Aristotle's Theory of the Unity of Science

MALCOLM WILSON

Aristotle's Theory of the Unity of Science

Aristotle's Theory of the Unity of Science

Aristotle was the first philosopher to provide a theory of autonomous scientific 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. MALCOLM WILSON 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 xxxvrn Tome supplementaire XXXVIII

MALCOLM WILSON

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. 2. Aristotle - Contributions in ontology. Science - Philosophy. 1. Title. II. Series: Phoenix. Supplementary volume (Toronto, Ont.) ; 38. B48SWS4 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 (BPIOP).

CONTENTS

ACKNOWLEDGMENTS ABBREVIATIONS

INTRODUCTION

vii

ix

3

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

I. Speed of Change 39 2. Value 41 3. Animal Locomotion 47 CHAPTER 2: ANALOGY IN ARISTOTLE'S BIOLOGY Problems with Analogy 53

I. Fixity of Analogy 60 2. Difficult Cases 67 3. Analogues and the More and Less 69 4. An~logues 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 Pcr 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 ?f Being 165 CHAPTER 6, MIXED USES OF ANALOGY AND FOCALITY

Matter 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

BIB L lOG RAP H Y I N D E X L 0 COR U M GENERAL

INDEX

243 255 265

175

ACKNOWLEDGMENTS

My first thanks go to my teachers at Berkeley, T any 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 encouragement 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 ma terial published in 'Anal ogy in Aristotle's Biology: Ancient Philosophy 17 (1997) .

......................------

ABBREVIA nONS

Works of Aristotle

APo APr Cat. DA DC DI EE

EN GA

GC HA IA Juv. 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 SGA WP

is predicated of species-genus-analogy 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

INTRODUCTION

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 modern scientific fields. His reasons for separating 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 desire 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. J shall contend that the isolating force of the subject-genus was so powerful that additional techniques 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, foeality, and cumulation,

of which the last three are the special concern of this book. J intend to study these techniques both at a specific and a general level. J 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 perfonn 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 funy 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 5,0 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 science. 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 71e-73a) . Likewise, in the Republic he supposed tha t 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 ambiguities 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.111138a4-b14). Similarly, Plato's universalization of virtue, which is manifested in the Republic's inclusion of women in the leadership of the state (4S1d-e), prompts Aristotle to distinguish between men's and women's tasks and therefore between their virtues (Pol. II.S 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. [n his later work, plato studied a second form of relational knowledge. [n the Sophist the Forms themselves are known through a process of division by their participation in Sameness and Difference with respect to other Forms. Here, the relations among the Fanns 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. [n order to know anything, therefore, one must know everything l 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 understanding, 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 highest 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 According to Aristotle (APo II,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· man, the less one retains of the particular kinds. And yet what a thing is spe"cifically 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 knowledge 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.' 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 I.l, where Aristotle draws the distinction between the specialized expert and the generaUy 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 J 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 demonstrative premiss, 'having wings' must appear in the definition of 'flier' or vice versa, e.g., wings are by definition the instrumental part for flying. s When

terms are so related, they are said to be per se (Ka8' aim5) or essentially related. Only essentially related terms may be joined in a demonstrative premiss, and a string of such premisses wi1l 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 Ti (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 chara([eristic fonn. 4 These issues will be discussed in greater detail in chapter 1 below. S In relating tenns within definitions Aristotle allows for some paronymy, Le., 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.' 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 I'ETa/3arJ'lS 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.' 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 connected 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· 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 related to one another through abstraction, but that nevertheless are separate and autonomous. Abstraction is a feature of Aristotle's philosophy familiar 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 (Le., 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 superordination 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, foeality, and cumulation operate. Analogy, strictly speaking, is a proportional relationship between four terms (A is to B as C is to 0), 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' 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 lO 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 obseJVation, 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.E.L. Owen (1960) first provided the current English translation of 7rpor tV A.EyOP.EVOV 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 (ov). 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 (ovcria). 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 instead 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 tenn (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 Aristotle 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.,ll 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. 12 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 thcologiac 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. l3 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 foeality, 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 autonomy 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.'

Genus, Abstraction, and Commensurability

In this chapter I shall first discuss two issues preliminary to 'semi-abstraction.' I shall begin by presenting in more detail the per se and qua relations, 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 (&'aipfCH&.(w 1I.2 and 3; a1foOzryiO'Kw II, as passive of a1fo/CTdvw). See also Goldin 1996, 1-14, for an overview of some of the problems involved in definitional inclusion. 4 Aristotle adds that /Cae' aim, and VaUTO are the same, and supplies examples (73b26-32): point and straight belong to line /Cae' airr~v (for they belong to it Vline) . McKirahan 1992, 97-8, argues that the VaUTO requirement does nOt add the distinctive feature of universality. This feature is instead described in 73b32-3: 'something holds universally (Ka80>..ov) whenever it is proved of a chance case and primitively.' Although Aristotle does not identify this feature with the Va1iro requirement here, they are identified at 1.5 74a12-13: '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 V 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, h6yo< KOro. rovvoJ.W.). This is an intensional condition and provides an imr0rtant restriction, since it is not

identical with the extensional condition. For as Aristotle points out (1.5 74al6--17), 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 yirtue of which 2R holds. As a result, even if 2R, triangle, and isosce les triangle were coextensive with one another, nevertheless 2R

would not belong to isosceles qua isosceles· So far, then, the terms of demoflstrative 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. Ll..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?

5 On this issue I side with Lennox 1987a and McKirahan 1992 against Ferejohn 1991 that the qlfa requirement has an intensional aspect. There are variations on these positions. Ferejohn (70-1; 149n9) claims that qlfa itself is an 'essentially extensional requirement: While he grants that it is not always purely extensional, he claims it is in APo IA. He cites 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.l1 1036a26-b3 using as an example a bronze circle. Here the abstraction must be made between the circular fonn and the bronze material, rather than between two mathematical fonns. 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. 6. .30 1025a30-32 cites 2R predicated of triangle as an example. APo 1.7 75a42-bl strongly suggests that the per sc accidents must be within the same genus as the subject. Most clear is Met. B .2 997a21-22: 'to investigate the per Sf accidents 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 tenns 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 (Ka8' aUTO. rrop./3