Plato's Method of Hypothesis in the Middle Dialogues 389665733X, 9783896657336

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Samuel Scolnicov taught at the Hebrew University of Jerusalem from 1974, rising to full Professor in 2005, and becoming Professor Emeritus in 2010. He held visiting positions around the globe. He was a founding member of the International Plato Society, of which he served as President (1998-2001). He specialized in Plato, and his works on Platonic subjects include: Plato’s Parmenides, Introduction, translation and commentary; Plato’s Philosophy of Education; and Euthydemus: Ethics and Language. He also published works on philosophy in several other languages, and edited, among other collections, New Images of Plato and From Theory into Practice: Plato’s Laws. He passed away in 2014, still planning further publications on Platonic philosophy. Harold Tarant taught at the University of Sydney from 1973 to 1993, after which he was Professor of Classics at the University of Newcastle Australia until 2011, but still has honorary positions at both universities. He was a member of the Executive of the International Plato Society (1995-2001). He has published and co-edited several books relating to Plato, most recently Proclus: Commentary on Plato’s Timaeus vol. VI and Brill’s Companion to the Reception of Plato in Antiquity.

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Samuel Scolnicov · Plato‘s Method of Hypothesis in the Middle Dialogues

The second decade of the twenty-first century has seen a revival of interest in Plato’s investigative methods in those dialogues where he appears to build substantially on foundations inherited from Socrates. Such works as the Phaedo and Republic have always in modern times been seen as ‘core Plato’, and the Meno has always had a claim to be considered alongside them, principally because of some rather obvious points in common with the Phaedo. The essential core of this ‘core Plato’, its methods and its metaphysics, had for over three decades become less fashionable, as new horizons opened up, than they were when Scolnicov and Tarrant learned their craft, and when Plato was treated as a thinker with a ‘system’, even if it changed later in his creative life. Scolnicov’s PhD thesis presents in a firm but lively way issues now being studied more intensely again. He remained committed to it, and built upon its foundations in such a way that it became seminal for his understanding of Plato. Many of its theses have found wider acceptance subsequently. Plato is not tailored to fit more comfortably with modern philosophical preconceptions, but is seen as one who made serious advances without these being steps towards Aristotle or ourselves. And the core of Plato’s philosophy, which some retreat from as if it were too ‘religious’, is linked here with a method of investigation that owed much to mathematics.

Plato‘s Method of Hypothesis in the Middle Dialogues Samuel Scolnicov

Edited by Harold Tarrant

Academia

Samuel Scolnicov Plato’s Method of Hypothesis in the Middle Dialogues

Plato’s Method of Hypothesis in the Middle Dialogues by Samuel Scolnicov

Edited and with an Introduction by Harold Tarrant

Academia Verlag

Baden-Baden

Cover design: by Bracha El-Hassid Grumer, based on the design of the Golden Section as principle of the harmonic rectangle.

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1. Auflage 2018 © Academia Verlag, ein Verlag in der Nomos-Verlagsgesellschaft mbH & Co. KG, Baden-Baden 2018 (räumlich, zeitlich und inhaltlich unbeschränkte, ausschließliche Nutzungsrechte). Internet: www.academia-verlag.de E-Mail: [email protected] Printed in Germany Alle Rechte vorbehalten Ohne schriftliche Genehmigung des Verlages ist es nicht gestattet, das Werk unter Verwendung mechanischer, elektronischer und anderer Systeme in irgendeiner Weise zu verarbeiten und zu verbreiten. Insbesondere vorbehalten sind die Rechte der Vervielfältigung – auch von Teilen des Werkes – auf fotomechanischem oder ähnlichem Wege, der tontechnischen Wiedergabe, des Vortrags, der Funk- und Fernsehsendung, der Speicherung in Datenverarbeitungsanlagen, der Übersetzung und der literarischen und anderweitigen Bearbeitung.

Table of Contents

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Table of Contents Foreword (Hanna Scolnicov) .................................................... Editor’s Introduction (Harold Tarrant) ...................................... Acknowledgements ...................................................................

7 10 38

Introduction ............................................................................... 1 Greek Geometrical Analysis ............................................... 2 The Meno ............................................................................ 3 Disagreement and Agreement ............................................. 4 The Phaedo ......................................................................... 5 The Republic ....................................................................... 6 Knowledge and Opinion ..................................................... 7 The Divided Line ................................................................ 8 The Objects of Mathematics ............................................... 9 Plato’s Method of Hypothesis ............................................. Appendix 1: Being and Truth .................................................... Appendix 2: The Upward Path .................................................. Bibliography ..............................................................................

39 45 67 85 96 120 150 163 197 206 213 222 224

List of the publications of Samuel Scolnicov ............................ 238 Index .......................................................................................... 250

Foreword

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Foreword Hanna Scolnicov This volume presents the Cambridge doctoral dissertation by Samuel Scolnicov, submitted as a graduate student of King’s College. The original title page gives the submission date of September 1973, and the degree was awarded the following year. It is presented here under the same title and with light editing only, but with footnotes and index for greater convenience, and with an additional Introduction by the Editor. Samuel maintained that the doctoral thesis is a work in which the young scholar develops his vision of the field he is exploring, expounds his new ideas, and maps out the directions he will pursue in the future. For the rest of his career, he will follow those venues he has adumbrated, follow his own road map. In this sense, publishing Samuel's unpublished thesis offers a broad perspective into which one can fit his numerous publications. He received his Ph.D. in Classics from the University of Cambridge (1974). In Cambridge, he had the best of supervisors: from Dr. Peck and Prof. Keith Guthrie (not an official supervisor, but a generous and meticulous reader), to Prof. Bernard Williams and Prof. Geoffrey Lloyd. He held them all in high esteem and benefitted from each of them in different ways. His Cambridge experience was total: he absorbed the English culture with great love and respect: the architecture of King's College Chapel (John Saltmarsh was his guide, as was Nikolaus Pevsner's book on Cambridgeshire) and the different colleges (he loved to guide friends who visited us in Cambridge around the old houses); punting on the river, at which he was very good; concerts (especially in King's College Chapel), theatre (we went to as many student performances as possible, in addition to our frequent outings to London); children's education (he was interested in this professionally, as well as personally, for our then

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toddler daughter). The two years in which he completed his doctorate (this was the short term of his British Council Fellowship) were truly formative years. He arrived in Cambridge with only a basic knowledge of English. But within those two years mastered the language, as can be witnessed by reading this thesis. He was born and raised in Brazil, so that his mother-tongue was Portuguese. There, he attended a Jewish school, where he acquired Hebrew and some Yiddish. When he emigrated to Israel at the age of seventeen, within a short time he was proficient enough to teach Hebrew language and literature at a leading high-school in Jerusalem. The foreign language he studied at school in Rio de Janeiro was French. English was hardly taught there, but he had taken part in the World Scouts Jamboree in 1957, in the UK, and had already then, as a teenager, fallen in love with the culture and landscape. His command of English was due to his genius for languages. Later in life, he both published and lectured in Hebrew, English, Portuguese, Spanish, French and Italian. To these must be added his knowledge of ancient Greek and Latin, and his passive knowledge of German and Dutch. His linguistic skills were put to good use in his various translations of poetry and prose, notably the pre-Socratic philosophers (into Hebrew), and culminated in his translation of Plato's Parmenides into English (University of California Press, Berkeley, 2003). Samuel's professional interests ranged from Greek philosophy to philosophy of education, philosophy of science, philosophy of language, Jewish philosophy and ethics. He saw himself as a latter-day humanist and philologist, devoted to the spreading of ideas and culture and, especially, to the teaching of children and young people. He was an enthusiastic and charismatic teacher, Socratic and ironic in his approach, and the students loved his lectures. He taught Greek philosophy and philosophy of Education at The Hebrew University of Jerusalem. At different periods, he was a visiting professor or fellow at Harvard, the Sorbonne, Dartmouth College, Catania, Cagliari (Sardinia), Sydney, Mexico City, Irvine, Toronto, and other universities that I can no longer recall. He was a fellow at the National Humanities Center in North Carolina and at the Bogliasco Foundation

Foreword

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(Italy) and was an invited lecturer in countless universities around the world. He was a founding member of the International Plato Society, and its President, from 1998 to 2001. I wish to thank Samuel's long-time colleague and friend, Prof. Harold Tarrant, who undertook to edit this book, believing in what was a young scholar's doctoral thesis. I am greatly indebted to another of Samuel's friends, Dr. Jürgen Richarz, director of the Academia Verlag, who, against all odds, decided to publish this volume. For both, this was a labour of love. Samuel would not have wished for a marble monument to commemorate him, but would have been immensely grateful for the posthumous publication of the first fruits of his scholarly journey.

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Editor’s Introduction Drama and Doctrine When conversing about Plato Samuel Scolnicov (1941–2014) not infrequently mentioned his doctoral thesis, and I suspect that I asked him more than once what the topic was. From his earlier essays on he had referred to it, and he published articles devoted to the hypothetical method in Kant-Studien and Methexis.1 He still remained committed to its principal claims in his treatment of Republic v-vii;2 and his book on the Parmenides, which was a natural dialogue to tackle as a sequel to the present work, reiterates many of its findings.3 However, he nowhere returned to these issues with the same thoroughness and scholarly acumen that is demonstrated in the present pages. When I finally read the thesis in Cambridge University Library I felt that here was the key to much else that he had published on Plato, a work that already showed his fundamental commitment to Plato – to a Plato that was importantly different from Aristotle, not just Aristotle’s more problematic precursor. The commitment to Plato led also to the commitment to allowing the dialogues, to the extent that they were willing and able, to speak on Plato’s behalf. While some passages may indeed have been enigmatic, others were conceived of as speaking much more directly to the reader, and Plato did not require the reader to read between the lines at the expense of reading the lines themselves. Since the thesis was written there has been considerable debate, sparked by an increasing awareness of the dramatic aspects of a Platonic dialogue and by the need to take an integrated view of each one, over the extent to which any character in a Platonic dialogue should be seen as communicating Plato’s own contribution directly to the reader (the

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Scolnicov (1975) and (1992). Scolnicov (1988), 88-97, where note 24 refers both to the thesis and to Scolnicov (1975). 3 Scolnicov (2003), 9-12; ‘hypotheses’ are central to Parmenides part II. 2

Editor’s Introduction

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so-called ‘mouthpiece-theory’).4 Most scholars, however, would still accept that Plato allows his principal speakers to communicate at least some of his recent advances (real or imagined) in at least some parts of the corpus. While Scolnicov would naturally have assumed that the dialogues he deals with are such that the Platonic ‘Socrates’ often does communicate Plato’s supposed discoveries, not only by his words but also by his confirmatory conduct,5 his principal concerns are with Plato’s methods of argument, and such metaphysical and epistemological theory as accompany them. While Plato may perhaps have held metaphysical theses to which no speaker in dialogues written at that period gives voice, it is highly unlikely that he will not have allowed his ‘Socrates’ all the dialectical weapons that he himself most cherished. Hence I believe that Scolnicov was entirely correct in treating the Platonic methods of any given period as something that could, with appropriate care, be deduced from the dialogues of that period, and usually from the words of the principal speaker6 as he explains the methods being applied. And one thing is certain: for the ‘Socrates’ who takes the protagonist’s role in each of the three dialogues tackled here methods mattered very much. The dramatic situations in each case and a personal involvement with the topics themselves endow the words of Socrates with some authority. Periods of Composition and Developmentalism As will be observed, Scolnicov’s title implies a three-fold division of Plato’s dialogues into early, middle and late. It is now generally recognized that the dialogues of the latest period can be identified from two notable stylistic shifts: (1) the avoidance where possible of hiatus, i.e. of placing words so that one ending with a vowel immediately precedes

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See in particular the collection of papers in Press (2000). Note the following words from Scolnicov (2017), 17: ‘In Phaedo Socrates’ death gives significance to all that is said. ... the proofs of immortality derive all their validity from Socrates’ behaviour …’. 6 Even so, note the words that begin the opening lecture of his book on Euthydemus (2013), 17: ‘Dialogue is drama. In every platonic dialogue, as in every drama, it is of maximal importance who speaks. … All that is said is said by someone to someone in a definite situation, and great part of the significance of what is said depends on who says what, to whom and when.’ 5

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one beginning with a vowel; (2) a shift away from certain kinds of clausulae, i.e. of certain kinds of rhythmic patterns at the ends of sentences involving the lengths of the final five syllables. The stylistic shift is so obvious that it has to stem from a deliberate decision. There are just six dialogues of largely undisputed authenticity that conform to these requirements: Sophist, Statesman, Timaeus, Critias,7 Philebus and Laws (in twelve books),8 but their total length accounts for a considerable part of the corpus. Two dialogues that do not conform to these stylistic features were then also presumed to be ‘late’, the Parmenides and Theaetetus, principally because they seem to be rethinking the metaphysical and epistemological theory of the Republic, theory that would not reappear in an unproblematic way in the other six late dialogues.9 Scolnicov’s own treatment of Parmenides does not see that dialogue as causing the abandonment of the theory of transcendent forms as some have supposed, but sees it simultaneously solving the difficulties of postulating forms and preparing the way for the Sophist’s notion that one must postulate both being ‘in itself’ and being ‘in relation to something’.10 Importantly, the method of hypothesis was seen as crucial background to the hypotheses examined in Part II of the Parmenides,11

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7 Rashed and Auffret (2017) have recently argued that the extant Critias is spurious, but on the basis of what they conceded to be only one substantial argument, involving an alleged anomaly between the Timaeus and Critias. Yet there is a widespread consensus that the styles of the Timaeus and Critias are virtually inseparable, whether ‘style’ is assessed on the basis of conventional philological comparisons or on the basis of computer-harvested data and analysis. Furthermore, Tulli (2013: 273), in dealing with the different accounts of the transmission of the Atlantis-story in the two dialogues, shows that such anomalies are common enough in Plato. The weakness of the case against authenticity when compared with the strength of the stylistic case for it means that few will give credence to the dissenting voice of Rashed and Auffret. 8 The authenticity of the Epinomis, which is admittedly similar stylistically to Laws, is regularly questioned on a variety of grounds and also on the strength of ancient reports that it is the work of Philip of Opus, Plato’s ‘promulgator’ (epigrapheus), who was also responsible for the final arrangement of Laws. Laws itself, however, was never treated as anything but Plato’s project. A similar style is also detectable in the Seventh Epistle, whose authenticity also remains a matter of debate. That, however, was not a dialogue. 9 I myself have very real doubts about whether the Republic was completed before these dialogues were begun, since I suspect that dialogues usually evolved, but as a convenient hypothesis it makes sense to place them both at this time. 10 See Scolnicov (2003), especially 8-9, 25-29, and 39. 11 Scolnicov (2003), 9-12, where a summary of his earlier research on the theory of hypothesis is presented; also 27, where we read: ‘Rather, Parmenides now [in part II of the Parmenides] raises the inquiry to a higher stage of generality (a “higher hypothesis”, in the terminology

Editor’s Introduction

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contributing to the solution of the Eleatic challenge and thereby preparing the path forward to the Sophist. No reliable stylistic criterion has ever been advanced for the separation of a distinct group of early dialogues, but ‘early’ for many scholars, particularly those influenced by Gregory Vlastos, has tended to mean ‘Socratic’, so that the principal criterion has been the rather awkward criterion of Socraticity, especially in the employment of the Socratic elenchus.12 On Vlastos’ view (1991: 47) the Meno is ‘early’, but nevertheless ‘transitional’, so that already he feels there is movement away from the earliest dialogues and towards the theories of a middle period that owe more to mathematics,13 becoming more ‘Platonic’ and metaphysical, even while working to some extent in Socrates’ footsteps. So the key thing is that while Vlastos may hold the Meno to be early, he still sees it leading directly forward to what has been called the ‘middle period’. And given that talk of hypotheses comes well after the abandonment of the elenctic method at 80e and the introduction of geometrical material, even Vlastos should allow the Meno to be treated as ‘middle’ for the purpose of examining hypothetical method. Furthermore he confidently assigns both Phaedo and Republic ii-x to a middle period, and is one of those who also allow that the Parmenides and Theaetetus are middle. In fact Scolnicov’s assignment of Phaedo and Republic vi-vii to a Platonic ‘middle period’ should only be controversial for those who are sceptical about the possibility of any advances towards an approximate Platonic chronology. While Scolnicov worked within a general chronological framework that had become commonplace at that time, this should not be taken to mean that he adhered to a strongly developmentalist view of Plato. Certainly he thought that Plato developed as a philosopher (what great philosopher would not make advances?), but he did not want to postulate a series of major turning points. At least as far as method was concerned

-------------------------------------------of Phaedo 101d5 and Republic vi 511a6). On this level, forms and sensible things are alike considered “ones”.’ 12 See in particular Vlastos (1991): 47 for the assignment of all relevant dialogues to compositional periods. 13 See here Vlastos (1991), 115 n.41, on the Meno’s employment of both elenchus (up to 80e) and non-elenctic, not to mention mathematical, methods thereafter.

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he took a holistic view of the dialogues, taken as a coherent corpus,14 which allowed steady refinements rather than crises and major shifts. In such circumstances the minutiae of chronological order lose some but not all of their importance. Scolnicov’s subtlety comes out when he distinguishes, like many others, ‘Plato’s Socrates’ from ‘the platonic Socrates’. ‘Plato’s Socrates’ is rather like Vlastos’ Socrates of the ‘early’ dialogues, Socrates as Plato wanted to remember him; ‘the Platonic Socrates’ is more like Vlastos’ middle-period Socrates. But Scolnicov rightly affirms that traces of the former may be found in the so-called ‘middle’ dialogues, and traces of the ‘latter’ in those usually thought early. And ‘Euthydemus gives us a mix of both Socrates.’15 The date of Euthydemus is much disputed, but Scolnicov here differs from Vlastos in cautiously assigning it to ‘around the time of the composition of the Republic’ on the assumption that it is ‘parasitical’, taking for granted some familiarity with dialogues that had preceded.16 So Scolnicov takes chronology seriously, but adopts a rather cautious and nuanced attitude towards it; he also takes development seriously, but finds the overall corpus much more coherent than one might expect from a ‘developmentalist’. With this attitude towards the corpus Scolnicov presents an integrated account of hypothesis from the Meno through to the Republic. To offer such a solution required determination, and I remember this as being precisely the kind of challenge that UK graduate students interested in Platonic logic and metaphysics at that time would have relished. The challenge, it seemed, was not simply to find a single Platonic theory, but to argue the case for its having been important. The result needed to be illuminating, and Platonic dialectic of the ‘middle period’ needed to hold its own not just against Aristotelian science but also against Plato’s own ‘late’ dialogues. It needed to hold the attention of philosophers, or at least those of them who were prepared to give it a careful hearing.

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But individual dialogues always had for him a stronger right to be considered as coherent wholes, Scolnicov (2013), 14. 15 See Scolnicov (2013), 19. 16 See Scolnicov (2013), 14; he specifically states that some parodies make no sense unless written after the Meno. I have cited this because it seems to me to be particularly insightful. Vlastos (1991), 47, had viewed the Euthydemus as ‘early’ but ‘transitional’.

Editor’s Introduction

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Philosophic appeal, however, never entailed, in Scolnicov’s mind, the abandonment of the dramatic and dialogical features of Platonic compositions. This can be seen when, in chapter iv.5, he wrote as follows: The hypothetical method is by its very nature dialectical, or should we say ‘situational’. It starts from a given concrete situation and follows its unique course according to the actual responses of the persons involved. The level of the philosophical discussion at each stage of the dialogue, the meanders of the analysis, the scope of the ethical or metaphysical outlook are dictated by Socrates’ interlocutor.

Hypotheses in late antique Platonism The topic of Platonic ‘hypothesis’ is by no means new. The word itself suggests something placed underneath, an ‘underpinning’ perhaps, something set down so that it could be built upon.17 If Plato was to be represented as a systematic philosopher then his system had to have foundations underpinning it, and the foundations would need explanation. In late antiquity it was the upper levels of reality were the Platonists’ principal goal of inquiry, so that its foundations would indeed have to be at a lower level. Their function and status of such hypotheses would require articulation. Until the fifth century CE, however, the extant remains of Platonic interpretation are not sufficiently extensive for us to expect to know much that is relevant. It is from commentaries that we expect to learn most, but we do not know of any on the Meno, and extant parts of the anonymous Theaetetus-commentary that makes good use of that dialogue only employ the term in column LXIV (12-36) where it refers to the Heraclitean hypothesis that all things are in flux, an hypothesis that leads to the conclusion that every perception is peculiar to the individual who perceives it. Surprisingly one of Plutarch’s Platonic Questions that interprets the Divided Line of the Republic fails to talk of hypotheses at all. This means that the Didascalicus of Alcinous,

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17 Note Plato’s own suggestion at Rep. 511b4 (Slings = b5 Burnet) that true hypotheses will be somehow below what they are used to discover.

Samuel Scolnicov

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to which Scolnicov sometimes refers,18 is the only work from the early Roman Imperial period to say much about Plato’s hypotheses (5.157.3643, 7.162.10-12). Later commentators use the term a great deal, usually as an ordinary part of a philosopher’s vocabulary rather than in any special Platonist sense. Sometimes it is also used like prothesis indicating the undertaking of a particular dialogue or part of it: what it proposed to achieve or investigate. In the works of Proclus the term hypothesis occurs over seven hundred times. It occurs in a variety of senses even in the Commentary on the Republic, where it naturally features in Proclus’ treatment of the Divided Line and of the types of cognition that it postulates.19 Proclus did not leave us a commentary on the Phaedo though Damascius preserves the key piece of information that he interpreted the key phrase ‘something sufficient’ (in Phd. II 74) as the Good itself. Damascius himself takes a much more general view, identifying it with any agreed or self-evident premises and principles; he then goes on to analyse the relevant argument in terms of these hypotheses qua premises. It is fairly obvious that Proclus’ discovery of the Good at this point stemmed from his reading the treatment of hypothesis in the Phaedo in close relation to the Divided Line passage, taking a more rigorously Platonic view; whereas Damascius seems to be understanding the term in closer relation to its ordinary philosophical sense. Hence he can speak of the argument from these hypotheses as a demonstration in syllogistic form. Olympiodorus finds much more need to discuss hypotheses in his Aristotelian commentaries than in his Platonic ones. However, at in Alc. 40.18-41.1 he clearly associates true philosophical argument with argument from an unhypothetical starting point, seeing the common notions as such a starting point. Other technai including medicine, he surmises, start from hypothetical assumptions. In general it seems that the prominence given to the Aristotelian curriculum at Alexandria since Ammonius had made it more difficult to understand Plato’s more distinctive notion. Occurrences of the term ‘unhypothetical’ (ἀνυπόθετος), however, do suggest a more Platonic framework. Such language is found

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Though in accordance with many at that time he took it to be the work of Albinus. See in particular in Remp. I 282.25-283.12, 292.1-15.

Editor’s Introduction

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four times in the in Alcibiadem but never in Aristotelian commentaries. In the Athenian school Damascius had made use of that term three times in section 225 of the in Philebum, where he appears to be correlating the classification of technai with the Divided Line. But Proclus had used it eight times in his in Rempublicam (283.11-284.20, 292.5), eleven times in his in Parmenidem and occasionally in other Platonic works. Syrianus also uses the term in an interesting passage relating to hypotheses (in Met. 65.10-20).20 What emerges is that in late antiquity Plato’s theory of hypothesis was indeed important, but nowhere in extant material well explained or well debated. It may be the case that the collection of ancient commentaries and treatises that has come down to us has been so randomly selected that all important discussions of Plato’s theory of hypothesis have been loss. A significant alternative is that the ancients, who did not shy away from trying to explain difficulties, simply did not regard the theory as especially difficult. They assumed that the meaning of the term had not changed so very much since Plato’s time, and that Plato did not actually mean by that term anything other than what he appeared to be saying. Plato’s methodological passages did not try to obfuscate, and consequently there was no need for the kind of deep interpretation that might be applied to the ‘Nuptial Number’ passage at the start of book VIII of the Republic or to the ‘Myth of Er’ at the end of book X. The purpose of the key passages was actually to explain what Plato was doing, and where Plato wanted to explain things openly he would have seen no need to make his language hard to understand. So perhaps the ancient commentators would have agreed with Scolnicov that these passages did not require us to seek for any understanding of the text other than the natural one.

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20 A little earlier Iamblichus spoke of things that are ‘unhypothetical’ in both his Protrepticus (22.7) and his De Communi Mathematicae Scientia (37.13, 39.24); in this last work the earlier case is from a Pythagorean (Pseudo-Archytas) imitation of the Divided Line passage, and the latter case in his own comment upon Pseudo-Archytas.

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Methodological passages and passages employing methods One of the most significant features of Scolnicov’s thesis is that it does not confine itself to these methodological passages in isolation. In seeing the Meno as a dialogue that introduces a method that can avoid some of the limitations of the aporetic dialogues, he sees a transformation in the way that Plato argues. Just as he later saw part II of the Parmenides as offering the insights necessary to avoid the aporiai of part I, so the Meno is now seen as able to make progress beyond the aporiai that characterised earlier dialogues. It is as if a critical stage, reminiscent of aporetic dialogues, had been reached at 79e where the need for a new beginning is acknowledged. The traditional problems are emphasised both by the comparison between Socrates and the stinging sea-creature (which are particularly relevant to how the interlocutor feels when aporia has been reached, but allegedly disguise the fact that Socrates suffers the same numbness, 80c), and by the difficulties in searching that are introduced informally by Meno and then in the form of a sophistic paradox by Socrates himself. The paradox seems to make all philosophic search pointless, whether or not the searcher knows what is sought. It is now, at this critical moment, that Scolnicov, in chapter ii, sees the use of hypothesis coming to be employed. The myth-like framework of the so-called theory of recollection is introduced as a possibility that would lead to the observation that there is nothing that the soul was unfamiliar with, then through its consequence that the process of searching and learning as a whole is just like a process of recollection, and on to the eventual conclusion that human beings can and should search for knowledge which currently escapes them. But Plato’s confidence in that conclusion is greater than his belief in the myth-like framework in which it had been grounded. That had supplied only a hypothesis, but as long as the hypothesis had some credibility it was enough to avoid the vicious dichotomy between knowledge and ignorance in which the sophistic paradox had been grounded. Plato was thus employing hypothesis already, six Stephanus pages before its explicit introduction.

Editor’s Introduction

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Having once found the application of a method in a passage that makes no direct claim to be using it,21 Scolnicov, like Benson (2015, especially chapter 8), has no reason to confine his treatment of either the Phaedo or the Republic to the key passages in which the hypothetical methodology is discussed. In actual fact that method is seen in chapter iv to be central to the overall argument concerning immortality in the Phaedo. Furthermore, Plato’s actual practice within the dialogue can be used as a test of theories about hypothesis itself (chapter iv.5). Likewise the method is seen as being central to the argument of the Republic from book iv or even before (see chapter v, from section 5), not simply from book v 471c as in Benson’s book.22 The result of Scolnicov’s discovery of quite a wide use of the hypothetical method is that each dialogue comes to warrant a plurality of chapters. The Republic in particular discusses the wider argument in chapter v, and the treatment of knowledge, opinion and ignorance in chapter vi – both before the extended discussion of the Divided Line passage in chapter vii, which considers the Line ‘not as a “container” but rather as a representation of quantitative relations.’ So Plato’s argumentative strategy is never considered in isolation from the epistemology and metaphysics, and all of them are studied in close relation to the text, and those whose interpretations have ignored the text itself attract regular criticism. This is nowhere more evident than in the discussion of the Divided Line. This discussion requires a further chapter beyond it, chapter viii, which will further explain Scolnicov’s hostility to any attempt to find mathematical intermediates behind the Line. His conclusion (chapter ix), however, will return to the basics of the theory of hypothesis, and to its relationship with the elenchus and with dialect. Here Scolnicov argues that the Phaedo and Republic, with their wider application of the method of hypothesis, will also go on to make such investigation a central plank of the philosophic life and of the life of the polis. These are the implications of method for ethics and for politics: a means of grounding aretê in epistêmê.

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21 For other claims to find a method of hypothesis beyond any methodological discussion, in the Charmides and the Theaetetus respectively (dialogues that do not actually offer a directly relevant methodological discussion), see Ostenfeld (1999) and Marcos de Pinotti (2016). 22 For book ii see Cambiano (2005).

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The importance of the ‘sought’ and its link with the τί ἐστίν On three occasions in his discussion of the Meno (chapter ii [4]) Scolnicov refers to ‘the “sought”’. Although we are not told exactly where this expression comes from, the Greek equivalent (τὸ ζητούμενον without a noun) occurs thirteen times in Pappus – more if one includes all cases. In fact Pappus’ definitions of analysis and synthesis (Syntaxis 7.634.11 and 22 (quoted by Scolnicov, chapter i [3]) include the genitive of the same phrase. Scolnicov notes that the ‘sought’ is the starting point of the geometer’s hypothetical procedure, which aims to convert ‘sought’ into ‘given’. With regard to the Meno he adds that at 87b5-6 the ‘sought’ is to be found in the protasis, and thus that it is that from which it would follow that aretê is teachable. The ‘sought’, it is implied, is found in the premise that aretê is some kind of knowledge (ἐπιστήμη τις). Though Plato’s protasis had in fact been talking of what sort of thing aretê might be (ποῖόν τι), it is actually presumed that it offers a view as to what it might be, in what looks like defiance of the dialogue’s key distinction between the ποῖόν τί ἐστίν and the τί ἐστίν. The identification of aretê with some kind of knowledge may go some way to saying what it is, but fails to specify which particular kind of knowledge (cf. Gorgias 462c10-e4). However, the key thing to be said for finding ‘the sought’ here is that it is usually just aretê that is the object of search (τὸ ζητούμενον) in the Meno, rather than the proposition that reveals what has been sought and found.23 That Scolnicov chose to speak of ‘the sought’ in this dialogue is highly appropriate. The verb ‘to seek’, ζητεῖν, occurs with considerably greater frequency in the Meno than in any other dialogue within the corpus,24 and its passive participle is found at 79d3 and d6 respectively. Of all those dialogues that we assume to have been completed prior to the Republic it is the only one to use any passive form of the verb. Let us examine the data (table 1):25

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23 But note the following in Scolnicov’s chapter ix.1: ‘we should keep in mind that the premise (or the “cause”) may be indifferently a term, a thing, a fact or a proposition.’ 24 Note that there is a much higher rate still (over 17 cases per thousand words) in one dialogue from the spuria, the Sisyphus, but there it is clearly thematic. 25 No cases occur in Crito, Alcibiades II, Hipparchus, Hippias Minor and Ion.

Editor’s Introduction

dialogue Meno Statesman Charmides Laches Philebus Sophist Epinomis Apology Hippias Major Theages Republic II-X Euthydemus Cratylus Clitophon Alcibiades I Theaetetus Symposium Republic I Phaedrus Epistles Amatores Phaedo Laws Protagoras Minos Gorgias Timaeus-Critias Menexenus Euthyphro Lysis Parmenides

21

words 10396 18592 8410 8021 19054 17414 6389 8854 8911 3650 79907 13030 19201 1575 11317 23803 17530 9451 17221 17213 2424 22633 106298 18077 3078 27824 29144 4908 5464 7319 16434

ζητεῖν [act.] 30 7 7 9 16 11 4 6 7 3 42 7 10 1 7 10 10 4 8 7 1 7 33 7 1 6 3 1 1 1 1

ζητεῖσθαι 2 14

3 6 1

other ζητ6 11 4 1 2 2 1 2 1

3

18 2 3

1

3 1 1

1 2 9

3

Total 38 32 11 10 21 19 6 8 8 3 63 9 13 1 7 14 10 5 9 8 1 9 42 7 1 6 6 1 1 1 1

/1000 3.655 1.721 1.308 1.247 1.102 1.091 0.939 0.904 0.898 0.822 0.788 0.691 0.677 0.635 0.619 0.588 0.570 0.529 0.523 0.465 0.413 0.398 0.395 0.387 0.325 0.216 0.206 0.204 0.183 0.137 0.061

Table 1: Frequency of ζητ-terminology in the Platonic Corpus

Samuel Scolnicov

22

Meno ref. 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

Skep-Skop0 0 0 1 0 1 0 0 0 0 0 1 1 0 1 1 4 4 3 1 1 1 0 4 1 0 1 1 1 0 0

Zêt0 0 1 2 2 2 0 0 0 2 6 4 0 0 3 0 6 0 0 3 2 0 1 1 0 0 2 0 0 1 1

Zêtein compounds

1 (su-)

1 (su-) 1 (epi-)

Table 2: vocabulary of ζητ- and σκοπ– etc. in Meno

Editor’s Introduction

23

There is a high rate in Meno partly because such vocabulary is closely linked with the search for virtue. It is associated with a particular thing that one is trying to find, as when one searches for a murderweapon or a perpetrator. It is not used for searching a particular area where the weapon or murderer might be found, as when one searches a farm-yard or forest. In such cases one already knows where the farmyard or forest is to be found, so that one cannot search for them; but one can hypothesize that they are where what one is searching for is to be found. Therefore one examines them. One searches for what is not currently at hand, but one can only examine what is now available to one. In the case of such examination of a potential search-area the Meno favours instead the verbs σκοπεῖν, σκέπτεσθαι, and their cognates. The vocabulary of searching and examining, treated by Fine (1992) without distinction as the language of inquiry, is not spread evenly throughout the Meno, but is concentrated in a few passages, as seen in table 2, which compares the frequency of the vocabulary of searching with that of σκοπεῖν, σκέπτεσθαι, and their cognates:26 It will be seen that there is a major concentration of searchvocabulary (ζητ-) at 79-81, with high figures also at 86, 89-90, and 7375. From 79d3 to 81e2 there are in fact thirteen cases of this vocabulary if one adds in the occurrence here of the compound συζητῆσαι (80d4). Socrates is inviting Meno to persist with a proper search for aretê prior to trying to discover whether or not it can be taught, Meno raises an allegedly sophistic problem that would make such searching impossible, and Socrates reformulates this difficulty. The theory of recollection, as seen from the four instances at 81d4-e2, is intended to answer that difficulty, and encourage searching. That is why at its conclusion there are another five cases at 86b4-c6. However, when Meno reiterates his desire to hear only about how aretê arises, the principal vocabulary for the discussion switches to that of investigation rather than search. It is relatively easy to see why this is so when one considers Socrates’ observation at 86d3-6 that, if he were in control of Meno as well as of himself, ‘we should not examine whether excellence is teachable or

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26 While I include compounds of ζητεῖν, I can find no occurrences even of the ἐπι– compounds of σκοπεῖν and σκέπτεσθαι.

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not teachable, until we have first searched for it—what it is.’ The verb for searching for something (ἐζητήσαμεν) is used in relation to the identity of some actual object of search; the verb for examining (ἐσκεψάμεθα) is employed rather for the subordinate questions that may be asked about that object of search; in the language of the Meno itself (71b4), the former is used of the τί ἐστιν (what it is), the latter of the ὁποῖόν τι (what sort of thing it is). For the next two Stephanus pages, during the illustration and application of the method of hypothesis, we have only the language of examining: 86d8-e1: ἔοικεν οὖν σκεπτέον εἶναι ποῖόν τί ἐστιν … 86e2-3: συγχώρησον ἐξ ὑποθέσεως αὐτὸ σκοπεῖσθαι, εἴτε διδακτόν ἐστιν εἴτε ὁπωσοῦν. 86e4-5: ... τὸ ἐξ ὑποθέσεως … ὥσπερ οἱ γεωμέτραι πολλάκις σκοποῦνται … 87b3-4: … ὑποθέμενοι αὐτὸ σκοπῶμεν εἴτε διδακτὸν εἴτε οὐ διδακτόν ἐστιν, … 87c11-12: δεῖ σκέψασθαι πότερόν ἐστιν ἐπιστήμη ἡ ἀρετὴ ἢ ἀλλοῖον ἐπιστήμης. 87d1: ἔμοιγε δοκεῖ τοῦτο μετὰ τοῦτο σκεπτέον εἶναι. 87e5-6: σκεψώμεθα δὴ καθ᾽ ἕκαστον ἀναλαμβάνοντες ποῖά ἐστιν ἃ ἡμᾶς ὠφελεῖ. 88a3 and 88b1: σκόπει δή, …27 88a6: ἔτι τοίνυν καὶ τὰ κατὰ τὴν ψυχὴν σκεψώμεθα. The vocabulary has changed because they are no longer trying to find some ultimate object of search (or the identity of that object), but the properties that such a thing exhibits; this much is indicated by words like ποῖόν τί (86e1) and ἀλλοῖον (87c12). They look within a searcharea, examining indisputably good things within the soul (88a6). The method of hypothesis treats the object of search as if it were already available to one, and proceeds to an examination of the area to which it is presumed to belong. The change of vocabulary applies to the introducti-

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27 For the most part little can be read into the the imperatives σκόπει (cf. 91b1) and σκέψαι (cf. 89d5, 90b7).

Editor’s Introduction

25

on and application of argument from hypothesis up to 89c4,28 which does not search for a direct answer, but makes an assumption about the goodness of the thing sought (87d2-3) and examines the area of goodness. After this argument’s conclusion we soon come to the beginning of the episode with Anytus. Here the verb for searching (ζητῶν, 89e6; ζητῶ, e8; ζητεῖν, 90b3; συζήτησον, b5) and the noun for search (ζητήσεως, e10) are immediately in evidence, but the object of Socrates’ search is now the teachers of virtue,29 and the search itself unsuccessful. When Socrates’ wishes to explain to Anytus the topic of their earlier examination (into the teachability of virtue) he noticeably reverts to his earlier language involving the verb σκόπειν, and explains as follows: 93b1-2: ἀλλ᾽ εἰ διδακτόν ἐστιν ἀρετὴ πάλαι σκοποῦμεν. τοῦτο δὲ σκοποῦντες τόδε σκοποῦμεν …. And the new question for examination is not who the teachers are, but whether men of excellence know how to pass on that excellence to their sons.30 Once Anytus has left, Socrates and Meno can resume their discussions. The indirect method of inquiry into the teachability of virtue is appropriately referred to by the verb ἐσκέμμεθα by Meno at 96d1, whereas the search for somebody to make them both better is still urged by Socrates at 96d8.31 At 97b10-11 Socrates refers to what was omitted ‘in the examination concerning excellence over what sort of thing it was (ἐν τῇ περὶ ἀρετῆς σκέψει ὁποῖόν τι εἴη), and at 98d7-8 to the question of whether it was teachable (ἐσκοποῦμεν τὸ μετὰ τοῦτο εἰ διδακτόν ἔστιν). Later Socrates talks of how excellence would come about ‘if now, in this whole discussion, we had searched and were making claims correctly’, coupling the verbs ἐζητήσαμεν (aor., with past reference) and ἐλέγομεν

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28 Here Meno includes κατὰ τὴν ὑπόθεσιν as well as εἴπερ ἐπιστήμη ἐστὶν ἀρετή, bringing a certain finality to this phase of the dialogue’s argument. 29 Also 92c8: ἐπιζητοῦμεν, and cf. ζητοῦντα μανθάνειν παρὰ τούτων. 30 It is in this context that the language of inquiry is used when Socrates wants to consider the example of Aristides too at 94a1. One might argue that the language is not quite consistent in the light of 93b6, where the verb of searching returns (τοῦτ᾽ ἔστιν ὃ πάλαι ζητοῦμεν), but it is possible to understand the object of search here once again as that thing which may or may not be handed down from father to son, i.e. excellence itself. 31 ζητητέον, but note at 96e1 (ζήτησιν) the reference to earlier discussion, which should perhaps be to the argument from hypothesis, or to its aftermath.

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(imperf., with present reference) in the protasis (99e5). But of course he does not believe that they have searched correctly because they have not first been searching for (ζητεῖν, 100b6) what excellence is. Proper searching goes straight to the matter of something’s or somebody’s identity. From the conclusion of the recollection passage, then, up to the end of the dialogue, Plato consistently distinguishes these two verbs, one favoured for the direct search that ends with identifying something, the other that aims at examining some other question about it on the assumption that it is such-and-such. What I have wanted to claim here is a matter of simple fact: that the dialogue applies the verbs for searching and examining in significantly different ways. I am not convinced that they can be precisely correlated with the dialectical (and mathematical) procedures discussed by Scolnicov, and Pappus used the term ‘the sought’ in his definitions of both analysis (7.634.11 and 13) and synthesis (7.634.22). So both these methods presume that there is something sought (in Pappus a proposition, since in analysis it can be true or false (7.636.5 and 7), and the difference is that the former starts with an assumption about ‘the sought’, while the latter ends in its establishment. It may be possible to clarify the roles of searching and examining further in relation to Platonic dialectical procedures, but it is not my purpose here. While it is with the argument from hypothesis that the distinction becomes clearest, it had perhaps been operating all along. There are in fact only six uses of skep- vocabulary prior to 86, all imperatives, one at 73d6, inviting the modification of an attempted definition, another at 75b9 inviting the evaluation of a definition, another at 81b2 inviting Meno’s comments about the truth of priestly and poetic tradition, another at 84c10 inviting Meno to observe the consequences of the slave’s being puzzled; and others at 82c7 and 85a4 telling the slave how to examine issues of simple geometry. The zet– terminology is used mainly for searching for a single concept of virtue (72a7, 73d1, d2, 74a8, a11, 79d6, 80d4); but likewise for a single concept of shape (75a4, b10, 79d3), or for the slave’s search for the line that will yield the square of size eight (84b10, c4, c11). It is used five times in the puzzles about the possibility of searching (80d5-e5) and four times in the answers to that puzzle (81d4 x 2, e1, e2), where it is implied that the process of sear-

Editor’s Introduction

27

ching and learning as a whole is not other than the process of ‘recollection’ (81d4-5). Searching’s intended result is therefore discovery, and it is no accident that the vocabulary of finding (εὑρίσκειν, ἀνευρίσκειν, ἐξευρίσκειν and cognates) is also commoner in the Meno than in most dialogues,32 even though its high rate in this regard cannot compare with its rate for the terminology of searching, so that it does not seem that discovery has been thematised in the same way as search. These findings invite the question of whether the vocabulary found in the relevant sections of Phaedo and of Republic vi mirror the way such terms had been used in Meno. The Phaedo employs the noun for ‘hypothesis’ at 92d7 and 94b1, then in the main methodological discussion at 101d2, d3 and d7, and finally at 107b5; the corresponding verb is found at 93c10, 100a3, b6 and 101d7, with a variant reading at 98a2.33 As soon as Socrates introduces his ‘second sailing’ we find the combination of the terminologies of searching, examination and hypothesis. This is turn follows shortly after an appearance of the terminology of search (99c2, ζητοῦσιν; cf. c5, ἐξευρεῖν) talking of the failure of the physicists to postulate an intelligent cause of the world’s goodness. We are dealing, in fact, with a passage about the search for the cause, in fact the ‘cause of coming-to-be and passing away’ (95e10). Here Socrates, unable to find a final cause for himself or learn about it from another, offers to show Cebes his δεύτερον πλοῦν ἐπὶ τὴν τῆς αἰτίας ζήτησιν ᾗ πεπραγμάτευμαι (99c9-d1). It is an alternative path that searches for the cause that Socrates requires, but this will be the last use of the vocabulary of searching for a while, since Socrates now goes on to discuss only the area on which the search will concentrate, not what he is looking for. In the context of this overall search, Socrates has been examining realities (99d5: τὰ ὄντα σκοπῶν), but desists, fearful that he will suffer the fate of those who examine the eclipse of the sun directly, rather than looking in reflections. His alternative method will be:

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32 The Meno uses such terminology approximately 0.96 times per thousand words, exceeded by the Statesman, Charmides, Cratylus, Laches, Hippias Major, Phaedrus, and some suspect dialogues, most notably Minos (4.55) and Alcibiades II (1.81). 33 The early examples concern the argument from recollection (92d7) and the hypothesis that the soul is a harmony (93c10, 94b1), perhaps preparing the way for more serious discussion of the method, but not yet entailing it.

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Samuel Scolnicov

P1) 99e5-6: … εἰς τοὺς λόγους καταφυγόντα ἐν ἐκείνοις σκοπεῖν τῶν ὄντων τὴν ἀλήθειαν. Τhis passage is still about the examination of realities, by understanding the truth of which Socrates hopes to discover the cause that is the object of his search. It had been implied by the reflection metaphor that it was somehow less direct, though Socrates has reservations about that metaphor: P2) 100a1-4: οὐ γὰρ πάνυ συγχωρῶ τὸν ἐν λόγοις σκοπούμενον τὰ ὄντα ἐν εἰκόσι μᾶλλον σκοπεῖν ἢ τὸν ἔν ἔργοις. ἀλλ᾽ οὖν δὴ ταύτῃ γε ὥρμησα, καὶ ὑποθέμενος ἑκάστοτε λόγον ὃν ἂν κρίνω ἐρρωμενέστερον εἶναι, … Whether this method is any more indirect than that of the physicists or not, Socrates proposes to build upon the foundations of whatever account he deems the most secure. These foundations will be his ‘hypotheses’. The primary ‘hypothesis’ is of course the existence of certain Platonic Ideas (100b5-7), and Cebes is invited to examine (100c3: σκόπει) whether he agrees about the consequences of such a hypothesis. Another imperative will be used to invite assent to a further refinement at 103c10. The major methodological passage is 101d1-8, and involves the examination of whether the consequences of a hypothesis are consistent or not (101d5: σκέψαιο). A higher-level hypothesis will be sought to justify the original hypothesis if it is challenged. The failure to act methodically will result in the disappointment of one’s hopes to find (101e3: εὑρεῖν). What this would mean in the case under consideration is not spelled out, but it would presumably mean a failed search for the final cause. It is not until 107b that the language of hypothesis and of searching will again be found. Here a more confident Simmias is encouraged to reexamine (107b6: ἐπισκεπτέαι) the primary hypotheses, however convincing they may seem. With sufficient precision over the hypotheses, they will be able to follow the argument through, so that ‘this thing itself’ (b8-9: τοῦτο αὐτὸ) will become clear, and they will no longer be searching for anything (107b9: οὐδὲν ζητήσετε περαιτέρω). The meaning of

Editor’s Introduction

29

the Greek could perhaps be clearer, and the nominative feminine plural ἐπισκεπτέαι has attracted suspicion, but the bulk of this is clear. It must be the hypotheses that are to be re-examined, and if they survive this there is hope that the search is at an end. If the search is at an end then their difficulties with the notion of an immortal soul must have been resolved, but previously the object of their search had been the not unrelated matter of the cause of coming-to-be and passing away (95e10). Finding this much must finally settle the issue of the soul’s inability to pass away itself. So the Phaedo resembles the Meno in making a fairly clear distinction between the object for which one searches and the area under examination, which it is hoped will bring that object to light. Hypotheses are again never what is truly sought, but facilitate areas of examination that may illuminate what is sought, if somewhat indirectly. Turning to the Republic, the relevant passage lasts only from 510b to 511e, and is considered more quickly. We meet the vocabulary of search three times here, and all cases involve geometrical and allied practice: R1) 510b4-5: τοῖς τότε μιμηθεῖσιν ὡς εἰκόσιν χρωμένη ψυχὴ ζητεῖν ἀναγκάζεται ἐξ ὑποθέσεων … R2) 510e3-511a1: τούτοις μὲν ὡς εἰκόσιν αὖ χρωμένη, ζητοῦντές τε αὐτὰ ἐκεῖνα ἰδεῖν ἃ οὐκ ἂν ἄλλως ἴδοι τις ἢ τῇ διανοίᾳ. R3) 511a4-5, 7-7: ὑποθέσεσι δ᾽ ἀναγκαζομένην ψυχὴν χρῆσθαι περὶ τὴν ζήτησιν αὐτοῦ, …, εἰκόσιν χρωμένην αὐτοῖς τοῖς ὑπὸ τῶν κάτω ἀπεικασθεῖσιν … The contexts are all very similar. One is trying to discover something non-sensible, but one cannot approach it directly, so the quest necessarily (R1, R3) involves things that had functioned as originals rather than images in the sensible segment (R1-3), employing them now as one employs images (R1-3) that will make an approach to the desired goal possible. These images do become objects of examination, but are not objects of search themselves. In this role they are called ‘hypotheses’ or ‘foundations’ upon which reasoning can be built. The identity of the objects of search are not obvious in R1, but for R2 they had been specified as things like ‘the square itself’ and ‘the diameter itself’

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(510d7-8), for they are ‘those things themselves’ (αὐτὰ ἐκεῖνα). And in R3 it had been something ‘intelligible in form’ (νοητὸν … τὸ εἶδος, 511a4). We appear, then, to be talking of the basic entities of geometry. Of the terminology of examination there are again three examples: R4) 510b2: σκόπει δὴ αὖ καὶ τὴν νοητὴν τομὴν ᾗ τμητέον. R5) 510d2-3: τελευτῶσιν ὁμολογουμένως ἐπὶ τοῦτο οὗ ἂν ἐπὶ σκέψιν ὁρμήσωσι. R6) 511c8-d1: διὰ δὲ τὸ μὴ ἐπ᾽ ἀρχὴν ἀνελθόντες σκοπεῖν ἀλλ᾽ ἐξ ὑποθέσεων, νοῦν οὐκ ἴσχειν περὶ αὐτὰ δοκοῦσι σοι … R4 involves only an imperative, inviting consideration. This is of no immediate relevance. R5, however, seems to involve the object of the geometers’ quest just as much as R1-3 had done, and we appear at first sight to be talking of an object of search of the kind that would normally follow ζητεῖν in the Meno. It may be objected that the indefinite construction with ἂν plus the subjective, talks of whatever the geometers examine, so that there is no reason why we could not be talking of problems that the geometers had set themselves rather than geometrical entities upon which they intend to focus, but one may require a fuller explanation than this. Perhaps the solution lies in the choice of the rather odd periphrasis ἐπὶ σκέψιν ὁρμήσωσι rather than the bare verb σκέψωνται. One might translate ‘They finish by general consent at that whatever they had rushed into examining.’34 There would in that case be a continuation of the implied criticism of contemporary geometrical method for going too fast and failing to give an account of its basic principles on the grounds that they are obvious to anybody. They might be examining some thing (e.g. the square of the hypotenuse) and this might in turn be a legitimate object of search, but they might rather be examining a property of that thing (e.g. whether it is identical to the sum of the squares on the other two sides). R6 involves the negative, specifying something that geometers would not do (and thus renewing the criticism), though it is something favoured by Socrates’ dialectic. The geometers are failing not only to

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34 I note that Reeve’s revision of Grube’s translation in Cooper (1997) has only ‘they arrive in full agreement’, without any attempt to translate ἐπὶ τοῦτο οὗ ἂν ἐπὶ σκέψιν ὁρμήσωσι.

Editor’s Introduction

31

search for the basic principles of their own discipline, but also to examine them, arguing instead, on the basis of what is agreed to be obvious, towards conclusions that are dependent on an unreflective view of those principles. While the situation is somewhat more complex in the Republic, the vocabulary of searching and examining there and in the Phaedo is used in a broadly similar manner to what we have seen in the Meno, with the verb of searching being used for the ultimate quarry of one’s philosophic activity, and hence usually of some thing rather than simply the answer to a question. The object of the search is therefore more akin to the missing person for whom a search is mounted than to the woods and moors that one seaches in the hope of finding them. The verb for examining is used mainly when one has abandoned the direct search and follows up other leads that might be expected, on adequate examination, to lead to whatever one cannot find directly. Given the methodological importance of these terms, I have checked the way that searching is conceived in the primary epistemological dialogue, the Theaetetus.35 The terminology of search is found there only fourteen times.36 Of these instances some have no methodological significance and may be ignored for our purposes, including 142a2 (concerning the search for a person), 170b3 (about searching for teachers and commanders) and 180a5 where Theodorus is noting the uselessness of seeking further explanation of what a Heraclitean has said. One instance, 174b5, confirms the kind of things that philosophers search for: what a human actually is and what is proper to a human as opposed to other natures (τί δέ ποτ᾽ ἐστὶν ἄνθρωπος καὶ τί τῇ τοιαύτῃ φύσει προσήκει), while two early instances (144b4, 148b) remind one that mathematicians may have different ideas from the philosopher about what an object of search is. Thereafter 187a3 confirms that knowledge is the primary ob-

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35 The Theaetetus is not directly relevant to method of hypothesis, as the vocabulary occurs only of Theaetetus’ proposed equation of knowledge and seeing at 165d1 and of a Heraclitean hypothesis at 183b4. 36 ζητεῖν at 142a2, 148b9, 170b3, 174b5, 180a5, 187a3, 188c10, 200c9, 201a1, 202d2, 210a7; ζήτημα at 191a6; ζήτησις at 144b4 and 196d9. I ignore here 142a2 (the search for a person), 170b3 (searching for teachers and commanders) and 180a5 (Theodorus on seeking further explanation of Heraclitean statements).

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ject of search,37 though at 188c10 the object of search has (temporarily) become false opinion, and it remains the object of search at 191a6. At 196d9 we are reminded that knowledge had been their initial object of search ὡς οὐκ εἰδόσι τί ποτ᾽ ἐστίν. That same phrase τί ποτ᾽ ἐστίν is repeated at 200d2, after Socrates had spoken of the error in searching (d1) for false opinion before knowledge had been found. At 201a1 τὸ ζητούμενον should still refer to knowledge, while right opinion is the area to be (briefly) examined in the hope that they may find it there (201a3-4: σκοπῶμεν, σκέψεως). Certainly at 202d2 knowledge is the thing that many wise persons have sought for, only to grow old before they find it. As the dialogue closes 210a7-8 confirms that knowledge is still the object of search. It can be said with some confidence, then, that there is no discernable difference between the Theaetetus and the Meno on the nature of an object of search, on its having to be something, and on the existence of a hierarchy of investigation that means some more primary objects of search should be found before other dependent ones are seriously investigated.38 However, when one examines those dialogues that present themselves as sequels to the Theaetetus, the Sophist and Statesman, one finds important differences, not least in the frequency of the passive participles (pres. and aor.): six and thirteen respectively. In the Sophist such participles refer to the sophist (223c2), the sophistic race (224c7), or an idea under which the sophist falls (235d2), but also angling (221c3), not-being in names (261d3), and a distinction between two types of teacher (229b11) or two types of statements or opinions. As for expressions like ὅτι ποτ᾽ ἔστι and τί ἐστί, they are no longer used at all in the Statesman, though the former (with ὅτι or τί) is fairly common in the Sophist.39 Given the presence of very different philosophic methods in the-

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37 At 187a3 Socrates discusses where we should be looking for knowledge, not in sensation any longer but in the internal discourse of the mind. At 196d9 we are reminded that at the start of the discussion knowledge had been their object of search ὡς οὐκ εἰδόσι τί ποτ᾽ ἐστίν. That same phrase τί ποτ᾽ ἐστίν is repeated at 200d2, after Socrates had spoken of the error in searching (d1) for false opinion before knowledge had been found. 38 I draw attention to the agreement between my findings here and the thesis argued by Marcos de Pinotti (2016). 39 These expressions are still directly coupled with the vocabulary of searching at 218b8-c1 and c6-7, but with a verb of definition at 217b2-3, and with a verb of finding at 221c7. After

Editor’s Introduction

33

se dialogues, it is perhaps only to be expected that differences in the vocabulary of search and examination would also be found. What I hope to have shown here is (i) the way in which the concept of searching for something is linked in the Meno with the direct study of what ‘the sought’ is rather than with the examination of the consequences of a hypothesis; and (ii) the consistency of this usage with the hypothesis-related passages of Phaedo and Republic. The first shows that hypothesis is closely bound up with the wider issues of method at the time of its introduction; the second shows that it continued to have approximately the same importance and meaning across the three dialogues tackled by Scolnicov. Notes on the editing process Scolnicov divided his chapters into sections marked (except in the case of the first) by a number followed by a stop at the beginning of the relevant paragraphs. This was thought to be a potential source of confusion, and I have replaced this by the same number in square brackets left-justified (numbering the first section also). The spelling ‘premiss’ then popular has been replaced by ‘premise’, which he is thought to have favoured later in life. The phrase ‘inasmuch as’ has been replaced by ‘in as much as’, and some more technical anglicized Greek terms that are not part of normal English, though left in roman in the thesis, are here in italics. With an increasing awareness that there is nothing in the Meno to establish that the slave is much younger than Meno himself, if at all,40 and that this is in any case irrelevant to the dramatic situation, I have changed all cases of ‘boy’ or ‘slave-boy’ (except within quotations) to ‘slave’. Though use of ‘boy’ was normal at the time, and an opportunity for welcome variation in one’s vocabulary, I prefer here to discourage any misunderstandings about what the term implies. Other

-------------------------------------------this they occur in contexts of saying, defining or grasping what something is (246a2, 260a8, 260e5, 263c2 and 263d10). 40 From 85e3-6 one might be tempted to deduce that Meno, still in his early twenties, had known the slave’s entire life-history, and thus was marginally older, but Meno’s assertion of knowledge may be based less on his personal observation than on that of others in a position to know. Meno would not have travelled to Athens with slaves who were very young or very old; see Nails (2002), 298; see also Nails (2007); Benitez (2016).

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small alterations have been made in accordance with notes in Samuel’s own copy of his thesis. Further Bibliography Given that Scolnicov has tackled a topic central to the development of Platonic metaphysics, it is inevitable that much that has a bearing on various aspects of his thesis should have been published since. I have no wish here to present myself as an expert on this particular aspect of Platonic philosophy, or to present a full appraisal of what has been done, but some indication of its scope ought nevertheless to be offered. Central to any such account would be the various methodological studies by Hugh H. Benson. It is interesting that he speaks (Benson, 2010: 194) of ‘Socrates’ explicit recognition that there is more work to be done.’ His work has culminated in a book that deals with dialectic and the method of hypothesis in the same three dialogues as Scolnicov’s thesis. Since Benson does not seem to have been aware of his predecessor’s work there is no direct engagement with it that might have helped one to evaluate the level of disagreement. Concerning the coherence and importance of the method across these three dialogues there is substantial agreement, as also regarding Plato’s willingness to use the method even before the actual passages that highlight it—though here Benson makes use of Republic 471c-502c (chapter 8). Otherwise most of the key work has tended to appear in articles or in books and commentaries devoted to individual dialogues: i.e. of Meno, Phaedo, or Republic. The Meno seems to have attracted by far the most attention in this context, and this is hardly surprising because scholars ordinarily assume that this was the dialogue in which the method of hypothesis was introduced. A new discovery can seem more exciting than a slight reworking of a weapon that is already in one’s armoury. Scolnicov himself published an article on the Meno (1975), and two more influential articles were published in the following decade by BéduAddo (1979, 1984). Studies of hypothetical method in altogether different dialogues included Ostenfeld (1999) and Marcos de Pinotti (2016); there was also a study relating to Republic ii by Cambiano (2005). Scolnicov (1992) himself has examined the role of hypothesis in the argu-

Editor’s Introduction

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ment in the Phaedrus. A periodical that has played an important part in disseminating ideas of the hypothetical method in the Meno in particular has been Apeiron, perhaps because it has sought to tackle ‘ancient philosophy and science’, and is therefore a natural home for a discussion of the mathematics involved. An early influential article in Apeiron was Meyers (1988), and this has been followed by Byrd (2007), Franklin (2010), and Iwata (2015).41 Franklin (87) argues that ‘we investigate from hypothesis when we study an item in a specific circumstance, or, as I shall call it, an investigative setting.’ This seems almost to mark the method with a Protagorean relativism, which might have proved unpalatable to Plato and Scolnicov alike. Iwata (2015) is sceptical about the extent to which any specific geometrical problem needs to have been alluded to in the ‘hypothsis’ section of the Meno. More directly on the philosophical argument from hypothesis here was Iwata (2016), arguing that the relevant hypothesis is simply that ‘virtue is good’, derived from Meno 77b-79a), and that the overall purpose of the section is protreptic in the sense of leading Meno to seek for the virtue that he so patently lacked. Ionescu (2018) contributes an interesting discussion to methodological discussion of the Meno insofar as it discusses elenchus, recollection, and the method of hypotheses as distinct but interrelated parts of Socrates’ total dialectical armoury in the Meno. Given below are those items referred to in this introduction, along with a few others that might be worth consulting in the course of any attempt to evaluate the contemporary state of the debate and the amount that Scolnicov’s thesis might still bring to it. Baltzly, D. (1995). ‘“To an Unhypothetical First Frinciple” in Plato’s Republic’. History of Philosophy Quarterly 13, 149-65. Bédu-Addo, J.T. (1984), ‘Recollection and the argument “from a hypothesis” in Plato’s Meno’, JHS 104, 1-14. Bedu-Addo, J.T. (1979), ‘The Role of the Hypothetical Method in the Phaedo’, Phronesis, Vol. 24, No. 2 (1979), pp. 111-132.

-------------------------------------------41

Also in that journal was Franklin (2011), on the Republic. The abstract speaks of hypothesis being ‘the basis for rigorous proof of general theorems, expressed entirely in terms of particulars, such as geometric figures.’ Such a description, not to mention the distinction between the objects of hypothetical method and dialectic, is unlikely to have found favour with Scolnicov.

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Benitez, E.E. (2016), ‘Boy! What Boy? (A Plea for Meno’s Slave)’, Ancient Philosophy 36, 107-114. Benson, H.H. (1990), ‘Meno, the slave-boy, and the elenchus’, Phronesis 35, 128158. Benson, H.H. (2003). ‘The Method of Hypothesis in the Meno’, Proceedings of the Boston Area Colloquium in Ancient Philosophy 18, 95-126. Benson, H.H. (2006). ‘Plato’s Method of Dialectic’, in H.H. Benson (ed.), A Companion to Plato, Oxford: Blackwell, 85-99. Benson, H.H. (2010). ‘Plato’s philosophical method in the Republic: the Divided Line (510b-511d)’. In M. McPherran, Plato’s Republic: a Critical Guide, Cambridge: Cambridge University Press, 188-203. Benson, H.H. (2015). Clitophon’s Challenge: Dialectic in Plato’s Meno, Phaedo, and Republic, Oxford: Oxford University Press. Byrd, M.N. (2007). ‘Dialectic and Plato’s Method of Hypothesis’, Apeiron 40, 141158. Cambiano, G. (2005) ‘La méthode par hypothèse en République II’, in M. Dixsaut (ed.), Études sur la République de Platon, Paris: Vrin, vol. 2, 9-24. Ebert, T. (2001). ‘Sokrates über seinen Umgang mit Hypotheseis (Phaidon 100a): ein Problem und ein Vorschlag zur lösung’, Hermes 129, 467-473. Fine, G. (1992). ‘Inquiry in the Meno’, in R, Kraut (ed.), The Cambridge Companion to Plato’, Cambridge: Cambridge University Press, 200-226. Fink, J.L. (2012). The Development of Dialectic from Plato to Aristotle, Cambridge: CUP. Fischer, F. (2002). ‘La “méthode” et les “hypothèses” en Phédon 99d-102a’, Révue philosophique de Louvain, 100, 650-680. Franklin, L. (2010). ‘Investigation from Hypothesis in Plato’s Meno: an unorthodox Reading’, Apeiron 43, 87-116. Franklin, L. (2011). ‘Particular and Universal: Hypothesis in Plato’s Divided Line’, Apeiron 44, 335-358. Ionescu C. (2018). ‘Elenchus, Recollection, and the Method of Hypothesis in the Meno’, Plato Journal 17, 9-29. Iwata, N. (2015). ‘Plato on Geometrical Hypothesis in the Meno’, Apeiron 48, 1-20. Iwata, N (2016). ‘Plato’s Hypothetical Inquiry in the Meno’, British journal for the history of philosophy, 24, 194-214. Judson, L. (2017). ‘Hypotheses in Plato’s Meno’, Philosophical Inquiry, 41.2/3, 2939. Landry, E. (2012). ‘Recollection and the Method of Hyothesis in Plato’s Philosophy’, Philosophia Mathematica 20, 143-169. Marcos de Pinotto, G.E. (2016). ‘La estrategia metodológica de Platón en la primera parte del Teeteto.’ Archai, 16, 43-75.

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Mehrizi, M.A. (2016). ‘The Method of Hypothesis in Plato’s Philosophy’, Philosophical Investigations 10, 1-26. Meyers, J. (1988). ‘Plato’s Geometric Hypothesis, Meno 86e-87b’, Apeiron 21, 17380. Nails, D. (2002). The People of Plato, Indianapolis: Hackett. Nails, D. (2007). Review of Cristina Ionescu, Plato's Meno: An Interpretation, NDPR 2007.11.15. Ostenfeld, E. (1999). ‘Hypothetical Method in the Charmides and in the Elenchus’, Classica et Mediaevalia 50, 167-180; reprinted in Human Wisdom:Studies in Ancient Greek Philosophy, Sankt Augustin: Academia Verlag, 2016, 149-161. Press, G.A. (ed.). (2000). Who Speaks for Plato? Studies in Platonic Anonymity. Lanham: Rowman and Littlefield. Rashed, M. and Auffret, T. (2017), ‘On the Inauthenticity of the Critias, Phronesis 62, 237-254. Schramm, M. (2007). ‘Hypothesen’, in C. Schäfer (ed.), Platon-Lexicon, Darmstadt, 154-56. Scolnicov, S. (1975). ‘Hypothetical Method and Rationality in Plato’, Kant-Studien 66, 157-62. Scolnicov, S. (1988). Plato’s Metaphysics of Education. London–New York: Routledge. Scolnicov, S. (1992). ‘Love and the Method of Hypothesis’, Méthexis 5, 69-77. Scolnicov, S. (2003). Plato’s Parmenides: translated with an introduction and commentary, Berkeley–Los Angeles–London: University of California Press. Scolnicov, S. (2013). Euthydemus: Ethics and language. Lecturae Platonis 8. Sankt Augustin: Academia Verlag. Scott, D. (2006). Plato’s Meno, Cambridge: Cambridge University Press. Tulli, M. (2013). ‘The Atlantis poem in the Timaeus-Critias’, in G. Boys-Stones, D. El Murr and C. Gill (eds), The Platonic Art of Philosophy, Cambridge: Cambridge University Press, 269-82. Vlastos, G. (1991). Socrates: Ironist and Moral Philosopher. Cambridge: Cambridge University Press. Williams, B. (1973). ‘The Analogy of City and Soul in Plato’s Republic’, in E.N.Lee et al. (eds), Exegesis and Argument: Studies in Greek Philosophy presented to Gregory Vlastos, Assen: Van Gorcum, 196-206.

Acknowledgements

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Acknowledgements Samuel Scolnicov included the following acknowledgements and dedication at the end of his introduction: To many I am grateful for a more personal kind of help. To my supervisor, Prof. B.A.Ο. Williams, I owe much of any accuracy and clear thinking there is in this work. Dr A.L. Peck supervised my work in its earlier stages and gave me much valuable advice. Dr G.E.R. Lloyd discussed with me the typescript at length; I have learned from him much about Plato and Platonic scholarship. Prof. W.K.C. Guthrie read one of the drafts and commented on it in great detail. They are responsible for much of what there is of value in this work – but, of course, for none of its faults. This work is dedicated to my wife Hanna.

The editor would like first to acknowledge the cooperation of the University Library, University of Cambridge, for making available the thesis by Scolnicov in electronic form. He has benefitted from discussions concerning this project with many scholars, among whom were Naoya Iwata, Aidan Nathan, Lloyd Gerson, and Rick Benitez, all of whom offered assistance if required, as well as pertinent ideas. Both Iwata and Nathan, as also François Renaud and Michel Narcy, have assisted me by supplying suggestions for further bibliography, some of which has been used in the introduction; Scolnicov’s original notes and bibliography, however, have been left largely to speak for themselves. The ongoing cooperation with Hanna Scolnicov on various matters, both practical and otherwise, has also proved extremely fruitful.

Introduction

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Introduction [1] It is to the credit of the Marburg neo-Kantians, and in particular of H. Cohen, P. Natorp and N. Hartmann, that they were the first in modern times to stress the importance of a comprehensive examination of Plato’s method and especially of his concept of hypothesis. They were led to this methodological approach to Plato’s philosophy, as is surely the case with every commentator, by their own philosophical interests, and, not surprisingly, their conclusions were not unaffected by these interests. For them, Plato’s hypothesis was the idea as objectivized principle of thought, whose function was to make possible scientific reasoning. There would be hardly any possibility of summarizing in this work the course of the history of the interpretation of Plato’s hypothetical method since the publication of Cohen’s Plato’s Ideenlehre und die Mathematik in 1878 and Natorp’s Plato’s Ideenlehre in 1903, through the many changes in Platonic scholarship and philosophical taste. On the one hand, virtually every writer on Plato’s philosophy was bound to pay attention to this aspect of Plato’s thought. And on the other hand, scholars like T. Heath and his nineteenth century predecessors and more recent followers, working on the history of mathematics, have approached the subject from a different angle. In this work I shall attempt a reinterpretation of Plato’s method of hypothesis and a new assessment of its importance for Plato as a philosophical technique. In the following chapters it will be necessary to deal in some detail both with the more restricted question of the various explanations of Plato’s description of the method of hypothesis and with the wider problems arising from the different accounts offered by scholars and philosophers of Plato’s development of his argument in the dialogues of the middle period. Here in this introduction it will suffice to survey briefly three of the more recent works which are especially concerned with general expositions of Plato’s method of hypothesis.

Introduction

40

[2] Robinson seems to have been by far the most influential of the recent writers on the topic. He summarized Plato’s hypothetical method in the five following points: (1) “We should adopt our opinions deliberately rather than slide into them unconsciously” and “we should adopt opinions rather than suspend judgement”. (2) Plato’s hypothetical method is a method of deduction as opposed to intuition. In that it is to be connected with what became known later as the method of “analysis”. (3) We must avoid contradictions, either direct or indirect. (4) The method consists in holding one’s opinion provisionally and not dogmatically. (5) It is a method of approximation.1 Robinson’s views have been already widely reviewed and discussed, and there is no need to dwell on them at the moment. The second and the fifth of the above points will be particularly questioned in this work, as well as the more general implications of this interpretation. And especially it will be argued that there is much more to the hypothetical method than is cautiously conceded by Robinson. (W. A. Williams2 applies in a rather mechanical way Robinson’s interpretation of analysis to a few earlier dialogues (Euthyphro, Laches, Charmides and Gorgias). While his understanding of Robinson is not always acceptable, yet his work shows well how difficult it can be, on Robinson’s terms, to tell elenchus from analysis.) H. P. Stahl based his interpretation on the concept of mutual implication or logical equivalence. He improves on Robinson by trying to show that the method of hypothesis has a wider application in the dialogues than the restricted contexts in which it was assumed by Robinson. He too, following Robinson and others, connects the method of hypothesis with later geometrical analysis. But he is unable to show that Plato in fact consistently used logical equivalence as the relation between hypothesis and consequence. He is then reduced to conclude that “Platon ging theoretisch aus von der Äquivalenz, wurde aber im Prakti-

-------------------------------------------1 2

Robinson (1953), 105-108. For full references, see bibliography at the end. W.A. Williams (1966).

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schen auf die Schlussformen des modus ponens und modus tollens hingefuhrt”, and that “Platon noch gar nicht sehen konnte, warum die zweiseitige Implikation, auf die die Geometrie Wert legen musste, bei seinen eigenen Deduktionen überflüssig war”. And although he claims that the hypothetical method is widely used in the dialogues, he is prevented by his interpretation of it as Konsequenzbetrachtung – sometimes hardly, if at all, distinguishable from elenchus – from finding either in the Phaedo or in the Republic examples of ἄλλην αὖ ὑπόθεσίν ὑποθέμενος (Phaedo 101D6-7).3 Κ. Sayre has recently offered the following account of Plato’s method of hypothesis: (1) “... Propositions (considerations, verbal formulations) can be justified on the basis of their relationships with other propositions (hypotheses) and ... there are two relationships on the basis of which such criticism is possible, corresponding to what we call ‘entailment’ and ‘consistency’.” (2) “The first step to take in defending an hypothesis that has come under question is to make sure that the hypothesis admit no inconsistency among its consequences.” (3) “The hypothesis should be justified by deducing it from other less problematic hypotheses which themselves can be shown to be consistent. Whether the relationship among consistent propositions in this method also includes mutual entailment is left ambiguous in the Phaedo but is cleared up emphatically in the Republic, where we are told (4) that the ‘higher’ propositions which provide the account of one under question entail the latter but are not entailed by it in turn (as is the case with some forms of mathematical reasoning).” (5) “The terminus of the dialectical procedure is in a starting point which itself stands beyond need of justification.”4 The crux of Sayre’s interpretation is his discussion of “agreement” at Phaedo 100A and its relation to Greek geometrical analysis. This will be examined in detail in ch. iii, below.

-------------------------------------------3 4

Stahl (1956), 44, 45, 68; cf. also 14, 32, 72. Sayre (1969), 55-56.

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Introduction

[3] If the more recent interpretations of the method of hypothesis put a greater emphasis on accuracy, they have nevertheless sacrificed to it the central position the method held in the earlier interpretations. The impression one has on first reading the descriptions of the method in the Meno, the Phaedo and the Republic is of a method which Plato thought of highly, perhaps as the method par excellence of philosophy. And yet, as recent commentators would present it, it turns out sometimes to be little more than an ingenious logical device, sporadically used for solving a few restricted problems. Still worse, it would seem from comparison of Plato’s methodological remarks in the dialogues with his actual practice there, that he was incapable of matching his advice with actual performance, and that the method of hypothesis so warmly recommended in these three dialogues was not actually used in its entirety in any one of them. This is not impossible. But good methodology and good will require that faults of this sort should sooner be imputed to the commentator than to the author. These three interpretations of Plato’s method of hypothesis share a few assumptions which seem to me questionable: i. The desire for greater precision of formulation led to a hasty interpretation of Plato’s procedure as corresponding somewhat rigidly to what we call today propositional calculus. There were, it is true, some protests, especially from less logicallyminded commentators, but they did not seem to have been sufficiently articulate. ii. More specifically, Plato’s dialectical procedures were deemed as necessarily expressible without remainder with the sole resources of the Principia Mathematica. Some of the more logically-minded commentators seemed oblivious to the fact that the material implication is a mere formal connective which does not necessarily define Plato’s concept of deduction or, for that matter, any other concept of deduction, and has certainly no absolute normative force as the definition of implication or deduction. That it may or may not be possible or desirable to render Plato’s συμβαῖνον or the like by an elaboration on the consequent of a material implication is at least arguable. (Patzig, for example, had based his interpretation of Aristotelian syllogistic on the material implication, but has now corrected his views. But, as he implies, we might have gone

Introduction

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already too far in that direction.) These two points will be pursued in more detail in ch. i especially pp. 35 ff., and again in ch. ix, and elsewhere in the body of this work. iii. All modern commentators assume a more or less intimate connexion between Plato’s method of hypothesis and the later method of analysis. But most of them accept the deductive view of analysis, and their interpretations of the method of hypothesis are influenced by it in one direction or another. However, the deductive interpretation of analysis is itself based on too modern a conception of the nature of logical procedures in general, and of ἀπόδειξις in particular. It will be necessary, therefore, to re-examine the current views on the method of analysis. This too is discussed in ch. i, below, and use will be made of the conclusions of that chapter in the rest of the work. **** [4] I shall argue in this work that the hypothetical method has a much more important role to play in Plato’s argumentation than has been assumed lately. It is my contention that the Meno, the Phaedo and the Republic develop one single method of philosophical inquiry and explore its epistemological and ontological implications. Plato’s method cannot be considered in isolation from these implications; for Plato, philosophy is the method. An examination of Plato’s method of hypothesis in the middle dialogues cannot avoid being to a great extent an examination of Plato’s philosophy in that period. It is to be expected that the importance of method in Plato’s philosophy should make itself felt in the actual use of the method of hypothesis in the dialogues. I intend to show that Plato’s use of the method of hypothesis as it is gradually developed in the middle dialogues is by no means confined to the immediate context of those passages in which it is discussed or exemplified. On the contrary, in these dialogues this method is the main, even if not the only, method of argumentation. I have restricted myself to the dialogues of the middle period – the Meno, the Phaedo and the Republic – for in them the method of hypothesis can be studied in its simplest formulation, following what may be presented as one single train of thought to its extreme conclusions.

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The Republic is clearly, in this respect, a watershed, whether one argues for or against a turning-point in Plato’s philosophy. I have tried as much as possible to refrain from basing my arguments on later developments. (I have done that at least once – but there the conclusion I draw is negative and does not depend on the turning-point discussion.) This is also the reason why I avoided commenting on the Third Man argument and related questions, although much of what I say bears directly on the controversy. But I felt that nothing short of a full discussion would do justice to the complexity of the problem. One middle dialogue is conspicuously missing: the Symposium. Opinions are divided on whether or not the Symposium contains an example of the hypothetical method. If it does, it is not obviously of the same variety which is discussed in the Meno and the Phaedo. This issue can be settled only by a thorough examination of the relation between the hypothetical method and the method of collection and division. Although I have touched this problem, it requires much more scope than is available at present. Whatever the results of such inquiry, there is I think a good prima facie case for not including the Symposium in a discussion of the hypothetical method based on the Phaedo and the Republic. From this point of view, and without going into questions of chronology, the Symposium is perhaps better examined together with the Phaedrus. [5] It is impossible to state the extent to which I have availed myself of the works of others. “The originality which any one man can show – said a recent writer, commenting on the very beginnings of philosophy – is astonishingly small, when measured against the enormous mass of ideas for which he is dependent on the past.”5 I have profited from those with whom I have disagreed perhaps more than from those with whom I eventually found myself in agreement. Where I was conscious of having borrowed some definite idea or piece of information, or where I felt the need of distinguishing my position from another, I have stated that in the notes. Many of the acknowledgements had to be relegated to the bibliography. But the more basic and pervasive influences will have to go unacknowledged.

-------------------------------------------5

C. H. Kahn, Anaximander, 134.

Greek Geometrical Analysis

45

Chapter i: Greek Geometrical Analysis [1] It has been widely assumed that the method of hypothesis as it is described in the Meno and in the following dialogues is somehow connected with the form of mathematical reasoning that was later to be known as ἀνάλυσις. As far as it goes, this assumption seems to me correct. When introducing his new method, Plato himself says that it is “the sort of thing the geometers often use in their inquiries” (Meno 86E4-5). And even if this is not sufficient reason for reading the later hellenistic analysis into Plato’s words, at least a clearer grasp of what geometrical analysis was is indispensable for a clarification of Plato’s own understanding of his new procedure and, as it will be shown, also of his later and more developed “inquiry into causes”. But the method of analysis itself has been variously understood by commentators, and their interpretations of it have played an important role in their expositions of what each believed Plato’s method of hypothesis to be. It would thus seem advisable to start by a fresh examination of the apparently rather remote question of the later method of analysis. The conclusions of this chapter would then be applied – most merely by way of disproving assumptions of earlier commentators – to problems bearing directly on Plato’s text. [2] Two main interpretations have been offered to the mathematical procedure known to the Greeks as “analysis”. The “traditional” interpretation is found, e.g., in Heath1 and was later defended most forcefully by Robinson.2 It seems still to be the generally accepted view on the nature of analysis. According to this “traditional” view of analysis, the method consisted in “hypothesizing the proposition to be proved and deducing the

-------------------------------------------1 2

Heath (1926), Introduction, 138 ff. Robinson (1936); (1953), 121.

46

Chapter i

consequences from that proposition until you have reached a consequence which you knew independently to be true or to be false. You could then, if the consequence was a true one, use it as the premise of a proof of your demonstrand; and if it was a false one, you could use its contradictory as a disproof of the proposition you had hoped to establish.”3 According to this account, analysis is a method of deduction, in which the demonstrand is taken as premise and from it a premise of the subsequent synthesis is deduced. This is possible, of course, only if the premises involved in this process are logically equivalent to their respective conclusions. Only in this case is the chain of reasoning strictly deductive in both directions, from the premises to the demonstrand as well as from the demonstrand to its premises. Reductio ad absurdum would be, therefore, a special case of analysis, in which a supposed premise, known as false, is reached, and the demonstrand is disproved starting from the contradictory of the supposed premise. The other interpretation of analysis has been offered by Cornford in his paper “Mathematics and Dialectic in the ‘Republic’ vi-vii” (1932), whose views on this point seem to have remained almost completely isolated.4 On Cornford’s view, analysis is not a deduction of consequences, but a divination of antecedents. The geometer does not search for what the given proposition implies, but for what would imply that proposition, and then for what would imply this new proposition, and so on. In analysis, the activity of the mind is not demonstration but intuition. In the synthesis, the geometer would be deducing consequence from premises; in the analysis he would be divining the premises that would lead to a given conclusion. The premises involved need not be, in this case, logically equivalent to the conclusion, though they may be so. “Analysis would be going the wrong way along a one-way street, and synthesis would be coming back in the right direction.”5 [3] Greek geometry has reached us in an eminently synthetic presentation, and the examples of analysis are scarce. There is little doubt that

-------------------------------------------3

Robinson (1953), 121. Cf. Lee (1935); Gulley (1958) tries to steer a middle course between the two opposing views. 5 Robinson (1936), 467, summarizing Cornford’s view. 4

Greek Geometrical Analysis

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Greek geometers did use analysis in discovering the proofs of their theorems and the solutions of their problems, but they were contented in most cases with the presentation of the synthetic proof or construction, omitting the preceding analysis. Nevertheless, there are a few examples of analysis in Greek mathematical practice, as well as some definitions and discussions of it. Unfortunately, the discussions of analysis in our possession are from hellenistic times. But it would not be correct to discard completely this evidence as being only of marginal relevance to Greek mathematics proper. Some of the theory and procedure of hellenistic mathematicians has been traced back to fourth and fifth century Greek mathematics. Hellenistic practice or theory should not be automatically read into earlier texts, but a careful study of later developments may help towards a better understanding of the texts we are primarily interested in. The fullest account of analysis that has reached us is in Pappus (4th ct. A.D.): Analysis is the procedure which starts from the desired conclusion, taken as agreed, διὰ τῶν ἑξῆς ἀκολούθων to something agreed upon in synthesis. For in analysis we suppose (ὑποθέμενοι) the desired result to be already accomplished, and look for that from which it results, and then again for the prior proposition leading to that, until, by tracing our steps backwards in this way, we meet with something already known or holding the rank of a first principle. Such a method we call “analysis” as being a “solution backwards” (ἀνάπαλιν λύσιν). In synthesis, on the other hand, reversing the process, we take as already done the last step reached in the analysis; the steps that followed one another in the former process (τὰ ἑπόμενα ἐκεῖ) we here put into their natural order as leading on one to another, and put them together one after another; so finally we arrive at the establishment of the desired result. This we call synthesis.

Analysis is either theoretical or problematical: In the theoretical kind we assume the conclusion sought as existent and true; and then, διὰ τῶν ἑξῆς ἀκολούθων, taken as true and as hypothetically existing, advance as far as something admitted. Then if that admitted thing is true, the conclusion sought will be true also, and the demonstration will correspond, in the reverse order, to the analysis; but if we come upon something admitted that is false, the conclusion sought will also be false. In the problematical kind, we assume the propounded as if it were known; and next advance διὰ τῶν ἑξῆς ἀκολούθων, taken as true, as far as something admitted. Then if the admitted

Chapter i

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thing is possible – “given” as the mathematicians say – the construction propounded will be possible too, and once more the demonstration will correspond, in the reverse order, to the analysis; but if we come upon something admitted that is impossible, the problem also will be impossible.6

The first part of this passage seems, on first inspection, to substantiate Cornford’s view. In analysis we look for that from which the conclusion results, and then to the prior proposition leading to the new proposition we have found, and so we trace our steps backwards until we come upon something already proved or upon a first principle (which amounts to the same, for that which was already proved was proved ultimately from the first principles and can be traced back to them again). Analysis is a “solution backwards”. This account indeed agrees with several other briefer accounts of analysis: Themistius defines analysis as “assuming a true conclusion and then finding out the premisses by which it is inferred”.7 Alexander describes analysis as a method which takes the conclusion as a starting point, and proceeds upwards, through the assumptions necessary for the demonstration of the conclusions, ἐπὶ τὰς ἀρχάς.8 So Ammonius, quoting Geminus to the effect that “analysis is the discovery of the demonstration”.9 Philoponus says of it that it is the discovery of the premises from which the truth of the conclusion is inferred; the conclusion is assumed as true and the analysis goes on until one reaches something admitted and the principles of geometry. His example is the analysis of the proposition that the three angles of a triangle are equal to two right angles into its prior conditions, viz. the definition of a straight line.”10 So also Eustratius and Proclus.11

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6 Greek text ed. by Hultsch (1877), ii 634-636. More readily available in Thomas (1941), ii 596-598. The translation quoted is that of Cornford in his above-quoted article of 1932. 7 In An. post, i 12, 26.23 Wallies. 8 In An. pr. i 7.11 ff. Wallies. 9 In An. pr. i 5.28 ff. Busse, and cf. his example there. 10 In Phys. ii 9, 333.3 ff. Cf. in An. post, i 12, 162.22 ff., in An. pr. i 319.6 ff. Cf. Arist. Phys. 200al5. 11 Eustratius in An. post, ii 1, 3-13 ff. Hayduck. Proclus in Eucl. i 382, 422 Friedlein.

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Albinus [Alcinous] states that in analysis we have to hypothesize the thing sought and consider which are the things prior to it, and prove (ἀποδεικνύειν) these proceeding from the posterior to the prior, until we come upon the first and accepted, and then, starting from this, we should descend (κατελευσόμεθα) to the thing sought in the synthetic manner.12 On the other hand, as Robinson pointed out very clearly, the latter part of Pappus’ account does not square with Cornford’s interpretation: According to Pappus, if, in analysis, “we come upon something admitted that is false, the conclusion sought will also be false”. But this is true only if the analysis is strictly deductive, i.e. if all the propositions involved in it are convertible. For, were analysis non-deductive, as Cornford would have it, then it would be impossible to conclude the falsity of the demonstrand from the falsity of the premise that would lead to it. As Aristotle had already noted, false premises might entail true consequences. But if analysis is deductive and the proposition arrived at from the demonstrated (taken in the analysis as premise) is independently known to be false, then the demonstrand itself is false, for whatever implies a false proposition is itself false. This is actually a reductio ad absurdum. That Pappus should have described analysis in the way he did, as a process that traces propositions backwards to their antecedents, is, to Robinson’s mind, not incorrect but merely unexpected. As the premises and the conclusion are logically equivalent, one may look at them either way. Pappus, as Greek geometers in general, looks upon geometrical proofs from the point of view of synthesis, and from this point of view analysis is seen to be going backwards. This is why Pappus says that synthesis takes the steps of the proof in their “natural order”. At first sight, Robinson admits, this statement favours Cornford’s interpretation. “But – he goes on – this can be given a good sense on the accepted view of analysis. The order in which propositions are taken in analysis is ‘unnatural’, in spite of the fact that it gives a necessary connection, because you start with a proposition that you do not know to be true and treat it as if you did know it to be true. This unnaturalness is very clear ... at the beginning of the analysis. The

-------------------------------------------12

Alcinous [then known as ‘Albinus’] Didaskalikos v, in Hermann (1853), vi 157-8.

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proposition that is set out in one line as to be proved is stated in the very next line as if it were already known.”13 But, already at this stage, it must be said that Robinson does not succeed in explaining why is it the order of the steps in the analysis that is unnatural. Pappus says: “in synthesis, ... we put the steps ... into their natural order ... one after another”. But in Robinson’s explanation there is no unnaturalness in the order of the steps, but only an unnaturalness concerning the first step of the analysis, namely taking as true what is as yet unknown. Such a supposition can certainly be said to be unnatural, but one can hardly see how this could be interpreted as constituting an unnaturalness in the order of the steps.14 One phrase in the above translation of Pappus’ account of analysis was left untranslated: διὰ τῶν ἑξῆς ἀκολούθων. The translation of this phrase depends on what view the translator has of analysis. The “traditional” translation of this phrase is “through the consequences”. So Heath, Hankel, Duhamel, Zeuthen, Gerhardt, Hultsch, Thomas.15 But, says Cornford opposing them, this forces us to accept that “the premisses of a demonstration can be the consequences of the conclusion”. Yet Pappus says clearly that the sequence of steps is the same in both the analysis and the synthesis, only that their order is reversed; “upwards in Analysis, from the consequences to the premises implied in that consequence, and downwards in Synthesis, when the steps are reversed to frame the theorem or demonstrate the construction ‘in the natural (logical) order’. You cannot follow the same series of steps first one way, then the opposite way, and arrive at logical consequences in both directions.”16 Therefore Cornford translates διὰ τῶν ἑξῆς ἀκολούθων “through the succession of sequent steps”. The word for “consequences” would have been, according to him, τὰ συμβαίνοντα. He concedes that τὰ ἀκόλουθα alone could mean “logical consequences”

-------------------------------------------13

Robinson (1936), 473. Pappus refers separately to this peculiarity of analysis when he says that τὰ ἑξῆς ἀκόλουθα are hypothetically taken as true and existent. 15 Heath (1926), loc. cit. Hankel (1874), 137-150. Duhamel (1865), 66 f. Zeuthen (1902), 77 ff. Gerhardt (1871), ad loc. 16 Cornford (1932), 72 n. 1 (Cornford’s italics). 14

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too and that this was perhaps why Pappus wrote διὰ τῶν ἑξῆς ἀκολούθων and not merely διὰ τῶν ἀκολούθων.17 Proponents and defenders of the “traditional” interpretation of analysis do not see any difficulty in having consequences at both ends of the chain of reasoning. Provided the premises are logically equivalent to the conclusion, you could follow the deduction in either direction, and what was at first a consequence may, in reversing the order of deduction, become a premise. This seems to be the main argument in Robinson’s reply to Cornford.18 In short: The overall textual evidence tends to confirm Cornford’s interpretation, especially by the repeated emphasis put on the different directions of analysis and synthesis (backwards, upwards and downwards, natural order, etc.). Nevertheless, each text in itself can be interpreted as referring to what in practice was a deductive procedure. Moreover, Greek mathematical practice shows that analysis was concerned with convertible propositions, and arriving at logical consequences at both ends of the chain of reasoning was common-place then as it is today. On the other hand, sustaining the non-deductive view of analysis (i.e. Cornford’s view) would imply accusing Pappus of a grave error in logic (Cf. pp. 18-19, above). [4] In revising this discussion several important things should be kept in mind: Nowhere in the extant accounts of analysis is mention made of the requirement of logical equivalence or convertibility. There is, though, at least one passage in which Aristotle comments on analysis and convertibility: Sometimes, no doubt, it is impossible to reason (συλλογίσασθαί) from premisses predicating mere attributes (ἐκ τῶν εἰλημμένων): but sometimes it is possible, though the possibility is overlooked. If false premisses could never give true conclusions ‘resolution (τὸ ἀναλύειν) would be easy, for premisses and conclusion would in that case inevitably reciprocate. I might then argue

-------------------------------------------17

As in the interpolation at the beginning of Eucl. xiii. Gulley surprisingly thinks this argument to be valid. One would expect from his position that he would think otherwise. 18

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thus: let A be an existing fact; let the existence of A imply such and such facts actually known to me to exist, which we may call Β. I can now, since they reciprocate, infer A from B. Reciprocation of premisses and conclusion is more frequent in mathematics, because mathematics takes definitions, but never an accident for its premisses – a second characteristic distinguishing mathematical reasoning from dialectical disputations.19

Here Aristotle could seem to be giving a very accurate account of the “traditional” interpretation of analysis: If premises and conclusion reciprocate, then it is possible to deduce (συλλογίσασθαί) the premises from the conclusion, and then, again the conclusion from the premises. Ross remarks that on this interpretation it is difficult to account for “the fact that A is represented as standing for one fact (τούτου) and Β for more than one (ταδί).” If Aristotle is describing a syllogistical procedure, “there must be some reason for the use of the singular and the plural respectively.”20 Now, it should be noted that Aristotle is clearly implying in this passage that not all mathematical reasoning admits of reciprocation. Reciprocation is more frequent in mathematics, but is not always possible. The second thing to be pointed out is that, when premises and conclusion reciprocate, analysis is “easy”. But Aristotle does not say that analysis is possible only when this condition is met. On the contrary, he seems to be taking analysis as possible also when there is no reciprocation, but in this case it will be more difficult. A further point is that, in introducing this question, Aristotle seems to imply that, in general, analysis is not syllogistical, though it may sometimes be so. Ross in his commentary remarks that ἀναλύειν in this passage cannot mean “the analysis or the reversal of a given syllogism but the analysis of a problem, i.e. the discovery of the premisses which establish the truth of a conclusion which it is desired to prove”. If false premises could never give true conclusions, analysis would be easy: whatever implies the conclusion would also be implied by it, and supposing the truth

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19 An. post. 78a5-13. Ross, ad loc.: “Though a syllogism with two affirmative premisses in the second figure is always, so far as can be seen from the form (ὁρᾶται), fallacious, yet, if the premisses are true and the major premiss is convertible, the conclusion will be true.” Cf. Cherniss (1951), 417: “These passages [sc. the passage from An. post, and Proclus in Eucl. 253.16-254.5, quoted below, p. 53], in the absence of evidence to the contrary indicate strongly that Plato and the Academic mathematicians did not assume that convertibility must be a universal law of geometry.” 20 Ross, ad loc. Contra, see Gulley (1958), 10.

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of the conclusion, if the premises found by analysis were true, the conclusion would be true, and if not – the conclusion would be false as well. But this is not the case in dialectic, although it is often (but not always!) so in mathematics.21 Other mathematical writers too recognized that there are mathematical propositions which are not convertible. E.g. the following passage from Proclus: Here, however, it must be observed that many false and improper conversions take place. E.g. ‘every hexagonal number is triangular’; but it is not also true that ‘every triangular number is hexagonal’. And the reason of this is that the one is more general, the other more particular, and one alone is predicated universally of the other. But those things in which the predication is primary are also convertible in this same respect. And these observations, indeed, were not unknown to Menaechmus and Amphinomus and their fellow-mathematicians. Of convertible theorems some are usually called precedents and others converse. For when hypothesizing a certain genus they demonstrate one of its properties they call this a precedent theorem. But when, on the contrary, they make the hypothesis the property and the conclusion the genus, they denominate the theorem to which this happens converse. For instance, the theorem which says ‘every isosceles triangle has the angles at the base equal’ is a precedent. For what precedes by nature is assumed; I mean the genus itself, or the isosceles triangle. But that which says ‘every triangle possessing two equal angles, has likewise the sides subtending those equal angles equal, and is isosceles’ is a converse theorem. For it changes the subject and its accident, hypothesizing the latter, and from this showing the former.22

Indeed, even the nineteenth-century historians of mathematics who are normally quoted in support of the “traditional” view have clearly seen that the unconditional reciprocation presupposed by this interpretation is not always sufficiently warranted. Duhamel sums up his account of Greek analysis by stating that Pappus’ method of analysis is so insufficient, “qu’en partant de la dernière proposition, reconnue comme, vraie, il n’en déduira jamais la proposée si les propositions successives ne sont pas toutes réciproques les unes des autres; circonstance fortuite, et dont il ne fait pas mention”. 23

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21 Nevertheless Ross commends Robinson’s note in Mind 1936 as a “clear discussion of analysis in Greek geometry”. 22 In Eucl. i 253.16-254.20. It should be noted that a distinction is made between the two different kinds of proof, even when the propositions are convertible. 23 Duhamel (1865), 67.

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Hankel voices the same complaint: “... alle der Geometrie Hauptsätze allgemein umkehrbar sind ... Doch sind nicht alle Lehrsätze in den Formen, in deren man sie zu geben pflegt, unbedingt umkehrbar.”24 Zeuthen deals with this question extensively, and shows that Eucl. vi 27, 28 are made convertible only on account of the diorismos in 28.25 Now, Aristotle seems to be saying that syllogism is possible in certain cases, viz. when premises and conclusion reciprocate. But analysis is possible, so he implies, also when no syllogism is possible. If the propositions happen to reciprocate, then analysis is easier, but this is not a necessary condition of it. Analysis is not syllogism, though it may sometimes, as it often does in mathematical reasoning, take the form of syllogism. [5] If Robinson were right in stating that analysis is essentially deductive, then reductio ad absurdum would be a kind of analysis. This was, indeed, widely recognized by the proponents of the “traditional” interpretation, and not least by Robinson himself. “The reductio ad absurdum – he says, repeating a well-accepted doctrine – is a special case of the method of analysis.” And elsewhere, in a passage already quoted above: “you could then, if the consequence [of the analysis] was a true one, use it as a premiss of a proof of your demonstrand; and if it was a false one, you could use its contradictory as a disproof of the proposition you had hoped to establish.”26 The symmetry is perfect, but this is certainly not a rendering of Pappus’ account. Pappus says clearly, speaking of theoretical analysis, that “if that admitted thing is true, the conclusion sought will be true also, and the demonstration will correspond, in the reverse order, to the analysis; but if we come upon something admitted that is false, the conclusion sought will also be false.” And here he immediately goes on to speak of problematical analysis. There is nowhere any hint of using the contradictory of the proposition arrived at in the analysis as a premise for the synthesis. On the contrary, “positive” analysis is always followed

-------------------------------------------24

Hankel (1874), 139. Zeuthen (1902), 78 ff. 26 Robinson (1936), 465; (1953), 121. 25

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by synthesis; reductio ad absurdum never is. All other accounts of analysis agree on this point. What is more, this seems to be confirmed by Greek mathematical practice: everywhere analysis is followed by synthesis (or only the synthesis is presented); nowhere is reductio ad absurdum seen as leading to a positive proof.27 Proclus, in a much-abused passage, gives us the following classification: It must be known that all mathematical proofs (πίστεις) are either from the principles or to the principles, as Porphyry says somewhere. The proofs from the principles are themselves of two types: they either follow from common notions and only by force of what is self-evident; or from what has been previously shown. Proofs to the principles either establish or destroy them. Those which establish the principles are called analyses; and to these syntheses are opposed. For it is possible to proceed in good order (εὐτάκτως) from those principles to what is sought, and this is the synthesis. But those proofs which destroy the principles are called reductions to impossibility. For it is the business of this method to destroy some of the things agreed, and of the objects of investigation. And in this also there is a certain syllogism, though not the same as in analysis. For in reduction to impossibility, the construction is according to the second mode of hypothetical syllogism. E.g.: If in triangles possessing equal angles the sides subtending the equal angles are not equal, the whole is equal to its part; but this is impossible. Therefore, in triangles possessing two equal angles, the sides subtending the equal angles are equal.28

The classification described in this passage is as follows:

/ from the principles

/

from what is self-evident

mathematical proofs

\

from what has been demonstrated

\ to the principles

/

analysis

\

reductio ad absurdum

It is immediately clear that at least in this classification reductio ad absurdum is coordinated to analysis and not a kind of it. In reductio ad

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27 There are more than eighty theorems in Euclid’s Elements proved by reductio ad absurdum (some of them involve two or more reductiones), and thirty theorems in Archimedes. None of them is accompanied by a positive proof. 28 In Eucl. i 255.8-256.8.

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absurdum there is syllogism, as there may be in analysis, but Proclus states expressly that the syllogism was not regarded as of the same kind. Similarly, in 211.12 ff., Proclus cites three methods for the solution of problems: (i) analysis to the principles, (ii) diairesis, and (iii) reductio ad absurdum, “which does not prove (δεικνῦσα) the thing sought in itself, but refutes its contradictory and finds the truth by accident”. [6] Still the question remains, if analysis may be syllogistical, and it seems that it could be so in a great many cases, why is the subsequent synthesis necessary? In the case that all geometrical propositions involved in the chain of implications are unconditionally equivalent, or can easily be made equivalent, then what is the point of going again through the whole series of propositions in the synthesis? If the series of propositions is one of mutual implications, then the analysis is as good a proof as the synthesis, and the repetition, in inverse order, of the whole process is superfluous. Just the same, the synthesis is expressly demanded by the theorists and laboriously carried out by the mathematicians. Hankel thought that this duplication of labour is to be explained by the fact that the Greeks “durch größte Vorsicht und völlige logische Strenge eine unangreifbare Gewissheit zu gewinnen suchten.”29 So Heath states that “in practice the Greeks secured what was wanted by always insisting on the analysis being confirmed by subsequent synthesis, that is, they laboriously worked backwards the whole way from Κ to A reversing the order of the analysis, which process would undoubtedly bring to light any flaw which had crept into the argument through the accidental neglect of the necessary precautions”.30 Robinson is more explicit about the nature of the precautions in question: “if in your analysis you should use any inconvertible propositions, you will discover that you have done so when you try to make your synthesis.”31

-------------------------------------------29 30

P. 145. Contra, see Klein (1968), 163. Heath (1926), 140.

31 Robinson (1936), 465. – Convertibility refers to the calculus of classes, not to the calculus of propositions. But Aristotelian syllogistic and the geometrical theory based on it seem to have restricted themselves mainly to relations of implication and equivalence between propositions that express relations between classes (or predicates). This means that, for example, for a syllogism of the first figure to be reciprocable, i.e. for its premises to be logically equivalent to its conclusion, its premises have to be convertible: [(S⊂Μ) · (Μ⊂P)] → (S⊂P); but {[(S⊂Μ) ·

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But Pappus does not imply anywhere that the synthesis is a mere confirmatory device. He seems to regard it as an integral part of the geometrical procedure, perhaps the most important part of it: it is the synthesis that is called “demonstration”, and through it alone is the desired result “established”. As a matter of fact, nowhere is analysis called “demonstration” (ἀπόδειξις).32 Proclus in 255.8 ff. uses the general word πίστεις for designating both mathematical proofs from the principles and to the principles (cf. αὐτόπιστος = “self-evident”, not “self-demonstrated”). Very characteristically, synthesis is insisted upon even when the propositions are clearly convertible, but analysis is most readily discarded also in cases when a diorismos is brought in so as to assure convertibility. On the “traditional” view, however, synthesis is to be expected especially when the propositions are only conditionally convertible, i.e. when there is a diorismos; but such a tendency is not apparent in the extant texts. As Duhamel remarks, the synthesis is valuable if some of the propositions involved are not convertible; but if the propositions involved happen to be unconditionally convertible, then there is nothing in the synthesis that would make it logically stronger than the analysis. Indeed, if synthesis and analysis were logically equivalent, then, as the synthesis alone can be presented as a sufficient demonstration of a theorem (or of the solution of a problem), so could the analysis be presented alone as a sufficient demonstration (or solution) of it. But this seems never to be the case in practice, and theorists always insist on supplementing analysis by synthesis. On the other hand, there seems to be little dispute over the fact that, in most if not all cases, Greek mathematical practice can be rendered fairly accurately by supposing analysis to be deductive. Heath, Robinson and others have shown this to be possible and, in fact, as most mathe-

-------------------------------------------(Μ⊂P)] ↔ (S⊂P)} ↔ {[(S⊂Μ) ↔ (Μ⊂S)] · [(Μ⊂P) ↔ (P⊂M)]}; and then of course (S⊂P) ↔ (P⊂S). The reason I prefer, where possible, to use the terminology of the calculus of propositions is that it will prove more useful for the understanding of Plato’s own method of hypothesis. However, I am not implying that Plato’s method was primarily connected with any sort of propositional calculus. 32 Albinus [Alcinous] (quoted above, p. 49) seems to be an exception. But he too insists in having the whole of the synthesis worked out, and says that the premise to be “proved” from the consequence has first to be “intuited” (θεωρεῖν).

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matical propositions are convertible,33 mathematical analysis could be thought to be essentially syllogistical. [7] To my mind, there is a measure of danger in looking at the mathematicians’ practice in order to find out what the Greeks meant by analysis. Even supposing they actually did what we think them to have done, this still does not instruct us about what they thought they were doing. What, according to our philosophy of mathematics (or one of our philosophies of mathematics), looks like one thing, could quite conceivably have looked very differently within a different conceptual frame. It is here that the ancient theorists of mathematics gain in importance. Our reconstruction of mathematical practice may be, to a great extent, correct, as far as the actual procedure goes; but for an understanding of the Greeks’ own interpretation of what they were doing we must look for what they themselves had to say on this subject. The only more so, as after Aristotle and probably by his influence, mathematics, as other sciences, became relatively detached from philosophy. The mathematics of the Pythagoreans and of Plato were eminently philosophical. But, as Stenzel has remarked, the great mathematicians of the classical period of Greek mathematics did not think it part of their business to philosophize about mathematics.34 Moreover, hellenistic mathematics were clearly characterized by a strong tendency – whose roots could perhaps be traced as far back as to the Sophists – to free themselves from philosophy and philosophical assumptions. But this process was slow. If H.D.P. Lee is right, Euclid may have abandoned Aristotle’s term “hypothesis” because he did not want to claim that all his “postulates” were necessarily indemonstrable and self-evident, especially the fifth and its preliminary, the fourth.35 But, in any case, the three first of Euclid’s postulates certainly conform to Aristotle’s demands regarding geometrical hypotheses. In fact, it seems that only Archimedes can be credited with a somewhat clearer view of a mathematical science divorced from phi-

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33 Problems can be made convertible with the aid of a diorismos. See, e.g., Euclid vi 28 and Zeuthen, 78 ff. 34 Stenzel (1933), 320-1. 35 Lee (1935).

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losophical premises, as a self-subsisting hypothetic-deductive system. Archimedes seems to have been the first to make his assumptions (λαμβανόμενα) in order that he might prove his theorems. In the introduction to his Quadrature of the Parabola he does not claim for the now so-called Axiom of Archimedes any privileged ontological or epistemological status, but claims that its assumption is warranted only by the results whose deduction it enables: For it is here shown that every segment bounded by a straight line and a section of a right-angled cone [a parabola] is four-thirds of the triangle which has the same base and equal height with the segment, and for the demonstration of this property the following lemma is assumed: that the excess by which the greater of (two) unequal areas exceeds the less can, by being added to itself, be made to exceed any given finite area. The earlier geometers have also used this lemma ... [here comes a list of theorems that had been proved by assuming this lemma or some other “similar to the aforesaid”.] And in the result, each of the aforesaid theorems has been accepted no less than those proved without the lemma. As therefore my work now published has satisfied the same test as the propositions referred to, I have written out the proof and send it to you, first as investigated by means of mechanics, and afterwards too as demonstrated by geometry. 36

Archimedes’ lemma is anything but self-evident. Nor does Archimedes claim it is. He assumes it on purely “pragmatic” grounds: the theorems in the demonstration of which it will be used can be seen to be true “by means of mechanics”, and this is enough justification for assuming the lemma. There is here no talk or assumption of a philosophical basis or of a self-asserting intuition. “The investigation by means of mechanics” does not prove the theorem. This is made even clearer in the introduction and in the concluding remark to the first proposition of the Method. Mechanical methods give “a sort of indication that the conclusion is true”. But once we “suspect” (ὑπονοοῦντες) the conclusion to be true (for we “know” it to be true only after we have demonstrated it from geometrical premises), we are justified in assuming lemmata that will enable us to demonstrate it. And these lemmata will be accepted solely on the force of their geometrical expediency.37

-------------------------------------------36

rals.

Heath (1912), 233-4. Cf. Introductions to On the Sphere and the Cylinder and to On Spi-

37 Cf. Dehn (1937-8), 19-22, who finds evidence that Archimedes’ axiom was actually disputed.

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But is not Aristotle’s logic such an hypothetic-deductive system? Patzig’s concluding remarks on Aristotle’s syllogistic are a good example of the bent of mind common among modern interpreters: “Keineswegs ist die aristotelische Syllogistik eine ‘philosophische’ Logik in dem Sinn, daß zu ihrem Verständniß gewisse philosophische Einsichten notig waren, oder die Wahrheit ihrer Satze von bestimmten Voraussehungen abhinge, die der Ontologie oder Metaphysik zugerechnet werden müssen ... Die aristotelische Syllogistik ist also die Theorie eines speziellen Gebiets der zweistelligen Relationenlogik.”38 In a certain sense this is true. Patzig has shown that Aristotle’ syllogistic is formalized enough to admit of being looked at somewhat independently of its philosophical context. Lukasiewicz, Bochenski and Patzig have succeeded in expressing accurately enough Aristotle’s syllogistic in modern formal terms.39 But they have done so at the price of neglecting the differences arising from the material content of the premises – which for Aristotle could be sometimes of great importance, if not in his syllogistic, at least in his logic, the whole of what he referred to as τὰ ἀναλυτικά. E.g., Patzig quotes An. pr. A 4. 25b30, to the effect that demonstration (ἀπόδειξις) is a special kind of syllogism,40 but he goes on to identify demonstration and syllogism.41 True, from the purely formal point of view, the distinction between a demonstrative and non-demonstrative syllogism is superfluous, and perhaps this is why this distinction is not prominent in the Analytica Priora. But the fact that Aristotle’s syllogistic can, in itself, be presented in this manner, must not be confounded with the claim that it is essentially independent of the wider philosophical context of Aristotle’s system.42

-------------------------------------------38

Patzig (1959), 198. But see n. 42 below. Lukasiewicz (1951); Bochenski (1951). 40 P. 137. 41 See, e.g., 143 n. 1: “Der Ausdruck δεῖξις steht also bei Aristoteles zunächst als das Allgemeine der in vollständiger Disjunktion das Gebiet der δεῖξις ausfüllenden Arten, ἀπόδειξις und ἐπαγωγή , wobei wegen der aristotelischen Gleichsetzung von ἀπόδειξις mit συλλογισμός τις fur ἀπόδειξις auch συλλογισμός eintreten konnte.” The unconditional substitution is unwarranted, even though Aristotle does not always specify the conditions under which συλλογισμός may be substituted for ἀπόδειξις. 42 In the preface to the second edition of his work, which reached me after the above text was written, Patzig writes: “It has been shown that the presentation of Aristotle’s syllogistic with the help of Russell’s ‘material implication’ ... and the logical quantifiers, (x) and (3x), 39

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The interpretation of Greek mathematical analysis seems to be a similar case. The concept of convertibility of propositions which leads to the view that consequences can be obtained in the chain of propositions no matter in which direction we deduce them from one another is based on a notion of entailment which disregards epistemic asymmetries:43 p entails q if and only if q is deducible from p.44 The consideration does not arise of course – although for Aristotle and his followers it was of great importance – whether p is “prior to” or “more knowable than” q. Now, to a great extent, the procedures of Greek mathematicians can be interpreted or reformulated as being of such a type, and so can indeed Aristotle’s syllogistic. But an attempt to present the whole of Aristotle’s logic as being a purely hypothetic-deductive, epistemologically neutral system is bound to leave many of its features without explanation in the wider context. And the same is true of Greek mathematical practice. It was already suggested that a reformulation such as that proposed by Patzig cannot cope with the difference between demonstrative and non-demonstrative syllogism. This difference may be unimportant from the formal point of view, but Aristotle stresses it several times: For – he says – though you may reason from true premisses without demonstrating, yet if your premisses are necessary you will assuredly demonstrate.45

-------------------------------------------allows most but not all the peculiarities of Aristotle’s system to be represented. Of the formal devices developed in the literature on mathematical logic, Lorenzen’s ‘logical implication’ now seems to me to come nearest to Aristotle’s ‘if ... then ...’ connective” (p. xv). “... My criticism of the nineteenth century interpreters who based Aristotle’s syllogistic on his metaphysics may easily be taken to imply that these two pillars of philosophy stand completely unrelated in Aristotle’s works. I never intended to advance this view, which is, historically speaking, evidently false; it is quite different from the thesis which I believe I have established: that the validity of the propositions in Aristotle’s syllogistic can, neither in fact nor in Aristotle’s opinion, be thought dependent on the truth of certain ontological propositions. It is consistent with this view both that Aristotle’s presentation of his syllogistic is unconsciously influenced in many ways by his ontological predilections, and also that the marrow of Aristotle’s ontology contains views which mirror his logical tenets” (pp. xvi-xvii). 43 I am indebted to Prof. B. Williams for this term. 44 This notion of entailment as defined by Moore should be sufficient: its exact relation to Lewis’ strict implication and other stronger connectives is irrelevant to our present purposes. 45 An. post. i 6. 74bl6. That this view is not confined to the An. post. is, I think, sufficiently shown by An. pr. I 4. 25b30: “Syllogism should be discussed before demonstration, because syllogism is the more general: the demonstration is a sort of syllogim, but not every syllogism

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Elsewhere in the Analytica Posteriora, Aristotle states the wellknown requisites of a demonstration, i.e. “a syllogism productive of scientific knowledge”: (i) The premises of demonstrated knowledge must be true; for what is not cannot be known. (ii) They must be primary and indemonstrable; otherwise they would themselves require demonstration in order to be known. (iii) The premises must be the causes (αἰτίαι) of the conclusion, since to possess scientific knowledge of a thing is to know its causes. (iv) They must be prior to the conclusion, meaning by this that they must be prior per se, not prior in relation to us. (v) They must be more known, i.e. they must be more intelligible per se. “Syllogism there may indeed be without these conditions, but such syllogism, not being productive of scientific knowledge, will not be demonstration.”46 Every demonstration is thus syllogistic,47 but not every syllogism is a demonstration. Demonstration is syllogism which, apart from being formally correct, has some further material specifications. So, for Aristotle, a syllogism may be valid, and moreover sound (its premises may be true), and nevertheless such a syllogism may fail to be a demonstration. In much the same way, Aristotle distinguishes between syllogism that proves the reasoned fact and syllogism that proves only the fact. A proof that planets are near because they do not twinkle is valid. But this syllogism, says Aristotle, proves not the reasoned fact but only the fact; for they are not near because they do not twinkle, but, because they are near, they do not twinkle.48 Here we have an epistemic asymmetry: one direction of inference gives us knowledge in its proper sense, while the oppo-

-------------------------------------------is a demonstration.” – On the bearing of this passage on the relative date of the Analytics, see Ross (1949), 9 ff. 46 i 2. For a detailed treatment of the conditions of demonstrative science in Aristotle, see Ross (1949), Introduction, ch. vi. See also von Fritz (1955), 23-4. 47 Cf. Patzig (1959), 142-4, and see there his remarks on the difficulties and exceptions to this affirmation. 48 An.post. i 13.

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site direction gives us only an inferior kind of knowledge.49 But science means knowledge of the reasons, not knowledge of the fact alone. In this respect, Aristotle’s Analytics as a whole (being wider than his formal syllogistic) present us with more than a hypothetic-deductive system of inferences. It seems that Aristotle had considered some possible system that would be merely coherent. In An. post. i 3, he considers a system in which there are no primary truths, for all truths are demonstrable, provided demonstration may be circular and reciprocal. But Aristotle rejects such a possibility, on the grounds that it obliterates the distinction between demonstration proper and non-demonstrative syllogism. He adds further that such a circular and reciprocal demonstration is possible only if all propositions are convertible. There seems, therefore, to be a certain difference between Aristotle’s epistemological approach to mathematical knowledge and the approach of the hellenistic mathematicians, best exemplified by Archimedes. But this difference, although useful in order to stress the shift that has taken place in mathematical theorizing from Aristotle to the Principia Mathematica, should not be over-emphasized. For one thing, Archimedes still regards synthesis as the proper demonstration of a proposition, and the few examples of analysis in his extant works are dutifully accompanied by their respective syntheses. Be it as it may, the idea of a hypothetic-deductive system, self-sufficient and claiming to demonstrate out of its own assumptions seems to have developed on the eve of hellenistic times, not without Aristotelian inspiration, as the Analytica Priora bear witness. But Archimedes, or any other contemporary, cannot be considered in this respect a clear watershed in the history of mathematics. Leaving aside the question of Archimedes’ and other mathematicians’ views on the philosophy of mathematics, it is at any rate clear that the “philosophical” trend in mathematical theorizing was still to be felt for a very long time, especially within the sphere of neo-Platonic influence. Proclus, for example, is very clear: No science demonstrates its own principles, nor gives account of them, but regards them as self-evident, and they are to it more manifest than what follows

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It should be noted that the syllogism in question admits of reciprocation.

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from them. These [sc. the principles] science knows by themselves; but what comes after them (τὰ δε μετὰ ταῦτα) by means of these ... And if one confounds principles and what comes from the principles into one and the same, one disturbs the whole order of knowledge,50 and mixes things which do not belong together; for a principle and what comes from it are naturally distinct from each other.51

Proclus acknowledges Archimedes’ attempt to free mathematical assumptions from their philosophical ballast, but he seems to be rather critical of it.52 When Proclus comes to describe the method which Plato allegedly handed down to Leodamas, he says that this was a method which analyses or reduces the thing sought to its arche In view of the “natural distinction” between principles and consequences, Proclus could never have implied in this phrase that an arche could be a consequence. Also here Proclus seems to view reductio ad absurdum as a method distinct from analysis, and not as a particular case of it. And he adds, furthermore, that this method “does not of itself show the thing sought, but refutes its opposite and discovers the truth by accident”. So Aristotle too preferred affirmative to negative proofs.53 Some of his arguments are mainly methodical;54 but some of them certainly are not: “the affirmative proposition is prior and better known than the negative”, he says.55 [8] It seems, then, that for Aristotle, as for the Greek mathematicians that came after him, the way up and the way down could not be regarded without much ado as the same way, even if mathematical practice would admit of such an interpretation. For them, there is a clear differentiation between the premises of a demonstration and its conclusion. A syllogism is a demonstration if and only if its premises are true and primary, are the causes of the conclusion, are prior to and better known than it.

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Cf. Phaedo 100E. In Eucl. i 75.14-26. 52 Ιn Eucl. i 181.16 ff. 53 An.post. i 25. 54 An.post. 86a33-b30. 55 b32 ff. That a negative proof may not be unconditionally regarded as a demonstration is, I think, witnessed by the intuitionist approach to mathematics. Cf., e.g., Beth (1959), 413 ff. I am not suggesting that Aristotle was an intuitionist after the Brouwerian manner, but neither must it be assumed that he was an orthodox logicist. 51

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But its premises can meet these qualifications only if the syllogism goes the right way – from the primary to the derivative, from the causes to the effect, from the prior and better known per se to the naturally posterior and less known. Otherwise, the syllogism can be formally valid and, if its premises are true, even sound; but it will not be demonstrative and conductive to episteme. And geometry, being the prototype of scientific knowledge, would certainly conform to these norms. On these assumptions, analysis, even when it is a valid syllogism, is not a demonstration. Analysis goes the wrong way and may give us, as Aristotle put it, knowledge of the fact, but it cannot give us knowledge of the reasoned fact. Therefore, once the premises of the argument have been discovered by analysis, it is necessary to demonstrate, i.e. to state the argument in its correct, natural order, from its natural premises to its natural conclusion. The synthesis is not only a precautionary device – it is the proof of the proposition. Synthesis may come without analysis, but analysis cannot come without synthesis, for, as Proclus implies, analysis is merely heuristic; synthesis, on the other hand, is demonstrative. If this is true, then Cornford should be corrected in one point, but he was right in what I believe was his main contention in saying that “you cannot follow the same series of steps first one way, then the opposite way and arrive at logical consequences in both directions” (his italics). If by “logical consequences” one means consequences in a system which disregards epistemic asymmetries, then, of course, you can arrive at logical consequences in both directions, provided the implications between your propositions are mutual. But Greek geometry was not indifferent to epistemic asymmetries.56 From what we could call today a purely logical or formal point of view, analysis and synthesis alike can be expressed (almost always) by a series of logical equivalences; nevertheless, the Greeks seemed to think that one end of the series was naturally prior and more intelligible, and per se the cause of the other end. In analysis we “trace our steps backwards”, looking for the proposition that is prior to the proposition given. And this proposition that is

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56 Cf. Arist. Phys. 200al5 ff.: “Since a straight line is what it is, it is necessary that the angles of a triangle should equal two right angles. But not conversely; though if the angles are not equal to two right angles, then the straight line is not what it is either” (tr. Hardie and Gaye).

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sought is prior to the proposition given, even if it is unconditionally logically equivalent to it. For there is a natural order in being, and logic and mathematics must comply with this order. Analysis is a “solution backwards”, going from what is a consequence per se to what is a cause per se. In synthesis, on the other hand, the steps are put in their natural order, and only in synthesis – so says Pappus expressly – do we arrive at the establishment of the desired result. For only synthesis is demonstrative. Synthesis is not formally stronger; in dealing with series of logical equivalences, there is no advantage to synthesis over analysis. The advantage is of another kind, namely the advantage of the “natural order” over the “solution backwards”. The natural order is the order from the more primary and, therefore, truer, to the derivative and less true. Pappus and the others make no mention of convertibility because convertibility is – from the theoretical point of view – irrelevant. It can make things easier for the mathematician, but it is not of the nature of analysis that the propositions involved in it are convertible, though they may be so, and, in most cases in mathematics, they in fact are. There remains one problem to be solved. If analysis is not primarily deductive, then why does Pappus say that “if you come upon something admitted that is false, the conclusion sought will also be false”? I suggest that Pappus was misled by the fact that propositions in mathematics are normally convertible and that, in practice, analysis would be, in a great many cases, deductive, although the theory behind this procedure would still carefully distinguish between the way up and the way down. I cannot, therefore, entirely agree with Gulley that these are “two different accounts of analysis”. If the above interpretation is right, mathematical analysis was not different, in principle, from philosophical analysis. Both were a divination of the premises supporting a given conclusion. This seems to be clear also from Eth. Nic. iii 3. 1112b.15 ff.: There geometrical analysis is spoken of not only as of the same kind as the analysis implied in practical deliberation, but also no mention is made of convertibility as essential to it. In practice, mathematical analysis, dealing normally with a series of equivalences, could be felt – sometimes – to be a special case of philosophical analysis. But the theory must have lagged behind the practice for quite a long while.

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Chapter ii: The Meno [1] The first mention of the method of hypothesis in Plato occurs in the Meno. Although the reference to it is short and by no means without its problems, it is clear from Plato’s words that he is now introducing a new method of philosophical inquiry, avowedly borrowed from the mathematicians. This method is subsequently used in the dialogue although without much apparent success. Nevertheless, the use of the method of hypothesis – and in a much wider scale than is usually assumed – marks off this from the earlier aporetic dialogues. The passage in question is as follows: ... allow me, in considering whether or not it [sc. excellence] can be taught, to make use of a hypothesis – the sort of thing, I mean, that the geometers often use in their inquiries. When they are asked, for example, about a given area, whether it is possible for this area to be inscribed as a triangle in a given circle, they will probably reply: Ί don’t know yet whether it fulfils the conditions, but I think I have a hypothesis which will help us in the matter. It is this. If the area is such that, when one has applied it to the given line of the circle, it is deficient by another rectangle similar to the one which is applied, then, I should say, one result follows; if not, the result is different. If you ask me, then, about the inscription of the figure in the circle – whether it is possible or not – I am ready to answer you in this hypothetical way’ (86E4-87B2, tr. Guthrie).

It is now widely agreed that the exact nature of the problem is not immediately relevant to the understanding either of the hypothetical procedure itself or its application in the dialogue. Bluck, in the Appendix to his edition of the Meno, offers a comprehensive summary of the attempted interpretations.1

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1 Bluck (1961a), 449 and 458, seems to consider it a drawback of the theories proposed by Heath and Cook-Wilson and by Farquharson that according to them the geometer would not have been in a position to ascertain whether the hypothesis is fulfilled or not. But, without committing myself to these theories, I should point out that, far from being a disadvantage, this feature shows even more clearly the nature of the hypothetical method as it is subsequently

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Otherwise, the text should be clear, and it will suffice to point out the main features of the method described in the above passage: A question is asked about the possibility of making a certain construction; in later terminology, a ‘problem’ is proposed: to inscribe a certain area as a triangle into a given circle. But the area is not given (presumably in respect of its size). In the terminology of the Meno, we are not given its τί. Nevertheless, we are asked about its ποίον, i.e., whether this (unknown) area is such that it can be inscribed in a given circle. The reasoning is patently regressive: Suppose the construction done. Now ask: What conditions must be satisfied in order that the construction be possible? The geometer’s answer is: If such and such conditions are fulfilled, then the construction is possible, and if not, “something else follows”. The starting point of the hypothetical procedure is the ‘sought’. Converting this ‘sought’ into ‘given’, the geometer sets himself to find the premises that would lead to it. 2 [2] This procedure is to be compared to Hippocrates of Chios’ solution of the problem of the quadrature of the lunes.3 His solution comprised five steps: (1) enunciation of the problem; (2) assumption as a principle of a proposition A, “useful for his purpose” (ἀρχὴν μὲν οὖν ἐποιήσατο καὶ πρῶτον ἔθετο τῶν πρὸς αὐτοὺς χρησίμων): “similar segments of circles have the same ratio to one another as the squares on their bases”; (3) demonstration of A by means of another proposition B: “squares on the diameters have the same ratio as the circles”; (4) demonstration of B;

-------------------------------------------used in the dialogue. As in the mathematical example, the problem of whether arete is teachable is reduced to another problem, that of whether virtue is knowledge. But, as it turns out, Socrates and Meno were not in a position to corroborate this hypothesis. 2 Robinson’s interpretation of this passage is based on his views on geometrical analysis. I have dealt with them above. Robinson (1953), 121; Bluck (1961a), 82-3. 3 Simpl. in Phys. 60 ff. Diels = Eudemus, fr. 140 Wehrli. Cf. Heath (1921), i 183-200; Cambiano (1967), 128-30.

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(3) distinction and resolution of four cases of the problem, by means of A. Although this procedure is not identical to what was later called analysis, it shares with it one important feature: Hippocrates does not demonstrate Β and then A, but, on the contrary, he demonstrates A by showing it to be dependent on B, in other words by showing the condition under which A is demonstrable. (It is worth noting, by the way, that Hippocrates also uses a few other propositions which apparently were not considered as “principles”.) The main characteristic of Hippocrates’ method seems therefore to have been the reduction of a problem or a proposition to be demonstrated or considered to be more easily demonstrable. This is especially apparent in his famous reduction of the problem of doubling the cube to that of finding two mean proportionals in continued proportion between two straight lines.4 [3] The procedure of 86E ff. has been often thought to be an early case of diorismos, namely, “the determination of the conditions or limits of the possibility of a solution of the problem, whether in its original form or in the form to which it is reduced”.5 It is perhaps worthwhile bringing two textbook examples in order to show how close they are to our passage:6 Euclid i 22 – Enunciation: From three straight lines which are equal to three given straight lines to construct a triangle. Diorismos (limiting condition): Thus (δεῖ δὴ) two of the straight lines taken together in any manner must be greater than the remaining one. Euclid vi 28 – Enunciation: To a given straight line to apply a parallelogram equal to a given rectilineal figure and falling short by a parallelogramic figure similar to a given one. Diorismos: Thus the given rectilineal figure must not be greater than that described on half the line and similar to the defect.

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Heath (1921), i 200-1. Heath (1921), i 303. Proclus, in Eucl. i 202: a criterion as to “whether what is sought is impossible or possible, and how far it is practicable and in how many ways”. Cf. further Cornford (1952), 64; Proclus ibid. 66. 6 Heath (1926), 130-1. 5

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Some commentators even found enough similarity between the last proposition and Meno 86Eff. to submit an interpretation of our problem as referring essentially to Euclid’s.7 Proclus and Diogenes Laertius8 somehow connect the discovery of the diorismos with Plato, although it seems that it is not actually attributed to him. Even so, it is not without significance that some such procedure should have aroused Plato’s interest. Another, more compressed, definition of diorismos is quoted by Proclus:9 “τίνος ὄντος τί ἐστίν”. Though far less accurate than the other formulations, it is probably closer to Plato’s conception of the procedure. On the other hand, some commentators10 would rather see here a case of reduction (ἀπαγωγή), basing themselves on An. pr. 69a20 ff., which seems to refer to our passage. Bluck notes that “one did not, so far as we can tell from the available evidence, make a series of διορισμοί”, so that the reduction of the question whether virtue is teachable to the (as yet open) question whether virtue is knowledge is a case of apagoge and not of diorismos.11 Elsewhere he concedes that diorismos is “closely associated with ἀπαγωγή”, but he does not show in what this association consists.12 This relationship, however, seems to be reasonably clear. The diorismos always states a limiting condition which is clear from a preceding theorem, or which is discovered in the course of the preceding analysis. So, Euclid i 22 has its diorismos from i 20, and vi 28, from vi 27. The most important characteristic of the diorismos in this context is that it is a feature of a synthetic system: it is deduced from preceding theorems and is introduced in order to limit the problem to cases in which it has a solution. As opposed to this, the apagoge is an analytical procedure: supposing the problem to have a solution, the (necessary) conditions for the solution are sought, and – if necessary – the conditions of these conditions, and so on. Strictly speaking, in a thoroughly analytical proce-

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Notably Cook-Wilson’s interpretation. See above, n. 1. So Gueroult (1935). Proclus in Eucl. i 211.18-23; Diog. Laert. iii 24-9. 9 Op. cit. 80.15-20. 10 See Bluck (1961a), 81 n. 2, 97. 11 Ibid., 81. 12 Ibid., 84. 8

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dure, a diorismos would be impossible, in as much as it is always proved from a preceding (prior) theorem. In other words, the diorismos is a synthetic device;13 the apagoge – in one of its uses – is its analytical counterpart. A fine example of the relationship between the apagoge and diorismos can be seen in Archimedes de sph. et cyl. ii 7: “From a given sphere to cut off a segment by a plane so that the segment may have a given ratio to the cone which has the same base as the segment and equal height.” Supposing the problem solved, the analysis brings us to the diorismos: Thus (δεῖ ἄρα), in order that a solution may be possible, it is a necessary condition that the given ratio must be greater than 3:2. And the synthesis follows. The difference seems therefore to be a difference of presentation, or rather of method. It is true that the canonical presentation of geometry was not yet established by Plato’s time, but it is also true that Plato was stating precisely the difference between a synthetic and an analytical approach. The difference between diorismos and apagoge may be small, but in this context it should be clear. If Plato was introducing analysis, then his procedure was apagoge and not diorismos (and this can be independently confirmed by comparing his procedure with Archimedes’ two complementary procedures in de sph. et cyl. quoted above). It should be noted, however, that the diorismos states a necessary condition of the solvability of the problem. As we shall see later, this is not always true of Plato’s hypotheses. [4] Now Socrates is ready to tackle the problem of arete. He says: And the same with regard to our excellence; as we know neither what it is nor how it is, let us inquire about it,14 supposing a hypothesis, whether it is teachable or not (87B2-4).

The original problem was: Is arete teachable? It is now reduced to the following problem:

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13 And one that can be done away with altogether. Cf. Arch. de sph. et cyl. ii 4, 214.16-20 Heiberg. 14 Understanding αὐτό as object of σκοπῶμεν , with Bluck against Friedländer.

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Problem II: Which of the things (ὄντα) in the soul is arete to be so that it shall be teachable (and if not – not teachable)? The Greek is clearer than the English: Εἰ ποῖόν τί ἐστιν τῶν περὶ τὴν ψυχὴν ὄντων ἀρετή, διδακτὸν ἂν εἴη ἢ οὐ διδακτόν; This is a question within the protasis of a conditional clause. It might be reformulated like this: If arete is x arete is teachable and if it is not x it is not teachable; and x is a thing (ὄν) in the soul. From this interesting formulation it is clear that Socrates is asking for the antecedent of the implication.15 The ‘sought’ appears in the protasis of the conditional clause. What is sought is therefore the premise from which it should follow that arete is teachable. In other words, arete is assumed as teachable and it is asked what would entail this proposition (“arete is teachable”) assumed as true.16 The parallelism to the mathematical example is clear: Suppose the construction possible, i.e. arete to be teachable, and ask for the conditions of the solution of the problem. It is interesting to note that the other example17 of a question within a conditional clause is Hipp. Ma. 288A εἰ τί ἐστιν αὐτὸ τὸ καλόν, ταὖτ’ ἂν εἴη καλά; Here too we have an analytical procedure, but more akin to that in Phaedo’s discussion of ideas as causes. The solution to Problem II: If (and only if) arete is a knowledge (ἐπιστήμη τις), it is clear that it shall be teachable (87B6, C5). The whole implication is proved by the assumption of the lemma: Nothing is teachable but knowledge (C2). Now it remains to inquire (δεῖ σκέψασθαι) whether arete is knowledge. This is Problem III. And this is done by assuming Hypothesis II: arete is good. The reduction is: If all good is knowledge and arete is good, then arete is knowledge.

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15 The implication is of course mutual, and Stahl thought this to be an essential feature of the method of hypothesis. But in fact, just as convertibility was not essential in geometrical analysis (ch. i, above), so was mutual implication too only accidental to Plato’s procedure, as Stahl himself had to recognize. 16 This shows that Robinson’s interpretation, (1953), 121, even if logically possible in this case, runs counter to the text. Cf. also Bluck (1961a), 77 n. 2. 17 Adduced by Stallbaum.

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The first part of the protasis is proved at length; the second part is agreed upon. Therefore, arete is knowledge, and, therefore teachable. In short: Assume that arete is teachable. The condition of the truth of this assumption is that arete be knowledge. Assume, therefore, that arete is knowledge. The conditions of this assumption being true are: (a) that arete is good; (b) that there is no good without knowledge. (b) is allegedly proved – mistakenly, as it turns out. (a) is assumed and is not retracted up to the end of the dialogue. The ‘synthetic’ presentation would be as follows: Hyp. II Lemma II Thus Hyp. I Lemma I Thus

arete is good nothing is good without knowledge arete is knowledge only knowledge is teachable arete is teachable.

I have abridged the argument in order to lay bare its main lines. The omitted steps are concerned chiefly with establishing Lemma II. To my mind, this proposition has been given undue prominence, even if one allows for the fact that Socrates himself blames it as being the weak link in the argument. It is important to note that of the four main premises of the argument, only two are actually called hypotheses.18 At 87D2-3 Socrates asks: ἄλλο τι ἢ ἀγαθὸν αὐτό φαμεν εἶναι τὴν ἀρετήν, καὶ αὕτη ἡ ὑπόθεσις μένει ἡμῖν, ἀγαθὸν αὐτὸ εἶναι; and at 88C2-4 Meno says: καὶ δῆλον, ὦ Σώκρατες, κατὰ τὴν ὐπόθεσιν, εἴπερ ἐπιστήμη ἐστὶν ἀρετή, ὅτι δίδακτόν ἐστίν.19 I have borrowed the word “Lemma” in its later, unPlatonic acceptation, to name the two other main premises. This exposition of the argument makes clear what other, more detailed expositions tend sometimes to obscure: the clear movement ‘upwards’, from hypothesis to hypothesis. Arete is teachable because it is knowledge and it is knowledge because it is good. It will be readily seen that, as in the

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18 Stahl (1956), 11, says Plato is here “etwas laxer in der Wahl seiner Termini”. It is difficult to believe he would be careless on this point precisely after introducing the term with so much ceremony. – On the term “hypothesis” being applied to only one premise in each step of the argument, cf. Hippocrates of Chios’ use of “ἀρχή”, pp. 68-69, above, and pp. 206-207, below. 19 The hypothesis is ἐπιστήμη ἐστὶν ἀρετή. Cf. Stahl (1956), 100 n. 9, contra Robinson, (1953), 117.

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geometrical example at 86E, only those assumptions are called hypotheses that relate to the nature of the subject under discussion, respectively the χωρίον or arete, but not other assumptions that may be needed as premises. L. E. Rose may, therefore, be right in pointing out that the decisive assumption in the above argument, “insofar as it is the one that eventually has to be withdrawn by the participants in order to avoid the conflicting results” that virtue is and is not teachable, is the assumption that “if something which is of the soul is profitable, it is knowledge”.20 But he seems to me unjustified in expecting Plato to call this assumption a hypothesis, for it is not an assumption as to the nature of the object of inquiry, but an auxiliary assumption, introduced in order to prove what I have called Lemma II. It has been objected that Socrates had tried to establish the hypothesis that excellence is knowledge by means of a higher hypothesis before testing the hypothesis itself for consistent conclusions. This, it is pointed out, disregards Socrates’ own (albeit later) recommendations in the famous passage in the Phaedo. But it should certainly seem strange that Plato, of all people, should disregard the importance of elenchus, and especially only one and a half pages after it has been so thoroughly applied in the slave’s lesson. It seems to me rather that the inversion in the procedure is premeditated. It is Socrates’ way of breaking Meno’s imperviousness. Meno, immediately after the demonstration that learning is recollecting, reverts, as if nothing had happened, to his original question: “But I would prefer to hear about what I asked in the first place, whether excellence is teachable, etc.” Socrates gives in for the time being; Meno has learned nothing. Meno must have his answer; only afterwards is the answer to be shown insufficient. Meno would not have been capable of understanding the full answer to his question; nor would he easily have understood the difference between his view of διδαχή and Socrates’. He must therefore be treated by shock. On the other hand, the hypothesis that arete is knowledge and the assumption that all good things are (ultimately) based on knowledge are not as bad as they seem. They are discarded only because of Meno’s misunderstanding of the nature of knowledge. Bluck surely must be

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Rose (1970), 3.

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wrong when he says that “δίδακτόν can hardly have lost its maieutic sense between 87B-C and 89C”.21 If Socrates is playing Meno’s game (and what else is dialectic?), it can hardly not have lost its meaning. Besides, Cornford’s argument22 offers a much better view of the movement of the dialogue than Bluck’s. [5] Bluck underestimates Plato’s craftsmanship when he says that “none of the devices proper to geometrical analysis or the hypothetical method is used to support or test the main suggestion of the dialogue, that knowledge comes by recollection”.23 Actually, the central contention of the dialogue – that knowledge is recollection – is arrived at by precisely the same analytical procedure that was described and exemplified in 87, and applied soon after to the question of whether virtue is teachable.24 Let us turn to the text in question: At 80D5, Meno objects to Socrates ad hominem:25 And which way will you look, Socrates, for that which you do not know at all what it is? What sort of thing26 among those you do not know will you aim at in your search? Or, even if you hit upon it, how will you know that this is what you did not know?

Socrates twists Meno’s restricted objection into a general philosophical issue: I see what you want to say, Meno ... That it is impossible for a man to search either for what he knows or for what he does not know; for he would search nei-

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Bluck (1961a), 21. Cornford (1952), 60 n. 1: “... This argument deliberately ignored the distinction between ‘teachable’ (διδακτόν) and ‘recoverable by recollection’ (ἀναμνηστόν) which Socrates had just established (87B-C). The fact that the Sophist cannot ‘teach’ virtue does not prove that virtue is not knowledge of the sort that is recollected under Socratic questioning. As in other early dialogues the true conclusion is masked.” 23 Bluck (1961a), 91. 24 Eckstein’s (1968) view “that neither Plato nor the Platonic Socrates accepts the doctrine of recollection” and “that Plato intends his slave-boy ‘demonstration’ to be taken as a farce and not as a paradigm of teaching” (p. 11) is stated rather than argued for, and the author seems to me hyper-sensitive to Plato’s irony, in a near-caricature of better commentators. 25 In a recent article, Moline (1969) has argued that the paradox is Socrates’ and not Meno’s. He was preceded by Phillips (1948-9). 26 Cf. Verdenius (1957) 294, on 80D6, and (1964), 267. 22

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ther for what he knows – for he knows it already and there is no need to search for such a thing; nor for what he does not know – for he would not know what to search for. (80E)27

The ἐριστικὸς λόγος introduces thus an aporia concerning the possibility of searching or learning. This is not, as Gulley would have it, “a request for a criterion of knowledge”.28 Gulley’s contention assumes that anamnesis is dogmatically accepted, when in fact it is not, and makes anamnesis serve as a criterion of knowledge. But this supposed criterion, apart from being far too simple-minded, is never actually seen to be applied in the dialogues. And our text certainly speaks about the possibility of engaging in inquiry, not about the related but distinct matter of the difference between knowledge and other states of mind. The problem is: Are inquiry, learning, knowledge, possible at all? In his reply to Μeno, Socrates starts from the paradoxical conclusion: οὐκ ἄρα ἔστιν ζητεῖν ἀνθρώπῳ, inquiry is impossible for man. The statement of the problem itself comes afterwards, as often in Plato: For one inquires either into what he knows or into what he does not know. Both are proved to be impossible. There is no way out. It is an “aporia”. Socrates’ business is to find a way out. He starts by abandoning the synthetic procedure into which the ἐριστικὸς λόγος was cast. Instead of trying to prove that learning is possible out of a set of agreed premises (introduced above by γάρ, three times, lines 3-4); he reverses the procedure. He negates the cogency of the argument (οὐκ ἔμοιγε 81A3), i.e. he assumes that the conclusion is false and that learning is, therefore, possible. Now it is required to find how (ὅπῃ, A4) this is so. Socrates’ solution: learning is possible if (in as much as) it is anamnesis. In as much as (ἅτε C5) the soul is immortal and was reborn many times and had seen all things here and in Hades, there is nothing she did not learn ... and in as much as (ἅτε γάρ Dl) nature is all of the same kind,29 and the soul has

-------------------------------------------27

Cf. Euthyd. 275D ff. Gulley (1954), 194-5, 199. 29 Cf. Tigner (1970), 4: “These are ‘akin’ (συγγενοῦς) in the perfectly straightforward sense that they all belong to the same ontological family. The prenatal exposure of the soul was to ‘one kind of thing’ (later, the Forms). “Now, it surely may be that a number of such ‘recollectables’ display all manners of logical relations, have a common origin, occupy the same ‘field’, and so on [respectively Allen’s, Klein’s and Moravcsik’s views], but Plato’s requirements here 28

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learnt all, nothing prevents her (οὐδὲν κωλύει D2), if she recalls one single thing – what men call “learning” – from finding out all the rest by herself, if only one is courageous and does not give up searching. For (ἄρα D5) searching and learning are nothing but (ὅλον) recollection. This hypothesis is itself very difficult to prove, but, says Socrates, it can be shown to be reasonable. As Socrates points out, the geometry lesson does not prove conclusively that knowledge is anamnesis. But then he did not want to prove it. He wanted only to resolve the aporia they were in. The contention was that knowledge is impossible. Socrates had therefore to show how it is possible. In assuming the premises of anamnesis at 8lD, he does not say that from these premises something necessarily follows (although this could be the case too). Rather, he says that granted these premises nothing prevents the soul from learning. He is interested in showing the possibility of the conclusion, or, in other words, in untying the aporia in order to permit a “free way”. Of course, in the process of “clearing the way” Socrates established some important points: The slave did have opinions that were his own (85D8-9). But, as it is agreed at C2-3, these opinions do not amount to knowledge. This distinction is important, for from it Socrates draws the conclusion that “he who does not know about any matters, whatever they be, may have true opinions on such matters, about which he knows nothing” (C6-7). The geometry lesson has thus shown that the dichotomy knowledge/ignorance presented by Meno and by the two sophists in the Euthydemus is untrue to the facts. True opinions are no less opinions because they are true: one may hit upon the way to Larissa without actually knowing it,

-------------------------------------------are surely not that stringent. All he needs is for ‘recollectables’ to be sufficiently alike that they can be approached by using the same (dialectical) method. They need to be ‘akin’ merely in the sense that they need to be of one ontological kind.” It might be added that Plato’s position is here essentially ambiguous. If he is working his way from epistemological distinctions to their ontological justifications, it is to be expected that the clarification of ontological issues will depend on epistemological points. Therefore, if his epistemological standpoint is the distinction between knowledge and opinion according to which knowledge is recollection of what is connected and opinion is the retrieval of single pieces of information, then the ontological justification for this distinction is a hypothesis that is to be explained and defended only later. This is actually done in the Phaedo. Cf. further p. 101, below. For a discussion of the myth itself (81A-E), see Gulley (1962), 6-11.

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perhaps by following a description of it, or by trusting some intuition. Adequatio is presumably a necessary condition of knowledge, but it is not a sufficient condition of it. Only recollection is knowledge stricto sensu, for it is ἀναλαμβάνειν αὐτὸν ἐν αὑτῷ ἐπιστήμην (85D6). This is opposed to opinion, which is acquired from without.30 Because he is incapable of grasping the change of meaning that “knowledge” has undergone in Socrates’ explanation of the experiment, Meno still understands knowledge as something that can be “acquired” from without, and his concept of διδαχή will correspond to his concept of knowledge. Socrates, however, intends knowledge here to be understood as recollection, and his concept of διδαχή is fitting to what he had just done to the slave-boy. Plato refuses, for good dramatic reasons, to clarify this ambiguity, and the aporia of this dialogue will result precisely from Socrates’ wilful play on it. But for the time being Socrates is content to show that the knowledge/ignorance dichotomy is ill-founded and that, as a matter of fact, it is possible to rid oneself of false opinions and eventually to pass from a state of having true opinions to a state of having knowledge. If the slave is asked many times about these matters he will in the end have the knowledge which he now lacks (C10-11). This may be a long process. Plato does not seem to allude in the Meno to the questions raised by the τι ἱκανόν of the Phaedo and the ὁμολογία of the Republic. But if knowledge in the Meno differs from opinion by the possibility of having a logos of it, then he sooner or later has to face the problem of the validity of a logos which is itself – as the Meno acknowledges merely a (true) opinion. For a moment (85D9-10) Plato indulges in considering the slave as already having made the whole way to knowledge. But at E7 he comes back to speaking of him as having only doxai, and at 86A7 as having had “true opinions which have only to be awakened by questioning to become knowledge”. Plato is not interested here in showing how knowledge actually arises in the soul, but in solving the aporia of knowledge, i.e. in showing how knowledge is possible. Once this is done, the problem, as far as Plato is concerned here, is solved.

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Cf. Euthyd. 304c παραλαβεῖν; Verdenius, (1964), 277 ad 96C10.

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It should be noted that the source of the slave’s opinions is irrelevant to the anamnestic process. The first solution proposed by the slave was probably one of his “stock opinions”, which he had spoken about, so Socrates jokingly presumed, many times before. His second and wrong solution was of his own invention. The correct solution is actually proposed by Socrates himself, which is perhaps rather unexpected, especially considering Socrates’ sustained claims that he is teaching the slave nothing. But viewed in its proper light, this solution is offered by Socrates as nothing more than yet another opinion that must be checked. As long as the slave accepts Socrates’ solution without checking it himself, this is for him only an opinion not different in respect of being an opinion (and not knowledge) from the other (false) opinions he had held. And although opinions (both false and true) can be handed over, the transformation of opinions into knowledge, involving ‘seeing’ the connexions between the statements leading to the confirmation of the opinion – this can only be done by the slave himself. His assent and his negation are solely his, and no one can perform them in his stead. In this sense, Socrates is perfectly justified in insisting that he did not teach the slave anything. In this sense too, the geometry lesson was a fitting ἐπίδειξις of learning as anamnesis, i.e. of the passing from opinion to knowledge. The geometry lesson shows that there is a difference between opinion and knowledge and that it is possible to pass from opinion to knowledge. But this means that the dichotomy between ignorance and knowledge is ill-founded. The experiment with the slave has shown that there are three states, not two: ignorance, opinion (false or true) and knowledge. Moreover, learning is not passing from ignorance to knowledge, but rather from opinion to knowledge. The difference between (true) opinion and knowledge, between those beliefs the slave entertained unreflectively and those he developed ‘out of himself’, this difference is a fact, as it was shown in the geometry lesson. But at the same time it is a fact too that it is possible to pass gradually from (true) opinion to knowledge. This means that although opinion and knowledge are different from each other, yet they are not completely separate states: knowledge is opinion plus “the calculation of the reason why”. And this can be done to a greater or a smaller degree.

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Complete opinion is held totally unreflectedly; absolute knowledge (which is not yet envisaged in the Meno) requires eventually the working out of the whole series of causes. Learning is a process leading from a (more or less) unreflected opinion to a state in which the logical causes or reasons of that opinion are made explicit – mostly only partially. Socrates’ problem is to account for this fact. This can be done, says Socrates, by supposing knowledge to be recollection. If learning is, strictly speaking, recollection, then true opinion is not knowledge. This is indeed the hypothetical procedure. In the terms of the inquiry into the question whether arete is teachable or not, the question would be posed: “What is learning to be, so that it should be possible?” The solution is: It is possible (οὐδὲν κωλύει), if learning is recollection. The corollary (“porismos”, as the later Greeks called it) would follow immediately that there is a difference between knowledge and opinion. [6] The difference we are now concerned with manifests itself in that he who has knowledge is capable of giving an account of what he knows, while he who has opinion only is not capable of that. This difference is explained at the end of the dialogue. By giving an account (λόγον διδόναι) Plato means showing the reason whereby a thing or a fact is as it is. Knowing excellence to be teachable and believing excellence to be teachable differ not in the content of the cognition but in the ability or lack of ability to give a reason for excellence being so. This reason is the hypothesis on which this property of excellence is based, namely, that excellence is knowledge. Thus, if anamnesis is the transformation of opinion into knowledge by binding them with “the calculation of the reason”, it should be clear by now that this calculation of the reason is precisely the psychological counterpart of analysis. For analysis is the figuring out of hypotheses to support a given conclusion, or, in the formulation of Oinopides, it is the procedure that inquires: τίνος ὄντος τί ἐστιν; excellence being teachable, what is excellence? So, anamnesis too is the process of discovery of what provides reasons and connexions to our disconnected world of opinions. Already at the beginning of the dialogue, Socrates asked for the “why”, the διὰ τί. At 72C6-7 he asked for ἕν γέ τι εἶδος δι’ ὅ εἰσιν

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ἀρεταί (Cf. Euthyph. 6D with the instrumental dative instead of διά). One may have a true opinion about excellence if one can enumerate examples of excellence and only examples of excellence when asked to do so. But one does not have any knowledge unless one can “think out the reason (αἰτία)” whereby (διά) all excellences are excellence. Meno, of course, does not even have a true opinion of excellence. But even if he had, he could not have gone much farther, because he does not understand the relation between the eidos and the particulars. The problem of the relation between the eidos and the particulars is to be developed in the Phaedo, and here we are given only a brief suggestion. Whether Plato was still working out the details of his doctrine by the time he wrote the Meno, or had them ready and refrained from writing them down for didactic or dialectical reasons – this is a question for which I have no use. The slave produced true opinions that were his own. He did not learn them in this life; he must have learned them “when he was not a man”. And this is only possible if the soul is immortal. Although the direction of the argument is from the slave’s opinions to the immortality of the soul (86B1-2 εἰ ἀεὶ ἡ ἀλήθεια ἡμῖν κτλ. ..., ἀθάνατος ἂν ἡ ψυχὴ εἴη), still the immortality of the soul is the cause whereby the slave has (or can have) true opinions of his own (cf. 85C ff.). The possibility of the solution of the problem of learning is accounted for by anamnesis and by the immortality of the soul. That the consequence (the actual fact of knowledge) is important and that there is no question of an actual ‘proof is shown by Socrates’ disclaimer at 86B6 f. It is not unimportant to note that here as elsewhere (e.g., 86B2, 81B5, esp. 81D5 ff.) Plato’s ultimate conclusion is practical. Bluck is then mistaken in saying that “the nature of the difference [sc. between ἀληθὴς δόξα and ἐπιστήμη] must depend, of course, on the validity of the theory of recollection”.31 Plato emphatically maintains the former and disclaims any certainty about the latter (as he does again in the Phaedo). And yet, if Plato’s procedure were dogmatic, setting himself to prove the possibility of learning and the difference between true opinion and knowledge from the doctrine of recollection, then Bluck’s

-------------------------------------------31

Bluck (1961a), 414.

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remarks would be certainly true. But Plato’s reservations about the doctrine of anamnesis make it abundantly clear that he viewed the conclusion as better established than the premises. If so – what did he need the premises for? The whole of the argument about knowledge and opinion seems to point clearly to the interpretation that Plato was not trying to produce a synthetic proof of the difference between true opinion and knowledge and of the possibility of learning, but that, on the contrary, he accepted these consequences from the beginning and was working his way “backwards”, from the consequences to the premises that would support them. And in doing so he believed he was not only offering a theoretical construction but primarily investigating the physis of things, the way things are, for only what is can serve as foundation to what is. [7] As we saw in the case of the slave’s opinions, the actual source of the hypothesis is irrelevant. Moreover, if the hypothesis is the antecedent (or one of the antecedents) of an implication not necessarily convertible, then its provenience could be expected to be ‘irrational’, a sort of divination. As a matter of fact, anything could, prima facie, be taken into account because everything is equally regarded as a provisional opinion till it is proved. Socrates can therefore allow himself to introduce his hypothesis as a myth. Moreover, he can afford to use an existing myth for his own purposes.32 If what he was after were a proof of the possibility of learning based on the immortality of the soul, he would have better presented it as a fact, as e.g. Empedocles and the Pythagoreans had done, instead of weakening his stand by submitting it as a notvery-well-accepted religious doctrine. But Plato did not want to offer a metaphysical proof of the possibility of knowledge.33

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32 Cf. Klein (1965), 166: “The nature of the tie between the thesis of the soul’s indestructibility and the thesis of recollection is by no means clear. This unclearness is not unrelated to the unambiguous use of the term ψυχή itself, the connotations of which range from φρόνησις to ζωή.” The connotations of the word in classical Greek certainly seem to allow Plato’s looseness of expression. But it would be misleading to attribute Plato’s latitude in the use of ψυχή to mere linguistic accident. The use of the doctrine of anamnesis as a hypothesis of the immortality of the soul in the Phaedo clearly makes the philosophical point that the principle of intelligence is the principle of life (or part of it). 33 Cf. Buchmann (1936), 71: “Die Tatsache, dass es Erkenntnis gibt, lässt sich für Platon nur beweisen durch ihre Begründung in der Metaphysik. Das ist für die ganze platonische Erkenntnistheorie charakteristisch. Ebenso wie später im Phaidon das Apriori nicht rein logisch gefasst

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Now, the account offered in the Meno is irrational not in the sense that it is mythical – this could be only a literary device – but in the sense that it is a divination rather than a deduction. By clothing it in a mythical robe Plato seems to be stressing the non-deductive aspect of this account. This is the same aspect of divination that is implied in every regressive reasoning, and Socrates does not fail to mark it everywhere in the dialogues by tracing back the sources of his hypotheses to dreams, quotations from poets or straightforward illumination. Therefore, this hypothesis cannot be presented as fact. Socrates makes quite clear that the anamnesis-hypothesis is not on an equal footing with the fact that the slave had previously had only opinions and he now has something more of a knowledge. The myth should not be taken, therefore, as relating things as they are, but rather as relating things in a figurative way. On the other hand, it would be difficult to maintain that there is in the Platonic corpus, and indeed in the Meno, no actual belief in the immortality of the soul. Whether there is here only a ‘modality of presentation’ I cannot say. This question can be clarified only within a comprehensive re-examination of the dialectical function of myth in Plato, into which we cannot go in the present study. I would just venture that there is an ambiguity in Plato’s mythical presentations, in as much as the myths refer to hypotheses which are, as such, to be distinguished from the consequences for the sake of which they are introduced, and deemed to be only provisionally true, but, on the other hand, buttressed not least by the fact that they are supposed to serve as the ontological basis of the world as we see it. One should note how this ambiguity is carefully guarded by Plato, e.g. in the precise formulation of the myth of anamnesis. As J. Klein pointed out, Plato does not say that the soul learned in a previous life

-------------------------------------------wird, sondern zeitlich und seine Erklärung in dem metaphysischen Tatbestand der Ideenschau in einem früheren Leben findet, so rechtfertigt Platon die Möglichkeit der Erkenntnis auch im Menon metaphysisch durch den Nachweis, dass wir schon einmal ein Wissen gehabt haben müssen. Ist das der Fall, dann besteht auch die Möglichkeit seiner Wiedererweckung im jetzigen Leben.” Plato’s a priori is certainly not “rein logisch”, but it is not plainly “zeitlich” either. The time of the a priori is mythical time, which cannot be equated without much ado with physical time. For related, but somewhat different views on Plato’s a priori, see Lion (1935), Moravcsik (1970).

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what she now knows, but he uses the perfect tense throughout: “she was in a state of having learned” (81C7, D2, 86A2, 8; also ἑωρακυῖα 8lC6).34 This squares well with Socrates’ later disclaimer of the ‘proof’ of the possibility of learning, as against his emphatic endorsement of the ethical superiority of inquiry over intellectual laziness. Indeed, the given is the consequence: Intellectual courage is better, learning is possible (and therefore, the dichotomy between ignorance and knowledge is spurious). For Socrates, as he stresses so many times during the dialogue, the possibility of knowledge is a conviction, not primarily theoretical but especially practical (moral): the first consequence Socrates draws from the assertion of the immortality of the soul is an ethical one: δεῖν δὴ διὰ ταῦτα ὡς ὁσιώτατα διαβιῶναι τὸν βίον (81Β5-6). But the foundation of this conviction is something that he can only propose as a hypothesis, not guarantee as truth.

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34 Cf. Klein (1965), 179: “... the assumption that the boy acquired knowledge ‘at some time’ (pote), that is, at some time before his birth, is made ambiguously equivalent to the assumption that the boy’s soul possesses that knowledge throughout all time (ton aei chronon). Does, then, the alternative suggested by Socrates reduce itself to the alternative of possessing knowledge always “throughout all time” (ton aei chronon) or possessing it always (aei) in a way which is not susceptible of any temporal measure, that is, strictly speaking, possessing it at ‘no time’? But is that latter possibility compatible with the mythical identity of the boy’s soul before and after birth?”

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Chapter iii: Disagreement and Agreement The Meno had pointed to a way out of the purely aporetic conclusions of the earlier dialogues, but the method that was to lead to positive results was only sketched. It is in the Phaedo that Plato elaborates on this method and actually shows its application on a large scale. However, the description of the method in the Phaedo has of late become something of a cause célèbre in the interpretation of this dialogue and of Plato’s middle period as a whole. The precise force of Plato’s methodological remarks has been the object of lively controversy, as have been also their relation to the remarks in the Meno and the Republic, and the extent to which they are in effect applied in the course of the dialogue. It is my contention that the methodological remarks of the Phaedo are an elaboration of those of the Meno and lead to those of the Republic, and that, moreover, the Phaedo is itself constructed throughout as a single unified example of the use of the hypothetical method it advocates. To substantiate this view, it would seem appropriate to begin by a close examination of Phaedo 100A and 101D, and then, in the next chapter, analyse the sequence of the argument in the dialogue and show that it conforms to Plato’s own methodological precepts. The two passages are as follows: 100A3-7 ἀλλ’ οὖν δὴ ταύτῃ γε ὥρμησα, καὶ ὑποθέμενος ἑκάστοτε λόγον ὃν ἂν κρίνω ἐρρωμενέστατον εἶναι, ἃ μὲν ἄν μοι δοκῇ τούτῳ συμφωνεῖν τίθημι ώς ἀληθῆ ὄντα, καὶ περὶ αἰτίας καὶ περὶ τῶν ἄλλων ἁπάντων [ὄντων], ἃ δ’ ἂν μή, ὡς οὐκ ἀληθῆ. 101D3-E1 εἰ δέ τις αὐτῆς τῆς ὑποθέσεως ἔχοιτο, χαίρειν ἐῴης ἂν καὶ οὐκ ἀποκρίναιο ἑως ἂν τὰ ἀπ’ ἐκείνης ὁρμηθέντα σκέψαιο εἴ σοι ἀλλήλους συμφωνεῖ ἢ διαφωνεῖ· ἐπειδὴ δὲ ἐκείνης αὐτῆς δέοι σε διδόναι λόγον, ὡσαύτως ἂν διδοίης, ἄλλην αὖ ὑπόθεσιν ὑποθέμενος ἥτις τῶν ἄνωθεν βελτίστη φαίνοιτο, ἕως ἐπί τι ἱκανὸν ἔλθοις, ...

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As Hackforth translates them, they could seem to be quite straightforward accounts of Plato’s method of inquiry into the “reasons”1 (aitiai) of things: Anyhow, it was on this path I set out: on each occasion I assume the proposition which I judge to be the soundest, and I put down as true whatever seems to me to be in agreement with this, whether the question is about causes or anything else; what does not seem to be in agreement I put down as false. And if anyone were to fasten upon the hypothesis itself, you would disregard him, and refuse to answer until you could consider the consequences of it and see whether they agreed or disagreed with each other. But when the time came for you to establish the hypothesis itself, you would pursue the same method: you would assume some more ultimate hypothesis, the best you could find, and continue until you reached something satisfactory.

2. The central problem in these passages is the question about the meaning of συμφωνεῖν and διαφωνεῖν. As Sayre has summarized it in a recent book, the problem is as follows: If Socrates’ procedure with regard to propositions that agree with the hypothesis is justifiable, then ‘agrees with’ here [in 100A] must carry the sense of ‘is implied by’. Yet if his procedure with regard to propositions that do not agree is justifiable then ‘agrees with’ must carry the sense of ‘is consistent with’. But it would appear that the term cannot carry both meanings at once, since consistency and implication are different logical relations.2

As Socrates uses the term symphonein only once in 100A, it is improbable that it is carrying both meanings at the same time, unless one wishes to accuse Plato of “a crude logical mistake”. It is, of course, possible to conclude that Plato was being deliberately vague, in order to “preserve conversational simplicity”, and that the term symphonein is

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1 Better than “causes”, though I shall be using this word too, as “reason” may sometimes translate also logos. 2 Sayre (1969), 15-16.

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doing double duty. This has been suggested, among others, by Robinson.3 Sayre contends that it is possible to make good logical sense out of the passage if we assume that the negation of agreement between propositions is not lack of agreement but actual disagreement, i.e. that Plato took the negation of ουμφωνεῖν to be not lack of entailment but actual inconsistency. Using the so-called “Polish notation”, Sayre explains: “There is no reason why Plato ... being innocent of a systematically developed logic of propositions, might not have thought of that which does not agree with the hypothesis as disagreeing with it – might not have constructed the negation at 100A7, that is, literally to qualify the verb ‘agrees with’ itself, and not to qualify the assertion of agreement between hypothesis and proposition. Not to agree with h, in this case, could be construed as disagreeing with h in such a fashion that if h is true then p is false. Failure of p to agree with h then would be asserted by LChNp. If this expedient of interpretation were adopted, LChp would assert the agreement of p with h, and LChNp would assert the lack of agreement of p with h, providing just the relationship needed to make good sense out of Socrates’ methodological remarks at 100A.”4 But Sayre himself points out three difficulties in the way of this interpretation: a. The interpretation of the denial of agreement as disagreement is not, in his view, as natural as the interpretation that disagreement means merely lack of agreement. “The term symphoneo – he says – or its equivalent in our language, seems inappropriate as a vehicle for the sense of logical entailment.”5

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3 Robinson (1953), 128. Crombie (1963), ii 539 ff., seems to be in general agreement with him. 4 Sayre (1969), 18-19. 5 P. 19. I cannot see why the denial of agreement is “more naturally” thought of as lack of agreement rather than as disagreement. Cf. ‘You must do it’ and ‘You must not do it’, as well as ‘You can do it’ and ‘You cannot do it’; both seem perfectly ‘natural’. There is however a further reason along these lines for not having symphoneo and diaphoneo meaning respectively ‘entailment’ and ‘inconsistency’. Any two sounds either symphonei or diaphonei, and there is no third possibility. But on the interpretation we are examining two propositions could neither entail nor be inconsistent with one another. The metaphor fails, therefore, to convey this meaning from the very start.

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b. As Robinson has shown, Plato’s use of symphoneo and diaphoneo in other contexts never clearly indicates entailment or its absence, but it seems clearly to indicate consistency or inconsistency.6 c. The most important objection brought by Sayre against his first interpretation is that in 101D it is quite implausible that symphoneo means ‘to be entailed by’. There one is instructed “to check the consequences of one’s hypotheses for mutual agreement (ἀλλήλοις συμφωνεῖ) before one turns to substantiate the hypothesis itself. Only rarely, if ever, would the consequences of a dialectician’s argument entail each other”.7 Therefore, Sayre proposes an alternative interpretation. He assumes that Socrates’ audience could be relied upon “to recall the technique of geometrical analysis upon hearing his description of method at Phaedo 100A”. Indeed, Cebes and Simmias, as well as Echecrates, were Pythagoreans and would certainly be familiar with this common mathematical practice. They would naturally think of the hypotheses and the propositions in agreement with them as convertible propositions. Sayre is assuming here that Greek mathematical analysis was a method “in which proof of a given proposition is sought by deducing consequences from it until one is reached which is known independently to be true.” Now, “as a point of procedure, geometers typically are concerned with deductions in which both premises and conclusions are statements of equality which are mutually convertible.”8 If this interpretation is right, two propositions are in agreement if they are consistent. This accounts for the second part of the statement at 100A: whatever does not agree with the hypothesis is posited as false. Now, the first part of the statement at 100A, i.e. that whatever agrees with the hypothesis is posited as true, “is accompanied by the assumption that members of Socrates’ audience are intended to draw upon an acquaintance with geometrical analysis in understanding that any proposition consistent with the hypothesis is also convertible with it and hence entailed by it”.9

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Robinson (1953), 127. See, e.g., Phaedrus 270C, Gorgias 457E. Sayre (1969), 20 n. 3. 8 Pp. 20-22. 9 P. 35. 7

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Sayre seems to waver between the two interpretations and he suggests at the end “that Phaedo 100A-101D, although not at all a piece of logical nonsense, remains vague as to how exactly it should be interpreted, and that this is as Plato intended it to be”.10 This does not seem to me to be a much better solution than Robinson’s, although it certainly is more elaborate. [3] I think, nevertheless, that there is no need to surrender so quickly. It seems to me that what vitiates the interpretations of both Robinson and Sayre is their assumption that the hypothetical method is related to mathematical analysis in being deductive and assuming convertible propositions. Robinson says that in the Phaedo it seems that Plato regarded the method of hypothesis, at least for mathematics, as consisting of nothing more than deduction.11 Sayre seems to think so too in his first interpretation and even more in the second. But I have already argued that Greek geometrical analysis was not deductive and was not intrinsically concerned with convertible propositions. If this is so, then Sayre’s second interpretation, which anyway leaves too much to the understanding of the listeners and the readers, lacks all foundation. On the other hand, if symphonein at 100A is supposed to mean ‘entailment’, then ἀλλήλους συμφωνεῖ at 101D cannot be understood but on the assumption of convertibility, the very assumption that led Sayre to abandon his other interpretation. What I am suggesting is that the interpretation of symphonein in both its occurrences should be rid of the misconceptions about Greek analysis that played such a great role in it. Symphoneo in Plato means in other contexts mere consistency.12 Why should it not mean the same here? The Platonic myth of the horror of precision will not suffice as an explanation. As a matter of fact, at 100A Plato is saying that whatever is consistent with the hypothesis (and is relevant to the subject under discussion) is provisionally posited”13 as true (ἀληθῆ ὄντα), and what is not – as not so. The important

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P. 39. Robinson (1954), 253. 12 See n. 6 above. Plass (1960) makes Plato sound even vaguer. 13 For the meaning of tithemi, see Robinson (1953), 93 f. 11

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and primary notion is here – as in the Socratic elenchus, of which the method of hypotheses is an avowed derivation – the notion of inconsistency. So, e.g., in Republic 436-7, 610A, in Sophist 259A, in Gorgias 457E, the main stress is always on the refutation of the hypothesis. In effect, no hypothesis ever receives a positive proof; there is only a lack of refutation.14 The hypothetical method by itself can only disclose inconsistencies, but it cannot, by its own nature, give us the truth. Only demonstration proves, but demonstration, if it does not follow from an unhypothetical beginning, is valueless.15 Sayre’s difficulty stems from the fact that he wants a positive conclusion to be implied in 100A5 τίθημι ὡς ἀληθῆ ὄντα. But there is no need to look for it at the expense of being entangled in grave exegetical confusion. For symphonein is a relation weaker than entailment but stronger than consistency. It is in fact consistency between propositions relevant to the case in discussion, which is certainly more than mere consistency between two propositions whatsoever. An important feature of Plato’s method as disclosed here is that he works within a restricted universe of discourse, and the limits of this universe of discourse are left for the hearer or the reader to understand from the context. This is not unlike Plato’s assuming a background of “standing assumptions” against which he proposes his hypotheses. Every proposition which is relevant to the case in discussion is either consistent or inconsistent with the hypothesis and its consequences. If it is inconsistent, one cannot affirm both this proposition and the hypothesis, and one must choose between them.16 If there is no contradiction between them, the new proposition is provisionally held as true. The same is said in the second passage: before one comes to the establishment of the hypothesis itself, one must check its consequences to see whether there is any inconsistency in them, or between them and our “standing beliefs”.17

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14 Robinson himself was quite aware of this fact. See, e.g., (1954), 255. Cf. further pp. 209212, above. 15 Cf. Republic 533C, Cratylus 436D. 16 See, e.g., Phaedo 92Bff. 17 On the consequences of the hypothesis conflicting with standing beliefs, see Robinson (1953), 133.

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[4] Up to this point the hypothetical method is very much akin to the Socratic elenchus. The final departure from it takes place at 101D5: If the proposed hypothesis remains unrefuted, then one should try to ‘establish’ it, to give it a reason, “in the same way”, namely in the same hypothetical way, by trying to justify it by a “higher” hypothesis. Robinson, faithful to his interpretation of analysis as deductive, stresses the first part of Plato’s hypothetical method and underestimates the importance of the second part. The method of hypothesis, he says, is a method of approximation, in that hypotheses are corrected in the light of the contradictions they might raise, and are thus gradually made more and more adequate. He seems to consider the establishment of the hypothesis as a sort of psychological enlightenment, a sudden apprehension of the particular hypothesis as clara et distincta, following months and years of hard work trying to refute it. The failure to refute the hypothesis seems to him to be the ultimate basis of its acceptance. In this interpretation intuition is underplayed. This is not to say, as Robinson himself reminds us, that intuition has no place in the hypothetical method. But it is restricted here to the repetition of one single sort of intuition: the intuition that this proposition logically entails that proposition. (Robinson does not mention another kind of intuition no less important in the method he is presenting: the intuition that this proposition contradicts that proposition.) But this interpretation of Robinson’s does not account for the fact that the text gives us two stages of the hypothetical method: the first stage is the verification of our hypothesis, much in the way described above; the second stage is the ‘giving of a logos’ to our hypothesis, by means of yet another hypothesis (and not only “correcting” or “revising” it). From this further process (logon didonai) it is clear that the establishment of the hypothesis is not merely negative, but that the failure to refute the hypothesis must be followed by a ‘giving of a reason’, without which the hypothesis cannot reach certainty. This logon didonai is prima facie the same procedure described in the Meno as “binding opinions αἰτίας λογισμῷ”. How do we arrive at this ‘higher hypothesis’? If my interpretation of geometrical analysis is correct, by the same way used in analysis – by intuition. But there is an important difference between this intuition and

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the Heraclitean intuition: this intuition does not give the truth, let alone self-contained truth. It gives us only a hypothesis, another doxa that must be given a logos, and can never pretend to be knowledge without being given such a logos. Plato stresses several times the difference between right opinion and knowledge. Right opinion, he says, e.g., in the Meno, is always right insofar as it is right opinion and will never be false. But, still, it is not knowledge. Poets, seers, politicians can all have right opinion, but they do not possess knowledge. Only the philosopher transforms his irrational intuition, his mania, into knowledge which can give an account of itself. Mere failure to show a contradiction is not enough. A homologia, says Plato in the Republic, will never be science. There is need of an intuition that will carry us ‘above’ our present hypotheses. But this intuition by itself will not give us knowledge. It will only provide us with yet another hypothesis, another doxa, which itself needs to be established. It should be noted that the term ‘intuition’ has acquired in my present usage a rather peculiar meaning: this is not an intuition that presents us with truth, it is an intuition that presents us with opinions to be tested. Nevertheless, I keep the term in order to stress that here we have an ‘irrational’ (non-deductive, non-inferential) feature of the method. The way you come to your hypothesis is irrelevant: you can take it out of a poem (Meno 77B), you can borrow it from religious myths (Meno 8lA), you can believe in it from authority (Meno 73C), it can be suggested to you by your interlocutor (Meno 84E). It is all one. The genesis of the hypothesis is itself outside the hypothetical method. This is why Socrates does not seem to be perturbed very much by the fact that it was he that suggested to the slave in the Meno the answer that was to be proved right. It makes no difference for the method whether Socrates or the slave proposes the hypothesis to be tested. In either case it is only a doxa that must be fettered αἰτίας λογισμῷ. There is therefore in the hypothetical method another kind of intuition besides what is acknowledged by Robinson, not unlike the Heraclitean intuition in that it presents itself with a prima facie credibility. But it is unlike it in that this credibility is open to attack because it does not purport to give us self-certifying truth, but only opinions to be

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tested.18 If our intuition survives the attack and does not raise any contradiction, it still has only its prima facie credibility to rely upon, as Socrates says very clearly in the Gorgias (527A): the reason why Socrates is right is that three among the wisest men in Greece could not offer a suitable alternative. [5] What is the relation between the ‘higher’ hypothesis and the lower one? The interpretation that sees analysis as deduction will naturally suppose that the higher hypothesis is higher in that it implies the hypothesis to be justified and that, since the propositions concerned are mutually convertible, is implied by it as well. But, although this might be the case in geometry, this seems not to be Plato’s actual procedure in the dialogue. I have already argued that less emphasis should be put on the implication between the premises and conclusion of a demonstration and more on their relation as cause and effect.19 The same is true of Plato. Plato’s hypotheses in the Phaedo are not sufficient conditions. But they are not necessary conditions either, as 98B ff. shows very clearly. Plato’s hypotheses are aitiai, brought in in order to διδόναι λόγον. What exactly this means can be seen only from a close examination of the dialogue in its entirety.20 The only way out of this seemingly endless string of hypotheses is to arrive at something ‘sufficient’. Whether this is supposed to be sufficient in relation to a given situation only, or it is intended as sufficient absolutely, is not made clear. There is indeed no open promise of an unhypothetical beginning. But this seems to me irrelevant. The hypothetical method is by its very nature dialectical, or should we say ‘situational’. It starts from a given concrete situation and follows its unique course according to the actual responses of the persons involved. The level of the philosophical discussion at each stage of the dialogue, the meanders of the analysis, the scope of the ethical or metaphysical outlook are dictated by Socrates’ interlocutor. Meno, being who he is, cannot carry the discussion further than it went. His inability to distinguish

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18 Against Vanhoutte (1949), 47: “... D’autre part ... [in the initial theory of ideas] ... les Idées se justifient par leur intelligibilité propre. Chacune d’elles est un ἱκανόν. 19 Cf. pp. 61-66., above. 20 Cf. also ch. ix, pp. 207 f., above.

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between learning as acquiring new doxai and learning as ‘recollecting’ puts a limit to Socrates’ attempt at attaining a satisfactory account of virtue and knowledge. It takes Theaetetus to raise the discussion to a higher level.21 Even in the Phaedo the relativity of the τι ἱκανόν is very marked. Simmias and Cebes see the case for the indestructibility of the soul as “sufficiently proved”.22 But not Socrates. What suffices for Simmias and Cebes does not suffice for Socrates. The τι ἱκανόν can, therefore, be interpreted situationally. And within the Phaedo there would be no reason for demanding an absolute principle. Socrates in the Phaedo had set before himself a task: to produce an apologia of his way of life before his friends. This, as any dialectical conversation, is fragmentary and is tied to the here and now. What is required of him is to satisfy his friends in this particular situation. But even when the discussion comes to an end, Socrates points further. The dialogue conducted here and now has reached a point that is psychologically sufficient for the characters involved in this particular conversation. But if the dialogue can be satisfied with interim premises, Dialectic cannot. Socrates-Eros always pushes the discussion still further, to a point that is not anymore what Aristotle would have called ἱκανὸν πρός τινα but ἱκανὸν ἁπλῶς.23 This transcendence from the existential limitations of the dialogue is clearly implied in Socrates’ remark at 107B. As a matter of fact, the corner-stone of Plato’s epistemology, as expressed as early as in the Meno, is the firm distinction between opinion and knowledge. But knowledge is possible only on a foundation that is sufficient absolutely. In any case, even if this absolute foundation is humanly unreachable (the text in the Republic seems to be against this view), still it exists as a real foundation of being and knowledge. Knowledge is really distinct from

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21 There is, of course, the further, fundamental irony of the dialogue as a premeditated work of art. As such, it is not in fact a live discussion. But as a written dialogue it strives to be the nearest possible approximation to it. The whole of Plato’s attitude towards the written word is implied here. See, e.g., Friedländer (1958), i, “Dialogue”. Rosen (1968), Introduction. 22 Simmias had done it before, at 77A5, and also at 72A4-8. 23 On τι ἱκανόν see Verdenius (1958), 231, and references there. But Verdenius’ adopted solution seems to me not to do justice to this dynamic aspect of the τι ἱκανόν.

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opinion, i.e. the distinction between them is founded in the nature of things. There is in Plato no possibility of making the absolute principle into a Kantian idea, a point in the infinite towards which our approximative analyses tend. All the stages of the analysis are equally devoid of epistemic value, unless they be related to an absolute beginning. Although Plato’s philosophical analysis starts from opinions, it is grounded in the ultimate distinction between opinion and knowledge.

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Chapter iv: The Phaedo [1] The purport of the Phaedo is patently ethical. Socrates’ first words to his friends are about pleasure and pain (59B). What men call pleasure is inevitably followed by pain and pain, by an ‘unreal’ pleasure. Immediately from the outset this theme is contrasted with its counter-theme: Socrates’ way of life – philosophia (61A). The opposition between the two ways of life is presented already here, at the very beginning of the narrative, and the question of the dialogue is posed: Which life should a man lead? Although the dialogue deals with death, its main preoccupation is man’s life. Were it not for this, as Dirlmeier remarks, the question about suicide would not have been raised, or it would have been answered differently. This is a long way from Stoic indifference in face of death, or indeed in face of life; even less is it the pessimistic outlook of Oedipus Coloneus: Μὴ φῦναι τὸν ἅπαντα νικᾷ λόγον· τὸ δ’, ἐπεὶ φανῇ, βῆναι κεῖθεν ὅθεν περ ἥκει, πολὺ δεύτερον, ὡς τάχιστα .1 There is not another dialogue in which the ‘story’ is so relevant to its contents.2 Openly, Phaedo is telling Echecrates the story of Socrates’ last day, from dawn to dusk, and the manner in which he died. As it turns out, Socrates’ death is the existential background against which a whole metaphysics is built. Every Platonic dialogue is ‘situational’ in that it is tied to a definite situation and context; but none is so eminently situational as the Phaedo. Socrates’ behaviour in front of what men call the ἔσχατον κίνδυνον (‘supreme danger’, ed.) is a given fact. By itself it can be meaningful or it can be meaningless. If Socrates is wrong in hoping that “there is a future for those that have died, and, as indeed we

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1 1. Oed. Col. 1224-7: “Not to be born beats all debate; once one appears, going back where one came from as quickly as possible is a clear second” (ed.); cf. also Theognis 425-8, Herod. i 31. Cf. Dirlmeier (1949), 238. 2 “In this dialogue, therefore, more than in any other, it is impossible to separate ‘what happened’ from ‘what was said’ (58C7), to distinguish between events and philosophical content, as in frame and picture.” Friedländer (1969), iii 35. Cf. i ch. viii. Klein (1965), 19 n. 51.

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have long been told, a far better future for the good than for the evil” (63C), then not only is he wrong in recommending to Evenus the philosopher’s way of life, but also in his own behaviour. If death is not better for the good than it is for the wicked, then Socrates “should be wrong not to complain of death” (63B). If it is not so, Socrates’ life and death are no more than a pathetic instance of emptiness. For Plato, as for the rest of Socrates’ friends, the intrinsic value of Socrates’ life and of his death was an indisputable fact, directly intuited.3 There is for them no question of negating this value. When later in the dialogue Simmias is faced with the choice between obliterating the difference between good and bad souls or abandoning a theory of soul which is not in itself contradictory, he chooses rather the second than the first. Because the first possibility would signify the negation of the very situation in which they found themselves. This is why Socrates opens the discussion by saying that he will again pronounce an apologia. He stresses this point by using the cognate verb twice in close sequence (63B2, 4). This dialogue will be a justification, a giving of reasons of his attitude which is taken for granted.4 This justification is, as I intend to show in this chapter, an analysis of the presuppositions on which Socrates’ philosophic way of life is based, presuppositions which alone, as Plato saw it, could guarantee the distinction between knowledge and opinion, between good and evil, in short the presuppositions upon which philosophia is based. In this sense, the hypothetical method is there from the start. On the other hand, of course, it is being gradually developed according to the needs and the possibilities of the argument. It is of the nature of dialectic that it explains itself as it proceeds. Therefore, Socrates does not come explicitly to the hypothetical method until much later in the dialogue. But if we are to analyse Socrates’ moves from the vantage point of an

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3 Cf. Robin (1926), p. xix: “Le lien qui les unissait [sc. les disciples de Socrate], c’était donc la personne même de Socrate ... Pour tous, sa conduite est un exemple surhumain; sa pensée, un objet de méditation et d’examen.” 4 Robin (1926) thinks that the apologia extends only for the first part of the dialogue. On his view, it is a matter of Socrates justifying his faith by plausible motives (pp. xxiv ff.). So Friedländer (1969), iii 43; but see also ibid., p. 473 n. 9. It seems to me that, rhetorical reasons apart, this attempt at justification runs through all of the dialogue, and I see no reason to restrict it to its first part only.

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overall view of the dialogue, we are bound to interpret his early arguments in the light of the later ones. Whether this interpretation is correct can only be evaluated by viewing again the reinterpreted parts in relation to the whole. Thus, in analysing Socrates’ argument, I shall use the terminology of the hypothetical method, without wishing to imply that Simmias or Cebes were deemed to be aware of what was being done. Fortunately we are not bound by the dramatic restrictions Plato puts on his characters. Here comes a short break, marking the end of the exposition of the main theme of the argument. Socrates will now, over the whole of the dialogue “give his grounds (τὸν λόγον ἀποδοῦναι, cf. the description of the hypothetical method 101D6 διδόναι λόγον) for thinking that a man who has truly spent his life in philosophy has good reason to be confident when he is about to die” (63E). [2] In order to prove his point at this stage, Socrates needs two όμολογήματα, which he proceeds to exact from Simmias: i. there is such a thing as death, and ii. death is the departure of soul from the body (cf. Gorgias 524B2). If this is granted, “perhaps you will find you share my view” (64C-D). Granted the division between soul and body, it is agreed furthermore that iia. the so-called pleasures of the body are not fit for the philosopher; iib. reasoning (as opposed to sensation) is the proper activity of the soul, and it is hampered by the body. In this respect, the philosopher’s tendance of his soul is a “rehearsal for death”. Third homologema: iii. We maintain that there are such things as ‘the just itself’, ‘the beautiful itself’, ‘the good itself’; these can be apprehended only through the soul and never through the bodily senses. “On all these grounds, then”, philosophers must long for the separation of the soul from the body. Hypothesis iib. has forced us to agree that we cannot know anything clearly while we are united to the body. If we accept this, we must choose between the two horns of the dilemma: either it is impossible to come to know anything altogether, or this is possible only after death. We shall see that the emphatic rejection of the first horn of the dilemma is a firm conviction of Plato’s. This rejection

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(unproved as it may be) is Plato’s reason for his endorsement of the second possibility. The first level of the argument was quite straightforward: If ii. there is a distinction between soul and body and if iii. there are ideas which are the objects of knowledge (as opposed to sensation), and if we agree furthermore that iib. sensation is bodily and knowledge is non-bodily and that iia. knowledge is more valuable for the philosopher than ignorance and the pleasures of the body, then the philosopher should long for the liberation of the soul from the body, i.e. death. The two last assumptions (iia. and iib.) are standing assumptions of Socrates and his friends,5 the two first are the hypotheses with which Socrates proposes to prove his case. [3] But Cebes, who “is forever hunting up arguments”, is not satisfied with the hypotheses. In order to be confident that philosophia is not a waste of time and in order that Socrates’ stance in front of death be not unwarranted, it is necessary to assume as well that Homer’s notion of the dead man’s soul being dispersed like breath or smoke is untenable. In other words, unless it be shown that “the soul exists when the man has died, and possesses some power and intelligence”, there is no justification for the philosopher’s way of life. One can, indeed, accept that death is the departure of the soul from the body without accepting iv. that it continues to exist after the death. And if this is so, then the consequence the philosopher draws from his hypotheses does not follow. The justification for the hypothesis that the soul exists when the man has died may be found provisionally in the ancient doctrine that v. “souls which have come from this world exist in the other, and conversely souls come and are born in this world from the world of the dead” (70C). This justification, as Socrates immediately goes on to explain, is itself in need of justification. Nevertheless, if such a justification can be given, this doctrine, for the time being only provisionally held, is “good evidence for what we have been saying”.

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5 Hypothesis iib. that knowledge is more valuable than ignorance is, in fact, a main assumption of philosophia. Is then the argument circular? I am rather trying to show it is analytical. But we are perhaps left with the contention that there is no justification for philosophia apart from philosophia itself. This has been argued, for example, by N. Rotenstreich (1969).

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The justification of the doctrine of palingenesis is given by vi. the doctrine that every opposite comes from its opposite (70D ff.). If this doctrine is true, then death comes from life and life from death. There is a balance in nature and soul too is subject to this balance.6 [4] The considerations of symmetry in nature lend a prima facie credibility to the doctrine that every opposite comes from its opposite. Nevertheless, this is a hypothesis that is itself in need of further justification. If this is true (and if the soul is subject to physical laws of generation and destruction), then the soul continues to live after the death of the body. At this stage, however, we still do not have the tools for corroborating this hypothesis. It was a physical hypothesis: it was formulated in physical terms and referred to physical things. But the question of the applicability or otherwise of physical doctrines to the soul requires a wider frame of reference, which would make possible the discussion of nonphysical entities. At this stage of the dialogue, when we have at our disposal only the physical terminology, this is still impossible. This line of argument seems to have run to its end. A new element is now introduced. Cebes turns to another hypothesis, a better one, it would seem, which “if true, points the same way” (Note the proviso!). This hypothesis will take us out of the physical level into another order of being, from ὄντα into λόγοι. The immortality of the soul follows also from vii. the doctrine of recollection.7 If learning is nothing more than recollection of what we have learnt at some previous time, then it follows that our soul existed before coming into the body.

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6 Antapodosis is of course not sufficient to prove Socrates’ point. It is dependent, at the least, on the question of the applicability of conceptual relations (such as opposition) to the material world. In this respect it is problematic, and if I am right in claiming, further below in this chapter, that the doctrine of methexis in the Phaedo is meant to deal with this question, then Plato knew it to be problematic, pending a solution to the problem of predication. This is a reason, I think, for maintaining that Plato is suggesting antapodosis as a hypothesis, although because of dramatic considerations he does not present it explicitly as such. 7 Gulley (1954) has argued convincingly that “anamnesis remained for Plato a fundamental postulate in his theory of knowledge”. (Contra Vanhoutte (1949), 306.) But I do not agree with his reasons “for not basing our view of that doctrine on the version of Phaedo 73C ff.” (p. 213).

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In order to overcome Simmias’ reluctance to accept this hypothesis, Socrates recurs to two further assumptions: viia. there is such a thing as recollection, and it is of several types; and, more important iii. there are ideas and we have knowledge of them. The question here is again that of the possibility of acquiring science as distinct from mere opinion. Socrates had already established that science is knowledge of ‘the just itself’, ‘the beautiful itself’, ‘the good itself’, in short knowledge of the ousia of each thing, be it greatness, health, strength or anything else. He had also established that such knowledge cannot be attained through sensation alone (65A ff.). The nature of these ideas and the difference between them and physical objects is elaborated in 74B ff. If we admit, then, that there are ideas, as distinguished from objects of sensation, and that in our bodily life we come to know about them, then we must admit also the doctrine of recollection, insofar as knowledge of ideas cannot be given by the senses alone. The alternative would be to assume that we retain the knowledge of the ideas throughout our lives (76A). There is, in fact, another possibility, which Socrates tacitly dropped: that we do not come to know the ideas at all. This possibility is raised once at 66E6, but there as here it is thought of as altogether impossible and put aside as utterly unthinkable.8 There the dilemma was between the impossibility of attaining knowledge at all and the sole possibility of attaining knowledge after death. A way between its horns was indicated in that Socrates spoke there of an “approximation unto knowledge” by means of our having as little to do with the body as possible. The possibility of this attainment of knowledge still during bodily life was accepted without questioning, and was not inquired into. Now the doctrine of anamnesis provides some of the basis on which this possibility is founded.9 Granted, therefore, that knowledge is possible, but, on the other hand, that we do not possess it at all times, then – If iii. those objects exist which are always on our lips, a beautiful and a good and all reality of that sort, and if it is to that that we refer the content of our sense perceptions ...it must follow that as surely as those objects exist so surely

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Cf. Parmenides 135B-C, Sophist 249C6-8. The argument for anamnesis in the Meno runs along quite similar lines.

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do our souls exist before we are born; but if the former do not exist, all our argument will have gone for nothing.10

And Plato stresses twice more the dependence of the doctrine of the immortality of the soul upon the doctrine of ideas and of participation. Here, as at the end of the dialogue, Simmias considers the proof as “sufficient” (ἱκανῶς ἀποδέδεικται 77A5). [5] The soul has been considered up to now as a physical object. This status is somewhat ironically presented in the Homeric simile of the soul dispersing in the wind like smoke. But the acceptance of anamnesis raises the necessity of a deeper inquiry into the nature of the soul. If the soul knows the ideas, it cannot be a physical object. The antapodosis hypothesis was put forward on the assumption that the soul is such a physical object. Its conjunction with the anamnesis hypothesis in 77A-C is somewhat strained, for the latter hypothesis is bound to bring the status of the soul into thorough reconsideration. The strain between the two parts of the proof cannot be apparent at this stage of the argument, as the exact status of the soul has not yet been considered. Socrates comes now to consider “to which kind the soul belongs” (78B ff.). There are two kinds of things which were considered up to now: the visible, composite, never constant, and the invisible, incomposite, unchanging. The soul, Socrates submits, is nearer to the second kind. viii. It is therefore nearer to what is incomposite and indecomposable. What exactly is the import of this argument? First it should be noted that the character of the soul which is being stressed is its affinity to the ideas. This affinity, summarized in the word ἀιδές, is explained after the argument has been formally completed: when the soul makes use of the body to investigate something through vision or hearing or some other sense ... it is dragged by the body towards objects that are never constant, and itself wanders in a sort of dizzy drunken confusion, in as much as it is apprehending confused objects ... But when it investigates by itself

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10 Against Stahl (1956), 36: No equivalence. If ... then ... But if not ... then ἄλλως ἂν ὁ λόγος οὗτος εἰρημένος εἴη. There is no immediate negation of the consequent.

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alone, it passes to that other world of pure, everlasting, immortal constant being, and by reason of its kinship thereto abides ever therewith ... (79C-D).

The proper activity of the mind αὐτὴ καθ’ αὐτήν is reasoning. And reasoning is possible only in the world of ideas, never in the world of sense. This activity is therefore of the same kind (συγγενής) as the ideas.11 For if it were not so, reasoning would be inexplicable. The affinity of the soul and ideas means that the soul is capable of attaining the ideas in their rationality.12 But it should be noted that Plato does not derive the rationality of the idea from the rationality of the soul (if I am permitted the slight ambiguity).13 The two are kept completely apart, and only an affinity is postulated between them. The ideas are not rational because they can be thought by the soul,14 nor does the soul take its capability of reasoning from the ideas. Ideas are “thinkable” (as opposed to visible) in themselves and by themselves. On the other hand, the proper activity of the soul in itself and by itself is reasoning. The two are independent, although there is between them a link of some sort, which can be explained only gradually, by analysing this relation as a condition of knowledge.15 This affinity is what makes anamnesis (that is to say knowledge in general) possible. From these considerations Socrates concludes that the soul cannot be a physical object, for the power of knowing and the possibility of being known are not to be found in physical objects. Not being a physical object, the soul is not subject to decomposition, for only physical objects can be decomposed.

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Cf. 75E5: reality is οἰκεῖον to the soul. As Meunier (1952) has put it: “C’est la ressemblance qu’a notre âme avec 1’essence des idées qui est le ressort secret de toute connaissance et de tout désir” (p. 102). And he rightly stresses that “Platon, en effet, ne nous dit jamais que l’âme est une idée, mais qu’elle est de même nature que l’idée” (p. 125). 13 Actually, the Aristotelian πρὸς ἕν ambiguity. 14 Cf. Parmenides 132B-C, Timaeus 52C. 15 The idea cannot thus be a “Setzung des Denkens” as Natorp would have it. If it were so, the objectivity of science would be destroyed. This is forcefully expressed in Plato’s “Refutation of Idealism” in Parmenides 132. Cf. Scolnicov (1971), 77-78. Bal (1950), 88-9, is wrong, to my mind, in identifying, with so many others, the world of ideas with a soul, as, e.g., the demiurge of the Timaeus. Even less possible is his view of Plato as precursor of Aristotle’s God thinking himself. The ideas are not “een geestelijk wezen” (p. 113). 12

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[6] The argument comes to a pause. The status sui-generis of the soul has been postulated as necessitated by the doctrine of recollection and ultimately by the essential difference between knowledge and sensation which is assumed from the outset. As only physical objects can be decomposed, it is clear that the soul cannot undergo decomposition, i.e. physical extermination. After this pause, Simmias probes deeper into the presuppositions of the immortality of the soul. It is not sufficient to assume the (conceptual) distinction between soul and body, not even the kinship of soul and ideas. In order to guarantee the existence of the soul after death, we must assume also ix. the substantiality of the soul. The positing of the soul as invisible and rational (or capable of reasoning) does not of itself secure the independent existence of the soul. As Simmias points out, it is quite conceivable that we may accept a distinction between soul and body and that the soul is incorporeal, without accepting at the same time the independent, substantial existence of the soul. One such possibility is the harmonia theory of the soul. The soul would then be, as A. E. Taylor has put it, an “epiphenomenon of the body”, conceptually distinct from it and invisible, but only the more perishable. If this theory is true, then the existence of the soul after death was a gratuitous assumption. Cebes goes even further. Even if the substantiality of the soul is granted, its immortality still does not follow from our premises. Indeed, all that was proved in the argument for the incorporeality of the soul was that the soul cannot suffer physical extinction. But it was not proved that the soul is essentially indestructible. For the soul may be substantial, and really distinct from the body, and outlive the body (or many bodies), and yet not be indestructible. We have thus to establish also the hypothesis that x. the soul is essentially indestructible. The warning against misology at this point of the dialogue – almost exactly at its middle – is not a mere interlude. It is, in fact, the main subject of the dialogue: the question that is being discussed is the question of philosophia as a whole, and it is rather she not Socrates that is endangered. The real tragedy is the death of the logos, not the death of Socrates, and it is for the logos, if it dies and cannot be brought back to life, that Phaedo must mourn. And again, as in the Meno, the conclusion is an exhortation to positive effort (90E). This is the actual spinal cord and

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raison d’être of the dialogue: Socrates as the supreme example of philosophia. Socrates’ behaviour is a given fact and is accepted as valuable. The dialogue is thus a search for explanations for the value of his behaviour. In the last analysis, philosophia is desired because of itself. As in the Meno, there is no proof to the effect that there is an argument that is sound and it is unthinkable that all arguments should be false. Rather this is assumed as a basic fact (a fact that is not, in truth, different, in Plato’s view, from the other basic fact in this dialogue – that there is a difference between good and evil) and the dialogue wants to point out the presuppositions of this fact. The answer to Simmias’ objection: The anamnesis theory is now part of our standing beliefs. But the consequences of the harmonia theory conflict with the assumption of anamnesis (92B). The two theories are therefore incompatible (οὐ συνᾴσεται 92C3. The elaboration on this word at C5 and C8 is not devoid of meaning, especially in view of 100A). Now, Simmias can have either of them, but he cannot have them both. Simmias gives his reasons for choosing the anamnesis and rejecting the harmonia (92D). The latter was adopted “merely because it seemed likely”. But the logos about anamnesis and learning was based on a hypothesis “worth accepting”, even though, for the time being, no proof of it has been given. The substantiality of the soul is a necessary condition of anamnesis. Were the soul a mere epiphenomenon of the body, it could not have existed before the body, and anamnesis would have been impossible. We accept, therefore, the substantiality of the soul because we believe in anamnesis. This is the sole ground for accepting this theory. Simmias prefers the reminiscence theory because (D6) it was proved δι’ ὑποθέσεως ἀξίας. The hypothesis is (D7) “That our soul existed before it came into the body just as (ὥσπερ) the reality which bears the title of ‘what is’ is hers”. Hackforth is wrong, I think, in accepting Mudge’s lectio facilior αὐτή for αὐτῆς , on grounds that “it would not be relevant here to remark that the Forms are apprehended by the soul”. On the contrary: this is exactly the ground for Simmias’ acceptance of the substantiality of the soul. Because he fails to see this, Hackforth states that “the hypothesis here referred to is of course the existence of the forms”. He is not do-

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ing justice to the independent hypothesis of the separate existence of the soul as subject of knowledge. As we have seen above, the affinity of soul and ideas consists of the very fact that ideas can be grasped by the soul, but, nevertheless, the soul is not an idea. As Loriaux comments on this passage, αὐτῆς need not imply possession in a strict sense but only “le fait que 1’οὐσία appartient à l’âme intentionellement, c’est a dire comme objet de connaissance”.16 Now comes an argument “from another aspect” (92E4). One of the consequences of the harmonia theory is that no soul will be “better” than another (94A). This passage has been the object of live controversy among scholars. The best treatment of it I know of is Hicken’s,17 which I shall follow: In the first place Socrates tries to establish a strict correlation between the degrees of success in attuning and degrees of attunement. “A perfect attuning implies a perfect attunement, an imperfect attempt at attunement implies an equally imperfect attunement.”18 This same point was made in the Gorgias 476C ff., in another context. But soul does not admit of degrees (93B4-7). On the other hand, souls are said to be good and bad, and this is certainly well said (“Ἀληθῶς μέντοι” is Simmias’ emphatic answer). Excellence and badness in the soul are conceived to be themselves attunement and lack of attunement. But this will lead to the conclusion that the good soul is an attunement that has an attunement and the bad soul, an attunement that lacks attunement. On account of the correlation established above, this is inadmissible. “For once we have agreed that if soul is an attunement, it is an attunement that does not admit of degrees, we must also allow that

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16 R. Loriaux, L’Etre et la Forme selon Platon, 28 ff., quoted by Verdenius (1958), 225. Cf. Phaedo 76E. Cf. further Moreau (1947), 320: “Aussi vrai qu’il y a des Idées, objets éternels de la connaissance, aussi vrai qu’il y a une vérité, une objectivité du savoir, autant il est vrai que le sujet pensant est irréductible au concert des fonctions organiques: le matérialisme est solidaire de l’empirisme et ruine 1’objectivité de la connaissance.” 17 See further on the interpretation of this passage Bal (1950), 111; Bluck (1956), 97, 100 n. 1, 223; Burnet (1911), on 93B1; Hackforth (1955), 115, 118; Moreau (1947), 320; Robin (1926), pp. xliii, on 93A8, and 61 n. 3; Tate (1956), 28; Verdenius (1958), 225. 18 Hicken (1954), 20.

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all souls are equally attuned (93D12-E3). But souls that are equally attuned cannot possess different degrees of attunement (93E4-6).”19 The harmonia theory leads to the conclusion that “in as much as it is the nature of every soul to be just as much soul as every other, all souls of all living beings will be equally good” (94A). This conclusion is unacceptable to Simmias, who rejects it most forcefully. Simmias wants to cling to the distinction between good and bad souls. But the harmonia theory will not back this distinction, in as much as naturalistic ethics are, to Plato’s mind, impossible.20 The upshot of this elenchus is that the substantiality of the soul is accepted as a necessary condition of morality. The possibility of learning and the distinction between good and evil are ultimately united in the concept of philosophia.21 These are the “standing beliefs”, which are to be justified. Therefore, as the substantiality of the soul is seen to be a condition of both facts, and since these facts are accepted as true and existent, their conditions are accepted as well. It should be noted that there is no other ground for the abandonment of the doctrine of harmonia. Were Simmias willing to accept its naturalistic consequences, he could very well hold this doctrine. As Socrates made it clear to Callicles in the Gorgias, naturalistic ethics are not, in themselves, self-contradictory. It is just a matter of holding on to the consequences to the very end – which Callicles himself was not prepared to do.22 Probably the same is true of the epistemological branch of the analysis. It seems that Plato did not see any logical contradiction in denying the possibility of learning. Had he seen one, he certainly would not have been loath to point it out. But there is, as the arguments here and in the Meno23 seem to imply, another kind of inconsistency: the in-

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Pp. 21-22. For a somewhat different argument, see Stahl (1956), 38 ff. This very point is the main argument of the Gorgias. 21 See, e.g., Bal (1950), 95: “Overal in Plato’s oeuvre is het streven naar kennis een praktische aspiratie”. See references there to further literature. 22 Cf. especially Gorgias 494A ff. 23 Cf. also Sophist 249C6-8. 20

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consistency inherent in knowing that knowledge is impossible – in fact, a variant of the notorious “liar’s paradox”. Without a proof of the indestructibility and immortality of the soul there is no reason for living a moral life, and the philosopher would have fared better if ἐν ἄλλῳ βίῳ βιοὺς ἐτελεύτα (95C3). The primary concern is here, as everywhere, moral, not metaphysical or eschatological. [7] As we have seen above, the conclusion that the soul is immortal and indestructible is still not warranted by the premises that were discovered. As Cebes’ objection makes clear, the fact that the soul is substantial and incorporeal is still not sufficient. For the most we can infer from that is that the soul is not dependent on the existence or non-existence of the body and that it cannot itself suffer physical extermination, viz. decomposition. But it remains to be proved that x. it cannot undergo extermination at all, that it is essentially indestructible (95A ff.). This doubt about the indestructibility of the immaterial soul is further deepened by its presentation in Cebes’ parable as a particular. In the harmonia theory soul was presented as an epiphenomenon, not as a self-subsistent particular. Socrates refutation of it only amounted to postulating the soul as independent from the body and as subsisting by itself. But it did not postulate it as a particular. Cebes himself seems to be stressing the particularity of the soul out of one’s immediate experience of one’s own personality. But there are further implications involved in this argument: Moral responsibility implies a person who is the subject of that responsibility. (Cf. the final myth, which stresses personal responsibility.) Were the soul proved indestructible but not as an individual, morality would still be unwarranted. Cebes’ objection points in this direction in that he proposes a concept of soul that is clearly that of soul as a particular, insofar as, unlike ideas or universals it cannot be predicated of anything.24 But, at this stage of the argument, whatever is not an idea must be presumed as classified in the second of the δύο γένη τῶν ὄντων. In this respect the

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24 This is not to say that ideas have instances. It is only to stress the difference between a personal soul and an Objective Mind. De Lacy (1939), 108, saw indeed that “on the Theory of Ideas the soul must be considered as an instance of particularity”. But he goes on to draw what seem to me to be the wrong consequences.

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soul is uncomfortably closer to the physical world than the argument for the affinity of soul and ideas would make one expect, and therefore subject once again to destruction (albeit non-physical destruction, viz. decomposition) insofar as it is a particular. Eventually in this dialogue the soul will emerge as a τρίτον τι, sharing with the material objects their particularity and with the ideas their incorporeity. This kind of argument necessitates a change in the level of the discussion. Cebes’ question cannot be answered on purely physical grounds. It calls for consideration of the aitia of becoming and perishing in general (ὅλως). Once we have widened the scope of being by admitting also souls and ideas as incorporeal beings, the physical (corporeal) explanation of nature ceases to be self-sufficient and it is at best derivative. But, as a matter of fact, this widening of the field of being towards the ideas is necessitated by the intrinsic incompleteness of the physical domain itself. Purely physical explanations are faulty not only in that they give rise to contradictions but also and primarily in that they do not afford any real explanation of how predication is possible. The question Socrates wanted to answer with the help of physical science was the question of being, becoming and perishing: Why is a thing what it is,25 why does it cease to be what it is and become something else? Why is a man taller than another? Why does a man cease to be short and become tall? Plato rejects the explanation by physical causes. For the physical ‘cause’ cannot explain how predication or change in predication are at all possible and it is there that his interest lies. If A is one and Β is one, then no physical manipulation can explain the fact that A and Β lose their predicate ‘one’ and are differently predicated as ‘two’. On the contrary, any attempt to explain predication by physical events will only entangle us in confusions and paradoxes.

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25 Rather than “Why does it exist?” Insofar as this question has any relevance to Plato, I think the question here is closer to a question about the essence than to a question about the existence of the thing. The ideas are described in this passage as being the aitiai of things being so-and-so, not of their being there at all. This is left to the demiurge of the Timaeus. Note that at 102B1-2 Phaedo summarizes the argument as follows: “ὡμολογεῖτο εἶναί τι ἕκαστον τῶν εἰδῶν καὶ τούτων τἄλλα μεταλαμβάνοντα αὐτῶν τούτων τὴν ἐπωνυμίαν ἴσχειν.” Things get their names from the ideas, not their existence. This problem is discussed more fully in App. 1.

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When a man grows taller, there is a physical as well as a logical aspect of this process. On the physical side there is physical change; on the logical side there is a change of predicates, from “short” to “tall”. In growing taller the physical aspect is an essential feature of the process. Not so with addition. Addition may have a physical aspect, but this aspect is irrelevant. Plato is interested in the logical or conceptual aspect of these processes, not in their physical aspect. And from the point of view of the problem of predication, Plato would probably deny the difference between growing taller and addition. Anaxagoras was close to the solution of the problem when he suggested (at least this is Plato’s interpretation of him) that the world is arranged in an intelligible manner, and that the intelligible order of the universe is due to Mind and not to matter. But Anaxagoras never showed that things are intelligible and why they are so. He came back to physical causes that are not in themselves intelligible and cannot explain anything. They are necessary conditions but nothing more. Socrates had therefore to appeal to a δεύτερος πλοῦς. As it is impossible to deal directly with the physical world, one must take a détour.26 Socrates is quite explicit about what the deuteros plous is: One cannot look at things directly; therefore, one must look away from things into logoi, only in order to come back later to things. The deuteros plous is second only in that it does not attack the facts directly. The protos plous would have been, if such a thing were possible, to study nature in the medium of nature itself.27 As this is impossible, Socrates tries to get at

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26 The well-known scholion on δεύτερος πλοῦς says: παροιμία, δεύτερος πλοῦς, ἐπὶ τῶν ἀσφαλῶς τι πραττόντων, παρ’ ὅσον οἱ διαμαρτόντες κατὰ τὸν πρότερον πλοῦν ἀσφαλῶς παρασκευάζονται τὸν δεύτερον. But, among other passages, it quotes Menander, fr. 241 Kock: ὁ δεύτερος πλοῦς ἐστὶ δήπου λεγόμενος, ἂν ἀποτύχῃ τις οὐρίου, κώπαισι πλεῖν. Cf. Goodrich (1903), 382: “According to its original signification deuteros plous indicates rather a change of method than a change of goal.” 27 Not Anaxagoras’ method. Contra Goodrich (1903), 382, and Murphy (1936), 42: “... although indirectness is a feature of the deuteros plous, and, as such, a feature of inferiority, we can scarcely say that the method is called deuteros in respect of its indirectness, since there is so little evidence in the text about the methodological character of the protos plous.” Indeed, if one accepts with Murphy that “the real main reason for depreciating it [sc. the deuteros plous] is not that stated in the present paragraph (99D-E), i.e., its indirectness of approach, but that stated in the previous paragraph (99C), i.e., its failure to demonstrate the reasonableness of things” (ibid. n. 1), then very little evidence is left. But I can see no reason for such an asser-

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nature via the ideas. The ultimate purpose of the theory of ideas is to explain nature – not what we call today nature but what the Ionians called the physis of things.28 Here comes the description of the method of hypotheses (100A). This I have discussed above. It was then said that the method of hypotheses had been used “in the present discussion” throughout. Why then is it brought in only here? I believe there is a reason for it, apart from compositional considerations. The hypothetical method is conducted purely within the realm of logoi. It is a conceptual, not a physical procedure. Of course, all dialogue is a conceptual not a physical process. But although people can use and follow the hypothetical method without being aware of it, it would have been premature to formulate this method before a clear distinction between the physical and the conceptual realms had been made, and the insufficiency of the physical realm pointed out. This particular application of the method of hypothesis which Socrates is about to deal with is especially important, because it provides itself the foundation upon which the method is based. That is to say that the hypothetical method itself is possible because of the hypothesis that ideas exist and that things participate in them. If there were no possibility of knowledge, or if this knowledge were not applicable to this world,29 the hypothetical method would be impossible or useless. In the first place Socrates assumes (ὑποθέμενος) the existence of a beautiful in and by itself, and a good, and a great, and all the rest. This

-------------------------------------------tion, and it is clearly against the bona fide reading of the text. Eventually, the failure to demonstrate the intelligibility of things stems from the impossibility of seeking it directly in the physical things themselves. But primarily the alleged inferiority of the method is in its “fleeing away” from things. Also against C. C. W. Taylor (1969), 53; L. E. Rose (1966); Crombie (1963), ii 531. Natorp (1903) has seen through it clearly: “Sein erster Weg nämlich war nach diesem Bericht kein andrer als der der bis dahin vorherrschenden Naturforschung: Erklärung nach den Analogien des Sinnlichen ...” (p. 147). “Nun, der Wink des Anaxagoras hatte ihm keinen wirklichen ‘Weg’, keine Methode eröffnet. Es war nur ein Ausblick, der sich alsbald wieder verhüllte” (p. 149). Cf. 97B, 99D. So Prauss (1966), 107: “... weil Erkenntnis dem Menschen nicht im ‘Wind’ der Wahrnehmung zufliegt.” 28 Of course, the physis Plato is left with is quite different from the Ionian physis; Plato could refer to the ideas as physis (Cf. Phaedo 103B5). But the underlying thought is always the same: to disclose ‘what the things are’, the ultimate ground of the intelligibility of the world (but not “to construct an a priori physics or physiology”, as Murphy (1936), 45, and Vlastos (1969) would have it; cf. further n. 46, below). 29 Plato comes back to this problem in the Parmenides.

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assumption was made already earlier in the dialogue, and we have seen that the purpose of such assumption was to ascertain the difference between knowledge and opinion, a difference which is a firm startingpoint of Plato’s epistemology. Now, if those exist and if something else is beautiful etc., besides those, then it is so only because xi. it participates in them (100C4-6). We assume the existence of the beautiful in itself. If besides this beautiful in itself we want to assert as well that something else is beautiful, we have to concede that the beautiful in itself is not completely cut off from what is said to be beautiful. In other words, Plato’s problem was to explain how it is possible to relate to a physical object characteristics that relate to another order of being, i.e. that are conceptual. His answer is that in order to relate concepts to the physical world we must allow for the possibility of some manner of inherence of conceptual determinations in physical objects. Of what this manner could be he gives only a few hints. This is exactly what Parmenides had denied and, after him, Gorgias. For Parmenides the world of Being and the world of becoming were completely separated. For Gorgias logos was completely dissociated from reality, even supposing reality to exist.30 Parmenides had started from the attributes of Being and deduced from them the absolute separation between Being and becoming. Plato goes the other way round. He starts by admitting the very conclusion Parmenides denied: He admits not only that there is a beautiful in itself but also that something can be said to be beautiful besides the beautiful in itself.31 The only way in which this can be true is by means of postulating a relation sui-generis between the idea and the physical thing. This is then the ‘naive’ explanation: A thing is beautiful because it participates in the beautiful. That is to say, a physical thing can be said to be beautiful because the concept is not severed from the thing but can be predicated of it. The ‘cause’ of predication “in general” (ὅλως) is not physical, but is the participation of things in ideas.32

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Cf. Parmenides 28 Β 6, Gorgias περὶ τὸ μὴ ὄντος ἢ περὶ φύσεως 82 Β 3. Not self-predication but systematic equivocation. 32 This is a general theory of predication and not, as Anscombe (1966) supposed, “a blanket thesis about the forms” (p. 404). Participation is the important feature of this explanation, and 31

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We have, then, two kinds of entities involved in this participation: the idea (“the beautiful in itself”) and the particular character (“the beautiful in us”). There are good grounds for supposing that Plato did not regard the particular subject (e.g. the rose which is said to be beautiful) as a separate kind of entity, somewhat like an Aristotelian substance.33 The idea is linked with the other ideas by xii. relations of contrariness and implication. Some ideas are contrary to one another, as ‘hot’ and ‘cold’; some imply one another as ‘three’ and ‘odd’. These relations are conceptual relations and they cannot be applied to physical objects without much ado. It is true that fire destroys snow but it would be wrong to say that fire and snow are opposites. For one thing, fire and snow are physical objects and contradiction is a relation between concepts. It would not even be of much use to say that the hot destroys snow, because as long as we are dealing with physical things the relation between the hot and snow is completely unintelligible. But if physical things participate in ideas, then the conceptual relations between the ideas can be valid for physical things and processes, by virtue of the conceptual characteristics particularized in these. If ‘the hot’ and ‘the cold’ are opposites in themselves, they will oppose each other also as particular characteristics of physical objects. Now the opposition between fire and snow is in fact the opposition between their characteristics, which is ultimately the opposition between ‘the hot in itself and ‘the cold in itself᾽. This opposition is, therefore, not physical but conceptual. This is, then, Plato’s solution for the problem of being, becoming and perishing. Things are what they are, and cannot be something else, because they participate in ideas. This is why things obey logical laws, even though they are not concepts. One physical thing is not contradictory of another physical thing, and there is nothing in it qua physical thing that prevents it from becoming something else, in fact anything else. In this sense, materialistic relativism, as proposed by the Sophists,

-------------------------------------------commentators should not be amazed not to find the word “χωρισμός” in the Phaedo used of the ideas and the particulars. As it happens, it occurs for this purpose only in the Parmenides. 33 Cf. Prauss (1966), 100; O’Brien (1967), 201. Contra Stahl (1956), 50: “In heutiger Terminologie ausgedrückt, geht es dabei um den Prädikatbegriff und die Subsumption des einzelnen Subjekts unter ihn.”

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is right. How then can logical relations (e.g. of contradiction, logical inclusion and implication) apply to things? For, as Socrates points out to the unnamed objector, only ideas are really contradictory to one another. Plato’s answer is that things are subject to logical relations because they participate in ideas, although they are not themselves ideas. Being, becoming and perishing are not without laws: snow cannot become hot because of logical connections. Philosophical analysis is an analysis of concepts but it bears on things. In this sense, then, Plato’s theory of ideas and of participation is a condition of the rationality of the world. In this same sense, it solves the problem implied in the Meno: How can the whole world be συγγενής? The δεύτερος πλοῦς started by fleeing from things to logoi, but came back full circle to things. [8] Now Socrates is ready to approach the problem of the essential immortality of the soul. Soul brings life to everything it occupies,34 and it will never admit the opposite of what it introduces. In other words, life is an essential characteristic of soul and cannot be dissociated from it. Soul is, therefore, ἀθάνατος. But τὸ ἀθάνατον is ipso facto τὸ ἀνόλεθρον. The immortal, being eternal (τό γε ἀθάνατον ἀίδιον ὄν), must be imperishable. That the imperishability of the soul is implied by its immortality is clear from the parallelism to ‘three’ and ‘odd’. Being ‘three’ implies odd’, but being ‘odd’ does not further imply being ‘imperishable’. If it did, the ‘three’, being odd would also be imperishable. And this is exactly what happens with the soul. The soul is immortal and being immortal does imply being eternal and imperishable. The soul is, therefore, imperishable. 35

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34 A point that was already made when death was defined as the separation of the soul from the body. 35 Crombie (1963), ii 521, thinks that the link between immortality and indestructibility is not suggested by Plato to be logically necessary. Cf. also Strato, fr. 123 (h), quoted by Hackforth (1955), 196. On the whole problem, see Erbse (1969), with whom I am in general agreement: Soul is a different substance from the body (as distinct, e.g., from the Aristotelian view), and extinction cannot mean for her but death. Cf. Proclus, ap. Damascius [known to Scolnicov as to Norvin as Olympiodorus], in Plat. Phaed. ii 78 W. = 226 N. = Strato 124 We: τὸ ἀπόλλυσθαι τῇ ψυχῇ θανατοῦσθαί ἐστιν, τὸ δὲ θανατοῦσθαι φαίνεται ὄν, ὡς καὶ αὐτός ὁ Στράτων φησίν, τὸ παθεῖν ἀποβολὴν ζωῆς τὸ ὑποκείμενον. O’Brien’s (1967) point seems to me to be similar, but I fail to follow his analysis of the metaphors (p. 230).

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In a certain sense this is, indeed, similar to an ‘ontological proof. The indestructibility of the soul is proved from “pure concepts”, through the analysis of the relations between them. The attribute ‘mortal’ is excluded from the soul by the mere definition of soul. But, as Moreau has stressed, the last conclusion, the imperishability of the soul, is not an attribute of the essence; it is a modality of the existence, viz. the infinite duration of the existence.36 Indeed, even granted the implication of ‘imperishable’ by ‘immortal’, for something immortal to be imperishable it still has to exist.37 As Descartes saw very clearly, “je voyais bien que, supposant un triangle, il fallait que ses trois angles fussent égaux à deux droits; mais je ne voyais rien pour cela qui m’assurait qu’il y eût au monde aucun triangle” (Discours IV, AT vi, p. 36). If God exists, he exists by necessity; but Descartes had no illusions about the scope of his proof.38 Plato’s ‘proof of the indestructibility of the soul is in a similar position: he has succeeded in showing that if soul exists and is such as it is presented in the dialogue, then it must be for ever, in as much as it must be immortal and being immortal implies being eternal (ἀίδιον). But has he proved that the soul exists and that it is of such a kind? He has certainly not given a synthetic proof of the existence of soul and of its characters. The existence of soul as distinct from the existence of the body was assumed from the start. On the other hand, this assumption was not unwarranted: it was necessitated by the distinction between knowledge and opinion (science and sensation). And this distinction was assumed as indisputable. The different characteristics or properties of the soul were ‘filled-in’ gradually, along with the gradual deepening of the analysis: ii. the soul is the principle of life; viii. it must not be physical, but incorporeal, so that it may know the ideas; and ix. it must be substantial and independent of the body, in order that it may be good or bad, and again in order that recollection may be possible. This soul, then, postulated as principle

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Cf. Moreau (1947), 328; Kant, KrV Β 620-630. Cf. Hackforth (1955), 163, and Strato fr. 123 (m), tr. by him at p. 196; Bluck (1956), 25. So also Keyt (1963), 169. 38 Cf. Wolfson’s (1934) interpretation of Spinoza’s ontological proof. 37

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of life, as incorporeal and as substantial, is, by logical necessity, out of its own characterization, immortal. But the soul so characterized is at the same time tacitly accepted as existing.39 The problem Plato was confronted with was not the problem of the existence of the soul but of what the soul is and what are its characteristics. As Plato has not yet drawn (if he ever was to draw) the distinction between essence, and existence, he could not identify them again in the concept of being cuius essentia est esse. But he could maintain that, given that there exists such a thing that cannot stop being what it is (in this case, the principle of life), this thing must exist for ever.40 [9] The thorough application of the method of hypothesis in the Phaedo can be summarized thus: The basic fact pervading the whole dialogue is Socrates’ impersonation of philosophia as intrinsically valuable. Philosophia has two aspects, the ethical and the epistemological, which are united in the Socratic dictum that virtue is knowledge. Philosophia can be defended only if it is better than relativistic ethics and epistemology. Now, Plato does not set himself to prove that philosophia is better (more valuable) than sophistry. He accepts this as given and wants to find out on what presuppositions this advantage of philosophia is founded. The first of these presuppositions is that the soul continues to exist after death and therefore it makes sense to care for one’s soul within a broader perspective than that offered by naturalistic ethics. In trying to ‘give a reason’ for this assumption, Plato puts forth the theories of palingenesis and antapodosis. This seems to bring him to a dead end. It is conceivable that this movement comes only in order to accentuate the

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39 This assumption is rather implicit. But the whole argument of the Phaedo depends on the assumption that the soul is not only such and such but also that it exists – two propositions that could be easily compressed into a single sentence. Cf. further App. 1. 40 For a somewhat different solution see Robin (1926), pp. lx, 82 n. 1, 83-4 n. 2. I think Robin does not do justice to the existential problem in the ‘ontological proof’. Cf. also O’Brien (1967). I cannot see Hackforth’s (1955) and Keyt’s (1963) point in taking soul as a form. Contra, cf. Dirlmeier (1949), 273, and especially Schiller (1967), 52: “It is to be noted that the usage of kataskhe here is different from that in 104D. The soul does not occupy the body in the sense in which trias occupies tria: the triad is the cause why three are three, the soul is not the cause why the body is body, but the cause why it is alive. The difference lies in this: the triad is the idea of three; the soul which quickens the body is not the idea of soul, but a particular soul, just as fever is a particular fever.” Cf. also Erbse (1969), 100.

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impossibility of dealing with the soul merely as with a physical object. But it is also possible that the doctrine of antapodosis is meant to find its justification in the thesis of the essential indestructibility of the soul. As Plato is silent about this point, it remains only as a speculation. The other arm of the argument states that anamnesis is a presupposition of the possibility of knowledge (hence the importance of the epistemological aspect of philosophia). Anamnesis itself presupposes the substantiality of the soul, in as much as it is incompatible with any theory such as that of harmonia which implies naturalistic ethics, which in turn is opposed to the ethical aspect of philosophia. Anamnesis presupposes as well the affinity between soul and ideas. This affinity between soul and ideas and the substantiality of the soul are grounded on a distinction between soul and body, paralleled by a distinction between knowledge and sensation. These hypotheses are supplemented by the postulation of the individuality of the soul. Of course, the identification of the soul as the knowing agent implies the recognition that the principle of intelligence is the principle of life, or part of it. Only this assumption permits the passage from anamnesis to immortality. Another presupposition of anamnesis is, of course, the existence of ideas as objects of knowledge. In their other aspect as ‘causes’ of things, the ideas are the hypotheses41 by means of which Plato gives an account of the possibility of conceptual relations holding in the non-conceptual world as well (including the physical world and the souls). This possibility is all-important in the conceptual analysis of soul in order to ascertain the validity of the conclusions for the soul itself and not only for the concept of soul.42 Is, then, the whole argument tautological? Does it amount to no more than positing a certain metaphysics and within it a particular conception of soul, and stating that in that conception and in that metaphysics soul is immortal and indestructible? Not quite. For Plato does not prove the immortality of the soul, but having accepted it as a presuppo-

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For the plural, see App. 1, pp. 275-9. That conceptual relations hold also in the non-conceptual world is in fact a presupposition of the possibility of the argument for the immortality of the soul, not a presupposition of the immortality itself; the latter is the hypothesis of the substantiality of the soul. 42

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sition of ethics and knowledge, works his way backwards to the kind of metaphysics that could support such a postulate. Plato has given us therefore a magnificent example of the hypothetical method. As in geometry the method of analysis consisted in a ‘resolution’ of the conclusion into its ‘causes’, so in philosophy the analytical method consists in a divination of the premises from which the conclusion follows. The metaphysics of the Phaedo is thus not the axiomatic basis upon which the epistemological, ethical and eschatological conclusions are based, but, quite on the contrary, it is the desideratum whereas the ethical and the epistemological conclusions are the data. That the doctrine of ideas is considered by the participants of the dialogue as sufficiently clear and acceptable is only in keeping with the method of geometrical analysis, which requires that the premises be traced back to a principle or to what is known to follow from a principle (what Socrates has called a τι ἱκανόν). But the doctrine of ideas is not itself beyond scrutiny, as Socrates hints in his remarks on the ὑποθέσεις αἱ πρῶται.43 ‘Causes’, as used, for example, in the Meno seem therefore to be exactly those antecedent facts (or propositions) that ‘support’ the conclusion.44 It is not a matter of being merely a necessary or a sufficient condition. For the notion of condition in itself does not do justice to the ontological priority of the cause over the caused. The aitia, in its general sense, is a condition as well but it is more than that: it is a πρότερον τῇ φύσει.45 When Plato speaks of the ideas as aitiai he seems to be using the term in a more restricted sense: the ideas are aitiai of being, becoming and perishing of things. In this sense the ideas are aitiai in a special way, as reasons of why things are what they are.46

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See also above, pp. 93-94 on τι ἱκανόν. The ‘higher’ hypothesis does not, therefore, destroy the lower, but, on the contrary, corroborates it. 45 Cf. further ch. i, esp. pp. 60-64, above. 46 For a good discussion of aitia in the Phaedo see Vlastos (1969). My few exceptions to his views should be obvious, especially in what refers to the notion of participation. So, I cannot agree with Vlastos that Plato was on the verge of a “reduction of physical to logical necessity”, in the manner of Leibniz, Bradley and Blanshard (p. 321). Miss W. F. Hicken voices a similar criticism in an unpublished paper. For one thing, Plato’s particulars are ontologically deficient (in type) and forever fall short of the ideas. In the Idealist position the particular is continuous with the universal and the difference between the intellectus archetypus and the intellectus ek44

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Socrates’ life and death are thus ultimately accounted for by the correlated assumptions of the existence of ideas (both as ‘causes’ of things and as objects of knowledge) and the distinction between soul and body as two independent entities. These hypotheses are brought in by Socrates immediately at the beginning of his analysis, and he hangs on to them to the end, filling in the intermediary links between them and the final conclusion, and refining them as he goes on. The result of this procedure is that when we come to the end of the dialogue we have not only a disclosure of the premises upon which the belief in the immortality and indestructibility of the soul is based, but also a fairly detailed account of the two main kinds of entities required by these premises: the ideas and the soul. Those could be indeed the ὑποθέσεις αἱ πρῶται. But it seems to me that Plato would be interested here rather in the question of the foundation of the doctrine of ideas than in the question of the justification for the postulation of a soul. That there is a soul (of some sort) is accepted without any questioning in the Phaedo, or indeed anywhere in Greek philosophy. The nature of the soul is argued mainly from its function as knowing agent and is thus, in a restricted sense, dependent on the existence of ideas as objects of knowledge.47 It would seem then that, at least according to the line of argument taken in the Phaedo, the ὑποθέσεις αἱ πρῶται would be the ideas themselves.48 And the call for re-examination of the first hypotheses could be the linking rope to the ἀνυπόθετος ἀρχή of the Republic.

-------------------------------------------typus is merely one of degree. – C. C. W. Taylor (1969) seems to think that Plato wants to distinguish logical from causal [mechanical?] necessity and that he fails to do so. Therefore, Taylor complains that “it appears ... to be impossible to discover any coherent method underlying Plato’s examples” (p. 54). 47 “In a restricted sense” because this is not to say that the soul can be reduced to an idea or to the ideas. It is one thing to say that the argument for the characterization of the soul as such and such is dependent on the assumption of ideas; it is quite another thing to say that the soul itself is dependent on the ideas. 48 Plato would be speaking here in the material mode, which could explain the plural as demanded by Bal (1950), 149 n. 1. Against Stahl (1956), 34, that “ihre Existenz [sc. of the ideas] bedarf offenbar nicht des Beweises”.

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Chapter v: The Republic [1] Apart from conducting the argument up to the hypothesis of justice, the Republic also inquires more deeply into the metaphysical foundations of the hypothetical method itself. As a matter of fact, the inquiry into justice and the inquiry into the foundations of knowledge are, from a certain point on, hardly distinguishable from one another. However, for the sake of the clarity of the overall picture, I outline in this chapter the main argument of the Republic, avoiding as much as possible the discussion of the central metaphysical passages. This is left to the next three chapters. In the next but one (ch. vii) I analyse the central passage of the Republic, the Sun, Divided Line and Cave, with special emphasis on the Divided Line, which, of the three similes, is the most closely connected with the method of hypothesis. That chapter is preceded by ch. vi, on the distinction drawn in book v between knowledge and opinion. The distinction is fundamental to the central similes of books vi-vii, and its discussion is preparatory to the discussion of the metaphysical core of the Republic. The interpretation of Plato’s doctrine of ideas as proposed there inescapably raises the vexed question of the “mathematicals” or “intermediates”. I attempt to deal with it in ch. viii, from which some further light should be thrown onto the main issues to be dealt with presently. [2] In any but the shortest works of Plato, picking up a particular line of argument in order to present it as “the main line of argument” of the work in question, is rightly to be regarded with suspicion. The danger which the interpreter faces is not only one of misplaced emphasis, but sometimes, through misrepresentation of intentions and inversion of priorities, one of downright falsification. This is particularly true in a book of such an immense scope and complexity as the Republic. This complexity has left room for the Republic to be variously described, and often quite aptly, as a treatise on education, a manual of politics, a disser-

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tation on metaphysics, an introduction to philosophy and to philosophical method, and more. This is not to say that it is impossible to isolate one line of argument and present it, for the purposes of a particular analysis, as the focus towards which all the other motifs of the work can be made to converge, and by which they and their place in the whole work can be explained. It is not thereby claimed that this is the only possible analysis of the work, nor even that it is the best. It is only claimed that a certain point of view – which still has to be justified by the very analysis that is being conducted – gives us certain advantageous insights into the work, into the whole of the Platonic corpus, and in some measure beyond that too. In this respect, and in this respect only, as a methodical term, I shall refer to “the main argument” or simply “the argument” of the Republic. In this chapter I shall try to show that the “main argument” of the Republic is one extended argument occupying most of the work, and, moreover, that this argument is essentially of the type of the argument of the Phaedo, namely, an argument conducted by the hypothetical method. It is not to be expected, of course, that the hypothetical method should be the only method used in this lengthy dialogue, although perhaps it is used more frequently than other types of argument. It will be shown, however, that the crucial steps of the argument from book ii to book x are framed in a conception of method which is essentially the same as was discovered in the Meno and perfected in the Phaedo. [3] For our purposes, we may disregard the first book of the Republic as not making any positive contribution towards the solution of the problem that it proposes. It is, to follow Cornford’s analysis, an aporetic examination of some current views of justice, viz. Cephalus’ implicit view of justice as honesty in word and deed, Polemarchus’ more selfconscious view of it as helping friends and harming enemies, and Thrasymachus’ attempt at presenting justice as the interest of the stronger. Thrasymachus maintains, moreover, that what is commonly called injustice is superior to what is commonly called justice, and, that, therefore, the unjust life is to be preferred to the just life. Towards the end of the book, Socrates raises his objections to Thrasymachus’ view, but he admits at the very end that the discussion was inconclusive and that “so

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long as I do not know what justice is, I am hardly likely to know whether or not it is an excellence (ἀρετή τις), or whether it makes a man happy or unhappy” (354C, tr. Cornford).1 Insofar as the structure of the Republic is concerned, and without entering into the historical-stylometrical discussion, we may, therefore, consider Republic i as introductory or preliminary2 to the main argument of the work, irrespective of whether it is an early dialogue or not. Book ii opens what is to be the main discussion with a restatement of the problem of the Republic: It stands to be proved that in every way it is better to be just than to be unjust (ὅτι παντὶ τρόπῳ ἄμεινόν ἐστιν δίκαιον εἶναι ἢ ἄδικον 357Β1-2). This is what Socrates had not succeeded in doing in the previous discussion and this is what Glaucon asks him to do now. He puts that later more explicitly: ἐπιθυμῶ γαρ ἀκοῦσαι τί τ’ ἐστιν ἐκάτερον καὶ τίνα ἔχει δύναμιν αὐτὸ καθ’ αὑτὸ ἐνὸν ἐν τῇ ψυχῇ (358Β4). As Socrates himself had pointed out at the end of book i, justice and injustice have to be defined and their effects on the soul are to be shown not by reference to external consequences but referring only to justice and injustice as they are in themselves. So Adeimantus too at 367 entreats Socrates to show not only that justice is superior (κρεῖττον) to injustice, but also “what good or evil each by itself causes in its possessor” (B3-5; cf. D3-4, El-5). It is important to see that here, even more markedly than in the Phaedo, the conclusion of the whole argument is firmly believed from its very beginning. What is being asked for is a proof of the conclusion. Glaucon and Adeimantus are portrayed as convinced of the superiority of justice (cf. also 368A8 ff.); Socrates too, of course, agrees with them in that (358A) and Adeimantus takes him at his word (367C5-6). The two brothers play the advocati diaboli explicitly in order to provoke Socrates into proving a conclusion they already believe to be true – although they themselves cannot give any explanation of their belief in the truth of this conclusion (much as Simmias and Cebes in the Phaedo).

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1 In this respect, the conclusion of Republic i is less advanced than the conclusion of the Gorgias, and stands on a par with the Meno. But Republic ii opens with a note that is reminiscent of Socrates’ (unproved) convictions in the Gorgias. 2 Cf. 357A2 προοίμιον.

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In the language of the Meno, the two brothers have alethes doxa or orthe doxa about justice and injustice, but they are not able to give an account of their doxa. They are themselves aware of the shortcomings of this state and they want to be led out of it into episteme. This is what Socrates does in the Republic. [4] As Socrates remarked at the end of book i, and as Glaucon and Adeimantus echoed in their requests, the inquiry into the superiority of justice implies a prior inquiry into the nature of justice itself. This is the same point as was made in the Meno about the impossibility of inquiry into the ποῖον of a thing without first inquiring into its τί. There this requirement was abandoned at Meno’s insistence, only to be complied with later, in a roundabout way. In the Republic there is no need for subterfuges: the importance of the τί ἐστίν question is immediately recognized. But the question, “What is justice itself?”, is a very obscure question, as Socrates puts it, presumably because we have no direct access to justice in itself, and we cannot see it as we can see other things that we use to define, like bees or colour or surface. So that this question too has to be approached indirectly. Socrates points out that “we say that justice is in the individual man, and is somehow also in the whole city” (368E2-3). This starting point is important, for on it the whole of the argument of the Republic is based. Socrates starts here from the (for them) accepted fact, from what is said: that justice is somehow (που) the same in the individual man and in the city. It is not sufficient that justice is analogous in both:3 the sameness of justice in the individual man and in the city is necessary, for only this sameness can warrant the later transfer of conclusions from the city to the individual soul.4 This is exactly the point of the simile of the small and the large letters. The letters written in small and in large characters are the same let-

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3 It is not presented as an analogy. Analogy is for Plato essentially a “rule of three”, in which, being given three terms and the point of comparison, the fourth term is sought. The Sun in book vi is a good example of Plato’s use of analogy. 4 The conditions of sameness are defined by the theory of ideas: x and y are “the same” if they participate both in the same idea.

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ters, otherwise the larger inscription would be useless. Accordingly, after reading the large characters one has to make sure that the letters are the same (368D7). And this is exactly what Socrates does later on when he makes sure that the soul has the same three kinds as the city. It is thus assumed that “justice” is not said of the individual and of the city by pure equivocation.5 But, for the time being, this identity of reference is assumed only, on the basis of common usage (φαμέν). The relation between the two kinds of justice is left as yet unspecified (που). Socrates proceeds then to develop the argument on this assumption, unproved as it is. An inquiry into the nature of justice in the city presupposes an inquiry into the nature and structure of the city itself. Only after the nature of the social organization is understood can one proceed to investigate what constitutes justice in this organization. The central and greater part of book ii inquires into the composition of the city and into the education of its citizens, which education, being the best possible, will inevitably bring about in the city all the aretai, and, among them, also justice. And at 433E12-13 justice is agreed (ὁμολογοῖτο) to be in some way (πῃ) “the having and doing what is one’s own and proper to oneself” (ἡ τοῦ οἰκείου τε καὶ ἑαυτοῦ ἕξις τε καὶ πρᾶξις). Socrates proceeds to explain and qualify this definition. By “doing what is one’s own” he does not mean that a cobbler should stick to his trade and should not engage also in carpentry; there would be no great harm in that (434A). But there is another kind of πολυπραγμοσύνη, that brings destruction to the city: that is the one that brings to the disruption of the natural organization of the city, as when someone who belongs by nature to a lower function of society tries to discharge functions that are not rightfully his (434A9B7). Justice is keeping the proper arrangement of society according to its natural order: “Where there are three orders, then, plurality of functions (πολυπραγμοσύνη) or shifting from one order to another is not merely utterly harmful to the community, but one might fairly call it the extreme of wrongdoing” (B9-C2, tr. Cornford).

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Cf. also 435A5-B3, quoted below, p. 125.

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[5] Socrates has thus solved the first part of the problem posed in his simile of the large and small letters: justice in the city was, if not defined, at least characterized. Now one must look into the small letters and see “whether they are the same” as the large letters. If, says Socrates (434D), we find this same eidos in the individual man and we can agree that is justice there too, then our search will have ended. And if not, we shall have to go back to the city and check our findings here with our findings there. Socrates seems prepared to lean quite heavily on the simile of the large and small letters, and at first sight this rather trivial comparison will not bear that much. But in fact, the simile is no more than an illustration and carries very little argumentative burden: the actual weight of the argument falls on the assumption behind 368E2-3, which is avowed only now at 435A5-B3: “If two things, one large, the other small, are called by the same name, they will be alike in that respect to which the common name applies ... Accordingly, in so far as the quality (εἶδος) of justice is concerned, there will be no difference between a just man and a just society.” Were it not for this assumption that speaking of an ἀνὴρ δίκαιος and a πόλις δικαία is not mere equivocation, the simile of the letters would be itself unfounded, for it would be impossible to show that the inscription is the same here and there without begging the question. I shall return to this point later. Justice in the city was said to be a certain interrelation among the parts of the city. If justice in the individual is supposed to be the same as justice in the city, then the individual soul will also be expected to have three parts or kinds, identical to those of the city (435B9-C3). But this inquiry into the nature of the soul, and indeed the whole inquiry into the presuppositions of the argument up to this point, necessitates a longer way (μακροτέρα ὁδός). Here, as with the δεύτερος πλοῦς in the Phaedo, the hypothetical method is explicitly introduced.6 Here as there, the ostensive cause for its introduction is the emergence of a problem which cannot, even on a primary level, be dealt with in the material

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6 The μακροτέρα ὁδός, as the δεύτερος πλοῦς, has of course a wider reference than just the hypothetical method. For the relation between the hypothetical method and the theory of ideas, see chs. iv and vi.

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mode, without overt reference to concepts and conceptual procedures. And, as there so here, although Socrates draws his company’s attention to the new method only at this particular point in the argument, he has actually been using it for quite a while. After this brief interlude, the investigation into whether or not the soul has those three kinds starts at 435 E. Socrates begins by proposing that “We must admit that the same qualities (εἴδη) and characters (ἤθη) that appear in the state must exist in every one of us; where else could they have come from?” (El-3). It has been suggested that Socrates is stating here what might be called “the whole-part principle”, viz. that a city has the characteristic F if and only if its citizens (all of them, most of them, an influential number of them) have the characteristic F, and because they have the characteristic F; and moreover that Plato intends this principle to hold for all the characteristics of the city. Prima facie the principle seems sound: a happy crowd of sailors (to use Prof. B. Williams’ example) is a crowd of happy sailors, and the crowd is said to be happy because the sailors are said to be happy. But – so runs the argument – if Plato intended this principle to have general application, so as to be able to use it in the proof that justice in the soul and justice in the city are the same, then it conflicts with Plato’s contention at 420, that not all characteristics of the city as a whole are necessarily shared by all, or by most, or, in extreme cases, by any of its citizens.7 But it rather seems to me that Plato did not intend this principle to have general application and that it has quite a restricted function in the argument. Firstly, the context in which this principle is used is not the context of the inquiry into the nature of justice, but that of the inquiry into whether the soul has the same three kinds as the city. And as we shall see later, Socrates infers the identity of justice in the soul and in the city at 441D5 not from the whole-part principle, but from the conclusion that the soul and the city have the same three gene. If justice is defined as the

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7 The difficulties of the whole-part principle were suggested by Prof. B. Williams in a forthcoming paper. [Apparently a reference to Williams (1973); see bibliography on p. 37 – ed.]

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good ordering of the parts of the soul/city, the condition for the identity of justice in the soul and justice in the city is that the parts of the soul and the city should be respectively the same (their sameness being determined within the framework of the theory of ideas; see p. 147, below). Secondly, the examples given immediately after the statement of the principle (435E3-436A3) show clearly that it is intended to apply only to some definite characteristics: the examples are of bravery, love of study and love of money, i.e. the three εἴδη or ἤθη corresponding to the three gene of the city and to the three gene of the soul that are to be proved in the sequel. Thirdly, by Plato’s own definition of justice, the whole-part principle cannot apply to it. For, if justice is some kind of organization of the parts of the city (or of the soul), then it is like a well-arranged crowd of sailors rather than like a happy or brave crowd of sailors: but a wellarranged crowd of sailors is not a crowd of well-arranged sailors. Moreover, if the just city is composed of just men and is just because the men are just, then either “just” is used homonymously or the whole-part principle applies also to justice in the individual man, and we have an infinite regress. This infinite regress can be avoided by reformulating the principle so that a city is F if and only if its citizens are F, but not necessarily because they are F. But this emendation runs counter to the text at 435E3 οὐ γάρ που ἄλλοθεν ἐκεῖσε ἀφῖκται (cf. Ε4 ἐκ τῶν ἰδιωτῶν), which can hardly be taken not to imply some sort of explanatory connexion. I do not think, therefore, that the principle has general application. It seems to me that it comes only to provide a provisional basis for the argument that is to follow. It is provisional in as much as it does not by itself support the conclusion that the soul has three gene or even that it has three εἴδη or ἤθη , but only presents a prima facie conclusion whose adequate proof it is Socrates’ business to devise. That this is so I shall try to show presently. At 435E Socrates has procured Glaucon’s admission that the city and the individual have the same characters (εἴδη, ἤθη). His argument is indeed of the sort that “a happy crowd of sailors must be a crowd of happy sailors”. Admitted then that we have these three characters, the

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question is raised whether we exercise (πράττομεν) each of these with something different in our soul, or with the whole soul. At 436B5 Socrates begins the examination of the proposition he has taken for granted a few lines above by asking for a determination whether these characters in the soul are identical to one another or not.8 In order to answer this question, Socrates resorts to a hypothesis (437A6 ὑποθέμενοι): “It is clear that the same thing cannot act or be acted upon in opposite ways in respect to [the same part of] itself,9 and in relation to the same thing, at the same time; so that if we should ever find (ὥστε ἄν που εὑρίσκωμεν) those [opposites] in them [i.e. the thing in consideration, now regarded as many] we shall know that it was not the same but many” (436B8-C1; cf. 436E8-437A2). It is important to note the difference between the hypothesis of noncontradiction and Aristotle’s correspondent law. In Aristotle’s formulation, τὸ γὰρ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτό (Met. Γ 3. 1005bl4. Cf. b26 and Ross’ note ad loc.).”10 What in his view is impossible is that the same thing should at the same time belong and not belong to the same subject, or – in another formulation – that opposites should belong at the same time to the same subject. If this seems to be the case, the opposites should be suitably qualified “to guard against dialectical objections”. In Plato’s version of the principle, it is the subject, not the opposite attributes, that is qualified; and if it cannot be adequately qualified, “we shall know that it was not the same but many”.11 It would seem that Plato held two versions of the principle of noncontradiction: the unqualified formulation of Phaedo 103B4-5, and the qualified formulation of Republic 437A6 (cf. also Sophist 230B7-8).

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8 436B5 αὐτά can only refer to A8 ἕκαστα. This interpretation is supported by the continuation of the argument at 437BC, where τὸ βούλεσθαι and τὸ ἀβουλεῖν are clearly εἶδη such as desire and spiritedness, not the corresponding gene in the soul. 9 B8 κατὰ ταὐτόν. 10 For a fuller statement of what a real contradiction is, see Soph. El. 167a23-27. 11 Prauss (1966) seems to think that this is a fundamental point in Plato’s conception of the sensible world. But it must be remembered that Plato is introducing this principle at this particular point with a restricted purpose in mind, as a hypothesis for the solution of this problem, and that, in this context, he is more interested in the unity or otherwise of the subject (namely, the soul) than in the genuineness or otherwise of the contraries.

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The ideas do not admit of opposites under any qualifications. By contrast, it is an essential feature of the sensible world that it does not admit of opposites only if suitable qualifications are added. Or, as Plato is more often inclined to view it, that it does admit of opposites unless suitable qualifications are added. Plato apparently thought this characteristic of the sensible world to be an index of ontological deficiency. His ontological criterion for distinguishing between the δύο γένη τῶν ὄντων seems to have been based on the principle of non-contradiction: beings which do not admit of opposites absolutely as against beings which do not admit of opposites only qualifiedly. The question asked at 436B5 whether the characters of the soul are distinct is tackled at 437B ff.: Assent and dissent, striving after something and refusing it, attraction and repulsion, and all such actions and passions (ποιήματα, παθήματα 437B4: cf. 436Β8 ποίειν ἢ πάσχειν, 437Α1-2 πάθοι ἢ καὶ ... ποιήσειεν) are posited (θείης) as opposites. Now thirst, insofar as it is thirst pure and simple is a desire for water, and hunger is a desire for food. The intervening argument at 433A-439A purports to isolate the desire for water in as much as it is merely a pure “craving for drink from a more complex desire whose object includes the pleasure or health expected to result from drinking”.12 This craving is the desire pure and simple without any admixture of elements extraneous to it, and only such can be, for Plato, the desire considered as one of the opposites in the soul.13 “Then the soul of the thirsty man, in so far as it is thirsty, wants only to drink, and longs and strives after this” (439A9-B1). But is being attracted and repelled by the same thing a case of “p and not-p”? Plato says they are enantia. What does he mean by that? One must examine Plato’s own examples to see what he probably had in mind. Plato makes clear that the opposition is between thirst (unqualified) as a desire for drink (unqualified) and some element of calculation about the pleasure or health to be expected from the drink, which counteracts

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12 Cornford (1941), 134. Not “blind craving”, as Cornford has it. Plato is making a logical, not a psychological, point. 13 Cf. 475E6 ff.

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thirst. This case is different from the case of, say, simultaneous thirst and hunger, of which only one can be satisfied at a time. For in the last case, the opposition between thirst and hunger is accidental, as they are not intrinsically connected with the same object (drink, food). Whereas in Plato’s case the attraction and repulsion refer to the same (intentional) object. For thirst, insofar as it is thirst pure and simple, is a “craving for drink”, not for “wholesome drink”. And “drink” is here anything that can be the intentional object of thirst. Therefore, as Plato uses the term “drink” here, according to his own purposes, if the soul wishes unwholesome drink (i.e. something which is not “objectively” drink), still the object of the soul’s thirst is, in any case, (“subjectively”) drink. And if the soul, at the same time, shuns this drink, it is being attracted and repelled by the same object. Thus it might be said that oppositions such as between thirst and hunger are not pros tauto [i.e. “with regard to the same thing”: ed.], while those such as between thirst and the calculation of pleasure or health expected from drinking are.14 Now, if there is something that prevents the soul from drinking, this must be, by our hypothesis, something different from what impels her towards drinking. That attraction and repulsion or wanting and notwanting are opposites has been agreed at 437B; that both cannot be true of the soul, in respect of the same part of itself, in respect of the same thing (namely, water, unqualifiedly), at the same time, follows from the hypothesis by simple substitution. 439C-D brings the argument to its conclusion by asserting that attraction and repulsion are true of the soul, as a matter of fact, at the same time, in respect to the same things, and that, therefore, one must distinguish between two different elements in the soul: reason and desire. A similar, though less convincing, argument supports the desired conclusion for the third γένος.

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14 The question remains of such cases as the fascination for the horrendous, where the attractive feature seems also to be the repulsive one. Leontius’ story at 439E could be an example of this. If this is so, I am inclined to say that Plato would consider such cases of ambivalence – which are by their nature cases in which the opposition is not accidental – as warranting a division in the soul. Although Plato accepts the traditional tripartition of the soul, he does admit she might be differently divided. His main point seems to be: a. that the soul – in its terrestrial life – has “parts” or “aspects”, and b. that it has (at least) a rational part and an irrational part.

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[6] Why is the principle of non-contradiction said by Plato to be hypothesized? Why does he say that “if we ever come to think otherwise, all the consequences based upon it [sc. upon the principle of noncontradiction] will fall to the ground”? (437A, tr. Cornford). What sort of evidence could Plato imagine to be valid as a counter-example to the law of contradiction, even in the form it is formulated by him? Indeed, if Plato were introducing here the principle as a general law of being or of thought, it would be necessarily impregnable to counterexamples, for it would itself have to serve as a criterion of what a counter-example is. The fact that Plato allows at this stage the possibility of counter-examples shows that he did not consider this principle, at this stage of the argument, as a supreme law of being or of thought. At 437A he is quite explicit about the status of this principle: it is a hypothesis that is to have consequences (συμβαίνοντα) deduced from it, and if it is subsequently proved false, all its consequences will be automatically “untied” (λελυμένα ἔσεσθαι). So far the principle of non-contradiction is not different from any other assumption that is made in the course of the argument. Indeed, like any other hypothesis, it is introduced for a very definite purpose: in order to have the three gene of the soul derived from it. This is not to say that Plato would not maintain the principle in a wider context.15 But two important reservations must be kept in mind: a. The principle is formulated specifically for the function it comes to fulfil, i.e. to serve as an important premise in an argument aimed at providing that the soul performs different acts in virtue of its different gene. Therefore, a general formulation of it might not coincide with this specific formulation.16 b. As any other hypothesis, this one too has to be supported in its turn by a higher hypothesis, and until this is not done its truth is only provisional. And therefore, even though the possibility of a counterexample might not be immediately apparent, still, in as much as this

-------------------------------------------15

Phaedo 102D is a case in point. Cf. also Sophist 230B7-8. Although it still might be claimed that this formulation is specific to the sensible world, not to this particular problem. But I cannot see why an Aristotelian hypothesis of noncontradiction would not be acceptable for the sensible world in general, were it not for the specific enunciation of this problem. 16

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principle is, at least in this particular context, only a hypothesis, it is open to refutation. It may be rightly asked: How can the principle of non-contradiction itself be proved? Is it not itself the principle that is implied in every proof? Unfortunately, Plato does not seem to answer this question in the Republic. But there can be no doubt that he considers the principle to be sound and, as it is apparent from 437A, to be in need of further support. It seems to me that an answer to this question may be elicited from the Republic, even though it is not explicitly stated. One should start by correcting the question: What is to be proved is not the principle of noncontradiction as a law of thought or of being which, as such, is implied in every proof. Rather, what stands to be proved is the hypothesis of non-contradiction as used in this particular proof. One important difference between the law and the hypothesis is in their modality:17 the law of contradiction is true (categorically or absolutely); the hypothesis of non-contradiction is only posited as true, it is hypothetically true. This gap between the absolutely true and the hypothetically true is essential to the hypothetical method. For every assertion in the “upward path” is made only hypothetically, is only assumed to be true, although the proposition asserted may in fact be true (categorically). This tension between the two modalities disappears only at the unhypothetical beginning, which, by being unhypothetical, is categorically true, and, by being a beginning, transforms the hypothetical truth of the dependent propositions into apodictic truth. In the language of the Sun, it is the source of their ousia as well as of their power of being known.18 The hypothesis of non-contradiction depends, therefore, at least on the possibility of transformation of hypothetical truths into apodictic truths. From a formal point of view, the difference between a hypothesis and a valid law is in their respective modalities. True as this is, one

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17 It should be noted that I am using the term “modality” as in classical syllogistic, referring to propositions as categorical, apodictic, or problematic, and not as necessary, possible, etc. 18 More on this point in the next chapter. – The transformation of hypothetical truth into apodictic truth has the same function, in Platonic dialectic, as the separation of the conclusion from its premises has in classical syllogistic. But for Plato there is no separation of conclusions, hence no categorization, even after the hypothetical beginning is reached. Cf. 511B ff., esp. D2 kaitoi noeton onton meta arkhes.

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might still feel the answer is unsatisfactory, for it gives no explanation as to what could count as a reason for this change of modality. Plato himself does not state whether he thought the hypothesis of noncontradiction to depend on some other hypothesis; but it seems improbable that he would not have given some thought to such a central point in his argument. I submit, then, that the principle of non-contradiction as assumed at 436B-437A is subordinated to the unhypothetical beginning and cannot be assumed without qualification to be the supreme law of thought or of being. And, of course, even when expressed as the law of non-contradiction, it is still not the supreme law of thought or of being, for it is a law only by force of the unhypothetical principle. Now, Plato has two versions of the Principle of Non-Contradiction. The one is implied in such remarks as: “What about this? The equals themselves – can they ever look to you unequal, or equality – inequality? – Never, Socrates.” (Phaedo 74C1-3). Namely, it is impossible that a thing (in this case, an idea) be A and not-A. Compare this with Parmenides’ version: “For this will never be forced: that it is without being” (fr. 7.1 DK). It is impossible for a thing to be and not to be. Anything that would break this principle is not and cannot be thought. It is to be noted that in this version of the principle of non-contradiction, at least as Plato presents it, the terms that can come in place of A are what we would call “unqualified descriptions (or predicates)”, such as “equal” as opposed to “equal to something” or “equal for someone” or “equal at a certain time”. The characters to which this principle applies are of the type “beautiful”, “equal”, and any qualifications such as “in respect of x” or “at time t” are considered as not forming part of the predicate itself, but as being qualifications to the principle of noncontradiction – and as such inadmissible by Parmenidean standards. The consequences of what would be named the “strong” version of the Principle of Non-Contradiction were drawn by Parmenides himself, and, if E. Hoffmann 19 is right, by Zeno:

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E. Hoffmann (1923).

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What do you mean, Zeno? You say that if being is multiple, it must be like and unlike, and this is impossible; for what is unlike cannot be like, and what is like unlike? Is this your argument? (Parmenides 127E)

So too in the fragments collected by Diels and Kranz: In his book which includes many proofs he shows in each of them that whoever says that the many are contradicts himself, etc. (Simplicius, Physica 139.5 ff. = 29B2 ff.)

Zeno showed once more that the sensible world does not comply with the “Parmenidean” Principle of Non-Contradiction: if the many are, then they are both like and unlike, both finite and infinite, and so on, in forty different ways, as far as his ingenuity would carry him. It is obvious that Zeno’s arguments prove nothing more than that the many are like or unlike in respect to different things, and that they are finite and infinite under different aspects. But to bring this up against Zeno would be to miss his point. For the point of the “strong” principle of non-contradiction of “Parmenides” is that what is A cannot be not-A – where “A” stands for an unqualified term. Predication is therefore impossible for “Parmenides”. He reckons two possibilities only: what is A is A (i.e. A = A), or what is A is not-A. The third way, according to which what is A is also B, is not seen by Parmenides as a real alternative. For this would require that A and Β be qualified in different respects. Six can be said to be both half and double if we supply the respective qualifications “of twelve” and “of three”; Socrates can be said to be both short and tall if we supply the qualifications “at time t1”, “at time t2”. But in “Parmenidean” terms these qualifications make no sense. On this view, the characters “beautiful at time t” or “beautiful in respect to x” – if they are to be allowed at all – are (ontologically) posterior to the character “beautiful”. Now, the character “beautiful” in itself does not give us any warrant for the possibility of its being at one time but not at another, or in one part (of the subject) but not in another. Thus, the qualifications of the simple character are seen as external to it and as contingent. Further, in an ontology that does not distinguish between substance and attribute, sentences such as “(the) man is man” and “(the) man is musical” would be on a par, unless there

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is some other way of maintaining that “to be” πολλαχῶς λέγεται. But “Parmenides”, taking “what is (A)” as unqualified and univocal, could not allow for what-is-man to be also what-is-musical. Plato accepts the unrestricted Principle of Non-Contradiction, and he sees, with Parmenides and with Zeno, that this principle does not hold in the sensible world. Its validity is limited to the world of ideas only. Only the beautiful itself is unrestrictedly beautiful, only the ideas fully are. For Plato, as for Parmenides, the intellected reality is undoubtedly real. But for Plato, as distinct from Parmenides, the sensible realm is not to be discarded as totally illusory. Sensible reality is of a derivative character. While the reality of the intellected realm is above doubt, the sensible world is, in a sense, merely factual. For it seems to me that, if anything is beautiful apart from the beautiful itself, it is not beautiful because of anything else, but because it partakes of that beautiful (Phaedo 100C4-6).

That the beautiful itself is beautiful (not “that there is a beautiful in itself”), this was accepted, at least at that stage of the argument in the Phaedo as evident, or at least as a “strong hypothesis”. What is being presented as problematic is the claim that “something is beautiful besides the beautiful itself”. That the beautiful itself is beautiful is clear, insofar as it follows directly from the Principle of Identity. But if, under pressure of the sensible world, we want to allow the character “beautiful” to something that is not the beautiful itself, say Hippias’ beautiful girl, or the beautiful sciences in the Symposium, we break “Parmenides’” prohibition. For this would mean to say of what is not the beautiful that it nevertheless is beautiful; in other words, to say of A not only that it is A (girl, science), but also that it is Β (beautiful). On “Parmenides’” assumptions, the first proposition is meaningful and necessary, the second is meaningless. Nevertheless, Plato is suggesting here the possibility that the relation between something different from the beautiful and the beautiful is not the same as that between the beautiful itself and itself. If it is possible that something that is not the beautiful be beautiful, then the relation

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between it and the beautiful has to be different from the relation between the beautiful and itself. Call this new relation “partaking”, “presence”, “communion”, or what you will. The difference between the two relations was already implicit in Plato’s former comments on the difference between the intelligible and the sensible (Phaedo 74B): sensible things look equal under one aspect (or to one person) but unequal under another aspect (or to another person);20 not so the equal itself. Plato’s conclusion is that the sensible equals are different from the equal itself. The Symposium has a long list of differences: the beautiful itself always is and never becomes or passes away, it does not augment or diminish, it is not beautiful here and ugly there, or beautiful at one time and ugly at another, or beautiful with respect to one thing and ugly with respect to another, or beautiful in one of its parts and ugly in another, beautiful to one person and ugly to another (211A1-5). This recognition of the possibility that something might be both beautiful and not-beautiful, albeit in different respects or at different times, is in clear contravention of the “Parmenidean” Principle of NonContradiction. This principle can be circumvented only if the sensible thing is what it is said to be in a different sense from that in which the idea is said to be what it is. This new sense of “being” requires also a new interpretation of the principle of non-contradiction. It is possible for things in the sensible world to be both A and not-A (where “A” stands for an “unqualified” term). But this is not to say that the sensible world is completely irrational and contradictory, as Parmenides would have it. As a matter of fact, the principle of non-contradiction is only differently understood: A and not-A can be qualified in so many respects. But for Plato the qualified character is still dependent on the unqualified, and this new understanding of the principle of non-contradiction amounted in Plato’s eyes to a weakening of it.21

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Or: “look sometimes equal, sometimes unequal” – apparently an old variant. The wording itself of Plato’s principle of non-contradiction in the Republic makes it clear that the predicate he is thinking of is “A” (unqualified), not “A-in-respect-of-x” or “A-at-timet”. But did Plato see the restrictions as applying to the predicates “A”, “not-A”, or to the principle “not (A and not-A)” as a whole? It seems to me that as Plato considered the qualified 21

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Plato saw in this weakening of the principle, as the Phaedo has it, a sign of the ontological “deficiency” of the sensible world as against the world of the ideas. These are the “deficiencies” listed in the Phaedo and in the Symposium. Accordingly, the “weak” Principle of Non-Contradiction includes several restrictions: “at the same time ... under the same aspect ... in relation to the same thing ...” It should be remembered that this version of the Principle of NonContradiction was introduced in order to inquire into the nature of the soul, i.e., into the nature of something which is not an idea, and to which, therefore, the “strong” Principle of Non-Contradiction does not apply. But, from a purely rational point of view, the ontological status of non-ideal entities is at the least precarious, as Parmenides had emphasized. In other words, the “strong” Principle of Non-Contradiction is firmly accepted by Plato, but it does not apply as it stands to the soul. On the other hand, the “weak” Principle of Non-Contradiction is problematic in the same manner and to the same extent that the sensible world is problematic. Plato does not doubt that “Parmenides’” “strong” Principle of Non-Contradiction is valid. But he cannot ascribe the same validity to the proposition that the Principle of Non-Contradiction can be restricted, i.e. that there might be a way in which things could be both A and not-A.22 Now we are in a position to answer the question raised at the beginning of this section. Firstly, what is put forward as a hypothesis is the restricted Principle of Non-Contradiction. The “Parmenidean”, “strong” Principle still remains a general principle of being and thought. But the restricted principle, posited for the first time at Republic 436 is presented as problematic. So far, the only basis for the restriction of the Principle of NonContradiction is factual; its status is as the status of the claim that something may be beautiful apart from the beautiful itself.

-------------------------------------------predicate as prior to the unqualified, at any rate the principle would not be intelligible in its own right if it referred primarily to qualified predicates, and therefore would turn up to be in any case a variant of the unqualified principle. 22 So Kant too maintained that the version of the (non-propositional) Principle of NonContradiction referring to temporal conditions is synthetic. The principle should rather be formulated: “Nothing can have a predicate which contradicts it.” Cf. KrV B190-2.

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Next, the proposition that it is possible that the Principle of NonContradiction be restricted is, at this stage, unproved, and it is posited in order that the required consequence might be drawn. We have seen above that the gist of the hypothetical method is in that it starts from the consequence required and looks for the premises that could support this consequence, and then again for the premises that could support the previous premises, and so on. The argument about the gene of the soul starts from the question whether the soul is “uniform” or “multiform”. The hypothesis from which the “multiformity” of the soul is derived is the restricted Principle of Non-Contradiction. The principle is actually built so that it might support the conclusion required. As we have seen, Plato could have stated the principle in a form somewhat closer to Aristotle (but not quite in Aristotle’s form, for Plato does not recognize in the Republic the distinction between the subject and what “belongs” to it). But were he to do so, he would be unable to use it in order to derive from it the “multiformity” of the soul. It seems, therefore, that even if the restricted Principle of Non-Contradiction has some application besides this case – in fact it is applicable to the whole of the non-ideal world – still the immediate intention in its being introduced here is that it serve as a hypothesis in the considerations about the nature of the soul. Lastly, it should be noted again that not all the premises on which Plato bases his argument are called by him hypotheseis. Actually, Plato never gives this name to more than one premise in each step of the argument. There are, of course, sections in his arguments, in which he does not use the term at all, and this is easily accounted for by the literary necessity of keeping the natural tone of the dialogue. But, as I have shown above in ch. ii, some consideration of Plato’s use of this term shows that it applies to the premise which Plato thought to be of special importance and which supports the conclusion, as it were, directly. It is also to be expected that this is to be, among the premises of the argument, the one that is problematic, at least for Plato. Indeed, as Robinson has shown,23 sometimes Plato states his chief premise only, and he seems to be deriving his conclusion directly from a single premise. In the case we are considering, among the premises Plato needed in order

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Robinson (1953), 29 ff.

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to prove the “multiformity” of the soul, this one about the possibility of restriction of the Principle of Non-Contradiction seemed to Plato to be questionable. The other assumptions are agreed among the hearers, and if Plato deals with them somewhat at length, it is in order to state them with adequate precision, not because they need to be argued. Thus, as Plato saw it, the hypothesis he needed to supply to his system of “standing assumptions” in order to draw the required conclusion, and will have to be argued for, is the restricted Principle of Non-Contradiction. But where, if anywhere, does Plato argue for the restricted Principle of Non-Contradiction? Explicitly, as far as I can see, nowhere. But, if I am right in pointing to the correlation between the epistemological and ontological status of the restricted principle and that of the sensible world, then an argument for the (restricted) reality of the sensible world is ipso facto an argument for the validity of the restricted Principle of Non-Contradiction. Now, the rationale for the very assumption of a sensible world is given in book v, in the discussion of doxa and episteme. As I show in more detail in the next chapter, the assumption of a sensible world is a necessary precondition of the distinction of doxa from both episteme and agnoia. And this distinction is accepted by Plato as a fact. The validity of the restricted Principle of Non-Contradiction is thus required by the fact that doxa is different from episteme, without being however agnoia. When all is said, one might still object that the ultimate ground for the distinction between the two Principles of Non-Contradiction is, after all, factual. It is. But then, this is the essence of the hypothetical method, that it seeks reasons for what is already believed to be true. [7] The soul has, then, three gene, and these are the same that exist in the city: the genos which is responsible for desire and luxury (cf. 372E ff., and esp. 373D6-10), those whose function is bravery, and that whose function is reasoning. But this is only “fairly agreed” (ἐπιεικῶς ὁμολόγηται 441C5), for it depends on unproved premises. Socrates is very careful to point out the provisionality of this conclusion; but, granted that, he proceeds immediately to draw the consequences from it: “Then is it not at once (ἤδη)

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necessary, that the city be wise in the same way and by the same (element) as the individual?” (441C9-10) And the same is true of courage. If, then, the gene are the same and the corresponding excellences are the same in the city and in the soul, it may be said also that a man will be just in the same way that a city is just: in the right order and interrelation of their three gene. And this was, of course, what was assumed at 368E2-3. At 443B6, Glaucon declares himself satisfied. Injustice is, accordingly, civil strife (στάσις 444BI) in the city or in the soul, and ἀλλοτριοπραγμοσύνη and rebellion of some part against the whole. At the present level, then, the discussion may be concluded and the problem solved: justice is natural order, injustice is unnatural disorder, much as health and disease of the body. For, “to produce health is to put the various parts of the body in their natural relations of authority or subservience to one another, while to produce disease is to disturb this natural relation. – Yes. – Then to produce justice, I said, is to put the parts of the soul in their natural relations of authority or subservience, while to produce injustice is to disturb this natural relation, is it not? – Surely, he said. – Then virtue, seemingly, will be a kind of health and beauty and good condition of the soul, vice a disease and ugliness and weakness. – That is true” (444D-E, tr. Lindsay). And if justice is natural order and health, then it is clear that it is superior to injustice and is more desirable than it, in the same way that health is more desirable than sickness. By comparing justice to health, Socrates classified it in Glaucon’s second class of goods (357C1-3), viz. those valued both for their own sake and for their consequences.24 This comparison provides the basis for the vindication of the rewards of justice and the myth of Er in the tenth book: justice, being “a kind of health”, is necessarily superior in itself and in its consequences. I shall return to this later.25

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24 That Socrates accepts the classification is clear from the passage itself. – For an analysis of justice in Republic ii – x as “Inbegriff der Ordnung” and οἰκεῖος κόσμος of the soul, see Krämer (1959), 83 ff. 25 Another interesting point in Glaucon’s classification is the three examples he gives: knowledge, health and sight (cf. also 367C) – all of them connected, at different levels, with the concept of justice.

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[8] Once the definition of justice has been arrived at, there is no need to look further for a definition of injustice. For the definition of justice is, by implication, the definition of injustice. “The eidos of excellence is one, those of badness are infinite” (445C5).26 Badness is, then, not so much the contradictory of excellence as a deviation from it, admitting of gradations. Plato supposes, of course, that, since “excellence” is for him univocal, the scale excellencebadness is unidimensional, and all the cities, possible and existing, and the souls corresponding to them, can be measured against this scale. His saying that the forms of badness are infinite suggests therefore that the scale is continuous. But, for the sake of classification, four among the forms of badness are worth considering (C6-7).27 And again the examination of the excellence or otherwise of the several cities is about to be undertaken for the sake of the classification of the different types of soul, when Socrates is interrupted. This interruption will take about one hundred pages and develop into the central and most important part of the Republic. In this central part, the metaphysical and epistemological justification will be stated for Socrates’ answer to Glaucon’s and Adeimantus’ problem. But, for our purposes, it will be more convenient perhaps to postpone the examination of this part of the Republic to the next chapters, where it will be dealt with in greater detail, from a different angle. On the other hand, the placing of the metaphysical justification at this point is crucial, as we shall see presently, and it will prove impossible to ignore that between 445C and 543C the distinctions between knowledge and opinion, between the one idea and the many participating in it, between the mathematical sciences and dialectic, all were agreed upon as true and accepted as justified by the unhypothetical idea of the Good. Keeping this in mind, we shall conclude the argumentation, resuming it from the point where Socrates himself picks up the thread at 543C.

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26 It is interesting to note the fluctuation of the sense of εἶδος in this sentence. In referring to “excellence” it must mean “idea” in the technical sense; for the εἶδος of excellence which is one is not its visible “form” or “appearance”, since these are obviously many. But in referring to “badness” it must mean “form” or “variety” in the non-technical sense: an idea can hardly be said to be infinite in number. 27 Presumably here because each has a peculiar eidos – cf. 544C8-D1 and 445C9.

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Not much has to be said on the conclusion of the argument that bears directly on our subject. The assumptions upon which justice had been defined and shown to be superior to injustice were now justified by the strict definition of σοφία as ἐπιστήμη and by the more general support – not worked out in detail – the doctrine of ideas lends to the other assumptions such as that of the analogy of soul and city. The difference in the modal status of the premises before and after the central metaphysical passage is well brought out by a small point in Socrates’ resumption of the argument: At 445C9-10 he is about to begin the classification of bad cities and souls by assuming again the parallelism of soul and city: Ὅσοι ... πολιτειῶν τρόποι εἰσὶν εἴδη ἔχοντες, τοσοῦτοι κινδυνεύουσι καὶ ψυχῆς τρόποι εἶναι. At 544D5-6 he starts the same argument over again: καὶ ἀνθρώπων εἴδη τοσαῦτα ἀνάγκη τρόπων εἶναι, ὅσπερ καὶ πολιτειῶν. Ιn the meantime, the analogy was accepted as proved, as the gene of soul and city can be seen, after the metaphysical interlude, to be (structurally) identical in the terms of the theory of ideas. (Cf. p. 147 below, and n. 36.) Plato goes back then to the analogy of soul and city and to his definition of justice, and draws the conclusions about the superiority of justice or injustice. It would be beyond our scope to examine the classification of the cities and the souls of the individuals corresponding to them. Plato’s main point is presumably not their accurate gradation,28 but the contrast of the extremes: the philosopher and the tyrant (contrast, e.g., 485A-487A with 577C ff.; and cf. 580C). The second and third proofs of the superiority of justice as the rule of reason do without the analogy of soul and city, at least explicitly, and are based on the distinction of the three gene in the soul. The second argument is probably only preliminary and seems not to be pressed very seriously. The third distinguishes between true and false pleasures and aims at establishing that only pleasures of the reason are real.29 The argument has been brought to its end, as Glaucon has requested. Socrates now reinforces his conclusion, after recalling Adeimantus’

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There is another gradation in the Statesman. Cf. 364A.

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original statement of the problem, by the simile of the man, the lion and the many-headed monster. After the excursus on philosophy and poetry, Socrates turns to Adeimantus’ reformulation of the problem (362E ff.), at which he had hinted earlier: after proving the intrinsic superiority of justice, one should also show that its effects in the soul of its possessor are better than the effects of injustice. Socrates intends to do more than that: he intends to show, following the theme introduced in the discussion on true and false pleasures, that the prizes and rewards of justice are real, those of injustice are illusory. He starts, as usual, by stating his conclusion, followed immediately by what is to be then developed into one of the premises of his argument: Yet greater prizes and rewards are reserved for virtue than mere intrinsic pleasure. And these rewards necessitate an infinitely longer span of time than that of a human life; i.e. they necessitate the immortality of the soul. That justice has also extrinsic rewards follows from its classification as a kind of health, namely as one of the goods which are desirable both for their own sake and for their consequences.30 If justice is the health of the soul, then it must also have desirable consequences. The theme of health and disease is reintroduced in the immediately ensuing proof of the immortality of the soul. Only the evil (κακόν) proper to each thing can destroy that thing. Injustice is the evil proper to soul. But injustice obviously does not destroy the soul. Therefore, the soul is destroyed neither by the evil proper to it nor by an alien evil. Therefore, the soul cannot be destroyed. The proof is based on the conclusions of the main argument: Justice and excellence are the health of the soul, injustice and badness its disease. But the main point of the proof is to show that the comparison breaks down in one important respect: Unlike disease of the body, injustice does not destroy the soul. This is clearly stated in 609C ff. And, conversely, if the soul were mortal (i.e. destructible), then in dying it would become worse, i.e. diseased; and the disease of the soul is injustice. Therefore if the soul is mortal, it becomes unjust in dying; which is

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Cf. p. 140, above.

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absurd. Consequently, death is not the disease of the soul. It is, as in the Phaedo, an affair of the body. The soul has a part in it only insofar as it is freed by it from the body. This argument assumes, of course, three gene in the soul, and in that it might be presented as conflicting with the argument given in the Phaedo. Plato shows that he is aware of the problem of the unity or multiplicity of the soul (612A4), and he seems to indicate that the soul as was described in the Republic is not the soul in her purity but “in the states and varieties which she manifests in human life”, in communion with the body “and with other evils”. “But we must rather fix our eyes, Glaucon, on her love of wisdom (φιλοσοφία,) and note how she seeks to apprehend and hold converse with the divine, immortal, and everlasting world to which she is akin (συγγενής)” (611E1-3, tr. Cornford). This would, indeed, seem to be the soul of the Phaedo, but I cannot here enter into a detailed examination of the problem.31 [9] The road is now clear for restoring to justice the rewards which belong to it by right, but were banned from the discussion by Glaucon’s strictness. But now the examination of the nature of justice not only has made room for, but also showed the necessity of, extrinsic rewards. They must, then, be reintroduced (612B). Once Glaucon’s restriction has been overridden, it is a necessary conclusion of the argument that justice be fittingly rewarded, if not during this life, then after death. Οὕτως ἄρα ὑποληπτέον περὶ τοῦ δικαίου

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31 Cf. 519, and 518D9-10: the excellences other than wisdom κινδυνεύουσιν ἐγγύς τι εἶναι τῶν τοῦ σώματος. – The crucial point of the argument is that it goes from the immortality of the soul to its simplicity, and not vice-versa. The simplicity of the soul is a requisite of its immortality, not a proof of it. Frutiger (1930) misunderstands this simplicity (here equivalent to incorporeality) when he says that, from the Republic onwards Plato has sacrificed “1’un des principaux arguments du Phédon en faveur de l’immortalité” (p. 68). The “parts” of the soul in the Republic, the Phaedrus and the Timaeus are not material parts, and this is all that is excluded by the Phaedo. In any case, in the Republic, as in the Phaedo, the argument is hypothetical (analytic), and the soul is postulated as simple or tripartite (albeit in different respects) according to the exigencies of the argument. – Archer-Hind’s (1882) suggestion that only the intellectual principle is immortal is modified and developed at length by Guthrie (1955), who maintains that the Phaedo and the Phaedrus show that the lower principles survive to some extent, so long as the soul is caught in the κύκλος γενέσεως and destined for another incarnation. Only when its φιλοσοφία has completely purified it does it shed the lower parts altogether. Of the three “parts” of the soul only νοῦς is immortal. – Cf. also Rodier (1907).

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ἀνδρός, ἐάντ’ ἐν πενίᾳ γίγνηται ἐάντ’ ἐν νόσοις ἤ τινι ἄλλῳ τῶν δοκούσων κακῶν, ὡς τούτῳ ταῦτα εἰς ἀγαθόν τι τελευτήσει ζῶντι ἢ καὶ ἀποθανόντι (613Α4-7): “In the same way, therefore, we have to assume, about the just man that, if he comes to poverty or illness or any of what are considered evils, these will end for him in some good, in his life or even after death”. Because justice, by its own nature, carries extrinsic reward, it has to be assumed that all the evils that may afflict the just man will necessarily be offset by future recompenses. Socrates depicts an optimistic picture of these recompenses in this life. But he allows for the all too frequent possibility of this life being too short for the recompenses to materialize. It is then necessary to assume that they are to come in a further extension of life. The move from the conclusion to the condition of the possibility and back to the conclusion is plain. “ὑποληπτέον” cannot but have here a marked technical sense, and the position of the assumption before the depiction of the recompenses of the just in this life, with the emphatic “ἢ καί” at A7, makes it clear that the immortality of the soul is assumed in order to prove the possibility of the conclusion that justice is superior to injustice not only in itself but also in its effects. 32 [10] By now, the hypothetical pattern of the argument of the Republic should have made itself clear. It is particularly evident from the position of the central metaphysical “digression” after the point in which the argument reached its conclusion. (The sections on women and on war are inserted after the first part of the argument obviously for reasons of rhythm.) The argument turned on the examination of the premises, namely of the conditions presupposed by the definition of justice as “natural order of elements under the rule of reason”. And once these conditions are followed up to the first unconditioned condition, Socrates comes back to the conclusion, now seen as incontestably proved.

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32 Cf. Kant, KpV, I Th., II Β., II. Hptst., IV. (ed. Hartenstein, p. 128). There is though one all-important difference between Plato’s reasoning and Kant’s. Immortality is for Kant a postulate of practical reason, i.e. of morality as distinguished from speculation. For Plato, immortality is necessitated by a conclusion that follows from a concept of justice that is no more practical, in Kant’s sense, than it is theoretical. Hence the possibility – and the necessity – of conducing Plato’s proof of the nature of justice and of the immortality of the soul to the unhypothetical beginning, transcending thereby their postulative character.

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And although the terminology of the hypothetical method is not introduced until 437A6, and the method itself is not discussed before the Divided Line, nevertheless it had actually been in use throughout the argument. The problem Socrates has taken upon himself to solve was to demonstrate that justice is superior to injustice. That this is so is accepted, only the proof is still to be found. This proof evidently involves an investigation into what justice is. Now, “justice” (or “just”) is said of two things: of the city and of the soul. The enunciation of Socrates’ problem refers to the soul, not to the city; i.e. Socrates is ostensibly interested in justice in the soul, not in justice in the city.33 However, justice in the soul is apparently more difficult to examine than justice in the city. But if justice in the soul and justice in the city are the same, then it is possible to conduct the inquiry in terms of the city and transfer the conclusions to the soul. This is, then, the first hypothesis: that justice is said not of the state and of the soul merely by equivocation. Granted this hypothesis, Socrates proceeds to examine the nature of justice in the city. But this inquiry presupposes another, viz. the inquiry into the nature of the city itself. Socrates proceeds therefore to construct his city and, taking again his construction for granted (hyp. ii.), he shows how justice is to be found in it.34 Having arrived at a characterization of justice in the city, Socrates turns now to transferring his conclusions to the soul. But this move depends on hypothesis i. that justice is the same in the city and in the soul. And this hypothesis can only be true if the soul too has in it the same three gene as the city (hyp. iii.).35 It is thus a matter of corroborating the

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33 This is not to say that Socrates is not interested in justice in the city. It is only to point out the ostensive formulation of the question. 34 Strictly speaking, Socrates has a preconception of justice, and he shows that his city is so built that it makes justice as he understands it possible. The nature of justice in the city should thus be hyp. ii. and the structure of the city itself, hyp. iii. But this is not the way the argument is actually construed in the text. Besides, it would be tedious to stick always to the rules, and whether Plato was aware of the deviation or not, no matter of great consequence follows from it. 35 Is hyp. iii. about the gene of the soul, or about the sameness of the gene of the soul and of the city? The difference between the two formulations seems irrelevant. As the gene of the city

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hypothesis that was at first assumed to be true. And this calls for an examination of the nature of the soul. This is done by introducing hyp. iv.: It is agreed that nothing can act or be acted upon in contrary ways, etc., and that if some one thing acts or is acted upon in contrary ways, etc., it is not one thing but many. From this hypothesis and from the acknowledged fact that the soul does act and is acted upon in contrary ways at the same time, the desired conclusion follows. Now, assuming that there is an identity of gene between the city and the soul and not a mere analogy, and that “justice” is not homonymous when said of both, then, indeed, it follows “at once”, that both will possess in the same manner and by virtue of the same genos any of the excellences. But these assumptions remain still to be proved. For what guarantees that “justice” is not purely equivocal is the doctrine that city and soul participate both in the same idea of justice. This idea, not being embodied in a particular soul or in a particular city, is a pure principle of order among the constituent elements of any soul/city. Likewise, the sameness of the gene of the city and the soul is guaranteed by their relative functions and by the interrelations between them. This formal identity was for Plato the sure sign of a single idea represented in different places.36 Are these two assumptions, that the gene of the city and of the soul are identical (in the context of the theory of ideas) and that justice is the same in both, really two distinct assumptions, or can the second be reduced to the first? For, it might be argued, the sameness of the gene of the city and of the soul is not only necessary but also sufficient for justice, as the natural good order of the gene, to be the same in the city and in the soul. This, indeed, appears to be Socrates’ position at 441. But at 443C ff. he seems to hint that this is not the whole story, and that the identity of gene of soul and city ensures the identity of justice in both only at a superficial level. At the level of external deeds, as the discus-

-------------------------------------------were already established, the question about the sameness of the gene of soul and city boils down in practice to the question about the gene of the soul. 36 In the same way the geometrical square figure and the arithmetical square number are both representations of the same idea of the Square. Cf. ch. vii, pp. 223 ff.

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sion was conducted up to that point, the φιλοθεάμων of book v might still have it his way. Justice is thus defined as the natural good order of the gene of the soul and of the city under the rule of reason (hyp. v.). On the one hand, this definition allows the immediate solution of the problem of the superiority of justice. On the other hand, once the conclusions have been drawn, the definition stands itself in need of support. This is done by an inquiry into the concept of reason, represented in the city by the philosopher and in the soul by wisdom. And that the rule of reason is the natural order will be supported by the identification of the aitia of being with the aitia of knowledge. Wisdom as the excellence of reason is knowledge (ἐπιστήμη), and (hyp. vi.) knowledge is distinct from opinion. This distinction implies, in its turn, an ontological distinction between ideas and sensibles (hyp. vii.). The whole chain of hypotheses culminates in the unhypothetical idea of the Good, which is the absolutely sufficient basis for all hypotheses.37 The theory of ideas supports not only the definition of justice by being presupposed by the concept of knowledge, but also the assumption of the identity of the nature of the city and the soul. But until their turn comes to be examined, these assumptions are agreed upon, and such consequences are drawn from them as are required by the formulation of the problem. This procedure is perfectly in line with that described and actually pursued in the Meno and the Phaedo: given a conclusion that one is required to prove, a hypothesis is selected which might lead to this conclusion; if the hypothesis entails contradictory consequences,38 it must be discarded; if not, it has in its turn to be proved by a higher hypothesis, till “something sufficient” is reached. In its first part the argument was pursued upwards to the hypothesis of the identity of nature of soul and city, and to a hypothetical definition

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37 See chs. vi and vii. For the sake of simplicity, I have omitted here the details of the arguments on the status of opinion and its object, on mathematical sciences and dialectic, and on the immortality of the soul. 38 On contradiction arising from a single proposition, see Robinson (1953), 30 f. In a work of the magnitude of the Republic, Plato seems to have spared himself the trouble of exploring blind alleys.

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of justice, and then downwards again to the desired conclusion. In the second part it was necessary to base these hypotheses themselves on the theory of ideas, and eventually on the unhypothetical beginning. The third part restates the conclusion, now proved, and completes the solution of the problem by postulating the immortality of the soul in order to make possible just reward.

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Chapter vi: Knowledge and Opinion [1] We must now examine Plato’s discussion in the Republic of the hypothetical method itself and its relation to the theory of ideas, and of dialectic as the science which is concerned with the hypothetical method as its proper method. But before we come to the central metaphysical similes of the Republic, we have to clarify Plato’s preliminary distinction between opinion and knowledge, on which the whole of the central section depends. This will be done in the present chapter. In the next chapter, the metaphysical similes and especially the Divided Line, and their implications will be considered. Justice was defined in the Republic as the natural order of the elements of the soul and of the city. This natural order consisted in the desire and the spirited element being controlled by reason, whether it be in the soul or in the city. Justice is thus made dependent on wisdom (σοφία) as the excellence of reason: for soul and city are “wise in virtue of that small part which rules and issues these injunctions, possessing as it does the knowledge of what is good for each of the three elements and for all of them in common” (442c5-8, tr. Cornford); and it is these rules that specify the soul’s or the city’s natural order of elements. The definition of justice which we were given assumed the presence of wisdom in the soul and in the city. But an adequate account of wisdom was lacking, and only after the argumentation was brought to its conclusion for the first time,1 does Plato come back – after an appendix on the status of women and on war – to the foundations of his argument. Once more Plato resorts to the common structure of city and soul, and begins (474) by identifying the element of reason in the city, where – again the simile of the large and small letters – it can be more easily recognized. The element of reason in the city is represented by the lover

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445B; cf. above p. 140.

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of wisdom, the philosopher, and, therefore, the ideal city should have philosophers as its rulers. But this contention must be defended by a detailed definition of what a philosopher is. Out of this definition, so Socrates hopes (474B), the demand that philosophers should be kings will become clear. On the other hand, a definition of the philosopher is, at the same time, a definition of wisdom as an excellence of the soul. And so the justification of the just arrangement of the city and of the just arrangement of the soul are one and the same. A philosopher is a lover of wisdom. As such he desires all wisdom, not only certain sorts of knowledge (474D ff.). But this very general characterization fails to distinguish the philosopher from others similar to him, but not worthy of the name: the φιλοθεάμονες and φιλήκοοι, the lovers of sights and sounds. They are sometimes presented as “dilettanti or mere amateurs of the art”,2 among other reasons no doubt also because of the derisive description of them in Glaucon’s mouth. But an examination of the ensuing discussion shows that the φιλοθεάμονες present a more serious philosophical problem than mere intellectual shallowness. Socrates proposes to distinguish between them by means of the distinction between what is in itself one and its many φαντάσματα: “... each of them [sc. the ideas] is itself one, but by communion (κοινωνία) with actions and bodies and with each other3 they each appear in many ways (πανταχοῦ φανταζόμενα), and seem many” (476A5, tr. Cornford). By this distinction (ταύτῃ τοίνυν), says Socrates, the philosopher will be set apart from those who superficially resemble him. The distinction Socrates is making is obviously that between the idea in its unparticipated aspect, recognized as one, and the appearance of that idea, which seems now to be many because of its communion with actions, bodies, and even with other ideas. The philosopher is, thus, he who is capable of seeing the one, over against those who can only see the multitude of aspects without grasping its essential unity. So, at 476B4 ff. the φιλοθεάμων is said to be able to take pleasure in beautiful

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Cornford (1941), 180. And cf. his remark on Thuc. ii 40: philosophia as “curiosity”. The text has been unduly suspected, as Adam (1902), 362 ff., rightly remarks.

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colours and shapes, but to be unable to grasp the beautiful itself and to delight in it. He sees only the beautiful as many, as it appears by virtue of its communion with bodies and actions. Because the φιλοθεάμων recognizes only beautiful things but not the beautiful itself, he equates the beautiful with its many appearances. In this respect he is dreaming. For dreaming is τὸ ὁμοῖόν τῳ μὴ ὁμοῖον ἀλλ’ αὐτὸ ἡγῆται εἶναι ᾧ ἔοικεν, whether one is asleep or awake (476C6-7). And this is exactly what the φιλοθεάμων does: he takes appearances to be not what they are but the realities of which they are appearances. He thinks that the beautiful which is seen multiplied in bodies and actions is the beautiful itself, for he recognizes no other beautiful apart from the beautiful that is many. By contrast, the philosopher never confuses the beautiful itself with τα μετέχοντα, with the beautiful in bodies or in actions, or τά μετέχοντα with the beautiful itself. The philosopher and the φιλοθεάμων each claim that the object of his cognition is beauty (or the beautiful). But while the philosopher knows beauty as being one, the φιλοθεάμων only δοξάζει (here the translation breaks down) beauty as being a plurality in colours and shapes. The cognition of the φιλοθεάμων is not knowledge in the Platonic sense, as it will be shown, but it cannot be said to be absolute ignorance either. His doxa is thus a state of cognition which is not knowledge because it does not attain the truth, and it is not ignorance because it is not completely false.4 Such a state calls for an explanation. Plato begins by stating that knowledge implies something (τι) that is known; and only what is, i.e. what has a determinate character, can be known absolutely; what has no determination whatsoever cannot be known in any way. Now, if something were of such a sort that it would both be (i.e. possess a determinate characteristic) and not be (i.e. lack that determinate characteristic), would it not be half-way between pure being (complete determinacy) and not being in any way (complete indeterminacy)? (477A6 ff.) There-

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4 It should be noted that the doxa Plato is concerned with in the Republic is, of course, the alethes doxa of the Meno. Plato assumes, as the context of the Republic makes clear, that doxa is not downright error. He had already set doxa apart from both knowledge and error, in the Meno. But there is still some ambiguity about agnoia as between error and ignorance.

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fore, if knowledge is of being and ignorance is necessarily of non-being, then one must look for something between knowledge and ignorance, that would be of (ἐπί) what is between being (say, F) and not being (F). The last part of the argument tries to show that the doxa of the φιλοθεάμων meets the requirement. Opinion, here as everywhere in Plato, is accepted as different from knowledge. Both are δυνάμεις – functions. And each function is distinguished by two criteria: ἐφ’ ᾧ τε ἔστι καὶ ὃ ἀπεργάζεται.5 Namely, (i) of what it is (or: to what it is correlated), and (ii) what it produces. These criteria are not explained by Socrates, and so we have to go to the development of the argument in order to try and understand what is meant by them. At 477E6-7 knowledge is said to differ from opinion as the infallible from the fallible. And Socrates goes on: ἐφ’ ἑτέρῳ ἄρα ἕτερόν τι δυναμένη ἑκατέρα αὐτῶν πέφυκεν (478Α3). It is clear from the context that ἕτερόν τι δυναμένη refers to the one being fallible, the other infallible. And that is “what each of them produces”, namely fallible or infallible cognition, respectively. The conclusion Socrates draws is that because each has the power of producing something different from the other, therefore (ἄρα) they are of (ἐπί) different things. This has been taken to mean that different dynameis, by the very fact of being different, must have different objects, and that if they “produce” different states of mind the difference must be due to the objects that the dynameis are related to. On this view, the two criteria are equivalent, and the inference from a difference in “states of mind” to a difference in object is immediate. [2] This seems to me a somewhat simplified view of Plato’s account of the matter. This view interprets 478A3 on its own, but disregards its context. As a matter of fact, the relation between the two criteria is more complex than is usually suggested, and the difference of objects follows from the difference of what the dynameis produce only in conjunction with other assumptions about the nature of knowledge and of opinion, some but not all of which are mentioned in the discussion.

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5 “ἐφ’ ᾧ” in itself need not imply a separately existing object; see 477A9-10 ἀγνωσία ... ἐπὶ μὴ ὄντι. The translation “function” is Crombie’s (1963), ii 57.

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One implicit assumption is that all cognition is recognition and naming (διονομάζειν). For Plato in his middle period, to know something is not merely to apprehend it or to have a representation of it but to recognize it as something,6 to know it as, say, F or G, i.e. to name it correctly. Error is mis-identification or misnaming, e.g. identifying as F or attributing the name F to what does not in fact have the character F.7 Another implicit assumption refers to the meaning of ὄν. As it will be shown below (App. 1), Plato – at least in his middle period – is not theoretically concerned in ascribing to εἶναι an independent existential sense (or, at any rate, he did not seem to use εἶναι in a purely existential technical sense). For him, at this stage at least, εἶναι has to be understood as incomplete, as “being (F)”. This is clear in this passage, e.g., from 479A5 ff.: there “being” and “not-being” are substituted by definite contraries such as beautiful and ugly, just and unjust, righteous and unrighteous. This is not to say, of course, that there is no existential εἶναι in Plato, nor even that the incomplete εἶναι does not have existential overtones. But this is not its primary import, and to interpret it as mainly existential would be to misplace the emphasis. The argument starts at 477B with a firm statement to the effect that opinion is different from knowledge. This is a point which, for Socrates and his company, needs no arguing (cf. 477E6-7). The second premise is stated at 477B10-11: Ἐπιστήμη μὲν ἐπὶ τῷ ὄντι, γνῶναι ὡς ἔστι τὸ ὄν, knowledge is of what is as it is. The conclusion came earlier at B7-8: Therefore (ἄρα) opinion is of something different from what knowledge is of, according to the dynamis of each.8 Socrates’ characterization of knowledge as cognition of what is as it is (or “that it is”) can be understood only on the implicit assumptions introduced above. Gosling, for example, thinks γνῶναι ὡς ἔστι τὸ ὄν to be a gloss by Plato himself on the first part of the statement.9 But this is surely strange, since this statement seems to be of great importance, re-

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A good example is Meno 82B9-10: γιγνώσκεις τετράγωνον χωρίον ὅτι τοιοῦτόν ἐστιν; Cf. Prauss (1966), 125 ff. 8 “δύναμις” is clearly seen here to be ambiguous: it means either function or (as here) its “power” to produce a certain state of mind (cf. 478A3 δυναμένη, quoted at p. 153, above). 9 Gosling (1968), 124 f. 7

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curring emphatically with both its parts twice: once at 477B10-11, before the discussion of the difference between the dynameis and again at 478A6, during the discussion. That it appears before the discussion of the difference between knowledge and opinion is important because, as we shall see, the argument that knowledge and opinion are of different things depends on it. Also, this conforms to Plato’s custom of stating the main premise at the beginning of the argument, even if it is only used later. In view of these considerations one should take this definition of knowledge as prima facie emphasizing two aspects of it: (i) ἐπὶ τῷ ὄντι πέφυκε, (ii) τὸ ὂν γνῶναι ὡς ἔχει (or ὡς ἔστι). Accordingly, the second part of this statement should be seen as an essential element in the definition of knowledge. This goes together with taking ἐφ’ ᾧ and ὃ ἀπεργάζεται as two separate criteria of cognition and not as redundant or implying each other immediately. I suggest therefore that Plato’s definition of knowledge bears on two distinct points: (i) knowledge is of what is, i.e. knowledge is of definite characters, say, F, G, (ii) having knowledge of definite characters F, G, (as opposed to having mere opinion about them), implies apprehending them as they are, as the definite characters F, G, ... It is then given that opinion is different from knowledge and that knowledge is of what is as it is. But the conclusion that opinion is of (ἐπὶ) something different from knowledge will not follow unless a further premise is granted: that a difference between functions is defined by a difference in “objects” and in “what they produce”. Granted this premise, the argument may be reformulated: knowledge and opinion are different from each other in that the one is infallible, the other fallible. Now, knowledge is apprehension of something as being F. Opinion too is apprehension of something as being F. However, if it is accepted that knowledge and opinion are different and that knowledge is of what is (F) as being (F), then opinion cannot also be of what is F, for then opinion would be indistinguishable from knowledge, both being then cognition of F as F. Therefore, although both opinion and knowledge are apprehensions of something as being F, they differ in that knowledge is always and infallibly of (ἐπί) what really is F, whereas opinion must be of (ἐπί) something else, if some such thing can be found.

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What the δοξάζων does is to take what is not truly F as if it were truly F. Having opinion (and not knowledge) of something as (truly) F, e.g., as “the beautiful” (pp. 151-152, above), means that the object of opinion is not (truly) F but something else. Plato points out that it cannot be, however, devoid of any character: opinion is of something, not of nothing. Here, Plato distinguishes implicitly – though not explicitly – between opinion and error.10 Error is misnaming, apprehending as F what is different from F. But this view does not appear here. Opinion too is misapprehension. But opinion is not error tout court: it is a very special kind of error. Like dreaming, it is such that τὸ ὁμοῖον τῷ μὴ ὁμοῖον ἀλλ’ αὐτὸ ἡγῆται εἶναι ᾧ ἔοικεν. It is apprehending as (truly) F what is not (truly) F but is similar to what is (truly) F. In a sense, then, the δοξάζων knows something (εἰδώς τί 476E6), in as much as what he apprehends can be called F with some measure of appropriateness, though his is not a fully adequate apprehension of it. “Then apparently we have still left to find that which partakes of both being and not being and which could not be rightly described as either absolutely” (478E1 ff.). “Then this having been established” (478E7 ff.), let the φιλοθεάμων, who believes in many beautifuls but not in one beautiful itself,11 answer whether any of these πολλὰ καλά is truly and invariably beautiful. He will find that no F that is multiplied in sensible things is (truly) F, but “tumbles about somewhere between what is not and what absolutely is” (479D5, tr. Lindsay). A crucial point in the argument is the definition of knowledge (emphasized twice) as apprehension of what is as it is. If knowledge were mere apprehension of what is (as opposed say, to opinion, as apprehension of what both is and is not), then the strict correlation between the two criteria for differentiating between functions, viz. “what they are of” and “what they produce” would be quite easily established. But once it is realized that knowledge is not mere apprehension of F, but apprehen-

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10 Again ambiguity between error and ignorance. An explication of this ambiguity would require the recognition of the double function of μὴ ὄν as “false” and as “indeterminate”, and the parallel, explicit recognition of εἶναι as an incomplete term. But this Plato does not do here. Nevertheless, is 476A5 ἀλλήλων ... κοινωνία a step towards the recognition of this distinction? 11 Cf. 476C2 ff.

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sion of F as F, it should be clear that the correlation between the “object” and what the function “produces” cannot be straightforward. In other words, it cannot be the case that different functions are automatically allocated different objects. For what makes knowledge infallible is the fact that it is of what is as it is. Now suppose, if possible, that knowledge and opinion differed in “effect” only, but not in object. Both would then be cognition of what is. But, in order to account for the fallibility of knowledge and the infallibility of opinion, we would have to suppose that it is of what is, not as it is (for this is knowledge and is infallible), but in a certain manner (ὡς ἔχει πως). But it is accepted Platonic doctrine that what is can only be known as it is (although this statement will be qualified later in the presentation of dianoia – and this explains perhaps why Plato thought it necessary to deal with dianoia at such a length). Therefore, in order that opinion be apprehension of an object as it is only in a qualified way, an object must be postulated that is susceptible of being apprehended in a qualified way. The two criteria for differentiating between functions are thus correlated, and in the particular case of opinion and knowledge they go together, but they are not equivalent. For example, if we represent by F what is F only “eponymously”, and disregard the cases of ignorance and error, which cannot be properly said to be cognition, we have four varieties of cognition: (i) apprehension of F as F, i.e. knowledge (ii) apprehension of F´ as F, i.e. opinion; (iii) apprehension of F as F´, viz. dianoia, or the mode of cognition of the mathematical sciences, which operate with sensibles while in fact dealing with ideas; and (iv) apprehension of F´ as F´, or the philosopher’s adequate apprehension of the sensible world, as described at 520C4-6 (cf. below pp. 159-160, and n. 13). The last two modes of cognition may need some explanation: (iii) It will be argued in the next chapter that the mathematical sciences deal with spatial representations of entities whose only adequate formulation is non-spatial. Therefore, if I understand by a square a four-cornered plane shape, etc., instead of apprehending it abstractly as, say n2, I am in fact apprehending F (i.e., n2) as F´ (i.e., as a four-cornered plane shape, etc.). Cf. pp. 181-183, below. (iv) The philosopher’s cognition of the sensible world cannot be knowledge, because (a) it is not of what is, and (b) it is not infallible, as

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there is no infallible cognition of the sensible world. But it is distinct from the opinion of the other dwellers of the cave in that it is accompanied by the consciousness of its not being knowledge. This consciousness is possible only as a result of the philosopher’s knowledge of the ideas and of the relation between the ideas and the sensible world. That this type of cognition is not mentioned in the Line only shows, firstly, that Plato’s conception of the relation between knowledge and opinion is more complex than is normally assumed, and, secondly, that the Line is not intended as an exhaustive classification of the modes of cognition. Our passage is concerned only with assessing two different modes of cognition both of which claim to be apprehensions of the same F, and none of which can be completely mistaken. This is done by introducing F´, as what is both F and non-F (both being and non-being). Modes (iii) and (iv) are not envisaged in our passage, nor were there, at the beginning of the passage the necessary conceptual tools for the formulation of the whole problem. This is left to the central similes of books vi–vii, after the necessary distinctions had been drawn in the present passage. A summary of the above argument might be helpful. The argument purported to show that doxa is of something “between” being and nonbeing, i.e. of something which can be said to be F without straightforward error, but, on the other hand, cannot be properly, or adequately, said to be F. The criterion for distinguishing between “functions” is double: (i) the object, (ii) the effect. Both are required for identity, and indeed book vii will give us an account of a dynamis which has the same object as episteme, but not the same effect, viz. dianoia. Thus, assuming (i) that opinion is different from knowledge (but is not error), the symptom of this difference being that knowledge is infallible, opinion fallible, (ii) that knowledge is of what is as it is, (iii) that an identity of both object and effect is necessary for there to be an identity of functions, these two criteria being, in this case, correlated, but not equivalent, and (iv) that opinion too, like knowledge, claims to have F as its object – it follows that the claim of the doxazon in (iv) that his cognition is of F cannot be true. But it cannot be unqualifiedly false either, for (i) opinion is not error. It must therefore be cognition of something which has some justification to be called F (hence opinion is not error), but is not properly F (hence opinion is not knowledge). If “prop-

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erly” is understood as implying “always”, “from all points of view”, “in all respects”, etc., the above conclusion accounts for the infallibility of knowledge and for the fallibility of opinion. [3] It seems then that it is not accurate to say that doxa in the Republic is the apprehension of the sensible world as such. Rather it is the apprehension of the characters in the sensible world which are in fact but a result of participation in the ideas, not as such, but as if they were the absolute and true, because only, characters F, G, .... Opinion is thus inadequate apprehension of the sensible world. This leaves open the question of the adequate cognition of the sensible world, and whether such adequate cognition is at all possible. Although Plato is not explicit on this matter, he does contrast the φιλοθεάμων, who confuses the many beautifuls with the beautiful itself, with the philosopher, who neither confuses the one with its μετέχοντα, nor the μετέχοντα with the one, and has presumably an adequate apprehension of both. One possible solution would be to take ὄν as the object of knowledge in a broad sense, as referring to the two γένη τῶν ὄντων, and to see only the παντελώς ὄν as a reference to the ideas. Knowledge could thus extend also to an adequate apprehension of the sensible world. But this would hardly be compatible with the assumed infallibility of knowledge. It seems thus that knowledge is of the ideas alone, and knowledge of the ideas, as far as the Republic is concerned, is always adequate. Opinion, on the other hand, is the inadequate apprehension of the sensible world.12 But the philosopher, because he has knowledge, differs from the φιλοθεάμων in his cognition of the sensible world.13 And even if he is still incapable of infallible knowledge of it, yet he can give an εἰκὼς λόγος, which is not completely devoid of reason, and which, because it

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12 It must be of the sensible world. If it were of the ideas as such it would not be inadequate. It is possible, of course, to have opinion about what knowledge is of, namely, about ideas. But this only means that the ideas are not attained in their purity but “in their communion with bodies and actions”. Still there is a point in distinguishing cognition that is specifically of the sensible world from cognition that is only accidentally of the sensible world. 13 Cf. 520C4-6 γνώσεσθε ἕκαστα τὰ εἴδωλα ἅττα ἐστὶ καὶ ὧν, διὰ τὸ ἀληθῆ ἑωρακέναι καλῶν τε καὶ δικαίων καὶ ἀγαθῶν πέρι.

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is only an εἰκὼς λόγος, is adequate to its subject-matter, not claiming knowledge of what cannot be strictly known. It should be pointed out that opinion of the sensible world is to be understood as of the ideas as participated in by bodies and actions. This participation accounts for the possibility of transition from opinion to knowledge. What has been presented in the Meno as a difference between modes of cognition is here given its metaphysical ground. The transition from doxa as mere unreflected opinion to knowledge through the giving of reasons is deemed possible because of the degree of rationality displayed by the material world, and this rationality is given its foundation in the theory of ideas and of participation. Were opinion exclusively of the sensible world as such, this transition would be at best unexplained. This is not to say that the sensible world is made to be wholly dependent on the world of the ideas. This impression might be left, for example, from Prauss’ description of Plato’s sensible things as an aggregate, with which the above interpretation goes a long way. From the purely epistemological point of view, insofar as knowledge is of ideas, and even apprehension in a wider sense is apprehension only of definite characters, this may be right. But from the ontological point of view one must not forget that the sensible world and the world of ideas are δύο γένη τῶν ὄντων. It is true that such a distinction might in itself amount to no more than that between the participated and the participating. But considerations about the nature of the opposition between the one and the many in Plato’s dialogues, about the concept of imitation and of space as the medium of imitation, and, above all, about the distinction that is fundamental in Plato’s thought between knowledge and opinion – these and others should make clear that the sensible world, while depending on the world of ideas, is separate from it. The importance of this dependence of the sensible world on the world of ideas is especially in that – as explained in the Sun – it receives from the world of ideas its ουσία and its possibility of being known. This is why opinion, i.e. the uncritical acceptance of what both is and is not as that which (truly) is can give way to the recognition that the shifting characters of this world have their reason in other characters which truly deserve the names that are applied to the sensible world only

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eponymously. And this, we read in the Phaedo, is recollection, and knowledge. This argument intended to show that, if we are to maintain the distinction between knowledge and opinion, we have to assume that this distinction is caused by a parallel ontological distinction (though not necessarily by means of the rule that different functions have different objects). The hypothetical procedure is clear: The conclusion sought is the (possibility of) distinction between the philosopher and the φιλοθεάμων, i.e., between knowledge and opinion. The conclusion is granted, and the premises leading to it are proposed: ideas and their images, knowledge as of what is as it is. By means of the auxiliary rule how to distinguish between functions by means of their “objects” and “products”, the lacking premise is found: opinion must be of the sensible world. But, of course, the argument depends on the acceptance of the two other premises, which have still to be investigated. [4] The section just analysed of book v established that σοφία, is ἐπιστήμη as distinguished from δόξα. In that much it has established the ground on which justice is dependent on wisdom. Wisdom is the excellence of reason and is thus the highest exercise of reason, i.e. knowledge. And, by the same argument, it can be nothing less than the highest knowledge: knowledge of the Good (505A ff.). This argument called for a detailed examination of the nature of knowledge. In the foregoing inquiry, knowledge was deemed sufficiently described as being of τὸ ὄν and as being “of what is as it is”. But this description is now avowed to be only a sketch (ὑπογραφή 504D6). And although the description of knowledge as of what is as it is was one of the basic assumptions of the argument to the effect that opinion is of what both is and is not, yet the very possibility of knowing something “as it is”, or, alternatively, “as it is in a certain way but is not in another”, still has to be accounted for. A related problem that has also been left open is the problem of the method itself which Plato is using in his argumentation. In starting from the conclusion that justice is superior to injustice and in moving from this conclusion assumed as true to the supporting premise about the nature of justice in the soul and in the city, from this to the non-homonymy

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of virtue and to the ideal identity of city and soul, and again from the nature of justice to the nature of knowledge – in all these moves from the conclusion to its premisees, Socrates cannot and does not claim to have ἐπιστήμη. He “suspects” only that his guesses are true. If this, then, is the philosopher’s method, it seems not to display the philosopher’s excellence, viz. knowledge. On what grounds, then, can the method itself be trusted? Moreover, the possibility of transition from opinion to knowledge, that was assumed but not explained in book v, is essential not only to the examination of the nature of knowledge, but to the much more fundamental task of proving the possibility of the very method by which the argument (including the one about knowledge and opinion) is being conducted. At this point the subject-matter of the argument and its method can no longer be distinguished. The highest object of knowledge, the idea of the Good, provides the solution for both problems: the problem of the semi-intelligibility of the sensible world (thereby also providing the basis for a complete definition of justice as the well-ordering of the constituent elements according to reason), and the problem of a method whose starting-point is opinion but which terminates in absolute knowledge.

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Chapter vii: The Divided Line Books vi and vii of the Republic contain, as it is well known, the important although short discussion of the status of hypotheses in mathematics and dialectic (510B4-511D5), which describes what is essentially the procedure of the Phaedo and the Meno. Indeed, the main purpose of the Line1 is to establish the difference between mathematical deductive proof and dialectical analysis. Although our interest is focused on the Line itself, it is impossible to consider this analogy apart from the whole complex of similes of which it is merely a part. As it is now widely recognized, no interpretation can be advanced which does not comprehend and explain the interrelations between the three parts of what A. S. Ferguson has called Plato’s Simile of Light.2 I shall, therefore, present first an exegetical exposition of the Sun, Line and Cave, and then come back to the Line and examine in greater detail some of the implications of Plato’s description of the upward path. I have already considered in the last chapter the important passage at 476 ff., on which, as it will be seen, the whole complex of similes is based. I shall also be concerned here with the passages on the sciences, and with the recapitulation of the Line at 534A. This recapitulation, by the way, seems by itself to indicate that the Line and the Cave are hardly intended to be taken as two separate similes.3 On the other hand, the Cave will be dealt with only in its broad lines, for, insofar as our special interest is concerned, it does not add much to the Line. [2] In answer to Glaucon’s request that he give an account of the Good, Socrates declares that he fears this account to be beyond his powers

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1 The capitalized words ‘Sun’, ‘Line’, ‘Cave’ refer to the similes, the words ‘sun’, ‘line’, ‘cave’, to the objects themselves. 2 A. S. Ferguson (1921-2), (1934). 3 There are other, weightier reasons. For a clear presentation of this case, see e.g. Raven (1953).

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(506D7 ὅπως μὴ οὐχ οἷός τ’ ἔσομαι) and beyond the élan (ὁρμή) of their present inquiry, and offers instead to tell him “what appears as the offspring of the Good and the thing most resembling it”. Socrates starts by distinguishing, as he has done in the Phaedo, between the many beautiful things and the beautiful itself; over against the many beautiful things, one idea is posited and is said to be ‘what is’ (ὃ ἔστιν). Further, the many things are visible but not intelligible, the idea is intelligible but not visible. All this is familiar ground to the readers of the Phaedo. So far, the distinction is the old one between the sensible and the intelligible. In order to make this clear, Plato proceeds to add hearing and other senses. But, having thus differentiated the intelligible from the sensible in general, he now singles out one sort of sensible things. Although sight and the other senses are all alike in that they are opposed to the intelligible, nevertheless sight is different from the other senses in one respect: while the other senses do not need ‘a third’ between them and their objects, sight does: sight cannot see but in light. This is a strange distinction, and not only from a modern point of view: Plato knew full well that air is the medium of hearing (cf. Timaeus 67B, 80A). However, Plato is not stating a scientific analogy, but is basing himself on the simple fact that sight is the only sense which requires a medium (better, a condition), viz. light, which is sometimes present and sometimes not. Sound needs a medium too; but (at least for Plato) this medium or condition is always present. And so with the other senses too. This peculiarity of vision, on which Socrates elaborates at such length, is, as we shall see, of maximum importance for the understanding of the function of the Idea of the Good in Plato’s philosophy.4 One may have the power of vision and colour may be present in the objects, and, nevertheless, nothing will be seen without light. Not because of a failure either of sight or of its object, but because of the lack of the condition under which alone the visible may be seen. Now, the reason for this light that enables both our eyes to see and the visible to be seen is the sun. “And it was the sun”, says Socrates,

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4 Cf. pp. 235 ff. Cf. A. S. Ferguson (1921), 135; Chambry (1932-4), 136, ad 507D2 (although his formulation is less felicitous). Cornford (1941), 218, ad loc, is very obscure.

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“that I meant when I spoke of that offspring which the Good has created in the visible world, to stand there in the same relation to vision and visible things as that which the Good itself bears in the intelligible world to the intelligence and to intelligible objects” (508B12-C2, tr. Cornford). When things are illuminated by the light of the day they are seen distinctly; but when they are under nocturnal lights (either natural or artificial),5 the eyes are dim and seem blind and clouded. In the same manner, when the object of the soul’s intelligence is illuminated by truth and reality, the soul knows and understands. But when it looks towards the sombre world of generation and passing away, then it has only unstable opinions, and seems without intelligence. And what gives both the objects of knowledge their truth and the knower his power of knowing is the idea of the Good. It is responsible for knowledge and truth alike. [3] The Line is a continuation of the Sun and a prologue to the culmination of the whole simile, the Cave. But, for our purposes it is, maybe, the most important of its parts. It starts with a brief restatement of the two fields (τόποι) of the previous analogy: the visible and the intelligible. The reference is unmistakably to the former analogues, in their former functions as analogues: “Conceive, then, these two (δύο αὐτώ), as we have said (ὥσπερ λέγομεν), one reigning over the intelligible realm, the other over the visible” (509D1-3). The picture recalled is the picture of the Sun. “Then take a line divided into two unequal segments and divide each segment again in the same proportion (ἀνὰ τὸν αὐτὸν λόγον), that of the visible class and that of the intelligible, and they will be related to one another as in respect of clearness and obscurity” (509D5-9). [Here the author presents a diagram of a vertical line divided into four segments, from the top, D, C, B, and A; these are represented according to Plato’s specified ratios, e.g. D 9, C and B 6, and A 4.]

The segment A represents images, namely “first shadows, then reflections in water or in any compact, smooth and polished surface, and

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5 Cf. A. S. Ferguson (1934), 194 n. 2, and Aeneas Tacticus X 25, quoted by him. But I do not think his reasons for taking νυκτερινὰ φέγγη as “artificial lights” alone are convincing.

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everything of that kind”. That segment A is not intended to comprehend also other objects of opinion was argued by Ferguson and Raven at length: the Line is an explicit continuation of the Sun, where the visible cannot be interpreted as an exemplification of the larger field of the objects of opinion in general. The segment A is explicitly called “visible”, not “sensible” or “opinable”. And the few examples given by Plato of the objects referred to in the lower subsection are exclusively visual.6 Segment Β stands “for what the first resembles (ᾧ τοῦτο ἔοικεν), the living things around us and the whole class of natural or manufactured things” (510A5-6). The relation between the two segments is then defined: “Would you also be willing to admit that it has been so divided (διηρῆσθαι) in respect of truth and lack of truth as the object of opinion stands to that of knowledge, so stands the copy to the original? – Yes, he said, I am quite willing” (510A8-10). In order to define the relation between A and B, namely between those objects that were introduced as copy and original, Socrates resorts to a ratio that was already established: the ratio doxaston:gnoston. At 476 ff. Socrates had established the difference between knowledge and opinion: Opinion is more obscure than knowledge, but not as dark as ignorance; likewise, its object cannot be called either purely real or purely unreal (ὄν, μὴ ὄν). Now the relation between copy and original in the lower segment, in respect of their truth (ἀλήθεια) or lack of truth, is as the relation of the object of opinion to the object of knowledge. The previous distinction of clearness (509D9 σαφηνεία) is now turned into a distinction in degree of truth. Having made this relation clear, Socrates moves on to the upper segments of the line. A mere glance at the page will show, judging from the number of lines alone, that Plato was primarily interested in the upper line and all that was said till now was subservient to the forthcoming discussion of the upper line.

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6 Cf. Raven (1965), 146-7. – δοξαστόν at 510A is introduced because of the definition of σαφήνεια in terms of ἀλήθεια . Cf. ibid., p. 25.

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The passage to the upper line is well marked: Σκόπει δὴ αὖ καὶ τὴν τοῦ νοητοῦ τομὴν ᾗ τμητέον (510Β2). And this is how he describes the upper line: “In one segment the soul, using as images what were there reproduced, is forced to search from hypotheses, not moving towards a principle but towards a conclusion; in the other – she goes from hypotheses towards an unhypothetical beginning7 without the images of the other segment, making her way through ideas themselves and ideas alone” (510B4-9). Glaucon is not to be blamed for his answer. And at this point the controversy grows so complex that we would do better to abandon the explanation of the text and tackle instead the several problems of interpretation one by one. [4] The first thing that should be clear by now is that the Line is not to be understood, in any case, as a classification. The traditional view of the Line8 sees it as a fourfold classification of reality. Such a view runs into insuperable difficulties already discussed in the immense literature on this passage. But, like the Sun, of which it is the sequel, the Line is an analogy. More exactly, it is a proportion. Its main characteristics are expressed in terms or proportions between its segments. The line has topological features, it is true. We hear about up and down in the line (ἄνω, ἀνωτάτω). But these topological features are more likely to be anticipations of the Cave: none of the relations in the terms of which the Line is established is topological, but only proportional.9 It is true, as Murphy pointed out,10 that Plato never refers to any segment as “longer” or “shorter” but only as “upper” or “lower”. He points out that opinions were divided already in antiquity over which segment was the shorter and which was the longer. Murphy seems to in-

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Omitting τὸ before ἐπ’ at B6 with Ast (and Cornford?). Jowett and Campbell, Adam and others, in a tradition dating back to the neo-Platonists. 9 511D4 μεταξὺ τι δόξης τε καὶ νοῦ would not be a counterexample. It does not refer to the Line but to 478D. Doxa is here not yet a technical term in the Line. The passage says only that dianoia is between doxa and episteme, just as doxa is between episteme and agnoia. The topological interpretation disregards the terms of the analogy: what symbolizes the degree of σαφήνεια and ἀλήθεια are the relative lengths of the segments, not their positions. 10 Murphy (1932), 99 n. 1. 8

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fer from the fact that we do not know which segment, if any, Plato thought of as longer that the inequality of the segments is extraneous to the purpose of the Line. He even goes as far as to suggest that the words “ἄνισα τμήματα” should be deleted as a gloss.11 Murphy is right if he is maintaining that the question which segment is the longer and which the shorter is irrelevant. But this is in itself no warrant for supposing that the difference in length between the segments is to be done away with. The only thing Plato is concerned with in this passage is the relations between the segments, not with the actual length of these segments The question what the terms of the proportion are in themselves, or whether the proportion is direct or inverse, is irrelevant to the point that is being made. It could be either way, as long as the proportions are maintained. These considerations notwithstanding, it is reasonable to suppose that, given that the point of analogy is the measure of clearness or lack of clearness, the clearer object would be represented by the longer segment. But there is no absolute reason why it should necessarily be so, and, in any case, no argument in the Line depends on this. Murphy sees the proportions, oddly enough, as obtaining between the objects “that fill the segments”, and, in his view, “it is not necessary to think of the diagram as having a corresponding shape”.12 Apart from textual difficulties, 13 his suggestion is intrinsically impossible. Proportions cannot obtain between objects as such, but only between welldefined quantitative aspects of objects. The aspect under consideration was carefully delimitated by Plato as “clarity and obscurity” or “truth and lack of truth”,14 and said to be represented – as any simple quantitative relation may be and actually was represented by the Greeks – as a proportion between the segments of a line. (The line is the standard presentation of a proportion in Euclid.)

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He was preceded by Beckman: see Adam (1902), ad loc. (1932), ibid. 13 It is difficult to see Murphy’s reason for saying that “the grammatical object of τέμνειν [t 509D77 ... is not a line or its sections, but this or that class of objects”: (1951), 157. The text is: πάλιν τέμνε ἑκάτερον τὸ τμῆμα ἀνὰ τὸν αὐτὸν λόγον κτλ. 14 Truth is seen here as an attribute of objects, not of sentences, and as admitting of degrees, as ἀ-λήθεια – the character of what is ἀληθές, unconcealed. See Appendix 1. 12

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As the proportion could be represented, more in keeping with later practice, by four separate segments, the question might be asked why Plato makes a point of having the four segments arranged on the same line. Were the proportion intended only A:B::C:D, the standard arrangement was perhaps to be expected. But, as we shall see, the proportion is established on the fundamental ratio A+B:C+D (i.e. doxaston:gnoston). Still, this could be adequately represented by two subdivided segments, not necessarily on the same line. The reason they are marked on one line is, I think, the need to emphasize that the doxaston and the gnoston are not completely cut off from one another. Although in the Line itself we do not have a passage from the one to the other, the Line prepares the setting for the Cave, and the Cave requires the possibility of passage from A+B to C+D. [5] The proportions in the Line are, then: A:B::C:D::A+B:C+D. That A+B:C+D is also a member of this proportion is shown not only by 534A but also by the instructions given by Socrates for the construction of the line: Let a line be cut in two unequal sections and let each of the sections be cut again ἀνὰ τὸν αὐτὸν λόγον. Of course, all depends on the interpretation of Ἀνὰ τὸν αὐτὸν λόγον and on the reading of D6 ἄνισα. I have given above my reasons for rejecting Murphy’s delection of ἄνισα τμήματα. Much the sane considerations should apply for discarding Ast’s and Stallbaum’s emendations. Their corrections sought to avoid the presumably embarrassing consequence of the proportion stated above, namely that B = C. But, although this conclusion is mathematically valid, it is invalid from the point of view of the analogy that is being drawn.15 Our analogy says only that as eikasia is related to pistis in respect of clearness and obscurity, so is dianoia related to nous. But it does not say whether there is any meaningful relation between

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Scolnicov gives the following mathematical proof, entailing that B = C: Α = A+B C = A+B B C+D D C+D Hence: B = C+D Hence: C = A+B A+B A+B+C+D C+D A+B+C+D Hence: Hence: B = (C+D) (A+B) C = (A+B) (C+D) A+B+C+D A+B+C+D

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pistis and dianoia. Mathematical proportion allows us to compare Β and C because it assumes that all the terms of the proportion are homogeneous and can be related to a common measure. But the states of mind that are the terms of the analogy do not fulfil this condition. The two great types of cognition, doxa and episteme, can be compared on their common ground as cognition. But if the subdivisions of these sections are not plainly classificatory, and dianoia is defined only in relation to nous, as indirect apprehension of ideas, it makes little sense to tear it out of this relation, as if it had an independent meaning of its own, and compare it with pistis, which too is a subdivision that was introduced solely for illustrative purposes.16 If, then, the line is to be cut in unequal parts, and if ἀνὰ τὸν αὐτὸν λόγον means “in the same proportion (as that between the two main segments)”, then A+B:C+D is, from the very beginning, also a member of the proportion. The established text of 509D6 is innocuous once the equality of Β and C is exposed for what it is. The meaning of τὸν αὐτὸν λόγον depends on this reading. If the line is cut in equal parts (Ast), then the subsections are cut “in the same proportion” presumably A:B::C:D, and then A=C and B=D, which is awkward, but not altogether impossible. In any case, this avoids B=C. But if the line is cut in unequal parts, the meaning of ἀνὰ τὸν αὐτὸν λόγον seems clear. [6] Nevertheless, R. S. Brumbaugh has proposed to cut the line in four unequal segments (though he bases the inequality on 511D5-6 ὡς μεταξύ τι δόξης τε καὶ νοῦ διάνοιαν οὖσαν, which seems to me irrelevant),17 so that the equality of the middle sections is avoided. His suggestion is

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This last point can also be put differently. The Line may be seen as construed by diairesis: cognition / \ doxa episteme / \ / \ eikasia pistis dianoia nous From the diairetical diagram it is clear that pistis and dianoia cannot be compared, as they belong to different “branches” of the diagram and have no immediate common measure. This series of dichotomies has been clearly recognized by Jackson (1882), Stocks (1911) and J. Ferguson (1963). – A. S. Ferguson (1921), 138 n. 3, is less clear and not so precise. 17 See n. 9, above.

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that one should “draw a figure with all segments unequal, which will illustrate the a:b::b:c::c:d proportion and defer reconciling it with the earlier direction for construction”.18 Brumbaugh supports his view from de anima 404b22, which he compares with Epinomis 991A, and takes to refer to Rep. 510-511. This progression, identified by him as 1-2-4-8 was used again in Laws 894A. Brumbaugh claims that it satisfies the proportion stated at 511D, which he takes to be a:b::b:c::c:d, as well as that stated at 534A, (a+b):(c+d)::a:c::b:d. Brumbaugh’s interpretation runs into several difficulties: a. The passage in de anima has nothing to do with the Republic, as has already been pointed out by reviewers.19 Nor has the fact that Plato used that same proportion again – if it was the same proportion – any bearing on the question whether this is the proportion intended here. b. Brumbaugh has to ask us explicitly to disregard Plato’s instructions at 509D, and to accept that Plato shifted from one proportion to another without as much as a warning. c. He seems to assume that 511D8-E2, and especially E2 καὶ τάξον αὐτὰ ἀνὰ λόγον, indicate a continued proportion. But all we are told to do there is to ascribe the παθήματα of the soul to the different sections of the line and to arrange them ἀνὰ λόγον, proportionally – presumably in the same proportion that is being considered throughout. d. On the other hand, that 509D7 ἀνὰ τὸν αὐτὸν λόγον does not refer to a continued proportion is clear: Socrates asked Glaucon first to cut a line in two unequal sections, and afterwards to cut each section again ἀνὰ τὸν αὐτὸν λόγον. Were this a direction for constructing a continued proportion, it would have been a strange direction indeed. A segment cut in two at any point would hardly be suitable for a continued proportion based on the subdivision of each of the two sections (or indeed for any continued proportion). For this cut would have to be exactly between a(l+m) and a(m2+m3); whereas any division would yield two segments m and n capable of being subdivided in the same ratio m:n so as to give n2:mn::mn:m2.

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18 Brumbaugh (1952), 531. Cf. also (1954), 91-107. He was preceded by Jowett and others: see Jackson (1882), 134. 19 Cherniss (1959-60), 171, 408-9.

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e. Brumbaugh’s suggestion does not satisfy the proportion (a+b):(c+d)::a:b::c:d. Brumbaugh thinks this proportion is not actually required by Plato’s line, but expresses only “crucial relations between the kinds of knowledge which the figure is supposed to represent. And these relations are so important that no scholiast or scholar has accepted the diagram with all the segments unequal”.20 Brumbaugh is probably right in implying that the ratio doxaston:gnoston is not to be referred primarily to the line.21 But the ratio (a+b):(c+d) is established by the first cut in the line, and this is the original λόγος according to which the subsections are formed. It will be seen, moreover, that this ratio is not only important for the general interpretation of Plato’s metaphysics (for if this were all, Brumbaugh would be right in dismissing it here), but it is also intrinsically important for the structure of the line, as I argue below. f. But the main objection to Brumbaugh’s interpretation is perhaps that it sacrifices without any warrant the consistency of the construction of the line in order to overcome a difficulty that is in itself fictitious. The equality of the middle sections of the Line is no real problem and has no significance whatsoever. L. E. Rose22 suggests that the divisions of the line are to be compared to Soph. 266A, and that Plato did not necessarily intend the “traditional quadripartite line”, but rather a cross-division κατὰ πλάτος and κατὰ μῆκος. He gives “graphic” reasons for not comparing the two middle segments, but does not ascribe any meaning to the graphic representation. And moreover, he starts by construing a diagram in which size is relevant, and then switches to ascribing meaning to the position of the figures. [7] Brumbaugh’s and Rose’s positions are extreme, and apparently have not attracted much support in the literature. More widely accepted is the interpretation of the Line, according to which the mathematical analogy is incapable of conveying the full range of relations between the various relata, for the proportion A:B::B:C::C:D::A+B::C+D – which is the pro-

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(1952), 532. See pp. 174-177. 22 Rose (1964). 21

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portion that is claimed was intended by Plato – is mathematically impossible. On these interpretations the analogy fails from start to convey Plato’s meaning. Because the relations in the lower line are established in terms of relations between objects, commentators assumed as a matter of course that the upper line too deals with a distinction of objects inside the field of the intelligibles. Even such scholars as agree that the lower line is purely (or mainly) illustrative still maintain with more or less conviction that it illustrates a distinction between objects in the upper line. As Raven has it: “The relation of each segment to that immediately above it [is] uniform throughout the whole Line ... A contains images of B, the objects of Β are images of the contents of C and C contains images of D. This is a neat feature of the analogy.”23 Raven is commenting on 510B4-9 and seems to be taking that passage to imply that “the objects of Β are images of the contents of C”, and, so it would appear, that the “contents of C” are themselves “objects” distinct from the contents of D. But the passage will not bear that much. It says only that “the soul uses as images the objects which, in the lower division, were themselves reproduced”, without saying anything about the nature of the objects that are ‘contained’ in this section, without even saying whether there are at all objects in this section. When we read further what is said of the upper segment, it becomes clear that there is no mention of objects: there it is only said that the soul does away with images altogether. Indeed, the assertion that, in the upper segment (C), the soul uses as images the objects of the lower segment (B) is not in any case equivalent to the assertion that the contents of this segment are the originals of those images, nor does it imply that this segment contains any objects at all. Plato’s wording at 510B suggests that he is interested in the soul’s activities rather than in the objects, and that objects, insofar as they appear at all, play an auxiliary role. As we shall see, the παθήματα in the lower line are defined by their objects, those in the upper line by analogy to the former.

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23 Raven (1965), 152. I have substituted my lettering for his. – I can find no support in the text for Tanner’s view (1970) that the “objects” or “contents” of C are “εἰκόνες ὑποθετικαί”.

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Now, if the Line is not concerned with objects, the relations within it cannot be presented as of straightforward reflection. For the relation of copy and original, or reflection and reflected, which is normally supposed to be the relation expressed by the line, obtains only between objects. It is perfectly intelligible to say that a figure in water or in a mirror is a reflection of a living creature or of an artefact. But it would be difficult, at first sight, to make good sense of the assertion that dianoia is an image of nous. Raven maintains, in the passage quoted above, that the relation of each segment to that immediately above it is uniform throughout the Line. His contention seems to hold only if we assume that he takes it that the Line establishes primarily analogies between the objects of the παθήματα, rather than between the παθήματα themselves. And indeed he seems to imply that much at the end of the passage I quoted. But it is my contention that the main point of the Line is not to establish analogies between the objects of the παθήματα, and that, accordingly, the proportion intended by Plato was not A:B::B:C::C:D::A+B:C+D, which is admittedly a mathematical impossibility. [8] The Line is an analogy which is concerned with the difference between the mathematical sciences24 and dialectic, as viewed through the states of mind (παθήματα ἐν τῇ ψυχῇ) related to them. In a sense, it may be said to be a definition of dialectic. As we are familiar with mathematics and mathematical procedure (Glaucon is so portrayed at 511B1), and as we are given a four-term proportion in which three terms are wellknown and the relations between the terms are carefully defined, we should be able to understand the nature of the fourth term in relation to the other three. The proportion is (509D, 511D-E; cf. above, p. 169): eikasia:pistis::dianoia:noesis. It is clear from the terms of the proportion that this is a proportion between states of mind, not between objects. So, in 534A, Socrates

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24 I.e. the μαθήματα, or what there is to be learned. For only the mathematical sciences can be the subject of knowledge as distinct from empeiria. Cf. Gorgias 462-4, Philebus 55 ff. I shall normally intend “mathematics” to refer to the five mathematical sciences recognized by Plato.

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evades speaking about the objects ἵνα μὴ ἡμᾶς πολλαπλασίων λόγων ἐμπλήσῃ ἢ ὅσων οἱ παρεληλυθότες. Whatever might be the case with the objects of these mental ‘abilities’, they are clearly not analogous to the states of mind themselves. If they were, there would be no reason why Plato should not say so in a short phrase. The fact that he does not, shows that the relation between them is not so simple – and that, at any rate, Plato was not interested in the objects for his purpose in this passage.25 When two terms are said to be analogous, they are said to be so only in a determined respect. It is in order to establish the point of analogy that Plato considers the objects of the παθήματα of the lower line. This procedure had been followed before: In the Sun, to which Socrates refers at the beginning of the Line (509D1 ff.), the analogy of vision and intelligence was arrived at by a distinction between, and correlation of, the visible (singled out from the sensible in general) and the intelligible. As at 477D, the states of mind are distinguished by “what they are correlated with” (Crombie) and by “what they produce”. The two first states of mind in the Line are defined by their objects: the first is correlated with images and reflections, the second with the originals of these reflections. Eikasia is indeed inference from appearances. It is the state of mind in which one sees the original through its image. Pistis, on the other hand, is the direct apprehension of the original. In this respect, then, eikasia is ἀσαφής as pistis is σαφής.26 As the original is clear and its apprehension is sure and unerring,27 so is the copy unsure and dubious.

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25 Even at the risk of displaying “the most amazing myopia”, I cannot see in 534A an “explicit ... reference to an ontological difference between the objects of διάνοια and νόησις”, and it takes a very sharp eye to agree with Brentlinger that “the passage is as clear and explicit a statement as one could hope for” (1963), 156. 26 Cf. Ferguson (1921), 144-5 and n. 1, quoting Thucydides iii 20, for εἰκάζω ἐκ or ἀπό τινος. Also Cooper (1966). Contra Cross and Woozley (1964), 219 ff.; Hamlyn (1958), but his position is vitiated by, among other things, his unwarranted and uncritical assumption of a strict parallelism between the Line and the Cave. 27 Cf. LSJ , s.v. σαφής. – What is σαφής: the object or the apprehension? It seems that both may be called σαφής. Is Plato then taking advantage of an ambiguity of the Greek? Not necessarily, since for him only the apprehension of a clear, sure object can be a clear and unerring apprehension.

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This distinction in clearness is also a distinction in ἀλήθεια , in reality and lack of reality. At 478E Socrates had stated how the objects of opinion are related to those of knowledge and of ignorance in respect of their reality and lack of reality (E2 εἶναί τε καὶ μὴ εἶναι). Now he recalls that distinction and states that as the objects of opinion relate to the objects of knowledge in respect of reality and lack of reality, so relates the resemblance to what it resembles (510A9-10). Once the relation between the two functions is clear, Socrates passes to the upper line. The objects are now dropped altogether; having served their function in defining the functions of pistis and eikasia, there is no more need for them. That the upper section is concerned with intelligibles is clear from 509D8, and this is enough for Plato’s purposes. The analogy is carried to the upper line: Ἧι τὸ μὲν αὐτοῦ τοῖς τότε μιμηθεῖσιν ὡς εἰκόσιν χρωμένη .... The contrast between the two subsections is well-marked: In the first the soul, using images, is forced to proceed from hypotheses towards a conclusion, whereas in the other the soul, without using images but through ideas alone, goes from hypotheses towards an unhypothetical principle. In one point at least the analogy with the lower line is clear: In A as in C the soul uses images, whereas in Β as in D she looks at the originals of these images. In C the soul inquires about the ideas, but by means of their reflections, namely by means of physical objects of Β (not by means of ‘mathematicals’). As I have argued above, this is not to be taken as implying that the contents of C are the originals of the contents of B. If anything can be said to be the ‘content’ of C, it is the πάθημα or δύναμις in the soul which studies ideas through their sensible representations. But I have already stated the case for considering the line not as a ‘container’ but rather as a representation of quantitative relations. Dianoia is thus not defined by the range of its objects – for in that it is indistinguishable from nous – but by the method whereby these objects are studied. While nous approaches the objects in themselves and inquires for the reasons of their being as they are, dianoia studies them only through their images, taking them for granted and following the chain of their consequences only.

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Whether the use of sensible images does force the soul to inquire from hypotheses towards a conclusion instead of towards a principle, and why this should be so, is a question that will be dealt with below. This interpretation also does away with “mathematicals” or “intermediates” – and this question too will be considered separately.28 [9] The recapitulation of the Line at 534A ff. confirms the movements of thought we have followed. Socrates starts by relating the functions to their objects: ... καὶ δόξαν μὲν περὶ γένεσιν, νόησιν δὲ περὶ οὐσίαν. It is to be noted that in this recapitulation no objects are assigned to the four subdivisions, but they are grouped in pairs and objects are assigned only to the main sections of the line. The ‘objects’ of eikasia and pistis had no further function than to define their respective abilities and the relation between them. After the main abilities, doxa and noesis, are defined by their objects, the relation between them is expressed by means of the relation between their objects: καὶ ὅτι οὐσία πρὸς γένεσιν, νόησιν πρὸς δόξαν. Once the relation of noesis and doxa is established, the objects are dropped altogether, and Socrates goes on to state, on the basis of the relation just established of noesis and doxa, the relations between the four abilities represented by the subsections of the line: καὶ ὅτι νόησιν πρὸς δόξαν, ἐπιστήμην πρός πίστιν καὶ διάνοιαν πρὸς εἰκασίαν. The movements in which the analogy is established are well marked: 1. τὴν μὲν πρώτην μοῖραν κτλ ... 2. καὶ συναμφότερα μὲν ... 3. καὶ δόξαν μὲν ... 4. καὶ ὅτι οὐσία ... 5. καὶ ὅτι νόησιν ... The καί at Α4 makes it clear that 5. is a new proportion and that 4. is merely introductory to it. The main proportion, towards which the whole passage is directed is 5. [10] Before we come back to the Line in order to examine the nature of the upward path described there, we should make mention of a few difficulties in the Cave. I shall deal with this allegory very briefly, as it does not seem to add to the understanding of Plato’s hypothetical method much more than we could gather from the Divided Line.

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See ch. viii.

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On the whole, the Cave is a continuation of the Line. Better, from the point of view of Plato’s purposes in the Republic, the Line is the prologue to the Cave. The latter is parallel to the former and is based on it, though the parallelism is not precise.29 In the Cave, we are back to the division between objects of opinion and objects of intelligence, and in this respect we do seem to have a classification rather than a single analogy. Moreover, in the Cave, the escaped prisoner is made to advance through all the stages, from the lowest to the highest, in what appears to be a single scale. But there is no real continuity in the Cave. Although the prisoner goes through the stages one after another, it cannot be said that each stage is a reflection of the stage above it. The shadows on the wall are indeed reflections of the statues carried behind the prisoners, as the reflections in the water outside are of men and things in the outer world. But this relation cannot apply between the upper stage of the cave and the lower stage of the outer world: the statues are not copies of the reflections in the water, but of the real men and things that cast these reflections. Moreover, if a continuous gradation is assumed in the Cave, the fire at the entrance is left without any function apart from that of a mere “stage property”.30 It is undeniable that the prisoner passes through the stages of the Cave in succession and that they are presented as ascending in clarity and value.31 But this is not a sufficient basis for the inference that the gradation of the stages themselves is one and continuous throughout. Indeed, as can be easily seen, the lower part as a whole is a reflection of the upper part. Each stage is related to the corresponding stage on the other world as ‘copy’ to original: the shadows inside to the shadows and reflections outside, the statues to the men and things outside, the fire to the sun. It is immediately to be noted that this parallelism is not perfect: in the upper world the ascent from the things to the sun is mediated by the

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29 I accept, in general, Raven’s exposition of the relations between the three parts of the simile. The minor points on which I disagree with him should be clear from what follows. See also J. Ferguson (1963). 30 So Notopoulos (1944), 237; perhaps also Diès (1932), p. lxvii. 31 Pace A. S. Ferguson (1922), 15.

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heavenly bodies, which have no counterpart inside the cave. It has been suggested that this expresses the gradual ascent of dialectic towards the Good through the hierarchy of ideas; this hierarchy exists of course only among the ideas and not among sensible things. It should be emphasized that this is a hierarchy of ideas, not of all being. As opposed to the neoPlatonic view, there is here no gradual passage from stage to stage embracing the whole scale of being. What happens to the released prisoner when confronted with the artefacts that cast the shadows is symbolic of his movement throughout. Outside, he looks at reflections – this is dianoia; but these are reflections of real things, not of artefacts. As in the cave he was dreaming, so is he still dreaming outside the cave – only now he is dreaming about being. The Cave emphasizes, “from the point of view of our state of education and lack of education”, the similitude as well as the difference between the two dreams. If this analysis is correct, then the Cave presents us with the same relations as the Line, and here as there no relation can be established between the second and the third stages. This means that the prisoner’s escape from the cave does not signify a passage from Β to C in the line, but a passage from the world of senses to the world of ideas. The break between the world of the cave and the outer world has been rightly pointed out by Ferguson.32 But he seems to me to have exaggerated this point, and to have drawn from it consequences that lack adequate support in the text. Only in the Cave is there an ascent from the objects of opinion to the objects of intelligence. Nothing of the sort was mentioned in the Line.33 In order that there may be an ascent, the Cave is, after all, classificatory, and includes objects of opinion and not only objects of sight.

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A. S. Ferguson (1922). Cf. Ross (1951), 70-71.

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But the ascent is from the cave to the outside world, i.e., from the sensible to the intelligible, and not, in any case, from stage II to stage III.34 [11] We can now come back to the Line and examine in greater detail the ‘upward path’.35 This is linked especially with the difference between mathematics and dialectic, and with the passage that is to be effected from the former to the latter. The difference between mathematics and dialectic is twofold: a. Mathematics uses sensible figures, whereas dialectic proceeds always through ideas. b. Mathematics is forced to proceed from hypotheses to a conclusion, dialectic goes from hypotheses to an unhypothetical beginning. Whether these two features are necessarily linked, and what their relation may be, this will be inquired into later.36 We should begin by examining the role these sensible figures play in mathematics. They themselves are not the objects of mathematics, but “those which they resemble”, and all the geometer’s utterances refer not to the figures he models and draws, but “to the Square itself and the Diameter itself”. The sensible figures are but aids for the mathematician in grasping the figures themselves (510D5 ff.). What is then the relation between the square the geometer draws in the sand and the Square itself? Commentators have suggested that this refers primarily to the geometer’s practice of drawing his diagram in the sand. This too is implied here. But this surely cannot be the point. It would be irrelevant, in the middle of a very condensed passage dealing with the relative degrees of clearness of geometry and dialectic, to disqualify geometry from being a science on the grounds of a procedure of geometers which is irrelevant to geometry itself and which can easily be done away with. Indeed,

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Diairesis again:

objects / \ of art of nature / \ / \ originals shadows originals shadows 35 Against Rosenmeyer’s (1960) suggestion that there is no upward path in the Republic, see Robinson’s reply, (1963). 36 See below, pp. 188-191.

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Greek geometers used to draw diagrams, but it is now recognized that the graphic aspect of ancient geometry has been greatly over-estimated.37 It seems rather that what we have here must be related to what deficiencies geometry has in itself, not to extraneous procedures of geometers. It may be true that Plato does not tell us much about what the ideas are, but he certainly does take great pains to tell us what they are not. One distinction Plato draws again and again, perhaps the main distinction between ideas and physical objects, is that ideas are not sensible, not corporeal, not spatial (i.e., neither extended nor located in space). And one of the central passages in which he comes back most forcefully to this distinction is this very passage of the Line, in which he speaks of the visible square and the Square itself. It must also be borne in mind that, as Plato clarifies time and again, it makes no sense to say that something is like something else without qualification. The relation of being alike implies some specified respect according to which things are like one another.38 From what has been said, it should be already clear that in one respect, at least, the visible square is not a resemblance of the Square itself; viz., in respect of being spatially extended, that is to say, in respect of having four sides, four right angles, etc. For, if the Square itself is a νοητόν, the one determination it cannot possibly have, by Plato’s own distinction between νοητά and αἰσθητά, is spatial determination. The Square itself, far from having four perfectly straight sides and four perfectly right angles, has no sides and no angles at all. If it had, it would be an αἰσθητόν, not a νοητόν.39 For Plato, shape (σχήμα) is always visible. Shape, Socrates defines in the Meno, is the only thing that always accompanies colour.40 In the Seventh Letter shape is associated once with bodies and once again with

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See, e.g., Neugebauer (1957). Cf. Archytas 47 Β4 DK. Parm. 129A5; cf. Soph. 259BD. 39 Of course, the property of being a square is not spatial. But the concept of property is not Platonic. The problem is to show, in Plato’s terms, that noeta cannot be in space or have shape. 40 75B10-11: ὃ μόνον τῶν ὄντων τυγχάνει, χρώματι ἀεὶ ἑπόμενον. This definition is rejected by Meno, but only because it uses unknown terms, not because it is presumed false. 38

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bodies and colour.41 In the Phaedrus colour and shape are emphatically excluded from intelligible being.42 In the first hypothesis of the Parmenides the one is said to be without shape.43 The dichotomy is for Plato complete: either a thing is visible, corporeal, in space, or it is invisible, incorporeal, in no space. Plato rebukes geometers for having to do with τοῖς ὁρωμένοις εἴδεσι (510D4), whereas their real concern is with the Square itself and with the Diagonal itself, not the squares and diagonals which are corporeal and cast shadows and reflections, but those that cannot be seen44 except τῇ διανοίᾳ. In order to have a Square itself that would ‘look’ like a square drawn in the sand, Plato would have to have another space in addition to, and distinct from the space of sensible objects. (Another solution, for example, would be something like Kant’s pure imagination. But this way was, of course, closed for Plato’s realistic outlook.) But there is no space for Plato apart from the public space of sensible corporeal objects, and anything that has a shape, must be located in that space.45 Even when we imagine a square, our φαντάσματα are still sensible.46 Imagination in geometry is not, in principle, different from drawings in the sand. The figures the geometer draws in the sand or merely imagines, all alike refer to something else. Even the imagination, insofar as it is imagination of a figure, is bound to be of a particular, and spatial. The

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41 342C6 οὐκ ἐν φωναῖς οὐδ’ ἐν σωμάτων σχήμασιν ἀλλ’ ἐν ψυχαῖς ἐνόν ... D4-5 περὶ ... περιφεροῦς σχήματος, καὶ χρόας ... καὶ περὶ σώματος ἅπαντος. I take the Seventh Letter to be authentic, pace Levison et al. (1968). 42 247C6 ἡ ... ἀχρώματός τε καὶ ἀσχημάτιστος καὶ ἀναφῆς οὐσία. – At Phaedo 79Α ff., MS. Β has the interesting variant ἀειδές contrasting with ὁρατόν, instead of the rather more obvious ἀιδές. 43 137D8 ἄνευ σχήματος. 44 ἰδεῖν ... ἴδοι τις ..., in close sequence, as opposed to the corporeal ὁράω. 45 Cf. further Allen (1960), 50 n. 2: “... For Aristotle the extended is substantial, real in its own right; and therefore it is for him feasible to adopt a relational view of space, with substances as relata. But for Plato extended entities are reflections, images; space, the medium of reflection, is a precondition of their existence, the receptacle in which the Forms are mirrored. It is therefore absolute, not a consequence of the mirroring.” So O’Brien (1967): “The Timaeus ... [provides] a receptacle in which the form of a substance can be particularized in something like the way in which the form of an attribute is particularized in the subject which it characterizes” (p. 202). 46 Philebus 39B classifies imagination alongside memory and sensation, and sees it as dependent on “sight or other sense”.

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actual drawing on the sand is not essential. In the Meno, Socrates presumably draws diagrams in front of the boy-slave; but Plato does not do so for his readers. And yet, when we, the readers, follow Socrates’ reasoning, we do not imagine the Square itself, whatever that may be, but we imagine a certain square, assumed to have a side two feet long, irrespective of whether we actually draw a square on a piece of paper or not.47 A still better example is afforded by the Line itself. When Socrates instructs Glaucon to cut a line in two different sections and again each of these sections etc., Glaucon presumably does not draw the line in the sand but performs these operations ‘in his mind’. Nevertheless, his φάντασμα is spatial. What is more important, it represents (is an εἰκών of) the non-spatial proportions that are to be discussed. Maintaining that the physical square imitates the shape of some other square (ideal or semi-ideal) not only creates the difficult because unnecessary problem of the “mathematicals”: it makes Plato incapable of distinguishing between the corporeal (spatial, visible, tangible) and the incorporeal (non-spatial, invisible, intangible), precisely in the passage in which he is drawing this very same distinction.48 [12] If so, an obvious question remains to be asked: In what respect, then, does the square resemble the Square itself? The answer is, I think, equally obvious, although it is, as we are warned in the Phaedo, disappointing: the square is a resemblance of the Square itself in the respect of being a square.49 But there is no reason why a square should be thought of primarily as a visual (or sensible) shape. Indeed, in Platonic terms, it is a contra-

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47 Cf. Ross (1951), 49: “Plato is at fault, no doubt, when he describes the geometer as necessarily drawing or modelling his particulars; he overlooks the fact that anyone with a lively visual imagination can make do with imaginary figures. But the recognition of this does not invalidate his general thesis, ...; for an imaginary figure is as particular as one that is drawn and seen.” 48 This is not to be construed as special pleading. It is no more than assuming that Plato meant what he said unless proof should be shown of the contrary. There is no prima facie reason to suppose that any square that is classified as intelligible should have spatial properties, when we are expressly told that noeta are not spatial entities. 49 ‘Square’ here is neither univocal nor equivocal; it is systematically ambiguous. Cf. below, n. 15 to ch. viii.

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diction that the purely intelligible essence of the square should be adequately expressed in spatial (i.e. sensible) terms. In other words, what makes the square in the sand a square is not the fact that it has four (perfectly or imperfectly) straight sides and four (perfectly or imperfectly) right angles. Similarly, what makes the number 4 a square number is not the fact that its units can be arranged in a square pattern. What makes them square is the fact that they are imitations or representations in another medium50 of the Square itself, which is the essence common to the square shape and the square number.51 We could perhaps say – although I fear this might look rather pedestrian from this end of History – that the Square itself is not very different from what in modern notation we would represent by n2. A good example, quoted with approbation by Plato, is Theaetetus’ attempt at a generalization of the theory of irrationals.52 I am not implying that Plato had some such formula in mind. We know too little about Plato’s own mathematical activities. But I think it is reasonable to assert that Plato was stating here that the essential nature of geometry is not spatial.53 The Square itself is thus the aitia of the square drawn in the sand. The spatially extended square is a representation of the Square itself, and insofar as it is such a representation it is intelligible and it is what it

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I.e. in (sensible) space. Cf. “images in water”, etc. This should not be understood as implying that Plato was on his way to analytical geometry. Our analytical geometry assigns coordinates to places and regards lines as mappings of functions. Plato did not think arithmetic and geometry to be merely intertranslatable by means of a useful convention: he thought numbered things and measured stretches were ontologically connected by a common cause. And, of course, the concept of variable, which is central in analytical geometry, was totally unknown to Plato. – Brentlinger (1963) is wrong when he says that “Pythagoras’ theorem is not about, in a simple sense, the ideal triangle” but about the “mathematical” triangle (p. 159). For, as geometry is not essentially spatial, Pythagoras’ theorem is in fact about triads of numbers (the so-called Pythagorean numbers) – which may, accidentally, be represented as sides of triangles. That the theorem was in effect originally numerical is argued, e.g., by Neugebauer (1957), 36. 52 Theaet. 174D ff. N.B. 174E1 συλλαβεῖν εἰς ἕν, the technical term for arriving at the idea. Cf. Heath (1921), i 155. 53 In a sense geometry is of necessity bound to spatial intuitions, insofar as it is geometry and not dialectic. But in another sense geometry is essentially non-spatial, insofar as it deals with entities that are essentially non-spatial and only by accident have also spatial determinations. The consummation of geometry is dialectic. But then, if you so wish, it is geometry no more. Epinomis 990D2-9 makes the same point (Cf. Scolnicov (1971), 93). Even if this work is not Plato’s, the passage gives a good example of the mathematical trends in the Academy and it is very probable that the view expressed there is, after all, Plato’s own. 51

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is. When the geometer draws a square in the sand or imagines it and sets out to prove theorems about this square, he is not proving anything about it at all; whether he is aware of it or not, he is referring to that other entity that can only be seen (ἰδεῖν) with the mind (τῇ διανοίᾳ).54 In effect, when the geometer uses “visible figures”, what he really has in mind are the originals of which these figures are ‘images’, namely the Square itself and the Diagonal itself. As we have seen, the dynamis which he displays is dianoia (in the strict sense of the word). And dianoia is to nous, the direct intelligence of ideas, as eikasia is to pistis, the direct apprehension of visible objects: it is an indirect, ‘mirror-like’ type of apprehension, which aims at the original through images that are less true and less clear than the original itself.55 The real object of study of mathematics is the Square itself and the Diagonal itself. That these terms refer to ideas has already been sufficiently argued, e.g. by Ross. Dianoia studies these ideas not by themselves, but through their images. And those images cannot but be the sensible figures, drawn or imagined. (Incidentally, Plato gives us one example of a science which studies ideas through images that are not visual: ‘harmony’, i.e. acoustics.) This is why the relation between A+B and C+D is intrinsically so important for the Line. Although Plato’s main intention in the Line is not ontological, nevertheless the distinction between dianoia and nous – and this is the distinction the Line seeks to establish – is based on the ontological dependence of the γιγνόμενα upon the ὄν, for dianoia is the study of the ὄν in the medium of γιγνόμενα. Therefore, mathematics effects the μεταστροφὴ ἀπὸ γενέσεως ἐπ’ ἀλήθειάν τε καὶ οὐσίαν (525C56) not because it deals with ‘intermediates’ but because it looks at οὐσία via γένεσις. Accordingly, the recapitulation of the Line is based on the relation genesis:ousia.

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54 Cf. also 327A6-B8 on geometrical ‘constructions’, and especially Β8 τοῦ γὰρ ἀεὶ ὄντος ἡ γεωμετρικὴ γνῶσίς ἐστιν. 55 Cf. Diès (1932), p. lxvi: “Or, la pensée moyenne ou διάνοια n’opère sur les intelligibles qu’à travers des symboles sensibles; elle est donc, relativement à 1’intuition directe des intelligibles, quelque chose comme une connaissance par images et, comparée a cette science parfaite, prend ainsi valeur d’opinion.”

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Thus, there are two kinds of objects involved in geometry, and those are the kinds referred to in the Line: the ideas aimed at, but only indirectly achieved, and the sensible images used by the soul in her inquiries. No room is left for ‘mathematicals’ or ‘intermediates’. ‘Intermediates’, apart from raising serious intrinsic difficulties and forcing the text, would disrupt the pattern of the Line, by supposing dianoia to aim indirectly not at ideas but at reflections of ideas.56 [13] The mathematical sciences are alike in that, having their place between opinion and strict dialectical knowledge, they “turn the eye of the soul” from the world of the senses to the intelligible world. Because these sciences deal with objects that can be adequately grasped only by the mind, notably with the concept of unity, they force the soul to go beyond what is apprehended by the senses. The passage at 523C ff. makes the preliminary point that there are at least some data of our senses which are contradictory. What is wrong with the senses is that they do not give us the impressions of, say, soft and hard, as two distinct (κεχωρισμένον 524C4) impressions, but as something confused (συγκεχυμένον τι). Unity is, of course, always experienced in contradictory contexts. Anything that is seen to be one is also seen to be many (cf. Phil. 14D). Every sensible unit contains parts, but the true unit contains no parts and is always identical to itself. True unity and true number are not to be found, therefore, in the sensible world. Arithmetic can be used in the sensible world, but its proper objects are ideal objects. As with arithmetic, so with geometry and stereometry (526C ff.). Geometry is “the knowledge of what eternally is, not of anything that comes to be this or that at some time and ceases to be”.

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56 The text says: “In the first [section] the soul uses as images those things which themselves had images in the visible world”. It is clear that a. dianoia uses visible objects, and b. these objects are used by dianoia as reflections (images). The question which is disputed is: what are these visible objects reflections of? If we try to insert intermediates into this pattern, we must do one of two things: 1. to have dianoia aiming directly at intermediates and thus indirectly at ideas; or 2. to have dianoia aiming at visible objects which are images of intermediates which in turn are images of ideas. In either case the pattern of the Line is disrupted. In the first, dianoia aims directly at intermediates, not at visible things as the text has it, and no relation is then stated between intermediates and visible things. In the second case, dianoia aims indirectly not at ideas but at reflections of ideas, i.e. at intermediates through visible things.

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Astronomy too is not to study “the traceries in the skies”. Although they are the most beautiful and the most exact of the sensible things, they are deficient in truth and being. For true velocity and slowness cannot be apprehended by sight, only by understanding. I should not take things so far as to suggest that Plato was heralding Leibniz’s differential calculus. But in this context, in which the sensible elements in the mathematical sciences are presented as “reflections” of true number, it is perhaps not unreasonable to understand “real velocity and real slowness in their true number” as referring tentatively to some sort of abstract, not necessarily spatial, proportion. The same is true of harmony. Consonance and dissonance are not primarily a matter of sounds, but a matter of abstract proportions. And as in arithmetic or geometry, empirical observation cannot produce an unequivocal unit of counting or measurement. When studied separately, each of these sciences seems to have its own subject-matter and its own axioms, forming each of them a system closed in itself. But this is only a superficial account of these sciences. For it is necessary to inquire into “the mutual relations and affinities (τὴν ἀλλήλων κοινωνίαν ... καὶ συγγένειαν) which bind all these sciences together” (531D1-2, tr. Cornford). As opposed to Aristotle, Plato seems to have held geometry and arithmetic as essentially the same. Aristotle has two definitions of number: (i) ὁ ἀριθμὸς σύνθεσις μονάδων (Met. Ζ 13. 1039al2; cf. I 1. 1053a30; 6. 1057a3, Μ 9. 1085b22, Ν 1. 1088a5; Phys. iii 6. 207b7. Euclid Elem. vii def. 2: ἀριθμὸς δὲ τὸ ἐκ μονάδων συγκειμένον πλῆθος). (ii) πλῆθος τὸ πεπερασμένον ἀριθμός (Met. Δ 13. 1020al3). This second definition, as Ross remarks in his commentary to this passage, refers back to the Academy, and more specifically to Eudoxus: The definition of number as πλῆθος πεπερασμένον is anticipated by Eudoxus’ definition of it as πλῆθος ὡρισμένον (Iambl. in Nicom. Ar., Introd. 10.17). Mr. F. Μ. Cornford (Class. Quart, xvii. 8n.) suggests (rightly, I think) that the present definition ‘goes back to the characteristically Pythagorean conception of number as the product of the union of πέρας and ἄπειρον’; whereas such definitions as σύνθεσις μονάδων, πλήθος μονάδων ... represent ‘the crude, and so to

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say materialistic, view, which may well have been shared by the Egyptians and the Pythagorean mathematicians or number atomists’ of the sixth century.57

The Platonic character of this definition was rightly pointed out by Wilpert.58 Plato’s non-atomistic concept of number enables him to bridge the gap between arithmetic and geometry, for both deal with relations. Accordingly, Plato held irrationals, such as √2, √3, etc., to be numbers (as opposed to Aristotle’s view on this point), because they express relations (even if those relations cannot be exhaustively expressed in a finite number of steps).59 It is not a question of Plato intending to perform the arithmetization of mathematics. Rather it seems that Plato saw in the mathematical sciences different sensible incarnations of an abstract theory of numbers. Two pebbles, two sticks one of which is half the length of the other, a horse which reaches the other side of the stadium in half the time as another, the musical interval C–C' – different as these may appear to the senses, they are all but representations in different media of the same abstract proportion. This number or proportion is the aitia of its several representations in the same sense that Simmias is the aitia of his portraits.60 Finding out the reality which in fact the mathematical sciences study means realizing that their inquiry is not about things that can be counted or stretches that can be measured, solids that can be gauged, relations between moving things in space or between audible sounds, but about abstract proportions that can be variously represented. [14] Now we are in a position to discuss the relation between the use of the senses and the impossibility of checking the hypotheses of mathematics. It would seem that the relation is not merely accidental. Plato is speaking as if there were something in the nature of mathematics that would “force” the soul to proceed from unchecked hypotheses to their conclusions, unable to verify the hypotheses themselves.

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Ross (1924), 323-4. Wilpert (1949), 177-8 n. 9. 59 Scolnicov (1971), 91-93 and further references there. 60 Cf. p. 203. 58

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Let us first examine the examples Plato gives us of mathematical hypotheses: the odd and the even, the figures and three kinds of angles. Indeed the only basis the geometer has for his assumptions is his sensible intuition: he posits three kinds of angles because he cannot draw (or imagine) an angle that would not be either equal to, or less, or greater than, a right angle. Similarly, that such and such figures ‘exist’ he proves by ultimately recurring to his spatial intuition. (As in the case that at least three straight lines are needed to form a figure. – I do not think this was necessarily the example Plato had in mind, but the general point seems to have been something like this.) And again, that numbers are either odd or even is supported by an appeal to an intuition that Plato probably thought to be based on sensory imagination: if to a collection of items that can be divided into two equal parts one more item is added, the resulting collection will no longer be divisible into two equal parts; but if to this new collection another item is added, the then resulting collection will be divisible again into two equal parts.61 And because the geometers can see these assumptions clearly, they take them as their starting-points ὡς παντὶ φανερῶν, since they are clear to all,62 when they should take as starting-points what is clear, that is intelligible, in itself, not what is apparent (φανερόν) to sensible intuition. Space and sensibility are for Plato intrinsically irrational.63 In as much as arithmetic and geometry have their basis on spatial sensible intuition, to that extent they are unintelligible, although they may be, in a sense, “apparent to all”. (Again, what is ἱκανόν for the geometer is not ἱκανόν for the dialectician.) Moreover, spatial intuitions are, in themselves, isolated from one another. If geometry and arithmetic are logically structured, this is not because of their sensible aspect, but in spite of it. As the Phaedo made clear, only ideas can be logically connected. Sensible things, situated in space, may participate indirectly in these logical connexions only insofar

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61 No doubt Pythagorean arithmetic had much to do with this; cf. Ross (1951), 49. But other philosophers came to much the same conclusions on somewhat different grounds: Kant, Brouwer, Beth. 62 So Lindsay: “on the ground that they are plain to everyone”. 63 See pp. 181-182, above.

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as they participate in the ideas. But as this participation is never complete, so the logicality of the sensible things is never complete. In the mathematical sciences Plato found a striking example of how strict logical relations could apply throughout in a medium that is essentially irrational. The irrationality of visual shapes and of audible sounds nevertheless gives way to relations that are completely rational. This could only be explained, for Plato, by understanding that the real subject-matter of mathematical science is not the sensible given or imagined, but the purely rational, of which the sensible is but a representation. For this reason, Plato maintains that the same object is studied by geometry and by dialectic. But the latter sees it as a full noeton because it can see it in its connexion with the arche (512D1). Mathematics as such cannot. If geometry and arithmetic cannot get rid of their sensible intuitions, they can never become fully intelligible. If geometers accept spatial sensible intuition as an essential element of their science, they are giving up all hope of ascending towards one principle, because this sensibility will always appear in their sets of assumptions as an irreducible residue. Intelligibility is unity and connectedness. Logical connexions can hold only between what is fully intelligible, and between any objects only insofar as they are intelligible. What is sensible, insofar as it is sensible, being opposed to the intelligible, is incapable of standing in logical connexions. What is sensible is thus necessarily disconnected, episodic. Therefore, as geometry and her sister sciences make use of sensible images in their procedures (though they do not in fact study the images themselves – which accounts for their intelligibility), they are restricted as to the direction of their inquiries. Prevented by the opaqueness of the images from going upwards towards an unifying principle, they proceed downwards towards a conclusion. This is their typical procedure. Of course geometry is not prevented from using analysis. But this analysis is of necessity sporadic and cannot bring geometry to the one unhypothetical principle. The irreducible residue of irrationality left by the sensible intuition puts a limit to the upward movement of analysis and unification. And once this limit is achieved (it would not seem very far for Plato, judging from his examples), only the way down would be left unobstructed.

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The relation between the “hypothetical” and the “aesthetic” aspects of the mathematical sciences is of great importance for Plato’s conception of the method of dialectic. In the Meno, the method of hypothesis could be interpreted in purely logical terms. Although in my interpretation of it above I tried to show that there it carries with it a metaphysical background, yet Plato’s description of the method as such is reasonably self-contained even without recourse to the metaphysical apparatus. The same case could be made – as indeed it was, not without some success – for the Phaedo. But in the Republic it is much more difficult to dissociate method from metaphysics. The way up and the way down cannot be satisfactorily explained without recourse to the participation of material things in the ideas. And if the Divided Line does not, the Cave certainly does combine inextricably the passage from opinion to knowledge with the passage from one degree of reality to another. This is understandable only if the two aspects of the transformation of opinion into knowledge, viz. the calculation of the reason and the turning of the eye of the soul from becoming towards being, are intimately connected. The mathematical sciences show indeed that the incapacity of questioning the hypotheses and the necessary appeal to sensible data are inseparable. Doing away with hypotheses is also doing away with sensible data. The transition from the almost uncommitted views on opinion and knowledge in the Meno to the heavily metaphysically loaded views of the Republic was effected, as I have tried to show, in the Phaedo, where Plato was led by what seemed to him to be demanded by the logic of his beliefs. The way is still open, of course, for those who would want to cut off the Meno and perhaps also the Phaedo from the Republic to claim that, on a minimal interpretation, the method in the earlier dialogues can be considered apart from the metaphysics. That may be so. But such possibility should not, to my mind, override the methodological consideration that, within the limits of one’s data, one should look for a maximum of coherence and continuity. [15] The nature of the highest principle is explained in the simile of the Sun. The sun, says Socrates, is the Good’s “offspring” and its analogue

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in the visible world. In that simile, as we saw, the point of analogy is as follows: The eye may have the power of vision and the object may have colour, i.e. the power of visibility, and yet, if light does not shine on them, the eye will not see its object. Similarly, the soul has intelligence and its object may be intelligible, but without the object being linked to the idea of the Good, the soul will fail to understand it fully. In both cases, there is no fault either in the eye or the soul or in their objects: it is only that the conditions for their abilities to be actualized were not present, or were present only imperfectly. This is precisely the case of the propositions of mathematics. When taken in themselves, as objects of a sensible apprehension, “there is no intelligence about them”. But as soon as they are taken μετ’ ἀρχῆς they become fully intelligible.64 And yet, the propositions have not changed in themselves. The assertion that every angle is equal to, or less or greater than, a right angle remains true (in our modern sense of “true”) as it was before. Only now it is not only true, but it is also seen as ἀληθές, as unconcealed, whereas formerly it was seen only darkly through the obscure vision of the senses. But, as the reflections in water are illuminated, however dimly, so also the hypotheses of mathematics have in them a degree of truth and reality. Yet, whatever truth and reality they possess is derived ultimately from the first unhypothetical principle. And to one who examines these hypotheses ‘from below’, without seeing their connexion to the first principle, their reality cannot be more than a provisional reality, a reality assumed much in the way we assume the features of a man whose shadow only we see on the wall. As long as the dialectician has not arrived at the unhypothetical principle, the reality of his hypotheses can be only assumed.65 It is only when he arrives at that principle and sees its connexion to his former hypotheses that their reality is given to him. We have thus a neat feature of the hypothetical method as we have seen it throughout. The reality (or truth) of a fact is assumed, and the reality of this fact is deemed to be caused by the reality of another fact. But this new fact too is only assumed to be true, although the dialecti-

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Geometry μετ’ ἀρχῆς is fully intelligible. But it is no more geometry; it is dialectic. Cf. Phaedo 100A5 τίθημι ὡς ἀληθῆ ὄντα.

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cian has perhaps ill-defined grounds for preferring this fact to other possible explanations.66 And so on, from assumption to assumption. This chain of assumptions cannot go on forever. If it did, it would be devoid of reality throughout. And that this cannot be is, I think, the most fundamental assumption of Plato’s epistemology. There is knowledge, and knowledge is of reality as it is (477B10-11 γνῶναι ὡς ἔστι τὸ ὄν). Therefore, in order that there be knowledge of reality, reality must, at some point at least, be given and not only assumed. Hypothetical reasoning, insofar as it starts from agreed assumptions, excludes reality. If every number is either odd or even, then the diagonal is incommensurable with the side of the square. But the reality of this fact can only be inferred from the reality of numbers that are such as to be either odd or even. And this assertion of reality is beyond mathematical ὁμολογία . It is dialectic therefore that must uncover the full truth of these assumptions.67 On the side of the knower, the first principle transforms his doxa into episteme (it should be remembered that dianoia is analogous to doxa when compared to nous). The difference between doxa and episteme is in being capable of giving a logos. But for the real dialectician, no logos is satisfactory (ἱκανός) short of the logos that is not itself in need of a logos, because it is no more an assumption but a statement of reality.68

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He chooses the hypothesis that seems to him in some unspecified way. Cf. p. 208. This view involves some difficulties. Festugière (1936), has already remarked, commenting on Parm. 132BC, that, for Plato, “dès là que le concept a un contenu et par force il en a un, ce contenu est aussitôt réalisé; pour l’intellectualisme platonicien, c’est même chose que penser, penser quelque objet, penser un objet qui est de l’être. Du moment qu’elle s’exerce, la pensée s’ordonne à l’être. Ne pas penser de l’être revient à ne rien penser, c’est à dire à ne pas penser du tout.” (pp. 212-3, n. 2; but see also p. 233.). However, the hypothetical method raises the question of the possibility of positing a concept only ὡς ἀληθές ὄν – as if it were real, explicitly allowing for the possibility of error. The middle dialogues avoid this problem and it is not until the Parmenides and especially the Theaetetus and the Sophist that the possibility of an unreal (or mistaken) concept is discussed. Festugière is right in maintaining that thought is, for Plato, always related to being. But he goes too far in stating that every concept necessarily has its content realized from the start. For the gist of the hypothetical method is precisely in a conscious provisional positing of the reality of the concept. 68 Contra Sayre (1969), 47: “For our purposes, it is enough to allow that teleological reasoning involving the Good might be implemented by the dialectical method of the Divided Line, but that there is no apparent necessity, and indeed no apparent sense, in the suggestion that all 67

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On his way down the dialectician now sees that what he took for assumptions on his way up, only suspecting their reality, were true facts.69 His ὁμολογία is now a true science because it is seen to be a knowledge of what is as it is. In this way the first principle is the source of knowledge. From this interpretation alone, it would seem that the function of the idea of the Good is mainly, or perhaps exclusively, epistemological. But, of course, the Sun tells us clearly that it is the source of being (οὐσία) as well as the source of knowledge. The first principle, as we saw, is the principle that knowledge must be knowledge of the real. But this assertion has a complementary aspect. On the part of the object, it means that the reality to which knowledge applies is such as to be knowable. The soul is such that she can attain reality by means of intelligence, and, conversely, reality is such that it is intrinsically intelligible. This seems to be some of the meaning behind affirmations such as that the Good is the cause of knowledge and truth: “You must agree that not only their knowability comes to the objects of knowledge from the Good, but also their being and reality come from the same source” (509B6-8).70 This problem of the relation between the soul and reality was already put forward in the Phaedo. There it was said that the soul is of the same kind (συγγενής) as the ideas (79D3).71 The proper activity of the soul is reasoning. And reasoning, it was argued in the chapter on the Phaedo, requires the affinity of soul and ideas. On the other hand, in order that knowledge can be knowledge of the real, ideas and soul must be kept distinct. In the Phaedo this correlation of soul and ideas was a hypothesis required by the assumption of anamnesis, i.e. of knowledge in general. The movement of thought in the Phaedo ended therefore in two

-------------------------------------------applications of this method in order to be successful must in some way culminate in the Form of the Good.” It all depends, of course, on what one understands by “successful”. 69 On ἀναιροῦσα see Ross (1951), 55-57; Robinson (1953), 162 f. But it seems to me reasonable to assume that Plato is referring in the anairesis passage to true hypotheses only, and discarding those that proved false, as a matter of course. One should not look for more precision than the text requires. 70 The very important question still remains why is the first principle of knowledge and reality also called the Good? But this is a question which I cannot deal with here. 71 Cf. Rep. 508B3 ἡλιοειδέστατον.

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separate but correlate hypotheses: the existence and nature of the ideas and the existence and nature of the soul. This duality was not resolved in the Phaedo itself. Although soul and ideas were described and characterized, and their relation somewhat commented upon, there is nothing in the way of an explanation of how these two might be separate yet correlate. The Sun comes to carry the argumentation one step – the last – further. If soul and ideas must be correlate, then her power of knowing and their power of being known could be explained for Plato only by means of a common cause. But – and Plato takes every possible care to get this point clear – this common source cannot be a common ousia. If it were, soul and ideas would be identified in their common ousia, and the soul’s knowledge would not be knowledge of reality but knowledge of herself. The common source of being and knowledge must be beyond ousia.72 [16] The concept of congruence of knowledge and reality was already implicit in Plato’s steadfast distinction between doxa and episteme. In a certain sense, it may be said that the assumption of a real difference between doxa and episteme implies as its ‘cause’ the acceptance of a first principle, and the Republic did nothing but spell out this implication. In this sense, the idea of the Good is the ultimate hypothesis of dialectic. But, on the other hand, it needs must be itself an unhypothetical principle. For the assurance that not all our propositions are hypothetical cannot itself be hypothetical. It is no doubt a methodical postulate; but it is also more than that. Kant could describe his Ideas of Reason as imaginary foci in the infinite, for the knowledge he was speaking of was of reality built by the intellect and insofar as it was built by the intellect Plato could not: his is

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Cf. Hartmann (1935), 74-75: “... der Ursprung des Seins und der Ursprung des Erkennens muss ein und derselbe sein, anders könnte es kein Wissen geben, dass seine Gewissheit in sich selbst trägt und der äusseren Gegebenheit entraten kann.” But there is no question of this being a “Gesetz des Denkverfahrens” (Natorp (1903), 33). – Crombie (1963) is thus not being accurate when he says in a Kantian vein that Plato “was convinced that the world owes such definiteness and tractability as it possesses to the activity of reason which is prior to and independent of the physical world” (ii 522). The rationality of the world, insofar as it concerns us, does not stem from the activity of reason, but from the affinity of soul and ideas which is prior to any activity of the soul on the world – indeed it is a condition of it.

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a knowledge of a reality that, although intelligible, is not ‘of the mind’, for the soul for Plato is essentially ‘apprehensive’ and can never create reality. She can, at most, in knowledge as in art, imitate reality. 73 Robinson starts his analysis of the Republic by stating that “Plato believed in the possibility of absolute incorrigible knowledge”. In itself, this statement is true. But Robinson goes on to say that “Plato’s methodology in the Phaedo is at variance with his epistemology as stated in the Republic and later works”. For the hypothetical method of the Phaedo can never attain to the absolute knowledge demanded in the Republic. More suitable to the Republic, so Robinson submits, would have been a methodology based on the belief in “absolute incorrigible starting-points”, like Aristotle’s or Descartes’, “guaranteed by an infallible intuition, from which certain conclusions could be deduced”.74 – But this claim is to a certain extent misleading. Plato did believe in the possibility of absolute incorrigible knowledge. But this was his postulate rather than his axiom. There is a difference between knowledge and opinion. This difference could be obliterated: some Sophists denied it altogether. Plato would not; and because he would not, he asked for the foundation that would guarantee such a difference. His approach must be distinguished from the Scholastic approach of Robinson’s interpretation: The Schools believed in absolute infallible knowledge because they believed in absolute incorrigible starting-points, guaranteed by intuition, from which this knowledge could be deduced. Plato, on the other hand, believed in an absolute starting-point because he believed in the difference between knowledge and opinion.

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73 This accounts for the fact that in anamnesis the soul, although active towards the sensible world, is passive towards the ideas and must receive her concepts without creating them. 74 (1953), 146.

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Chapter viii: The Objects of Mathematics Our main evidence for Plato having held that mathematics deals with its own objects, separate from both the ideas and the sensible things comes, of course, from Aristotle. Robin1 has collected and analysed this evidence. The relating of τὰ μαθηματικά to the Line is as old as Proclus2 or perhaps Syrianus.3 But, as Ross remarks, this interpretation is difficult to accept. Were the Line intended to distinguish between ideas and mathematicals, this distinction could surely have been brought forth much more forcefully than it supposedly was in our text. The fact remains that Aristotle attributed ‘intermediates’ to Plato, a fact that is hard to dispute or to dismiss. Yet no explicit mention of them is made in the Platonic dialogues, and commentators who have found concealed hints of a doctrine of mathematicals have done so by avowedly importing the Aristotelian interpretation into the Platonic text. Even so, their harvest is meagre: Phaedo 74C, on “the equals themselves”, which could be no more them a convenient Greek idiom;4 Rep. 510B, implying a classificatory interpretation of the Line, and involving a misreading of the text; Rep. 526A and Phil. 56D, on units existing in the plural, yet distinct from sensible things, but not necessarily implying mathematicals; and especially Tim. 50C τὰ εἰσιόντα καὶ ἐξιόντα , which are much more plausibly interpreted as the μορφαί of the Phaedo. If the interpretation of the Divided Line which I have adopted is correct, then the doctrine of intermediates in the Republic falls as a matter of course.5 But there are also independent considerations pointing to the

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Robin (1908). See also Ross (1924), Introduction. Proclus in Eucl. i 4.14-5.10 Friedlein. Cf. Ross (1924), 59. 3 Syrianus, 4.16. Cf. Ross (1924), i 167, ad Met. 987bl4. 4 There is a wealth of recent literature on this subject. But I do not think anyone has succeeded in showing any appreciable difference between αὐτὰ τὰ ἴσα at 74C1 and αὐτὸ τὸ ἴσον at 74C4-5, Ε7, 9. See Tarrant (1957). For further discussion and some literature see, e.g., Haynes (1964), Rist (1964). 5 For all those that ascribe to Plato the doctrine of intermediates necessarily see the Line as classificatory. E.g. Wedberg (1955), 14. 2

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conclusion that this doctrine is unwarranted in itself and has been derived, at least for modern interpreters, from a misconception of the nature of Plato’s theory of ideas. A consideration of all or even most writers that would have Plato holding some doctrine of intermediates would be repetitive, and is impossible in a work like this. Instead, I shall examine one – perhaps the most comprehensive – modern attempt at vindicating the doctrine of intermediates, namely Wedberg’s. Although I am aware of the range of opinions even among those who believe Plato held such a doctrine, still Wedberg’s attempt seems to me to exhibit clearly the main traits of all or most similar interpretations of Plato. Wedberg has tried to rehabilitate the theory that Plato did postulate the existence of “certain ideal Euclidean objects, i.e. ideal spatial objects which exemplify, or partake of, the Euclidean Ideas”.6 His analysis of the core of Plato’s argument is as follows: a) Euclidean geometry is true. b) The truth of Euclidean geometry presupposes the existence of perfect instances of the Euclidean Ideas. c) Hence, such perfect instances exist.7

These “perfect instances” are the “intermediates” or “mathematicals”, defined by Wedberg as “ideal Euclidean objects”. But, as Wedberg readily admits, “Premise b) is stated nowhere in Plato’s published writings, nor is it mentioned by Aristotle”. Nevertheless, “there are a number of reasons which make it plausible that premise b) was – more or less consciously – assumed by Plato.”8 I shall try to show briefly that Wedberg’s reasons stem mainly from a misunderstanding of the nature of Plato’s ideas. Wedberg adduces four reasons for assuming mathematicals:

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Wedberg (1955), 14. P. 54. 8 Ibid. 7

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a. “From the relatively unsophisticated point of view from which the Greeks of Plato’s time looked upon science, it would appear self-evident that any science must study a certain class of actually existing things. Cf. Post. An. I 7.”9

From the chapter of the Analytics one is entitled only to affirm that Aristotle thought each science to be concerned with a different genus. That the subject-matter of each science need not be an “actually existing thing” (I take this to mean “existing by itself”, i.e. a substance) is clear from Aristotle’s concept of genus. And whatever might have been Aristotle’s position regarding this question, I cannot see that it implies Plato’s acceptance of a separate substantial object of mathematics. A better argument would have been, perhaps the argument ἐξ ἐπιστημῶν . But even this was probably aimed at proving the existence of ideas (in general), not of objects of particular sciences.10 And if arithmetic and geometry would require, “from the unsophisticated point of view ... of Plato’s time ... a certain class of actually existing things”, it is not clear why (pure) astronomy and harmonics would be exempt from such a requirement. Wedberg’s answer is that “whereas the postulation of intelligible arithmetical and geometrical objects can be presented in such a light as to appear plausible in some degree, a parallel postulation of intelligible astronomical or musical objects shocks us as grotesque and must, it seems, have made the same impression on the minds of Plato and his contemporaries”.11 But surely there is nothing more grotesque in pure mathematical objects than in pure astronomical objects, and ‘a sky besides this sky’ is no more ridiculous than ‘a space besides this space’. Ever since Archimedes classical mechanics has been based on assumptions of ideal mass-points and the like. The a priori objection seems to lean solely on the fact that Aristotle tells us about mathematical objects only. Wedberg’s contention seems to be that mathematicals must exist if arithmetic and geometry are to have something they are true of. But, as I have already argued in the last chapter (section 12), geometry and the other mathematical sciences are true of ideas – only, being the product

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Ibid. Cf., e.g., Alex. in Met. 79.3-15 Hayd. 11 Pp. 90-1. 10

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of dianoia, they deal with ideas through sensible reflections. Geometry is not true of the diagonal drawn on the sand, but of the idea it represents. However, not being dialectic, geometry cannot attain the idea directly. Geometry and dialectic are thus true of the same objects, and there is no need to postulate separate objects for geometry. As for the difference between geometry (and the other mathematical sciences) and dialectic, it lies, as I have already argued, in the manner in which they attain their object, not in the object itself. b. ‘Some A are B’ clearly states that there exist some objects which simultaneously exemplify both the concept A and the concept B. If Aristotle’s doctrine is applied to the universal propositions of Euclidean geometry, these are made to entail particular propositions asserting the existence of Euclidean objects. c. Every Idea ... is a ‘one over many’. In one sense, to partake of an Idea is merely to have some inferior degree of a quality of which the Idea represents the highest degree ... But in another, and that the primary, sense, to partake of an Idea is to have that very attribute which is the Idea. From this point of view, the sensible objects that pass for circles do not suffice: the Idea of the Circle requires the existence of a multiplicity of perfect circles which as such are not to be found in the world of senses.12

In b. and c. Wedberg makes his misinterpretation of Plato’s theory of ideas explicit. He takes Plato’s ideas to be attributes or classes,13 and the relation of particulars to ideas as of imperfect exemplification. Ideas are not classes. Sensible things cannot be said to be members of ideas. This much should be clear. But they are not attributes either. As R. E. Allen and others have shown at length, the particulars and the ideas have the same name, but this name is systematically ambiguous. Wedberg’s interpretation is explicitly based on the assumption that the name of the idea and the name of the particular are univocally the same – from which follows easily enough the aporia of the Third Man.14

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Pp. 55-6. Cf. p. 34 and esp. p. 35: “We might perhaps say that the Platonic Ideas are something in between what we call attributes and what we call classes but, on the whole, closer to the former than to the latter.” 14 Cf. Wedberg’s analysis of the assumptions of the theory of ideas with Vlastos (1954), and especially Assumption 3 of the Addendum (1963), in Allen (1965), 261. 13

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But the relation between the idea and the particulars is not exemplification, nor is it imperfect exemplification. A bed is not an exemplification of the idea of the Bed, because both cannot be said to be ‘beds’ in the same sense. This ambiguity is clearest precisely in dealing with mathematical examples: A straight line drawn in the sand and the ideal Straight Line are not straight in the same sense. For whereas the straightness of the line drawn in the sand is spatial and visual, the straightness of the ideal line – in as much as this line is invisible and not in space – is purely conceptual. Even the name ‘line’ cannot be univocally applied to both. And yet, if ‘y = ax+b’ is not, in Platonic terms, a straight line, what else is it? In the same manner, the particular bed and the Bed itself are not beds in the same sense, as it is apparent from the fact that the Bed itself cannot have any physical characteristics whatsoever.15 Even less can there be any question of imperfect exemplification in the sense intended by Wedberg. He seems to assume that there is only one possibility of imperfection, viz. imperfection within the same kind. For him, the negation of a Euclidean circle is a Euclidean non-circle; he does not seem to consider the possibility of the negation of a Euclidean circle being instead a non-Euclidean circle. A material circle is therefore, for Wedberg, a Euclidean non-circle and not – as it would be far easier to assume – a non-Euclidean κύκλος . Wedberg runs therefore into trouble when he recognizes that “there are no truly Euclidean objects in this world”, but goes on to add that, if a

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15 Cf. pp. 183-186, above. – Already Robin (1908), 607 had very aptly remarked on Met. A6. 987b8-10, that the relation between the idea and the particulars is neither homonymy nor synonymy. Homonymy there would be between a model and its copy; but “en ce qui concerne les Idées et les choses sensibles, les copies n’ont pas une nature entièrement distincte de celle de leur modèle”. Here the relation is prior to the relata. As the Phaedo stresses, if there is a sensible world, it is because of participation. Robin is therefore right in negating the dilemma: “... les choses sensibles ne sont ni proprement univoques, ni simplement équivoques avec les Idées: elles sont équivoques, mais en ce sens, précisément, que celles-ci sont modèles, celleslà, copies, et que les copies possèdent non essentiellement ce que appartient essentiellement aux modèles” (p. 71). – It is impossible to go here into a discussion of the Third Man Argument. A good selection of papers and an ample bibliography may be found in Allen (1965). For discussion of the suggestion that the relation between ideas and particulars is neither simple homonymy nor synonymy, see Allen (1960), Moravcsik (1963); contra Shiner (1970), where the bibliography is brought up to date. For the concept of πρὸς ἕν ambiguity, or “focal meaning”, see Owen (1957), (1960); Owens (1963).

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circle is a Euclidean object and as such cannot be found in the sensible world, a non-circle too is a Euclidean object and is thus likewise inexistent in the sensible world.16 One wonders what then, on his classification, does exist in the world? Wedberg readily admits that Plato “must ... have had some suitable restriction” to this assertion. But Wedberg does not attempt to show what the restriction might have been. On the other hand, he points out that no such restriction would have circumvented the paradox of Phaedo 74-75, according to which no two sensible objects are perfectly equal to one another, nor perfectly greater or smaller than one another. These paradoxes arise from the failure to grasp that the imperfection in question is an imperfection of kind, not one of degree, as a reflection is in comparison to the original not in having in a lesser degree the reflected properties of the original, but in the very fact of being a reflection. A reflection may lack some of the properties of the original, e.g. three-dimensionality, and have additional properties, as inversion of leftright relations. But the reason why Simmias’ reflection in water is not Simmias himself is not that the reflection is shorter or paler than the original, but that it is another sort of thing. The fact that the name of the idea and of the particular is ambiguous precludes a consistent theory of imperfections of degree. For what is not quite a circle cannot be properly called a circle, even in a derivative sense, any more than it can be called a non-circle. But a theory of imperfections of kind is compatible with such an ambiguity. The sensible circle is deficient in relation to the ideal circle because it is susceptible to change, to destruction, to points of view, in short, because it is material, not because it is imperfectly circular (although this too may well be the case). That this last consideration is unimportant may be readily seen if one examines arithmetical instead of geometrical concepts. Three sensible items can hardly be said to be an imperfect triad in the sense that there are not quite enough of them.17 But they certainly do not measure

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Pp. 49-50. Cf., e.g., Field’s (1951) view of the idea as “a limit towards which they [sc. the things] converged to a greater or lesser degree, without ever quite reaching” (p. 33). 17

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up to the Platonic standards of immutability, independence from point of view, etc. Wedberg writes in a very long tradition that puts the relata before the relation. For him, as for most of Plato’s commentators, the ideas and the particulars have both substantial existence, and the relation of imitation or participation links them to one another. But Plato’s conception is different: the particular is a reflection, a pure representation of the idea in the spatial medium: ‘it has its being’ from the idea. The particular is thus purely relational,18 not being in itself anything (rather than ‘not existing in itself’), but being completely dependent upon the idea for its being a so-and-so.19 The fact that Plato’s ideas are neither classes nor attributes does not mean that they are not ‘one over many’. The concept of ‘imitation’ provides a good description of the relation between the one and the many. The many imitate or represent the one, and the one – not being identified with the physical – ‘participates’ in the many, much in the same way that each of Simmias’ portraits is, in a way, Simmias, and the cause of its being Simmias’ portrait (not the cause of its being a portrait) is Simmias himself. If imitation is taken to be resemblance of the imperfect to the perfect as a matter of degree, then the relation of the particular square to the mathematical square is explained (exception made for the Third Man). But then this is not the same relation as that which holds between the mathematical square and the Square itself, for the mathematical square is certainly not an exemplification of the Square itself in the same sense that the particular sensible square is supposed to be an exemplification of the Square itself. d. Wedberg’s fourth reason for assuming that Plato held a doctrine of mathematics is that Euclid’s axiomatization of geometry has implicit

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18 By this I mean that every particular has an essential property that is a relation, the other relatum being an idea. But the use of “essential property” here should be qualified to allow, contrary to the Aristotelian use, for the particular being at one time and not being at another. 19 Cf. Aristotle de memoria 450b20, on the two aspects of a picture. Plato’s conception of the particular is that of a pure representation, which is always dependent and can never be considered to be anything in itself. For, to be considered as such-and-such is ipso facto to be related to an idea.

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existential assumptions.20 But this reason will support the conclusion only in conjunction with the first three reasons. Only if particular triangles are (imperfect) exemplifications of the perfect triangle, is it necessary to assume that the entities presupposed as existent by Euclid’s axiomatization are “Euclidean objects”, or mathematicals. And that this was not the case for Plato, I have argued above. The theory of intermediates, therefore, far from being implied in Plato’s assumptions about the ideas, has its foundations on a deep misunderstanding of their nature. Once these misunderstandings are clarified, there is no reason for a theory of mathematicals. On the contrary, the viability of this theory depends on these misunderstandings. Wedberg has shown quite clearly that the theory of intermediates assumes the view that the relation between ideas and particulars is one of exemplification, and depends on that view. But once this interpretation falls, the theory of intermediates falls with it. It is worth noting that when Plato does give some sort of a classification of being, in Letter vii 342A7-C4, the mathematical or intermediates are conspicuously missing. If the theory of intermediates was held by Plato in the Republic, it would have been strange indeed if no mention of it were made here, in so appropriate a context. Wedberg has, of course, to explain away this passage: The concept of the circle is considered by Plato merely as an example of a concept in general, and what he says about the example is intended to apply to any concept whatsoever. It would have been misleading if, in discussing the example of the circle, Plato had taken into account such features of this concept as are not found in all concepts. Now, intermediate objects are associated with mathematical concepts only – if with any concepts. Hence, even if the author of the Seventh Letter believed in the doctrine of intermediate mathematical objects, it is quite comprehensible why he does not mention it in the letter.21

Wedberg’s interpretation of the Letter assumes precisely what is under discussion: that mathematical concepts are unlike other concepts in that they need ‘intermediates’ between them and their sensible ‘instantiations’. The whole point of the interpretation that does away with in-

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P. 56. P. 116.

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termediates altogether lies in maintaining that mathematical concepts are exactly like any other concept: they are themselves non-spatial and their particular representations are ‘imitations’ of them in the sensible space, the only space known to Plato; there is no intermediate between them. Indeed, in the list offered by the Letter, the physical image is contiguous with the knowledge of the object “in the soul”, raising no need, and leaving no room, for an intermediate between them. And were not this mathematical example perfectly adequate, could not Plato have chosen some other idea, say the Shuttle or the Ox? In what concerns the Seventh Letter, it is better perhaps to accept Ross’ conclusion, that the passage we have been discussing “suggests that it was not till very near the end of his life that Plato formulated the doctrine [of intermediates], though he had long been on the point of formulating it”.22 But this verdict amounts to an acceptance of the fact that all we know about Plato’s intermediates derives from Aristotle, and any support we find for their presence in the dialogues is the result of our reading – or misreading – into the text what is not there, and what seems to me cannot be there. On the other hand, Aristotle is not to be thrown overboard. However, a full reappraisal of the relation between Aristotle’s account and Plato’s text is well beyond our scope and our forces.

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(1951), 62.

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Chapter ix: Plato’s Method of Hypothesis [1] The main feature of Plato’s method of hypothesis, as it emerges from the analysis of the dialogues is negative: It is not a method of demonstration, but – as the Phaedo makes abundantly clear – a method of inquiry into causes. As distinct from deduction, here Plato is not primarily interested in what consequences can be deduced from given premises. On the contrary, the conclusion of the argument is always given from the start, and it is its premise or premises that are sought. Dialectic does not start from the premises, because it is its business to discover and clarify the premises. In this respect, then, the hypothetical argument is never a proof. Rather, it is the discovery of a proof. The hypothetical procedure may be described as a “solution backwards”, i.e. against the normal direction of deduction. As we have seen, unless the propositions involved entail each other, which is not always the case in philosophical inquiries, there is no method of arriving at the desired premises. This has to be left to intuition or divination. And even when the premises and the conclusion entail each other, this is not considered an essential feature of the method, and cannot be relied upon. These characteristics are common to the method of hypothesis and to later geometrical analysis. Analysis too “starts from the desired conclusion, taken as agreed”, and looks “for that from which it results, and then again for the prior proposition leading to that, until, by tracing our steps backwards in this way, we meet with something already known or holding the rank of a first principle”.1 That in Pappus’ account of analysis it is the conclusion that is said to be hypothesized and not the premise from which it follows is to my mind irrelevant.2 The important similarity lies in the acceptance of the solution as true and the subsequent search for premises that would imply that solution. The comparison of

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Cf. ch. i, pp. 47-48, above. Cambiano (1967), 137, seems to consider this an important difference.

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the hypothetical procedures of the Meno with the “reductions” of Hippocrates of Chios is very instructive on this point.3 The first condition the envisaged premise has to satisfy is that it has to lead to the desired conclusion. It might be thought that Plato was concerned only with relations of consistency and inconsistency. Such interpretation does not take into account that every hypothesis is chosen as a logos for its conclusion, as providing an account of its “reason why”. Consistency is too weak a relation for this purpose. Some kind of implication is obviously called for. But once the hypothesis is chosen, any proposition can be considered and tested for consistency with it. It is not easy to say what is the precise relation between the hypothesis and the conclusion. It is certainly not one of material implication. Clearly something stronger is needed here, closer perhaps to Lewis’ strict implication, or Moore’s entailment.4 But this is still not accurate, for, as was shown, Plato gives the name of “hypothesis” to only one of the premises which conjunctly entail the conclusion, and sometimes even looks for only one of these premises, presumably that which in his eyes is the most important. Plato is not looking for the set of propositions whose conjunction is sufficient to entail the conclusion. He is interested in the main premise (which he calls the “reason” or the “cause”), which, in conjunction with the set of “standing assumptions”, entails the conclusion. Sometimes, as in the Meno, he specifies these assumptions. Sometimes he does not, as in the Republic. In the Meno the term “hypothesis” was used of an assumption about the nature of the thing under consideration. This use of the term is borne out by the examination of the structures of the three dialogues we have been concerned with. Moreover, Plato distinguishes in the middle dialogues neither between propositions and single terms, nor between the formal and material modes of speech.5 Therefore, the term “hypothesis” is used by him

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See ch. ii, pp. 68-69, above. It is interesting to note that Patzig in the preface to the second edition (1963) of his Aristotle’s Theory of the Syllogism has abandoned the material implication for Lorenzen’s “logical implication”. 5 See App. 1. 4

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indifferently of propositions or states of affairs (Meno 87D2-3, 88C2, Rep. 437A6), or of single terms or things (Rep. 510C3-5), without paying attention to the formal-material distinction: Rep. 533C8 τὰς ὑποθέσεις ἀναιροῦσα is a good example of a sudden slip into the material mode.6 This means that, although for reasons of neatness in presentation we still interpret Plato’s arguments as being propositional, we should keep in mind that the premise (or the “cause”) may be indifferently a term, a thing, a fact or a proposition, and the same is true of its συμβαίνοντα. For Plato, a thing, if it is a cause, can have consequences not less than a proposition. What is the strength of the chosen premise? The hypothesis is evidently chosen with a view to solving the given problem, i.e with a view at arriving at the solution which is already given. This is a “problematical” as opposed to a “deductive” approach: the arrangement of the propositions is not univocally given as in an axiomatic system, but is determined also by the problem to be solved.7 The “strength” of the hypothesis (cf. Phaedo 100A4 ἐρρωμενέστατον) is thus judged by reference to its contribution to the solution to the problem. But, of course, even if the hypothesis does entail the conclusion – in conjunction with an unspecified set of standing assumptions – this is yet no guarantee of its truth, let alone of the truth of the conclusion. The hypothesis itself has to be checked for consistency. And although the consistency of the hypothesis with itself and with the set of standing assumptions is necessary for it to be accepted, it is still not sufficient guarantee either of its truth or of the truth of the conclusion. It has therefore to be supported in its turn by another hypothesis, until the end of the process at the unhypothetical principle. [2] Thus, in the hypothetical method, elenchus and analysis are complementary. Elenchus disproves the hypothesis; analysis confirms it. But analysis can confirm it only to the extent to which the confirmatory hypothesis is itself acceptable. Complete confirmation is possible only in linking up with the unhypothetical principle. However, as philosophical

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Cf. n. 69 to ch. vii, and App. 1, pp. 219-221. Cf. Cambiano (1967), 139.

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problems have their place on the way to the unhypothetical principle rather than on the way from it, Plato’s position as to what consists the solution of a problem is rather peculiar. In a system which develops conclusions from given premises, a solution to a problem is a valid derivation from some or all of the premises of a conclusion which fits the specifications of the enunciation. In such systems, the conclusion has to be actually produced (sometimes – if there is such a rule in the system – by proving its contradictory to be false). Plato’s is not such a system. On the way to the unhypothetical principle the premises are not given, but sought. A problem is unsolved when there is aporia, when there is “no way”. The solution to the problem is the creation of euporia, “free way”.8 This is done not by actually producing a solution out of premises, but by showing that a proposed solution is possible under certain conditions. For Plato these conditions took the form of hypotheses. In the method of hypothesis, elenchus and analysis are related as aporia and euporia. Elenchus blocks the way to proposed solutions; analysis shows their possibility. Hence the important part elenchus plays in the examination of proposed hypotheses. But, while elenchus is purely negative, attempting to prevent solutions, analysis tries to go beyond the mere failure to disprove, in order to arrive eventually at what cannot be disproved. The method of hypothesis does not intend to prove anything. It only purports to offer support for a proposition which is accepted at first on grounds that may be irrelevant to the process of argumentation. Strictly speaking, no proposition in Plato can be proved: it can be either refuted by elenchus or supported by analysis. Strict demonstration would require deduction from premises of which we have absolute knowledge. But, as Protagoras stressed, any premise can be challenged. And in as much as it is open to challenge and persuasion, there is no knowledge of it but mere opinion. The only premise that cannot be challenged is the unhypothetical principle. But no proof can start from the unhypothetical principle given as an axiom. For it is of its nature that it cannot be disso-

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8 On aporia and euporia, see Owens (1963), 211-219. Phil. 15C is normally quoted as the source of this couple of terms, but they appear already in the same context at Phaedo 84C9-D3. Cf. DK 63.11-12.

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ciated from the upward path. It is the last hypothesis, and is of no use in starting a chain of deductions separate from a previous analytical procedure. There are, of course, proofs in a weaker sense: i.e. deductions from agreed premises. But those proofs are only as good as their premises, and these are never absolutely sufficient, but only sufficient in a given limited situation. It seems, then, that the only possible demonstration that would not be mere ὁμολογία would be a demonstration from the unhypothetical principle which is consequent upon the analysis which led to this principle. This means, in effect, that no problem can be adequately solved in a purely axiomatic, deductive way; any adequate solution or proof is dependent on the preceding analysis, and loses its value as knowledge if dissociated from it. [3] Here the personal aspect of the method of hypothesis is well seen. It is not only a matter of “problematical” as against “systematic” approach. It is also and foremost a matter of the personal aspect of knowledge as against the indifferent nature of doxa as information. On the one hand, then, Plato’s method of hypothesis precedes the establishment of a system, at least a parte subiecti. On the other hand, philosophizing must conform to the objective interconnexion of ideas. This objective cosmos of ideas cannot be given to the subject beforehand, but has to be reconstructed (recollected) in the soul. Hence the two concepts of διδαχή in the Meno. The tension between the objective and the personal aspects of the hypothetical procedure is also apparent in the discrepancy in the assertion of the premise on the way up as merely hypothetical and the assertion of the same premise on the way down from the unhypothetical principle as apodictically true. Regarding the content of their propositions, the way up and the way down may be the same: they differ only in the modality of what is asserted.9

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Of course, they could also differ in that the way up is tentative and may contain false starts and errors in the order of the hypotheses, which would disappear in the way down. But this is not its essential characteristic in Plato’s eyes. If by a successful series of divinations there were no such deviations, there would still be a difference between the way up and the way down. Cf., e.g., Rep. 445C9-10 with 544D5-6.

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Every hypothesis is put forward only provisionally. Within the framework of the hypothetical method there are only two truth-values, that were taken over from the Socratic elenchus: refuted or unrefuted. As in the elenchus, the basic notion is the notion of refutation or contradiction: Whatever entails its own contradiction is false, and no two contradictory opinions should be held together. What is not refuted stands as true as long as it is not contradicted – or until the analysis goes up to the unhypothetical principle and the demonstration brings the argument back again to the proposition in question. When this is done, the proposition itself does not change, but its modality changes: instead of being asserted hypothetically it is now asserted apodictically. But, of course, the proposition was true from the start. Here we have the double aspect of the concept of ἀλήθεια as correspondence and as Unverborgenheit.”10 Insofar as it corresponds to the real state of affairs, the hypothesis was of course true also when only hypothetically considered. But a parte subiecti it was not known as true (as opposed to merely believed as true). From the dialectician’s point of view, the proposition is a hypothesis that could be either true or false, and until the whole process is terminated he himself cannot do more than accept his hypothesis provisionally and be prepared to change it for another if this proves false or inadequate. Only the unhypothetical principle can bridge the gap between the two modalities of truth which the dialectician is forced to employ: truth as being so-and-so and truth as merely posited following a failure to detect inconsistency. Only the derivation of the series of hypotheses from the unhypothetical principle transforms their hypothetical truth into apodictic truth. Until this derivation is effected, the dialectician has to be content with avoiding inconsistency, while groping – by some sort of divination – for the right way up. [4] Although the method of hypothesis is introduced by Plato as a general method of inquiry, it is apparent from his actual use of the method that there is a definite sort of problems for the sake of which the method is introduced and for the solution of which it is especially adequate. The

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Cf. App. 1.

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common theme of the three dialogues we have been discussing is one: philosophia as a way of life. In the Meno it is merely adumbrated in the possibility that excellence is knowledge. In the Phaedo this way of life is accepted as the best for the individual, and in the Republic the conception of philosophia is extended to cover the whole city. From the point of view of the method of hypothesis, the Phaedo and the Republic do more than just perfect a method that was introduced in the Meno. These dialogues actually apply the method of hypothesis to Plato’s main philosophical problem in this period. In them, the hypotheseis of philosophia are sought, i.e. the epistemological and ontological presuppositions of the conviction that excellence is knowledge. These hypotheseis are found in the theory of the ideas, the soul and the sensible world, as it is developed in the Phaedo and the Republic. Philosophy is not called upon to demonstrate that justice and knowledge are better than injustice or ignorance. But conversely, given that no one has consistently maintained that injustice or ignorance are better, the role of philosophy is to show under what conditions the opposite claim is possible. On the other hand, philosophia as the type of life advocated by Socrates consists precisely in negating that unreflected opinion, even if true, can ever be ethically sufficient. The highest ethical value is attached to the inquiry itself into the logoi of the opinions we hold. Philosophia as a way of life and as an intellectual discipline means the giving of a “reason why” to every opinion, without being ever satisfied with reasons that are themselves in need of reasons. The way of life and the method of inquiry go together. This was Plato’s interpretation of the Socratic dictum that arete is episteme.

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Appendix 1: On Being and Truth [1] Republic 479C7 “between being and not being” must be understood in the sense that sensible things never have univocally determined characters, but may always be predicated in contrary ways. It is not the existence of sensible things that is being challenged, but their being univocally this or that. What Plato is denying then is not their being fully posited ex nihilo (as if something could be halfway between naught and aught), but their being capable of full characterization as such-and-such. For Plato, what fully is admits of no contradiction. It can never be said of it that it both is and is not (say, F), in any circumstances. Therefore, the principle of non-contradiction fully applies only in the intelligible world. It does not apply unqualifiedly in the sensible world: sensible things obey the principle only when it is qualified in so many respects.1 In this sense, then, they are only qualifiedly F, precisely as they are also qualifiedly non-F. Or, as Plato put it, they are between what fully is and what is not in any way. That ὄν and εἶναι in this and the precedent passages are to be taken as incomplete expressions is clear, e.g., from 479B. Moreover, the primary function of the ideas is to account for the sensible things being such-and-such, and only secondarily, if at all, for their existence. This has already been pointed out in the chapter on the Phaedo. In fact, it would seem that the Greek verb ‘to be’ did not have a purely technical existential meaning. Or, as C. H. Kahn puts it more exactly in a recent paper: ... if by a word for existence one means simply an expression which we would normally render into English by ‘there is’, then it is clear that the Greek verb esti often has this sense. But if we understand the phrase ‘there is’ as representing a univocal concept of existence for a subject of predication, as distinct from the content of the predication itself – as distinct from the ‘essence’ of the subject or the kind of the thing it is (as we often do, for example, when we read the

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Cf. p. 133, above.

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existential quantifier ‘(∃x)’ as ‘there is something of which the following is true’) – if this generalized positing of a subject as ‘real’ is what we mean by existence, then I would be inclined to deny that such a notion can be taken for granted as a basis for understanding the meaning of the Greek verb.2

Indeed, the hard and fast distinction between essence and existence was first made by Al-Farabi and Avicenna, although it seems to have been felt in varying degrees much earlier. But this distinction, natural though it was for the Arabs, cannot be taken for granted with the Greeks.3 Nevertheless, even if the distinction cannot be taken for granted on philological grounds, still the question remains, whether Plato consciously distinguished these two senses of einai, and if he did not distinguish them consciously, whether he consistently used the verb in one of its senses, or switched occasionally from one to another. That Plato does not expressly distinguish between the esse essentiae and the esse existentiae before the Sophist, I take to be today common ground. Whether or not he does this in the Sophist has been lately object of much dispute. G. E. L. Owen, in a recent article, reviews the recent interpretations and agrees especially with Frede and Malcolm that Plato’s study in the Sophist “is essentially preliminary to, and not based on, the isolation or construction of the difficult notion ‘exist’.”4 His main argument is based on his contention that “Plato does not say that his problems about not-being come from understanding ‘being’ in a certain way; he says that they come from understanding ‘not’ in a certain way”.5 This is why Plato “nowhere suggests, and by implication he consistently denies that he has found a use of the verb ‘be’ in which only its positive occurrences have significance.”6 On this showing, “‘what is not’ is not equated with ‘what does not exist’ (nothing) but with ‘what is not anything, what not-in-any-way is’: a subject with all the being knocked out of it and so unidentifiable, no subject”.7

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Kahn (1966), 248. For Aristotle’s εἶναί τι and ἁπλῶς εἶναι, cf. ibid., Postscripta, 263 f. Graham (1965), 227; Gilson (1952), ch. iii. 4 Owen (1970), 248. 5 Ibid., 231. 6 Ibid., 229. 7 Ibid., 247. 3

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It should be noted that already in Republic 477 ff. ὄν and μὴ ὄν carry those senses of being some determinate, identifiable thing, and not being determinate in any way. Moreover, the denial of the compatibility of being and non-being as applied to semblances is precisely the subject of Republic 479C. In the Sophist, the not-being passes from the sensible substances to the ideas considered as ‘other’.8 The difference is in the range of the μὴ ὄν rather than in its meaning, although in the Republic this meaning remains always implicit, and is explicated only in the Sophist. It would, of course, be impossible to maintain that εἶναι and ὄν never have existential implications or overtones – even if we limit ourselves to the “technical” uses of the verb, if such could be agreed upon. Rather, what is being maintained is that Plato’s primary technical use of the verb or the participle is in the same sense of ‘being so-and-so’. But there is no denial that, for Plato, what is so-and-so also exists, although this existence, at least in the middle dialogues, does not attract his philosophical attention. Plato’s is what Gilson has called “an existentially neutral conception of being”.9 [2] Along these lines it is possible better to understand Plato’s “degrees of reality”. The foregoing considerations, among others, support Vlastos’ claim that there is no evidence for degrees of existence in Plato.10 And accordingly he seems to me right in maintaining that “forms are more real because they are never F and non-F”.11 But he goes on to add that Plato’s ontology leaves no room for degrees of reality, for his was an ontology of degrees of being when he should have had an ontology of kinds of being. Some of his line of thought may be found developed in a little more detail in a previous paper by Bröcker: Die copula meint die Teilhabe, oder, modern gesprochen, die Subsumption eines Gegenstandes unter einen Begriff. Aber daraus folgt nun, dass das esse es-

--------------------------------------------

8 The problem of the not-being of the ideas as the “other” is already implied in the Republic in the tacit distinction between opinion and error. But this distinction is not explicitly drawn. 9 Gilson (1952), 6. 10 Vlastos (1965), 8-9. 11 Ibid., 10: cf. Rep. 479 AD, Symp. 211A, Phaedo 78D-79E, Hipp. Ma. 289D, Rep. 523E.

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sentiae keine Möglichkeit hergibt für einen ontologischen Komparativ. Denn man kann nur subsumieren oder es lassen, aber man kann nicht mehr oder weniger subsumieren. Und etwas hat an einer Idee Teil oder nicht.12

At this point Bröcker misses the mark. Platonic ‘predication’ is not subsumption in the sense Bröcker is using the term. The relation between the particulars and the idea has three aspects, of which two are common to it and to the relation of ideas among themselves, and one of which is peculiar to this relation alone. Sensible things as well as ideas are said to participate in, and to have communion with, ideas. These relations do not imply nor rule out any ontological disparity between the relata. But particulars are also said to imitate ideas, and to be ontologically deficient in this respect. Ideas, on the other hand are not said to imitate other ideas. So that, even if ‘participation’ and ‘communion’ designate something like Bröcker’s Subsumption, ‘imitation’ certainly does not. I have argued above that this imitation does not imply a deficiency of degree, but a deficiency of kind. It is true that the sensible and the intelligible “können nicht mehr dadurch unterschieden werden, dass das eine und nur das eine zugleich Nichtseindes ist, vielmehr sind beide Seiendes und Nichtseiendes zugleich”.13 But this means that discourse is possible only if ὄν and μὴ ὄν are taken to mean F and its complement: that is, that discourse about being and non-being is confined to the intelligible domain and that the sensible world can be referred to only in relation to the intelligible world, as what is other than intelligible. This is indeed consistent with the doctrine of the Phaedo. [3] Again according to Kahn, the primary sense of εἶναι is not ‘to exist’ but ‘to be the case’, ‘to be so’, and, when applied to statements, ‘to be true’. In this sense, for example, he suggests that one should understand Protagoras’ dictum that man is the measure τῶν μὲν ὄντων ὡς ἔστιν, τῶν δὲ οὐκ ὄντων ὡς οὐκ ἔστιν. This is the sense of the verb in the expressions ‘τῷ ὄντι’ = ‘really, truly’, ‘ἔστι ταῦτα’ = ‘these things are so’.14

-------------------------------------------12

Bröcker (1959), 422. Bröcker, loc. cit. 14 Kahn (1966), 249-250. 13

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On the other hand, truth, ἀλήθεια , is not conceived as a predicate of statements, but of things. The first to point this out in modern times seems to have been N. Hartmann: he suggested that ἀλήθεια still carried for Plato its etymological associations as ἀ-λήθεια , ‘Unverborgenheit’, the quality of what is unconcealed, of what is not forgotten (cf. λανθάνω) or of what is recovered in anamnesis.15 His lead was followed by Heidegger,16 who blamed Plato for the decay of the concept of truth from its primaeval objectivity as ‘Unverborgenheit des Seins’ into a mere subjective ‘correctness of apprehension’. For Heidegger himself, truth is ἀ-λήθεια,17 a basic aspect of reality, rather than a human attitude towards it. And in his view, although Plato still felt the etymology, he already meant by ‘truth’ mere ὀρθότης , in the epistemological sense. Friedländer18 questioned Heidegger’s interpretation by arguing against his etymological derivation. He even suggested that the word might not be Indo-European at all, hence that the α is not an α privativum. On the philosophical plane, Friedländer has redressed the balance, in pointing out that “truth, in Plato’s system, is always both: reality of being and correctness of apprehension and assertion.”19 In recent years, the philological interpretation of ἀλήθεια as ἀλήθεια has regained ground. Heitsch has produced a wealth of new or forgotten evidence from Homer to Lycurgus and Xenophon, aiming at showing that this etymology, whether justified or not, underlined the Greek common literary usage. And although Plato does not explicitly produce an etymology for ἀλήθεια, a number of places may show that he felt quite strongly the connexion with λανθάνω and its cognates.20

-------------------------------------------15

Hartmann (1909), 239 n. 1. Heidegger (1927), 52 ff., 219 ff.; (1947). 17 For the etymology, cf. Et. Magnum; Sextus Emp. adv. logicοs viii 8; Damascius [known to Scolnicov as to Norvin as ‘Olympiodorus’] in Plat. Phaed. 156.15 Norvin. 18 Friedländer (1958), vol. 1, ch. xi. 19 P. 227. 20 Heitsch (1962), 24-39. Among his examples: Apol. 17A, Crito 51A, Prot. 339D, Phaedo 64AD, Lysis 216C, Phil. 52B, 63D, Phaedr. 248B, 275A. See also G. Jäger (1967), 47; Prauss (1966), 44, 130, and further bibl. there. 16

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As a predicate of things or of facts, ἀλήθεια is identified with ὄν: what is so, what is the case.21 The “truth”, or genuineness, of an object consists precisely in its being fully what it is, and the truth of our apprehension in our apprehending it as it is (cf. τὸ ὂν γνῶναι ὡς ἔστι). τὸ ὄντως ὂν is τὸ ἀληθῶς ὄν – what fully and unqualifiedly is what it is; i.e. the ideas, which alone can be said to be ‘truly’ F. [4] It is worth noting that both εἶναι and ἀλήθεια, and their cognates, are freely used of facts or states of affairs as well as of things, εστί. ταῦτα refers normally to a fact, although we obligingly translate it often by ‘these things are so’, and the emphatic ἔστι Σωκράτης μουσικός is best rendered as ‘it is the case that Socrates is musical’. “It is not so much that the Greeks lack our notion of existence, as that they lack our sense of distinction from essence or from the being-so, of fact and predication.”22 Whatever may be the case in the Sophist, this distinction is certainly lacking in the middle dialogues. There, the logos is a mere string of ὀνόματα, whose function is διονομάζειν, ‘to distinguish by a name’.23 Knowledge is knowledge of ὄντα. And by ὄντα Plato understands in the middle dialogues indifferently things or facts apprehended as thing-like. Facts like, e.g., Socrates’ being musical, are seen as not essentially different from things, say the musical Socrates, and therefore what the logos does in both cases is to name the fact/the thing by its corresponding string of names, answering to an objective communion of ideas. This is why Plato may refer to the objects of cognition, or to his hypotheses, etc., indifferently as things or as propositions or states of affairs. There is for him no difference between knowing the square and knowing that the square has such and such properties. Because knowing the square means knowing it as it is, namely as square, as having such and such properties. And this knowledge can be equally described as knowledge of the square or knowledge of the fact that the square has such and such properties.

-------------------------------------------21

From the purely linguistic point of view, cf. ἔστι ταῦτα with ἀληθῆ ταῦτα. Kahn, 262. 23 Prauss (1966), 46. 22

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[5] That Plato’s hypotheses may be things, propositions or states of affairs is shown also by an independent examination of the textual evidence. The controversy is well known: Robinson has assumed that Plato’s hypotheses are propositions, and Stahl has followed him with reservations. Bluck and Tredennick have thought them to be “provisional conceptions (or notions) of Form-causes”. Murphy preferred “theories”. This latter interpretation is not of much help, as it certainly does not refer to theories of the modern type, and, on the other hand, it is not at all clear what type of theories these are. Robinson has been at some pains to show that Plato’s hypothesis need not be an existential affirmation. Meno 87A2 ff. certainly is not, nor is Protagoras 339D2-3, nor are Euthyphro 9D8, Meno 87D2, Sophist 238D9-E2. On the other hand, there is at least one example that can be taken as an existential hypothesis at Parmenides 136B1-2 ἐὰν ὑποθῇ εἰ ἔστιν ὁμοιότης ἢ εἰ μὴ ἔστιν. Phaedo 100Β5-6 ὑποθέμενος εἶναί τι καλὸν αὐτὸ καθ’ αὑτό might be existential too, but it seems that the bulk of the evidence is against purely existential propositions in Plato’s middle period. But what Robinson takes for granted is that hypotheses are propositions. Some of them are indeed. But some are presented in a different linguistic form. Republic 510C3 ff. ὑποθέμενοι τό τε περιττὸν καὶ τὸ ἄρτιον καὶ τὰ σχήματα κτλ ... is the obvious example. Another is Theaetetus 191C8-9: θὲς δέ μοι λόγου ἕνεκα ἐν ταῖς ψυχαῖς ἡμῶν ἐνὸν κήρινον ἐκμαγεῖον. We could, of course, as we do almost automatically, read these sentences as elliptical for existential propositions. This has been disputed at least in the first case and there is no reason for doing it in the second. It seems that in Plato the verb ὑποτίθημι and the noun ὑπόθεσις are indifferently applied to the things or to the proposition about the thing. Indeed, the non-propositional use of hypothesis survives in Aristotle and had a great revival with the later Neo-platonists. Bonitz’ note is still very apt: “in doctrina politica (quoniam ἐν ταῖς πράξεσι τὸ οὗ ἕνεκα ἀρχή, ὥσπερ ἐν τοῖς μαθηματικοῖς αἱ ὑποθέσεις ΕΝ vii 9. 1151al7)

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ὑπόθεσις non multum differt a notionibus τέλους et ὅρου.”24 So, e.g. Pol, vii 2. 1317a40: ὑπόθεσις τῆς δημοκρατικῆς πολιτείας ἐλευθερία. And in a sense much closer to Plato’s: Phys. i 6. 189a28 πρὸς δὲ τούτοις ἔτι κἂν τάδε τις ἀπορήσειεν, εἰ μή τις ἑτέραν ὑποθέσει τοῖς ἐναντίοις φύσιν. cf. 189bl, iii 4. 203al7, de gen. et corr. 1 1. 314b26, Met. A 7. 988a25. Also de caelo iii 5. 303bl0. It is true that in his logical writings Aristotle uses the term hypothesis to designate propositions alone. But it seems clear that the term could have other designations as well, in political, physical or metaphysical contexts. A term used much in the same way is ἀρχή, which sometimes seems to be quite close in meaning to hypothesis. In logical contexts it refers to propositions; in other contexts it does not. At least with this term the propositional use is derivative. But even if Aristotle made the distinction between the logical and the ‘material’ use of the hypothesis (which I doubt), there is no reason why Plato should have done so too, especially if his logic was not necessarily propositional. Nevertheless, we speak about the world in sentences that express propositions and so did Plato. His hypotheses can be cast in the form of propositions – in the last analysis we cannot escape it for very long – and Plato actually did that most of the time. But he would sometimes speak in the material mode, calling hypothesis not the proposition about the thing or the event25 supposed as a basis to the explicand, but the thing or the event itself. This distinction between the hypothesis as a proposition and the hypothesis as a thing or a fact may be unimportant in most cases, for we could, as Plato does, shift at will from the material to the formal mode. But in certain cases, as in ὑποθέσεις αἱ πρῶται of Phaedo 107B5, or τὰς ὑποθέσεις ἀναιροῦσα Rep. 533C8, it is good to keep this ambiguity in mind.26 Thus, the interpretation of Plato’s logical procedures in the middle dialogues as rigidly connected with some sort of propositional calculus is misguided. It is not only that “Plato was not as proposition-conscious as some of his critics”,27 but that he was still not aware of the difference

-------------------------------------------24

Bonitz (1870), s.v. ὑπόθεσις. At Prot. 339D2-3 it is an event that is hypothesized. 26 Bluck (1957), 21 n. 3. 27 Bluck (1957), 21 n. 3. 25

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between a mere string of names and a proposition as composed of ὀνόματα, and ῥήματα. On the other hand, in principle, we can easily translate Plato’s statements about non-propositional hypotheses into more manageable propositional hypotheses. In particular, we should not be surprised by finding hypotheses that are clearly propositions side by side with hypotheses that are clearly single terms (or things: Plato would prefer the material mode).

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Appendix 2: The Upward Path Robinson classifies the interpretations of the “upward path” of the Republic in four groups: a. the synthesis-theory, b. the mathematical theories, c. the Phaedo-theory, and d. the intuition-theory. He accepts with reservations the last two and rejects the others. From my expositions of the Phaedo and the Republic, it should be clear that I see the upward path in the Republic as being the hypothetical method of the Phaedo. It is however to be noted that this view implies an interpretation of the Republic and especially of the Phaedo which is different from Robinson’s. The same remarks apply to the intuition-theory of the upward path. I think Robinson is certainly right when he affirms that: the hypothetical method of the Phaedo does not seem to exhaust the upward path as Plato conceived it in the Republic, because it cannot give, and does not claim to give, the infallible certainty, the sure grasp of the ‘unhypothesized beginning’, which is emphasized in the Republic ... [Nevertheless] I believe that Plato in the Republic claims the possibility of certainty for the dialectician without having any more method at his command than the Phaedo gave him.1

But I heartily disagree with Robinson’ conception of this method. It is not a matter of months or years of labour, trying to refute a hypothesis without success, until “it dawns on him [viz. the dialectician] that this hypothesis is certainly true, that it is no longer an hypothesis but an anhypotheton”.2 Here “intuition” has a purely negative meaning, as “knowledge not reached by method”. However, if the interpretation I suggested is correct, there is more to the anhypotheton than the mere subjective failure to disprove it: the anhypotheton is not only nonhypothetical, but it is also ἀρχή – first principle and cause. Intuition does

-------------------------------------------1 2

Robinson (1953), 172. So Stahl (1956), 88-9. P. 173. For criticism, see Stahl (1956), 91; Sayre (1969), 52.

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not demonstrate, and Socrates is very careful about this, but nevertheless, the upward path has a method, albeit not a deductive one. This brings us to the analysis-theory of the upward path, the only one among the mathematical theories with which we are concerned. Robinson rejects it out of hand, because of his views on mathematical analysis. I have dealt with this question in the first chapter. If we renounce Robinson’s view, which he claims “is really as certain as anything in the history of thought”, and adopt instead an interpretation closer to that of Cornford, we can easily see that the intuition-theory, the Phaedo-theory and the analysis-theory are one: the method of mathematical analysis is the method used in the Phaedo and described in the Republic, and it consists essentially in the divination of the premises of an argument, the conclusion of which is given. It was this identification that was argued at length in this work. As to the synthesis-theory, Robinson’s criticisms apply to it in all its forms only if the synthesis is supposed to be performed from particulars to an Aristotelian genus. That ideas are not Aristotelian genera has already been shown. But the inquiry into the exact relationship between the upward path in the Republic and the later dialectic of the Phaedrus and the Sophist falls outside the scope of this work.

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Bibliography Abbreviations AJPh ArchBeg ArchGeschPhil CPh CQ CR CW IPQ JHPh JHS JPh Mnem NewSchol PQ PR QS RevEtG RevMet RevMetMor RevPhil RevPhil Louvain RivFil

American Journal of Philology Archiv fur Begriffsgeschichte Archiv fur Geschichte der Philosophie Classical Philology Classical Quarterly Classical Review Classical Weekly International Philosophical Quarterly Journal of the History of Philosophy Journal of Hellenic Studies Journal of Philology Mnemosyne New Scholasticism Philosophical Quarterly Philosophical Review Quellen und Studien zur Geschichte der Mathematik Revue des Etudes Grecques Review of Metaphysics Revue de Métaphysique et Morale Revue philosophique Revue philosophique de Louvain Rivista di Filosofia

DK LSJ3

see Diels (1951) see Liddell and Scott (1968)

Texts Albinus [Alcinous, ed.]: Hermann (1853) Archimedes: Heiberg (1908)

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Aristotle: Bekker (1837) Anal. Ross (1949) Met. Ross (1924) Phys. Ross (1936) Comment. in Arist. Graeca (1882-1909) Diels-Kranz (1951) Eudemus: Wehrli (1969) Menander: Hock (1880-8) Olympiodorus [Damascius, ed.]: Norvin (1913) Pappus: Gerhardt (1871), Hultsch (1877), Thomas (1941) Plato: Burnet (1900-7) Meno Bluck (1961), Thompson (1901) Phaedo Archer-Hind (1894), Burnet (1911), Robin (1926) Republic Adam (1902), Chambry (1921-4), Shorey (1930-5) Scholia Greene (1938) Proclus: Friedlein (1873) Sextus Emp.: Bury (1935) Strato: Wehrli (1969)

Translations Archimedes: Heath (1912) Aristotle: Smith and Ross (1908-52) Euclid: Heath (1926) Plato: Meno: Guthrie (1956) Phaedo: Bluck (1956), Dirlmeier (1959), Hackforth (1955), Meunier (1952), Robin (1926) Republic: Chambry (1932-4), Cornford (1941), Lindsay (1935), Shorey (1930-5)

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(1981) A Short History of Greek Philosophy: The Pre-Socratic philosophers. 221 pp. Yahdav, Tel-Aviv. (Hebrew) (1988) Heraclitus and Parmenides: Testimonia and fragments. Introductions, Hebrew translation and notes. 265 pp. Bialik Institute, Jerusalem. (1988) Plato’s Metaphysics of Education. 157 pp. Routledge, London and New York. (1994) Essência e Existência: Oito palestras sobre a filosofia grega e a filosofia medieval judaica. 88 pp. Perspectiva, São Paulo. (2003) Plato’s Parmenides. Introduction, English translation and commentary . x + 193 pp. University of California Press, Berkeley. (2006) Platão e o Problema Educacional (Plato and the Problem of Education). Edições Loyola, S. Paulo. (2008) Method and Idea: Twenty-eight studies in Plato Magnes, Jerusalem. (Hebrew). (A collection of articles previously published in Hebrew and in other languages.) (2013) Euthydemus: Ethics and language. Lecturae Platonis 5. Academia Verlag, St. Augustin.

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(1963) C. Rabin, Biblical Hebrew Syntax. Mif’al Haschichpul, Jerusalem. 123 pp. (Hebrew) (1964) P. Haezrahi, On the Perfect Being. Mif’al Haschichpul and the Faculty of Humanities of the Hebrew University of Jerusalem. 399 pp. (Hebrew) (1974) Iyyun 24: In memoriam P. Haezrahi. (Hebrew) (1975) S. Rivière, Studies in Greek Philosophy. Ed. by M. Brinker, S. Pines and S. Scolnicov. Magnes, Jerusalem. 125 pp. (Hebrew)

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(1980) I. Scheffler, Conditions of Knowledge. Hebrew tr. by D. Heyd; philosophical revision by S. Scolnicov. The School of Education of the Hebrew University of Jerusalem. 172 pp. (1987–8) The Israeli General Encyclopedia. Philosophy editor. Keter, Jerusalem. 4 vols. (Hebrew) (1992) Aristotle, Metaphysics Book I. Tr. into Hebrew by Leon Roth, revised by S. Scolnicov. Magnes, Jerusalem. 98 pp. (1996) Education for Critical Thinking. Ed. and tr. by Y. HarpazPE, Scientific advisor: S. Scolnicov. Magnes and Branco Weiss Institute, Jerusalem. 144 pp. (Hebrew) (2001) Crossroads: Values and Education in Israeli Society. Ed. by Y. IramPE, S. Scolnicov, J. Cohen and E.P. Schachter. Ministry of Education, Jerusalem. 723 pp. (Hebrew) (2001) Greek Philosophy. Vol 4: A collection of essays. Ed. by S. ScolnicovPE and E. Weinryb. The Open University of Israel, TelAviv. 247 pp. (Hebrew) (2002) New Images of Plato: Dialogues on the Idea of the Good. Ed. by G. Reale and S. ScolnicovPE. Academia Verlag, St. Augustin. 444 pp. (2003) Plato’s Laws: Political theory into practice. Ed. by S. Scolnicov and L. Brisson. International Plato Studies. Academia Verlag, St. Augustin. 365 pp.

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(1977) The simile of the large and small letters. In: The Just and the Unjust, ed. by A. Kasher and M. Dascal, pp. 79–83. Tel-Aviv University, Tel-Aviv. (Hebrew) (1978) Truth, neutrality and the philosophy teacher. In: Growing Up with Philosophy, ed. by M. Lipman and A.M. Sharp, pp. 392– 404. Temple University Press, Philadelphia. (1981) The true political man: Socrates on knowledge and politics, in: The Humanist as Citizen: Essays in memory of Charles Frankel, ed. by J. Agresto and P. Riesenberg, 26–34. University of North Carolina Press, Chapel Hill.

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(1982) Socrate: La conoscenza e la politica. In: Atti dell’Istituto Universitario Orientale. Napoli. (1983) Eraclito e la preistoria del principio di non-contraddizione. In: Atti del Symposium Heracliteum 1981, ed. by L. Rossetti, 97– 110. Edizioni dell’ Ateneo, Roma. (1985) Learning rules and learning concepts. In: School and Education: Essays in honor of Seymour Fox, ed. by Z. Lamm, 257– 264. The School of Education of the Hebrew University of Jerusalem. (Hebrew) (1988) Maimonide et le Dieu des philosophes. In: Individu et société: L’influence d’Aristote dans le monde méditerranéen, ed. by T. Zarcone, 77–82. Editions Isis, Istanbul and Paris. (1991) ‘To me, Callicles, he seems exceedingly in earnest’: On taking Socratic irony seriously. In: The Philosophy of Socrates, ed. by C. Boudouris, 324–332. International Center for Greek Philosophy, Athens. (1991) The seriousness of Socratic irony, Iyyun 40:137–149. (Hebrew) (1992) What is Pythagoras doing in Plato’s Parmenides? In: Pythagorean Philosophy, ed. by C. Boudouris, 195–204. International Center for Greek Philosophy, Athens. (1993) What is education? In: In memoriam Zvi Adar, 5–12. The School of Education of the Hebrew University of Jerusalem. (Hebrew) (1994) Grace, justice and weakness of the will: Religion and philosophy in Maimonides. In: Between Religion and Ethics, ed. by D. Stetman and A. Sagi, 157–170. Bar-Ilan University, Ramat-Gan. (Hebrew) (1994) Derrida’s drug and Plato’s antidote: Socratic dialogues as moral philosophy. In: Reflective Commitment: Essays in literature and moral philosophy, ed. by L. Toker, 3–23. (1995) Le parricide déguisé: Platon contre Parménide (The disguised parricide: Plato against Parmenides). In: Contre Platon II: Renverser le platonisme, ed. by M. Dixsaut, 215–234. J. Vrin, Paris.

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14a (1995) On humanism. In: The Role and Place of the Humanities in Education, ed. by Y. Iram, 599–606. Bar-Ilan University and the World Association for Educational Research, Ramat-Gan. 14b (1996) On humanism. In: Moulding and Rehabilitation: Papers in memory of Prof. Akiva Ernst Simon and Prof. Carl Frankenstein (1996), ed. by Z. Lamm, 303–318. The School of Education, The Hebrew University of Jerusalem. (Hebrew) 15 (1996) Humanistic education as total education. In: Educational policy planning, ed. Y. Danilov, 63–81. Ministry of Education and Culture, Jerusalem. (Hebrew) 16a (1996) The private and public logos. In: The Philosophy of the Logos, ed. by C. Boudouris, 196–204. International Society for Greek Philosophy, Athens. 16b (1996) The private logos and the public logos: Philosophy and the other in Greek thought until Socrates, Iyyun 45:463–470. (Hebrew version) 16c (2000) Si_ré de he gōnggòng de lúokési: qián sūx_là si_xiăng zhōng de zhésué xie* geti*(The private and public logos: Philosophy and the individual in Greek thought until Socrates). In: Xi_fāng zhéxué jiăngyănlù (Western Philosophy), ed. by Li Chaojie, 1–11. Peking University, Beijing. (Chinese translation by Li Chaojie) 17 (1996) The ‘bookcase’ of the Jewish humanist. In: Judaism and Humanism, 53–61. Ministry of Education and School of Education, The Hebrew University of Jerusalem. (Hebrew) 18 (1997) S. ScolnicovPA, N. Gover and I. Soreq, Teacher education as total humanistic education. In: Educational Policy Planning: Position papers 1995–1996, ed. Y. Danilov, vol. 2, 125–136. Ministry of Education and Culture, Jerusalem. (Hebrew) 19 (1997) Freedom and education in Plato’s Timaeus. In: Interpreting the Timaeus/Critias, ed. by T. Calvo and L. Brisson, 363–374. International Plato Studies. Academia Verlag, S. Augustin. 20 (1997) ‘And if not— to be put over him from without’: The Socratic roots of Plato’s violence of reason. In: Plato’s Political Philosophy, ed. C. Boudouris, vol. 2, 175–181. International Society for Greek Philosophy, Athens.

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(1998) The contribution of the study of philosophy in high-schools to education for democracy. In: Philosophie et democratie en Europe, 155–163. Commission nationale de la Bulgarie pour UNESCO, Sophia. (1998) Plato: Diseases of the soul, diseases of the body. In: Philosophy and Medicine, ed. by C. Boudouris, vol. 2, 198–205. International Society for Greek Philosophy, Athens. (1998) Plato and modern education. In: Plato’s Philosophy of Education and Its Relevance to Contemporary Society, ed. by J.D. Gericke and P.J. Maritz, 457–465. The South African Society for Greek Philosophy and the Humanities, Pretoria. (1998) Plato on education as the development of reason. In ΠΑΙΔΕΙΑ: 20th World Congress of Philosophy. http://www.bu.edu/ wcp/Papers/Anci/AnciScol.htm (1999) Plato: Education as the development of reason. In: Education and History: Cultural and political contexts, ed. by R. Feldhai and I. Etkes, 23–32. Zalman Shazar Centre for the History of Israel, Jerusalem. (Hebrew) (1998) Plato against tragedy. In: Greek Philosophy and the Arts, ed. by C. Boudouris. International Society for Greek Philosophy, Athens. (1999) A anamnese e a estrutura das idéias: O Teeteto e o Parmênides. In: Anamnese e Saber, ed. by J.G. Trindade Santos, 172–200. Imprensa Nacional— Casa da Moeda, Lisboa. (2005) Anamnèse et structure des idées dans le Théétète et dans le Parménide. In: La philosophie de Platon, vol. 2, ed. by Michel Fattal. L’Harmattan, Paris, 139-158. (2000). Rúhédú băilátú de dùihuà (How to read a platonic dialogue). In: Xi_fāng zhéxué jiăngyănlù (Western Philosophy), ed. by Li Chaojie, 12–25. Peking University, Beijing. (Chinese tr. by Li Chaojie.) (2003) Como ler um diálogo platônico, Hypnos 11: Platão, Ética e Conhecimento II, 49-59. (2010) Comment lire un dialogue de Platon. In: Aglaïa. Autour de Platon, Mélanges offerts à Monique Dixsaut, ed. A.Brancacci, D.

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El Murr et D.P. Taormina. Bibliothèque d’Histoire de la Philosophie. Vrin, Paris, 83-91. (2000) Direitos e o conceito de pessoa moral: As raízes judaicas. In: Direitos Humanos no Limiar do Século XXI: Os judeus, ed. by A. Novinsky. Universidade de São Paulo, São Paulo. (2000) Euthydemus’ philosophy of language. In: Plato’s Lysis, Charmides, Euthydemus, ed. by T.M. Robinson and L. Brisson, 115–122. International Plato Studies. Academia Verlag, St. Augustin. (2001) Samuel ScolnicovPE and I. Soreq, Values. In: Crossroads: Values and Education in Israeli Society (2001), ed. by Y. IramPE, S. Scolnicov, J. Cohen and E.P. Schachter, 9–38. Ministry of Education, Jerusalem. (Hebrew) (2001) Truth and faith: Pluralistic value education. In: Crossroads: Values and Education in Israeli Society (2001), ed. by Y. IramPE, S. Scolnicov, J. Cohen and E.P. Schachter, 702–715. Ministry of Education, Jerusalem. (Hebrew) (2003) New images of Plato. In: New Images of Plato: Dialogues on the Idea of the Good, ed. by G. Reale and S. Scolnicov, 15–25. Academia Verlag, St. Augustin. (2003) Pleasure and responsibility in Plato’s Laws. In: Plato’s Laws: Political Philosophy into Practice, ed. by S. Scolnicov and L. Brisson. International Plato Studies. Academia Verlag, St. Augustin. (2004) Plato’s ethics of irony. In: Plato ethicus, ed. by M. Migliori, 289-300. Academia Verlag, St. Augustin. (2005) The conditions of knowledge in Plato’s Parmenides. In: Plato’s Parmenides, ed. Aleš Havliček, 165-180. Oikoumene, Prague. (2007) Wyller's henological interpretation of the Parmenides. Afterword to the 2nd ed. of Egil A.Wyller, Platons Parmenides in seinem Zusammenhang Symposium und Politeia: Intrepretationen zur Platonischen Henologie, 221-225. Königshausen & Neumann, Hamburg.

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(2008) Autonomy and humanistic education (Response to Ilan GurZeev). In Autonomy and education: Critical aspects, ed. Sheila Scheinberg. Resling, Tel-Aviv. (Hebrew). (2010) Plato’s use of irony. In: Philosophy and dialogue: Studies on Plato’s dialogues, vol. 2, ed. by Antoni Bosch-Veciana and Josep Monserrat-Molas. Barcelonesa d’Edicions – Societat Catlana de Filosofia. (2012) Time, man and God: Father Dubois’ Aristotle. In: Le chrétien poète de sion: In memoriam Marcel-Jacuqes Dubois, ed. A. Wohlman, Yossef Schwartz, 71-76. The Van Leer Jerusalem Institute / Hakibbutz Hameuchad Publishing House, Tel-Aviv. (Hebrew) (2016) Beyond Language and Literature. In: Plato’s Styles and Characters: Between Literature and Philosophy. ed. G. Cornelli, 514. Berlin: de Gruyter. (2016) What Socrates learned from Aristophanes (and What he left Behind). In: Plato in Symposium: Selected papers from the Tenth Symposium Platonicum, ed. M. Tulli, M. Erler, 178-182. Academia Verlag, St. Augustin. (2017) Atemporal teleology in Plato. In: Teleology in Antiquity: Philosophic and Medical Approaches, ed. J. Rocca, 45-57. Cambridge, Cambridge University Press.

Articles 1a 1b 2 3 4 5

(1969) On the epistemological significance of Plato’s theory of ideal numbers, Iyyun 20:186–210. (Hebrew) (1971) On the epistemological significance of Plato’s theory of ideal numbers, Museum Helveticum 28:72–92. (1971) Towards a new formulation of the problem of semantic fields and tropes, Lešonenu 35:254–271. (Hebrew) (1971) On education and non-education, Megamot 17:311–320. (Hebrew) (1973) Gorgias, or on the absolute scepticism of P. Haezrahi, Iyyun 24:1–9. (Hebrew) (1973) Plato on A and not-A, Iyyun 24:217–226. (Hebrew)

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(1974) Philosophy studies in high-school, Iyyunim be-Hinuch 5:119–24. (Hebrew) (1975) Plato’s Phaedo as an example of the hypothetical method, Eshkolot 7:45–64. (Hebrew) (1975) Philebus 15B1–8, Scripta Classica Israelica 1:3–13. (1975) Hypothetical method and rationality in Plato, Kant-Studien 66:157–162. (1975) Hypothetical method and rationality in Plato. In: The Rational and the Irrational, ed. by M. Dascal and A. Parush, 123–128. Ben-Gurion University, Beer-Sheva. (Hebrew). (1976) Three aspects of Plato’s philosophy of learning and instruction, Paideia 5:50–62. Plato issue. (1977) Razão e emoção na psicologia platônica, Revista latinoamericana de filosofia 3:145–158. (1978) Reason and passion in the platonic soul, Dionysus 2:35–48. (1978) Changing the concept of conceptual change, Philosophy of Education 1978, 259–266. (1981) Perfection and its image: Nature and reason in Plato’s Timaeus, Iyyun 30:227–260. (Hebrew) (1982) An image of perfection: The good and the rational in Plato’s material universe, Revue de philosophie ancienne 9:35–67. (1982) Plato’s Euthydemus: A study on the relations between logic and education, Scripta Classica Israelica 6:19–29. (1983) Dilemas de la universidad moderna. CINTERPLAN, Caracas. (1983) Knowledge and opinion in Plato’s Republic, Iyyun 32:230– 239. (Hebrew) (1984) Il Parmenide di Platone: Prolegomeni ad una reinterpretazione, Symbolon 1: Momenti e Problemi di Storia del Platonismo, ed. F. Romano, 9–36. (1984) Plato’s Parmenides: Prolegomena to a new interpretation, Iyyun 33:459–479. (Hebrew) (1986) I searched myself (Heraclitus 101 DK), Scripta Classica Israelica 7:1–12. (1986) Socrates on the unity of the person, Scripta Classica Israelica 7:13–25.

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(1986) ‘All is a name’: Parmenides on language and the world, Iyyun 35:90–100. (Hebrew) (1988) The curriculum and the democratic idea, Iyyunim Behinuch 19. (Hebrew) (1990) The logical and the psychological in Plato, Hermathena 149: The Heritage of Platonism, 7–17. (1992) Love and the method of hypothesis, Méthexis 5:69–77. (1993) Friends and friendship in Plato:Some remarks on the Lysis, Scripta Classica Israelica 12:67–74. (1994) Socrates, Plato and the development of reason: A rejoinder to Professor Sichel, Studies in Philosophy and Education 13:177– 184. (1996) Is education for pluralism incompatible with real disagreement? In: Education and Change, eds. J.H. Coetzee and T.G. Smith, 59–64. University of South Africa, Pretoria. (1999) Ist eine Erziehung zum Pluralismus unvereinbar mit realer Nichtübereinstimmung? Toleranz, Minderheiten, Dialog. Teil II. Mitteilungen des Instituts für Wissenschaft und Kunst 54:27–32. (German tr. by F. Wimmer.) (2000) How is an education for pluralism compatible with real disagreement? In: Education for culure ina multi-cultural society. Issues in teachers' continuing education IX, ed. Miraim Barlev, 3140. Jerusalem: The Hebrew University of Jerusalem, School of Education. (1997) Prophetic parables and philosophic falsehoods, Scripta Classica Israelica 16:227–238. (1998) Distortion and miscomprehension: On Dudi Mahlev, ‘A retardation-causing theory’ (Haaretz, 15.7.97), ‘Alalei hinuch 2. (1998) A opinião do outro: Os gregos e os judeus, Nova Renascença 18.69–71: A Diáspora Judia, ed. by A. Novinsky, 153–169. (1999) A problemática comunidade de investigação: Sócrates e Kant sobre Lipman e Dewey. In: Filosofia para Crianças em Debate, ed. by W.O. Kohan and B. Leal, 89–96. Vozes, Petrópolis. (2000) The problematic community of inquiry: Socrates and Kant on Lipman and Dewey, Thinking 15:41-45.

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(2003) ‘Things worth wondering at’:Sandra Peterson’s Parmenides, The New Schoolman 30: 279–287. 32 (2004) The two faces of Platonic knowledge, Plato: The internet journal of the International Plato Society 4. www.nd.edu/~plato 33a (2004) Platão contra o atomismo lógico, Veritas 49:641-652. 33b (2005) Plato against logical atomism, Iyyun 54: 363-374 (Hebrew). 34 (2004) Review of G.J. Reydams-Schils, ed., Plato’s Timaeus as Cultural Icon (Notre Dame, IN: University of Notre Dame Press). The Classical Review, 54: 317-320. 35 (2005) Posmodernismo y responsabilidad, El Olivo 29:267-273. 36 (2005) Plato on language and doxa, Ordia Prima 4:75-87. 37 (2006) Review of Christopher Bobonich, Plato’s utopia recast: His later ethics and politics (Oxford: Clarendon Press). The European Legacy 11:557–598. 38 (2006) Tempo e educação em Platão, (Time and education in Plato), Hypnos 17: O Tempo, 1-13. 39 (2007) How do we know a good deed? Einaim 85:15-17. (Hebrew) 40 (2011) You can because you ought, Hed Hahunuch 85:120-122 (Hebrew) 41 (2011) After irony: Reading Plato seriously, Arctos, Acta Philologica Fenica 45, 123-131 42 (2011) Review of Christopher Bobonich, Plato’s Laws: A Critical Guide. AHB online reviews 1, 1-3. 43 (2012) Review of Stephen G. Miller, The Berkeley Plato: From neglected relic to ancient treasure. An archaeological detective story. (Berkeley, Los Angeles and London: University of California Press, 2009), The European Legacy 17:709-711. 44 (2012) Man creates worlds, Hed Hahincuh 86:96-100. (Hebrew) 45 (2012) On the rational and the not rational in education, Hed Hahinuch, ‘Great educationalists’, Plato, 40-43 (Hebrew). 46 (2012) Review of Victor Ehrenberg From Solon to Socrates: Greek History and Civilization during the Sixth and Fifth Centuries B.C. The European Legacy 17:849-850. 47 (2013) Review of Holger Thesleff, Platonic patterns: A collection of studies Iyyun: The Jerusalem Philosophial Quarterly, 62:277281.

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(2013) Positive educational sins: Review of Israel Scheffler, The question of education. A collection of articles, tr. A. Zuckerman, Y. Farkas, A. Katzman (Jerusalem: Mandel, 2011), Gilui Da’at 14: 153-153. (Hebrew) (2013) Review of K.R. Moore, Plato, Politics and a Practical Utopia. Social Constructivism and Civic Planning in the Laws. The Classical Review 63:62-64. (2013) As grandes revoluções no judaísmo, WebMosaica 5:10-14. www.seer.ufrgs.br/webmosaica.

Text-books Samuel ScolnicovPA and Elazar Weinryb, Greek Philosophy. The Open University of Israel, Tel-Aviv. (Hebrew) Vol 1: (1997) Before Socrates. 134 pp. Vol 2: (1997) Socrates and Plato. 367 pp. Vol 3: (1998) Aristotle. 301 pp. Vol 4: (2001) A Collection of essays Edited text-books Sources for the Study of Philosophy in High School. Texts, notes and questions. The School of Education, The Hebrew University of Jerusalem, and the Ministry of Education and Culture. (Hebrew): (1977) What Is Philosophy. Ed. by Y. Ben-ShlomoPE, D. Heyd and S. Scolnicov. 53 pp. (1978). Ethics. Ed. by Y. Ben-Shlomo, D. Heyd, Y. Ofrat and S. ScolnicovPE. 99 pp. (1979) Theory of Knowledge. Ed. by Y. Ben-Shlomo, M. Binnenstock, D. Heyd, S. ScolnicovPE and E. Yakira. 136 pp. (1984) Political Philosophy. Ed. by M. Binnenstock, D. Heyd, S. ScolnicovPE and E. Yakira.145 pp. (1986) Aesthetics. Ed. by D. Heyd, Y. Mathias, R. Shusterman and S. ScolnicovPE. 88 pp. (1995) Philosophy of Religion. Ed. by D. Heyd, Y. Mathias, S. ScolnicovPE and E. Yakira. 124 pp.

List of Publications

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(1996) Philosophy for the Upper Grades of State High School: Teacher’s Guide. Ed. by M. Binnenstock, D. Heyd, Y. Mathias, S. ScolnicovPE and O. Schwarz. The School of Education, The Hebrew University of Jerusalem, and the Ministry of Education and Culture. 130 pp. Entries in Encyclopedias 1

2 3 4

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(1987-88) Entries: Catharsis, Celsus, Clemens of Alexandria, Cosmology and cosmogony in Greek philosophy, Critias, Cynics, Cyrenaic school, Parmenides, Plotinus, Prodicus, Pythagoras of Samos and Pythagoreans, Thales, Themistius, Theophrastus, Therapeuts, Zeller (Eduard). In: The Israeli General Encyclopedia. Philosophy ed. S. Scolnicov. Keter, Jerusalem. 4 vols. (Hebrew) (1996) Plato. In: Philosophy of Education: An Encyclopedia, ed. J.J. Chambliss, 483–489. Garland, New York. (1998) Education. In: Lexicon of Education and Teaching, ed. Y. Kashti, M. Arieli and S. Shleski. Ramot, Tel-Aviv. (Hebrew) (2004) Plato. In: Encyclopedia of children and childhood in history and society, ed. in chief Paula S. Fass. Macmillan, New York . 2: 681-682. (2014) Plato. In: Encyclopedia of Theory and Philosophy of Education, ed. D. C. Phillips. Sage Publications, Thousand Oaks CA, 630633.

250

Index

Index Note: This index is intended to assist in finding select concepts, passages, and authors (ancient and modern) referred to in the main text or quoted at length in the notes. Many epistemological or metaphysical concepts occur too frequently for inclusion. aitia: 109-110, 118, 148, 184, 188 aitias logismôi: 80, 91 Al-Farabi: 214 Alcinous: 15-16, 49 Allen: 200 analysis: 43, 45-66, 118, 206-208 Anaxagoras: 110 Anscombe: 112 antapodosis: 100, 102, 116, 117, Archimedes: 58-59, 63, 199 de sph. et cyl. ii 7: 71 arête: 71-74 teaching of: see Plato Meno Aristotle: 58, 51, 62-65, 94, 196, 197-199, 205, 219 An. pr. A 4. 25b30: 60 An. pr. 69a20 ff.: 70 An. post. i 6. 74bl6: 61 An. post. I 7: 199 An. post. 78a5-13: 51-52 De An. 404b22: 171 Eth. Nic. iii 3. 1112b15 ff: 66 Met. Γ 3. 1005bl4-26: 128 Met. Δ 13. 1020al3 Met. Ζ 13. 1039al2 Avicenna: 214 becoming and perishing: 109-114 Bluck: 67, 70, 74-75, 219 Bonitz: 219 Bröcker: 215-216 Brumbaugh: 170-172 Buchmann: 82 calculation of the cause: see aitias logismôi

Cave: 158, 163, 169, 177-180 Cherniss: 52 chronology: 11-14 convertibility: 49, 51-58, 61, 63, 66, 82, 88-93, Cornford: 46, 49-51, 65, 75, 187, 223 Damascius: 16-17 Descartes: 115, 196 deuteros plous: 110, 114 developmentalism: 11-14 Divided Line: 19, 146, 163-196, 197205 dramatic aspects: 10-11, 33, 78, 96, 98 Duhamel: 53 elenchus: 19, 35, 40-41, 74, 90-91, 107, 208-209 Euclid: 58, 69-70, 168, 198-204 i.22: 69-70 vi.28: 69 vii.2: 187 Eudoxus: 187 Evenus: 97 Ferguson: 168 Festugière: 193 Friedländer: 217 Geminus: 48 geometry: 46-66; 180-186; see also Divided Line Gilson: 215 Good (the): 16, 141, 150, 161-165, 181, 192-194 Gorgias: 112 Gosling: 154

Index

Gulley: 66, 76, Hackforth: 86 Hankel: 54, 56 harmony (soul as): 104-107, 117 Hartmann: 217 Heath: 45, 59 Heidegger: 217 Hellenistic period: 58 Hicken: 106 Hippocrates: 68-69, 207 Hoffmann: 133 immortality (of soul): 81-84, 100 intuition: 92-93, 222-223 justice: see Plato Republic Kahn: 213-214, 216 Kant: 97, 184, 195 Klein: 82-84 Lee: 58 Lewis: 207 literature (updated): 34-37 logon didonai: 91, 93 Lorenzen: 61 Loriaux: 106, maieutic: 75 mathematicals: 120, 176-177, 183, 186, 197-205 Moore: 207 mouthpiece theory 10-11 Murphy: 110, 168, 219 myth: 18, 82-83 Natorp: 111 non-contradiction: 128-139 Olympiodorus: 16 Owen: 214 palingenesis: 100, 116 Pappus: 47, 55, 57, 66, 206 ii 7.634-6: 20, 48-49 Parmenides: 112, 133-137 fr. 7.1: 133 Patzig: 60-61 Philoponus: 48 philosophia: 96-99, 104-107, 116117, 144, 212 philotheamôn: 151-153, 156, 159 Plato: Critias: 12 Epinomis:

251 991a: 171 Euthydemus: 14 Euthyphro: 9d: 219 Gorgias: 457e: 90 476c-d: 106 524b: 98 Hippias Major: 288a: 72 Laws: 894a: 171 Letters vii 342a-c: 205 Meno: 13-14, 18, 20-27, 45, 6785, 191, 207, 210, 212 72c: 80 75b: 181 80d-e: 75-76 81a-d: 76-77, 84 85c-86a: 77-78, 84 86e-87b: 67-71 87a: 219 87b-c: 71-72 87d: 208, 219 88c: 208 Parmenides: 12-13, 127e: 134 136b: 219 Phaedo: 16, 19, 27-29, 74, 85-95, 96-119, 121-122, 137, 164, 189, 191, 196, 212, 216, 222-223 59b: 96 61a: 96 63b: 97 63e: 98 64c-d: 98 65a-b: 101 66e:101 70c: 99 70d-72d: 100 74b-76e: 101-102, 202 74b: 136 74c: 133, 197 77a-c: 102 78b-79b: 102 79c-d: 102-103, 194

252 90e:104 92b-d: 105-106 92e-94a: 106-107 95a-c: 108 98b-99d: 93 100a: 85-88, 90, 111, 208 100b: 219 100c: 112, 135 101d-e: 85-88, 91, 98, 103b: 128 107b: 94, 220 Phaedrus: 223 Philebus: 56d: 197 Protagoras: 339d: 219 Republic: 12-14, 17, 19, 29-31, 120-149, 150-162, 163-196, 197-205, 207-208, 212, 222-223 Book i: 121-123 357b-358e: 122, 140 358a-e: 122 362e-367e: 143 368a: 122 368d-e: 123-124, 140 372e-373d: 139 420: 126 433a-439a: 129 433e-434c: 124 434d-435c: 125 435e-436a: 126-127 436a-437e: 90, 128-129, 133 437a: 131-132, 146, 208 437b: 130 439a-b: 129 439c-d: 129 441c: 139-140 441d: 126 442c: 150 443b: 140 444b-e: 140 445c: 141-142 474a-d: 150-151 476a: 150 476c: 152 476e: 156 477a: 152

Index

477b: 154-155, 193 477d: 175 477e: 153 478a: 153, 155 478e: 156, 176 279b-c: 213, 215 479d: 156 485a-487a: 142 504d: 161 505a-b: 161 506d: 164 508b-c: 165 509b: 194 509d: 165-166, 170-171, 174176 510a: 168, 176 510b: 167, 173, 197 510b-511d: 163-196 510c: 219 510d: 180 511b: 174 511d-e: 170-171, 174 520c: 157 523c-527b: 186 525c: 185 526a: 197 531d: 187 533c: 208, 520 534a: 163, 169, 171, 174, 176 543c: 141 544d: 142 577c-e: 142 580c: 142 609c-d: 143 610a: 90 611e: 144 612b: 144 613a: 145 Sophist: 32-33, 214-215, 218, 223 230b: 128 238d-e: 219 259a: 90 266a: 172 Statesman: 32 Symposium: 44, 137 211a: 136 Theaetetus: 12-13, 31-32

Index

191c: 219 Timaeus: 50c: 197 67b: 164 80a: 164 Platonism, late antique: 15 Prauss: 111 Proclus: 16, 48, 197 in Eucl. 75.14-26: 63-65 in Eucl. 211.12 ff, 56 253.16-254.5: 52, 53 255.8-256.8, 55 Raven: 166, 173 Recollection: 75-81, 117 reductio ad absurdum: 46, 54-55, Robin: 197 Robinson: 40, 45, 49-51, 54, 56, 8891, 196, 219, 222-223 Rose: 74, 172 Ross: 52-53, 128, 187, 197 Sayre: 41, 86-90, 193 Schiller: 116 Scolnicov, other writings by: 9-14 simile of the letters: 123-6, 150 slave, examination of: 77-79, 82

253 Sophocles: OC 1224-27: 96 ‘sought’: see zêtoumenon Stahl: 40-41, 73, 219 Stenzel: 58 Sun: 160, 165, 191-195 syllogistic: 60, Syrianus: 197 Taylor: 104 ti hikanon: 16, 94, 118, 148 Tigner: 76 Tredennick: 219 unhypothetical principle: 16, 90, 93, 119, 132-133, 141, 148-149, 167, 176, 180, 190, 192, 195, 209, 222 Vlastos: 13-14 Wedberg: 198-205 Williams, B.: 38, 61, 126 Williams, W.: 40 Wilpert: 188 Zeno of Elea: 133-135 B2: 134 zêtoumenon: 20-33, Zeuthen: 54