Aristotle’s Theory of the Unity of Science 0802047963, 9780802047960

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Aristotle's Theory of the Unity of Science

Aristotle was the first philosopher to provide a theory of autonomous sci­ entific disciplines and the systematic connections between those disciplines. This book presents the first comprehensive treatment of these systematic connections: analogy, focality, and cumulation. Wilson appeals to these systematic connections in order to reconcile Aristotle's narrow theory of the subject-genus (described in the Posterior Analytics in terms of essential definitional connections among terms) with the more expansive conception found in Aristotle's scientific practice. These connections, all variations on the notion of abstraction, allow for the more expansive subject-genus, and in turn are based on concepts fundamental to the Posterior Analytics. Wilson thus treats the connections in their relation to Aristotle's theory of science and shows how they arise from his doctrine of abstraction. The effect of the argument is to place the connections, which are traditionally viewed as marginal, at the centre of Aristotle's theory of science. The scholarly work of the last decade has argued that the Posterior Analytics is essential for an understanding of Aristotle's scientific practice. Wilson's book, while grounded in this research, extends its discoveries to the problems of the conditions for the unity of scientific disciplines. m a l c o l m W i l s o n is an assistant professor in the Classics Department at the University of Oregon.

PHOENIX Journal of the Classical Association of Canada Revue de la Societe canadienne des etudes classiques Supplementary Volume xxxvm Tome supplem ental xxxvm

MALCOLM W ILSO N

Aristotle's Theory of the Unity of Science

UNIVERSITY OF TORONTO PRESS Toronto Buffalo London

© University of Toronto Press Incorporated 2000 Toronto Buffalo London Printed in Canada ISBN 0-8020-4796-3

© Printed on acid-free paper

Canadian Cataloguing in Publication Data Wilson, Malcolm Cameron Aristotle's theory of the unity of science (Phoenix. Supplementary volume ; 38 = Phoenix. Tome supplementaire, ISSN 0079-1784 ; 38) Includes bibliographical references and index. ISBN 0-8020-4796-3 1.

Aristotle - Contributions in methodology. Aristotle - Contributions in ontology. Science - Philosophy. I. Title. II. Series: Phoenix. Supplementary volume (Toronto, O n t.); 38. 2.

B485.W54 2000

185

C99-932973-1

University of Toronto Press acknowledges the financial assistance to its publishing program of the Canada Council for the Arts and the Ontario Arts Council. University of Toronto Press acknowledges the financial support for its publishing activities of the Government of Canada through the Book Publishing Industry Development Program (BPIDP).

CONTENTS

A C K N O W L E D G M E N T S ABBREVIATIONS

INTRODUCTION

Vl i

IX

3

CHAPTER 1: GENUS, ABSTRACTION, AND COMMENSURABILITY 14 Demarcating the Genus 15 Abstraction 29 1. 3.

Speed of Change 39 2. Value 41 Animal Locomotion 47

CHAPTER 2: ANALOGY IN ARISTOTLE'S BIOLOGY Problems with Analogy 53 1. Fixity of Analogy 60 2. Difficult Cases 67 3.

Analogues and the More and Less 69 4. Analogues and Position 69 5. Analogy of Function 72 6. Genus as Matter 74 A Solution 77 A Challenging Case 83 Analogy and Abstraction 86

53

vi Contents CHAPTER 3: ANALOGY AND DEMONSTRATION

89

Analogy in APo: Passages and Discussion 91 Analogy in the Biology 99 Analogy and the Scala Naturae 109 CHAPTER 4: THE STRUCTURE OF FOCALITY

116

Focality and Per Se Predication 122 The Limits of Focality in the Biological Works 129 CHAPTER 5: METAPHYSICAL FOCALITY

134

The Genus of Being 136 Categorial Focality in Metaphysics Z 144 Demonstration in the Science of Being 158 The Wider Focal Science of Being 165 CHAPTER 6: MIXED USES OF ANALOGY AND FOCALITY M atter and Potentiality 177 The Good 194 CHAPTER 7: CUMULATION

207

Souls 208

1. The Analogical Account 210 2. The Cumulative Account 214 Friendship 224

1. Eudemian Ethics and the Problems of Focal Friendship 225 2. The Nicomachean Version 231 The Place of Theology in the Science of Being 235 Conclusion: Analogy, Focality, and Cumulation 239

BIBLIOGRAPHY INDEX

LO CO RUM

GENERAL

INDEX

243 255 265

175

ACKNOW LEDGM ENTS

M y first thanks go to my teachers at Berkeley, Tony Long, John Ferrari, and Alan Code, who supervised the dissertation from which this book arose. Mary Louise Gill and James Lennox also kindly read my entire dissertation and provided encourage­ ment and advice. Friends and colleagues have read and commented on various parts in various stages of completion: Andrew Coles, William Keith, John Nicols, Scott Pratt; and my wife, Mary Jaeger, who conquered 'philosophy-induced narcolepsy' to read the entire manuscript more than once. Two anonymous reviewers for the University of Toronto Press provided much detailed and general comment useful in improvement. Finally, I should also like to thank Ancient Philosophy for permission to use material published in 'Analogy in Aristotle's Biology,' Ancient Philosophy 17 (1997).

A BBREVIATIO NS

Works of Aristotle APo APr Cat. DA DC Dl EE EN GA GC HA 1A )uv. Long. MA Met. Mete. MM PA Phys. PN Pol. Resp. SE Sens. Somn. Top.

Posterior Analytics Prior Analytics Categories de Anima de Caelo de Interpretatione Eudemian Ethics Nicomachean Ethics Generation of Animals Generation and Corruption History of Animals Progression of Animals On Youth, Old Age, Life and Death On Length and Shortness of Life Movement of Animals Metaphysics Meteorologica Magna Moralia Parts of Animals Physics Parva Naturalia Politics Respiration Sophistical Refutations Sense and Sensibilia de Somno Topics

x Abbreviations

Other Works LSJ H.G. Liddell and R. Scott. A Greek-English Lexicon. Revised and augmented by H. Jones. Oxford: Clarendon Press, 1996. ROT J. Barnes. The Complete Works of Aristotle. The Revised Oxford Translation (Bollingen Series LXXI.2). Princeton: Princeton University Press, 1984.

Acronyms and Summary of Per Se Relations IPO is predicated of SGA species-genus-analogy WP wholes-parts per se (1) predicate: is contained in the definition of its subject, e.g., linear is predicated of triangle. per se (2) predicate: contains its subject in its definition, e.g., female is predicated of animal. per se (3) is self-subsistent subject, e.g., man. per se (4) predicate: is predicated of something on account of itself, e.g., dying is predicated of being slaughtered.

Aristotle's Theory of the Unity of Science

IN TR O D U C TIO N

Aristotle is renowned for having been the first to create autonomous sciences and independent disciplines. By distinguishing physics, political science, and many other areas of study, he circumscribed and identified some of the most important modem scientific fields. His reasons for sep­ arating such sciences and their subject matters were not the social and practical reasons familiar today. He did not worry about the limitations of the individual human mind faced with the explosive growth of knowledge and the consequent drive towards ever-increasing specialization. Quite the contrary, he thought humans were naturally capable of fulfilling their de­ sire for understanding and he did not view the sheer amount of knowledge as an impediment to this end. His concern lay instead with the form that that understanding takes. He denied that all of our knowledge falls into a single undifferentiated domain, a single universal science, and he developed a solution, the subject-genus, which served to separate and isolate each subject matter. But his solution created problems of its own. I shall contend that the isolating force of the subject-genus was so powerful that additional tech­ niques were required to provide for the legitimate causal and explanatory links between sciences and subject-genera. To effect the happy compromise between universal science and genus-isolation, Aristotle developed four techniques of connection: subordination, analogy, focality, and cumulation, of which the last three are the special concern of this book. I intend to study these techniques both at a specific and a general level. I am first of all interested in the use Aristotle makes of them. The specific passages in which he explicitly puts these techniques to work are among the most controversial in the Aristotelian corpus. They concern such fun­ damental questions as the unity of the science of Being and metaphysics.

4 Aristotle's Theory of the Unity of Science the definition of the soul, the organization and nature of goods, and the kinds of friendship. In treating each technique in turn and with an eye to the larger picture, I shall offer new interpretations of specific areas of Aristotelian philosophy. At a more general level, I gather these techniques together and provide a single comprehensive theory for them. This theory arises out of my reflections on recent developments in Aristotelian scholarship. One of the most important trends of the last several decades has been the realization that Aristotle's theory of science contained in the Posterior Analytics is not an abstract ideal without practical application, but in fact is used in important ways in the special sciences, especially in the biological works. Many of the basic concepts of Aristotle's formal scientific methodology, like demonstration and definition, have been found to inform the practice and presentation of specific sciences. This research has been very fruitful, but it has focused primarily on the single isolated genus. There is good reason for this focus. While the APo does discuss the subordination technique at some length, it only briefly notes analogy and never mentions focality or cumulation at all. And yet these are important organizational tools in the several sciences. In view of the success in applying the APo's single-genus theory to Aristotle's scientific practice, I want to reverse the hermeneutic process, as it were, and ask whether the widespread use of analogy, focality, and cumulation in the special sciences can be given any theoretical account within the terms of the APo. I believe that this is possible, and shall adduce evidence and argument to show that Aristotle had the APo in mind when he formulated these techniques. I shall also argue that this fact yields important results. Not only do we obtain a theoretical account of these techniques, but we also discover that, far from being a random assortment of tools of various vintages scattered haphazardly throughout the corpus, they perform interlocking and complementary functions. Moreover, they are all logical developments of the most important concepts in the APo, per se and qua predication. This fact both confirms our belief in the relevance of the APo for these techniques and also allows us to provide a general and unified account of them, for they are variations on a single logical theme. Finally, by describing these techniques in terms of the central concepts of the APo, we can provide a richer and more powerful account of Aristotle's theory of science, one that is more fully integrated into all aspects of his scientific practice. Such an interpretation is founded on an assumption hermeneutically confirmed that Aristotle's philosophy forms a basically consistent unity, and that there are few radical changes in his views. The unsuccessful attempts of this century to impose a chronology on Aristotle similar to

5 Introduction the one that so successfully applies to Plato lead me to view the historical question as less interesting than the philosophical question concerning the logical organization of concepts. It would be absurd to deny that any philosopher underwent intellectual development, but I am inclined to believe that Aristotle's development is more like the articulation of basic ideas than the repeated creation and destruction of whole systems of thought. The story begins with Aristotle's objections to a single universal sci­ ence. These objections arose out of the historical context of debates with his older contemporaries Plato and Speusippus, heads of the Academy. It was a common supposition of ancient Greek epistemology that we know something when we know how it is related to other things we know. This relational view of knowledge manifests itself in two patterns. First, Plato held that we know the particulars best (to the extent that we actually can know them) when we understand how they imitate the Forms, and since we understand the particular in virtue of the universal, Plato exalted the Form or universal and depreciated the sensible particulars. Since we can understand only what is common and universal among the particulars, the variations among them are relegated to the shadowy realm of opinion. With the quip that Meno was providing a whole swarm of virtues, Plato's Socrates compelled him to avoid examples, like manly virtue and womanly virtue, and state instead the single definition of virtue that covers all these cases. For virtue, Socrates claimed, must be the same whether it is present in a man or a woman (Meno 7le-73a). Likewise, in the Republic he sup­ posed that justice will have the same nature wherever it is found, and as a result, he argued, justice in the soul will be the same as justice in the state (368c-369a). In the drive for the universal definition, Plato often overlooked genuine ambiguities in terms. For Aristotle, detecting and disarming these ambi­ guities became something of a philosophical obsession. He faults Plato on the grounds that justice exists properly as a relation between two people, and exists between the parts of the soul only by a metaphorical extension (EN V .ll 1138a4-bl4). Similarly, Plato's universalization of virtue, which is manifested in the Republic's inclusion of women in the leadership of the state (451d-e), prompts Aristotle to distinguish between men's and women's tasks and therefore between their virtues (Pol. II.5 1264b4-6). For Plato, then, the possession of any common characteristic among particulars was a sufficient condition for positing a Form and universal, and as a result he failed to detect other more subtle relationships. The preference for the universal over the particular is recapitulated in the preference for the more general Form over more specific Forms, as is clear in the example

6 Aristotle's Theory of the Unity of Science of Meno's virtues, in which man's virtue, even though a universal itself, was rejected as too particular. As a result, important demarcations between fields and sciences were blurred, and in the Republic all knowledge became an articulation of the unified politico-philosophical super-science of the Good, in which the Form of the Good made all other Forms intelligible. In his later work, Plato studied a second form of relational knowledge. In the Sophist the Forms themselves are known through a process of divi­ sion by their participation in Sameness and Difference with respect to other Forms. Here, the relations among the Forms themselves are the source and ground of knowledge. Plato's nephew, Speusippus, while rejecting the Forms, elaborated this system of division and used it to drive even harder in the direction of scientific unification. He argued that all knowledge is relational, and that everything is known in virtue of its sameness and difference from all other things. In order to know anything, therefore, one must know everything.1 Knowledge is articulated through a universal scheme of division, and a thing just is its relational position within this universal scheme. As a member of Plato's Academy and as a philosopher in the Platonic tradition, Aristotle was engaged in this common quest for systematic un­ derstanding, but he was suspicious of both the generalizing and unifying tendencies he found there. On several grounds he argued the inadequacy of the Academic project. He claimed that there was no universal subject matter to provide an object for a universal science; there was, that is, no one genus of Being. And even if there were, he claimed, this general science would tell us nothing about the manifold nature of reality. Nor would it be useful, since we do not even need it in order to know about specific pieces of reality. As Aristotle presented it, Plato identified Being and Unity as the high­ est genera of things, under which all Forms fall. He also identified Being and Unity as the elements of things, since he supposed that the Forms were somehow constituted out of them. Being and Unity, then, were at the same time both principles and the highest genera (Met. B.3 998b9-21). For Plato, the more universal a thing was, the more of a principle it was and the greater its generative and explanatory power. Aristotle, by contrast, argued that there was a limit to the degree of universalization attainable among all objects. Neither Being nor Unity, he thought, form a genus with a single unambiguous definition, and therefore neither can be a principle for a universal science (998b22-28).1

1 According to Aristotle (APo 11.13 97a6-19). See my 1997a.

7 Introduction Aristotle was also concerned about the epistemological etiolation that attends increasing universalization. The more one grasps at what is com­ mon, the less one retains of the particular kinds. And yet what a thing is specifically is as much a part of its Being as what it is at a high level of generalization. For being biped is as much, if not more, part of the Being of a man as being a substantial unity, the actuality of a potentiality. This is not to say that Aristotle rejected general understanding altogether, but he did not think that we know something solely in virtue of its membership in a genus. Nor did he believe that the genus always provides the cause and explanation for a thing. He preferred instead the constitutive element and the various kinds of cause as explanatory principles, and in his theory of science the genus comes to denote the extension of the explanation, rather than the explanation itself. Aristotle also took issue with the Academic doctrine that all knowl­ edge forms a single science. He made the observation —hardly original considering Socrates' frequent appeal to it - that there were experts who understood their own field but not others. It was clearly not necessary to know everything in order to have expertise in a single field.2 Nor was it necessary to know the most general science. Plato, for his part, had been scandalized that the mathematicians simply accepted the principles of their science without investigating its foundations. He supposed that their hypothetical principles could be perfected by an unhypothetical science, philosophical dialectic, which would remedy the deficiency of mathematics and indeed all hypothetical sciences. Only the philosopher, then, could legitimately lay claim to true knowledge of the special sciences. Aristotle, though he recognized a first philosophy that examined the first principles of the special sciences, thought it right and proper that the special sciences should merely presuppose and not examine their own first principles. Accordingly, Aristotle sought to redress the imbalance apparent in the Academic prejudice towards the universal. He attended more equally to both the specific and the general levels of inquiry and studied the causes of things in addition to their similarities and differences. These new concerns found logical expression in his theory of scientific understanding, whose foundation is the demonstrative syllogism. A syllogism is composed of at least three terms, a major (e.g., having wings), a middle (e.g., fliers), and a minor (e.g., birds), arranged in at least two premisses and a conclusion; for example, 2 See PA 1.1, where Aristotle draws the distinction between the specialized expert and the generally educated layman. Also Balme 1972, 70, on the connection with Plato and Speusippus.

8 Aristotle's Theory of the Unity of Science having wings is predicated of (henceforth, IPO) fliers fliers IPO birds therefore, having wings IPO birds.3 In order for a syllogism to be demonstrative, the relationship between the terms of its premisses (e.g., 'having wings' and 'fliers') must be necessary.4 This necessity is understood in terms of essential, definitional relationships: in order for 'having wings' and 'fliers' to be terms in the same demonstra­ tive premiss, 'having wings' must appear in the definition of 'flier' or vice versa, e.g., wings are by definition the instrumental part for flying.5 When terms are so related, they are said to be per se (καθ' αυτό) or essentially related. Only essentially related terms may be joined in a demonstrative premiss, and a string of such premisses will form a string of essential relations. Terms that are not essentially related are said to be accidentally related, and cannot be connected in a demonstrative premiss. In addition to this per se requirement Aristotle introduces the rule that terms in a demonstrative syllogism must be proved of the subject as such and universally, indicating this criterion by the use of the relative pronoun ■p {qua). The effect of this requirement is to restrict further the terms admissible to a demonstration and therefore to a science. A triangle, for example, can be demonstrated as having interior angles equal to two right angles (following the custom, I shall call this the 2R theorem), because it possesses this property as or qua triangle. By contrast, a demonstration that proves this attribute of isosceles triangle is defective because the property does not belong to isosceles triangle qua isosceles, but qua triangle. Such a proof is said to be an accidental proof, because 2R does not belong to isosceles triangle qua isosceles. The term 2R, then, belongs in the science of triangle and not in the science of isosceles triangle. These two restrictions on the admission of terms to a demonstration constitute the identity conditions of a science and provide the foundations for the autonomy of disciplines. Since not all terms are per se related to one another, and since they are different in their qua designations, they 3 This syllogism is frequently presented differently by modem commentators: birds are fliers fliers have wings birds have wings. This is not, however, Aristotle's presentation, and it will be most convenient for our purposes to adhere to his characteristic form. 4 These issues will be discussed in greater detail in chapter 1 below. 5 In relating terms within definitions Aristotle allows for some paronymy, i.e., flying for flier.

9 Introduction cannot all be included in one universal science. Each science has a subject or a subject-genus. This is what the science is about and the subject of which the predicates are predicated. A science is the sum of the demonstrative syllogisms that concern the same subject.6 The subject of the science is indicated by the qua expression, and the per se criterion for including other terms in a science implies that each science is autonomous and has its own and unique set of principles. When these restrictions are violated, when there is an attempt to introduce a term that is not per se and qua related to the other terms into a demonstrative syllogism, the result is an error, which Aristotle calls μΐτάβαχης or kind-crossing, and this will destroy the demonstrative power of the syllogism and the cogency of the science. In contrast to Plato's and Speusippus' universalizing and inclusive tendencies, Aristotle's theory of demonstration is a powerfully isolating force. The qua requirement especially entails that understanding occurs within a single subject-genus, and not in relation to other genera through an analysis of sameness and difference.7 Each science will be specialized and isolated from every other except by incidental connections, and there will be no communication between disciplines. Each subject-genus, bound by necessity solely to its own principles and predicates, will form an island in the sea of Being. The view of the world that this theory of science represents will be that of a heap of subjects, in which one genus is only incidentally related to another. It is clear, however, that Aristotle never advocated such a degree of isolation. In fact there are a multitude of ways in which sciences are con­ nected with one another and share principles. The axioms, like the principle of non-contradiction, are common to all sciences, and are the precondition for any understanding at all. More elaborately developed within the APo is the connection between a more abstract, superordinate science and a less abstract, subordinate science. A superordinate science, usually a branch of mathematics, supplies principles and explanations for a fact or conclusion found in a distinct and subordinate natural science, for instance, harmonics or optics. Since this technique and its place in the APo has been well studied

6 I am deliberate in avoiding the claim that a science is the sum of demonstrations which have the same minor term for reasons which will be discussed in chapter 4. 7 No doubt, division remains an important part of Aristotle's epistemology, but it plays a preliminary role in establishing the extent of the subject-genera and the attributes that are coextensive with them. It is not the primary form of understanding. See Ferejohn 1991, who places division in the 'framing' or pre-demonstrative stage of science. See also chapter 2 below.

10 Aristotle's Theory of the Unity of Science by the secondary literature, I shall not treat it in the same depth as the three other techniques.8 It will provide, however, a useful stepping-stone to those techniques. In the first chapter of this book I shall begin by laying out in more detail the conditions for a unified subject-genus and what makes two subject-genera different. I shall then consider subject-genera that are re­ lated to one another through abstraction, but that nevertheless are separate and autonomous. Abstraction is a feature of Aristotle's philosophy famil­ iar from his theory of mathematics. According to Aristotle, mathematical objects are ontologically dependent on their physical substrate, but can be mentally abstracted from that substrate so that they maintain absolutely no conceptual connections (i.e., per se relations) to it. Mathematics and physics, then, are a pair of subject-genera related by pure abstraction. I shall argue that abstraction has a much broader application than merely to mathematics and, more importantly, that there are several degrees of abstractability, depending on the nature of the subject matter. I shall focus on several pairs of subject-genera in which the conceptual abstraction is not absolute, cases in which there are per se relations between the abstracted genus and its substrate. I call this situation 'semi-abstraction.' The super­ ordination technique will provide us with the first step along this road. It is precisely in the realm of abstraction and semi-abstraction, in which two subject-genera can be treated as autonomous and yet maintain per se connections to one another, that analogy, focality, and cumulation operate. Analogy, strictly speaking, is a proportional relationship between four terms (A is to B as C is to D), that expresses a common relation between each of the two pairs. The formal structure of the relationship does not dictate the content, and an analogy can express any commonality from an exuberant metaphor of poetry to a trivial numerical identity. Nevertheless, I argue that Aristotle has a more specific function in mind for analogy, one closely related to demonstration. Analogy arises between subject-genera. Where genera are different, their qua designations are different, and there are no per se connections between them. As a result they cannot be treated by a common science. In the face of the injunction against metabasis or kind-crossing, analogy provides us with the means of treating subjects that are generically different in a parallel way. In the Parts of Animals, for example, Aristotle discusses the analogous parts, wing and fin. These parts are predicated respectively of bird and fish in virtue of the final causes or functions, flying and swimming. Bird, wing, and flying have obvious universal and per se connections; so also do fish, fin, and swimming. We

8 See e.g., Lear 1982, McKirahan 1978, Cartwright and Mendell 1984, and Lennox 1986.

11 Introduction can prove that wing is predicated of bird by using the proper principles of the subject genus, bird; similarly with the fish's fin.9 In spite of the independence and autonomy of the demonstrations, there is a parallel in the proofs, an analogical identity of relation: as wing is to bird, so fin is to fish. This identity, however, cannot be abstracted from, and must always be per se related to, the subject-genera in which the demonstrations take place. This is a result of the fact that the subjects, bird and fish, determine the qua level at which the attributes and causes are treated. At the same time, behind the generic difference there is the intimation of a more abstract subject-genus to which both bird and fish are related. This subject-genus arises from the fact that flying and swimming are forms of locomotion, and that wing and fin are instrumental parts of locomotion. The second and third chapters of this book will be devoted to explaining how analogy facilitates this limited degree of unity among different scientific subjects. The second object of our investigation, the focal relationship, is a method for drawing together in a single subject matter objects that are of different genera.10 According to Aristotle's favourite example, the term 'medical' applies to many different kinds of objects. For instance, we call an operation medical, a doctor medical, a scalpel medical, not because they possess the same attribute, medical, but because they are all related to the thing that is called medical in the primary sense, the medical art. The other medical things are so called because they are the work of the medical art, the possessor of the medical art, or the instrument of the medical art. The definitions of these derivatively medical things contain in themselves the primary term or its definition. Chapter 4 will be devoted to analysing the focal relationship in terms of Aristotle's theory of science and showing that medical is predicated of the derivative medical things in virtue of a variety of per se relations. Although all the medical objects do not form a single genus, in the sense that they are not of the same kind or similar to one another, the definitional relations among them show how they form a genus in another important sense of the term, objects related by per se connections to a single subject-genus.

9 This is Aristotle's standard pattern of demonstration in the PA. We perceive that a bird has wings from observation, but to know in the fullest sense we must know why, and this knowledge comes from relating the cause to the fact in a demonstration. We cannot prove that a bird has wings from observation, because only demonstration provides proof. 10 G.EX. Owen (1960) first provided the current English translation of irpos ev Kcyopevov as 'focal meaning.' It is also known as 'relational equivocity.' Most recently Shields 1999 has called this (as well as cumulation) 'core dependent homonymy.'

12 Aristotle's Theory of the Unity of Science The most important consequence of this interpretation of the focal relationship in terms of the APo theory is a reassessment of Aristotle's famous application of focality, the science of Being (cw). This will be the task of chapter 5. Though they do not form a single genus. Beings can be treated under a single science because they are all per se related to a single primary term, substance (ουσία). The focal relation has traditionally been treated as a very special case, found only in exceptionally difficult circumstances like the science of Being. But the fact that the focal relation is basically a per se relation suggests that focality should be viewed in­ stead as a simple application of the logical and causal relations of normal Aristotelian demonstrative science. The terms (subjects, attributes, causes) of demonstrative premisses are bound together by necessary, definitional relations, whereby one term (or its definition) is included in the definition of another. This is the structure of any ordinary Aristotelian science, and the binding relations found in ordinary or normal science are of the same kind as those by which focal science, including the focal science of Being, is constituted. In the sixth chapter I shall consider groups of objects that Aristo­ tle treats both analogically and focally. These cases have a long history of controversy. Aquinas, for example, made analogy invariably into a relation between prior and posterior, assimilating it to focal and serial schemes, which he called 'analogy of attribution.'11 More recently, G.E.L. Owen sharply distinguished analogy and focality and tried to set them in a chronological sequence within Aristotle's philosophical development.1112 Neither, however, studied analogy and focality in terms of per se relations and demonstrative science. And though Owen was right to reject the terms of Aquinas's assimilation of the techniques, there are other and deeper structural connections that have escaped the notice both of Aquinas and the moderns. In this chapter I shall argue that, far from being independent or even incompatible means for the unification of a subject-genus, focality is logically prior to analogy and a necessary precondition for it. Analogy and focality are two basic ways in which Aristotle treats different genera in conjunction with one another. But there is another 11 Summa theologiae 1.13.6c: 'In the case of all names which are predicated analogously of several things, it is necessary that all be predicated with respect to one, and therefore that that one be placed in the definition of all. Because "the intelligibility which a name means is its definition," as is said in the fourth book of the Metaphysics, a name must be antecedently predicated of that which is put in the definitions of the others, and consequently of the others, according to the order in which they approach, more or less, that first analogate.' For passages and discussion see Klubertanz 1960, 68-9. 12 Owen 1960.

13 Introduction important means that employs elements of focality and analogy to create a series of similar objects. I call this method 'cumulation/ and it will be the subject of the final chapter.13 It is a special form of a series, which is arranged in order of priority and posteriority, and is used in Aristotle's discussions of souls and friendships. It is also important for determining the place of theology within metaphysics. The prior members of the series are logically and ontologically contained in the posterior members, as for example the nutritive soul is contained in the sensitive soul. The latter cannot exist without the former, and the latter contains the former in its definition potentially. Members of cumulative series do not form standard genera, but they all share some essential attributes with one another, as analogues do; they are also per se related among themselves, since the definition of a later member contains the definition of a prior member, just as focally related objects do. In spite of the features of cumulation that are common with focality, cumulative objects cannot form a focal genus. The reasons for this will emerge in my interpretation of the soul series. The chapter will be filled out with an examination of Aristotle's two discussions of friendship and an argument that he abandoned the focal analysis of friendship he provided in the Eudemian Ethics for a cumulative view in the Nicomachean Ethics because of the intractible difficulties in applying focality in this context. Finally, I shall use the lesson of cumulation and focality to shed light on the problem of the place of theology in the science of Being. Together, analogy, focality, and cumulation provide Aristotle with the means to balance the claims of the universal science advocated by the Academy and the isolation of the subject-genera, which arises within the logic of his own theory of science. This solution, by preserving the auton­ omy of sciences without creating a chaotic heap of subject matters, allows each subject to be treated separately while still maintaining its place in the intelligible architecture of the world.

13 Grice 1988, 190-2, has called this 'recursive unification.'

1

Genus, Abstraction, and Commensurability

In this chapter I shall first discuss two issues preliminary to 'semi-abstrac­ tion.' I shall begin by presenting in more detail the per se and qua re­ lations, and show how they make a subject-genus a single subject-genus distinct from other subject-genera. Aristotle illustrates these relations by the familiar 2R example and the proof for alternating proportionality. In both cases the per se and qua relations provide an adequate set of criteria for identifying and demarcating subject-genera. Next, I shall introduce abstraction (aaipeais) through Aristotle's theory of mathematics, and analyse this concept in terms of per se and qua relations. Abstraction will provide a means of moving or shifting between qua levels and between subject-genera, not just among mathematical and physical objects, but wherever two subject-genera are related. These preliminary discussions provide the background for semi-abstrac­ tion, and allow for a distinction between semi-abstraction and pure ab­ straction. In pure abstraction, such as the abstraction of mathematicals from their physical substrates, the abstracted subject-genus maintains no per se connections to the substrate from which it was abstracted. In semiabstraction, by contrast, the abstracted subject-genus does maintain some per se connections to its substrate. I shall argue that, precisely because these per se connections are maintained, the lines of demarcation between a semi-abstracted subject-genus and its substrate cannot be sharply drawn. As a result ambiguity arises in determining which subject-genus is under consideration, the semi-abstract or its substrate. We shall see this problem first arising with the proof for alternating proportionality, and then more acutely in the 'mixed' or subordinate sciences, like harmonics and optics. In these latter cases more than one subject-genus is involved in the same proof, and therefore proofs in such sciences do not occur clearly within one or the other subject-genus, but rather occur in both.

15 Genus, Abstraction, and Commensurability There are different degrees of semi-abstraction. By enlisting commen­ surability as a sign of generic unity (i.e., objects in the same genus can be compared directly with one another, while objects from different genera cannot) I shall examine abstraction and resistance to abstraction in several graduated cases. While mathematicals can easily be abstracted from their physical substrate and be compared as quantities, some other objects resist abstraction to a greater or lesser extent. I shall consider three such objects. First, kinds of change cannot be abstracted from their substrate and cannot be compared one with another. Next, the exchange value of manufactured goods can be abstracted from the proper function of the goods sufficiently to allow commensuration for the purpose of exchange and trade. Finally, causes of animal locomotion can be abstracted from the instrumental parts of locomotion to the extent that at the upper reaches of abstraction there remain no per se connections with the specific instruments. But each level of abstraction from the parts allows for commensuration within that level. By establishing the possibility of semi-abstraction and degrees of abstractability and by describing them in the theoretical terms of the Posterior Analytics, I shall have identified the fundamental concepts in Aristotle's theory of relations among subject-genera.

Demarcating the Genus A demonstrative science is constructed out of demonstrative syllogisms. A demonstrative syllogism, in turn, is constructed out of terms that are organized into premisses and a conclusion. The terms of the premisses are related to one another by necessity. In order to explicate the notion of necessity, Aristotle introduces three relationships between terms in a demonstrative syllogism: Demonstration, therefore, is deduction from w hat is necessary. We m ust therefore grasp what things and what sort of things demonstrations depend on. And first let us define w hat we mean by holding in every case (κατά τταντό?) and what by in itself (per se; καθ' αυτό) and what by universally (καθόλου). (APo 1.4 73a24-27; modified Revised Oxford Translation [ROT])

Necessity, then, is explicated in terms of the relations holding in every case, holding in itself, and holding universally. It is not clear from this passage whether each of these relations by itself is a sufficient condition of necessity, or whether they are sufficient only as a group. However, they appear to be arranged in order of increasing stringency and, to some extent, inclusion. We may, therefore, leave at least the holding-in-everycase relation (κατά ttovtos) safely aside, on the grounds that it is subsumed

16 Aristotle's Theory of the Unity of Science under the other forms of necessity. Our main interest lies with the in itself (or per se as I shall refer to it; καθ' αυτό) and universal (καθόλου) relation, and since the in itself I per se relation is logically prior to the universal relation, let us follow Aristotle and consider it first. In a controversial passage (1.4 73a34—bl6), Aristotle distinguishes four kinds of in itself or perse relationships, which in accordance with the recent convention I shall call per se (l)-(4).1 Three of the four describe a relation between the terms of a demonstrative syllogism, and in these three cases the terms are related by definition. Indeed, it is precisely because these per se predicates are definitionally related that they are necessary and so useful in demonstrations. In the first form (73a34-37) B is predicated per se of A, if B appears in the account that makes clear the essence or the 'what is it' of A (eu τω λόγω τω λίγουτι τ ί etm), as, for example, line is present in the definition of triangle, since triangle is a figure bounded by three straight lines. The proposition, 'triangle is linear' or 'line is predicated of triangle,' then, passes the per se test as a demonstrative premiss. In the second form (73a37-b3), B is predicated per se of A, if A is present in the account of B, as curved is predicated of line, because line appears in the definition of curved.12 In this case, the proposition 'line is curved' passes the perse test as a demonstrative premiss. A third thing (73b5-10), that which is not predicated of a substrate, is called per se, but this hardly provides us with a description of a predication at all, and so cannot be relevant to demonstrative premisses. But the fourth use of per se, that which belongs to each thing on account of itself (6t’ αυτό, 73bl0-16), clearly involves predication. Aristotle cites as an example death (άποθανεΐν) belonging per se to slaughter (σφάττΐσθαι). Accordingly, 'to be slaughtered is to die' passes the per se test as a demonstrative premiss. Though there is no small amount of controversy surrounding these relationships, we can reasonably maintain that to the extent that they are relevant to predication, all involve definitional relations. Only the fourth case is problematic in this respect, since it has sometimes been taken to refer to a causal rather than a definitional relationship. According to the causal interpretation, something dies because it is slaughtered or sacrificed.

1 This list may be compared to Met. Δ.18, which arguably covers all the four kinds of APo 1.4, For detailed discussions of these relationships, see Ferejohn 1991, 75-130, and McKirahan 1992, 80-102. 2 Aristotle later qualifies this form (1.6 74b8-10) by saying that these predicates are opposites. There is some controversy whether so restricted a relation is useful. 1 agree with McKirahan (1992, 90) that the more general formulation of 1.4 captures the important aspects of this relation.

17 Genus, Abstraction, and Commensurability But since σφάτπσθαι can simply mean 'to be killed/ and since αητοθανύν also admits of that meaning, they may be synonyms or close synonyms, and one may be implied in the definition of the other.3 Moreover, even if σφάττΐσθαι means to sacrifice, there is clearly a definitional connection between sacrificing and killing, since to sacrifice means to kill an animal dedicated to a god. In general, then, the per se relations make definitional inclusion of one term in another a necessary condition for joining those terms in a demonstrative premiss. The next and most important relation of necessity for the purposes of abstraction is the universal or καθόλου relation. The universal predicate is described as belonging in every case, per se, and qua its subject (ρ αυτό).4 As such, it includes the first two forms of necessary predication, and adds something new. Aristotle makes clear what this is by his favourite example. A triangle has interior angles equal to two right angles (2R) qua triangle, because all and only triangles have 2R. By contrast, an isosceles triangle does not have 2R qua isosceles, because other triangles also have 2R. In general, an attribute belongs qua its subject when it belongs to all and only that subject. This is an extensional condition, and such attributes are said to be coextensive or commensurate with their subjects. In addition, an attribute also belongs qua its subject when it belongs to that thing in 3 This fourth per se relation has sometimes been interpreted as providing for external cause (McKirahan 1992, 95): T he point is that in one case an event (the animal's dying) happened on account of or because of another event (the cutting of its throat) ... Since there is no suggestion that any of these events happened on account of or because of itself, what is the point of calling any of them "per se"?' McKirahan has misinterpreted the passage. Careful attention to the parallel examples in the text reveals that they are not events predicated of a single subject, but one event predicated of another, and they are not related as external cause and internal effect. Barnes 1994, 117, is succinct and correct. On my interpretation we must suppose that σφάττerSai and άττοθανιΐν are synonyms, which they certainly can be (LSJ σφάζω II.2 and 3; αποθνήσκω II, as passive of άττοκτ(ίνω). See also Goldin 1996, 1-14, for an overview of some of the problems involved in definitional inclusion. 4 Aristotle adds that καθ' αυτό and p αύτό are the same, and supplies examples (73b26-32): point and straight belong to line καθ' αυτήν (for they belong to it ή line). McKirahan 1992, 97-8, argues that the p αυτό requirement does not add the distinctive feature of universality. This feature is instead described in 73b32-3: 'something holds universally (καθόλου) whenever it is proved of a chance case and primitively.' Although Aristotle does not identify this feature with the p αύτό requirement here, they are identified at 1.5 74al2-13: 'I say a demonstration is of this primitively and as such when it is of it primitively and universally.' It is also Aristotle's practice everywhere to indicate this feature by the p expression, See Mignucci's thorough discussion (1975, 81-4), which attenuates the force of the identification. Barnes 1994, 118-19, argues briefly for the identification.

18 Aristotle's Theory of the Unity of Science virtue of the definition or the account in accordance with the subject's name (in the language of the Categories, λόγος κατά τουνομα). This is an intensional condition and provides an important restriction, since it is not identical with the extensional condition. For as Aristotle points out (1.5 7 4 al6 -l7), if there were no other kind of triangle besides isosceles, the 2R predicate would seem to belong to isosceles qua isosceles, because all and only isosceles triangles would have interior angles equal to 2R. But, in fact, it would not, since the definition of isosceles triangle includes having two sides equal, and it is not in virtue of this fact that the 2R predicate holds. The distinctive differentia of isosceles triangle is irrelevant to the predicate. That two of those sides are equal in length is not the part of the definition in virtue of which 2R holds. As a result, even if 2R, triangle, and isosceles triangle were coextensive with one another, nevertheless 2R would not belong to isosceles qua isosceles.56 So far, then, the terms of demonstrative premisses must be both per se and qua related. But as yet I have made no comment about the relation between the terms of a demonstrative conclusion. Whereas the terms of a premiss are related by definitional inclusion, the terms of a conclusion are not. For the conclusion is what is proved from the definitions of things. For example, 2R is predicated of triangle as a conclusion, but 2R is not present in the definition of triangle (APo 1.9 76a4-7; Met. Δ.30 1025a30-32). In the strict sense of definitional inclusion, then, 2R cannot be predicated per se of triangle. However, as the same 2R example makes clear, the predicate in the conclusion of a demonstration is predicated qua the subject, and so is commensurately universal with the subject.7 5 On this issue I side with Lennox 1987a and McKirahan 1992 against Ferejohn 1991 that the qua requirement has an intensional aspect. There are variations on these positions. Ferejohn (70-1; 149n9) claims that qua itself is an 'essentially extensional requirement.' While he grants that it is not always purely extensional, he claims it is in APo 1.4. He dtes as evidence the bronze isosceles triangle example, which shows that commensurate universals are the only concern. Lennox (92) claims that both per se and qua requirements are intensional. McKirahan (102) agrees, claiming that the qua requirement derives its intensionality from its connection with per se. 6 Compare a similar passage at Met. Z .ll 1036a26-b3 using as an example a bronze circle. Here the abstraction must be made between the circular form and the bronze material, rather than between two mathematical forms. 7 The examples cited by Bonitz 1961 all point in this direction. There are no cases to my knowledge in which 2R is said to be a per se accident of isosceles triangle. Met. Δ.30 1025a30-32 dtes 2R predicated of triangle as an example. APo 1.7 75a42-bl strongly suggests that the per se accidents must be within the same genus as the subject. Most clear is Met. B.2 997a21-22: 'to investigate the per se acddents of one subject-genus, starting from one set of beliefs, is the business of one science' (modified

19 Genus, Abstraction, and Commensurability We have a situation, then, in which the terms of a legitimate scientific proposition are qua related, but not per se related. Aristotle seems to recognize such a class of connections called per se accidents (καθ’ αύτά σνμβεβηκότα), which follow from strict per se premisses and belong qua the subject:8 2R IPO {per set qua) having angles around the apex of the triangle = 180° having angles around apex of triangle = 180° IPO {per se!qua) triangle 2R IPO {per se accident/qua) triangle So long as we keep the distinction between premiss and conclusion in mind, these qualifications to the theory present little difficulty. But there is another form of argument, important for analogy, called an 'application argument/ in which certain tensions arise between the per se and qua criteria.9 In such an argument a predicate can be proved to belong to the

ROT); explicitly too in the context of qua. Met. M.3 1078a5~8 (cf. PA 1.1 639al5-19). Phys. II.2 193b26-32 clearly mentions mixed sciences as dealing with per se accidents. APo 1.22 83bl9-20 comes the closest to extending the formulae to all necessary concomitants, but it is unclear, and even if it does, it seems to connect only a string of genus terms. 8 Per se accidents (καθ’ αυτά συμβφηκότα) such as 2R predicated of triangle are not under consideration in APo 1.4, where Aristotle is only concerned with immediate connections (73a24-25), which indeed must be either per se or accidental. He is not talking about conclusions, though, admittedly, 2R, which is not an immediate predicate, is discussed in this context. At Met. Δ.18 Aristotle seems to grant a per se accidental connection an unqualified per se status: a man is alive per se, because the soul is a part of the man, and in it primarily is life (1022a31-32). This example, however, is found together with a dear case of per se (2) predication. A stronger claim is made at APo II.4 91al8-21: 'if A belongs to every B in what it is (tv ™ ri t