and further bibliography, see Holmes 2010b, 157–159, 182–183. 87 Corp. Hipp., Vict. I 35 (Littré 6.518=154,20–21 Joly-Byl).

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patients and form the raw material of expert knowledge. What we can mark is the fact of their disembodiment in these terms. We can mark, too, the resulting identification of these voices with observation, reasoning, and expert judgment, as well as with the capacity to exercise technical agency. The result is a more nuanced portrait of the role of the physician, according to which that role serves as a position from which a reasoning agent extends efficacious control over the unruly physicality of human nature. What are the implications of the elaborated physician role that we have been tracing? I would venture, first, that it tells us something about a particular way of situating the self vis-à-vis the study of nature. It is misleading, we have seen, to call the voice of medical authority in the rhetorical Hippocratic texts impersonal. To the extent that the stance of the early medical writers is characterized by an aggressive “egotism,” it would seem to preclude them being “objective” in the modern sense of “aspir[ing] to knowledge that bears no trace of the knower.”88 Nevertheless, the definition of the knower in these texts may stand as a significant and perhaps foundational moment in the early history of objectivity in Western medicine and science. On the one hand, the knowing subject lays claim to his position of authority through his identification with a type of technical expertise, rather than through knowledge defined by the fusion of the knower with the objects of knowledge, as we see in some representations of godlike wisdom in early Greek philosophy.89 He does not, in seeking knowledge, go in search of himself, as Heraclitus does (fr. 22 B101 Diels-Kranz).90 On the other hand, the role of the physician is organized around the absence of the physical body. What this means is that the knowledge and the power associated with that position are cut off from the sea of physical forces that dominate the descriptions of the body in the medical texts and determine the fate of patients. The position of the physician is thus protected by a kind of “structural disembodiment.” Yet insofar as the role of the physician is defined not just vis-à-vis the larger physical world but vis-à-vis human nature, it also creates new opportunities for the self – that is, for subjectivity alongside objectivity. The physician role, as we have seen, moves beyond the clinical encounter to spheres of oral and written performance in the later fifth century . It is mobile in other ways as well. While I do not have sufficient space to analyze its migration into other contexts in detail here, I would like to close by indicating briefly two related areas where the transformed “physician role” may have been influential for concepts of the self in classical antiquity. 88 Daston & Galison 2007, 17. 89 See Miller 2011, esp. 27–42, 48–51, 70–77, 85–113. 90 For Plato, physicians know the body without knowing themselves (Alc. 1 131a5–7; Charm. 164a9c2). Part of the problem for Plato is that the body does not constitute the self: the self is the soul. But even to the extent the body is virtually synonymous with human nature in the medical writers, it is not a route to self-knowledge for the physician.

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In considering lay audiences, we have focused on contexts where the speaker addresses a general public presumed to be interested in medicine. But there are other treatises where the layperson is addressed as someone who is involved in the care of his own body.91 The treatise On Affections begins: ἄνδρα χρή, ὅστις ἐστὶ συνετός, λογισάμενον ὅτι τοῖσιν ἀνθρώποισι πλείστου ἄξιόν ἐστιν ἡ ὑγιείη, ἐπίστασθαι ἀπὸ τῆς ἑωυτοῦ γνώμης ἐν τῇσι νούσοισιν ὠφελέεσθαι· ἐπίστασθαι δὲ τὰ ὑπὸ τῶν ἰητρῶν καὶ λεγόμενα καὶ προσφερόμενα πρὸς τὸ σῶμα ἑαυτοῦ καὶ διαγινώσκειν· ἐπίστασθαι δὲ τούτων ἕκαστα ἐς ὅσον εἰκὸς ἰδιώτην. (Corp. Hipp., Aff. 1 [Li 6.208=6 Potter]) Any man of intelligence, having taken it into account that health is of the greatest value to human beings, must know by means of his own understanding how to help himself in diseases, and to know and to judge what is said by physicians and what they administer to his body, and to know each of these things to the extent that is fitting for a layperson.

The address bears striking similarities to the opening line of Airs (the use of χρή, “one ought to”; the ὅστις, “whoever,” clause modifying the subject of the χρή construction) with a crucial substitution: the aspiring physician is replaced by the intelligent layperson who is an object of medical care.92 But the layperson turns out to be not so distant from the physician in this context. For the author invites the addressee to occupy a position that, at least in a modified way, mimics the physician role insofar as it is defined by reasoning, knowledge, and judgment. The layperson, in other words, becomes like a physician, but in relation to his own body. He thus internalizes the split within the clinical relationship, which is transformed, accordingly, into a relationship to the self. By laying claim to the structural disembodiment of the physician, the informed layperson isolates his capacity to judge and to reason from the volatile dynamics of the cavity – richly described in the rest of On Affections – and ceases to be simply an object of others’ actions. The role of the physician thus becomes a position from which to exercise a modified medical authority, underwritten by the tekhnē, over oneself – a model of self-reflexive care. The appeal of such a position seems to have become widespread by the end of the fifth century . The treatise On Regimen, for example, is addressed to laypersons who seek to manage their bodies in health as well as in disease. The author envisions an audience comprising elites, who are convinced that there are no benefits of wealth without health, and non-elites, who are not in a position to neglect everything to take care of themselves.93 And Socrates rails against the

91 See Wittern 1998, 30, who draws a useful distinction between the layperson interested in medicine and the layperson qua potential patient. 92 Some scholars have seen the proem as a frame alien to the body of the treatise, which is fairly technical and addresses the physician in the second-person: see esp. Potter 1988, 4–5. But most scholars now accept the unity of the treatise and see the proem as further evidence of public interest in medical knowledge. See van der Eijk 1997, 86–87; Schiefsky 2005, 41–42; Cañizares 2010. 93 Corp. Hipp., Vict. III 69 (Littré 6.604–606=200,23–27 Joly-Byl).

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“excessive” care of the body (ἡ περιττὴ αὕτη ἐπιμέλεια τοῦ σώματος) among elite Athenians in the Republic (III, 407b8-c6). Yet for all of Socrates’ ire towards the growing influence of medicine, he also provides evidence for its cultural capital. Indeed, the concept of the “physician role” seems to serve a function in early philosophical ethics, as Plato’s own writings show.94 Plato, we will recall, believes that the physician does not treat a body with a body but with a soul. The soul on this model takes over the role of the physician; the split between physician and patient is mapped onto the split between the body and the soul. That it is the responsibility of the soul to take care of the body is suggested elsewhere in the Republic; the idea appears as well in the fragments of Democritus.95 In these cases, the position of authority occupied by the physician, to the extent that it is taken over by the soul, appears fully internalized.96 But the emergence of the soul’s therapeutic function does not mean the role of the physician becomes irrelevant. In other dialogues, and especially in the early “Socratic” dialogues, Plato often introduces the idea that, in addition to techniques of caring for the body, there are techniques of caring for the soul that resemble those used in medicine.97 He does draw a distinction between the kind of technical knowledge commanded by a physician and the knowledge required for the flourishing of the soul.98 Nevertheless, the idea that a philosophical ethics might provide a technique both for maintaining the health of the soul and for curing its ills runs through the Greco-Roman ethical tradition, from Plato through Aristotle to the Hellenistic and Roman philosophical schools.99 In some versions of the medical analogy, technical expertise is associated with an external figure – such as a teacher – who stands in relationship to the subject

94 For a fuller treatment of the relationship between early Greek medicine and early philosophical ethics, see Holmes 2010a; 2010b; and forthcoming. 95 Plato, Res publ. III, 403d8-e2; Democritus fr. 68 B159 Diels-Kranz. 96 See, here, too, Aristotle’s formulation of the soul as an entity exercising its functions without being affected itself in terms of a craftsman exercising his craft, and esp. the analogy to the physician at Gen. corr. I 7, 324a24-b6. The passage is fascinating insofar as it suggests that the agent – technically, the tekhnē of medicine, but Aristotle also speaks directly of the physician – does not have the same matter (hylē) as the patient and thus is not affected when he exercises the tekhnē. Even when Aristotle speaks of the artisan, the artisan’s body is present only as an instrument of the tekhnē, as Menn points out (2002, 124–125), much as we have seen with the physician. 97 See Holmes 2010a, with further bibliography. 98 The extent to which technical knowledge differs from moral knowledge is a source of contention. For the opposing positions, see Irwin 1995, who privileges the craft analogy; Roochnik 1996, drawing a sharp distinction between technical knowledge and Socratic wisdom. The point I make here is a more general one about how the care of the self is conceptualized. 99 See Jaeger 1957 (on Aristotle); Nussbaum 1994 (on the Hellenistic schools); Tsouna 2009 (on Epicureanism).

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like a physician to a patient.100 But the analogy can also include a subject position from which techniques are applied reflexively to the self. Self-reflexivity here is underwritten, in part, by an implicit cut between the subject and the object of care and the premise that reason and judgment can be isolated from the tumult not only of the body but of the appetitive and emotional soul. Of course, once the clinical relationship has been internalized, there is always the threat that the barrier between physician and patient will collapse, contaminating the technical expertise and knowledge of the former with the volatile physicality of the latter. Nevertheless, the possibility of even erecting that barrier, however indebted to developing ideas of dualism in the classical and Hellenistic periods, may draw, I suggest, on the expansion of the physician role in early medical speeches and texts to encompass a disembodied authority to speak about and manage human nature.101 The rise of ethical philosophies organized around reflexive attention to the self brings us back to the scene with which we began: Odysseus’ encounter with Hermes. The episode came to enjoy a rich afterlife in the hands of those who sought allegorical meaning in the Homeric poems.102 One of the most extensive readings of the scene is found in Stobaeus, who attributes it, perhaps wrongly, to the Neoplatonist philosopher and literary critic Porphyry.103 The allegorist reads Odysseus’ adventures on Aeaea as an incredible story of things having to do with the soul, its care, and especially the repercussions of failing to take care.104 He is working with a set of assumptions that, while Platonist in slant, share much with the foundations of other ethical philosophies of the first centuries . ἔνθα δὴ τὸ μετὰ παιδείας ἑκάστῳ καὶ φιλοσοφίας ὄφελος ἀναμνημονεύουσα105 τῶν καλῶν ἡ ψυχὴ καὶ δυσχεραίνουσα τὰς αἰσχρὰς καὶ παρανόμους ἡδονὰς δύναται κρατεῖν καὶ προσέχειν

100 See, e.g., Plato, Crit. 47d6–48a4. 101 It may be in the contribution that medicine makes to “techniques of the self” that it is most relevant to the story told about objectivity in Daston & Galison 2007. Daston and Galison introduce ancient techniques of the self as a model for the practices they find integral to the subject position of objectivity in eighteenth-, nineteenth-, and twentieth-century science. They see the ancient self as purely ethical, occupied with the imperative to “know thyself” (2007, 37–39); the “scientific self” is a later development, taking us “far beyond” the ancient directive. The Delphic maxim is indeed crucial for ancient ethics. But perhaps the very notion of a technique of the self begins with a variant of the scientific self, who knows and controls the physical world while standing outside its dynamics. The Hippocratic texts offer an early version of this persona. 102 On early allegorical interpretations of Homer, see Ford 1999. On allegorical interpretations of the Circe episode, most of which offer some variant of the interpretation in the extract from Stobaeus, see Buffière 1956, 292, 324, 379; Yarnall 1994, 73–78, 93–97; Gosserez 2003 focuses on the early Church Fathers. See Pépin 1982 on the Neoplatonist Odysseus more generally (drawing attention to the salvation theme). 103 Helmig 2008 makes a good case for attributing the reading to Plutarch. 104 On the passage, see Buffière 1956, 506–515; Lamberton 1986, 115–119. 105 ἀναμνημονεύουσα Meineke. ἂν μνημονεύουσα FP2 ἂν μνημονεύσα P1.

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αὑτῇ καὶ φυλάττειν, μὴ λάθῃ θηρίον γενομένη καὶ στέρξασα σώματος οὐκ εὐφυοῦς οὐδὲ καθαροῦ πρὸς ἀρετὴν φύσιν ἄμουσον καὶ ἄλογον καὶ τὸ ἐπιθυμοῦν καὶ θυμούμενον μᾶλλον ἢ τὸ φρόνιμον αὔξοντος καὶ τρέφοντος. (Stobaeus, Ecl. I 41.60) By virtue of what each of us gains through education and philosophy, the soul, remembering the good and repelled by shameful and illicit pleasures, is able to prevail and watch itself carefully and take care lest through inattention it be reborn as a beast and fall in love with a body badly suited for virtue and impure, nurturing an uncultivated and irrational nature and encouraging the appetitive and passionate elements of the soul rather than the rational. (transl. R. Lamberton)

Odysseus’ companions, transformed into pigs, offer a cautionary tale about souls that fail to conquer their appetitive desires. Odysseus himself is spared their fate only because Hermes, the symbol of reason (logos), “meets the soul and clearly points the way to the good,” encouraging the soul to remember what it already knows.106 The allegorist thus transforms the meeting in the forest into a scene in which the god transmits the art of philosophy as a prophylactic drug that allows the soul of the hero to guard against bestialization by “watching itself.” Odysseus emerges as an ethical hero who succeeds in protecting himself in the strange lands of the soul’s appetites and the unruly body by adopting techniques of care that are symbolized by reason, transmitted by education, and enacted through the practice of philosophy. In the end, it is precisely because Odysseus anticipates the subject of ethical philosophy that he is not a physician. The role of the physician in antiquity remains distinct from that of the philosopher.107 His authority is defined by an expertise that moves outward rather than reflexively, targeting the vulnerability of others and human nature in the abstract. If the authority of the philosopher is often premised on his own mastery of the body and the appetitive self – we can think here of figures like Empedocles, Socrates, and the Stoic sage – the authority of the physician rests on the structural suppression of the body, that is, the suppression of the fluid and volatile substratum where selves are made and unmade in early physiological thinking.108 The structural disembodiment of the physician role tells us something about the difference between technical or even “scientific” authority about human nature and what we might call philosophical wisdom. And yet, the story of the soul that Odysseus’ adventures on Aeaea come to illustrate may build, I have suggested, on the elaboration of the physician role in

106 The allegorical interpretation of Hermes goes back at least to Socrates, who, according to Xenophon, identified the god with Odysseus’ own capacity to master his appetites in the face of temptation (Mem. I 3.7); see also the specific equation of Hermes with reason or philosophy in the Homeric Allegories of Heraclitus (72.4). 107 Galen brings these roles together in fascinating and probably innovative ways without, I would argue, eliminating the sense that they are two separate roles. 108 On the long history of bodily management as part of the philosopher’s or the intellectual’s identity, see Dillon 1995; Shapin 1998.

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texts and speeches about medicine in the classical period, a process shaped by the specific discursive, intellectual, and performative context in which it unfolds, as well as by the emergence of the physical body as an object of specialized knowledge and, perhaps, as a cause of difficulty for the rational self. However much the physician role is taken over by the soul, it continues to be informed by the intuition that the soul requires techniques to manage its own appetites and the body, techniques developed and transmitted by philosophy. If philosophy often uses medicine to describe its own authority and efficacy, it may be because, by the later fifth and early fourth centuries , medicine has become about more than the encounter between healer and patient. It has become an integral part of the history of how we came to stand outside ourselves to take human nature as an object of inquiry, manipulation, and care.

Bibliography Texts quoted Abbreviations and Editions of Classical Texts Diels-Kranz: Diels, H. 1951–1952. Die Fragmente der Vorsokratiker. 6th ed., revised by W. Kranz. Berlin. Kühn: Kühn, C. 1821–1833. Claudii Galeni opera omnia, 20 vols. Leipzig. Littré: Littré, É. 1839–61. Œuvres complètes d’Hippocrate, 10 vols. Paris. LP: Lobel, E., & D. Page 1955. Poetarum Lesbiorum fragmenta. Oxford. Hippocratic Texts What follows are the Hippocratic editions I have used, together with the most convenient English translations. Other editions that are cited are included in the bibliography. Aer.: Airs, Waters, Places (Littré 2.12–93). Jouanna, J. 1996. Hippocrate, Airs, eaux, lieux. Paris. Jones, W. 1923. Hippocrates. Vol. 1. Cambridge, MA. Aff.: On Affections (Littré 6.208–271). Potter, P. 1988. Hippocrates. Vol. 5. Cambridge, MA. Ars: On the Tekhnē (Littré 6.2–27). Jouanna, J. 1988. Hippocrate, Des vents; De l’art. Paris. Jones, W. 1923. Hippocrates. Vol. 2. Cambridge, MA. Artic.: On Joints (Littré 4.78–327). Kühlewein, H. 1894–1902. Hippocratis opera quae feruntur omnia. 2 vols. Leipzig. Withington, E. 1928. Hippocrates. Vol. 3. Cambridge, MA. Carn.: On Fleshes (Littré 8.584–615). Joly, R. 1978. Hippocrate, Des lieux dans l’homme; Du système des glandes; Des fistules-Des hémorroïdes; De la vision; Des chairs; De la dentition. Paris. Potter, P. 1995. Hippocrates. Vol. 8. Cambridge, MA. Dec.: Decorum (Littré 9.226–243). Heiberg, I. 1927. Hippocratis opera. Corp. med. Gr. I.1. Leipzig. Jones, W. 1923. Hippocrates. Vol. 2. Cambridge, MA. Epid. I: Epidemics I (Littré 2.598–717). Kühlewein, H. 1894–1902. Hippocratis opera quae feruntur omnia. 2 vols. Leipzig. Jones, W. 1923. Hippocrates. Vol. 1. Cambridge, MA. Epid. V: Epidemics V (Littré 5.204–259). Jouanna, J. 2000. Hippocrate, Epidémies V et VII. Paris. Smith, W. 1994. Hippocrates. Vol. 7. Cambridge, MA. Epid. VI: Epidemics VI (Littré 5.266–357). Manetti, D., & A. Roselli 1982. Ippocrate, Epidemie: libro sesto. Florence. W. D. Smith, ed. & transl. 1994. Hippocrates. Vol. 7. Cambridge, MA.

In Strange Lands

467

Flat.: On Breaths (Littré 6.90–115). Jouanna, J. 1988. Hippocrate, Des vents; De l’art. Paris. Jones, W. 1923. Hippocrates. Vol. 2. Cambridge, MA. Genit./Nat. Puer.: On Generation/On the Nature of the Child (Littré 7.470–543). Joly, R. 1970. Hippocrate, De la génération; De la nature de l’enfant; Des maladies IV; Du fœtus de huit mois. Paris. Lonie, I. 1981. The Hippocratic Treatises “On Generation,” “On the Nature of the Child,” “Diseases IV.” Berlin. Iusi.: Oath (Littré 4.628–632). Heiberg, I. 1927. Hippocratis opera. Corp. med. Gr. I.1. Leipzig. Jouanna, J. 1996. “Un témoin méconnu de la tradition hippocratique: L’Ambrosianus Gr. 134 (B 113 Sup.), fol. 1–2 (avec une nouvelle édition du Serment et de la Loi).” In: A. Garzya (ed.), Storia e ecdotica dei testi medici greci: Atti del II Convegno Internazionale, Parigi 24– 26 maggio 1994. Naples, 253–272. Jones, W. 1923. Hippocrates. Vol. 1. Cambridge, MA. Lex: Law (Littré 4.638–642). Heiberg, I. 1927. Hippocratis opera. Corp. med. Gr. I.1. Leipzig. Jouanna, J. 1996. “Un témoin méconnu de la tradition hippocratique: L’Ambrosianus Gr. 134 (B 113 Sup.), fol. 1–2 (avec une nouvelle édition du Serment et de la Loi).” In: A. Garzya (ed.), Storia e ecdotica dei testi medici greci: Atti del II Convegno Internazionale, Parigi 24– 26 maggio 1994. Naples, 253–272. Jones, W. 1923. Hippocrates. Vol. 2. Cambridge, MA. Medic.: Physician (Littré 9.204–220). Heiberg, I. 1927. Hippocratis opera. Corp. med. Gr. I.1. Leipzig. Morb. I: On Diseases I (Littré 6.140–205). Wittern, R. 1974. Die hippokratische Schrift “De morbis I.” Hildesheim. Potter, P. 1988. Hippocrates. Vol. 5. Cambridge, MA. Morb. sacr.: On the Sacred Disease (Littré 6.353–397). Jouanna, J. 2003. Hippocrate, La maladie sacrée. Paris. Jones, W. 1923. Hippocrates. Vol. 2. Cambridge, MA. Mul. I: Diseases of Women I (Littré 8.10–233). Grensemann, H. 1982. Hippokratische Gynäkologie. Die gynäkologischen Texte des Autors C nach den pseudohippokratischen Schriften De muliebribus I, II und De sterilibus. Wiesbaden. Hanson, A. 1975. “Hippocrates: Diseases of Women I.” In: Signs 1, 567–584. Nat. hom.: On the Nature of a Human Being (Littré 6.32–69). Jouanna, J. 2002. Hippocrate, La nature de l’homme. 2nd ed. Corp. med. Gr. I.1.3. Berlin. Jones, W. 1931. Hippocrates. Vol. 4. Cambridge, MA. Off. med.: In the Surgery (Littré 3.272–337). Kühlewein, H. 1894–1902. Hippocratis opera quae feruntur omnia. 2 vols. Leipzig. Withington, E. 1928. Hippocrates. Vol. 3. Cambridge, MA. Praec.: Precepts (Littré 9.250–272). Heiberg, I. 1927. Hippocratis opera. Corp. med. Gr. I.1. Leipzig. Jones, W. 1923. Hippocrates. Vol. 1. Cambridge, MA. Vict.: On Regimen (Littré 6.466–663). Joly, R., with S. Byl 2003. Hippocrate, Du régime. 2nd ed. Corp. med. Gr. I.2.4. Berlin. Jones, W. 1931. Hippocrates. Vol. 4. Cambridge, MA. Virg.: Diseases of Young Girls (Littré 8.466–471). Lami, A. 2007. “[Ippocrate], Sui disturbi virginali: testo, traduzione e commento.” In: Galenos 1, 15–59. Flemming, R., & A. Hanson 1998. “Hippocrates’ Peri Partheniôn (“Diseases of Young Girls”): Text and Translation.” In: Early Science and Medicine 3, 241–252. Vet. med.: On Ancient Medicine (Littré 1.570–637). Jouanna, J. 1990. Hippocrate, De l’ancienne médecine. Paris. Jones, W. 1923. Hippocrates. Vol. 1. Cambridge, MA.

468

Brooke Holmes

Works quoted Alexander, C. 1991. “A Note on the Stag: Odyssey 10.156–72.” In: Classical Quarterly 41, 520– 524. Althoff, J. 1993. “Formen der Wissensvermittlung in der frühgriechischen Medizin.” In: Kullmann & Althoff 1993, 211–223. Altman, L. 1972. “Auto-experimentation: An Unappreciated Tradition in Medical Science.” In: New England Journal of Medicine 286, 346–352. Reprinted in: R. Bulger (ed.), Hippocrates Revisited: A Search for Meaning (New York, 1973), 193–210. Amundsen, D. 1977. “Images of Physicians in Classical Times.” In: Journal of Popular Culture 11, 642–655. Asper, M. 2007. Griechische Wissenschaftstexte. Formen, Funktionen, Differenzierungsgeschichten. Stuttgart. Bakker, E. 2005. “Homeric Epic between Feasting and Fasting.” In: F. Montanari & A. Rengakos (eds.), La poésie épique grecque: Métamorphoses d’un genre littéraire. Geneva, 1–30 (Discussion, 31–39). Bakker, E. 2009. “Homer, Odysseus, and the Narratology of Performance.” In: J. Grethlein & A. Rengakos (eds.), Narratology and Interpretation: The Content of Narrative Form in Ancient Literature. Berlin, 117–136. Baltussen, H. 2000. Theophrastus against the Presocratics and Plato: Peripatetic Dialectic in the “De sensibus.” Leiden. Baragwanath, E. 2008. Motivation and Narrative in Herodotus. Oxford. Barton, T. 1994. Power and Knowledge: Astrology, Physiognomics, and Medicine under the Roman Empire. Ann Arbor. Bensel, J. 1923. “Hippocratis qui fertur De Medico libellus ad codicum fidem recensitus.” In: Philologus 78, 88–130. Boudon-Millot, V. 2009. “Galen’s Bios and Methodos: From Ways of Life to Path of Knowledge.” In: Gill et al. 2009, 175–189. Brain, P. 1982. “The Hippocratic Physician and His Drugs: A Reinterpretation of AΠΟΡΕΙΣΘΑΙ and ΔΙΑΜΑΡΤΑΝΕΙΝ in Chapter 2 of ΠΕΡΙ ΑΕΡΩΝ, ΥΔΑΤΩΝ, ΤΟΠΩΝ.” In: Classical Philology 77, 48–51. Bremmer, J. N. 2002. “How Old is the Idea of Holiness (of Mind) in the Epidaurian Temple Inscription and the Hippocratic Oath?” In: Zeitschrift für Papyrologie und Epigraphik 141, 106–108. Buffière, F. 1956. Les mythes d’Homère et la pensée grecque. Paris. Calame, C. 2005. Masks of Authority: Fiction and Pragmatics in Ancient Greek Poetics. Transl. P. Burk. Ithaca. Cañizares, P. 2010. “The Importance of Having Medical Knowledge as a Layman: The Hippocratic Treatise Affections in the Context of the Hippocratic Corpus.” In: Horstmanshoff 2010, 87–99. Chaniotis, A., & J. Mylonopoulos 2005. “Epigraphic Bulletin for Greek Religion 2002.” In: Kernos 18, 425–474. Clay, J. 1972. “The Planktai and Moly: Divine Naming and Knowing in Homer.” In: Hermes 100, 127–131. Curtis, T. 2009. “Didactic and Rhetorical Strategies in Galen’s De pulsibus ad tirones.” In: Taub & Doody 2009, 63–79. Daston, L., & P. Galison 2007. Objectivity. New York. Davies, M. 2008. “Hermes the Helper Figure: Odyssey 10.275–308.” In: Prometheus 34, 27–32. Dean-Jones, L. 2003. “Literacy and the Charlatan in Ancient Greek Medicine.” In: Yunis 2003, 97– 121. Dean-Jones, L. 2010. “Physician: A Metapaedagogical Text.” In: Horstmanshoff 2010, 53–72.

In Strange Lands

469

Debru, A. 1992. “La suffocation hystérique chez Galien et Aétius: Réécriture et emprunt du ‘je.’” In: A. Garzya (ed.), Tradizione e ecdotica dei testi medici tardoantichi e bizantini: Atti del Convegno Internazionale, Anacapri, 29–31 ottobre 1990. Naples, 79–89. Debru, A. 1995. “Les démonstrations médicales à Rome au temps de Galien.” In: P. van der Eijk et al. (eds.), Ancient Medicine in its Socio-Cultural Context, 2 vols. Amsterdam, 69–81. Demont, P. 1993. “Die Epideixis über die Techne im V. und IV. Jh.” In: Kullmann & Althoff 1993, 181–209. Dewald, C. 1987. “Narrative Surface and Authorial Voice in Herodotus’ Histories.” In: Arethusa 20, 147–170. Diller, H. 1932. “ΟΨΙΣ ΑΔΗΛΩΝ ΤΑ ΦΑΙΝΟΜΕΝΑ.” In: Hermes 67, 14–42. Reprinted in: Kleine Schriften zur antiken Literatur (Munich, 1971), 119–143. Diller, H. 1975. “Das Selbstverständnis der griechischen Medizin in der Zeit des Hippokrates.” In: L. Bourgey & J. Jouanna (eds.), La Collection hippocratique et son rôle dans l’histoire de la médecine: Colloque de Strasbourg, 23–27 octobre 1972. Leiden, 77–93. Dillon, J. 1995. “Rejecting the Body, Refining the Body: Some Remarks on the Development of Platonist Asceticism.” In: V. Wimbush & R. Valantasis (eds.), Asceticism. New York, 80–87. Ducatillon, J. 2001. “Le Serment d’Hippocrate, problèmes et interprétations.” In: Bulletin de l’Association Guillaume Budé 2001.1, 34–61. Edelstein, L. 1967. Ancient Medicine: Selected Papers of Ludwig Edelstein. Baltimore. van der Eijk, P. 1997. “Towards a Rhetoric of Ancient Scientific Discourse – Some Formal Characteristics of Greek Medical and Philosophical Texts (Hippocratic Corpus, Aristotle).” In: E. Bakker (ed.), Grammar as Interpretation: Greek Literature in Its Linguistic Contexts. Leiden, 77–129. Fausti, D. 2003. “‘Epidemie’ Ippocratiche e mancanza di contagio: un’aporia della medicina antica.” In: Fontes 11–12, 41–61. Fleischer, U. 1939. Untersuchungen zu den pseudohippokratischen Schriften ΠΑΡΑΓΓΕΛΙΑΙ, ΠΕΡΙ ΙΗΤΡΟΥ und ΠΕΡΙ ΕΥΣΧΗΜΟΣΥΝΗΣ. Berlin. Forcht Dagi, T. 1995. “Autoexperimentation.” In: W. Reich (ed.), Encyclopedia of Bioethics, rev. ed., 5 vols. New York, vol. 1, 211–215. Ford, A. 1999. “Performing Interpretation: Early Allegorical Exegesis of Homer.” In: M. Beissinger et al. (eds.), Epic Traditions in the Contemporary World: The Poetics of Community. Berkeley, 33–53. Gill, C., et al. (eds.) 2009. Galen and the World of Knowledge. Cambridge. Gleason, M. 2009. “Shock and Awe: The Performance Dimension of Galen’s Anatomy Demonstrations.” In: Gill et al. 2009, 85–114. Goldhill, S. 2002. The Invention of Prose. Oxford. Gosserez, L. 2003. “Une métamorphose allégorique, les bêtes féroces de Circé vues par les Pères de l’Église.” In: Gaia 7, 447–459. Graziosi, B., & J. Haubold 2010. Homer. Iliad, Book VI. Cambridge. Griffith, M. 1983. “Personality in Hesiod.” In: Classical Antiquity 2, 37–65. Guillén, L. 1992. “Hipócrates y el discurso científico.” In: López Férez 1992, 319–333. Hankinson, R. 1995. “Pollution and Infection: An Hypothesis Still-born.” In: Apeiron 28, 25–65. Heinimann, F. 1945. Nomos und Physis. Herkunft und Bedeutung einer Antithese im griechischen Denken des 5. Jahrhunderts. Basel. Helmig, C. 2008. “Plutarch of Chaeronea and Porphyry on Transmigration – Who is the Author of Stobaeus I 445.14–448.3 (W.-H.)?” In: Classical Quarterly 58, 250–255. Heubeck, A., & A. Hoekstra 1989. A Commentary on Homer’s Odyssey. Vol. 2: Books IX–XVI. Oxford. Hine, H. 2009. “Subjectivity and Objectivity in Latin Scientific and Technical Literature.” In: Taub & Doody 2009, 13–30.

470

Brooke Holmes

Holmes, B. 2010a. “Body, Soul, and Medical Analogy in Plato.” In: K. Bassi & J. Euben (eds.), When Worlds Elide: Classics, Politics, Culture. Lanham, MD, 345–385. Holmes, B. 2010b. The Symptom and the Subject: The Emergence of the Physical Body in Ancient Greece. Princeton. Holmes, B. forthcoming. “Causality, Agency, and the Limits of Medicine.” In: Apeiron (ahead of print: DOI: 10.1515/apeiron-2012-0016, March 2013). Horstmanshoff, H. 1990. “The Ancient Physician: Craftsman or Scientist?” In: Journal of the History of Medicine and the Allied Sciences 45, 176–197. Horstmanshoff, M. (ed.) 2010. Hippocrates and Medical Education: Selected Papers Read at the XIIth International Hippocrates Colloquium, Universiteit Leiden, 24–26 August 2005. Leiden. Humphreys, S. 1996. “From Riddle to Rigour: Satisfactions of Scientific Prose in Ancient Greece.” In: S. Marchand & E. Lunbeck (eds.), Proof and Persuasion: Essays on Authority, Objectivity, and Evidence. Turnhout, 3–24. Ihm, S. 2002. “Drei Anmerkungen zum hippokratischen Eid.” In: A. Thivel & A. Zucker (eds.), Le normal et le pathologique dans la Collection hippocratique: Actes du Xème colloque international hippocratique, Nice, 6–8 Octobre 1999, 2 vols. Nice, 671–692. Irwin, T. 1995. Plato’s Ethics. New York. Isaac, B. 2004. The Invention of Racism in Classical Antiquity. Princeton. Jaeger, W. 1944. Paideia: The Ideals of Greek Culture. Vol. 3: The Conflict of Cultural Ideals in the Age of Plato. Transl. G. Highet. Oxford. Jaeger, W. 1957. “Aristotle’s Use of Medicine as Model of Method in His Ethics.” In: Journal of Hellenic Studies 77, 54–61. Jones, H. 1973. “Homeric Nouns in – sis.” In: Glotta 51, 7–29. Jones, W. 1923. Hippocrates. Vol. 1. Cambridge, MA. de Jong, I. 2001. A Narratological Commentary on the “Odyssey.” Cambridge. de Jong, I., & R. Nünlist 2004. “From Bird’s Eye View to Close-Up: The Standpoint of the Narrator in the Homeric Epics.” In: A. Bierl et al. (eds.), Antike Literatur in neuer Deutung. Munich, 63–83. Jouanna, J. 1984. “Rhétorique et médecine dans la Collection hippocratique: Contribution à l’histoire de la rhétorique au Ve siècle.” In: Revue des études grecques 97, 26–44. Jouanna, J. 1988. Hippocrate, Des vents; De l’art. Paris. Jouanna, J. 1990. Hippocrate, De l’ancienne médecine. Paris. Jouanna, J. 1996a. Hippocrate, Airs, eaux, lieux. Paris. Jouanna, J. 1996b. “Un témoin méconnu de la tradition hippocratique: L’Ambrosianus Gr. 134 (B 113 Sup.), fol. 1–2 (avec une nouvelle édition du Serment et de la Loi).” In: A. Garzya (ed.), Storia e ecdotica dei testi medici greci: Atti del II Convegno Internazionale, Parigi 24– 26 maggio 1994. Naples, 253–272. Jouanna, J. 1999. Hippocrates. Transl. M. DeBevoise. Baltimore. Jouanna, J. 2001. “Air, miasme et contagion au temps d’Hippocrate et survivance des miasmes dans la médecine posthippocratique (Rufus d’Éphèse, Galien et Palladios).” In: S. BazinTacchella et al. (eds.), Air, miasmes et contagion: Les épidémies dans l’Antiquité et au Moyen Âge. Langres, 9–28. Jouanna, J. 2003. Hippocrate, La maladie sacrée. Paris. Kingsley, P. 1995. Ancient Philosophy, Mystery, and Magic: Empedocles and Pythagorean Tradition. Oxford. Kirk, G. 1985. The Iliad: A Commentary. Vol. 1: Books 1–4. Cambridge. Kollesch, J. 1979. “Ärztliche Ausbildung in der Antike.” In: Klio 61, 507–513. Kollesch, J. 1991. “Darstellungsformen der medizinischen Literatur im 5. und 4. Jahrhundert v. Chr.” In: Philologus 135, 177–183. Kudlien, F. 1970a. “Medical Education in Classical Antiquity.” In: C. O’Malley (ed.), The History of Medical Education. Berkeley, 3–37.

In Strange Lands

471

Kudlien, F. 1970b. “Medical Ethics and Popular Ethics in Greece and Rome.” In: Clio Medica 5, 91–121. Kullmann, W., & J. Althoff (eds.) 1993. Vermittlung und Tradierung von Wissen in der griechischen Kultur. Tübingen. Lamberton, R. 1986. Homer the Theologian: Neoplatonist Allegorical Reading and the Growth of the Epic Tradition. Berkeley. Lara Nava, D. 1992. “Función literaria del prólogo en los tratados hipocráticos más antiguos.” In: López Férez 1992, 343–350. Laskaris, J. 2002. The Art is Long: “On the Sacred Disease” and the Scientific Tradition. Leiden. Lateiner, D. 1986. “The Empirical Element in the Methods of Early Greek Medical Writers and Herodotus: A Shared Epistemological Response.” In: Antichthon 20, 1–20. Lattimore, R. 1957. Homer. The Iliad. Chicago. Lawrence, C. 1998. “Medical Minds, Surgical Bodies: Corporeality and the Doctors.” In: Lawrence & Shapin 1998, 156–201. Lawrence, C., & S. Shapin (eds.) 1998. Science Incarnate: Historical Embodiments of Natural Knowledge. Chicago. Leith, D. 2007. “The Hippocratic Oath in Antiquity and on Papyrus.” In: H. Froschauer & C. Römer (eds.), Zwischen Magie und Wissenschaft: Ärzte und Heilkunst in den Papyri aus Ägypten. Vienna, 35–42. Lloyd, G. 1979. Magic, Reason, and Experience: Studies in the Origin and Development of Greek Science. Cambridge. Lloyd, G. 1987. The Revolutions of Wisdom: Studies in the Claims and Practice of Ancient Greek Science. Berkeley. López Férez, J. (ed.) 1992. Tratados hipocráticos: estudias acerca de su contenido, forma, e influencia; actas del VIIe colloque international hippocratique, Madrid, 24–29 de septiembre de 1990. Madrid. Marincola, J. 1987. “Herodotean Narrative and the Narrator’s Presence.” In: Arethusa 20, 121–137. Martin, R. 1989. The Language of Heroes: Speech and Performance in the “Iliad.” Ithaca. Mattern, S. 2008. Galen and the Rhetoric of Healing. Baltimore. Menn, S. 2002. “Aristotle’s Definition of Soul and the Programme of the De anima.” In: Oxford Studies in Ancient Philosophy 22, 83–139. Miller, P. 2011. Becoming God: Pure Reason in Early Greek Philosophy. London. Moisan, M. 1993. Édition critique et commentée avec traduction française, de deux œuvres de la Collection Hippocratique: Preceptes et Médecin. Thèse, Université de Paris IV, Sorbonne. Paris. Naddaf, G. 2005. The Greek Concept of Nature. Albany. Nussbaum, M. 1994. The Therapy of Desire: Theory and Practice in Hellenistic Ethics. Princeton. Nutton, V. 1983. “The Seeds of Disease: An Explanation of Contagion and Infection from the Greeks to the Renaissance.” In: Medical History 27, 1–34. Nutton, V. 2009. “Galen’s Authorial Voice: A Preliminary Enquiry.” In: Taub & Doody 2009, 53–62. Page, D. 1973. Folktales in Homer’s “Odyssey.” Cambridge, MA. Pépin, J. 1982. “The Platonic and Christian Ulysses.” In: D. O’Meara (ed.), Neoplatonism and Christian Thought, Norfolk, VA, 3–18. Potter, P. 1988. Hippocrates. Vol. 5. Cambridge, MA. Potter, P. 1995. Hippocrates. Vol. 8. Cambridge, MA. Pucci, P. 1987. Odysseus Polutropos: Intertextual Readings in the “Odyssey” and the “Iliad.” Ithaca. Roochnik, D. 1996. Of Art and Wisdom: Plato’s Understanding of Techne. University Park, Pa. Schaffer, S. 1992. “Self Evidence.” In: Critical Inquiry 18, 327–362. Schaffer, S. 1998. “Regeneration: The Body of Natural Philosophers in Restoration England.” In: Lawrence & Schaffer 1998, 83–120.

472

Brooke Holmes

Schiebinger, L. 2004. “Human Experimentation in the Eighteenth Century: Natural Boundaries and Valid Testing.” In: L. Daston & F. Vidal (eds.), The Moral Authority of Nature. Chicago, 384–408. Schiefsky, M. 2005. Hippocrates, On Ancient Medicine. Leiden. Shapin, S. 1998. “The Philosopher and the Chicken: On the Dietetics of Disembodied Knowledge.” In: Lawrence & Shapin 1998, 21–50. von Staden, H. 1994a. “Anatomy as Rhetoric: Galen on Dissection and Persuasion.” In: Journal of the History of Medicine and Allied Sciences 50, 47–66. von Staden, H. 1994b. “Author and Authority: Celsus and the Construction of a Scientific Self.” In: M. Buján (ed.), Tradición e innovación de la medicina latina de la antiguëdad y de la Alta Edad Media: Actas del IV Coloquio Internacional sobre los Textos Médicos Latinos Antiguos. Santiago de Compostela, 103–117. von Staden, H. 1996. “‘In a Pure and Holy Way’: Personal and Professional Conduct in the Hippocratic Oath?” In: Journal of the History of Medicine and Allied Sciences 51, 404–437. von Staden, H. 1997. “Character and Competence: Personal and Professional Conduct in Greek Medicine.” In: H. Flashar & J. Jouanna 1997 (eds.), Médecine et morale dans l’Antiquité. Geneva, 157–195 (Discussion, 196–210). von Staden, H. 2007. “Physis and Technê in Greek Medicine.” In: B. Bensaude-Vincent & W. Newman (eds.), The Artificial and the Natural: An Evolving Polarity. Cambridge, MA, 21–49. von Staden, H. 2008. “‘The Oath’, the Oaths, and the Hippocratic Corpus.” In: V. Boudon-Millot et al. (eds.), La science médicale antique: nouveaux regards. Paris, 425–466. von Staden, H. 2009. “Staging the Past, Staging Oneself: Galen on Hellenistic Exegetical Traditions.” In: Gill et al. 2009, 132–156. Stehle, E. 2005. “The Addressees of Empedokles, Katharmoi Fr. B112: Performance and Moral Implications.” In: Ancient Philosophy 25, 247–272. Strickland, S. 1998. “The Ideology of Self-Knowledge and the Practice of Self-Experimentation.” In: Eighteenth-Century Studies 31, 453–471. Taub, L., & A. Doody (eds.) 2009. Authorial Voices in Greco-Roman Technical Writing. Trier. Temkin, O. 1953. “Greek Medicine as Science and Craft.” In: Isis 44, 213–225. Thesleff, H. 1966. “Scientific and Technical Style in Early Greek Prose.” In: Arctos 4, 89–113. Thomas, R. 1993. “Performance and Written Publication in Herodotus and the Sophistic Generation.” In: Kullmann & Althoff 1993, 225–244. Thomas, R. 2000. Herodotus in Context: Ethnography, Science and the Art of Persuasion. Cambridge. Thomas, R. 2003. “Prose Performance Texts: Epideixis and Written Publication in the Late Fifth and Early Fourth Centuries.” In: Yunis 2003, 162–188. Tsouna, V. 2009. “Epicurean Therapeutic Strategies.” In: J. Warren (ed.), The Cambridge Companion to Epicureanism. Cambridge, 249–265. Wittern, R. 1998. “Gattungen im Corpus Hippocraticum.” In: W. Kullmann et al. (eds.), Gattungen wissenschaftlicher Literatur in der Antike. Tübingen, 17–36. Yarnall, J. 1994. Transformations of Circe: The History of an Enchantress. Urbana, Ill. Yunis, H. (ed.) 2003. Written Texts and the Rise of Literate Culture in Ancient Greece. Cambridge.

Notes on Contributors Markus Asper is Professor of Classics at Humboldt-Universität zu Berlin. He has published on Hellenistic poetry and ancient Greek literature of science. Steffen Bogen is Lecturer of Art History at the University of Konstanz and also designer of board-games. He studied Art History, Comparative Literature and Semiotics at the Universities of Stuttgart, Bologna and Marburg (PhD 1997, Habilitation 2007). His research focuses on diagrammatology and narratology. Among his publications are “Schattenriss und Sonnenuhr. Überlegungen zu einer kunsthistorischen Diagrammatik“ (2005); Rom. Eine Stadt in Karten von der Antike bis heute (with F. Thürlemann, 2009); “Zwischen innen und außen. Für eine Pragmatik des Diagrammatischen” (2011). Alan C. Bowen, Director of the Institute for Research in Classical Philosophy and Science (Princeton), is a historian of ancient Greco-Latin science and philosophy. His most recent books are New Perspectives on Aristotle’s De caelo (2009, with Christian Wildberg) and Simplicius on the Planets and Their Motions: In Defense of a Heresy (2012). He is currently writing a monograph on Hellenistic astronomy. He is also the editor of the journal Aestimatio: Critical Reviews in the History of Science and co-editor of the series Interpretatio: Sources and Studies in the History and Philosophy of Classical Science. Karine Chemla is currently a senior researcher at CNRS, France. Her interest is in the history of mathematics in ancient China within the context of world history. She also researches modern European mathematics, focusing on the relationship between mathematics and professional culture from the viewpoint of historical anthropology. Chemla and Guo Shuchun published Les neuf chapitres (2004), which was granted the 2006 Hirayama Prize from the Académie des Inscriptions et Belles-Lettres. Chemla also received the Prix Binoux from the Académie des Sciences in 2006 and the silver medal from CNRS in 2008. She serves on editorial boards of several scholarly journals. Serafina Cuomo is Reader in Roman History at Birkbeck, University of London. She has published on the history of ancient mathematics and technology, and is currently working on a project entitled Ancient Numeracy. Counting, Calculating and Measuring in Greece and Rome. Apostolos Doxiadis is a fiction writer, who has also worked in the theatre and cinema. Though he studied mathematics, he was never an active mathematician but has often dealt with mathematical subjects in his works, especially in the novel Uncle Petros and Goldbach’s Conjecture (Faber, 2000) and the graphic novel (with

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Christos Papadimitriou) Logicomix (Bloomsbury, 2010). He is keenly interested in various aspects of the relationship of mathematics and narrative on which he has lectured and published, also editing (with Barry Mazur) the book Circles Disturbed: The Interplay of Mathematics and Narrative (Princeton University Press, 2012.) Philip van der Eijk is Alexander von Humboldt Professor of Classics and History of Science at Humboldt-Universität zu Berlin. His particular research interests are in ancient medicine and in the relationship between Aristotelian philosophy and Greek medical thought. He currently directs a project on concepts of health in the ancient world and is general editor of a new series of scholarly translations of works of Galen, to be published by Cambridge University Press. Thorsten Fögen is Reader in Classics at Durham University (UK) and Privatdozent at the Humboldt-Universität zu Berlin. He is the author of Patrii sermonis egestas. Einstellungen lateinischer Autoren zu ihrer Muttersprache (Munich & Leipzig 2000) and of Wissen, Kommunikation und Selbstdarstellung. Zur Struktur und Charakteristik römischer Fachtexte der frühen Kaiserzeit (Munich 2009) and the editor of seven volumes. Brooke Holmes is Associate Professor in Classics at Princeton University. Her first book, The Symptom and the Subject: The Emergence of the Physical Body in Ancient Greece, appeared in 2010. She is also the co-editor (with W. V. Harris) of Aelius Aristides between Greece, Rome, and the Gods (2008). In 2012, she has published a short book entitled Gender: Antiquity and Its Legacy and an edited volume (with W. H. Shearin) on the reception of Epicureanism in the West. She has published on Lucretius, Greek tragedy, the history of medicine, the history of the body, and Homer. Paul T. Keyser studied physics and classics at St. Andrews’ School, Duke, and Boulder. After a few years of research and teaching in Classics, at Edmonton, Cornell, and other places, he returned to his first love, programming. He is crafting Java, patents, and papers, until recently for the IBM Watson Research Center, and currently for Google. His publications include work on gravitational physics, stylometry, and ancient science and technology. Reviel Netz was trained in Tel Aviv and Cambridge and is now professor of Classics at Stanford. He is the author of many studies in Greek mathematics (in particular of Archimedes, most recently “The Archimedes Palimpsest”, Vols I-II, Cambridge 2011). His research focuses on science as a literary phenomenon, from a formalist/ cognitive perspective (“The Shaping of Deduction in Greek Mathematics”, Cambridge 1999) and from the perspective of aesthetics and genre (most recently in “Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic”, Cambridge 2009).

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Ralph M. Rosen is Rose Family Endowed Term Professor in the Department of Classical Studies at the University of Pennsylvania. He has published widely in various areas of Greek and Roman literature, with particular focus on comic genres, intellectual history and ancient medicine. He is co-founder of the Penn-Leiden Colloquia on Ancient Values, and co-editor of the five published volumes (Brill) based on these events. His most recent book is Making Mockery: The Poetics of Ancient Satire (2007). Michalis Sialaros was born in Cyprus, in 1981. He studied mathematics at the National Technical University of Athens, and history and philosophy of science at the University of Athens. He has recently completed a PhD thesis on ancient Greek mathematics at Birkbeck, University of London, entitled ‘Revisiting Euclid: a Contextual Study of Greek Mathematical Authorship’. He is currently preparing a new English translation (with commentary) of Euclid’s Elements. Ineke Sluiter (PhD 1990, Vrije Universiteit Amsterdam) is Professor of Greek at Leiden University. Her research focuses on ancient ideas on language (grammar, rhetoric, ancient literary theory and ancient exegetical practices). Her other major research interest is ancient and modern public discourse on norms and values. She is the co-director of the “Penn-Leiden Colloquia on Ancient Values” (with Ralph Rosen); so far five volumes have appeared on this topic, most recently Valuing Others in Classical Antiquity (2010). In 2010 she won the Spinoza-prize, the highest academic distinction in the Netherlands. Liba Taub is Professor of History and Philosophy of Science and Director and Curator of the Whipple Museum of the History of Science at the University of Cambridge. In 2010 she received an Einstein Foundation Visiting Fellowship to work with the Topoi Excellence Cluster, Berlin. The author of Ptolemy’s Universe: The Natural Philosophical and Ethical Foundations of Ptolemy’s Astronomy (1993), Ancient Meteorology (2003), and Aetna and the Moon: Explaining Nature in Ancient Greece and Rome (2008), as well as numerous articles, she co-edited Authorial Voices in Greco-Roman Technical Writing (with Aude Doody, 2009) and Structures and Strategies in Ancient Greek and Roman Technical Writing (with Aude Doody and Sabine Föllinger, a special issue of Studies in History and Philosophy of Science, 2012). Heinrich von Staden is Professor emeritus of Classics and History of Science at the Institute for Advanced Study, Princeton. The principal subject of his current research is the diverse roles of animals in the development of human medicine, biology and natural history in the ancient Mediterranean. He also is continuing his research on the roles of individuals and collectivities in ancient science and medicine, his work on the ‘physiology of morality’ in antiquity, and his investiga-

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tion of ancient reflections on the sources and consequences of medical and scientific errors.

General Index account 255–275 accountability 255, 262–264, 266–268, 274–275 acrobatics 177, 180 addressee 166, 245, 418, 431, 434, 438– 439, 442–444, 448, 455–456, 462 agora 256 aids, non-verbal, visual 113–119, 138, 350 allegory 186–187, 464–465 ambiguity 112–113, 123, 125, 127, 138, 274– 275, 356 anadiplosis 396, 398 analemma 313–317 analogy, medical 463–464 analysis 344, 347, 360 animals 33, 111–139, 452 announcements 158, 166 anonymity 120–121, 123, 367 apodeixis 155, 345, 380 appropriation 191, 197–203, 208, 309 architecture 310–318 Aristotelian, terminology 150, 154, examples 150, style of reasoning 158 Aristotelianism 150–158, 246 artillery 46–48, 411, 415, 419 arts, high 177, useful 50, 177–178, banausic 177 assessment 255, 264, 269 astrologia 299, see astrology astrology 299, 301, 303, 305–309, 311, 314–317, 322–326 astronomia, see astronomy astronomy 51, 239–240, 243, 245–248, 299, 300, 303, 306, 318, 319, 324, 327, 335, 359 athletics 177, 183–184, 378 Atticism 217, 231 auction lists 255, 271 audience 92–93, 104, 112–113, 124, 128, 134–135, 146–148, 158–173, 192, 194, 197, 202, 231, 239, 242, 249–250, 258, 265–275, 291, 333–334, 339, 341, 345, 350–351, 376, 379, 395, 412, 418, 428, 434, 440–443, 447–448, 453, 458, 462 Augustus 19, 90, 245, 310–312, 317, 424 author 63–81, 124–139, 145–147, 158–173, 217–232, 289–291, 301–302, 333–360, 426–427, absent 223, impersonal 223,

implied 227, of inscriptions 258–259, mathematical 223–224, 367, 403–404, medical 443, poetic 177, 179, 181, 184, scientific 18, 134, 230, 412, 426 authoriality 4, 227–232, 250, quantification of 132–133 authority 4, 85–86, 89, 92, 98, 102, 104– 105, 113, 124, 131–135, 155–157, 191, 193, 299–300, 302, 305, 311, 318–319, 322, 327, 339, 375, 377, 412, 417–426, 431–466, construction of 422, 433, 443, disembodied 431, 434, 444, 459– 466, disregard of 22, 24, established 102, invocation of 423, medical 433– 435, 440, 443–444, 447, 449, 452–453, 458–462, past 423, poetic 177, 180– 184, 188–189, scholarly 104, scientific 113, 135, 139, 465 authorship, scientific 4, 113 autobiography 125, 421, 441–442 automaton 291–296 autopsia / autopsy 102–103, 445–448, 453 axiomatic-deductive 368 bia 204, 208–211, see violence bibliography 71–73 biography, of an author 219–220, 227, 231, as a genre 333, 341, 359 bios / life 334, 359, 456–458 body 431–435, 444–466, absence of 434, 439, 444, of the physician 431, 433, 439, 444–450, 455–462 botany 95, 102–103 calculating 257, 275 canon, Confucian 69, mathematical 68, 416 canonicity 230–231 canonization 192, 195 capital, cultural 195, 202, 207, 463 capstone theorem 225 carelessness 147 categories, human 112 center, authorial 217 chiasmus 390–392, 394–403 Circe 435–438, 441, 464 circle, area of 76–78 citation, poetic 177–189 clarification 125, 151, 153

478

General Index

class, social 24–26, 32 classic, Confucian 69 classification 225–226, 335, 352 clay tablets, Babylonian 267, 371 client-advisor 310–311 closure 392, 398, 415, 418, 421 collection genre 420 collectivity 128 commentary genre 192–193, 196, choice for the 193, generic expectations of the 193 commentary 63–81, 191–208, 351–353, didactic purpose of 194, lemmatic 194, marginal 193, relation between source and 191–195, 203, 205, selection of text as the object of 194– 195, stand-alone 193 commentator 66–72, 191–208, 351–353, creation of the poet by the 194–195, grammarian 195, 200–203, 207–208, power of the 192–195, power dynamic between source and 191–193, 203, 207–208, secondary material provided by the 193, violent 191, 206, see violence commercial mode 25, 28, 30, 32, 48–49, see guardian mode communication, forms of 333, 336, 339, 360, peer-to-peer 247, 249 competition 184, 203–210, 217, 236, 308, 375, 418–427, see interpretation competitiveness 83–105 compilation 63, 68, 71–72, 78, 80, 88, 102, 117, 246 conclusion, compared to enunciation 345, 380–381, 389, 400, 402–403 confidence, rhetoric of 168–172 consensus 92, 300 conservatism 49 constellations 314, 316 construction, of authorial authority 422, of a deficient past 419, graphical 285– 286, 289–290, 296, of group cohesion 421, of legitimate succession 422, of narratees 418, of the scientist’s self 412, technical 286, 289, 294, 296 constructionism, social 1 contagion 432 contents, table of 84–85, 87, 90–91 contradiction 38, 395

cosmology 93–95, 321, 377 counter-narratives 386, 388, 395 counter-propositions 388 cross references 127–128, 158, 166–168 culture, deuteronomic 7, 417, 424–425 mathematical 224, 247 decline 21, 27–29, 52–53, 96–97 dedication 89, dedicatory epistle 90 deduction 379–384, 395–396, 400 definition 145, 204, 223, 320, 322, 334, 340, 343, 359, 389 democracy 21–23, 255–256, 261, 264–265, 274–275 deontology 434–435, 453–458 design, authorial 222–226 development 22, 24, 27, 40, 46–47, 49, 52, 66–67, 96, 103, 148, 199, 280, 367, 378–379, 411–412, 425, 427, 434, 440, 450, 453–454 diagram(s) 113–119, 217, 239–241, 244– 245, 279–297, 335, 340, 342, 350, 368, 370, 380, 382–383, 390, 399–402, authoring of 289–291, combination of text and lettered 280, Greek mathematical 241, pictorial embellishment of the 296, reading 289–291, in technical writings 296, transformation of the 287, 289, 294, visual 113, see reasoning diairesis 386 dialogue 147, 341, 349, 358, 371, 376–377, 424 diaporein 169 didaskalia 149 dietetics 149–150, 449–450 dihorismos 345–346, 380 disembodiment 432–433, 444, 450, 460– 461, structural 461–462, 465, see authority, knowledge, observation disparagement 205 dissection 116, 134–137 distribution of works 222 divination, science of 318, 323 doxography 27, 419–420 drawer (zōgraphos) 283 drawings, schematic 285, 296 dunameis 423, 437–438, 443, 451 eclipse 93–94, 248, 308, 320, 325

General Index

edition 63–81 education 177, 179, 195–196, 203, 222, 240, 243–244, 305, 307–308, 320, 360, 421, 435, 465, of the architect 311–313, 316–317, astronomical 247, 307, Chaldaean 307, general 312, Greek 307, mathematical 243, medical 447, 459–460, philosophical 246, scientific 244 ego, authorial 124, 128–129, 146–147 egotism 433, 461 eisagōgē 334, 358, see introduction ekthesis 345–346, 380 encounter, clinical 434, 449, 452–453, 458–459, 461 encyclopedia 27, 84, 87, 93, 333, 340, 360 enthymeme 377, 398 enumeration, rhetoric of 132 enunciation / protasis 345–347, 349, 353, 380, 382, 388–389, 400–402 epideixis 420 epigram 201–202, 338, 354–357 epilogos 387 epimerism 197, 199 epistēmē 18, 290, 335 epitome 145, 321, 333, 351 ethos 95, 99, 104, 147, 376–377, 383, 385 Euclid 224, see Homer, mathematical evolution, biological 30–32, 52, scientific 17–30–33, 49 exhaustion, method of 34, 38–39, 41 expertise 182, 197, 208, 258–260, 306, 311, 322, 379, 433, 435, 440–441, 443, 450–451, 458, 460–461, 463–465 extraction 24–25 failure 33, 302, 304, 307, 460 falsification 31, 33 festivals: dramatic 230, Athenian 230, PanHellenic 238 figuration 123, 139 figurative, the 138–139, see literal first person 124–125, 127–128, 130, 158– 160, 164, 166–167, 224, 318, 339, 432– 433, 441, 443, 446, 448, 451, 453, 456, 459 force, verbal 204 forensic speech 368, 378, 384–390 form, literary, choice of 112 formula 37, 48167, 171–172, 223–225, 266, 342, 382, 411

Fortune / tykhē 177 fragmentation 194 generality 120–121, 280, 334, 348, 377 genre(s) 145, 147–149, 151, 179, 192–193, 196, 198, 217–218, 229, 231, 240, 244– 245, 250–251, 280–281, 297, 333–360, 376, 378, 420, 442, 445, 456, authorial choices of 193, 333, 336, 338–340, categorization of 338, contamination of 135, conventions of 135, 146, 148, 334, 337, expectations of 112, 148, 172, 193, 337–339, 456–458, of mathematical texts 333–360, of scientific texts 334, system 217, 251, 337 geometers, catalogue of 415 geometry 118, 126, 239, 241, 245, 247, 279–280, 286, 303, 305, 311–312, 319– 320, 324, 341–343, 347–348, 350–351, 354, 360, 370–374, 379–384, 388–389 Gorgianism 394 grammar 194, 201–203, 207–208, 210 guardian mode 25–26, 49, see commercial mode Han dynasty 69–71, 73, 80 handbook 341, 351, 358 herbal medicine 99–103 Hermes 177, 233, 435–439, 443, 456, 464– 465 Hippocratic Oath 451, 454, 456–458 history, pattern of 412 Homer, mathematical 224, see Euclid hupomnēma 149, 160 hybrids, textual 338 hupomnēmatikon 383 ideology, imperial 28 illustration 101, 114, 116–117, 119, 234–235, 237–241, 249–250, 279, 284, 296, 345, of books 233–237, 280 immunity, authority of 441, 444, of the physician 432, 439 impersonality 125, 128, 138, 146, 164–167, 223–224, 247, 318, 339, 368, 374, 404, 433 infinite 33–41, 414 innovation 18, 21–25, 31, 47, 49–50, 52, 86–87, 95, 101, 120, 124, 129–130, 135,

479

480

General Index

307, 333, 335, 404, 412, 422, 446, 465, see novelty inscription 89, 240, 245, 255–275, 340 instructions 44, 50, 149, 164–167, 195, 304, 374, 376, 438–439, 442–443 integrity 87, 89, 95, 111, 147, 443 intent, statements of 158, 166–168 intention 70, 89, 181, 186, 191–192, 194– 195, 203, 227, 334, 338, 413 interpretation, destructive 207, violent 203–208, see competition introduction 92, 193, 222, 224, 225, 245– 246, 299–303, 318–319, 321, 324, 326, 333–334, 342, 358–359, 385, 387, 389, 415, 419–420 inventor / prōtos heuretēs 21, 413 inventories 261, 265–268, 271, 274 invisible hand 32 kataskeuē 345–346, 380 knowledge / epistēmē 18–19, 35, 41, 66– 67, 70, 80, 83, 85, 93, 95–96, 98–99, 101–102, 104–105, 112, 129, 132–134, 137, 178, 182, 194–195, 199, 202–203, 207, 247–249, 257, 264–265, 290–291, 296–297, 305–306, 324, 335, 340, 345, 352, 367, 369, 376, 397, 413–416, 422– 427, 431–466, accumulation of 98, 415, authorial 132, body of 70, 80, 203, 207, 413, claims to 290, 297, 432–434, 442, classifications of 335, 352, disembodied 435, 444, 446, expert 102, 432, 434–435, 452, 461, imparter of 85, mathematical 41, 66, 67, 248, 369, 416, medical 434, 446, 460, 462, objective 367, philosophical 178, poetic 178, privileged 437–438, 442, progress of 101, scientific 98, 129, 178, storing of 96, technical 129, 133, 207, 290–291, 296, 414, 450–451, 463, theoretical 178, 335, types of 335, transmission of 96, 99 language 23, 26, 30, 83, 88, 100–113, 119– 129, 133–139, 146, 148, 195, 199–206, 243, 279, 297, 335, 339–340, 377–378, 384, 446, 451, 453, counter-authorial 223, formulaic 223–225, 342, mathematical 223–224, technical 124– 125, 134, 340, theories of 138

layperson 182, 434–435, 445, 448–449, 462 lecture 147, 165, 242–249, 290, 300, 333– 334, 341, 350–352, 358–360, 420 legō 125, 382, see also first person lemma 37–38, 344 letter 85, 92, 129, 145, 147, 247, 333–334, 338, 341–342, 353–356, 358, 360 literacy, cultural 195, 197 literal, the 138–139, see figurative literature, anonymous 217–218, 220, distinction of 147, 338–339, 434, nonperformative 217, 240, 249, performative 227, 229, 241–242, 250, 434, 456, 458, 466, oral character of 232, 358, technical 87, 90, 92, 111, 114, 129, 138–139, 158, 339, 360 makhesthai 211–212 manipulation 271, 275, 452, 466 mathēma 374 mathematicians 217, 224–225, 232, 241– 250, 280, 297, 324, 333–335, 338, 341– 343, 349, 352–353, 355, 360, 367–368, 370–371, 374, 384, 389, 403, 415–416, 418, 425, 427 mathematics, Greek 63, 217, 223, 225–226, 232, 241, 244, 247, 249–250, 280, 333–335, 337, 339–342, 348–349, 353, 360, 367–375, 381–382, 384, 389, 403, Babylonian 247, 266, 340, 371, Chinese 63–81, Egyptian 368–371, Greek practitioners of 341, 368, 374, influences on the creation of Greek 374, lack of specialization in Greek 374, non-Greek 375, in philosophy 246, practical 368, 374 mathēmatikos 334, 374 mechanics 279–281, 285, 290, 297, 350, 418 medium 113–114, 230, 289, 296, 334, 375, 434 memory, art of 391 metaphor 4, 123, 138–139, 149, 390 metatext 193, 208 ming bian 377 mixtures / kraseis 150–155 monument 245–246, 248, 266 myth 25, 51, 184, 186–187, 210, 233, 392, 397, 412–413

General Index

namelessness 113, 120–129, 134, 138 narration / diēgēsis / prothesis 385–387, compared to construction 388–389 narrative 4, 83–84, 94, 112, 114, 132, 198, 217, 226, 231, 233, 235, 300–301, 341, 359, 368, 375–378, 384–389, 392, 394–395, 397, 403, 411–428, 440–441, 443, 453 narrativist turn 411 narratology 411 narrator 134, 411–412, 414, 417–418, 420, 424–426, 436, 440–441, 443 necessity 225–226, 280, 284, 441 neologisms, technical 123 network 222, 230, 232, 245, 456 nine parts of mathematics 66–67, 70 noise, rhetorical 433, 451 novelty 21, 24, 51, 86–87, 424, see innovation number 34–41, 225, 255, 257–258, 266, 268, 271, 275, 340–341, 343, 356–357, 360 numeracy 27, 255, 257–259, 264, 266, 274– 275, 340 obscurity 125, 138, 398 observation, disembodied 453 observer, expert 446 occasion 146–147, 150, 158, 231–232, 300 Odysseus 357, 391, 395, 397, 431, 435–441, 443, 464–465 orality 256 originality 88, 124, 129–130, 133, 135, 446 palaioi 155–156 papyri 193, 218–241, fragments 218, 220, Greek literary 220–221, 227, 229, 232, herbal 240, magical 240, mathematical 241, 247 paradeigma 115–116, 392–393, 400 paradigm 33, 52, 281, 414, 421–422 para-medical 180 parapēgma 245, 315–318, 321, 323–325 paratext 193, 342 passive future 167 passive perfect 167 patron 27, 234, 247, 310, 333, 336, 339, 341 performance 114, 136, 207, 217, 227, 229– 232, 237–239, 241–250, 266, 274, 431,

434–435, 440–443, 451, 453–454, 458–459, 461 peripeteia 424 person-to-person relation 247, 250 persuasion 3, 204, 368, 376, 385, 392, 394, 398 pharmacology 85, 100–103, 150, 154 pharmakon 436, 438 philosophia 20–21 phusiologia 18 phusis 436, 450, 454 physician role 433, 435, 444, 447, 453–454, 459–466 pistis 385–388 pivot 314, 390, 393, 395 plagiarism 88 plague 431–432, 444, 447 plot 231, 414–418, 421–426 pneuma, psychic 186 pneumatics 279, 290 poetry, attitudes towards 178, mathematical 333, 354, 354–357 polarity 394–395 polis 229, 242, 256, 260, 263, 265, 304, 308, 375, 378–379, 384, 404 polutropos 437 polysemy 123, 125, 127 popularity 218, 220 porism 344 postulate 334, 343, 389 practice, mathematical 249–250, 335, 340, 368, 38, rational 4 practitioners 30, 32, 46, 299, 301, 307, 326, 335, 339–341, 368, 374, 423 pragmateia / tractatus 145–150, 169, 172, 334, 358 predecessors 23, 70, 83–84, 86, 89, 91–92, 94, 99, 102, 104, 130, 135, 145–146, 148, 151, 187, 339, 348, 355, 374, 416, 419–420 preface 64, 66–73, 83–92, 102, 124–125, 129, 131, 133, 317, 415 presence, authorial 217, 227, 232, 239, 250 priamel 386–387, 390, 402 proanaphōnesis 385, 390 problem 27, 34–35, 41, 69–70, 74, 76, 79, 147, 169, 341–357, 369–373, 381–382, 389, 399–403 progress 23–24, 48–52, 94–95, 101, 411– 428

481

482

General Index

prolegomena 145, 193 proof 37–39, 115, 222–225, 244, 301, 306, 314, 334, 338, 342–343, 345–348, 351, 353–355, 367, 370, 380–383, 385, 388–390, 400, 402, language of 23, 446, structure of 225, 388 prooimion 385 proposition, geometrical 347–348, 379, 381 prose, mathematical 340, 343 publication, of research 333 punctuation 237–238 Pythia 181–182 quarrel, between poetry and philosophy 178 Quellenanalyse 104 question-and-answer text 333–334, 341, 349–351 reader 85–94, 97, 99, 102, 104–105, 112– 113, 128–134, 145, 147, 161, 164–166, 169, 173, 177, 181, 184, 193–194, 196– 197, 218, 227, 238–239, 241, 243, 258, 269, 271–272, 279–280, 287, 290, 294, 296–297, 299–303, 305, 308–312, 314, 317–322, 325–327, intended 266, 319, 338 reading, as a medical tool 424 reasoning, diagrammatic 279 reception by audiences 334 recipe 17, 29–31, 46, 52, 91, 102, 333, 370 representation, of animals 113 researchers 95, 98, 103 revolution 21, 413, 416 rhetoric 368–369, 375–379, 384–390, 392, 395–396, 398, 400, 402, 403 rhetorician 183 ring-composition 389–394, 399–403 Rome 19, 27–28, 83, 93, 96, 99–101, 104, 135–136, 257, 305, 424 rule of three 74–75 sages 67–68, 71 Schadenfreude 184 scholarship, decline of 96–97 scholia 191–192, 197–198, 207, 209–210 scholiast 191, 194, 197–199, 202, 207–210 science 1, 4, applied 29, 33, celestial 299–327, drawing of 279, exact 114, 217, 219, 222, 232, 239, 240, 243–244, 248–250, flourishing of 22, 29, 53,

pure 29, rhetoric of 188, Roman assimilation of Greek 27 second person 152, 160, 163, 165–167, 173, 247, 443, 462 Second Sophistic 221, 227, 231, 242, 423– 424 self-advertisement 88, 92–93, 95, 104 self-presentation 83, 89, 113, 123, 132, 139, 193, 339, 426, 433, 453–456, 458 setting-out (ekthesis) 345–348, 380, 382– 383, 388 skholion 334 society, closed 24–26, indigenous 26–27, non-industrial 26, non-literate 26, open 25–27, 29, 49, oral 26, smallscale 26, traditional 26, 52, 404 sophia 20, 51 source(s) / auctores 32, 65, 69–70, 74–78, 80–81, 84–88, 90–91, 93, 101, 104, 117, 131–132, 160, 181, 191–199, 201, 203, 205–208, 235, 281, 307, 343, 352, authority of 193, documentation of 91, evaluation of 104, 146, 155, list of 87, 91, use of 87, 131 sovereign 375 specification 345–346, 380, 382–383, 388, 400, 402 speech, public 228, 231, 242, 245, 248 spiral 222–224, 227 stasis 31, 33 strategies, authorial 114, rhetorical 169, 180, 183, 198, 318, 326, 411, 447–448 STS (science and technology studies) 3 style, mathematical 247, 368, 374 subcommentary 65, 68, 72, 74–79 sub-narratives 386, 388, 397 sub-propositions 388 success 30, 33, 47, 169, 230, 302, 304, 307, 375, 414–415, 421–422, 427, 439 Sumerian adversarial literature 376 sumperasma 345, 347, 380 sungramma 149 survival, cultural 192, 195–196 susceptibility to influence 404 syllogism 377, 398 synthesis 244, 344, 420 teachers 201, 207, 243–244, 246, 335–336, 351, 360, 457 tekhnē 51, 178, 180, 265, 290, 358, 391

General Index

terminology 4, 150, 153–154, 191, 200, 343–344, 347, 349, 353, 358, lack of 123 testimony, poetic 177–180, 184, 186–187 texts, visual 232 textual formats / types 334, 338, 360 textualizing 111, 113, 136, 138 theorem 18, 37, 39, 225, 257, 305, 334, 344, 347–349, 373, 381–382, 384, 389, 399, 402–403, 425 theōria 18, 152, 187 theorists 317, 320, 324, 360, 422–423 third person 152, 160, 164–166 title, choice of 88–89 tradition 18, 22, 24–26, 28, 49, 52, 87, 145, 182, 193, 199, 202, 205 transformation 28, 197, 202, 235, 280, 286–289, 294, 318, 396 treasurer 260–262, 269 treatise 91, 112, 114–116, 119–120, 123–125, 127–131, 135–139, 146–150, 158–159, 166–169, 172–173, 177, 180, 183–184, 193, 223, 225, 240, 242, 281, 285, 300, 304, 310, 318–322, 334, 341, 343, 351,

358, 367, 369, 372, 376, 378, 415, 419, 422, 434–435, 438–439, 443–444, 447–449, 451, 453, 456, 458, 459, 462 tribute list 255–256, 266–267, 272 usefulness / utilitas 86, 91–92, 97, 191, 285, 451 utilitarianism 100 variety, formal 145–147, 333 viniculture 95–99 violence 191–192, 203–211, 242, 442, 459, see bia visualization 113–119 vivisection 116, 134–137 voice, authorial 226, 238, 250–251, 339, 343, 360 word-boundaries 237 wound-treatment 41–46 writing science 1–4 Zhou dynasty 66–67 zoology 111–139

483

Index Locorum Aelian Nat. anim. VI 19 133 Aelianus tact. Tact. 1.5 285 Aelius Aristides To Rome 60 28 Aeschines or. 3.16 205 3.35 205 3.59 266 3.72 204 Aeschylus Pers. 213 263 Prom. 442–506 413 686 124 Alexis (Poet. Com. Graec. II) fr. 15.12 133 Ammonius In Arist. Cat. (Comm. Arist. Graec. 4.4) 15.3–20.12 201 Anaxagoras (59 Diels-Kranz) B 1 34 B 4 34 Anaximander (12 Diels-Kranz) B 1 34 Anaximenes hist. (ed. Fuhrmann) fr. 10 373 Annales Sangallenses breves Mon. Germ. Hist. Script. I, p. 64 417 Anthologia Graeca IX 168 (Palladas) 201 169 (Palladas) 201 173 (Palladas) 201 174 (Palladas) 201 XI 139 (Lucilius) 202 279 (Palladas) 201 400 (Lucianus) 201 401 (Lucilius) 201 Antiphon or. or. 2 (Tetr. 1).115.4 386–388, 395–396 115.5 387 or. 5.69–71 262 Antiphon soph. (87 Diels-Kranz) A 13 35 Apollonius Dyscolus (Gramm. graec.) Adv. (ed. Schneider) 140.6f. 211 Synt. (ed. Uhlig) 48.12 205 327.11 205 365.4 205 Apollonius Pergaeus Con. I introd. 245 II introd. 245 Appian praef. 24–28 28 Aratus Phaen. 537–540 324

Archimedes Dim. circ. 1.138.5–1.139.4 388 Meth. III 84.8 373 Probl. bov. 355–357 Quadr. parab. 23–24 39–40 Sphaer. cyl. praef. 342 I praef. 38–39 I 1–6 39 I 9.3 373 Spir. introd. 245 Aristophanes Av. 992–1019 246 Eccl. 218–220 21 456–457 21 577–580 21 586–587 21 Nub. 896–898 21 Vesp. 655–663 272 665–712 272–273 655–718 266 Aristophanes Byz. Epit. 2.29 119 Aristotle Cat. 1.1a1 201 Int. 10.19b5–12 120 Anal. pr. I 24.41b14–26 348 Anal. post. I 5.74a8–10 120 7.75b14–17 335 II 13.96b6–8 120 Soph. el. 11.171b16 373 172a2 373 172a3–9 35 14.173b17ff. 199 34.184b3–8 165 Phys. I 2.185a14–18 35 185a17 373 II 1–2.192b8–194b15 30 2.193b23 352 194a7–8 335 III 6.206b3–33 35–36 V 2.226a29–b1 120 VI 2.232a23–233a21 34 2.233a21–32 34

486

Index Locorum

9.239b9–30 34 10.240b8–9 118 VII 4.249b22–26 120 VIII 6.258b25 118 8.263a4–b9 34 Cael. I 3.270b19f. 414 Gen. corr. I 7.324a24–b6 463 II 2.330a12 123 Mete. I 3.339b27–30 414 Anim. I 3.406b22 128 II 5.417b32–418a3 120 7.418a26–29 120 7.419a2–6 120 7.419a30–32 120 III 2.426a11–15 120 Mem. 2.451b10–452a30 391 452a17–30 391, 398 Respir. 8.474b2–3 122 474b9 116 12.476b30–32 126 16.478a26–b2 116 17.478b28–31 126 Hist. anim. I 1.486a5–8 124 3.489a17–19 121 5.490a6–11 121 5.490a12–13 121 6.490b7–12 121 6.490b15–20 121 6.490b31–32 121 6.491a22 128 11.492a13–16 121 13.493a25–30 121 15.494a2–3 122 15.494a13–14 122 15.494a23–24 127 16.494b20 128 17.497a30–32 115 II 1.499b21 128 8.502a26 128 11.503a24 128 14.505b18–22 134 17.507a1–2 128 III 1.509b21–24 116 1.510a29–35 118 1.511a11–14 116 IV 1.525a6–8 116 3.527b7 128 4.528a11–13 126

4.529b18–19 116 4.530a30–31 116 6.531a28–29 128 V 5.541a5–6 128 11.543b10 128 14.545a14–15 127 18.550a23–27 117 20.552b30–553a2 123 22.554b2–3 128 32.557b1–2 128 VI 5.563a7 373 5.563a8 128 10.564b18–19 128 10.565a6–7 128 10.565a12–13 116 11.566a9–10 128 11.566a10–15 116 13.567a18 128 29.578b6–7 128 VII 10.587a24–25 128 VIII 1.588b11–12 128 17.600b18–19 128 IX 1.608b15 128 Part. anim. I 1.640a2–3 128 1.640a13–14 127 1.641b19–20 128 5.644b24–645a5 128 5.645a2–3 128 5.645b3–4 128 5.645b11 127 5.646a1–2 127 II 2.648a31–b1 123 2.648a35 128 2.648b10–649b9 123 2–3.649b5–11 123 3.650a31–32 116 8.654a27 127 10.656a8 128 13.657b3–4 122 16.659a14–15 127 16.659a34 127 16.659b21–22 127 16.659b36 127 17.661a30 127 III 1.661b16 127 1.662a19 127 3.664b20 127 4.665b31 128 4.666a8–10 116

Index Locorum

4.666b16–17 127 4.666b25 127 4.667a8 127 5.668a10 127 6.668b28–30 116 7.670a3–4 127 14.674b15–17 116 IV 2.677a8–10 116 4.678a6–11 122 5.678b23 128 5.679b32–680a2 116 5.680a14–15 122 5.682a2–3 128 7.683b22–24 122 8.684b1–5 116 10.689a16–20 116 11.692a20 127 13.696b14–16 116 Mot. anim. 1.698a16–b1 118 4.699b20 128 8.702a12–13 127 9.702b25–703a1 118 11.703b29–33 119 704b2 127 Inc. anim. 4.705b22–23 126 6.706b25–28 126 7.707b22–30 119 8.708a12–14 127 15.713a2–3 127 16.713a26–27 127 Gen. anim. I 1.715a1–4 127 2.716a4 127 2.716a21 128 5.717b33 128 13.720a24 128 15.720b19–20 128 16.721a26–27 128 18.723a22 128 18.723b22 127 18.724b23–28 126 18.725a3–7 126 18.725a22 128 18.726a9 128 19.726b2–3 128 19.726b19 128 19.726b34 128 19.727a33–34 128

20.728b32–36 126 21.730a3 127 23.731b7–8 127 II 1.733b17–18 128 1.734a23–29 127 2.736a18 128 3.649b12–28 123 4.740a23–24 116 4.740b18–24 127 6.741b25 128 6.742b36–37 128 6.743a33 128 6.743b16 127 7.745b23 128 7.746a14–15 115 8.747b27–30 127 8.747b8 128 8.748a13 128 III 3.754b33 127 8.758a21–25 117 9.758a30–31 128 10.759a15–20 126 IV 1.763b28 128 1.764a33–36 116 1.765b8–14 127 1.765b35–766a4 123 1.766b7–12 126 4.771a36 127 4.771b32–33 116 V 1.778a16–20 126 1.778b1–2 128 1.779a6 127 1.779a7–11 116 1.779b22 128 6.785b16–21 126 Metaph. A 1.981b23 368, 374 1–2.981b13–982b27 178 2.983a12–16 291 3.984a8 373 10.993a15–17 426 α 3.995a5–7 341 Ζ 7.1033a8–16 120 Ι 5.1056a24–25 120 Λ 8.1073b17–1074a14 309 8.1074b8–14 414 Μ 6–8.1080a12–1085a2 35 Eth. Nic. I 7.1098a22–25 414 12.1101b27 373

487

488

Index Locorum

II 7.1107b1–2 120 7.1107b28–31 120 7.1108a4–6 120 7.1108a16–19 120 III 6.1115b24–26 120 IV 4–5.1125b17–29 120 6–7.1127a11–14 120 V 2.1131a8–9 204 Eth. Eud. II 3.1221a28–31 120 3.1221a3 120 3.1221a38–40 120 8.1224a18–20 120 III 2.1231a39–b2 120 6.1233a38–39 120 7.1233b19–22 120 IV 14.1247a17 374 Pol. I 3.1253b8–11 120 II 8.1268b34–40 414 8.1269a3–4 24 III 1.1275b29.32 120 3.1282a3–5 434 VII 6.1327a18–28 24 10.1329b25–30 414 Rhet. I 1.1354a–b 398 2.1355b35–1356a23 377, 385 2.1357b3–5 120 3.1358a36 378 II 21.1394a26–27 376 22.1395b 398 23.1398a 386 III 2.1405a33–b5 123 2.1405a34–b5 120 3.1406a35–36 120 9.1410a20–25 396 14.1414b 384 19.1419b10–13 387 Poet. 1.1447a28–b2 120 19.1456b15ff. 199 21.1457b25–33 120 24.1460a33 210 Ath. pol. 4.2 263 7.3 260 8.1 260 8.4 263 23.4–5 264

26.2 261 27.1 263 30.2 261 47.1 260 47.2–3 260 47.5 260 48.1 260 48.3–4 262 48.4 263 50.2 259 54.1 259 54.1–2 262 Ps.-Aristotle Probl. mech. 847b18f. 287 848a20–22 287 848a6–8 287 Probl. phys. XV 10.912b4–10 350 Aristoxenus Harm. II introd. 246 Athenaeus Deipn. XIII 89.5 373 Athenaeus mech. 39.7 285 Augustine Civ. II 21 19 Autolycus Sphaer. 3 382–383 3.1 383 Babylonian clay tablet A.O. 6770 371 Berossus (FGrHist 680, ed. Jacoby) F 1 (4) f. 413 Chaeremon (Trag. Graec. Frag. 71) fr. 21 414 Cicero De orat. II 161 20 Fam. IV 5.5 456 Leg. I 53 20 Nat. deor. III 43–44 20 Off. II 12–15 51 Pro Flacc. 15–18 20 Rep. II 7–9 24 III 8 20 III fr. 9 20 Tusc. II 2.4 20 2.5 19 2.6 20 Cleomedes Cael. II 2.7 358 7.12 358 Columella De re rust. I 1.13 101 Corpus Hippocraticum (ed. Littré)

Index Locorum

Acut. 64.1 (2.364.3) 124 Aer. 1 (2.12) 438 2 (2.14) 438–439 8 (2.36) 443 10 (2.48) 438 10 (2.42–44) 438 12 (2.56) 438 13 (2.56–58) 443 16 (2.62) 438 (2.64–66) 443 16.3–5 (2.64–66) 23 20 (2.74–76) 443 23.4 (2.86) 23 24 (2.90) 443 (2.92) 439 24.9 (2.92) 164 Aff. 1 (6.208) 462 Aph. I 1 (4.458) 201 VI 19 (4.568.4) 122 Ars 1 (6.2) 22 7 (6.10–12) 460 9 (6.16) 454 12 (6.24) 453 Artic. 8 (4.94–98) 452 Carn. 1 (8.584) 435, 451 8 (8.594) 452 9 (8.596) 452 15–17 (8.602–606) 445 18 (8.608) 446–447 19 (8.610.614) 446 Coac. 109 (5.606.4) 124 494 (5.696.20) 122 Dec. 2 (9.228) 455 3 (9.228) 455 4 (9.230) 455 7 (9.236) 455 11–12 (9.238–240) 455 16 (9.242) 455 Epid. I 11 (2.636) 449 V 16 (5.214–216) 44 27 (5.226) 44 28 (5.226–228) 44 46 (5.234) 446

97 (5.256) 44 VI 8.17 (5.350) 445 VII 35 (5.402–404) 44 Flat. 1 (6.90) 445 7 (6.100) 447 14 (6.110) 447 14 (6.112) 448–449 Genit./Nat. puer. 13 (7.488–490) 446 (7.490) 453 (7.492) 446 Iusi. 4 (4.630) 456 8 (4.632) 457 Lex 3 (4.640) 455 Loc. hom. 32 (6.324) 44 Medic. 1 (9.204) 455 (9.206) 455, 457 Morb. I 1 (6.140) 458 II 23–25 (7.38–40) 44 IV 55 (7.604.6) 122 Morb. sacr. 3 (6.366) 447 11 (6.382) 452 14 (6.388) 445 14–17 (6.386–394) 44 Mul. I 6 (8.30) 452 Nat. hom. 2 (6.34) 447 5 (6.42) 452 6 (6.44) 452 Off. med. 1 (3.272) 445 4 (4.284–288) 454 Praec. 6 (9.258) 455 10 (9.266) 455 Ulc. 12.4 (6.412.23) 122 14.3 (6.418.3) 122 Vet. med. 1 (1.572) 448 2 (1.572) 449 (1.572.9–14) 422 (1.572–574) 23 4 (1.578) 449 6 (1.582–584) 449

489

490

Index Locorum

7 (1.584) 448 (1.584–586) 450 9 (1.588) 450 (1.588–590) 450 13 (1.600) 443 15 (1.604) 448 18 (1.612–614) 448 (1.614) 448 20 (1.620–622) 448 21 (1.624–626) 450 Vict. I 2 (6. 468–470) 451 2 (6.470) 450 35 (6.518) 460 III 69 (6.606) 23 69 (6.604–606) 462 Virg. 2 (8.466–468) 447 Vuln. cap. 3 (3.194) 44 4–6 (3.194–204) 44 7 (3.194–210) 44 8 (3.210) 44 9 (3.210–212) 44–45 12 (3.222–228) 44 13.1–2 (3.228–230) 45 13.3–14 (3.232–242) 45 19 (3.252–254) 46 19.3 (3.254) 45 20 (3.254–256) 45 21 (3.256–260) 45 Ps.-Demetrius Eloc. 4 201 Democritus (68 Diels-Kranz) B 155 34 B 159 463 Ps.-Democritus (68 Diels-Kranz) B 299 368 Demosthenes or. 4.10 (= Phil. I) 21 or. 18.229 266 Dicaearchus (ed. Mirhady) fr. 56A.39– 44 413 Dio Chrysostomus or. 11.35f. 200 Diocles On Burning Mirrors (ed. Toomer) introd. (34) 245 Diodorus Siculus Bibl. I 1.1–2 304 1.1–2.8 303 1.3 304, 309 1.4 304 1.4–2.8 304 2.1 309

3.1–4.5 304 3.1–8 304 3.2–3 304 3.4–8 304 4.1–5 304–305 4.8 50 28.1 306 69.1–2 305 69.3 306 69.3–4 305–306 69.5–7 305 70.1–80.6 305 81.1–4 305 81.4 305 81.4–5 305 81.5 309 81.6 306 96.1–3 306 96.1–98.10 306 98.3–4 306 II 1.2–3 306 1.3–28.8 306 29.1 306 29.2.4 307 29.2–3 307 29.4–6 307 29.5 307 30.1–2 308 30.3–5 308 30.4 308 30.5–6 308 30.6 308 30.6–7 308 31.1–3 308–309 31.6–7 308 31.7 308 31.7–9 308 XI 47.2 264 XIV 41–43.4 46, 48 42.2 46 XVII 112 309 112.4–5 309 XIX 55 309 55.9 309 XXXX fr. 3.1–2 19 Diogenes Laertius I 14.1–16 373 16.6 373 23 93 24.10 371

Index Locorum

III 5

230 24.8 373 IV 29–32 244 V 2.36 242 VII 144–146 321 155–156 321 185 248 VIII 84 373 86.1 373 IX 12–14 19 31 34 34 373 53f. 199 55 50 Dioscurides Mat. med. praef. 3 102 4 102 7–8 102 II 52 133 IV 153.4 122 Empedocles (31 Diels-Kranz) B 23.3 126 B 100 444 B 112 442–443 B 146 442 Ennius Ann. V fr. 156 Skutsch 19 Euclid Dat. 5 401–402 Elem. I 1 399–400 I 2 400–401 3 403 6 347 7 369–370, 380 19 402 47 225 241–242 346 IV 10 347 IX 35 37 36 225 X 1 38 1–20 225 42–47 225–226 85–90 226 XII 2 38 10 38 XIV introd. 245 Euripides Heracl. 329–332 21 Med. 1078–1079 188

Suppl. 339–345 21 347 204 403–455 23 576–577 21 Eustathius Ad Iliad. 1016.45 211 Eutocius (ed. Heiberg) In Archim. Dim. cir. III 228.15 373 In Archim. Sphaer. cyl. 78.13–84.11 373 88–96 354 88.8–10 354 96.10–27 355 Galen Adv. Lycum (ed. Kühn) 18A.196f. 206 Anat. adm. (ed. Kühn) I 1 (2.215–218) 136 2 (2.218–219) 136 III 9 (2.396.6–7) 137 IV 3 (2.430–431) 137 VI 1 137 1 (2.537) 137 3 137 7 137 12 (2.581.1–6) 423 VII 16 (2.644–646) 248 X 1 137 7 137 XI 2 137 8 137 12 137 XIII 4 137 XIV 1 115, 137 XV 2 137 Ars med. (ed. Kühn) 37.9 (1.408.15– 16) 137 Bon. mal. suc. (ed. Kühn) 6.800 150 Cur. rat. ven. sect. (ed. Kühn) 11.257 150 Diff. puls. (ed. Kühn) III 6–7 (8.670– 694) 138 Diff. resp. (ed. Kühn) 7.825 149 854 149 Hipp. elem. (ed. Kühn) 1.489 150 In Hipp. Acut. (ed. Kühn) 15.515 149 In Hipp. Aph. (ed. Kühn) 17B.345–356 201 17B.870f. 205 In Hipp. Epid. I (ed. Kühn)

491

492

Index Locorum

I (17A.6) 191 (17A.15–37) 201 In Hipp. Epid. III (ed. Kühn) I (17A.507) 191, 206 In Hipp. Epid. VI (ed. Kühn) I (17A.793) 206 (17A.822) 149 II (17A.993) 206 In Hipp. Fract. (ed. Kühn) 18B.548 154 In Hipp. Nat. hom. (ed. Kühn) 15.9 149 15.68 115 15.136 115 15.188 150 In Hipp. Off. med. (ed. Kühn) III (18B.783) 211 (18B.784) 211 In Hipp. Prog. (ed. Kühn) 18B.17f. 191 In Hipp. Prorrh. I (ed. Kühn) 16.532 149 Lib. prop. (ed. Boudon-Millot) 4.38 (154.1–2) 137 20.1 (173) 139, 178 Lib. prop. (ed. Kühn) 19.20 120 19.28 149 19.30 149 19.31 149 19.32 149 19.33 149 19.37 149 19.41 149 Loc. aff. (ed. Kühn) 8.7 173 8.9 173 8.20 173 8.39 173 8.48 173 8.63 173 8.81 447 8.84 173 8.88–89 459 8.131 173 8.133 173 8.141 173 8.182 173 8.190 173 8.222 173 8.223 173 8.284 173

8.295 173 8.308 173 8.356 173 8.364 173 8.365 173 Meth. med. (ed. Kühn) I (10.15) 150 VIII (10.531) 150 IX 8 (10.632.1–4) 423 (10.632.12–633.13) 424 Ord. lib. prop. (ed. Kühn) 2.6 (19.55) 137 Plac. Hipp. Plat. (ed. De Lacy) I 8 (92.25–26) 154 II 2.5 179 5.94–95 185 III 2.18 188 3.2 188 8 186 8.13 (226.12) 186 8.28 186 8.29–32 186 8.33 187 8.34 187 8.35.10 187 8.38 187 IV 6.10 187 6.18–38 187 6.19 188 6.20–27 188 V 7.42–43 179 Plen. (ed. Kühn) 7.552 150 Praecogn. (ed. Nutton) 5.21 (100.2ff.) 420 Protr. (ed. Barigazzi) 3 177 9 177, 180 (130.25–26) 178 (130.25–27) 180 (132.2–6) 180 (132.8–12) 180 (132.12–14) 181 (132.18) 181 (132.22) 181 (133) 181 10 184 (134.7–8) 181 (134.9–10) 182 (134.18–26) 182 (136.1–8) 182

Index Locorum

(136.8–19) 182 184 (144.4–5) 184 14 177 (146.15–16) 184 (146.17–148.9) 184 (148.10) 184 14.4 177 14.5 177 San. tu. (ed. Kühn) 6.372 150 Simpl. med. (ed. Kühn) 11.379 150 Temp. (ed. Helmreich) 1.1–10 151 1.6 155 1.7–10 159, 169 2.4 167 2.5ff. 151 2.22ff. 151 4.9 169 4.23 150 5.20ff. 151 7.3–5 151 7.24–28 152 7.25 169 7.27–28 159 8.10 169 9.1 158 9.1–26 152 9.16 158 9.26–10.3 156 9.27–28 152 10.1–5 152 10.4–7 159 11.24–12.1 160 12.6 155 12.12 155 13.20–22 159 13.26ff. 152 14.7 169 14.10–12 161 14.24–25 161 15.1ff. 152 16.4–5 160 16.24–17.21 153, 157 17.4 155 17.10 155 17.11 155 17.22 153 17.22–23 159 17.22–25 159 13

20.8–21.9 150 27.10–16 166 27.22 167 28.20 155 28.22 155 29.8–9 163 31.3–5 160 31.27–29 172 31.28–32.4 153 32.8–10 165 33.13–16 162 34.3–4 165 34.5–19 170 34.6–7 157 34.24–25 154 36.3–6 156 36.8–37.8 153 36.16–17 157 36.19 169 37.21–25 162 37.23–25 165 37.25 159 39.10 159 40.3 151 40.11 151 41.17–19 163 43.12–16 167 44.11 163 44.12 163 46.10 156 46.26 169 49.23 169 50.17–19 160 52.12–53.18 164 54.17–55.10 161 55.2 163 55.6 163 55.8 163 55.26–29 160 57.11 158 58.11 163 58.16 163 58.17 163 60.12–13 160 61.6–9 165 61.27–62.5 166 61.28 156 62.6–8 162 63.3 158 64.7 158

493

494

Index Locorum

65.19–29 162 66.27–67.5 163 69.19 158 70.5–7 170 71.12–13 165 72.19 156 72.24 156 75.3 156 75.12–13 165 75.22 158 76.11–13 160 77.13 165, 169 79.18–80.6 157 82.11 155 82.11–12 160 84.18 159 84.18–20 167 85.8–18 168 86.5 151 86.6 151 87.10 163 87.17–29 164 87.21 163 88.15–16 158 88.20–21 152 89.15–21 162 90.3–13 163 90.29–91.1 159 93.3–4 170 94.5–8 170 95.26–96.13 170 97.14–98.12 171 98.23–24 156 99.8–9 158 99.13–16 165 100.2 158 102.13 169 102.15–16 156 103.5–8 171 103.6–14 158 103.14–17 172 106.13 166 106.22–24 172 106.27–30 172 107.13–14 172 107.18 165 107.18–19 163 107.21–23 172 108.24–109.1 165 109.26–27 154

111.5–7 163 113.27–114.2 163 114.27–29 159 Temp. (ed. Kühn) 1.544 150 1.571 150 Περὶ ἀλυπίας (ed. Boudon-Millot) 20– 29 178 Gellius Noct. Att. praef. 4 89 4–10 89 5 89 10 89 25 92 XVII 17.2 100 Geminus Introd. astron. 1 325 1.22 318 1.40 318–319 2 321 2.1 322 2.4–6 322 2.5 322 2.8 323 2.8–11 325 2.9–11 323 2.13–14 323 5.14–15 319 5.17 319 5.24 319 6.5 318–319 6.11–12 324 7.8 324 8 325 8.4 318 8.29 318 8.29–30 319 8.30 318 8.38 318 8.38–39 319 8.39 318 8.47 318–319 9–11 325 12.14–19 321 16.19 318 16.19–20 319 16.20 318 16.21–23 321 16.21–24 324 16.22 324

Index Locorum

16.23 324 16.29 321 16.32 319 17 316, 321, 323–324 17.1 324 17.2 323 17.5 318–319 17.6 323 17.9 323 17.15 321 17.16 324 17.17 319 17.18 318 17.18–23 324 17.21 323 17.23 323 17.25 324 17.26–45 325 17.27–29 325 17.30–31 325 17.32–35 321, 325 17.33 321 17.36 325 17.37–44 325 17.46 319, 325 17.46–49 325 17.48 319 18 325 18.7 318–319 18.9 322 Gilgamesh epic XI 86 413 Gorgias Hel. 6 204 8–14 204 11.6 386, 394 12 204 Pal. 11a6 397 11a25 395 Hecataeus Abd. (FGrHist 254, ed. Jacoby) fr. 6 19 Hecataeus Mil. (FGrHist 1, ed. Jacoby) fr. 1 21 Heraclitus (22 Diels-Kranz) B 101 461 B 123 437 Heraclitus Alleg. 72.4 465 Hermogenes Stat. 3.110 204

73.16–74.4 204 74.1–4 204 Hero Alex. Autom. (ed. Schmidt) 1.1 (338.3– 6) 291 Belop. (ed. Wescher) 73.6–11 419 75 46 81–83 47 84–86 46 86–90 46 112–113 48 Def. (ed. Heiberg) 137.1.1 381 137.3 381 138.11.1 373 138.11.3 373 Pneum. (ed. Schmidt) I 16 292 I 16.90 292 I 16.90–92 294 I 16.92–96 295 Herodotus I 65.3 181 153 24 197 450 207 374 II 41.3 19 86 115 109 368 III 80–82 23 86.2 124 131–137 19 V 62 115 78 23 VII 10a.1 23 Hippias (86 Diels-Kranz) B 4 420 B 6 419 Homer Il. I 1 197 1–5 200, 202, 385 12ff. 194 366ff. 194 II 119 208 484 442 494–759 267 761–762 441 III 323 208 IV 539–542 441 IX 507 209 570 212

495

496

Index Locorum

XI 218–220 441 515 434 XIV 508–510 441 XV 298–299 211 XVI 787 442 XIX 86ff. 209 94 209 95 209 XXI 328ff. 209 362f. 209 XXIV 339–469 436 601–612 392 601–618 393 Od. I1

441 1–10 385 5 17 6–10 357 VI 201 208 VIII 491 441 X 232–243 440 281–286 436 303 436 305–306 436 329 437 330 437 XI 171–203 391, 398 368 441 XII 127ff. 357 XIII 439 437 XVI 437 208 XVII 382–385 434 Schol. Hom. A 1 (AT) 197 A 1b, bT 198 A 1c, AbT 198 A 1d (AT) 198 A 1e (1 and 2, bT) 198 A 1f, bT 198 A 1g–i (AT) 198 A 366a bT 194 B 865 (A) 205, 210 E 329a (A) 205, 211 O 299 (T) 211 T 94a (A) 205, 209 Ξ 221a (Α) 205, 208 Ξ 221b (bT) 208 Ξ 437a (A) 205, 211 Φ 363e (Gc) 209

Horace Epist. II 1.156–157 19 Hypsicles see Euclid Elem. XIV Iamblichus In Nicom. 100.23 373 Inscriptions ATL III 13–18 263 Inscriptiones Delicae 1442 B.42 245 1443 B II.109 245 Inscriptiones Graecae I2 374.248 115 I3 32 261 34 263 52 255, 261 52.13–15 260 64 255 68 263 71 255, 269 71.45–50 260 73 255 77 255 100 255 101 255 130 255 248 269 259 269 259.2 261 259–290 255 260 269 260.1 261 261.1 261 263 269 264 269 296–299 255 377 261 383 271 397–400 255 421–430 255 433 255 435 255 436–451 255 455–458 255 460–470 255 472 255 474–478 255 1144 267 1146 267 1147 267 1149 267 1150 267

Index Locorum

1162 267 1180 267 1184 267 1186 267 1190 267 II2 120 259 212 259 847 262 1667.95 115 1675.23 115 XI(2) 161 A 43 115 161 A 75 115 203 B 95 115 SIG3 239 256 Isagoga in Aratum (ed. Maass) 329.19 283 Isocrates or. 4.32 50 40 50 40.2 204 41–43 24 or. 8.1 205 or. 9.10 385 or. 11.4 205 or. 13.21 265 or. 15.254 375 Josephus Contra Ap. I 3.15–5.27 21 8.42 21 II 13.135 21 19.181 21 20.182–183 21 31.225–231 21 36.259–261 21 Lactantius Div. inst. V 14.3–5 20 Liu Hui Commentary on The Nine Chapters (ed. Chemla-Guo Shuchun) 66–79 Livy II 32 44 XXV 1.9–11 19 Lucian Hist. conscr. 47 103 Var. hist. II 20 200 Lucretius V 332–336 50 332–337 414 1107 414 1241–1378 51 1452–1453 51 1457 414 VI 1179 432

Lysias (ed. Carey) or. 1.92.4 385 95.34 393 95.37–42 386 fr. 101a.10 124 Manuscripts Bibl. Nat. Cod. supp. gr. 1294 233 Cod. Laurentianus 74.7 114 Marcellinus Vita Thuc. 54 248 Michael Eph. (Comm. Arist. Graec. 22.2) 125.14–126.25 119 130.8–26 119 Moschion (Trag. Graec. Frag. 97) fr. 6 50 Nicomachus Ger. Ar. I 13 357 I 16 37 The Nine Chapters (ed. Chemla-Guo Shuchun) 74–75, 371 Oppian Hal. I 212 134 Pappus Coll. (ed. Hultsch) III praef. (30.17–22) 247 (34.1–2) 247 (34.1–8) 247 IV (250.33) 373 V praef. 1–3 348 VII (650.14–20) 381 (672.12–674.19) 373 32 (676.25ff.) 416 Papyri Johnson Papyrus 240 P. Cair. Zen. 445.9 115 665.2 115 P. Colon. 179 234 P. Edwin Smith Case 1 42 Case 2 42 Case 3 (col. 1r, line 18) 42 Case 4 43 (col. 2r, line 2) 42 (col. 2r, line 8) 43 Case 5 42 (col. 2r, line 11) 42 Case 6 42 (col. 2r, line 18) 42 (col. 2r, line 23) 43 (col. 2r, line 23–24) 42 Case 7 42 (col. 3r, line 2) 42 (col. 3r, lines 7–8) 43 (col. 3r, lines 9–10) 45 (col. 3r, line 15) 43

497

498

Index Locorum

Case 7b 43 Case 8 42 (col. 4r, line 5) 42 (col. 4r, lines 6–7) 45 (col. 4r, lines 7–9) 45 Case 9 (col. 4r, line 19) 42 Case 10 42 Case 13 42 Case 15 42 Case 16 42 Case 17 42 Case 18 42 Case 18 (col. 7r, line 9) 42 Case 19 (col. 7r, lines 14–15) 42 (col. 7r, line 17) 42 Case 20 42–43 (col. 7r, line 23) 42 (col. 8r, line 3) 42 Case 21 (col. 8r, lines 6–7) 42 Case 22 42 (col. 8r, line 9) 42 Case 38 42 P. Herc. 154 247 1042 247 1044 (col. 25 lines 4–8) 244 P. Hibeh 1.27 302 P. Oxy. 1235 230 2331 233 2547 457 2652–2653 234 2891 232 3001 234 P. Parisinus gr. 1 301, 303 P. Rhind probl. 26 369 P. Soc. Ital. 485 115 847 234 1368 233 P. Tebt. 679 240 P. Turin 55001 233 Parmenides (28 Diels-Kranz) B 1 442 B 8 444 Philo Alex. De aet. mundi 76.1–84.5 322 Philo Byz. Belop. (ed. Diels-Schramm) 51.11–22 310 59.34–45 310

Belop. (ed. Thévenot) 49.13–50.6 415 50–51 48 50.24–26 415 56 48 56–67 48 67–73 48 73–77 48 77–78 48 Pneum. 18–21 285 Philoponus In Arist. An. post. (Comm. Arist. Graec. 13.3) 112.8 373 149.10 373 In Arist. Phys. (Comm. Arist. Graec. 16) 31.3 374 Photius Bibl. 244 (380a) 19 Schol. Pind. I 1.15b 210 Plato Alc. 1 131a5–7 461 Charm. 164a9–c2 461 Crat. 436cd 203 Crit. 47d6–48a4 464 Euthyd. 305c–307c 265 Gorg. 456b1–5 458 520d9–11 265 Hipp. mai. 281d3–7 414 Leg. III, 677cd 413 701c 204 IV, 705ab 24 720d1-e2 458 IX, 857d2–4 458 XII, 949e-950a 24 Men. 70a 265 82a–85d 335 86c–d 265 89c-90b 265 91b 265 93a–94e 265 96d 265 99e–100b 265 Phaed. 78c3–8 124 Phaedr. 229d3–e4 187 266b 386 266c 384

Index Locorum

274c–275e 256 275e 192, 205 366d 384 Pol. 288e5 124 Prot. 319e–320b 265 320c8–323a4 50 339a3ff. 206 339a–347b 178 339e1f. 206 340a 207 340a1 206 340a7 207 347c3 178 347e5 178 Res publ. I, 341b 204 III, 403d8–e2 463 407b8–c6 463 408d10–e2 447 408e2–4 459 IV, 433a-434c 25 VI, 500e 115 X, 607b–c 178 Soph. 219c2–7 324 241d 203 Theaet. 147c7–d7 243 147d2 373 203–205 35 205c7 124 Tim. 28c 115 88c 374 88c1 324 Plato (Trag. Graec. Frag. 46) fr. 1–3 Ps.-Plato Amat. 132a1–b3 243 Pliny the Elder Nat. hist. praef. 93 1 86, 129 3 90 5 90 11 90 12–13 89 14 130 14–15 86 17 85, 131 17–18 85 20 92

230

21–23 87, 90 24 88 26–27 89 28 92 33 91 II 1–101 93 51–55 93 53 94 54 94 62 94 71 fin. 95 72–76 95 89 90 102–153 93 117 95 118 95 154–211 93 191 94 192 94 212–234 93 235–241 93 VII 35 103 36 fin. 103 76 103 83 103 88 100 113 19 VIII 1–3 112 1–34 112 IX 79 134 X 68 133 73 134 120 134 XIV 3 96 4 96 4–6 96 20 97 XVI 67 134 XVII 137 132 XVIII 22 101 159 133 317 421 XXI 2 101 50 133 52 133 XXII 14 97 15 97 147 133 XXIV 29 133 90 133

499

500

Index Locorum

91 133 130 133 XXV 1–2 99 4 100–101 4–15 100 5 100 5–7 100 6 100 7 100 8 101, 114 8–15 101 9 102 16 99 18 102 27 102 116 102 XXVI 2 133 100 133 XXVIII 22 133 XXIX 1 131 14 19 XXX 49 133 94 134 117 133 XXXII 1–6 134 140 133 154 133 XXXIV 65 133 XXXV 2.11 237 XXXVII 205 87 Pliny the Younger Epist. III 5.10 105 5.7 90 Plutarch Glor. Ath. 346f 238 Vita Arist. 4.2–5 264 24.2 264 24.4 264 Vita dec. orat. 832b-852e Vita Num. 12.4.1 204 Polyaenus Strat. 2.38.2 47 Polybius I 5.5 305 III 58–59 98 59.3–5 99 59.6–8 99 IX 12.1–20.10 302 14.5 303 14.6–19.4 303

373

fr. 2.5 50 X fr. 47.12 50 X frr. 43–47 50 XI fr. 12.4 47 XXXVI fr. 13.3 50 Porphyry Vita Plot. 14.10–14 352 Proclus In Eucl. (ed. Friedlein) 64.18 368 65.11–68.7 416 65.15–21 373 65.15–67.2 373 65.21 373 65.7 371 66.2–67.1 373 66.8 383 67.2 373 67.20–23 416 68–70 352 72.24 373 77.7 381 77.7–81.2 344 78.9 373 79.20–26 381 81.5 381 81–84 351 83.1 358 203 347 203.1–15 344 203.1–210.6 344 203.12–13 345 203.17 388 203–204.23 379 204 347 208–210 345 210 347, 351 210.19 351 210.616 381 211.21 373 211–213 344 233.112 381 241–244 348 250.20–251.19 425 255–266 344 272.7 373 283.7 373 352 371 356.11 373 375.9 351 426 373 426.6–10 373

Index Locorum

Procopius Bell. VIII 11.28 51 Protagoras (80 Diels-Kranz) A 1.55 50 Ptolemy Alm. I 5 114 I 1 335 Geogr. I 2.2 114 3.3 114 VII 5–7 114 VIII 1–28 114 Quintilian Inst. I 1.12–14 134 IV 2.31 385 XI 2.50 100 De rebus bell. prol. 4 51 Rhet. Her. I 1 19 Rufus Eph. Onom. 101–102 122 Sappho (ed. Lobel-Page) fr. 31 442 Scribonius Largus Comp. (ed. Sconocchia) praef. 15 (6–16) 92 Seneca Ep. mor. 88 322 88.40 200 Nat. quaest. VII 25.4–5 51 30.5–6 98 31.1–32.4 97 32.4 98 Sextus Empiricus Adv. math. I 131–140 201 133 201 VIII 80–82 201 IX 350–351 201 Simplicius In Arist. Cat. (Comm. Arist. Graec. 8) 21.1–28.11 201 In Arist. Phys. (Comm. Arist. Graec. 9) 53.28–69.34 383 290.1–5 352 453–455 35 Sophocles Ant. 332–375 50 Phil. 563 204 Stobaeus Anth. I 8.2 49 Ecl. I 41.60 465 Strabo Geogr. I 1.21 303

II 3.8 322 VI 2.1 357 XII 8.11 310 XIII 1.54 (608 f.) 426 XIV 2.5 310 XVI 1.6 307 2.24 322 Suetonius Vesp. 18–19 90 Testamentum Novum 1 Cor 1.20–22 20 9.20–21 20 2 Cor 11.22 20 Acts 17.21 20 Col 2.8 20 Eph 4.14 20 Gal 1.13–14 20 Phil 3.4–7 20 Rom 2.28–29 20 11.1 20 Testamentum Vetus 1 Macc 12.5–23 21 14.16–23 21 Sir 19.20 20 28.9 20 Themistius In Arist. An. post. (Comm. Arist. Graec. 5.1) 19.11 373 Theo Math. Plat. 201.25 373 Theophrastus Hist. plant. I 1.1 103 14.4 103 III 12.4 103 Thucydides I 4–18 50 6 21, 23 18.1 21 20–23 103 22.1–3 103 22.2 103 70 21, 23 71.3 414 102.3 23 II 13 274 15 274 37.1–2 21 37.2–3 23 38.2 24 40.2 21, 23 41.1 21 47 431 48 432

501

502

Index Locorum

III 37.2–4 23 37–48 23 38.5 21 38.7 21 42.1–2 23 V 18.5 264 26.5 103 VI 2.2 357 9.3 21 18.3 21 18.6–7 21 35–40 23 87.3 21 VIII 96 21 96.5 21 Tragicus anonymus (Trag. Graec. Frag. 2) fr. 166 354 Valerius Soranus Epopt. (ed. Morel-BüchnerBlänsdorf) fr. 2 91 Vergil Aen. VI 847–850 20 851–853 20 Georg. III 548–550 432 Vitruvius Arch. I praef. 1–3 310 praef. 2 310 praef. 18 310 1.1–2 311 1.3 311 1.4–10 312 1.7 312 1.8 310 1.10 312–313, 316 1.11 312 1.12 312 1.12–16 312 1.16 312 1.18 310, 312 6.1 316 II 1 51 1.2 51 1.6 51 VII praef. 310 IX praef. 1–2 313

praef. 3–4 313 praef. 5 313 praef. 6–8 313 praef. 9–12 313 praef. 13–14 313 praef. 14 315 praef. 15–17 313 praef. 18 313 1.1 313–314 1.2 314 1.3 314 1.5 314 1.5–10 314 1.6–7 314 1.14–15 314 1.16 314 2 314 3 314 4 314 5 314 6.1 314 6.2 314, 316–317 6.3 315–317 6.11–13 317 7 315 7.7 316–317 8.1 316 8.8–15 316 X 10–11 310 XIX 1.11–13 314 Xenophanes (21 Diels-Kranz) B 11 22 B 12 22 B 14 22 B 16 22 B 18 49, 414 B 23 22 B 28 34 Xenophon Apol. 29–31 265 Cyrup. IV 3.20 124 Mem. I 3.7 465 Ps.-Xenophon Ath. Pol. 2.7–8 21, 24 Zeno Eleat. (29 Diels-Kranz) A 25–26 34