Aristotle's Theory Unity of Science

MALCOLM WILSONAristotle's Theoryof theUnity of Science

Aristotle's Theory of the Unity of ScienceAristotle was the first philosopher to provide a theory of autonomous scientificdisciplines and the systematic connections between those disciplines.This book presents the first comprehensive treatment of these systematicconnections: analogy, focality, and cumulation.Wilson appeals to these systematic connections in order to reconcileAristotle's narrow theory of the subject-genus (described in the PosteriorAnalytics in terms of essential definitional connections among terms) withthe more expansive conception found in Aristotle's scientific practice. Theseconnections, all variations on the notion of abstraction, allow for the moreexpansive subject-genus, and in turn are based on concepts fundamental tothe Posterior Analytics. Wilson thus treats the connections in their relationto Aristotle's theory of science and shows how they arise from his doctrineof abstraction. The effect of the argument is to place the connections, whichare traditionally viewed as marginal, at the centre of Aristotle's theory ofscience.The scholarly work of the last decade has argued that the PosteriorAnalytics is essential for an understanding of Aristotle's scientific practice.Wilson's book, while grounded in this research, extends its discoveries tothe problems of the conditions for the unity of scientific disciplines.MALCOLM WILSON is an assistant professor in the Classics Departmentat the University of Oregon.

PHOENIXJournal of the Classical Association of CanadaRevue de la Societe canadienne des etudes classiquesSupplementary Volume xxxvrnTome supplementaire XXXVIII

MALCOLM WILSONAristotle's Theory ofthe Unity of ScienceUNIVERSITY OF TORONTO PRESSToronto Buffalo London

@ University of Toronto Press Incorporated 2000Toronto Buffalo LondonPrinted in CanadaISBN 0-8020-4796-3Printed on acid-free paperCanadian Cataloguing in Publication DataWilson, Malcolm CameronAristotle's theory of the unity of science(Phoenix. Supplementary volume ; 38 = Phoenix. Tome supplementaire,ISSN 0079-1784; 38)Includes bibliographical references and index.ISBN 0-8020-4796-31. Aristotle - Contributions in methodology.2. Aristotle - Contributions in ontology.Science - Philosophy. 1. Title.II. Series: Phoenix. Supplementary volume (Toronto, Ont.) ; 38.B48SWS4 2000 185 C99-932973-1University of Toronto Press acknowledges the financial assistance to its publishingprogram of the Canada Council for the Arts and the Ontario Arts Council.University of Toronto Press acknowledges the financial support for its publishingactivities of the Government of Canada through the Book PublishingIndustry Development Program (BPIOP).

CONTENTSACKNOWLEDGMENTS viiABBREVIATIONS ixINTRODUCTION 3CHAPTER 1: GENUS, ABSTRACTION, ANDCOMMENSURABILITY 14Demarcating the Genus 15Abstraction 29I. Speed of Change 392. Value 413. Animal Locomotion 47CHAPTER 2: ANALOGY IN ARISTOTLE'S BIOLOGY 53Problems with Analogy 53I. Fixity of Analogy 602. Difficult Cases 673. Analogues and the More and Less 694. An~logues and Position 695. Analogy of Function 726. Genus as Matter 74A Solution 77A Challenging Case 83Analogy and Abstraction 86

vi ContentsCHAPTER 3, ANALOGY AND DEMONSTRATION 89Analogy in APo; Passages and Discussion 91Analogy in the Biology 99Analogy and the Scala Naturae 109CHAPTER 4, THE STRUCTURE OF FOCALITY 116Focality and Pcr Se Predication 122The Limits of Focality in the Biological Works 129CHAPTER 5, METAPHYSICAL FOCALITY 134The Genus of Being 136Categorial Focality in Metaphysics Z 144Demonstration in the Science of Being 158The Wider Focal Science ?f Being 165CHAPTER 6, MIXED USES OF ANALOGY AND FOCALITY 175Matter and Potentiality 177The Good 194CHAPTER 7, CUMULATION 207Souls 2081. The Analogical Account 2102. The Cumulative Account 214Friendship 2241. Eudemian Ethics and the Problems of Focal Friendship 2252. The Nicomachean Version 231The Place of Theology in the Science of Being 235Conclusion: Analogy, Focality, and Cumulation 239BIB L lOG RAP H Y 243I N D E X L 0 COR U M 255GENERAL INDEX 265

ABBREVIA nONSWorks of AristotleAPoAPrCat.DADCDIEEENGAGCHAIAJuv.Long.MAMet.Mete.MMPAPhys.PNPol.Resp.SESens.Somn.Top.Posterior AnalyticsPrior AnalyticsCategoriesde Animade Caelode InterpretationeEudemian EthicsNicomachean EthicsGeneration of AnimalsGeneration and CorruptionHistory of AnimalsProgression of AnimalsOn Youth, Old Age, Life and DeathOn Length and Shortness of LifeMovement of AnimalsMetaphysicsMeteorologicaMagna MoraliaParts of AnimalsPhysicsParva NaturaliaPoliticsRespirationSophistical RefutationsSense and Sensibiliade SomnoTopics

x AbbreviationsOther WorksLSj H.G. Liddell and R. Scott. A Greek-English Lexicon. Revised andaugmented by H. jones. Oxford: Clarendon Press, 1996.ROT j. Barnes. The Complete Works of Aristotle. The Revised OxfordTranslation (Bollingen Series LXXI.2). Princeton: Princeton UniversityPress, 1984.Acronyms and Summary of Per Se RelationsIPOSGAWPis predicated ofspecies-genus-analogywholes-partsper se (1) predicate: is contained in the definition of its subject, e.g., linearis predicated of triangle.per se (2) predicate: contains its subject in its definition, e.g., female ispredicated 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

INTRODUCTIONAristotle is renowned for having been the first to create autonomoussciences and independent disciplines. By distinguishing physics, politicalscience, and many other areas of study, he circumscribed and identifiedsome of the most important modern scientific fields. His reasons for separatingsuch sciences and their subject matters were not the social andpractical reasons familiar today. He did not worry about the limitations ofthe individual human mind faced with the explosive growth of knowledgeand the consequent drive towards ever-increasing specialization . Quite thecontrary, he thought humans were naturally capable of fulfilling their desirefor understanding and he did not view the sheer amount of knowledgeas an impediment to this end. His concern lay instead with the form thatthat understanding takes. He denied that all of our knowledge falls into asingle undifferentiated domain, a single universal science, and he developeda solution, the subject-genus, which served to separate and isolate eachsubject matter.But his solution created problems of its own. J shall contend that theisolating force of the subject-genus was so powerful that additional techniqueswere required to provide for the legitimate causal and explanatorylinks between sciences and subject-genera. To effect the happy compromisebetween universal science and genus-isolation, Aristotle developed fourtechniques 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 specificpassages in which he explicitly puts these techniques to work are amongthe most controversial in the Aristotelian corpus. They concern such fundamentalquestions as the unity of the science of Being and metaphysics,

4 Aristotle's Theory of the Unity of Sciencethe definition of the soul, the organization and nature of goods, and thekinds of friendship. In treating each technique in turn and with an eyeto the larger picture, I shall offer new interpretations of specific areas ofAristotelian philosophy.At a more general level, I gather these techniques together and providea single comprehensive theory for them. This theory arises out of myreflections on recent developments in Aristotelian scholarship. One of themost important trends of the last several decades has been the realizationthat Aristotle's theory of science contained in the Posterior Analytics isnot an abstract ideal without practical application, but in fact is used inimportant ways in the special sciences, especially in the biological works.Many of the basic concepts of Aristotle's formal scientific methodology, likedemonstration and definition, have been found to inform the practice andpresentation of specific sciences. This research has been very fruitfuL butit has focused primarily on the single isolated genus. There is good reasonfor this focus. While the APo does discuss the subordination technique atsome length, it only briefly notes analogy and never mentions focality orcumulation at all. And yet these are important organizational tools in theseveral sciences. In view of the success in applying the APo's single-genustheory to Aristotle's scientific practice, I want to reverse the hermeneuticprocess, as it were, and ask whether the widespread use of analogy, focality,and cumulation in the special sciences can be given any theoretical accountwithin the terms of the APo. I believe that this is possible, and shall adduceevidence and argument to show that Aristotle had the APo in mind whenhe formulated these techniques. I shall also argue that this fact yieldsimportant results. Not only do we obtain a theoretical account of thesetechniques, but we also discover that, far from being a random assortmentof tools of various vintages scattered haphazardly throughout the corpus,they perfonn interlocking and complementary functions. Moreover, theyare all logical developments of the most important concepts in the APo, perse and qua predication. This fact both confirms our belief in the relevanceof the APo for these techniques and also allows us to provide a general andunified account of them, for they are variations on a Single logical theme.Finally, by describing these techniques in terms of the central concepts ofthe APo, we can provide a richer and more powerful account of Aristotle'stheory of science, one that is more funy integrated into all aspects of hisscientific practice.Such an interpretation is founded on an assumption hermeneuticallyconfirmed that Aristotle's philosophy forms a basically consistent unity,and that there are few radical changes in his views. The unsuccessfulattempts of this century to impose a chronology on Aristotle similar to

5 Introductionthe one that 5,0 successfully applies to Plato lead me to view the historicalquestion as less interesting than the philosophical question concerningthe logical organization of concepts. It would be absurd to deny that. any philosopher underwent intellectual ' development, but I am inclinedto believe that Aristotle's development is more like the articulation ofbasic ideas than the repeated creation and destruction of whole systems ofthought.The story begins with Aristotle's objections to a single universal science.These objections arose out of the historical context of debates withhis older contemporaries Plato and Speusippus, heads of the Academy. Itwas a common supposition of ancient Greek epistemology that we knowsomething when we know how it is related to other things we know. Thisrelational view of knowledge manifests itself in two patterns. First, Platoheld that we know the particulars best (to the extent that we actually canknow them) when we understand how they imitate the Forms, and sincewe understand the particular in virtue of the universaL Plato exalted theForm or universal and depreciated the sensible particulars. Since we ·canunderstand only what is common and universal among the particulars, thevariations among them are relegated to the shadowy realm of opinion.With the quip that Meno was providing a whole swarm of virtues, Plato'sSocrates compelled him to avoid examples, like manly virtue and womanlyvirtue, and state instead the single definition of virtue that covers all thesecases. For virtue, Socrates claimed, must be the same whether it is presentin a man or a woman (Meno 71e-73a). Likewise, in the Republic he supposedthat justice will have the same nature wherever it is found, and as aresult, 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 genuineambiguities in terms. For Aristotle, detecting and disarming these ambiguitiesbecame something of a philosophical obsession. He faults Plato onthe 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, whichis manifested in the Republic's inclusion of women in the leadership ofthe state (4S1d-e), prompts Aristotle to distinguish between men's andwomen's tasks and therefore between their virtues (Pol. II.S 1264b4-6). ForPlato, then, the possession of any common characteristic among particularswas a sufficient condition for positing a Form and universal, and as aresult he failed to detect other more subtle relationships. The preferencefor the universal over the particular is recapitulated in the preference forthe more general Form over more specific Forms, as is clear in the example

7 IntroductionAristotle was also concerned about the epistemological etiolation thatattends increasing universalization. The more one grasps at what is com·man, the less one retains of the particular kinds. And yet what a thing isspe"cifically is as much a part of its Being as what it is at a high level ofgeneralization. For being biped is as much, if not more, part of the Beingof a man as being a substantial unity, the actuality of a potentiality. This isnot to say that Aristotle rejected general understanding altogether, but hedid not think that we know something solely in virtue of its membershipin a genus. Nor did he believe that the genus always provides the causeand explanation for a thing. He preferred instead the constitutive elementand the various kinds of cause as explanatory principles, and in his theoryof 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 knowledgeforms a single science. He made the observation - hardly originalconSidering Socrates' frequent appeal to it - that there were experts whounderstood their own field but not others. It was clearly not necessaryto know everything in order to have expertise in a single field.' Nor wasit necessary to know the most general science. Plato, for his part, hadbeen scandalized that the mathematicians simply accepted the principles oftheir science without investigating its foundations. He supposed that theirhypothetical principles could be perfected by an unhypothetical science,philosophical dialectic, which would remedy the deficiency of mathematicsand indeed all hypothetical sciences. Only the philosopher, then, couldlegitimately lay claim to true knowledge of the special sciences. Aristotle,though he recognized a first philosophy that examined the first principlesof the special sciences, thought it right and proper that the special sciencesshould merely presuppose and not examine their own first principles.Accordingly, Aristotle sought to redress the imbalance apparent in theAcademic prejudice towards the universal. He attended more equally toboth the specific and the general levels of inquiry and studied the causes ofthings in addition to their similarities and differences. These new concernsfound logical expression in his theory of scientific understanding, whosefoundation is the demonstrative syllogism. A syllogism is composed of atleast three terms, a major (e.g., having wings), a middle (e.g., fliers), anda 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 andthe generaUy educated layman. Also Balme 1972, 70, on the connection with Plato andSpeusippus.

8 Aristotle's Theory of the Unity of Sciencehaving wings is predicated of (henceforth, IPO) fliersfliers IPO birdstherefore, having wings IPO birds JIn order for a syllogism to be demonstrative, the relationship between theterms of its premisses (e.g., 'having wings' and 'fliers') must be necessary.4This necessity is understood in terms of essential, definitional relationships:in order for 'having wings' and 'fliers' to be terms in the same demonstrativepremiss, 'having wings' must appear in the definition of 'flier' or viceversa, e.g., wings are by definition the instrumental part for flying. s Whenterms are so related, they are said to be per se (Ka8' aim5) or essentiallyrelated. Only essentially related terms may be joined in a demonstrativepremiss, and a string of such premisses wi1l form a string of essentialrelations. Terms that are not essentially related are said to be accidentallyrelated, and cannot be connected in a demonstrative premiss.In addition to this per se requirement Aristotle introduces the rule thatterms in a demonstrative syllogism must be proved of the subject as suchand universally, indicating this criterion by the use of the relative pronounTi (qua). The effect of this requirement is to restrict further the termsadmissible to a demonstration and therefore to a science. A triangle, forexample, can be demonstrated as having interior angles equal to two rightangles (following the custom, I shall call this the 2R theorem), because itpossesses this property as or qua triangle. By contrast, a demonstration thatproves this attribute of isosceles triangle is defective because the propertydoes not belong to isosceles triangle qua isosceles, but qua triangle. Sucha proof is said to be an accidental proof, because 2R does not belong toisosceles triangle qua isosceles. The term 2R, then, belongs in the scienceof triangle and not in the science of isosceles triangle.These two restrictions on the admission of terms to a demonstrationconstitute the identity conditions of a science and provide the foundationsfor the autonomy of disciplines. Since not all terms are per se related toone another, and since they are different in their qua designations, they3 This syllogism is frequently presented differently by modem commentators:birds are fliersfliers have wingsbirds have wings.This is not, however, Aristotle's presentation, and it will be most convenient for ourpurposes 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 forflier.

9 Introductioncannot all be included in one universal science. Each science has a subject ora subject-genus. This is what the science is about and the subject of whichthe predicates are predicated. A science is the sum of the demonstrativesyllogisms that concern the same subject.' The subject of the science isindicated by the qua expression, and the per se criterion for includingother terms in a science implies that each science is autonomous and hasits own and unique set of principles.When these restrictions are violated, when there is an attempt tointroduce a term that is not per se and qua related to the other termsinto a demonstrative syllogism, the result is an error, which Aristotle callsI'ETa/3arJ'lS or kind-crossing, and this will destroy the demonstrative powerof the syllogism and the cogency of the science.In contrast to Plato's and Speusippus' universalizing and inclusivetendencies, Aristotle's theory of demonstration is a powerfully isolatingforce. The qua requirement especially entails that understanding occurswithin a single subject-genus, and not in relation to other genera throughan analysis of sameness and difference.' Each science will be specializedand isolated from every other except by incidental connections, and therewill be no communication between disciplines. Each subject-genus, boundby necessity solely to its own principles and predicates, will form an islandin the sea of Being. The view of the world that this theory of sciencerepresents will be that of a heap of subjects, in which one genus is onlyincidentally related to another.It is clear, however, that Aristotle never advocated such a degree ofisolation. In fact there are a multitude of ways in which sciences are connectedwith one another and share principles. The axioms, like the principleof non-contradiction, are common to all sciences, and are the preconditionfor any understanding at all. More elaborately developed within the APois the connection between a more abstract, superordinate science and a lessabstract, subordinate science. A superordinate science, usually a branch ofmathematics, supplies principles and explanations for a fact or conclusionfound in a distinct and subordinate natural science, for instance, harmonicsor optics. Since this technique and its place in the APo has been well studied6 I am deliberate in avoiding the claim that a science is the sum of demonstrations whichhave 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 apreliminary role in establishing the extent of the subject-genera and the attributes thatare coextensive with them. It is not the primary form of understanding. See Ferejohn1991, who places division in the 'framing' or pre-demonstrative stage of science. Seealso chapter 2 below.

10 Aristotle's Theory of the Unity of Scienceby the secondary literature, I shall not treat it in the same depth as the threeother techniques· It will proVide, however, a useful stepping-stone to thosetechniques. In the first chapter of this book I shall begin by laying out inmore detail the conditions for a unified subject-genus and what makes twosubject-genera different. I shall then consider subject-genera that are relatedto one another through abstraction, but that nevertheless are separateand autonomous. Abstraction is a feature of Aristotle's philosophy familiarfrom his theory of mathematics. According to Aristotle, mathematicalobjects are ontologically dependent on their physical substrate, but can bementally abstracted from that substrate so that they maintain absolutelyno conceptual connections (Le., per se relations) to it. Mathematics andphysics, then, are a pair of subject-genera related by pure abstraction. Ishall argue that abstraction has a much broader application than merelyto mathematics and, more importantly, that there are several degrees ofabstractability, depending on the nature of the subject matter. I shall focuson several pairs of subject-genera in which the conceptual abstraction is notabsolute, cases in which there are per se relations between the abstractedgenus and its substrate. I call this situation 'semi-abstraction.' The superordinationtechnique will proVide us with the first step along this road.It is precisely in the realm of abstraction and semi-abstraction, in whichtwo subject-genera can be treated as autonomous and yet maintain per seconnections to one another, that analogy, foeality, and cumulation operate.Analogy, strictly speaking, is a proportional relationship between fourterms (A is to B as C is to 0), that expresses a common relation betweeneach of the two pairs. The formal structure of the relationship does notdictate the content, and an analogy can express any commonality from anexuberant metaphor of poetry to a trivial numerical identity. Nevertheless,I argue that Aristotle has a more specific function in mind for analogy, oneclosely related to demonstration. Analogy arises between subject-genera.Where genera are different, their qua designations are different, and thereare no per se connections between them. As a result they cannot be treatedby a common science. In the face of the injunction against metabasis orkind-crossing, analogy provides us with the means of treating subjectsthat are generically different in a parallel way. In the Parts of Animals, forexample, Aristotle discusses the analogous parts, wing and fin. These partsare predicated respectively of bird and fish in virtue of the final causesor functions, flying and swimming. Bird, wing, and flying have obviousuniversal and per se connections; so also do fish, fin, and swimming. We8 See e.g., Lear 1982, McKirahan 1978, CartWright and Mendell 1984, and Lennox 1986.

11 Introductioncan prove that wing is predicated of bird by using the proper principlesof the subject genus, bird; similarly with the fish's fin' In spite of theindependence and autonomy of the demonstrations, there is a parallel inthe proofs, an analogical identity of relation: as wing is to bird, so fin is tofish. This identity, however, cannot be abstracted from, and must always beper 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 thequa level at which the attributes and causes are treated. At the same time,behind the generic difference there is the intimation of a more abstractsubject-genus to which both bird and fish are related. This subject-genusarises from the fact that flying and swimming are forms of locomotion,and that wing and fin are instrumental parts of locomotion. The secondand third chapters of this book will be devoted to explaining how analogyfacilitates this limited degree of unity among different scientific subjects.The second object of our investigation, the focal relationship, is amethod for drawing together in a single subject matter objects that areof different genera lO According to Aristotle's favourite example, the term'medical' applies to many different kinds of objects. For instance, we callan operation medical, a doctor medical, a scalpel medical, not because theypossess the same attribute, medical, but because they are all related to thething that is called medical in the primary sense, the medical art. The othermedical 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. Thedefinitions of these derivatively medical things contain in themselves theprimary term or its definition. Chapter 4 will be devoted to analysing thefocal relationship in terms of -Aristotle's theory of science and showingthat medical is predicated of the derivative medical things in virtue of avariety of per se relations. Although all the medical objects do not form asingle genus, in the sense that they are not of the same kind or similar toone another, the definitional relations among them show how they forma genus in another important sense of the term, objects related by per seconnections to a single subject-genus.9 This is Aristotle's standard pattern of demonstration in the PA . We perceive that a birdhas wings from obseJVation, but to know in the fullest sense we must know why, andthis knowledge comes from relating the cause to the fact in a demonstration. We cannotprove that a bird has wings from observation, because only demonstration providesproof.10 G.E.L. Owen (1960) first provided the current English translation of 7rpor tV A.EyOP.EVOVas 'focal meaning.' It is also known as 'relational equivocity.' Most recently Shields1999 has called this (as well as cumulation) 'core dependent homonymy.'

12 Aristotle's Theory of the Unity of ScienceThe most important ·consequence of this interpretation of the focalrelationship in terms of the APo theory is a reassessment of Aristotle'sfamous application of focality, the science of Being (ov). This will be thetask of chapter 5. Though they do not form a single genus, Beings canbe treated under a single science because they are all per se related to asingle primary term, substance (ovcria). The focal relation has traditionallybeen treated as a very special case, found only in exceptionally difficultcircumstances like the science of Being. But the fact that the focal relationis basically a per se relation suggests that focality should be viewed insteadas a simple application of the logical and causal relations of normalAristotelian demonstrative science. The terms (subjects, attributes, causes)of demonstrative premisses are bound together by necessary, definitionalrelations, whereby one tenn (or its definition) is included in the definitionof another. This is the structure of any ordinary Aristotelian science, andthe binding relations found in ordinary or normal science are of the samekind 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 Aristotletreats both analogically and focally. These cases have a long historyof controversy. Aquinas, for example, made analogy invariably into arelation between prior and posterior, assimilating it to focal and serialschemes, which he called 'analogy of attribution.,ll More recently, G.E.L.Owen sharply distinguished analogy and focality and tried to set them ina chronological sequence within Aristotle's philosophical development. 12Neither, however, studied analogy and focality in terms of per se relationsand demonstrative science. And though Owen was right to reject the termsof Aquinas's assimilation of the techniques, there are other and deeperstructural connections that have escaped the notice both of Aquinas andthe moderns. In this chapter I shall argue that, far from being independentor even incompatible means for the unification of a subject-genus, focalityis logically prior to analogy and a necessary precondition for it.Analogy and focality are two basic ways in which Aristotle treatsdifferent genera in conjunction with one another. But there is another11 Summa thcologiac 1.13.6c: 'In the case of all names which are predicated analogously ofseveral things, it is necessary that all be predicated with respect to one, and thereforethat that one be placed in the definition of all. Because "the intelligibility which a namemeans is its definition," as is said in the fourth book of the Metaphysics, a name mustbe antecedently predicated of that which is put in the definitions of the others, andconsequently of the others, according to the order in which they approach, more orless, that first analogate.' For passages and discussion see Klubertanz 1960, 68-9.12 Owen 1960.

13 Introductionimportant means that employs elements of focality and analogy to createa series of similar objects. I call this method 'cumulation,' and it will bethe subject of the final chapter. l3 It is a special form of a series, which isarranged in order of priority and posteriority, and is used in Aristotle'sdiscussions of souls and friendships. It is also important for determiningthe place of theology within metaphysics. The prior members of the seriesare logically and ontologically contained in the posterior members, as forexample the nutritive soul is contained in the sensitive soul. The lattercannot exist without the former, and the latter contains the former in itsdefinition potentially. Members of cumulative series do not form standardgenera, but they all share some essential attributes with one another, asanalogues do; they are also per se related among themselves, since thedefinition of a later member contains the definition of a prior member, justas focally related objects do. In spite of the features of cumulation that arecommon with foeality, cumulative objects cannot form a focal genus. Thereasons for this will emerge in my interpretation of the soul series. Thechapter will be filled out with an examination of Aristotle's two discussionsof friendship and an argument that he abandoned the focal analysis offriendship he provided in the Eudemian Ethics for a cumulative view inthe Nicomachean Ethics because of the intractible difficulties in applyingfocality in this context. Finally, I shall use the lesson of cumulation andfocality to shed light on the problem of the place of theology in the scienceof Being.Together, analogy, focality, and cumulation provide Aristotle with themeans to balance the claims of the universal science advocated by theAcademy and the isolation of the subject-genera, which arises within thelogic of his own theory of science. This solution, by preserving the autonomyof sciences without creating a chaotic heap of subject matters, allowseach subject to be treated separately while still maintaining its place in theintelligible architecture of the world.13 Grice 1988, 190--2, has called this 'recursive unification.'

Genus, Abstraction,and CommensurabilityIn 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-genusdistinct from other subject-genera. Aristotle illustrates these relations bythe familiar 2R example and the proof for alternating proportionality. Inboth cases the per se and qua relations provide an adequate set of criteriafor identifying and demarcating subject-genera. Next, I shall introduceabstraction (&'aipfCH

15 Genus, Abstraction, and CommensurabilityThere are different degrees of semi-abstraction. By enlisting commensurabilityas a sign of generic unity (i.e., objects in the same genus can becompared directly with one another, while objects from different generacannot) I shall examine abstraction and resistance to abstraction in severalgraduated cases. While mathematicals can easily be abstracted from theirphysical substrate and be compared as quantities, some other objects resistabstraction to a greater or lesser extent. I shall consider three such objects . .First, kinds of change cannot be abstracted from their substrate and cannotbe compared one with another. Next, the exchange value of manufacturedgoods can be abstracted from the proper function of the goods sufficientlyto allow commensuration for the purpose of exchange and trade. Finally,causes of animal locomotion can be abstracted from the instrumental partsof locomotion to the extent that at the upper reaches of abstraction thereremain no per se connections with the specific -instruments. But eachlevel of abstraction from the pans allows for commensuration within thatlevel. By establishing the possibility of semi-abstraction and degrees ofabstractability and by describing them in the theoretical terms of thePosterior Analytics, I shall have identified the fundamental concepts inAristotle's theory of relations among subject-genera.Demarcating the GenusA demonstrative science is constructed out of demonstrative syllogisms.A demonstrative syllogism, in turn, is constructed out of terms that areorganized into premisses and a conclusion. The terms of the premissesare related to one another by necessity. In order to explicate the notionof necessity, Aristotle introduces three relationships between terms in ademonstrative syllogism:Demonstration, therefore, is deduction from what is necessary. We must thereforegrasp what things and what sort of things demonstrations depend 00. And first letus define what we mean by holding in every case (Kanl 7TaVn:lS') and what by initself (peT se; Ka8' a;'To) and what by universally (Ka80Aov) . (APo 1.4 73.24-27;modified Revised Oxford Translation [ROT])Necessity, then, is explicated in terms of the relations holding in everycase, holding in itself, and holding universally. It is not clear from thispassage whether each of these relations by itself is a sufficient conditionof necessity, or whether they are sufficient only as a group. However,they appear to be arranged in order of increasing stringency and, to someextent, inclusion. We may, therefore, leave at least the holding-in-everycaserelation (KarCz. 1TavTo~) safely aside, on the grounds that it is subsumed

16 Aristotle's Theory of the Unity of Scienceunder the other forms of necessity. OUf main interest lies with the in itself(or per se as I shall refer to it;

17 Genus, Abstraction, and CommensurabilityBut since ()(p(hUCTea~ can simply mean 'to be killed,' and since a:7To8av€lValso admits of that meaning, they may be synonyms or close synonyms,and one may be implied in the definition of the other. 3 Moreover, evenif 0"

18 Aristotle's Theory of the Unity of Sciencevirtue of the definition or the account in accordance with the subject'sname (in the language of the Categories, h6yo< KOro. rovvoJ.W.). This is anintensional condition and provides an imr0rtant restriction, since it is notidentical with the extensional condition. For as Aristotle points out (1.574al6--17), if there were no other kind of triangle besides isosceles, the2R predicate would seem to belong to isosceles qua isosceles, because alland only isosceles triangles would have interior angles equal to 2R. But, infact, it would not, since the definition of isosceles triangle includes havingtwo sides equal, and it is not in virtue of this fact that the 2R predicateholds. The distinctive differentia of isosceles triangle is irrelevant to thepredicate. That two of those sides are equal in length is not the part of thedefinition in yirtue of which 2R holds. As a result, even if 2R, triangle,and isosceles triangle were coextensive with one another, nevertheless 2Rwould not belong to isosceles qua isosceles·So far, then, the terms of demoflstrative premisses must be both perse and qua related. But as yet I have made no comment about the relationbetween the terms of a demonstrative conclusion. Whereas the terms of apremiss are related by definitional inclusion, the terms of a conclusionare not. For the conclusion is what is proved from the definitions ofthings. For example, 2R is predicated of triangle as a conclusion, but 2Ris not present in the definition of triangle (APo 1.9 76a4-7; Met. Ll..301025a30-32). In the strict sense of definitional inclusion, then, 2R cannotbe predicated per se of triangle. However, as the same 2R example makesclear, the predicate in the conclusion of a demonstration is predicatedqua the subject, and so is commensurately universal with the subject?5 On this issue I side with Lennox 1987a and McKirahan 1992 against Ferejohn 1991that the qlfa requirement has an intensional aspect. There are variations on thesepositions. Ferejohn (70-1; 149n9) claims that qlfa itself is an 'essentially extensionalrequirement: While he grants that it is not always purely extensional, he claims it isin APo IA. He cites as evidence the bronze isosceles triangle example, which shows thatcommensurate universals are the only concern. Lennox (92) claims that both per seand qua requirements are intensional. McKirahan (102) agrees, claiming that the quarequirement 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 bronzecircle. Here the abstraction must be made between the circular fonn and the bronzematerial, rather than between two mathematical fonns.7 The examples cited by Bonitz 1961 all point in this direction. There are no cases tomy 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-blstrongly suggests that the per sc accidents must be within the same genus as thesubject. Most clear is Met. B.2 997a21-22: 'to investigate the per Sf accidents of onesubject-genus, starting from one set of beliefs, is the business of one science' (modified

19 Genus, Abstraction, and CommensurabilityWe have a situation, then, in which the tenns of a legitimate scientificproposition are qua related, but not per se related. Aristotle seems torecognize such a class of connections called per se accidents (Ka8' aUTO.rrop./3

20 Aristotle's Theory of the Unity of Sciencesubject through per se premisses, although it does not belong qua thesubject:2R IPO (per se I qua) having angles around apex of the triangle ~ 180"having angles around apex of triangle ~ 180" IPO (per sel qua) triangletriangle IPO (per se) isosceles triangle2R IPO isosceles triangleThe peculiarity of this demonstration lies in its third premiss. Triangle ispredicated of isosceles triangle by the per se (1) connection, since triangleis present in the definition of the isosceles triangle. Indeed, in general, theper se (1) connection admits predicates that extend further than the subject,for example, the genus of the subject. And since other predicates, like theessence and properties of the genus, belong to the genus per se and quathe genus, these also can be proved to belong to its species in the samemanner as the example above. 2R clearly belongs necessarily to isoscelestriangle in the sense that all isosceles triangles have 2R, but it does notbelong to isosceles qua isosceles. Such proofs apply wherever there areinvariably concomitant features of a subject whether coextensive or not.Now, Aristotle did not seem to have a name for these kinds of predication.He clearly denies that they are predicates of the subject qua the subject.Nor can they be per se predications in the strict sense, since per se isan immediate definitional relationship. We might, therefore, characterizethem as non-coextensive (non-qua) perse accidents. lO As we shall see, theyform an important class of predication in the context of abstraction.A demonstrative science is constructed out of demonstrative syllogisms,and the terms of a demonstrative syllogism are per se and qua relatedin the manner described above. When the terms of the science are sorelated, the science is unified with respect to its genus or subject-genus. llThe subject-genus is the underlying subject matter of a demonstration,that which is identified by the qua expression. It is the subject of whichthe attributes are proved (APo 1.7 7Sa39- b2), the minor term of thedemonstrative syllogism. But it may also be extended to include all thosepredicates that are immediately predicable of the subject matter per se anduniversally, and ultimately to all those predicates that can be proved ofthe subject qua what it is through immediate premisses, since, as Aristotle10 Cf. Met. ~.2 1014al-3, where Aristotle says that classes that include (711 7r~Pt£XOV1'o. ) theaccidental causes are causes, e.g., animal is the cause of the sta tue, because Polyditus isa man, and man is an animal.11 For an excellent discussion of the significance of the genus, see McKirahan 1992, 50--63.

21 Genus, Abstraction, and Commensurabilitysays, 'it is necessary for the extreme and the middle terms to come fromthe same genus' (APo I.7 7SblO-ll). Aristotle explains in more detail·howthe identity of a science is determined by the genus:A science (f7TLUT~,U:1J) is one if it is of one genus (EVO~ yivov!O) - of whatever thingsare composed from the primitives and are parts or attributes of these in themselves(.!Cae' aimi). One science is different from another if their principles depend neitheron the same things nor the ones on the others. There is evidence for this whenone comes to the non-demonstrables; for these must be in the same genus as thethings demonstrated. And there is evidence for this when the things that are provedthrough them are in the same genus and of a kind. (APo 1.28)It is an important point made clear in this passage that this sense of 'genus/the identity condition of a science, is not the same as the sense in which agroup is divided into species by differentiae. This' genus' includes a subject,its principles, its parts, and its attributes. Many of these will not be in thesame divisionary genus, and will not even be in the same category as thesubject itself. Whereas members of a divisionary genus like animal are allsimilar and share some characteristics, members of a scientific genus arerelated to one another by per se relations. 12The terms of a single science, then, all belong in the same genus,because they are related per se and qua the subject. Conversely, terms thatare not related per se and qua the subject do not belong in the genus.What is not related per se is incidental (APo 1.4 73b4-S), and since it isimpossible to demonstrate anything with incidental premisses, one can onlydemonstrate with terms from the same genus. Each thing must be provedfrom its own principles (A Po 1.9 7Sb37-38), and the principles used mustbe coextensive with the subject. Aristotle repeatedly warns about breakingthis rule: what is proved must not be proved of a subject narrower inextension than the predicate:One cannot, therefore, prove anything by crossing from another genus (E~ aAAOVyivovS' flETaj3a.vTa) - e.g. something geometrical by arithmetic ... For this reasonone cannot prove by geometry that there is a single science of opposites, nor even12 For further comments, see McKirahan 1992, 61-2. The senses of the tenn are hardlyexclusive, and as Andrew Coles has pointed out to me they are central to two momentsof a single inquiry. The first, the divisionary moment in which subjects are connectedwith attributes at various levels of generality, requires that a genus be divisible intospecies. After this stage each level becomes a genus-subject of demonstration. Seeespecially Lennox 1987a.

22 Aristotle's Theory of the Unity of Sciencethat two cubes make a cube, nor can one prove by any other science the theoremsof a different one, except such as are related to one another that the one is underthe other - e.g. optics to geometry and harmonics to arithmetic. Nor can one proveby geometry anything that belongs to lines not as lines and as from their properprinciples - e.g. whether the straight line is the most beautiful of lines or whetherit is contrarily related to the circumference; for that belongs to them not as theirproper genus but as something common. (APa 1.7 75a38-39; 75b12-20)Aristotle calls this error metabasis. Further elucidation of the probleminvolved comes later:Since it is evident that one cannot demonstrate anything except from its ownprinciples if what is being proved belongs to it as that thing, understanding is notthis - if a thing is proved from what is true and non-demonstrable and immediate.(For one can conduct a proof in this way - as Bryson proved the squaring of thecircle.) For such arguments prove in virtue of a common feature which will alsobelong to something else; that is why the arguments also apply (i.cpapiJ.OTTOvUW)to other things not of the same kind. So you do not understand it as that thingbut accidentally. (APa 1.9 75b37-76a2)13Again, if we use a general proof for a specific subject and suppose thatwe are proving the attribute of that subject as such, we commit metabasisand prove the attribute only inCidentally. The per se and qua requirementsfor predicates demand that attributes and proofs be adapted to their appropriategenus (icpap!lOTTEW hr' TO YEVO,) and not cross to another kind(y.,m/3aiv,w Ei, ail.il.o yEVO,). It is clear from the examples Aristotle providesthat, practically speaking, metabasis does not usually occur betweenunrelated genera, since it is unlikely that we would look for principlesamong irrelevant objects. Instead the danger of metabasis is most acutebetween closely related genera, like a sub-group and a more extensivegenus (e.g., straight lines and beautiful things). Although they are closelyrelated, the sub-group forms a different genus from that of the larger13 There is a long-standing difficulty with the case of Bryson. Heath (1949, 47-50)discusses the possibilities and despairs of a solution. More recently, Mueller 1982supports Proclus' interpretation that Aristotle's objection stems from Bryson's notproviding a constructive proof to correspond to the intuition that the circle has thesame area as a certain polygon intermediate between the i.nscribed and circumscribedpolygons. In short, Bryson moved from premisses to conclusion without using theimmediate premisses. But it is not clear on this explanation how Bryson then is provingin virtue of a common feature. Mueller admits that this is a weakness in Prod us'interpretation (160-4).

23 Genus, Abstraction, and Commensurabilitygroup. The suh-group may be a species of the more extensive genus, asisosceles is a species of triangle, or it may not, as straight lines are beautifulthings, but are not species of beauty. In either case the genera must bekept separate, and metabasis is forbidden.This is not to say that we cannot prove that straight lines are the mostbeautiful or that the isosceles triangle has 2R. We can prove that straightlines are the most beautifuL but not qua lines.14 Beauty, even if it is aninva riable concomitant of straight lines, does not belong to lines qua linesnor qua geometrical entities. Beauty belongs to straight lines because theyare a particular set of beautiful things. Beauty is common to many otherthings besides, namely to beautiful things qua beautiful, a genus with itsown principles. In order to prove that straight lines are beautiful, we needan application argument. As we saw, this applies a predicate that is provedof a genus to a species or instance of that genus. It must have one morepremiss than the argument that proves the attribute of the genus qua thegenus. The application argument for straight lines being beautiful mightbe something like the following: .beauty IPO intelligibilityintelligibility IPO symmetrysymmetty IPO straight linebeauty IPO straight lineThe first two premisses are sufficient to prove that symmetrical thingsgenerally are beautiful and the third premiss merely applies the generalconclusion to the species. This is a perfectly legitimate proof. But if we ttyto prove straight lines beautiful without the intermediaty of symmetty,we shall have committed metabasis. 1514 The contrary relation of straight line and circumference may be an allusion to DC 1.2268h17-19, which sta tes that they are the only simple motion s. This, then, will be aphysical rather than a geometrical proposition.15 Aristotle provides an interestingly different analysis of thi s situation at Met. M.3l 078a31-b5: 'Now since the good and the beautiful are different (for the fonneralways implies conduct as its subject, while the beautiful is found also in motionlessthings), those who assert that the mathematical sciences say nothing of the beautifulor the good are in error. For these sciences say and prove a very great deal aboutthem; for if they do not expressly mention them, but prove attributes which aretheir results or their formulae, it is not true to say that they tell us nothing aboutthem. The chief fonns of beauty are order and symmetry and defin iteness, whichthe mathematical sciences demonstrate in a special degree. And since these (e .g. orderand definiteness) are obviously causes of many things, eVidently these sciences musttreat this so rt of cause also (Le. the beautiful) as in some sense a cause.' Mathematics

24 Aristotle's Theory of the Unity of ScienceAristotle recognized that errors frequently occur because the appropriatesteps of proof are not followed, and this happens when we misidentifythe appropriate qua-level for demonstration and produce a mismatch betweenthe subject and the property proved of it. Sometimes these errorsoccur through carelessness, sometimes because of the difficulty of theproblem involved. Aristotle discusses one especially difficult case:And it might seem that proportion alternates for things as (i1) numbers and as linesand as solids and as times - as once it used to be proved separately, though it ispossible for it to be proved of all cases by a single demonstration. But because allthese things - numbers, lengths, times, solids - do not constitute a single nameditem and differ in sort from one another, it used to be taken separately. But nowit is proved universally; for it did not belong to things as lines or as numbers, butas (n) this which they suppose to belong universally. (APo 1.5 74a17-25)Aristotle introduces this case as a parallel to the triangle / isosceles-2R case,but one in which there was no obvious universal corresponding to triangleover the particulars kinds of triangle. Formerly the law of alternatingproportion (if A:B::C:D, then AC::B:D) had to be proved separately foreach of the species to which it applied, because these species did not appearto constitute a single universal genus. This general kind escaped notice,Aristotle says, because it did not have a single name. The definitions andproofs for alternating proportionality had to be couched in terms of thespecific magnitude, length a or time b or volume c. Because of the lack ofa common name the laws of proportionality masqueraded as a problem requiringmultiple parallel solutions, though in fact it was a generic problemand required a general solution. For, as Aristotle says, the general proofwas subsequently discovered. 16Aristotle was familiar with the general proof that had been developedby Eudoxus, a friend of Plato and member of the Academy.l7 Subsequently,Euclid incorporated Eudoxus' di?coveries along with the earlier,seems to provide some of the causal material for the science of beauty. It explainswhy a straight line is symmetrical. Other principles will be necessary to show whysymmetry is beautiful, i.e., what symmetry, order, and definiteness have in common,say, intelligibility, which makes them all beautiful. This passage also makes clearthat one science may say a lot about another science without being the same as thatscience.16 But even for Aristotle the general kind, though constituting a common nature, doesnot have a general name. By the time Euclid composed the fifth book, however, thegeneral teon JlfYf.8os was in use.17 For the professional activities of Eudoxus, see Heath 1981, I, 322- 7.

25 Genus, Abstraction, and Commensurabilityless-developed work on proportion into two books of the Elements, book Von general magnitude and book VII specifically on number.18 As a resultwe can compare the general treatment of alternating proportion with oneof the specific treatments, and make observations regarding the appropriateper se and qua predications.We find that the error in proving a theorem on the specific level ratherthan the general is not so clearly an error in this case as it was in the caseof 2R proved of isosceles rather than of triangle. This is because there arelegitimate proofs both on the general and the specific levels, and as a resultthe predicate, proportionals alternate, belongs at both qua-levels, thoughin different ways. This case provides a good introduction to situations inwhich qua-levels of predicates are not perfectly demarcated.In his introductory definitions to the two books Euclid provides both ageneral and a specific definition for 'part':V. def. 1: A magnitude is a part of a magnitude, the less of the greater,when it measures the greater.VII. def. 3: A number is a part of a number, the less of the greater, whenit measures the greater.The term 'part' is defined in different ways in each case. If we applyAristotle's language of necessity to these definitions, the terms in thedefinition are related to the definiendum, part, by the per se (1) relationship.As a result, in V def. 1 a part is magnitudinal, and in VII def. 3 a part isnumerical. 19 It is dear, then, that the per se relationships of the generaland the specific sciences are different, and although Euclid has preservedfor us the specific science governing only discrete quantity, it is easy to seehow the definition can be modified to be appropriate for time and so on:A time is a part of a time, the less of the greater, when it measures thegreater.The subject-genus is different in each of the specific sciences, and theterms that enter into the demonstrations concerning the subject-genus18 See Heath 1956, II, 112-13; Mueller 1970a. For the general proofs of Eudoxus, seeProdus, In primum Ellclidis 67, 3- 5: 7rPWTM TWV Ka86.\ov Ka.\ov}J.EvWV 8€wpruuiTwv TO7J'.\i180S' 'YJU{'YJfT€v.19 So also V. def. 2: 'The greater is-a multiple of the less when it is measured by theless,' and VII. def. 5: 'The greater number is a multiple of the less when it is measured·by the less.' Translations from Heath 1956.

26 Aristotle's Theory of the Unity of Sciencemust be defined in a correspondingly restricted way. Since the term 'part'has different definitions, it is ambiguous, and yet the ambiguity is farfrom random. The meanings of part correspond to one another: the rolethat a part-number plays in the genus of number corresponds to that ofa part-time in the genus of time, and so on. This arrangement in whichterms are adapted to a specific subject-genus is comparable to Aristotle'sremarks about another class of scientific principles, the axioms:Of the things they use in the demonstrative sciences some are proper to eachscience and others common - but common by analogy, since things are useful inso far as they bear on the genus under the science. Proper: e.g. that a line is suchand such, and straight so and SOi common: e.g. that jf equals are taken from equals,the remainders are equal. But each of these is sufficient in so far as it bears onthe genus; for it will produce the same result even if it is not assumed as holdingof everything but only for the case of magnitudes - or, for the arithmetician, fornumbers. (APo 1.10 76a37-b2)Comparison with a passage at APo 1.11 77a26-35 shows that the commonitems discussed here are axioms, one of the three kinds of principles indemonstrations, and that without which no learning is possible (1.2 72aI6-17). Though these axioms, such as the 'equals taken from equals' axiom,are common to many genera (or common to all genera in the case of theprinciple of non-contradiction), they are not used in their common formwithin a specific genus. Instead they are adapted to the genus in whichthey operate.'o When there is a multiplicity of such adaptations in manydifferent genera, the axioms are analogically the same, since they performcorresponding functions in each genus. The issue is similar in the caseof alternating proportion. Each proof is conducted within its own propergenus, but each part of one proof corresponds to that of another. Prior toEudoxus analogy was the nearest one could come to a general proof amongthis group of subject matters.The substitution of the appropriate terms in order to adapt the definiendaof one specific-genus to another specific genus seems to be fairlytrivial. The general science of proportionality, however, accomplishes farmore than merely introdUCing a general term that will adequately cover allthe specific cases. Eudoxus developed a science that holds good for irrational20 Ross 1949, 538: 'other {principles are} common, but common in virtue of an analogy,since they are useful just in so far as they faU within the genus studied.' Cf. Met. r .31oo5a26--27: 'men use [common axioms} JUSt so far as to satisfy their purposes; that is,as far as the genus whose attributes they are proving extends.'

27 Genus, Abstraction, and Commensurabilityquantities as well as rational, and in order to accomplish this he had tomodify some definitions fundamentally. Take, for example,V. def. 6: Let magnitudes which have the same ratio be called proportional,where being in the same ratio is defined asV. def. 5: Magnitudes are said to be in the same ratio, the first to thesecond and the third to the fourth, when, if any equimultiples whateverbe taken of the first and third, and any equimultiples whatever of thesecond and fourth, the former equimultiples alike exceed, are alike equalto, or alike fall short of, the latter equimultiples respectively taken incorresponding order.We are instructed to multiply the first and third quantity by any equalfactor, and multiply the second and the fourth quantity by any other equalfactor. If the quantities stand in proportion, then, no matter what factorswe use, the first and third will always be likewise smaller than, equalto, or larger than the second and the fourth respectively. This definitionis expressly formulated in terms of equimultiples in order to overcomethe challenge of incommensurability, which arises in the environmentof irrational quantities. For this reason the definition requires neither arational relationship between the first and the second term, and the thirdand the fourth, nor between the two pairs of magnitudes. Compare thiswithVII. def. 20: numbers are proportional when the first is the same multipleor the same part, or the same parts of the second that the third is of thefourth,which assumes that all the members of the proportion are commensurablerational numbers.For the single theorem Aristotle is referring to, that if A:B::C:D, thenA:C::B:D, Euclid's proofs are parallel in broad outline, both depending onfinding some means of measuring the first quantity by the third. Theyaccomplish this in different ways: V. prop. 16, the general proof, usesequimultiples to establish the proportion between A and C, and Band 0,while the theorem for discrete number, VII. prop. 9, can show this moredirectly, since A is the same part of B that C is of 0 , and wholes with thesame number of parts have their parts proportional with their wholes.

28 Aristotle's Theory of the Unity of ScienceEuclid's presentation tells us a great deal about the relationship betweenthe general and the specific science, but not about the relationshipbetween specific sciences. Unfortunately we are prevented from comparingtwo special definitions or proofs, because we only have the special science ofnumbers. But there is nothing in VII prop. 9 that would prevent a simplesubstitution of number for time, area, and so on, so long as irrationalquantities are avoided. This theorem is the same by analogy for all generaof quantity.This passage teaches that the law of alternating proportion appearedat one time to be capable of only analogical proof. In fact, this was neverso, it only appeared so. If, however, there had not been the more generalgenus, magnitude, the legitimate proofs would have been analogical. Asit is, the legitimate proof for alternating proportion is to be found atthe general level, since alternating proportion belongs to magnitude quamagnitude. This does not, however, make the specific proof, such as we findin Euclid VII, illegitimate, since it is specifically adapted to discrete quantityand depends upon the nature of discrete quantity to make its proof. Butit would be illegitimate to prove the general theorem in the context ofdiscrete quantity qua discrete quantity or to prove the specific theorem inthe context of magnitude generally. For discrete quantiry, there are nowtwo legitimate proofs for alternating proportion, the original specific proof,and a proof through an application of the general proof. Though Aristotledoes not recognize the possibility of two legitimate proofs in the passagefrom APo 1.5, he does later:Why do proportionals alternate? For the explanation in the cases of lines and ofnumbers is different - and the same: as lines it is different, as having such andsuch an increase it is the same. (APo 11.17 99a8-10)Furthermore, just because one theorem is the same by analogy doesnot mean that all the theorems in a genus will have analogous proofsin the other genera. Most of the definitions in Euclid's two books onproportion are peculiar to their own science. For example, VII. def. 6:I An even number is that which is divisible into two equal parts' is trueand relevant only on the supposition that we are dealing with discretenumbers. It has an analogue neither in the general science nor in thespecific sciences of continuous quantity. Likewise VII. prop. 2, 'Given twonumbers not prime to one another, to find their greatest common measure,'which depends upon commensurability of quantities, has no analogue inthe general science. Eudoxus' discovery of the general science of proportiondid not, therefore, completely eliminate the need for the specific sciences.

29 Genus, Abstraction, and CommensurabilityOnly certain theorems could be proved at the general level. Others still hadto be treated specifically. Still others, as we just observed, could be treatedboth ways. The question 'In what genus is the theorem of alternatingproportion proved 7' does not have a single unambiguous answer. Ratherit is proved in two genera in two different ways. As a result, numericalproportion, for example, cannot be treated within a single genus, but insteadsome theorems must be proved in a more general genus, others in amore specific. This is a very frequent occurrence in Aristotelian science aswell.AbstractionConfusion in determining the correct qua-level for a demonstration arisesmost frequently among qua-levels that are related to one another by abstraction(acpatpftTls). We can move from one qua-level to a more generalqua-level when we abstract certain features of the object under consideration. For example, to move from isosceles triangle to triangle we abstractthe general triangular nature and ignore the fact that it has two sides equal.Similarly, from the straight line we may eliminate all of its geometricalnature, including its genus, line, and leave only a necessary accident, itsbeauty. As this last example makes clear, the process of abstraction occursnot just among the qua-levels of mathematics, but among objects moredistantly related as wel l. In fact, Aristotle's most famous application of theprocess abstracts mathematical entities from their physical substrates:Just as the universal part of mathematics deals not with objects which existseparately, apart from magnitudes and from numbers, but with magnitudes andnumbers, not however qua such as to have magnitude or to be divisible, clearlyit is possible that there should also be both formulae and demonstrations aboutsensible magnitudes, not however qua sensible but qua possessed of certain definitequalities. For as there are many formulae about things merely considered as inmotion, apart from the essence of each such thing and from their accidents, andas it is not therefore necessary that there should be either something in motionseparate· from sensibles, or a separate substance in the sensibles, so too in the caseof moving things there will be formulae and sciences which treat them not quamoving but only qua bodies, or again only qua planes, or only qua lines, or quadivisibles, or qua indivisibles having position, or only qua indivisibles. (Met. M.3l077b17-30jAccording to Aristotle mathematical objects are ontologically dependent onnatural substances. We abstract the quantitative nature of substance and

30 Aristotle's Theory of the Unity of Sciencetreat it as if it were separate en XWPLtJ'Tov) from substance, even thoughit is not (Phys. II .2 193b22-194a12; Met. M.3)21 Although quantity isdependent on substance, we can mentally separate it (Tn VO~

31 Genus, Abstraction, and Commensurabilitya different genus from isosceles triangle. And since 'a science (E 7TlCTT~lq )is one if it is of one genus' (1.28 87a38), it follows that these genera willalso form different sciences. If it seems strange to say that the study oftriangles and isosceles triangles are different sciences, we shall have to waituntil we can provide a fuller explanation in the context of focality.Aristotle distinguished this conceptual abstraction, in which the abstractedgenus maintains no per se relations to its ontological substrate,from the concrete attribute, emblematized by the 'snub: which is definedas curvature in the nose. 23 The name snub (UL,uOV ) contains nose in itsdefinition, and insofar as we are treating snub, nose will always be a perse part of it. We may certainly study snub without the nose, but we shallno longer be studying snub qua snub, but rather snub .qua curved in itsabstracted geometrical nature.This same fact can be expressed in another way: once we have abstractedmathematicals from their natural substrate and developed thescience of mathematics, we can play the process of abstraction in reverse,and add (7rPOCTTL8EvaL ) the mathematics back into the natural substance. WemaYI as it were, add the CUIVe back to the nose in order to get the snub.The contrast is drawn at DC I1I.1 299a13-17, where Aristotle says thatmathematics deals with abstracts (Tel E~ a.c/JaLpEIIEw,), physics with concretes(Ta EK 7rpoII8E"EW, ).24 The science of optics for Aristotle is analogous to thesnub nose (phys. 11.2 194a7-15). Lines and points, the stuff of geometry,when added to the optical subject matter, become rays and eyes. Similarlywith nature in general (194a12-15):Since two sorts of things are called nature, the form and the matter, we mustinvestigate its objects as we would the essence of snubness, that is neither independentlyof matter nor in terms of matter only.23 So also DA 1.1 403a25-b19; Met. E.1 1025b30-1026a6.24 In fact, the contrast is extended to the barest logical applications in Met. M.2 l077b4-11,according to which white is logically prior to white man, because it is by the addition(EK 7fpou8iufwr) to the white that we speak of the white man. In a dIfferent formulation,Aristotle says (Met. A.2 982a25-28): 'Those [sciences] which involve few er principlesare more exact than those which involve additional principles (b: 7fpo

32 Aristotle's Theory of the Unity of ScienceThe 'snub' serves metonymically to refer to a broad variety of terms thatmight be called 'embedded: It is the general character of the embeddedterm that it is a predicate (snub) applied to its subject qua that subject(nose). Some embedded terms are also necessarily (and perhaps per se)related to other, abstract, objects that serve as subject-genera themselves(curved). The abstract subject-genera are, however, not coextensive withthe embedded term or its substrate, and so cannot be included in thescience of the embedded term and its subject. 25 In short, there is a tensionbetween the per se requirement of definitional inclusion (for an element ina definition can extend beyond the definiendum) and the qua requirement,which demands coextension.When we abstract from one kind of object we are usually abstractingsome named feature common to many other kinds of objects as well.Sometimes, however, the common feature, while having a common name,also has a name peculiar to the specific genus from which it is abstracted.So, for example, in abstracting the geometrical curve from the snub nose,we abstract a feature that is common to many things besides noses. But solong as the curve is in the nose, it goes by the name snub, and until snubis abstracted into curved, it cannot be treated as something common. Onlya nose may be snub and only a leg may be bandy. Snub and bandy cannotbe treated together in a common science, since they are per se attributesof different subjects:For 'concave' has a general meaning which is the same in the case of a snub nose,and of a bandy leg, but when added, in the one case to nose, in the other to leg,nothing prevents it from meaning different things; for in the fonner cannexion itmeans snub and in the latter bandy. (SE '31 181b37- 182a2)It is within this context that Aristotle recognizes one legitimate kindof m etabasis, that between general and specific sciences, in which theprinciples of a superordinate and abstract science are used to provide aproof in a subordinate and concrete science:If this is not so [if the attribute and middle are not in the same genus as thesubject], then the theorems are proved as harmonical theorems are proved througharithmetic. Such things are proved in the same way, but they differ; for the factfalls under a different science (for the underlying ge nus is different), but the reason25 Bahne 1987b, 311, arrives at the same conclusion through a different path, noting thatsnub is properly a description of nose-flesh in a ce rtain state, rather than a qualityabstracted from nose-flesh.

33 Genus, Abstraction, and Commensurabilityunder the higher science under which fall the attributes that belong in themselves.Hence from this too it is evident that one cannot demonstrate anything simpliciterexcept from its own principles. But the principles of these sciences have the commonfeature. (APo 1.9 76a9-15)In this passage, Aristotle discusses the so-called mixed sciences, in whicha branch of mathematics and a branch of natural science are mixed together.In other passages Aristotle considers a similar mixing between solidgeometry and mechanics, between mathematical and nautical astronomy,and between geometry and optics. 26 In these cases the conclusion of thedemonstration, which is the fact to be proved, comes from a natural science,while the reason or cause, the middle term, is located in a mathematicalscience. Two different genera are operative within the same demonstrationand the same science. As such these sciences are different from a simplescience like mathematics, in which only one genus is involved.This form of metabasis is important for the present purposes, becausethe understanding in one genus directly bears on the understanding in another,and there is not the ·tidy separation of genera we find with trianglesand isosceles triangles or with mathematicals and natural objects. It is oneof a group of cases I shall consider in which the autonomy of generabecomes weaker and the demarcations less clear. It has been commonto characterize these mixed sciences as forms of application argument, inwhich the general conclusion proved at a higher, mathematical qua-level isapplied to a natural species or instance. On this interpretation the generalconclusion can be immediately applied to the specific instance without anyfurther premisses or explanation. I shall argue, however, that the generalattribute cannot be immediately applied to the specific genus, but that thisconnection itself requires proof, and that the predication of the generalattribute requires that some explanatory work be done at a specific level.On this interpretation the mixed science combines explanatory elementsfrom both subject-genera, rather than merely applying the explanation ofone to the other.In order to understand how one science can provide the explanationor reason for a fact that is found in another, we may once again turnto a comparison of Aristotle and Euclid. To the extent that Euclid providesclarification for points Aristotle is making, we may use him forcorroborating evidence. We may start by turning to the proofs for opticalphenomena found in his Optics, which at once clarify Aristotle's discussion26 APo 1.7 75bl4-17; 1.12 77a40-b6; 1.13 78b32-79a16.

34 Aristotle's Theory of the Unity of Scienceof mixed sciences and raise the further questions I have mentioned. Ofcourse, Euclid's proofs are not arranged as syllogisms, but they start witha statement of a proposition, which corresponds to an Aristotelian fact orconclusion of a syllogism. For example, proposition 23 begins:When any sphere is seen by a single eye it will always be seen as lessthan a semicircle and that very part which is seen will appear bounded bya circle. 27The proposition clearly contains optical terms (e.g., eye, seen) and as suchbelongs in the science of optics. There follows in Euclid's proof the settingout (heECTL'), which ~rovides a bridge from the optical proposition to thegeometrical solution. 8 The eye, for example, is hypothesized as a point.Thereafter, the proof (cbr61\"t,,) is conducted purely in geometrical terms,and the conclusion finally relates the geometrical proof to the optical fact.To make the distinction between optics and geometry in a Euclideanproof is fairly straightforward, since they are separated in the stages ofthe proof. In an Aristotelian demonstration, however, it is much moredifficult, since the requirement for immediacy in the premisses is so strict.But we get some clue how this is done by examining Aristotle' 5 treatmentof various meteorological phenomena in Mete. 111.2-6 29 He begins his explanationof the shape of a halo in the following way (III.3 372b34--373aS):The visual ray is reflected from the mist that forms round the sun or the moon,and that is why the halo is not seen opposite the sun like the rainbow. Since thereflection takes place in the same way from every point the result is necessarily acircle or a segment of a circle; for if the lines start from the same point and end atthe same point and are equal, the points where they form an angle will always lie 'on a circle. 30As with Euclid there follows a purely geometrical proof:Let ACB and AFB and ADB be lines each of which goes from the point A to thepoint B and forms an angle. Let the lines AC, AF, AD be equal and those at B -27 My translation of Hayduck's edition of Euclid.28 For the ElCeffItS see Heath 1981, I, 370.29 Lennox 1986 has pointed out the importance of this passage for these issues, and mydiscussion relies heavily on his.30 ROT translates oo/tS as 'sight' instead of 'visual ray.' lowe the correction to ananonymous reader.

35 Genus, Abstraction, and Commensurabilityviz. CB, FB, DB - equal too. Draw the line AEB. Then the triangles are equal; fortheir base AEB is equal. Draw perpendiculars to AEB from the angles; CE from(, FE from F, DE from D. Then these perpendiculars are equal, being in equaltriangles and all in one plane; for they are all at right angles to AEB and meetat the single point E. So if you draw the line it will be a circle and E its centre.(373a6-16)Aristotle concludes with some principles that allow us to interpret thegeometrical proof in optical and natural terms:now B is the sun, A the eye, and the circumference passing through the pointsCFD the cloud from which the visual ray is reflected to the sun. (373al6-19)SuperfiCially it is easy to see just what kind of explanation Aristotle hasin mind when he says that geometry provides the cause for the opticalfact. One common and plausible interpretation argues that in the contextof a demonstrative syllogism, the major and middle terms of thedemonstration will come from geometry, while the minor term will beoptical, and the minor premiss will state that the optical phenomenonfalls under the geometrical explanation.31 Consequently, the demonstrationwill have the same sort of structure as that applying the general2R theorem to the specific case of the isosceles triangle, an applicationargument. But isosceles is a species of triangle, and the application ofthe genus and its properties to the species does not require any furtherexplanation, since the genus-species connection is immediate. By contrast,the connection between optics and geometry is not immediate and requiresexplanation. 32I should like to suggest that, because of the presence of embeddedterms in the proof, this mixed science cannot be a case of simple applicationargument. First of all, at Phys. II.2 194al-12 Aristotle clearlyplaces mixed sciences among those that behave like the snub. In this samepassage he claims that, 'while geometry investigates natural lines but notqua natural, optics investigates mathematical lines, but qua naturaL notqua mathematical.' The difficulty in setting a determinate qua-level forsuch demonstrations is illustrated by his contradictory claim that 'neither31 This is the interpretation given by McKirahan 1978, 201, and Lennox 1986, 48. Lennox1987a, 94, notes the similarity between 2R-isosceles and mixed science, but rightly doesnot identify their structure.32 McKirahan 1992, 178, 184, recognizes that application arguments need not be to species,but does not deal with cases where the application may not be immediate.

36 Aristotle's Theory of the Uniry of Science[optics nor harmonics] considers its objects qua light-ray or qua voice,but qua lines and numbers' (Met. M.3 1078a14-16). At what qua-leveloptical phenomena are to be proved is clearly in doubt. By contrast, 2R isclearly proved of isosceles triangle qua triangle. Optics cannot be studiedpurely qua geometry (i.e., those mathematical proofs that apply to optics),since then we should merely cull proofs from the Elements, and withoutadapting their terms in any way, call them optics. No reference couldbe made to rays or eyes. Obviously, neither Aristotle nor Euclid doesthis, since this would not make clear how they explain optical phenomena.Alternatively, we might cull proofs from the Elements and briefly applythem to optical instances by identifying, for example, point A as centre ofa sphere, B as eye, and so on. Again, neither Aristotle nor Euclid does this,since it would still not be clear what we were trying to prove, namely,why this optical phenomenon exists. Instead, in both authors we beginwith an optical phenomenon to be explained. 33 Optical nature is deeplyembedded in the explanation in a way isosceles nature is not embeddedat all in the explanation of 2R. It is clear, then, that optics studies opticalphenomena but makes use of geometry in its explanations. How is thisthe case?We have already seen both the setting out of Optics 23 and the mannerin which Aristotle in Mete. III.3 begins his explanations of halos. It isclear that geometry is not the only explanatory factor in these explanations.Instead, part of the explanation is optical and part is geometrical.In demonstrative form we may represent the explanation for halos asfollows:forming a circle IPO equal lines falling from one pointequal lines falling from one point IPO a haloforming a circle IPO a haloBut this is not yet a demonstration, since neither premiss is immediate.Between .the major and the middle term we must 'pack' or insert furthergeometrical premisses. Equally, between the middle and the minor termswe require packing of premisses containing optical terms in order to explainwhy optical terms can be described in geometrical terms. These premissesmight be something like the following:33 Cf. PA 1.1 639b5-10, where Aristotle asks whether the procedure in biology should besimilar to that in astronomical mathematics, in which the astronomical mathematicianfirst makes the obselVations and collects the phenomena, and then supplies the cause.

37 Genus, Abstraction, and Commensurabilityequal lines falling from a point IPO equal rays falling from a light sourceequal rays falling from a light source IPO equal rays falling from the sunequal rays falling from the sun IPO equal rays reflected by mist to the eyeequal rays reflected by mist to the eye IPO halo.These premisses will be explanatory of why halos exhibit this particulargeometrical nature.We now have an explanation of how these mixed sciences may haveboth geometrical and optical explanatory components, and as a result it willnot be possible to say that the explanation resides either at the qua-level ofgeometry or at the qua-level of optics: it resides at both. In a correspondingway we can redescribe Euclid's Optics 23 in a schematic demonstrativefashion:smaller than the diameter IPO circle at the tangent from a pointcircle at the tangent from a point IPO appearance of sphere from one eyesmaller than the diameter !PO appearance of sphere from one eyeAgain the cone shape of the optical field will serve as a principle to explainthe connection between the middle and the minor terms.As Lennox has rightly pointed out, the form of explanation in these'mixed' sciences differs from the application of 2R to isosceles in thathalos are not species or determinate forms of circles. 34 In fact, circle is noteven part of the definition of halo. For this reason, the transference ofper se attributes of common features (geometry) to the instance (halo) isnot an immediate fact, but itself requires explanation. Aristotle describesthe situation in terms of facts and causes, because he is interested inthe reason why the halo takes a circular shape, rather than why it fall sunder geometrical analysis at alL Nevertheless, the example illustrates thatwhere the subordinate science is not a species of the superordinate science,the subordinate science makes a genuine and unique contribution to theunderstanding of why the major term belongs to the subordinate subject.In proving that halos are circular, we are studying halos qua halos, thatis, we are studying what belongs to halos in virtue of their halo nature,but we are proving attributes that extend beyond halos, attributes that arenon-coextensive per se accidents. Owing to the inconcinnity between theper se and qua requirements, the distinction between the mathematical34 1986,41.

38 Aristotle's Theory of the Unity of Sciencegenus of circle and the natural genus of halo cannot be sharply drawn inthis case.The mathematical component of mixed sciences is treated as snub, thatis, as unabstracted from the natural substrate. But that mathematical componentcan also be completely abstracted and treated as pure mathematics.Such is the nature of mathematical entities. Other objects are susceptible toabstraction in different ways and lie somewhere in between embeddednessand complete abstraction. These objects [ call 'semi-abstracts.' The degreeof abstractability depends on both the subject matter from which theabstraction is made and the abstraction itself. Some abstractions simplycannot be made, in which case demonstration can only proceed within asingle genus. Other abstractions can be made but only to the most limiteddegree; still others, while not complete like mathematical abstractions, formost explanatory purposes leave their concretes behind.'5 A study of thesecases is important, because they illustrate the basic principles of scientificunity, focality and analogy.[n the examples we shall now consider we are helped in determiningthe limits of abstraction by the presence or absence of commensurability. Itis a peculiar feature of quantified things that they can be compared as lessand greater. 36 This is true, however, only if we are making comparisonswithin a single genus or subject matter, for instance, one nose may be moresnub than another, but a nose cannot be more snub than a leg. So long asthe discourse concerns snub and bandy, there can be no comparison and nocommensuration between them, 'for things which differ in genus have noway to one another, but are too far distant and are not comparable' (Met.1.4 1055a6-7). [t is only as abstracted mathematicals, i.e., qua curved, that. they form a single subject, a new genus, and so can be compared. Aristotlemakes the same point in the context of the parts of animals: parts of animalsin the same genus differ only by more and less (HA 1.1 486a21-23). Suchdifferences are contrarieties of affections or incidental attributes (naerj.uaTa486b5). Excess or defect of these contrarieties does not affect the essentialnature of their substrate, and the per se attributes remain undisturbed by35 Aristotle's example of snub has an ambiguous status in this scheme. Inasmuch as snubis an accident of nose, it behaves as a predicate of the subject-genus nose. As such, itis completely embedded. But inasmuch as it is emblema tic of fonn in a "matter-fonncompound, it behaves as a semi-abstract, since, like soul and the form of natural objectsgenerally, it can be abstracted to the extent that it forms a subject of discourse with itsown per se predicates.36 Cat. 6 6a19-25 claims that quantities themselves do not admit of the more and the less,i.e., one three cannot be more three than another three.

39 Genus, Abstraction, and Commensurabilitychanges in the affections. A wing may be longer or shorter without ceasingto be a wing. Commensurability, then, is a mark of genus.Aristotle recognizes degrees of abstractability according to how easilythe proposed object can be removed from the per se connections that bindit to its substrate and how easily this new object forms a commensurablegenus. Let us consider three cases drawn from a wide range of contexts,which illustrate the varying degrees to which semi-abstracts maintain perse connection with their substrate .1. Change is impossible to abstract, and so does not even qualify as a semiabstract.What it is to be a change is completely embedded in the specificinstance, its primary recipient. One cannot remove change from its perse and qua connections to its substrate. This is indicated by the factthat change is only commensurable within the genus of its substrate,and different kinds of change, such as alteration and locomotion, areincommensurable with each other.2. The value of manufactured goods is only slightly easier to abstract.Manufactured goods cannot form a single genus, because they performa great variety of functions. Their value is dependent on theirfunction, and so value is per se and qua related to each specific kindof good. But their exchange value in barter must be commensurable ifexchange is to occur. Nevertheless, exchange value, though common, isnot conceivable apart from the specific goods to be exchanged. Value iscommensurable, but it is dependent upon the specific goods, and cannotbe abstracted even conceptually from their manifold specific variety.3. In the case of animal locomotion there is a series of abstractions thatfall short of mathematical completeness, but are more separable thanchange or exchange value. Because the series of abstractions neverleaves the natural domain, each new abstraction remains a hylomorphiccompound, but they become increasingly general and increasingly focusedupon the form. Accordingly, the abstracts always serve as causesfor the substrate, although their per se relations with the substratebecome less direct. As the qua-level changes, the basis for commensurationalso changes.1. Speed of ChangeIn one of the more important and searching passages for issues concerningabstraction, Physics VIl.4, Aristotle argues that the forms of change(alteration, locomotion, etc.) must be specifically identical in order tobe commensurable. The chapter begins with an aporia: is every change

40 Aristotle's Theory of the Uniry of Science(K,vrycn

41 Genus, Abstraction, and CommensurabilityThe general tenn and definition only appear to be common to the variousforms of change. In fact, since they have different per se connections ineach case, they will be ambiguous.The reason for the strict standards on commensurability is the factthat the affection or kind of change cannot be abstracted from the primaryrecipient, what the change occurs in. Three elements are present in thedefinition of speed of change: the time in which it takes place, the affection,like white or health, and the substrate, like surface or man (249a29-b26).Speed is measured by the amount of the substrate changed to the affectionin a certain time: 10 square feet of surface changed to white in 40 seconds.The affection and substrate must be related to one another per se andnot incidentally.'" Therefore, the affection and the substrate must both bespecifically the same in the cases compared, and equality of amount will bedenominated in amount of substrate. Thus the white of dog and the whiteof horse are commensurable because both dog and horse have surface, andsurface, not dog or horse, is the primary recipient of white. The surfacebecomes the single subject that allows for commensuration, and we are notcomparing dogs and horses.Speed of change is bound by its necessary relations to be treated atthe same qua-level as its affection and primary recipient. Because thesethings differ from change to change, and change is defined in terms ofthem, change is necessarily ambiguous, and there is no one definition inaccordance with its name. The confusion arises because there is a singlename, change, which suggests that there will be a single definition, and aSingle commensurable genus. But, in fact, there is no abstract change apartfrom the specific changes. Therefore, speed of change, too, is unabstractable.2. ValueThe concept of value admits of a greater degree of abstraction than change,but remains nevertheless bound to its substrate. Aristotle's discussion ofthis subject at Politics 1.9 1257a6ff. is aimed at showing how wealth properlyspeaking must always be bound to its substrate, property, which fulfilssome specific function for its owner:Of everything which we possess there are two uses (XP7jffl:tS'): both belong to thething as such (KaO' aUTO). but not in the same manner, for one is the proper (oLKEia),and the other is not the proper use of it (OVK OLKEla). For example, a shoe is usedfor wear, and is used for exchange; both are uses of the shoe. He who gives a shoe40 Cf. Cat. 6 Sa38-bIO.

42 Aristotle's Theory of the Unity of Sciencein exchange for money or food to him who wants one, does indeed use the shoeas a shoe (1J7Too~J.lan ii inroolU.l,a), but this is not its proper use, for a shoe is notmade to be an object of barter. The same may be said of all possessions, for theart of exchange extends to all of them, and it arises at first from what is natural,from the circumstance that some have too little, others too much. Hence we mayinfer that retail trade is not a natural part of the art of getting wealth. (1257a6-18;modified ROT)The first problem is to provide an account for the apparent confusion ofterms, according to which a per se (Ka8' aim)) use of an object, one in whichthe object is used qua that named object, is, however, not proper (olKda).It is clear that the wearer of the shoe is using the shoe as a shoe. But theexchanger is not wearing the shoe; he is instead using it for exchange. Thisis not the proper use of it, because the shoe was not made for the purposeof exchange. This, however, cannot be the whole story, because nothingprevents the cobbler from making shoes expressly to exchange them.In spite of the confusion in the technical expression, Aristotle's thoughtseems to be this: 41 there is a natural circumstance in which some have toomuch and others too little of some natural good (1257al4-17), and this iscaused by the practice of the crafts. The cobbler makes shoes. He wearsthem (a per se and proper use of shoes). But he keeps on making them,because he is a cobbler and cobblers make shoes to be put on feet. Butnow he has too many, and other people are unshod. In trading his shoeshe is treating his shoes qua shoes, and they are achieving their per seuse, because they are protecting feet, the reason the cobbler made themin the first place. But in the act of exchange he is also treating them asexchange goods to fulfil his own natural needs other than shoes. This isnot the purpose for which they were made (OUK oiKfia), but they serve thispurpose because others need them and he needs what they have more of.The exchange comes to an end when everyone has what they need. Theshoe can serve as an exchange good precisely because it is being treated as ashoe and is needed as such, for otherwise it would have no exchange value.The retail trader, by contrast, is neither interested in shoeing the worldas the cobbler is, nor in fulfilling his natural needs. He buys shoes not .towear them, but to sell them again at a profit, and since he sells themneither to supply himself with other necessaries nor in accordance withthe art of seeing people shod, he is neither using the shoe as a shoe norusing it in one of its two per se uses.41 lowe this interpretation to Meikle 1995, 68-81.

43 Genus, Abstraction, and CommensurabilityNatural wealth cannot be abstracted from the specific good and thepurpose for which it is intended. That is what makes it natural wealth:the wealth is derived from the inherent purposes of the objects. And evenwhen the shoe is being used for exchange, it is being treated qua shoe, sinceit is fulfilling a natural need, and this is what gives it value in exchange.The exchange value cannot be abstracted from the natural need. The sameobject is at one and the same time treated both as a shoe and more generallyand abstractly as an exchange good 42 This is as far as one may abstractand still be concerned with natural wealth.Exchange within the context of natural wealth is possible, but Aristotledoes not discuss how it occurs in the Politics. We can instead draw on histreatment of rectificatory justice in EN V.5. It is clear from here that someform of equality must be established in order for exchange to take place."But since the goods are of different kinds, absolute equality is impossible.Instead rectificatory justice, like distributive justice, must be expressed byproportional analogy:Now proportionate return is secured by cross-conjunction. Let A be a builder, B ashoemaker, C a house, D a shoe. The builder, then, must get from the shoemakerthe latter's work and must himself give him in return his own. If, then, first thereis proportionate equality of goods, and then reciprocal action takes place, the resultwe mention will be effected ... And this proportional will not be effected unlessthe goods are somehow equal. All goods must therefore be measured by some onething, as we said before. Now this unit is in truth need {)(pita), which holds allthings together ... but money has become by convention a sort of representativeof need. (113307-29; modified ROT)Now in truth it is impossible that things differing so much should become commensurate,but with reference to need they may become so sufficiently. Theremust, then, be a unit, and that fixed by agreement (for which reason it is calledmoney); for it is this that makes all things commensurate, since all things aremeasured by money. (1133bl8-23; rnodined ROT)In contrast to distributive justice, in which different people receive differentamounts of goods in proportion to the difference in their excellence,42 Cf. EE VIL13 1246a26-31 for the gruesome example of the eyeball in its proper purposeand in its beitig sold or eaten.43 Meikle 1995, ch. 1 and 2, has denied that Aristotle provides a positive theory ofcommensuration in this chapter. He takes 1133b18--20 as a denial of 'epistemic'commensurability. See Judson 1997, 158n21, for an argument contra.

44 Aristotle's Theory of the Unity of Sciencerectificatory justice depends on each party receiving equal shares. But inthe analogy, housebuilder:cobbler::house:shoe, it is difficult to see just whatthe relationship between the housebuilder and the cobbler is so that theycould have a proportion of one. As Meikle has pointed out, for Aristotletheir most natural relationship is mediated through the political art, whichsituates each craft within the activity of the polis." But that relationshipcannot be described by analogy, since, as we shall see, it is the job of thefocal relationship. Likewise, because houses are not shoes, a simple commensurationand equation between them is impossible. Yet the relationshipbetween the cobbler and the housebuilder must be some form of equalityfor exchange to take place. We might think to express the relationship asfollows: the claims of and demands on the cobbler are equivalent to those ofthe housebuilder. 45 But considering Aristotle's suspicion concerning equalityin the context of change, he is likely to be wary of this formulation,since the demands and claims of the exchanging partners are oppositeto one another (the cobbler claims a house, the housebuilder a pair ofshoes). Since need is bound to its object Aristotle puts strong emphasison the commensurating power of money, which mediates and measuresthe goods exchanged. In the Politics Aristotle aids this commensuratingpower by making exchange a per se use of a good, thereby essentiallyjoining the common function with the specific good. The EN manifests asimilar tension. The commonality between goods of exchange is positedhypothetically (i~ inroe€cr,ws), a matter of convention rather than nature.Need w,ia) as measured by money provides the equation between thecraftsmen and between the goods. While there is a natural analogy, housebuilder:house::cobbler:shoe(as artisan is to artefact), this analogy does notexpress the commonality necessary to effect an exchange. This can onlybe achieved when we treat the goods as objects of need:"44 Meikle 1995, ch. 4.45 Judson seems to concur (1997, 168-69): 'the ratio of the strength of their needs for thegoods in question .'46 I am in fundamental disagreement with Meikle's basic views on commensurability. It isthe basic thesis of his book that Aristotle's economic theory was not that of neo-c1assicalutilitarianism, according to which goods in exchange can be fully commensuratedthrough the 'satisfaction a subject derives from possessing or consuming an object'(38). So intent is he on shOwing that Aristotle viewed goods only in their proper use,that he denies that Aristotle intended a quantitative commensurability at all, declaring1133h18-20 as an 'unambiguous' denial of commensurability (35-6). The problem withhis analysis, as I see it, is that though he is trying to support Aristotle's economicswith an Aristotelian 'metaphysics' of substantial ends, he should also have consideredAristotle's theory of science, and especially the role of the universal, the pcr sc, and

46 Aristotle's Theory of the Unity of Sciencenature. 48 Just what that common nature is is not made dear, but Aristotlesuggests that it is expressed analogically: as five shoes are in the fulfilmentof the house builder' s natural needs, so one house is in the fulfilment of thecobbler's natural needs. The analogical structure allows Aristotle to treatas a limited commonality what must be treated as generically different"And yet there are more abstracted ways of dealing with wealth. Aristotleviews retail trade and usury as successive deviations from naturalwealth-getting, and as a result he does not recognize them as abstractedsubject matters that have a per se existence. Although he does recognize48 Cf. Judson 1997, 171, for a rather different view: 'Aristotle means that, if one considers"houses and shoes in isolation from human needs, there is simply no fact of the matteras to what a house is worth. This is quite compatible with thinking that there can besuch a fact of the matter when houses and shoes are considered as objects whicl;l satisfyhuman needs.'49 A similar analogical relationship is discussed at GC II.6 (333a20--34), where Aristotleis criticizing Empedocles for holding that the elements are commensurable andnon-transfonnable:'If it is meant that they [the elementsI are comparable in their amount, all thecomparables must possess an identical something whereby they are measu red. If, e.g.,one pint of Water yields ten of Air, both are measured by the same unit; and thereforeboth were from the first an identical something. On the other hand, suppose they arenot comparable in their amount in the sense that so much of the one yields so much ofthe other, but comparable in power of action (a pint of Water, e.g., having a power ofcooling equal to that of ten pints of Air); even so, they are in their amount, though notqua amount, but qua having power. Instead of comparing their powers by the measureof their amount, they might be compared as tenns in an analogy: e.g., as x is hot, so Yis white. But "as," though it means equality in quantity, means similarity in quality.Thus it is manifestly absurd that the bodies, though they are not transformable, arecomparable not by analogy, but by a measure of their powers; Le. that so much Fire iscomparable with many times that amount of Air, as being equally or similarly hot. Forthe same thing, if it be greater in amount, will, since it belongs to the same kind, ha~eits ratio correspondingly increased.'If the elements cannot undergo mutual transfonnation, then they can only be comparedby analogy. There seem to be tWO kinds of analogy under consideration, one thatallows for commensuration by quantification on the basis of measure of power, and onethat does not (as x is hot, so Y is white), since there is no similarity of the qualities.Though the elements are not transfonnable, they may still be capable of eHectingsome common thing in a similar manner, and on that basis a ratio may be establishedbetween the amounts necessary to bring about the similar effect. The commensurationof the elements in question cannot be separated from the elements they are, since weare not trying to commensurate cooling power, but the elements that bring about thecooling. Commensuration through analogy is possible when some common attributeis shared by different subjects, and can be partly abstracted from the subjecrs it isfound in.

47 Genus, Abstraction, and Commensurabilitydiscrete crafts, like retail sale and usury, governing each, he clearly thinksthese crafts are perversions. And yet as a result of the close connectionsbetween the crafts of exchange and retail, he says, some people confusethe different forms of wealth-getting (Pol. 1.9 1257b35). Usury is for himthe most unnatural form of wealth-getting just because it makes a gainfrom money itself, rather than from the natural object of wealth (1.101258a38-b8). It is unnatural because it has become completely conceptuallyseparated from the only source of value per se, the manufactured good.For Aristotle the subject matter of economics is natural wealth, and otherthings, like money, may be included in the study to the extent that theyare relevant to natural wealth. Money is included because it measures theneed for natural wealth and therefore is per se related to natural wealth.But it has no legitimate function apart from its relation to natural wealth.And yet we see how easily usury and even capitalism can be made tofit into Aristotle's scheme of abstraction. We are more inclined todayto view usury as part of the art of finance, and would consider it as amore completely abstracted craft. The subject matter of finance is capitaland its properties, and these properties are different from those of shoes.Banking is more abstract too in the sense that it gives principles to themanufacturing arts, like those of capital investment or deficit finanCing.But Aristotle did not abstract finance from manufactured goods, becausehe did not conceive of value abstracted from some fairly primitive naturalneeds of man. Value maintains its per se connections to the specific genusof good, and a commensurable commonality is attainable only by analogyand the convention of money.3. Animal LocomotionIn the case of animal locomotion, Aristotle treats a series of subjects relatedto one another by abstraction as he proceeds from the PA to the lA, MA,and DA. Though these subjects are more abstractable than the arts ofwealth-getting, the abstraction is never as great as with mathematics, andthe per se connections to less abstract levels are not abandoned: the form,no matter how abstract, is always conceived of as part of a hylomorphiccompound, and is always in a causal relationship, however distant, withthe lowest concrete object. soThe PA studies the parts of animals and their causes. The investigationtakes place at a concrete material level, and the treatise supplies reasons50 See Peck's (1983, 8-10) comments on the organization of the biological treatises.

48 Aristotle's Theory of the Unity of Sciencefor the material nature of the parts. 51 Broadly speaking, these reasonsare couched in terms of function (form) and constraints (matter). Thetreatise is organized largely part by part starting with the head and movingdown, and each greatest genus, like bird and fish, is treated more or lessseparately. Aristotle does not devote much energy to the instrumentalparts of locomotion in the PA, but he does, for example, say that birdshave a pair of wings because it is part of their nature to be able to fly(IV .l2 693blO--13) . Wings in their material constitution are commensurableamong themselves: rapinous birds have unusually large wings, otherbirds have smaller wings. As such, they form a genus. Fishes' fins formanother genus, commensurable among themselves, but incommensurablewith birds' wings. Aristotle explains the differences among wings by referenceto the differences in the way of life (/3io

49 Genus, Abstraction, and CommensurabilityThe IA is a problem-based inquiry. As in the PA the problems are material,concerned with the instrumental parts, but now at a general level. Certainfacts are clear from the HA and this treatise must provide the cause (1704b9-11 ). The questions concern the number of points of motion (someanimals have more, others fewer), the convexity or concavity of limbs,and the way in which the limbs move. The point theory of movement is acommon explanatory principle and must account for the different featuresof various animals taken now as a group. Features of locomotion are stillcorrelated to the broad divisions used in the PA (sanguineous animals moveat four points, birds have convex legs, and so on), but since the IA choosesa different basis of comparison from the PA , the various genera of animalsbecome commensurable.Whether the locomotions of animals are commensurable is not a questionAristotle explicitly addresses in the IA. It arises instead at Phys. VilAin the context of determining the commensurable substrate tor change:{Locomotion is specifically differentiated} also accordingly as the instrument of thelocomotion is different: thus if feet are the instrument, it is walking, if wings itis flying. Or is that not so? Is locomotion different only according to the shape ofthe path? (Phys. VII.4 249a17-19)Aristotle hardly gives an unequivocal answer in this passage, but he clearlyleans towards commensurability, instrument of locomotion not making aspecific difference. We can say, then, that birds move faster than dogs (asthe crow flies). Commensuration is possible, but what is commensuratedhere is obviously different from what we find in the PA. The genus haschanged from wing to locomotion. But in the IA Aristotle is not interestedin the quantitative aspects of locomotion, since these problems extendmore widely than animal locomotion, and belong in physics rather thanbiology.At the end of the IA Aristotle claims that after having investigatedthe parts, we must move to investigating the soul (19 714b20-23).S4 But,in fact, it is clear that the MA, not the DA, is methodologically the nexttreatise, since it begins with an explicit statement that seems to assumethe IA:Elsewhere we have investigated the movement of animals after their various kinds,the differences between them and th e causes of their particular characters (forsome animals fly, some swim, some walk, other move in various other ways);54 This reference may suggest that the MA was not written at the time of the reference.Cf. Nussbaum 1978, 27.3-4.

50 Aristotle's Theory of the Unity of Sciencethere remains an investigation of the common cause (ICOW7}S- alTius) of any sort ofanimal movement whatsoever. (1 698al-7)Aristotle shows in the first chapter that there must be a point of rest in theanimal that is the origin of motion. In addition there must be somethingoutside it that is absolutely at rest (ch. 2). This is a fact that extends beyondanimals even to physics in general, and is treated as useful for the presentscience. 55 The MA will also consider how the soul moves the body. Accordinglythere is a brief discussion of the practical syllogism (7701a7-bl),which provides the psychological part of the answer. The corporeal part ofthe answer is found in the expansion and contraction of the connaturalspirit (a1JJ.'CPVTOV '1TVEvJ.'a) located in the origin of movement (i.e., the soul)which pushes and pulls and thus causes other movements in the instrumentalparts. Absent from this common treatment is any mention of thespecific kinds of instrumental p~rts. Instead we learn about some commonmaterial conditions for movement in general (not just locomotion), theinternal and external unmoved, and the joint; and some common formalconditions, desire and the practical syllogism; and that which mediatesbetween formal and material, the connatural spirit. How and in what waythe soul is moved is the subject of the DA (MA 6 700b4-6).In the treatment of movement in the DA all material considerationsare absent on the grounds that I examination of it falls within the provinceof the functions common to body and soul' (!IUO 433b19-21). Insteadthe DA asks what part or parts of the soul are responsible for movement.No one faculty by itself is sufficient, Aristotle avers, but appetite initiatesthe movement and together appetite and thought or imagination suffice.In general. then, the DA merely considers which faculties of the soul areresponsible for movement and the nature of the conflict between variousdesires and faculties.These four treatises, then, are organized in order of increasing generalityand formality, away from what is specific and material towardswhat is common and forma1. 56 Each step in the abstraction provides a55 Cf. Nussbaum 1978, 107-14, who argues that the MA is 'a deliberate and fruitful'(113) departure from Aristotle's strictures on metabasis; Kung 1982 correctly repliesthat this does not constitute metabasis in any usual sense, that it is assimilable to thesubordinate-science model.56 In organizing a subject matter, Aristotle sometimes identifies two levels of principles,the first of which might roughly be characterized as internal to the subject matter,the second as external. Patzig referred to this technique in the context of metaphysics,which he called a 'doppelt paronymische Wissenschaft' (1961, 196). Here all beingdepends on substance and cannot be separated from substance. Substance is, as it

51 Genus, Abstraction, and Commensurabilitynew genus and qua-level, and new per se predicates. And yet for tworeasons abstraction of the mathematical kind is never attained. First, neverdoes Aristotle suggest that the ·abstraction of the soul faculties from theirmaterial substrates can be fully effected in definition. Soul faculties mustalways be defined as actualities of material potentialities. And yet it isclearly legitimate to consider appetites and imagination separately fromthe instrumental parts of locomotion in a way it was not appropriate formoney to be considered separately from specific exchange goods. Whereasvalue is always tied to the specific good of exchange, the material conditionsof locomotion become increasingly abstracted and generalized from theirspecific manifestations as Aristotle generalizes the formal components. Theincreasingly abstract formal sequence, flying, locomotion, motion, desire,is per se and qua related to the increasingly abstract material sequence,wing, limb, joint, potentiality for desire. 57Second, the more abstract and formal subject matters provide the causesfor the more concrete, and for this reason they remain necessarily connectedto the more concrete. The soul provides a principle of animals (DAL1 402a6-7) in several ways, being the formal, final, and moving cause ofliving things. The instrumental parts are ultimately explained by referenceto the faculties of the soul, though they are not the subject of the DA.The examples we have considered in this chapter develop the notion ofscientific autonomy. The case of 2R belonging to triangle is the simplestcase of 'pure generic autonomy,' in which a per se predicate is proved tobelong to a subject qua that subject. Alternating proportion shows thatthe same predicate can be proved of two subjects of different extensionthrough generically different causes. This is a case of 'mixed autonomy,'since the proof in each genus is autonomous and independent of the other.The case of optical proofs and mixed science introduced the notion of the'mixed genus,' in which two different but related genera were active withina single proof. The genera are no longer treated as autonomous, but bothcontribute to the same proof.were, an internal cause. But in addition, god is the first substance and an externalcause of all other substances. Similarly, general and internal causes of the organs oflocomotion are considered, then the external causes of their motion. For desire andperception are not part of the wing, etc., but instead are present in the heart. Soalso Met. A.10 1075al4-15: 'For the good [of the army] is in the order and in theleader, and more in the latter: for he does not depend on the order but it depends onhim.'57 Cf. Met. H.3 1043a34-37, which by using the example of animal rather than manor horse, implies that different levels of generality in form imply different levels ofgenerality in matter and composite. See Loux 1991, 163.

ob"e.52 Aristotle's Theory of the Unity of ScienceSpeed of change, value, locomotion, and mathematics form a graduatedseries of sciences, which illustrate the issue of autonomy from a differentperspective. Instead of a reduction in autonomy as two genera become fusedinto 'Jne, this series marks the degrees to which autonomous genera canbe abstracted from the mixed genera in which they reside. In differentcontexts, certain aspects of the natures of things can be more or lessabstracted so as to form new subject matters. In the case of speed there isnothing common that can form a subject matter over the various speeds.In the case of mathematics, we can completely abstract the quantitativenature of objects and treat it as if it had no per se connections with itssubstrate. Since mathematics loses its per se connections to its substrate,it forms a science independent from physics. It genuinely has its ownprinciples and per se attributes. In the case of locomotion, and to a lesserextent value, common features can be abstracted, but not to the extent thatthey lose all their per se connections to their substrate. Such semi-abstractsubject matters do not form wholly independent sciences, even thoughtheir subject-genera have different per se and qua relations from those oftheir substrates. Semi-abstract subject matters are related to the science oftheir substrate, and are really parts of the science of the substrate. To thisextent, as we shall see, they embody the principles of focality.At the same time, in those cases where either abstraction or semiabstractionis possible (value, locomotion, mathematics), related terms existand function both at concrete and at abstract levels. The concrete term islogically embedded in a specific genus, the wearing of a shoe, the flight ofa bird, the snubness of a nose. But they are all instances of more abstractterms which are not embedded in the specific genus, though the degree ,of the abstraction varies in each case: exchange value, locomotion, curve.Where there are two or more terms that embed the same abstract conceptin different subject matters, those terms will be considered analogous, asthe snub is analogous to the bandy.(

2Analogy In Aristotle's BiologyProblems with AnalogyIn this chapter I turn to analogy and its role in Aristotle's biological works.The biological works serve as a good introduction to analogy, since the conceptand the term are most frequently and systematically used here l I ·shallfirst review some of the prominent interpretations of biological analogy,and then provide some observations on its use derived from a thoroughexamination of the evidence. These observations will form the foundationfor a new interpretation, one that fits analogy into the most basic organizationalschemes of Aristotle's biology, the genus-species scheme and theho!e-parts scheme. This interpretation exploits the t~nsion between theper se and qua requirement and shows how this tension operates to bindtogether discrete genera of objects.The clearest exposition of the role of analogy in biology is provided inthe first chapter of the HistoriaAnimalium:or animals, some resemble one another in all their parts, while others have partswherein they differ. Sometimes the pa rts are identical in form, as, for instance,::me man's nose or eye resembles another man's nose or eye, flesh flesh, and bonebone; and in like manner with a horse, and with all other animals which we reckonto be of one and the same species; for as the whole is to the whole, so each to~ach are the parts severally. In other cases the parts are identical, save only for a1 The biological works represent 26 per cent of the Bekker edition. The uses ofavclhoyol1 / avahoyia. in these same· works represent 36 per cent of the uses. The otherextensive use of the tenn is in the discussion of justice in the ethical works (EN andMM, 12 per cent).

54 Aristotle's Theory of the Unity of Sciencedifference in the way of excess or defect, as is the case in such animals as are ofone and the same genus. By 'genus' I mean, for instance, Bird or Fish; for each ofthese is subject to difference in respect of its genus, and there are many species offishes and of birds.Among them, most of the parts as a rule exhibit differences through contrarietyof properties (TGS Ti;w 7Ta(fryj1.aTwV €VavnwO'Hs-), such as colour and shape, in thatsome are more and some in a less degree the subject 0'£ the same property; andalso in the way of multitude or fewness, magnitude or smallness, in short in theway of excess or defect. Thus in some the texture of the flesh is soft, in othersfirm; some have a long bill, others a short one; some have abundance of feathers,others have only a small quantity. It happens further that, even in the cases we areconsidering, some have parts that others have not: for instance, some have spursand others not, some have crests and others noti but as a general rule, most partsand those that go to make up the bulk of the body are either identical with oneanother, or differ from one another in the way of contrariety and of excess anddefect. For the more and the less lJ,tnAAov KaL 11nov) may be represented as excessand defect.There are some animals whose parts are neither identical in form nor differingin the way of excess or defecti but they are the same only in the way of analogy(KaT' avaAoytav), as, for instance, bone is only analogous to fish-bone, nail to hoof,hand to claw, and scale to featheri for what the feather is in a bird, the scale is ina fish. (HA 1.1 486al4-b22)Though this system of identity - £lOO~ -yEvos-d.vaAoyia - seems intuitivelyapt for biological phenomena, 2 it present us with two challenges. The firsthas to do with the meaning of genus in this context. This challenge is. one my account faces because I have treated genus strictly as subjectgenus,while here Aristotle is talking about a divisible genus. The secondchallenge, the one that has most occupied scholars and will be the startingpoint for my own interpretation, has been to justify 'more and less' as aconsistent demarcation between genus and analogy.The last chapter focused on genus in the sense of subject-genus, whichI distinguished from the genus that is divisible into species. In the formercontext species of a genus are relevant only in application arguments,and their differentiae, that which makes them species, are not considered.Instead, the differentiated species are treated as different subject mattersfrom their divisionary genus. As we saw, the differentiated species (likeisosceles triangle), when treated as a subject of demonstration, becomes a2 See Thompson's (1961) chapter on the theory of transformation, esp. p. 273.

55 Analogy in Aristotle's Biologysubject-genus in its own right. In light of recent research, there is littledispute that the HA and PA make use of such subject-genera. These worksare organized according to subject-genera, and Aristotle is seeking coextensiveuniversals to join in demonstration. 3 There remains, however, a greatdeal of dispute concerning the technical terms genos and eidos. Eidos isextensively used in the biological works and has been a source of confusionand perplexity. Balme was the first to argue that Aristotle's genus-speciessystem was not a precursor of the Linnaean taxonomic system, and thatAristotle's use of the terms, outside of what he called the 'programmaticpassages' (like the one above) was not consistently taxonomic. In fact,Balme so despaired of finding a hierarchical use for these terms that heopted for the etymological sense of genos as lineage group and eidos asappearance, and he dismissed as later additions the 'programmatic' passages,in which eidos, genos, and analogia are placed in a clear hierarchy.4Pellegrin thought that he could discern a consistent order in Aristotle'suse. 5 Genus and species were not fixed levels of generality, but wererelative to one another. The same group of objects could be consideredboth as a genus and as a species. The difference was that the genus isdivisible into species, and the species are determined by differentiae. Bothscholars produced their work before the insights of the Posterior Analyticswere widely applied to the biological works, and so, for all the progress intheir battle against the taxonomic view, they never completely abandonedthe concept of genus as divisible. If, however, we distinguish the use of theterm in the HA and the PA, and especially if we distinguish the first bookof the PA from the other four books, we find some remarkable results.It is reasonable that we should make this distinction, for, as Lennox hasshown, the HA provides the facts of biology, an enumeration of the kindsand sub-kinds of animals together with their coextensive attributes. PA!I-IV takes these facts and provides demonstrations for them. PA I is atreatise on general biological method, and so is different in character fromboth HA and the rest of the PA. Now, eidos is hardly used at all in PAll-IV, just six times, and on four of those occasions it clearly does notmean a determinate kind, but, as Salme remarked, means appearance. 6In two cases it arguably means species, but in neither of these cases isit found in the context of a biological demonstration. Rather, on these3 See especially the work of Lennox (1987a).4 Programmatic passages include HA I.1 486al4-b22 (quoted above), 1.2 488b29-32, 1.6491.14-19, PA 1.4644.16-23, .nd 1.5 645b20-28.5 Pellegrin 1986a, 1987.6 665b8; 680.15; 687b6; 692b13.

56 Aristotle's Theory of the Unity of Scienceoccasions Aristotle is introducing discussions of the great kinds, testaceaand crustacea, and 50 is recapitulating the findings of the HA? By contrast,genas is widely used in PA II-IV and frequently in demonstrative contexts.In short, genos, as we would expect, is the only term used in the contextof demonstration in the PA. When we turn to the HA, we find bothterms in fre~uent use. This is to he expected in view of the purpose ofthat treatise. The HA is pre-demonstrative. Since it establishes genera,divides them into species, and identifies coextensive attributes for bothlevels, it is natural that in this context we should find extensive use ofeide as species into which a genas is divided. This divisionary stage isfollowed by the demonstrative stage in the PA. We take each group ofwhatever extensi

57 Analogy in Aristotle's Biologythe possibility that analogues share any properties and restrict analogicalSimilarity to identity of function. This might be called the orthodox, realist,or functionalist position.A second interpretation, that of the relativists or formalists, holds thatspecies and genus constitute a coherent pair of concepts by themselves towhich analogy has nothing genuine to contribute. David Balme and PierrePellegrin are the principal advocates of this view 10 They have emphasizedthat Aristotle's use of the terms genus and species in the biological works isnot the same as the Linnaean, taxonomic use of genus and species, and thatAristotle is not interested in constructing a taxonomy based on fixed levelsof generality. For our purposes it is important to note that Balme extendedhis argument to analogy: since Aristotle frequently claimed that the samegroups both differ by more and less and are analogically identical, thedistinction between genus and analogy is just as confused as that betweenspecies and genus. To cite one of Balme's more difficult examples: 'oo-ToBvand xovopo, are "vaAoyov at P.A. 653b36 ... but differ Tcr P.UAAOV Kat ~TTOVat 655a32.' Moreover, Balme thought - if rather inconsistently -thatanalogy was wholly dependent on the genera of whole animals, so thatany similarity in part or function between animals of different genera,say, birds and fish, was ipso facto an analogue. Pellegrin, by contrast,argued that the biological use of species and genus was consistent withtheir hierarchical use elsewhere in the corpus: species and genus are onlyfixed relative to one another, and are tools of analysis that can be appliedof analogy, p. 87). He explicitly calls the more and less a criterion of generic identity(73-4). According to Gotthelf (1985, 48), the distinction between a part and its analogueis precisely one between two parts with (essentially) the same function but whichdiffer in material constitution and structure, and do so by more than 'the more and theless'; d. a similar description in Lennox 1987b, 341n8, who rightly stresses that thefunction is the same at a very abstract level. Also see Ross 1949, 670. Cf. Nussbaum1978,83: 'When [Aristotle] so frequently users] the phrase "the x or its analogue" [heis] emphasizing that we are interested in a functional state of the organism, which isrealized in some suitable matter or other. An artificial pump might perform the heart'sfunction, whereas a non-functioning heart would be only homonymously a heart.' Thisposition is supported by Cohen 1992, 59, and Charles 1990, 157, who holds that thegenera are based on distinctive modes of discharging some function.10 Balme 1962; also important for issues in this chapter are Balme 1961 and 1987a.Pellegrin 1986a, 88--94. The English edition contains extensive revisions of his sectionon analogy, and so I omit reference to the original French edition (La Classificationdes animaJlx chez Aristote: Statllt de fa biologie et unite de l'aristotelisme. [Paris: LesBelles Lemes, 1982]). For a quick summary of most of the main issues in his book seePellegrin 1987. Balme 1987a, 79n8, said that he came to agree with Pellegrin on theissue of analogy.

58 Aristotle's Theory of the Unity of Scienceto groups of objects of any extension. Analogy completes the series byallowing Aristotle to compare man, who forms the standard of biologicalintelligibility, with other genera on the lower rungs of the scala naturae.In general, the relativists have focused their attention on the relationshipbetween genus and species and as a result tend to trivialize the role ofanalogy to the extent that it merely recapitulates the function of genus. Itsimply becomes a higher order of generality than genus and can easily betransformed into a genus if we generalize in the appropriate way.Still a third interpretation has provided a deep 'scientific' reason fordemarcating generic from analogical identity. On the grounds that speciesof a common genus develop out of a common physical matter, somescholars have argued that this matter will provide the criterion of genericidentity. According to the embryological interpretation, there is some pointearly in their development when all embryos of a genus have a commonform which later becomes differentiated into the various specific forms.This common form is the matter for further differentiation, and will bedifferent for each genus. Thus, all and only birds are generated from birdmatter, all and only fish from fish matter and so on. If this were true,then generic boundaries could be determined by a thorough study of theembryos. Analogues, then, would be parts that perform the same function,but come from animals of different generic matter. Lloyd, Rorty, and, atone time, Lennox have supported this interpretation,l1 Like the orthodoxinterpretation it is functionalist, but it grounds generic difference, not inthe more and the less, but in facts of embryological development. Like theposition of the relativists, it has the consequence of making all transgenericsimilarities into analogues.All three positions share the assumption that analogy is an interpretativeproblem. Aristotle nowhere provides a clear and extended treatment ofanalogy, and we are forced to piece his theoretical remarks together with hisactual practice in order to produce a coherent account. The functionalistinterpretation is prima facie most plausible, not least because it is mostclosely based on the text, but its supporters have done little to defend itagainst attack. Indeed the major stumbling block to maintaining analogyas a Significant part of the system of identity has been the fact that thedistinction befween analogy and the generic 'more and less' simply cannotbe maintained without further qualification. For, as has been repeatedlyand correctly remarked, analogues frequently differ by more and less inmany ways. Though Aristotle does not call them analogues, the beak in11 Lloyd 1962; Rorty 1973; Lennox 1980, and for his revised position see 1987b.

59 Analogy in Aristotle's Biologybirds and the lips and teeth in humans are surely beyond differences ofdegree, and yet Aristotle transforms one into the other in a remarkablepassage (PA II.16 659b23-27):For supposing that one were to cut off a man's lips, unite his upper teeth together,and similarly his under ones, and then were to lengthen out the two separatepieces thus formed, narrowing them on either side - then we should at once havea bird-like beak. 12In fact, differences of more and less are pervasive throughout all levels ofgenerality. Within a single species one animal is taller, darker, and thinnerthan another. And even within an ~ndividual animal variations are found,for instance, in the temperature of blood, the lower parts being cooler thanthe upper pans (PA IL2 647b29-35). Difference of degree is, therefore, notsufficient in itself to distinguish generic from any other form of identity.It was precisely by seizing on this problem that the relativists extendedtheir argument. Balme began with the observation that species and genushad no hierarchical sense, and then pointed out that analogues too differedby the more and the less, and so could be treated as belonging to thesame genus. The confusion that started with species and genus spread togenus and analogy. It was likewise in response to this problem that theembryologists invoked the material from which organisms develop as thebasis for drawing generic lines. For they realized that the 'more and less'could not be trusted as a steadfast criterion, and cast about for a more securefoundation for generic distinctions. The functionalists for their part, sincethey deny that analogues are similar, have sidestepped the problem.My own interpretation will attempt to combine the virtues of thesethree accounts: remaining close to the text and respecting analogy as asignificant part of Aristotle's system of difference (as the functionalistsdo), embracing the more and less of analogues (as the relativists do), andproviding a theoretical framework in hylomorphism and qua-levels thatwill account for the fixity of analogy (as the embryologists do). But beforeproceeding to that positive step, I shall argue against the relativists that (1)12 Cf. also Pol. V.3 1302b33-1303a2: 'Political revolutions also spring from adisproportionate increase in any part of the state. For as a body is made up of manymembers, and every member ought to grow in proportion so that symmetry may bepreserved. but it loses its nature ($8f'pfTal) if the foot is four cubits long and the restof the body two spans; and, should the abnormal increase be one of quality as well asof quantity, it may even take the fonn of another animal; even so a state has manyparts, of which some one may often grow imperceptibly; for example, the number ofpoor in democracies and in constitutional states.'

60 Aristotle's Theory of the Unity of Sciencethey are inconsistent in claiming that analogy is a relative designation, andthat (2) in spite of a couple of difficult cases, the analogues are fixed and donot vary. I also wish to show, against the functionalists, that (3) analogues,in a certain sense, are related by the more and the less, that (4) relative positionis of fundamental importance in assigning analogical status, and that(5) identity of function in different matter cannot be a criterion for analogues,because there are analogues of function as well as of parts. Finally,(6) I shall provide some arguments against the genus-as-matter position.1. Fixity of AnalogyIn the passage quoted above Aristotle describes analogy as a form ofidentity in a descending scale together with generic and specific identity.But in one important respect analogy is quite different l3 Whereas wholeanimals can be specifically and generically identical, analogical identityapplies only to the parts of animals14 For analogy depends on two objectsbeing compared as parts of two different systems, in this case wholeanimals. But inasmuch as Aristotle groups analogy together with specificand generic identity, he invites comparison between them. And to makethem comparable he presents all three kinds of identity in terms of theparts of animals. Indeed in this passage he draws an explicit correlationbetween parts and wholes and claims that as the parts are to the parts, sothe whole is to the whole (486a20-21). But while whole animals can onlybe specifically or generically identical, parts can be specifically, generically,or analogically identical.Although Aristotle says here that there is a correlation between thelevels of analysis, it is by no means perfect. Speaking of generically identicalanimals, he says, 'as a general rule, most parts and those that go13 In addition to the three common kinds of difference in animals - specific, generic, andanalogical- Aristotle adds several others: position, arrangement, possession/lacking.These are not often included in the standard list because they do not fit logically intothat series. They are similar to analogy in that they deal prinCipally with parts ratherthan wholes. So, for example, in viviparous quadrupeds teats may be found in thebreast or dose to the thighs (HA I.1 486b24-487a1). Identity of relative position isalmost always a condition for analogical identity.14 Muskens 1943, 33. There is only one case where Aristotle calls whole animalsanalogous. At GA 1II.1l 761a24-32, testacea and plants are said to be analogous (T~V4>ucnu a.uaAoyov iXH) because the nature of testacea is to be in such a relation to wateras plants are to earth, as if plants were, so to say, land shell·fish and shell· fish waterplants. In this case the analogy is between the organisms and their environment, ratherthan between pans a~d whole organisms.

61 Analogy in Aristotle's Biologyto make up the bulk of the body are either identical with one another,or differ from one another in the way of contrariety and of excess anddefect' (HA 1.1 486bl4-16). Among generically identical animals, then,Aristotle says that some of their parts are either the same or differ byexcess or defect. Although fewer than fifteen lines before he had saidthat whole animals are related as their parts are, here he qualifies hisprevious statement and divides the parts of generically identical animalsinto three categories, those that are the same, those that are present insome and absent in others, and those, the majority, that differ by moreand less. We can envisage cases like the following: among species A,B,C,Dof a genus, A and B may have a certain part the same, which C hasto a lesser degree and D has not at all. 15 Generic attributes that areexactly the same represent the limiting case of more and less, and solong as not all members of the genus share the same attribute to thesame extent, the more or less distinction stands, because it holds goodfor the most part. At either end of the generic scale there will be attributesthat are so little distinct between two animals as to be exactlythe same, or so much distinct that they are possessed to a negligibledegree by some members, and indeed are completely absent from them.'6Evidence from the text overwhelmingly shows that some parts are morewidely distributed than others and that between two animals of the samegenus not all their parts need have exactly the same degree of difference.Indeed, this fact can be observed in the organization of the PA, forwhile the internal parts of blooded animals are treated in common, theirexternal parts are treated separately for each greatest genus (p.€YWTOVyiVD', viviparous quadrupeds, oviparous quadrupeds, birds, fishes). Notonly within a genus are some parts more similar than others, some greatestgenera simply display a greater degree of internal similarity than others.Aristotle's paradigm cases of genera, birds and fish, have by far most oftheir parts the same or differing by more and less. This is especially sowith birds:The differences of birds compared one with another are differences of magnitude,and of the greater or smaller development of parts. Thus some have long legs,others short legs; some have a broad tongue, others a narrow tongue; and so onwith the other parts. There are few of their parts that differ, taking birds by15 Pellegrin prOVides a similar analysis in 1986b, 151.16 This is suggested by Met. I.4, where the various fonns of opposition are arranged inan order: contradictories, posseSSion/privation, contrariety, and relatives. The limitingcase of contrariety is possession/privation. See Pellegrin 1986a, 59-60.

62 Aristotle's Theory of the Unity of Sciencethemselves. But when birds are compared with other animals the parts presentdifferences of form also (Tfj flOpfj TWV flopiwv). (PA IY.12 692b3-9)Other genera, like viviparous quadrupeds, do not show this same degreeof internal unity.At HA 11.1 497b6-12, Aristotle says that some organs and parts arecommon to all animals, and some common only to a particular genus:With regard to animals in general, some parts or organs are common to aU, as hasbeen said, and some are common only to particular genera ... For as a general ruleall animals that are generically distinct have the majority of their parts differentin form; and some of them they have analogically similar and diverse in genus,while they have others that are alike in genus but specifically diversei and manyexist in some animals but not in others. 17This passage clearly implies that if generically identical species can haveparts that are specifically the same, vary by degree, or are missing fromsome members altogether, some parts of generically distinct animals willbe more closely related than others (e.g., the eyes of fish and birds aremore closely related than their scales and feathers)'8 Likewise, a part ofan animal in one genus may simply not have an analogue in an animalof another genus. For example, cephalopods simply do not have analoguesof hair; testacea do not have analogues of lungs. Alternatively, a certain17 The last part of the passage reads: UXEOOV yap oa-a y' fUTl yivEt Eupa TWV '~WV, Kat TO.7TAftt1Ta rwv P.fPWV (Xft EUpa Tip dOft, I(al TO. ,!.tEV l(aT' avaAoyiav aOta.cpopa p.Ovov, Tlf yivEto· EUpa. Til Of T~ yivEt }lfV TaVra r~ f!'Oft 0' fUpa.18 The passage is nOt without controversy. In comparing it with HA 486al4--b22 quotedabove, Balme took issue with those who interpret them together and claim thatgenerically distinct animals have some partS generically distinct, others specificallydistinct (1962, 91): 'Thompson, ad loe.: "In the opening sentences, which must be readtogether with those of Book I. brevity leads to a certain appearance of confusion: weare reminded that a generic difference between two animals carries with it genericdifference between certain parts as wdl as specific difference between many others." Butthe words which I have italicized are nOt in accord with I. 486316f. (above). yivEt Eupaare, for example, opw~ and 'XOvs (486a21 ). Their pans are to be compared ouu fWEtOUTE KaO' inrfPOX~V I(al (hAEt",'V, ahAa I(ar' ava,).,oyiav ... 0 yap f V opvt8t 7TTfpOV. ToilTOfV ;''X!JVl fO"T ~ hf1Tls. KaTa. ,!.tfv o~v .uDPla a. fXOtXnv (lC.aO"Ta TWIJ (~WIJ. TOVTOV roy rpinrovfUpO. fO"Tll(a~ mimi (486bl8-23). The expression fUpa T

63 Analogy in Aristotle's Biologypart shared by animals in two different genera may not be analogically,but generically the same, for example, blood, which is shared by man,viviparous quadrupeds, oviparous quadrupeds, and fish.19In general, then, the relations of similarity among parts are fixed andprimary, and the similarity among whole animals is dependent upon these.Since different parts have different extensions, there may be some ambiguityin assigning identity status to groups of whole animals. Since Balmewas concerned with problems of whole animal taxonomy, he tended todevalue the importance of parts in determining identity status. Pellegrin,by contrast, took the parts as primary. When a certain generic part is unclerconsideration, he argued, the animals which have that part form a genus,and when a modification or species of that part is under considerationthe animals which have that part form a species. It follows that the sameanimal group may be a species or a genus depending on which part isunder consideration. So, considered as an animal having a liver, birds forma species of the genus blooded animals, but as having wings they area genus. The identity status of whole animals depends on the identitystatus of parts, and these must be fixed. So, if a group of animals is calleda species, it is because the part that these animals have is a species, adetermination of a type; if they are called a genus, the part that theyhave is a genus, a determinable type. To some extent, then, the passageswe have discussed corroborate Pellegrin's controversial thesis concerningAristotle's 'moriology: the claim that the parts of animals are ontologically19 There is one statement which suggests that analogies are ubiquitous, since all similaritiesbetween genera are analogues: TOVTO ~E 7rOLt:tV i1rl1TdCTul au pq.~tDlr TO. yap 'lTo.\M (~aava..\oyolJ ravTo wf:rrov8f:v (PA 1.4 644a22-23). Peck translates: 'It is not easy to do this inall cases, for the corresponding analogous parts of most groups of animals are identical.'This is a rather difficult construal of the text, but he seems to mean that in mostanimals (Le., between mOSt animals groups, however you take them) the proportionalrelation is really identity (i.e., not analogy). So, e.g., as wing is to sparrow, so wing is tofinch, and the relationship, even if set in analogical form, is really identity. That is whyit is. difficult .to find genuine analogies, because most of them are really identities. If thisis what Peck has in mind, it strains the meaning of the words. The ROT translation ('Itis not easy to do this in all cases; for in most animals what is common is so by analogy';W. Ogle) makes good sense of the last sentence, but it does not seem to fit the context.The TOVTO 11"Otf:IV almost certainly refers back to the beginning of the chapter, meaningthat it is difficult to comprehend two groups into a single kind (so Balme 1972, 121),and since it is difficult, presumably the common lot of men have not done it, and theywere right not to do so. The implication of the passage is that it is difficult to find acommon nature among distinct groups (animals that breathe do fonn such a commonnature). Among such groups analogy is a much more common relation. This passage,then, does not constitute evidence that every transgeneric Similarity is an analogy.

64 Aristotle's Theory of the Unity of Scienceand epistemologically basic and that whole animals, species or genus, arederivative.'o But when Pellegrin discusses analogy, he fails to apply thisscheme consistently and ignores the fact that analogy is a relationship thatexists between parts only, and not, as species and genus, between both partsand wholes. While he rightly makes the genera of wholes dependent upontheir parts, when he treats analogy, he reverses the order of dependencyand makes the identity status of parts dependent on whole animals. He citesthe example of bone (to which I shall return) in order to show that underone description a group of parts (bone and cartilage) may be consideredonly analogically identical, while under another they may be genericallyidentical. He claims that there is no simple answer to the question whetherbone and cartilage are related analogically or by difference of degree, sincethe contexts in which Aristotle talks of analogical difference are quitedifferent from those in which he talks of more and less. Inasmuch, hesays, as 'we have two genet .bony animals and cartilaginous animals,' thereis 'between them an analogical relation,,2l For Pellegrin, the determination20 I cannot follow him in his argument regarding the use of the tenns genos and ddosoutside the programmatic passages for the reasons given at the beginning of the chapter.Here Balme is basically correct: eido5 as used of whole animals very rarely designatesthe technical 'species,' and the text does not support his claim that gene are ne

65 Analogy in Aristotle's Biologyof genus' is largely a matter of decision: 'from the moment one decides totake' these groups as genera, parts common to both become analogous?2But from a different perspective, he says, Aristotle considers the natureand function of skeletons in general, and from this perspective 'bone andcartilage are now two different "species" of material used by nature as"support.'" Pellegrin's comments are brief and not altogether clear.23 HeThe animals which do not have [boneJ have something analogous: in the fishes, forexample, in some there are spines, in others cartilage (11.8 653b35, after P.P.)The nature of cartilage is the same as that of bone, but they differ according to themore and the less. (11.9 655a33, after P.P.)'Is there between cartilage and bone an analogical difference or a difference of degree?That is not an Aristotelian ques tion. In the first case we have two gene, bony animalsand cartilaginous animals, which have between them an analogical relationship; but inthe second case the point of view is not the same. Chapter 9 studies the nature andfunction of the skeleton: from this perspective bone and cartilage are two different"species" of matter employed by nature as "suppOrt" of the body ... Within thegenos constituted by "parts" assuring the "support" of flesh, there are variations ofdegree, particularly according to size and hardness, which relates, among others, tothe difference between bone and cartilage. And one may find other examples of thesechanges in perspective which have the effect of "declassing" the analogical relationship,even if these examples are less explicit from a terminological point of view. Comparetwo texts:In some animals the parts are not of the same ddos and do not differ by excess anddefect, but differ by analogy: that is the case, for example, of bone in relation to spine,of nail in relation to hoof .. . (HA I.l 486b17, after P.P.)We have here an example very close to the doctrine which we found above at PA644a16 [not quoted here]: that which is nail for genos A, is hoof for genos B. But as inthe example given above, the point of view can change:There are some parts which to the touch resemble bone, for example nails, hoofs, clawsof lobsters, horns, beaks of birds. All these parts at e possessed by animals for theirdefense. (PA 11.9 655h2)Although he does not say so explicitly, Aristotle now considers these different parts aseide of the genos "organs of defense", and from this perspective nail and hoof are nolonger analogous. One may even suppose that when a little later Aristotle reminds usthat these parts are all composed of earth (655bll), that is a way of saying that theyform one genos:22 1986a, 88: 'A logical examination of the concepts of genos and analogia shows us .that feather and scale can be said to be analogues from the moment one decides to take"bird" and "fish" as gene.' The italics are Pellegrin's.23 The immediate context of the passage he quotes for this second perspective, PA 11.9655a32-34, discusses the use of bone and cartilage in the same animal (i.e., in additionto bones, we have cartilage which supports our ears and nose).

66 Aristotle's Theory of the Unity of Scienceseems to be aiming at a contrast between the way parts are treated whenthey are considered as parts of animals of different genera (analogues)and when they are considered as a group of parts that perform the samefunction (members of a genus). Considered just as flesh support they differby the more and the less, harder and softer, and as such they are speciesof a genus. But inasmuch as they discharge the same function in differentgenera of animals, they are analogically related.Taking another example, Pellegrin claims that the organs made of nailstuff, including teeth, can be considered as species of the genus 'organs ofdefence,' so making analogous organs fall into a single genus (EV TOlmp ni>YEVEl 655b8). But inasmuch as they appear in different animal genera theyare considered analogous. This cannot be right. For while nail, horn, hoof,claw, and bird beak are clearly made of a similar material necessitated bytheir being defensive organs, Aristotle never says they are all analogues.In fact, only nails, hooves, and claws are.24For Pellegrin a solution lies ready at hand. It is one of the centraltheses of his book and later work that the identity status of whole animalsdepends upon the identity status of their parts. 25 Thus if we decide to takea certain part as a genus, it will logically follow that the animals that havethis part will form a genus. This whole edifice falls unless it is based uponthe fixed identity status of parts, and for this reason Pellegrin should nothave abandoned this principle when dealing with analogy. According to hisgeneral argument, Pellegrin should say that bony and cartilaginous animalsare placed in different genera only if the parts they have, bone and cartilage,are generically different. He should remain faithful to this general principleand claim that just as genus applies primarily to parts, and derivatively towhole animals, so also analogy applies to parts first and foremost, andis not something that logically follows from a predetermination that' twogroups of whole animals constitute different genera. This position is morein accordance with the spirit of his interpretation and the evidence fromthe text. So, from the general argument provided by Pellegrin, we cansee that the relativists, since they are relativists only in regard to wholeanimals and not in regard to parts, have no need to insist on the relativityof analogy. Analogues are fixed at the level of parts, a wing just is an24 Aristotle says (PA II.9 65Sb2-4; HA IILll 517b21-26) that nail etc. are the same asbone with respect to hardness or to the touch, but at HA III.9 517a6-10 he goes $0 faras to say that though these parts do not have the same nature, it is not too far removedfrom that of cartilage and bone.25 Pellegrin 1986a, 1987.

67 Analogy in Aristotle's Biologyanalogue of a fin, hair of scale, and so on. Pellegrin is generally correctabout the primacy of parts in determining group affiliation in the HA andthe PA. HA I- IV and PA II-IV are, after all, about parts, so it is naturalthat the animals should be discussed in these terms."2. Difficult CasesThough the relativists, in order to maintain their basic thesis concerningthe primacy of parts over wholes, must" concede that the identity relationbetween analogues is absolutely fixed and unchanging, there are severalcases in which the demarcation between analogy and genus seems far fromfixed. For example, the distinction between flesh (TCipt) and its analogueusually follows that between blood and its analogue (PA III.5 668a25-27;HA 1.4 489a23-26). But on one occasion Aristotle divides among bloodedanimals, and makes the division correspond to bone and fish-spine, thusmaking fish-flesh only analogous to other blooded flesh rather than genericallyidentical (HA II1.16 519b26-30). Likewise, there are variant accountsabout chests (aTijea,). On the one hand, 'all animals have a part analogousto the chest in man, but not similar to his; for the chest in man is broad, butthat of all other animals is narrow. Moreover, no other animal but man hasbreasts in front; the elephant, certainly, has two breasts, not however inthe chest, but near it' (HA I1.1497b33-498a2; d. HA 11.12 503b29-32). Thedifference in the arrangement of the elements of the parts and the shapeof the whole parts are sufficient in this case to make the parts analogous.Since the breasts are the major component of the chest in man, and this isa major part of what chest is, without the breasts 'chest' can only deSignatea position. 27 Alternatively, when all perfect animals are divided in threeparts, the middle is called the chest in the largest animals, and in othersit is the analogue Uuv. 2 468a13- 17). In this context, the chest is invoked26 For good reasons we need not, and should not, follow him in his ontological claim:Aristotle clearly says that the whole individual C!idos is primary (PA I.4644a23-27).Moreover, pans are often the explananda, not the explanantia, and so ultimi'!!ely maynot form pan of the definition of the animal. While pans are methodologically the firstway of looking at animals, they are not the last or best way. Cf. also G.E.R. Lloyd1990.27 Cf. HA I.12 493a12-16, which mentions the breasts as the only component of the chest:'Next after the neck in the front part is the chest, with a pair of breasts. To each of thebreasts is attached a nipple, through which in the case of females the milk percolates;and the breast is soft. Milk is found at times in the male; but with the male the fleshof the breast is tough, with the female it is spongy and porous.'

68 Aristotle's Theory of the Unity of Scienceas the seat of the nutritive faculty. Thus, the demarcation between chestand its analogue can be drawn either (i) between man and other animals,or (ii) between big perfect animals and other perfect animals.Again, there are two quite different levels of analogy among wombs.Copulating female insects frequently have a part that is extended into themale, and this is called an analogue of a womb (GA 11.4 739a18-20). In whatis obviously a remoter analogy, an eggshell is also called an analogue of thewomb (GA 111.2 753b35-754a3). Some analogues even extend beyond animals.Without giving explicit examples Aristotle says that mouths amonganimals may be analogous (HA 1.2 488b29- 32), but more remotely, theroots of plants are analogous to the mouth in animals (Juv. 1 468a9-12).It is clear from these examples that analogical distinctions can be madeat different levels, and that there is no precise degree of similarity thatcharacterizes analogous parts.As a result, Aristotle is sometimes not clear whether the relationship isone of analogy or something closer. Urchins have black fonnations attachedto the starting point of the teeth. Other animals like tortoises, toads,frogs, and cephalopods have something like this or analogous (rowvrovi) .lv/IAoyov HA IV.S S30b31-33). We may compare this to the case offish-flesh above, which may be considered either analogously or genericallyrelated to the flesh of other blooded animals.These cases present an important challenge to the fiXity of analogy andgenus, and suggest that the distinction is universally interchangeable orrelative. However, most analogues do not admit of these variations, andthere are good reasons why these cases are peculiar. Each part has a definitionin accordance with its name (AOYOS- Karel TOVVO/la), and for most partsthe essential features of the definition are clear enough. But with someparts, and especially those with nameless analogues, it is often difficult toset a demarcation with exact precision, and sometimes essential featuresfloat in and out of the definition according to the demands of grouping andexplanation. So chest may be defined either as the place where breasts arelocated or as the seat of nutrition. Because named analogues like wing andfin pick out clearly defined objects, there is never a question whether theseare analogues or form a genus. A nameless analogue, however, is invokedbecause, though it corresponds to the named part, Aristotle feel s that itis inappropriate to extend that name to it. In these cases the demarcationhas not been set by common usage. Without a definite contrast pair, thedefinition of one member may vary. While this flux in definition is quitemarked in the cases of analogues, it is endemic to Aristotle's whole method,which does not provide full definitions from the outset, but uses partialdefinitions in an often ad hoc manner.

69 Analogy in Aristotle's Biology3. Analogues and the More and LessHaving considered the arguments of the relativists we must now turn tothe functionalists, and show that analogy involves not only identity offunction, but also material and structural similarities. 28Most commentators have recognized that analogues exhibit materialsimilarities that may be characterized by the more and the less, and this isthe source of the problem of analogy. It hardly needs lengthy proof and afew examples will suffice: bone and cartilage, though they are analogues,share the same nature and are related by the more and the less, bonebeing earthier and harder than cartilage (PA [1.9 655a23-34). Feathers,hair, and scale all arise from the moist material under the skin (GA V.3783b2-8). Talons and hooves are made of the same basic horny material(PA [1.9 655b2-4). Blood and its analogue have a close material relation:'The watery part of the blood is serum «xwp), either owing to its not beingyet concocted, or owing to its having become corrupted' (PA [1.4 651a17-18). Blood is a further concoction of ichor together with fibre, which isadded or formed in the concoction, and this fibre aids coagulation in theblood (HA [[[.19 521a17-18; 520b25-26). The blood of the very youngis ichor-like (521a32-33). Ichor is at once materially similar to blood andthe analogue of blood. As Aristotle says, even among animals in differentgenera there are common affections (EOT' yap fmQ, 7ra8'r] /cOLVa Kal. TOVTOtS-PA 1.4 644al4-16).29 .4. Analogues and PositionWhile the material similarities are notorious, the importance of position,the arrangement of a constituent part within a whole, in determininganalogues has been underrated. 30 But the importance of. position is not28 In the following review I have nOt included uses of a1.'Ti or any other looser expressionwhere one part is substituted for another that performs the same function. To do sowould immediately prejudice the results in favour of a purely functional interpretationof analogy. I do not assume that Aristotle explicitly used avaAOYov on every appropriateoccasion, any more than he explicitly calls every genos YfllOr and so on, but anyeven-handed study must start from his actual use of the tenn.29 Among other examples that indicate the material similarity of analogues, we find DA11.11 423aI2-15: 'For no living body could be constructed of air or water; it must besomething solid. Consequently it must be composed of earth along with these, which isjust what flesh and its ana/oglle tend to be.'30 Richard Owen (1804-92) first drew the distinction between homology (structuresdiffering in function and appearance but deriving from the same part in the 'archetype')

70 Aristotle's Theory of the Uniry of Sciencesurprising, when we consider that the organization of the HA and the PAis largely based on the position of parts within animals. Analogous organsin generically different animals cannot, of course, have identical positions,since the position is always relative to the particular kind, but their positionscan correspond. While viviparous quadrupeds have hair, oviparousquadrupeds have the analogue horny scales: these scales correspond inposition (o!,owv XWp'f) with the scales of fishes (PA IV.U 691a16).31Still, neither similarity of function nor similarity of position is individuallya sufficient condition of analogy. For a function may be dischargedby a variety of different parts without those parts being called analogous.And though parts may occupy the same relative position, they are notnecessarily analogues. Humans have hands (X"P«), and polydactylousanimals have paws closely analogous to hands (jJ.a.)"'TTa ava.,\oyov HA[1.1 497bl8-20). For they use their paws for some of the same functionsas hands, such as grasping things and defending themselves (PA IV.10687b28-688a2). Aristotle draws a contrast between them and hooved animals,which explicitly do not have such analogues (PA IV.10 688a2-4).They have forelegs (7rpou$,a) instead of arms (avTl TWV /3paX'ovwv HAII.l 497b18-19). So, even though the forelegs occupy the same relativeposition, since they do not perform the same function as hands, they cannotbe analogues.Conversely, though hooved animals use their back legs for defence (PAIV.lO 688a2), these are not called analogous, because, even though theyperform some of the same functions as hands, they are not in the samerelative position. Again, though elephants have a trunk (jJ.VKT~p) insteadof a hand, it is never called analogous (HA II.l 497b26-27), in spite of thefact that the elephant uses it as a hand (PA 11.16 658b35-36). Likewise,mouths and teeth are used for defence, but are not called analogous tohands (PA III.1 661b3-6). .By contrast nail (iivvt) and hoof (67r'\~ ) are analogous (HA I.l486b20).Both are organs of defence (PA 11.9 655b4-5), but this is not sufficientand analogy (structures performing similar functions, but not necessarily derived fromthe modification of one and the same part in the 'plan' or 'archetype' according towhich the ' two animals compared were supposed to be constructed). Aristotle does .notmake a distinction between homology and analogy. His examples, however, are usuallyobvious cases of homology rather than analogy, although they do not involve thenotion of archetype. LeBlond mistakenly claims that Aristotle did draw this distinction(1973, 221). Nor is Aristotle concerned with visible fonns of ideal prototypes (contraThompson 1929, 55; d. Lennox 1980, 327-9).31 Cf. wings and fins at fA 18 714b3-7.

to make them analogues 171 Analogy in Aristotle's Biologyfor it is clear that they occupy similar relativepositions and are made of similar material (655b4-15).Even among internal organs, analogues share relative position in ad~dition to having similar material constituents. The most frequently mentionedare the heart, blood, blood vessel, and flesh and their analogues.Together they form the most basic nutritive and sensitive system of ananimal. Heart and its analogue are the principle of nutrition, movement,and sensation; flesh and its analogue are the medium of touch. Blood andits analogue are food for flesh and its analogue, and must be contained in ablood vessel or its analogue. Among these analogues shared function is notthe only consideration. The /lUTtS in cephalopods is clearly the analogueof the heart because it occupies the same position (PA IV.5 681b28-30on o· furl TO aVO,AOrOV Tff KapOiq. TOVTO TO jJ.0PLOV, 017AOL (; T07TOS' (O~TOS'yap f(rnV 0 aUTOS)). 2 The position of the P:UTtS' is not incidental to itsfunction: the heart and its analogue occupy the central position of thebody, because they are the sources of control (PA IV.5 681b33-34). Again,the fact that the fluid in the /lUTtS is sweet and has undergone concoctionshows that it is the analogue of blood. 33 Likewise, it is necessary that bloodand its analogue should be contained in a vessel (PA III.5 667b18- 20). AtHA 1.4 489a19-22 Aristotle mentions various similarities between blood(aT/la) and its analogue, ichor (ixwp).34 They are both found throughoutthe body, and they exhibit various material similarities. But ichor, whenpresent in blooded animals, does not serve the same function as blood. Itis only as parts of systems that parts can be analogous.The brain is the only clear case of an inference to the existence of ananalogous organ on the basis of principle without any perceptible evidenceof position or material. All animals have sense perception, and since noactivity can be continuous, sense perception must occasionally rest, andthis state is called sleep. Although Aristotle cannot say with certaintythat all animals sleep, he accounts for those in which sleep is observed,namely all the blooded animals, cephalopods, and insects, and says thatif his argument from sensation is persuasive (7HeaVOS'), it will persuade32 That position plays an important role in analogy was recognized and briefly commentedon by Lones (1912, 211): 'It cannot be decided to what extent, if any, Aristotle wasthinking of the plan of structure of the parts, when he compared them [by analogy], butit is clear that he was rderring chiefly to their functions, positions, and mere externalresemblances.' Cf. also Leblond 1945, 41-2.33 For sweetness of the blood, HA III.19 520bl8-19.34 Elsewhere he mentions the counterpart of blood without calling it ichor (e.g ., 645b8-10,648a4-5, 650a34-35). At PA IVA 678a8-9 blood's analogue is said to be without name.

72 Aristotle's Theory of the Unity of Scienceus that testacea sleep as well, though their sleep is not evident (Somn. 1454bl4-23). Moreover, he explicitly makes the assumption that the causesof sleep are the same or analogous in blooded and bloodless animals, and arethe same in blooded animals as in man (Somn. 2 455b32-33: inroil:rI7TT€ov€ivat TO. aina TOU 1Tci8ovs. ~ ravro'ry TO. Q.vaAoyov TOtS B' €Vai}lOLf!: a.7f'fP TOtSav8pw7ToLS). Nevertheless, he never mentions any features of the analogousparts, except to say that since the bloodless animals lack blood, they havelittle heat, and so presumably require smaller brain analogues. Aristotleseems more certain in the PA that bloodless animals have an analogue ofthe brain (PA Il.7 653a10--12). But apart from the octopus he mentions nocase of a brain analogue (652b23-25). It is clear that if Aristotle did notsee the brains of bloodless animals, then they could hardly be genericallyrelated, that is, related by difference of degree. Nevertheless we can assumethat, since sleep is caused by the rising vapours of food to the brain, brainanalogues will have to be situated in the upper region of rhe body. Thus,while analogues frequently exhibit obvious perceprual similarities, in thiscase they are assumed on the basis of a principle. Although Aristotle doesnot discuss how bloodless animals sleep, it is clear from his assumption ofa brain analogue that he supposed that the mechanism and position wouldbe much the same as in blooded animals.There are examples of more remote analogies. An eggshell is called ananalogue of a womb (GA III.2 753b35-754a5), but even this is not a purelyfunctional analogy. The embryo must be in contact with the mother, andin the case of the egg the mother is in the womb, namely the yolk inthe egg. But in spite of the inversion the analogy is partly based on thesimilarity of structure, since the womb and its analogue, the shell, encloseand protect the embryo.Even the roots of plants, which are the analogue of the mouth, are inthe same relative position Uuv. 1468a9-12), since plants are simply upsidedown (PA IV.IO 686b31-687a1). The notion of shared relative position isso basic to analogy that Aristotle is willing to view plants as invertedanimals to achieve the parallel.5. Analogy of FunctionSo it is clear that analogues are based on more than shared function. Buteven the function that analogues share cannot be identical, for there areanalogies of functions as well as of parts. Alrhough the passage is neitherclear nor consistent, Aristotle at least recognizes that activities (7TpatHS')may be analogically, generically, or specifically identical (PA 1.5 645b20--28):

73 Analogy in Aristotle's BiologyWe have, then, first to describe the common activities, and those which belong toa genus or to a species. By 'common' I mean those which belong to all animals;by 'to a genus,' those of animals whose differences from one another we see tobe matters of degree - Bird is a genus. Man is a species, and 50 is everything notdifferentiated into subordinate groups. In the first case the common attributes maybe called analogous, in the second generic, in the third specific.If we can assume that Aristotle is talking about activities throughout thispassage, then the 'common activities' in the first line is to be glossed by'analogically,' as he explains in the last sentence. It is strange that he explainscommonality in terms of whole animals rather than their activities,but perhaps we can suppose that he has in mind generic bird activities andspecific human activities. Elsewhere Aristotle considers the pOSSibility thatplants perform an action analogous to sleep (GA V.1 779a2-4). Althoughhe thinks this is a far-fetched analogy, he does not say that functionscannot have analogues.Other passages make the same point more clearly. Along with theactivities, the ways of life (f3iOL) and habits (~e~) are said to admit of thesame kinds of identity as the parts (HA VII (VIII).l 588a25-31). But littleactual use is made of the scheme. Most of the habits seem simply to beshared more and less among various animals. This is because the analysisby activities and habits tends to ignore the instrumental parts, and so thecorrespondence between the parts on the one hand and the activities andhabits on the other becomes less clear, especially with the emotions. Theexception is intelligence, which man has primarily and the other animalshave analogically. Aristotle draws correspondences between intelligenceand material conditions. Art (T'XV~), wisdom (rroia), and understanding(UVV€ULS-) are peculiar to man, but other animals have analogues. In general,colder and thinner blood is conducive to sensation and intelligence, andthe same applies to the analogue of blood in bloodless animals. So bees areintelligent (POVL!'OL) because of the coldness and thinness of their bloodanalogue (PA 11.2 648a4-8).While it is easy to see how the function of walking is determinedby the particular material constitution of the leg, it is much less easyto see how psychological functions like thought and the emotions couldhave analogues, and for this reason Aristotle rightly leaves this part of hisscheme undeveloped. Nevertheless, analogues of function limit the degreeto which parts that perform these functions can be the same, and make clearthat Aristotle did not intend the functions to serve as higher genera underwhich the analogues could be species. If functions can be analogues, theycannot be abstracted from the instrument that performs them. Walking,

74 Aristotle's Theory of the Unity of Sciencefor instance, is a function that only legs can perform, and only wings canfly. Since the function of parts cannot be considered separately from thoseparts, function cannot provide the genus-creating unity that the orthodoxaccount (or Pellegrin) suggests.6. Genus as MatterLike the functionalist account we just considered the genus-as-matter approachtries to establish a clear demarcation between generic and analogicalidentity, but it rejects as arbitrary or ad hoc the more and less criterion.Instead it finds an empirical solution in certain facts about embryologicaldevelopment. Aristotle does, in fact, provide some tantalizing hintsthat embryos develop towards greater articulation and specification froma more common and generic form . But according to the genus-as-matterinterpretation there is some point in their development when all embryosof a genus will have a common form that later becomes differentiated intothe various specific forms. This common form is the matter for furtherdifferentiation, and will be different for each genus. Thus birds are generatedfrom bird matter, fish from fish matter, and so on. If this were true,then generic boundaries could be determined by a thorough study of theembryos.There are two variations on this account, corresponding to two ratherdifferent views of division. The first treats the differentiations on the modelof Metaphysics Z.12 and successive divisions, for instance, footed, clovenfooted.On this model embryos become successively differentiated from acommon genus, and the history of this development can establish thosecommon attributes that are truly generic from those that are analogicaL 35The second account begins from the system of differentiation laid out inPA 1.2-4. 36 Starting from a group of generic characteristics that all embryosof a genus have in common, each species takes on its specific differences.This account would seem to be more consistent with the basic approach ofthe biological works. Both accounts, however, face the problem that thereis no clear evidence in the GA that Aristotle seriously tried to establish or35 A.c. Lloyd (1962) argues for a physical process of differentiation from the genus thathe identifies with matter to the ultimate species, identified with fonn. M. Grene (1974)has pointed out difficulties that Lloyd and those who identify matter and genus face.Though there are clearly passages where they are identified (Met. 6..28 1024b6-9; Z.121038a3-9; H.6 1045al4-25; 1.8 1058a21-26), it is not dear that matter must meanmaterial substrate. While these kinds of genus may be related by analogy, they are notthe same (Grene 1974, 65).36 Once championed by Lennox: 1987h, 358. Since that time he has repudiated this view,hut it is important to consider it for the lessons it teaches about analogy.

75 Analogy in Aristotle's Biologyjustify his demarcations through an appeal to the facts of embryologicaldevelopment.While Aristotle does discuss the order of development in individualcases, there is no mention of fish matter or bird matter becoming specified,and instead he confines himself to the order in which different parts of anorganism develop. He makes use of the basic principle that parts whichmake other parts (i.e., the heart) must be the first to be formed; parts thatare the purpose of the animal (i.e., organs of sensation) are formed second,and finally those parts that are instrumental to the end (e.g., legs, viscera)are formed last (GA II.6 742a18-b17). He addresses his remarks here ata very high level of generality, and he believes that this basic order is acommon feature of all animals. He clearly cannot have intended the orderof development as a practicable empirical criterion, since he expressly sayshe has observed the formation of the heart only in blooded animals Uuv.3 468b28-30), and nowhere does he consider specific differentiations froma generic type.The only suggestive evidence within the biological works is the passageat GA II.6 743b18- 25:The upper half of the body, then, is first marked out in the order of development; astime goes on the lower also reaches its full size in the sanguinea. All the parts arefirst marked out in their outlines (a7To.vTa. Of TatS 7Tfptypacpa'is OtOpiC€To.t 7TPOT€POV)and acquire later on their colour and softness or hardness, exactly as if nature werea painter producing a work of art, for painters, too, first sketch in the animal withlines and only after that put in the colours.Though this passage offers some superficial support for the position, thegenus that is differentiated here is animal, not one of the greatest genera.Yet it was essential for the argument that it be the matter of the greatestgenera that is differentiated, if the matter is to be that which distinguishesthe genera. In fact, all of the parts whose development Aristotle describesin this chapter are parts common to all animals, and not generic parts orattributes at all. ROT translates a:rravTa as referring to all the parts, butthis passage as a whole is found in a discussion about the formation ofhomoiomerous parts, and Aristotle is describing the changes that occurin the nutriment to form these parts. It is far more likely then thatQ.7TavTa refers to these homoiomerous parts, and this is corroborated by thedifferences these parts later take on: differences of hardness and colour areassociated with flesh, skin, nails, and so on. 37 And homoiomerous parts,37 Cf. GA Its 741bll-lS, which clearly says as much.

76 Aristotle's Theory of the Unity of Scienceas we have observed "above,. have only a very loose correspondence to thegreatest genera of whole animals.The strongest argument against the genus-as-matter view is that itwould entail that all parts of two different genera could only be analogicallyidentical, which seems unlikely in view of the evidence adduced above.When the matter of each genus is what separates the genera from oneanother and all the parts of each genus are generated out of this matter,analogy can be the only level of identity among parts of animals of differentgenera.To look to embryological development to solve the problem of genericidentity is to ignore more obvious evidence close at hand. The genera of animalsare distinguished by their external form. The fact that some animalsare internally and externally viviparous, others oviparous or laxviparoll5simply corroborates most of the other internal and external differences. Notonly is the embryological approach implausible, it is contrary to Aristotle'sstated method (PA I.1 640a10-19), which begins by taking the phenomena,then goes on to consider how each animal comes to be formed. 38 From suchmaterial and efficient causes we can explain and demonstrate the phenomena,but it would be a mistake to suppose that we can use embryologicalresearch to establish or justify the demarcations. 39Although Aristotle did not exploit the physical application of thegenus-as-matter approach, the logical formulation, in which, for example,hooked beak is a differentiation of the generic beak, turns out to bevery important, since it provides the basis of an order of explanation thatdistinguishes analogical from generic similarities. Differentiations of a partmust be treated together, and different parts must be treated separately.The logical formulation distinguishes these patterns on the basis of theadult form rather than embryological development, and ultimately what38 A similar point is made by Preus 1983, 344. Preus treats the 'genotypiC' (roughlythe account through embryological development) and the 'phenotypic' (common-sensedivisions of genera) to be rival methods of classifying animals, rather than two parts ofan explanation of phenomena.39 Compare what Balme (1961, 208) says about the dualiZing animals: 'They are notdismissed as exceptions that prove the rule, nor are they assigned to both sides of adivision .. . [T]hey compel a more precise definition of the division ... Their propergrouping is rarely decided, and they seem to be brought into the discussions, not inorder to be classified, but in order to bring out sharper distinctions in the differentiaeconcerned, or more precise statements of the ways in which the differentiae can becombined.' Aristotle's method allows for increased accuracy and finer distinctions, buteven in a thoroughly empirical study such as biology, common-sense distinctions mustremain more or less intact.

77 Analogy in Aristotle's Biologyqualifies as a variation or an entirely different part is a matter of definitionand first principle.The physical and logical formulations of the genus-as-matter interpretationcorrespond to two different notions of potentiality. Aristotle in theGA traces the development of embryos from menstrual fluid (KaTaI':'Ivia)to the articulated organism. This development involves a transformationof matter and potentiality through the addition of form: Karal''lvia is thematter and potentiality for the formation of homoiomerous parts. Thematter and potentiality in this case is a substrate for transformation, andas such is quite different from the kind of genus that is determined bythe more and the less. For in the latter case there is no transformation,only a specification of a more general form. This general form isa potentiality, but it is not a potentiality to be transformed as KaTa/J:ryviais transformed into flesh or skin: a long or short wing is still actuallya wing, whereas KaTafJ.1Jvia transformed into flesh is no longer actuallyKUTuIlTfvia.A SolutionAristotle, then, recognizes analogy as a legitimate and distinct level of generalitybased on perceptible similarities as well as functions. The weaknessof the functionalist, the relativist, and the genus-as-matter interpretationsis their failure to provide a convincing theoretical framework that accommodatesthese facts.Analogy was not always a part of Aristotle's system of identity anddifference. Neither the Categories nor the Topics makes use of it. 40 But inthe biological works, as we have seen, it is clearly ·introduced in contrast tothe relationship between genus and species. However inadequate the moreand less is as a criterion of generic identity, the very fact that Aristotleinvokes it shows that he intends the species-genus and the genus-analogyrelationships to be different. The relationship between genus and analogyis not intended to be a recapitulation of the relationship betweengenus and species, and the efforts to make it so, especially to view analogyas a functional genus, silence Aristotle on a point he seems urgentto make.A simple observation about the species-genus-analogy hierarchy mayserve as a starting point towards providing a reason for this difference. Thespecies-genus-analogy system (let us call this the SGA system) is a narrow40 If these works are early and represent a pre.hylomorphic stage of Aristotle's thought,there is good reason, as we shall see below, for the absence of analogy in them.

78 Aristotle's Theory of the Unity of Scienceand limited system'! Although species, genus, and analogy represent differentlevels of generality, the hierarchy cannot be expanded upward ordownward. We do not find extended divisions of successive genus andspecies terms as we do with dichotomy. The system of multiple genericdifferentiae discussed in PA I has done away with that. As a result we findthe following sort of SGA string:analogygenusspecieswing: bird: : fin: fishwinglong wingThe system is limited to three and only three steps, and there is nothingmore specific than long wing or more general than the analogy,wing:bird: :fin:fish. It is also a narrow system in the sense that the genusterm appears at all three levels of generality. These genus terms are particulardenominated parts: wing, blood, hoof, and so on. They form the pivotor centre of the system, and of these there are determinations of 7Tae~fJ.aTa(species) and correspondences (analogues).The parts, which are the cornerstone of the system, are those pickedout by common language. What Aristotle says concerning whole animals(PA 1.3 643b10-13) applies equally to the parts:We must attempt to recognize the natural groups, following the indications affordedby the instincts of mankind, which led them for instance to form the class of Birdsand the class of Fishes, each of which groups combines a multitude of differentiae,and is not defined by a single one as in dichotomy.The common names pick out the appropriate groups, and although birdsand fish share some common features, these groups should be separated andvariations on the basic type should be taken together (PA 1.4 644a12-23).Importantly, the various great genera of animals are not in turn speciesof some higher genus like animal, nor are they distinguished amongthemselves by contraty differentiae of more and less. Instead, birds aredefined by the generic differentiae 'having wings: 'having beaks: and soon. The sum of these differentiae provides an autonomous characterizationof the genus defined in its own terms rather than by its difference fromother genera. Each genus, then, is other than, and not different from,the other genera. The situation is exactly similar with the parts. Aristotle41 Balme 1962, 88-9, makes this observation in support of his claim that the eidos' andgenos are not used in the biological works as they are in the logical works.

79 Analogy in Aristotle's Biologyconsistently uses common names and maintains the common distinctionsbetween them. Each part constitutes a genus and is defined by its genericdifferentiae. Each is autonomous and other than, rather than differentfrom, all others. Since difference operates only within the genus, it followsthat one generic part cannot differ from another by more and less.Conversely, a part may differ by more and less only within the determinatelimits of the genus. For a wing can be a long wing or a short wing, butit cannot be modified so as to cease to be a wing. The requirement thata part must remain what it is in spite of its modification is reflected inthe way Aristotle describes the more and less in the passage from HA 1.1:they are contraries of affections «vavnw

80 Aristotle's Theory of the Unity of ScienceThe SGA system is one of the great organizational hierarchies in thebiological works. It is a system of identity and difference dependent uponthe genus term, and each genus is autonomous and incommensurable withevery other genus. But just because there are no relations of differencebetween one genus and another does not mean that there are no relationsat all between genera. For all these genera are organized in the other greathierarchy, the hierarchy of composition, the whole-parts (WP) system.Aristotle describes this at the beginning of HA 1.1 (486a5-14) and PA Il.1(646a13-24), and it is clear that it informs the conception and presentationof the biological works. Whole animals, like birds and fish, are constitutedfrom complex parts, like wing, fin, stomach, hand, kidney, and so on. Intum these are made of homoiomerous or simple parts, feather, scale, skin,horn, flesh, bone, etc., which are shaped from stuffs often of the samename, horn, blood vessel, bone, ichor, etc., and these finally arise from thepowers or 3vvaJ.'Ets, hot, cold, sticky, brittle, wet, dry, etc.:Whole animals Birds Fish Testacea CrustaceaComplex parts wing fin stomach hand kidneySimple parts feather scale flesh tooth skinSimple stuffs horn flesh bone bloodPowers hot cold sticky brittle wet dryTo some extent this is an organizational hierarchy of matter and form. Eachitem consists of matter from a lower level and is formally detennined byits contribution to a higher level. Nevertheless, it does not distinguish andseparate the formal and material components of each part; each level issimply a more highly organized hylomorphic compound. Primarily it isa hierarchical system of biological subjects. Each of the terms providessubjects for biological predicates or serves as a predicate for some otherterm on the table. At various places in the biological works Aristotle talksabout the attributes of blood, kidneys, wings, and birds. These are theentities whose existence must be hypothesized and whose -essence must bedefined 4 ' As such, they serve as the first principles of this part of biologicalscience, and this is why they are introduced first in both the HA and thethat do not make for differences in species. These 'Iralhjp.am are not species-creatin&because they are not backed by teleological causes (Lennox 1980). They are 71"a87/p.aranot only with respect to the genus, hut also with respect to the species.44 These are the hypotheses and definitions discussed in APo 1.2 72a14-24.

81 Analogy in Aristotle's BiologyPA. If Aristotle does not expressly posit their existence or provide theirdefinitions, that is not unusual, for as he says at APo 1.10 76b16-19:Nothing, however, prevents some sciences from overlooking some of these things[statement of principles}, - e.g. from not supposing that its genus is, if it is evidentthat it is (for it is not equally clear that number is and that hot and cold is).Each of these parts has per se predicates that belong to it qua itself, andeach is found in the demonstrations characteristic of the PA. Each of thelevels of the table provides definable subjects, and none can be reduced toanother: wholes cannot be eliminatively reduced to their component parts.Moreover, it is dear that Aristotle intended to map the SGA system ontothe WP system. He explicitly describes this mapping in HA 1.1 (486al4-487a10), where he first discusses the SGA levels of complex parts, thenthe SGA levels of simple parts: we find species, genus, and analogy at themiddle levels of the whole-parts system, the complex and simple parts.We do not find analogy at the level of whole animals for reasons alreadyconsidered, and we do not find analogues at the level of powers for reasonsthat will be important below.Since the WP system is a system of composition, not difference, eachpart is not different from, but other than, all others. They are certainlyrelated to one another, but not by sameness and difference. They are beyonddifference, and as such provide grounds for the application of analogy.At the same time, the WP system displays the correspondences typical ofanalogy. For as we saw, analogy depends on relative position and similarityof material as well as function, and these are displayed by the WP levelsabove and below a part. So a feather is a certain simple part of the wholeanimal bird, just as a scale is of a fish, and they correspond in their relativeposition in their complex whole. Likewise, they have a similar materialorigin in horny stuff and moisture, which appear at a lower WP level.The WP system displays the parts of animals as a table of interrelatedsubjects, and it is the task of the PA to explain these parts and theirproperties. It is dear from the first lines of HA 1.1 and PA 11.1 that westart from the material composition of the animals, saying first what thoseparts are, and then why they are the way they are and why animalshave them. We start from the common conception, what is familiar tous, the sensible and particular, and work towards the formal. intelligible,and universal. These parts are the subject of our inquiry, and they are,of course, not randomly chosen. They all belong to the same broad type,organic physically isola table components of animals. They would certainlyall be found in the same category of existence. But there are good reasons

82 Aristotle's Theory of the Unity of Sciencewhy they do not form a genus of the 'programmatic' variety. That systemof phenomenal identity and difference would fail to capture their mostimportant essential nature, namely their compositional relationships. Ifwe were to gather generic parts into higher genera based on function wewould immediately upset the compositional WP hierarchy. For lung andgill, for example, do not have identical compositional relations.In the presentation of the HA and PA, Aristotle gives precedence tocomposition over function. The WP system, organized on the basis ofcomposition rather than difference, provides the theoretical ground foranalogy. The SGA system, as we have seen, is a system of difference, butlike the WP system, it is based on material and phenomenal features, asthe relationship between species and genus makes clear. As such the SGAsystem makes a good yoke-mate for the WP system: together they providean interlocking hierarchical organization of the material nature of animals.But biological nature can be studied from perspectives other than materialparts. At a later stage in the investigation, when Aristotle comes to the MA,the PN, and the DA, he chooses new subjects that are more formal, moreuniversal, and less familiar to us, the soul activities, nutrition, sensation,thought, and locomotion 4 S In the DA, for example, matter is consideredonly to the extent that it is a potentiality for these activities. We seehere a different set of subjects, and as a result a different set of analogies,primarily among the sense organs and their operation. 46 We cannot, asthe relativists would have us do, casually form a new genus from theanalogues on the basis of the common function those analogues perform.For to do so would be to change the subject of discourse and the qua-levelof the science. In the HA and PA the parts are the subjects and each has adefinition in accordance with its name. Functions are important, of course,especially in the FA , but they are not subjects, they are middle terms.Aristotle's method involves a fairly strict division of labour betweenmatter and form." Considering that HA and PA deal with material parts,45 The investigation begins with what is more familiar to us and moves towards what ismore familiar without qualification. The order of the treatises as I have laid them outhere does not, therefore, reflect a logical priority. Indeed, Aristotle makes clear (Met .Z.10 1035bl4-22) that the parts of the soul of the animal are prior to the compositeand that parts of the body (with the exception of the heart [or brain}) are posterior.This same passage, however, clearly distinguishes the parts of the body from the partsof the soul, and so wa rrants their being treated as different subjects.46 For example, there is the analogy, sharp I flat: hearing:: sharp I blunt : touch at DA 11.8420b1-4; we find the analogy between taste and smell and their sensibilia at II.9421016-20.47 See Peck 1983, 9-10, for one interpretation.

83 Analogy in Aristotle's Biologythere is little surprise that their species are distinguished by material'lfa8"Jlam and that analogues should be materially and structurally based.We can also understand why Aristotle studiously avoids any functionaldescription of analogy: analogues are merely proportionally related beyonda difference of degree. There is also no surprise that functions thatare treated universally in the VA are discussed as analogous in the PA.For :within the qua-system of commensurate universals that lies at thefoundation of demonstration in the PA, the cause must be coextensivewith the subject and the attribute. And 'things the same by analogy havetheir middles the same by analogy' (APo 11.17 99a15-16). Since functionsprovide the middle terms in the PA, there will be analogues of functionsas well.A Challenging CaseLet us return to the case of bone and its analogues, which has been widelycited as an instance of hopeless confusion in Aristotle's use of analogy andgenus just because of the close similarities they exhibit. As we shall see,this case illustrates some of the factors Aristotle had in mind in callingparts analogous: the dependence on definition in accordance with the nameand the tendency to choose as analogues parts that are similar in materialand relative position.As we might expect, Aristotle does not always give the same accountof what the analogues are. In the APo (11.14 98a20-23) he says thatbone (OOTOVV), fish-spine (aKav8a), and pounce (cn)1TWV in cephalopods)are analogous. [n his main treatment of bone in the PA they are bone(OO"TOVV), fish-spine (aKav8a) in some fishes, and cartilage (xovopo

84 Aristotle's Theory of the Unity of Sciencewe move from viviparous quadrupeds through birds, oviparous quadrupeds,fishes, and cephalopods. Moreover, there are variations in the hardnessof bones among viviparous quadrupeds and among serpents (PA 11.9655a12-14; a20-23).Again, the materials are very similar. Bone and cartilage have thesame nature (~ 4>vO'« ~ aVT~) and differ by more and less and for thisreason neither continues to grow when cut off (PA 11.9 655a32-34). Theseanalogues also share relative position: they are clearly contrasted with theexoskeletons of crustacea and testacea, which though they discharge thesame function are not called analogues, because their relative positions aredifferent (PA 11.8 653b35-654a19). For all these reasons these analoguesare as close as any Aristotle offers and could conceivably be treated as agenus. But at the same time, there are reasons why they are not. Thoughthey share many attributes, they are parts bearing different names, andeach has its own definition. At APo 11.14 (98a20-23) Aristotle says thatone may excerpt commonalities according to analogy: ffor you cannot getone identical thing which pounce and spine and bone should be called.'There is no common term that can be applied to all three kinds of fleshsupport, But the lack of a common name is merely a sign of the lackof a genuinely common nature. One reason for denying that these partsdiffer by more and less is the fact that there are sharp discontinuitiesin the 'series of graduated changes' from small cartilaginous animals tolarge bony animals. Aristotle clearly does not think that the kinds offlesh support are determined solely as a function of the size of the animalthey are found in. Dolphins, for example, which are no larger than manyselachia and oviparous fishes, have bone rather than fish-spine (PA 11.9655a16- 17).Moreover, as corresponding parts of different systems, bone, fish-spine,and cartilage have a claim to autonomous genera. One of the major externaldifferences between selachia and oviparous fish, and one that marks themoff as different genera, is the presence or absence of gill coverings. Whilefish have them, seIachia do not, since the gill coverings require fish-spinefor their formation, and the selachia have a skeleton invariably madeof cartilage-spine (nl oE O'€AO.Xry 71'avTa xovopaKavGa PA IV.13 696b2-6).The difference in material has other effects in their 71'pat

85 Analogy in Aristotle's Biologydistinguishes them not only by their skeletons but also by their modes ofreproduction, skin covering, and gills. This, however, concedes the argumentto Pellegrin, that cartilaginous and spiny animals are analogous assoon as we select those groups as genera.But perhaps a more convincing solution to this difficulty lies in theWP system:simple partbonecartilage/ ~ / ~affection harder softer harder softerpower hard softAs Aristotle's description makes clear, the powers are paired in contraryqualities (PA ILl 646b20-22): 'one part will be soft, another hard, anotherfluid, another solid,' and so on. As such, in their very nature theyare relative and on a scale of more and less. But the simple parts, likebone and cartilage, have different powers, and inasmuch as the powerscontribute to the 'what-is-it' of a part, they are essential features of thatpart. Aristotle's description in PA 11.1 treats the participation of the powerin the generic part as essential. So bone will be essentially (absolutely)hard, blood essentially (absolutely) fluid. But, in addition, each part maydiffer by contrarieties of affections (n;'v 7Tae'lllaTwV EVaVTLW(Tm). Like thepowers, these are contraries, but they are not essentiaL A part may varymore and less in respect of these affections while still maintaining itsessential power, which is its nature as that part. Now it often happens thata part may have the same quality both essentially and non-essentially.There is, for example, an absolute hardness of bone that is necessary forbone to maintain its essential nature and a different hardness that, whilenot being essential to bone, makes lions' bone especially hard. While thepower is absolute, the affection differs by more and less within the genus.The confusion for bone and cartilage arises because the power, which isnecessary and absolute for the simple part and its nature, may be consideredby itself separately from any part 4 ' When it is so considered it is simplya contrary quality admitting of more and less (some parts are hard, somesoft, some wet, some dry). For this reason, the statementbone is harder than cartilagemay be taken as ambiguous betweenI49 Cf. Mary Louise Gill 1997, 154-7, who makes similar observations about flesh based ondifferent levels of organization.

86 Aristotle's Theory of the Unity of Science(1) bone qua bone is a harder form of the same essential nature ascartilage qua cartilage and(2) bone qua having the power hard is harder than cartilage qua havingthe power soft.According to Aristotle, (1) is false, (2) is true. By keeping in mind that thevarious compositional levels of the WP system are causally related but notreducible to one another, we can see why parts may be analogues whileexhibiting material similarities to one another.· Analogy and AbstractionThe SGA system of difference based on common names for parts andwhole animals is combined with the WP system of composition. Variationswithin each part are important and revelatory of nature, but differencesbased on affections among the parts (e.g., the liver is softer than the heart)do not reveal much of scientific significance. Rather it is the compositionalrelations and finally the causal relations among the parts that explain mostabout their nature. For this reason it seemed most profitable to Aristotle tolimit the study of difference to the generic part, then continue with otherforms of relation among the parts. Analogy has a liminal position in thisdual system. It is placed within the SGA system of difference, but it islogically dependent on the WP system in a way that neither species norgenus is. The compositional system is not necessary in order to identify thegenera and species of parts, but it is necessary in order to identify analogies,since analogies are determined by material and positional factors, and theseare determined within the WP system.This liminal position between the two systems is mirrored by analogy'sdual nature. Analogues fall into different genera, because each analoguehas its own per se predicates (that is, the predicates contain the term ofthe analogue in their definition) and these are treated qua that genus.This makes each analogue an autonomous subject, and explains (or at leastmakes manifest) that they do not fall into a single genus. But there arealso reasons why analogues are gathered together as analogues of eachother. They have something in common, of which the WP table providesintimations. As I noted above, the WP table is to some extent a table ofform and matter, but each component is itself a hylomorphic compound.The table has arranged the parts in such a way as to make the causalrelationships among them graspable without explicitly stating them. Thelower levels of the table provide part of the material cause for the higherlevels. The higher levels point towards the final and formal cause, sinceposition within a whole is an important ' clue to function. The WP table,

87 Analogy in Aristotle's Biologythen, is not explicitly causal, but points towards cause. Analogies belong inthe WP system for this very reason: their similarities are pointed towards,but not made explicit. Functions within this system are fully embedded inthe parts.Analogues, while not haVing any term in common, point towards acommon term. There are two sets of related terms, a proper set, per se andqua related to the special substrates, as snub and bandy are related to noseand leg, and a common set, no longer qua related to the substrates. Thetwo sets are related because the common set is per se predicated of its ownparticular manifestations (as curved is contained in the definition of snupand bandy). The common set, then, is abstracted from the proper. Analogyarises in this context, when terms specifically embedded in certain generaare per se related to other terms that are more general and therefore ata different and more abstract qua leveL So, for example, wing belongs tobird qua bird; and fin belongs to fish qua fish. Wing and fin have their ownpeculiar per se and qua relations. The sciences that study these featuresare the science of wing and the science of fin, or morely properly thescience of bird qua winged and the science of fish qua finned. But wingand fin have per se features in common. They are both instrumental partsfor locomotion that have joints and are related to the anterior pair ofthe points of motion. These features extend beyond either of the particulargenera, and although they may be useful in proofs concerning theparticular genera, attributes cannot be proved of the particular genera atthe qua-level that corresponds to these general features. If we want toconsider rather than just use the general causes and attributes, we mustselect a more abstract and general genus, for instance, animals qua jointedor animals qua progressing. Otherwise, to cross between the general andspecific genera is to commit metabasis. It is just within the tension betweenthe per se and the qua requirements that analogy operates. Analogues areof different and autonomous genera in virtue of the qua requirement, butare treated together in virtue of their common per se relation.As we move from lower to higher subject-genus we are not moving upa genus-specie.s chain. It is clear from the series wing, joint, heart, desirethat the more abstract entity is not the genus of the less abstract. A jointis not what a wing and fin are, and even less is a heart what a joint is. Buteach more abstract term is in one way or another a cause for the moreconcrete tenn, and each is per se, but not qua, related to the subject beforeit in the series. Each, therefore, forms a different but related subject, partlyabstracted from its predecessor.Analogues exist in this no man's land between the level of lower andstrictly autonomous genera and a higher common genus. This no man's

3Analogy and DemonstrationWhile the relationship between the SGA and the WP systems seems toaccount for the phenomenal demarcation of analogy from other forms ofidentity, the place of analogy in demonstration is more difficult to accountfor. There are clear indications in the Posterior Analytics that analogy playsa distinctive role in demonstration, but just what that role is, and whetherand how it is worked out in the biological writings is far from clear. Partof the difficulty lies in the fact that analogy was not a central interest toAristotle when composing the APo. In fact, of the three passages in whichanalogy in the appropriate sense is discussed, all seem to have the status andimportance of footnotes to major discussions. Moreover, the passages donot all point in the same direction. Some suggest that analogy is manifestedin a distinctive form of demonstration, others seem to present analoguesas specific instances to which general principles and causes are applied.The same difficulty, too, arises in Aristotle's analogical demonstrations inthe biological works. We often find distinctively analogical demonstrations,but more frequently general explanations seem to be applied universallyto several analogues.As we saw, the underlying genera of the PA are whole animals andtheir parts, each with its own definition in accordance with its name. Wecan now fill in some details from the Analytics 1 APo 1.4-10 discussesdemonstration in terms of the most stringent conditions, demonstrativesyllogisms in Barbara, where all the terms are related per se and qua thesubject. Proofs that fall short d this are incidental. Now the predicatesof animals and their parts apply at various levels of generality. Some1 For more elaborate attempts to organize single.genus biological proofs on the APomodel see Gotthelf 1997 and Dete11997.

90 Aristotle's Theory of the Unity of Sciencepredicates belong to a part qua that part, or to a species qua that species,while other predicates will belong qua something more common. If weuse a specific part as a subject of demonstration, then attributes and middlesmust belong qua the part, that is, they must be in the same genusas the part (1.7 75blO-ll). Predicates that belong commonly must havea common subject, and belong qua something common. These commonsubjects will be different from the specific subjects and will form differentgenera, subjects of different sciences. If we try to prove something of onesubject through the per se predicates of a different subject, we will commitmetabasis. An example of a final-causal syllogism will help us to explicatesome of these relations:wing IPO flierflier IPO birdtherefore, wing IPO birdWe learn that being a flier is in the oVlIia of a bird, and therefore it willappear in the account of its essence (PA IV.12 693bl3-l4). The relationshipbetween having a wing and being a flier is one of hypothetical necessity:if something is to fly, it must have wings. We may express this hypotheticalnecessity through definitional inclusion in the following way: wingis predicated of flier because in the definition of wing we find the termflier (or a paronym thereof), since a wing is by definition an instrumentalpart for flying. In the conclusion that birds have wings, wing will be a perse accident of bird. The proof will have proceeded within the genus. Theproof concerning fish, fin, and swimming will be exactly parallel but in adifferent genus, and clearly we must not use terms proper to birds in aproof concerning fish.Analogous parts, though they share common features, do not form acommon subject. Each constitutes its own separate genus. The predicatesthat apply to it must apply at its qua-level and must be adapted to thatgenus. Any common features that analogues share cannot be treated asstrictly common. So, if the subject is bird, then wing and flying willbe predicated of it universally, but if the term locomotion is used ofthe subject bird, that term must be adapted as 'locomotion for a bird,'that is, 'flying,' since bird is not the appropriate subject for the generalpredicate, locomotion. Terms predicated of each analogue must be predicatedcommensurately with the analogues. For if a Single general term isunambiguously predicated of two subjects, then, at least insofar as thatpredicate is concerned, the subjects are instances of a genus rather thananalogues. Indeed in such cases the general term cannot be predicated of

91 Analogy and Demonstrationthe instance qua what it is, but only through an application argument.Analogy arises, then, within the strictest conditions for demonstrationslaid out in the core of Aristotle's demonstrative theory.Analogy in APo: Passages and DiscussionSince the APo is primarily interested in demonstration within a singlesubject-genus, and analogy is an exception to or special form of demonstration,it is treated rather briefly in that text. In fact there are only threepassages that make direct reference to analogy:Of the things they use in the demonstrative sciences, some are proper to eachscience and others common - but common by analogy (KOWa Of Kar' avaAoyia.u),since things are useful (XP";UlJ.LOV) in so far as they bear on the genus under thescience. Proper: e.g. that a line is such and such, and straight so and so; common:e.g. that if equals are taken from equals, the remainders are equal. But each ofthese is sufficient (LKavov) in so far as it bears on the genus; for it will produce thesame result, even if it is ' not assumed as holding of everything, but only for thecase of magnitudes - or, for the arithmetician, for numbers. (1.10 76a37-76b2)Again, another way [to grasp problems] is excerpting in virtue of analogy (KanlTO avaAOYOV EKAtyUV); for you cannot get one identical thing which pounce andspine and bone should be called; but there will be things that follow them too, asthough there were some single nature of this sort. (11.14 98a20-23)And things which are the same by analogy will have their middle terms the sameby analogy (KaT'

92 Aristotle's Theory of the Unity of Scienceprinciples, like the 'equals' axiom, extend beyond numbers, when we treatthis restricted subject-genus, we require that the principle hold good onlyfor number. Does Aristotle mean by this that in applying the commonprinciple we should retain its general formulation (if equals are taken ... ),and simply use it in the special subject-genus, or that we should adaptit to the specific subject matter (if equal numbers are taken from equalnumbers, equal numbers remain)? By describing the commonality as 'byanalogy' Aristotle indicates that he prefers the latter alternative: whenthe common principle is used, it must be specifically adapted, not merelyapplied. Nevertheless, the equals axiom seems to be quite intelligible in itsgeneral formulation, and its adaptation to the specific subject-genus seemsto be a trivial matter of substitution of terms. It is true that Aristotleheld to the common opinion that arithmetic and geometry were separategenera and studied quite different objects, but the common principle willbe analogical only because the genera in which it is used are differentand not because the principle itself is ambiguous. If this is so, then thecause of the analogy of the principles in this case is the subject-genera towhich they are adapted, and the common prinCiple, even if it admits of ageneral account, is given analogical formulations only because the subjectsto which it attaches are analogues.This is surprising, since what we have learned about analogy so farwould lead us to expect that analogical identity would be reflected in adistinctive pattern of demonstration. At least this seems to be the importof the third passage from 11.17. The fact that the middles of analogues areanalogues implies that the causes of analogous phenomena are themselvesanalogous. But again Aristotle is not clear in his expression, and thisstatement can be interpreted in at least two ways: that the middle termsare analogous in their own right, that is, though they are not identicalwith one another, they hold identical relations within their correspondingdemonstrations. On this interpretation the fact that the middles areanalogous will explain why the major terms are analogous. Alternatively,the middles may be analogous merely because they apply to subjects thatare themselves analogous, and because the rules of demonstration requirethem to be adapted to their genus. In this case it is the analogous subjectsthat explain why the middles are analogous.This interpretative dilemma clearly corresponds to that between therelativist and orthodox views discussed in the last chapter. The relativistinterpretation claims that demonstrations and tenns in demonstrations areanalogous just because their subject-genera are treated as different genera.This thesis is the demonstrative correlate of the relativist analogy theotyof Pellegrin and Balme. On this view, attributes are analogously the same

93 Analogy and Demonstrationwhen they are predicated in different genera. If we take this as a sufficientcondition of analogy, there will be every reason to suppose that genericattributes can be analogously adapted to species. This is precisely Balme'sand Pellegrin's contention. But, if there is one thing that Aristotle makesclear it is that generic features are not adapted to species by analogy(e.g., the 2R theorem is not adapted analogously to the three kinds oftriangle).The second passage provides little clarification for our problems. Superficiallyonly the lack of a name to apply commonly to pounce, fish-spine,and bone seems to prevent their forming a genus. But the mere lack of aname is no bar to establishing a generic nature, and if there is a nature itcan be named at least in principle. Malakostraka (HA 1.6 490b10-12) forma genus, but they do not have a single name (avwvvl'a ivi ovol'an). Theproblem with bone and its analogues is not the lack of a common nameto apply to a common nature. Aristotle simply does not think that theseobjects form a single genus, and that is the reason why they do not havea common name. And yet, as he says here, there are items that followbone, pounce, and spine as if they were a single nature, and this suggeststhat for some purposes analogues may be treated as species of a genus. So,again, it is not clear whether these common items are generically commonor common only by analogy.The third passage is found in Aristotle's discussion of whether thesame thing may have different explanations, and it deserves to be quotedmore extensively (II.1? 99al- 16):Is it possible for there not to be the same explanation of the same thing for everycase, but a different one? or not? Perhaps if it has been demonstrated in itself andnot in virtue of a sign or accidentally it is not possible (for the middle term isthe account of the extreme), but if it has not been demonstrated in this way, itis possible? One can inquire accidentally both about what it is explanatory of andabout what it is explanatory for - but these do not seem to be problems. Otherwise,the middle term will have a similar character - if they are homonymous, the middlewill be homonymous; if they are in a genus, it will have a similar character.E.g. why do proportionals alternate? For the explanation in the cases of linesand of numbers is different - and the same: as lines it is different, as having suchand such an increase it is the same. And so in all cases.The explanation of a colour's being similar to a colour and a figure to a figureis different in the different cases. For what is similar is homonymous in thesecases; for here it is presumably having proportionate sides and equal angles, butin the case of colours it is that perception of them is single, or something else ofthat sort.

94 Aristotle's Theory of the Unity of ScienceAnd things which are the same by analogy will have their middle term thesame by analogy too.In a lax sense of 'same' and 'different' it is possible to explain the samething in different ways, but, in fact, in two explanatory demonstrationswith the same explanandum (major term), the explanandum is a unityonly to the extent that the explanation (middle term) is. When the majoris ambiguous, the middle too is ambiguous, and where the major is genericallythe same, the middle is generically the same. The examples Aristotleprovides are not intended to correspond precisely with these degrees ofidentity, but they clarify his general point.' The alternation of proportionalsamong lines and numbers are given different explanations whentreated as different genera. The alternation of proportionals among thesegenera will be analogous, and the explanations will be analogous, as wesaw above. But when the genus, magnitude, is abstracted, the alternation ofproportionals will be generic and the explanation generic. Fully ambiguousterms, like similarity among similar figures and among similar colours,will have two unrelated explanations.Aristotle goes on in this chapter to discuss the relationships betweenthe terms of a demonstrative syllogism, outlining the schema for applicationarguments (99a16-37), and cases where a single major term belongsfor different reasons to different subjects (99a37-b7). These latter caseshave strong affinities to analogical explanation, and the example Aristotleoffers may provide some insight into the demonstrative structure of analogy(99b4-7):It is possible for there to be several explanations of the same thing, but not forthings of the same species - e.g. the explanation of longevity for quadrupeds istheir not having bile, but for birds their being dry or something else.The fact that this example is based on the genera of the biological workssuggests that it might be relevant to our problem, although it does notdeal with any of the standard analogues we have seen. Aristotle does notmake explicitly clear which, if any, of the three candidates for multiplecauses the longevity case corresponds to, but the context indicates that itis not an application of a generic feature to an instance, nor does longevityseem to be radically homonymous in the way that similarity is (TO Ol'owv)when applied to similar triangles and similar colours. After all longevity2 Contra, Ross 1949, 668.

95 Analogy and Demonstrationin both birds and quadrupeds is judged by the same criterion (they livefor several decades), whereas similarity in figures and colours is judgedby quite different criteria. Analogy, therefore, seems to be the most likelycandidate.'The explanation for longevity is different in the case of quadrupeds andbirds. Now in the second book of the APo Aristotle regularly identifies thedefinition of a major (or minor) term with the middle, that is, the cause.If this doctrine may be applied in such cases as these, the definition oflongevity will be different for birds and quadrupeds, since the cause willbe different in each case. That is, longevity has a different significance inthe two genera' We can fill in the details of longevity from elsewhere:life is dependent on vital heat Uuv. 6 470a19-20; Resp. 17 478b32-33),which can be exhausted or extinguished Uuv. 5 469b21-22). And it can beextinguished by excessive moisture (d. Resp. 20 479b19-26) or by bUe. Bileis a useless residue, the opposite of nutriment, which fuels the vital heat.Bile, therefore, causes impurity in the blood and contributes to shortnessof life (PA IV.2 677a25-35).' Dryness and bilelessness both contribute,therefore, to the preservation of vital heat.The subjects of our demonstrations here are birds and viviparous quadrupeds.The demonstrations are analogical, not merely because birds andviviparous quadrupeds belong to different genera, but because dtyness andbilelessness are different. That is, the cause of longevity is not merelystipulated as different because the subject-genera are different. The causesjust are different and they discharge a corresponding function within theirgenera. To be sure, longevity is an item that follows these two differentsubjects. This folloWing term has a common nominal definition (say,longevity is the capacity for long life in each case) that offers a commonaccount and reveals some fact about the object that is more familiar to us,but that requires further explanation. But in spite of this common account,3 McKirahan 1992, 171-2, treats longevity, but does not comment (except hriefly inn. 39) on its connection with analogy.4 This is the conclusion that Goldin 1996, 147, comes to from an examination of therelationship between the nominal definition (the major) and the causal explanation. Hedenies, however, that Aristotle 'envisages the possibility of this sort of homonymy' inwhich one nominal definition might have two causal definitions (147n13).5 Cf. PA 11.2 648b2-8: 'There ought, then, to be some clear understanding as to the sensein which natural substances are to be termed hot or cold, dry or moist. For it appearsmanifest that these are properties on which even life and death are largely dependent,and that they are moreover the causes of sleep and waking, of maturity and old age, ofhealth and disease.' Even among vivipara dryness may contribute to long life; d. ENVIl.3 1147a5-6: dry food is the most healthy.

96 Aristotle's Theory of the Uniry of Sciencelongevity remains ambiguous because it has different causes. The nominaldefinition provides the fact, and the causal definitions, bilelessness anddryness, provide the cause 6 The common fact is an effect of differingcauses. 7 The subjects, bird and quadruped, are conceived of as different invirtue of their being bileless or dry and it is from these different causes thatwe can infer the common effect, their capacity for long life. It is, however,in virtue of the familiar fact of their longevity that birds' dryness andquadrupeds' bile less ness are gathered together as analogues, since this is aconclusion that follows from both of them SAnd yet that is hardly the end of the story, for it is clear that we neednot settle for' capacity for long life' as a common definition of longevity.Instead, 'preservative of vital heat' seems to provide a common cause forlongevity in birds and viviparous quadrupeds, and this can serve as thecommon middle and the causal definition of longeviry. We would now havean unambiguous (generic) middle explaining an unambiguous (generic)major. What, then, would be wrong with accepting the general explanationof longeviry, that which preserves vital heat, and applying it directly tothe specific instances? The reason has to do with the asymmetry of causalexplanation. We can construct the following explanatory syllogism for it:1) longevity IPO preservative of vital heat2a) preservative of vital heat IPObilelessness3a) bilelessness IPOviviparous quadrupeds2b) preservative of vital heat IPOdryness3b) dryness IPO birdstherefore,4a) longevity IPOviviparous quadrupeds4b) longevity IPO birds6 There has been a considerable amount of attention given to the issue of nominaldefinition: Bolton 1976; Demos and Devereux 1988; Goldin 1996.7 Similarly in PA 1.4, in his defence of the common division of animal groups, Aristotlesays that water animals and feathered animals, though their correspondence is only byanalogy, share some 7ralhj .8 In Long., Aristotle actually does discuss the causes of absolute longevity. He explainswhy generally larger animals are longer-lived than smaller animals, viz., they containmore moisture and this moisture is hotter and less liable to freeze or congeaLBilelessness is not mentioned in Long. as a cause of longevity, nor is dryness a cause inanimals (though it is in plants 16. 467a6-8}). The scenario Aristotle lays out in Long.does not involve the same examples as in the APo.

97 Analogy and DemonstrationWe can see that in contrast to the single-genus proofs for triangleshaving 2R, there is here an additional premiss (2a and 2b) providing adistinct reason in each case. It is ultimately not in virtue of one causethat longevity is predicated of birds and viviparous quadrupeds. Thereare two sets of middle term s: preservative of vital heat is the same inboth cases, but bilelessness is different from dryness. According to thefollowing chapter, APo 1l.l8, when there is more than one middle termbetween major and minor (e.g., preservative of vital heat and bile lessness/dryness), the proper explanation is the middle term that is closestto the minor. The scheme of explanation is asymmetricaL because wecannot invert preservation of vital heat and bilelessness in the order ofexplanation. Bilelessness explains preservation of vital heat in quadrupeds,not the other way around. This principle is stated immediately after theII.17 example of longevity, and is clearlyintended to block an attempt tofind a universal explanation for the analogous term. The reason we choosethe middle closest to the subject is clear: the more specific middle explainsthe more general but not vice versa. Thus, if we were to choose the middlenearest the major, the analogy (or homonymy) could easily escape ournotice.There are some important similarities and differences between thelongevity case as I have interpreted it and Aristotle's treatment of analogyin the biological works. In both cases, common features are attributed todifferent genera for different reasons, thus making these features analogous.We also find a similar distinction between general and specific cause,where the latter is appropriately adapted to the subject-genus, and theformer is not. In all the important formal respects longevity is a case ofanalogical explanation.But there are also some significant differences that point to the varietyof forms and degrees of abstraction in which analogy can be found. Inthe case of longevity, the common feature is the major term or the fact,while the middle terms or causes are distinct. This is not always thecase in the biological practice. Frequently, to all appearances the causesfor which features belong to analogues are common. On other occasionsthe entire demonstration has analogous terms throughout, the commonterms being explicitly nowhere in sight. Moreover, in the PA, which isdevoted primarily (though by no means exclusively) to explaining biologicalphenomena through the final cause, this cause tends, as we shallsee, to be more common and universal than the phenomena it explains. Inthe case of longevity, by contrast, the causes, being material and efficient,constitute different explanations for a common explanandum. And indeedit is generally the case that the relationship of common and specific terms

98 Aristotle's Theory of the Unity of Scienceare oppositely arranged in demonstrations that involve final. from thosethat involve efficient/material causes.So the variation apparent throughout Aristotle's brief discussion ofanalogy in the APo is mirrored in his practice in the biological works.Aristotle tends to identify the form with the function as common anduniversa l, and the material conditions with plurality and specificity" Indemonstrations that relate form and matter (i.e., causal demonstrationsinvoking the final and material cause) there will often be a tension betweenthe formal terms, which are more general, and the material tenns,which aTe more specific. In such cases it is not clear whether the COIDmanterms are analogous in a merely relative sense or whether theyare naturally or really analogous. Aristotle's answer within the highlyconstrained criteria of demonstration is that common terms when predicatedin different genera will always be common by analogy unless anapplication argument is used. As we saw with the case of alternatingproportion, it is possible for a predicate to be treated in both ways: alternatingproportion is proved of lines and number by separate but anal-·agaus demonstrations, but alternating proportion also can be proved ofgeneral magnitude and then applied to the species, line and number, byapplication argument. This answer is made more plausible through theobservation that definitions are first principles of demonstrations and donot admit of proof or justification. As a result, when we adapt a termfor a demonstration, that adaptation becomes a part of the definition ofthe term and a first principle. The question, then, whether the adaptedterm is 'naturally' analogous (the orthodox position) or analogous merelybecause it has been formally adapted to different subject matters (therelativist position) makes little sense. Since the adaptation is part of thedefinition, the adaptation is as much a part of the essence of the termas any other part, and so there is no further need to argue for theterm's being analogous. In this way Aristotle's theory of demonstrativeunderstanding, which concerns the relations between terms and betweenpremisses, imposes constraints on the meanings and significance of terms.The formal language of qua and per se captures some of the commoninsight that terms mean different things in different contexts, and whenwe say something about some subject, what we say applies only to thatsubject and no further. The use of a term, for Aristotle, is to a large extentits meaning.9 It is important to distinguish the material cause in the sense of the components thatmake up the developed form from the materials that undergo change so as to becomeIlew materials. It is the former that are identified as plural and specific.

' 99 Analogy and DemonstrationAnalogy in the BiologyAs in the APo, so also in the biological works there is good evidence thatAristotle often used a distinctive form of demonstration when treatinganalogues. But, as in the APo, here too there is no one single pattern.Instead, we can discern three basic forms, in which the importance ofanalogy is displayed to a greater or lesser degree:L Analogous attributes proved of analogous parts by parallel demonstrations.2. Systematic variations on analogous parts that are covariant with acommon feature proved by parallel demonstrations,3, Apparently common attributes proved commonly by a general causeand applied to analogues, 'The progression from the first to the third is a progression fromgreatest to least importance of analogy in demonstration, and from theorthodox to the relativist conception of analogy, As a result of this varietyof form, the interpretative difficulties we faced in the APo presentation aremanifested again in the biological works:(a) While there are cases in which analogy clearly has a profound influenceon the proof structure, there are other cases in which the traitsbeing discussed appear to be absolutely common. In the latter cases theintroduction of analogues seems to be irrelevant to the proof at hand.(b) Not all the terms of a demonstration are explicitly analogous, Indeedthere are usually common terms involved, and the analogues are oftentreated together under some common designation, as, for example,blood and its analogue are often discussed together as nutriment(TPOCP~), in spite of the fact that this is a functional designation,(c) Analogues are not introduced on all appropriate occasions, Often thelesser analogue (the unnamed one) is not mentioned or is droppedmidway through a discussion,(d) In spite of what Aristotle says at APo IL14 (98a20-23), analoguesare not always treated together for every purpose. Sometimes theircommon aspects are treated together and their peculiar traits separately.So, for example, heart and its analogue (when nameless) are treatedtogether, but the analogue, when named (}.tVH,), is treated separately,One observation at the outset strongly suggests that analogy hasan effect on demonstration. Aristotle often says that certain parts and

100 Aristotle's Theory of the Unity of Sciencefunctions are in the essence of an animal. Gotthelf has assembled a listof such essential parts and functions and it includes such principles asbeing blooded (PA IV.5 678a31-34), having a claw (PA IV.8 684a33-35),or having a lung (PA 1ll.6 669b8-12). 1O Other principles mention functions,like being a flier (PA IV.12 693b4-13), a swimmer (PA IV.13 695b17-19),or a thinker (PA IV.lO 686a25-28). All of these, whether functions orparts, are mentioned elsewhere as having analogues. Now, since they areirreducibly part of the essence of an animal, they are starting points ofexplanation and mark first principles in demonstration. Since they formpart of the definition of the animal groups, they are predicated of theanimal subjects per se and universally. It is not the more general termsthat are part of their definitions. The general term 'having nutriment,'for example, is not part of the definition of blooded animals, but rather'having blood.' For this reason we should expect to find separate ratherthan common demonstrations concerning and involving analogues.In the first form of analogical explanation, Aristotle explicitly followsthe prescription of APo 11.17, that analogous attributes have their middlesthe same by analogy. So, for example, at PA 1ll.5 668a4-7 Aristotle givesthe reason why the blood vessels are distributed all over the body:[T]he reason for the vessels being distributed throughout the entire body is thatin the vessels, or in parts analogous to them, is contained the blood, or the fluidwhich in bloodless animals takes the place of blood, and that this is the materialfrom which the whole body (CTw!'aTo,) is made. (modified ROT)We may safely assume, in view of the second use of 'vessels,' that thefirst use is lax, and properly should be 'blood vessels or their analogue.'In this passage we find two entirely analogous demonstrations appearingin parallel. The analogous major terms - blood vessels being distributedall over the body, and blood vessel-analogues being distributed all overthe body - are predicated of blooded and bloodless animals respectivelyin virtue of the channelling of blood and its analogue. Major, middle,10 Gotthelf 1987, 190-1. Without providing the details, his list is the follOwing: sensationis in the definition of animal; lung is present in the OWI.a. of lunged animals; blood isin the logos defining the oixT{a of blooded animals; having many origins (of movementand sensation) is present in the oixrla of insects; the reason lobsters have claws is thatthey are of the kind that has claws; one kind of octopus has only one row of suckersbecause of the length and slimness of its nature; thinking and reasoning is in the natureor owla of man; being a flier is in the oUrT{a of bird; being a swimmer is in the logosof the ourria of fish; being disproportionate in length relative to the rest of the bodilynature is pan of the ourria and essence of snakes.

101 Analogy and Demonstrationand minor are all analogous. ll Again, later in the same section Aristotleexplains why veins appear during emaciation (668a23--28): since blood andits analogue are potentially the body (which is flesh and its analogue),the former may actually become the latter and disappear until starvationmakes them reappear.Elsewhere we find a more telegraphic form of parallel explanation (P AII.12 657al8-23):In birds, on the other hand, there are only the auditory passages. This is becausetheir skin is hard and because they have feathers instead of hairs, so that theyhave not got the proper material for the formation of ears. Exactly the same is thecase with such oviparous quadrupeds as are clad with scaly plates, and the sameexplanation applies to them (0 yap a.UTOS ap}J.O(JH Kat E7r' EKEtVWV "-OYOII).ap/J.o(€w is often used where corresponding or analogous arguments areimplied 12 It is clear in view of APo II.17 that" atJT'" Myo, must meanthe same by analogy, but the fact that Aristotle does not express himselfaccurately is an indication of how lax he can be in practice.In the second group of demonstrations not only do we find analoguesbetween parts, but also among the 'more and less' variations. These variationsare the same by analogy because they are covariant with somecommon feature. In this group common explanatory terms are frequentlyused. So, for example, the demarcation between lungs and gills is clear, bothfrom their shape and from the kinds of animals that possess them. They arementioned as analogous in a programmatic passage (PA 1.5 645b6). Whilelung is treated among the internal parts of blooded animals (PA III.6),the gill is considered an external part of fish (PA IV.13). The functionsof the organs are also called analogous (HA VII [VIII].2 589b18- 19): asair passes in and out of the lung, so water passes in and out of thegill (Resp. 21 480a23-b20). We can provide a common formulation thatcovers both cases: the fact that all blooded animals are hot accounts forthe need for respiration, but neither this formulation nor any variationupon it can account for the materially and formally specified organs.11 Strictly speaking, this passage seems to involve a double demonstration: provingfirst that blood is transported allover the body, and then using that as a premiss toshow that blood vessels are distributed all over the body. The first conclusion willhypothetically necessitate the second conclusion. Double demonstrations are commonin the biology, but no provision is made for them in the APo. There is a great dealabout packing, but APo recognizes only purely transitive fonns of inference.12 E.g., Phys. IV.1 209.9; IV.8 214b22-23; Pol. IV.11288b12; d. Pol. III.1 1275033-34.

102 Aristotle's Theory of the Unity of ScienceThey must each be referred to their own proper function: only the factthat one group breathes air and the other respires water explains thepresence of each organ: two different, but parallel final causes explainthe analogous parts. For this reason merely respiring is not a sufficientexplanation, and having a lung must be in the o1)(ria of those animals thathave them (PA Il1.6 669b8-12). Variations on these organs likewise canbe explained in parallel ways, and we can show that common propertiesfollow upon this grouping of analogues. Since viviparous quadrupeds areespecially hot, they have bloody and large lungs, and since ovipara arecooler, their lungs are small and spongy (PA III.6 669a24-32). By analogyfish that are hotter have more numerous gills, while cooler fisheshave fewer (PA IV.13 696b16-20). Thus, we find attributes common byanalogy shared by both of the analogues. On the one hand, lung andgill meet the common need to cool the animals, but they also displayvariations according to an analogous principle: the hotter the animal, thelarger the lung or the greater the number of gills. The two analogues aretreated as different subjects, but they vary in analogous ways accordingto the same principle. In this case analogies exist both at a general anda specific level. So not only do we find correspondences in the explanatorystructure between the analogous parts, the animals to which theybelong, and their causes, but we also find correspondences among thevariations.Again, throughout the HA, PA, and GA, Aristotle discusses variouskinds of body covering: hair, feathers, scaly plates, and fish scales. Some ofthese analogues are more closely related than others. Some attributes areanalogously common to them all, others just to some. At HA 1.l486b21-22Aristotle says that what the feather is in a bird, the scale is in a fish,and it is clear that they are not related by difference of degree. At ageneral level, they share a function, external covering for the animal, butthey also share certain material and structural similarities. They form acovering over the skin, made of many discrete identical parts of similarbasic material lodged in the skin. To this extent hair among viviparousquadrupeds is also analogous. The hair is said to protect from the heatand cold (PA Il.14 658a6-7). Treating oviparous quadrupeds separately,Aristotle says that they are covered with horny scales for the same reason.Crocodiles and tortoises have especially hard and bony horny scales (PAIV.ll 691a17-19). Aristotle tentatively says that the shell acts as a lid forthe heat (PA 11.8 654a5-9)."13 Note that this is also a function of exoskeletons and shells, which are, of course,nowhere called analogues of hair and feathers.

103 Analogy and DemonstrationSome animals have more or less hair, longer and shorter hair, justas other animals have more or fewer feathers or scales, and so on. Thesevariations on the generic type are explained by the varying amounts ofmoisture and earthy deposits from which they all are formed. Especiallyinteresting is a passage at GA V.3 782al4-20:Men go bald on the front of the head, but turn grey first on the temples;. noone goes bald on these or on the back of the head. Some such affections occurin a corresponding manner also in animals which have not hair but somethinganalogous to it, as the feathers of birds and scales in the class of fish.Balding, whether of hair or its analogues, occurs because, as the animalgrows older, it becomes drier, the skin becomes harder and thicker, theheat fails, and the moisture, which is the material cause of the hair, failsas well (GA V.3 783b2-8). There is no suggestion in these examples thatthe moisture itself has analogous manifestations. One kind of moisture, itseems, plays the same role in all the demonstrations, and the definition ofmoisture is not explicitly adapted to fit each demonstration. 14At PA II.2 648a2-7, Aristotle describes the differences in blood: thickand thin, dear and muddy, cold and warm. There is also the differencebetween those animals that have blood, and those that have instead someother such part «TEPOV TL }lOpWV TawilTav):The thicker and the hotter blood is, the more conducive is it to strength, whilein proportion to its thinness and its coldness is its suitability for sensation andintelligence. A like distinction exists also in the fluid which is analogous to blood.(T~V aVT~v 0' EXEt otacpopav Kat TO ava'\oyov {nrapxov 7rPOS TO aip.a.) This explainshow it is that bees and other similar creatures are of a more intelligent nature thanmany sanguineous animals.We see here that intelligence is predicated of animals in virtue of the middleterms, cold blood / cold blood-analogue. The intelligence which bees haveis in some ways similar to man's, but it too is analogous. In this case it isnat perfectly dear whether the major term (intelligence) is generically oranalogically common. The result may be two entirely analogical demonstrationsor two partially common demonstrations.14 Likewise, differences in hair and its analogues correspond to differences in gender. AtHA IV.11 538b8-9 Ariswtle remarks that the female is more delicate in hair ~nd wherethere is no hair she is less strongly furnished in some analogous substance. Here againwe observe analogous parts covariant with common features.

104 Aristotle's Theory of the Unity of ScienceFinally, we find analogies of the senses of hearing and touch, whichalso involve variations of more and less. These analogies do not involvedemonstration, but they illustrate the general point that analogies are oftensystematic, involving not just the general case, but also variations upon it.They are also peculiar in another respect. They concern sense perception,which is an activity of the soul, rather than a part of the body. Thisrepresents a higher level of scientific generalization, but here too there areanalogies. The terms sharp (at.,) and flat (j3a.pv) are applied metaphoricallyto sound from the realm of touch,where they mean respectively what moves the sense much in a short time, and whatmoves the sense little in a long time ... There seems to be an analogy (auQ.Xoyov)between what is sharp or flat to hearing and what is sharp or blunt to touch; whatis sharp as it were (oLov) stabs (KEVTf'i), while what is blunt as it were (orov) pushes(Weft), the one producing its effect in a short, the other in a long time, so that theone is quick, the other slow. (modified ROT; DA II.S 420a3D--b4)Although there is no explicit demonstration here, it is clear that there is anexplanation of what makes sounds sharp or flat. The explanation is parallelin the case of hearing and touch, and there is even a general explanationof a sort available: what moves the sense in a long or short time is sharpor flat/ dull. Notice that in spite of the general explanation Aristotle avoidsusing language in one genus that properly belongs to another genus. Forthis reason he uses the expressions oiov KEVT€~ and orov weft.Likewise, .it seems that there is an analogy between the senses of smell and taste, and that thespecies of tastes (7(1 EWl1 TWV XlJ,uwv) run parallel to those of smells ... As flavoursmay be divided into sweet and bitter, so with smells. In some things the flavourand the smell have the analogous (civa.\.oyov; not as ROT, the same) quality, e.g.sweet smell and sweet taste, and their opposites. Similarly a smell may be pungent,astringent, acid, or succulent. But, as we said, because smells are much less easyto discriminate than flavours, the names of these varieties are applied to smells invirtue of similarity. (DA II.9 421a17-bl)Again, the same features are apparent, including explicit mention of thefr~l1 of tastes corresponding to those of smell. No causal explanations areat work in this case, but we may safely assume that Aristotle would feelobliged to give a common account of these variations. We do see someexplanations at work in the following passage (Sens. 5 443b3-12):

105 Analogy and DemonstrationIt is clearly conceivable that the moist, whether in air (for air, too, is esser:ttiallymoist) or in water, should imbibe the influence of, and have effects wrought init by, the sapid dryness. Moreover, if the dry produces in moist media and air,an effect as of something washed out in them, it is manifest that odours must besomething analogous to savours. Indeed, this analogy is, in some instances, a fact;for odours as well as savours are spoken of as pungent, sweet, harsh, astringent,rich; and one might regard fetid smells as analogous to bitter tastes; which explainswhy the fonner are as unpleasant to breathe as the latter are to drink.All the explanations canvassed above invoke different kinds of cause(final, material, and efficient). In each of these cases some common formulationcan be provided, and each group of analogues can conceivablybe denominated by some functional description, for instance, blood-cooler,external surface residue, that which has intelligence, sensation. Clearly,then, some common account can be substituted even in these cases, andvariations on this new common item can be accounted for by variationsin some other common feature, more or less heat, more or less moistresidue, longer or shorter time. But to provide a common account wouldbe to abstract beyond the appropriate subject matter of the sciences, for ineach case Aristotle is talking about the specific part or function.The third and final form of demonstration, in which the major andeven middle terms are apparently treated as common and in which thereare no systematic variations, is the most frequent. It is a common practicefor Aristotle to provide a general argument that ends with a mention ofthe analogues to which the argument applies. At PA 11.1 647a24-33, forexample, Aristotle says[A]s the sensory faculty, the motor faculty, and the nutritive faculty are all lodgedin one and the same part of the body (EV TaVTC{J j.L0pl.'fl TOV (J'wj.LaTos) it isnecessary that the part which is the primary seat of these principles shall on theone hand, in its character of general sensory recipient, be one of the simple parts;and on the other hand shall, in its motor and active character, be one of theheterogeneous parts. For this reason (Ot07T€p) it is the heart which in sanguineousanimals constitutes this central part, and in bloodless animals it is the analogue.For it is divided into homoiomeries like each of the rest of the viscera, and yet itis anhomoiomerous on account of its shape. (modified ROT)Aristotle provides a general argument concerning the common seat ofsensation and movement. At the beginning of the argument the parts havenot been given their proper names, and only subsequently are analogues

106 Aristotle's Theory of the Unity of Scienceidentified. They are treated as a single nature throughout. The last twosentences of the passage seem to constitute an application argument: sinceboth the heart and its analogue have a homoiomerous and anhomoiomerousnature, they qualify as the seat of these faculties 1sThis pattern of explanation is also found very frequently in the GA.We see Aristotle discussing and explaining various common traits of theprinciple (apx~), then stating that this principle is the heart or the analogueof the heart. So, for example, 11.1 735al6-26:Hence it is that only one part comes into being first and not all of them together.But that must first come into being which has a principle of increase (for thisnutritive power exists in all alike, whether animals or plants, and this is the sameas the power that enables an animal or plant to generate another like itself, thatbeing the function of them all if naturally perfect). And this is necessary for thereason that whenever a living thing is produced it must grow. It is produced, then,by something else of the same name, as e.g. man is produced by man, but it isincreased by means of itself. There is, then, something which increases it. If this isa single part, this must come into being first. Therefore if the heart is first made insome animals, and what is analogous to the heart in the others which have no heart,it is from this or its analogue that the first principle of movement would arise.Here the general argument extends not only beyond the analogues themselves,but even beyond animal to encompass everything capable of nutrition.Again, the general argument seems to be applied to the heart and itsanalogue as to species.These examples of demonstration seem to belie the claim that a COIDmangenus and a common explanation cannot be given for analogues. ForAristotle seems to be perfectly capable of articulating the cause at a generallevel and applying it directly to the analogues. These cases, then, supportthe relativist interpretation whereby analogues can with no modificationbe gathered into a genus.How are we to account for this wide variation in practice, where sometimes,as we see, purely general arguments seem to be applied to analoguesas if to species, sometimes general features seem to be adapted to genera15 So also at PA 11.1 647al4-21 we are told the reason for the existence of flesh and itsanalogue, but in general terms; sensation takes place in the simple parts, but tou ch takesplace in the least simple of the parts. This part must be more complex, because thissense deals with more than one sensible. Only after providing this general explanationdoes Aristotle say that the sense organ of these, the flesh and it s analogue, is the mostcorporeal of the sense organs.

107 Analogy and Demonstrationto a greater or lesser extent, and sometimes again demonstrations are fullyanalogo.us? One is tempted to fall back on the common and correct claimthat the biological works are not syllogized in the formal way that wouldbe necessary in order to reveal the intricacy of analogical demonstration.Formalization would involve the tedious and unnecessary process of statingexplicitly all the per se and qua relationships. The mention of analogues incontexts where demonstrations are not fully formalized may represent asort of promissory note, an indication of the mode of proof to be pursuedif one wishes to formalize.No doubt, this view explains the variation in practice to some extent.Aristotle throughout the biological works prefers to use a non-technicaland non-formal language, and the logical apparatus of the APo to theextent that it is present remains largely implicit. But our difficulties are notsolved by this means alone. The other, more important reason is that anygiven item must enter into causal relationships with several other items atvarious levels of generality.16 This fact is made clear by the organizationof the WP system. The lower levels on the table provide the matter andare the material cause for the higher levels. But the matter often has adifferent extension from that for which it is the matter. Horny material,for example, provides the stuff for a variety of different organs, fingernails,talons, and horns. Horny material, that is, extends further than anyone ofthe homoiomerous parts for which it is the materia1. 17 This situation occursnot just among the components of the WP system, but also in the processof generation, as the following passage makes clear (GA 1.19 726bl- S):We have previously stated that the final nutriment is the blood in the sanguineaand the analogous fluid in the other animals. Since the semen is also a residue ofthe nutriment, and that in its final stage, it follows that it will be either blood orthat which is analogous to blood, or something formed from these.Though in many demonstrations semen will be related to other termsthat have the same level of generality as itself, this is not the case herewith its material cause. Now, it would not be difficult to analyse this16 This problem is discussed by Goldin 1996, 148- 51, who solves it by claiming thatAristotle is not consistent in his injunction against metabasis, and that he frequentlyinvokes principles from other sciences. Goldin assimilates such cases [0 the use ofmathematical middles in optical demonstrations.17 PA II.9 655b2-4; cf. ILl 646b3O-34, where some of the viscera are made of a commonhomoiomerous material, differentiated presumably just by their shapes. So also Met.H.4 1044a25-31, where a single matter may have. two forms and two different mattersmay have the same form.

108 Aristotle's Theory of the Unity of Sciencecase in accordance with the model of longevity and assume two differentbut parallel causal processes of concoction whereby blood and its analogueare transformed into semen. Semen will then have one general cause andtwo analogous causes. As a concoction of nutriment it has one cause, butas a transformation of blood and a transformation of blood's analogueit will have two, and semen in this case will be ambiguous 1 8 But evenif we can provide an adequate analogical analysis for these cases, andclaim that for the sake of brevity Aristotle chose not to do so himself,we are merely evading a more pervasive problem. We have seen thatanalogues have their origin in the phenomenal analysis of the WP andSGA systems. There each part was hypothesized as existent and fitted intoa compositional network. Generically different parts with similar materialand compositional constitutions were deemed analogous. The analogueswere hypothesized as generically different, but were called analogous becausethey fit into corresponding positions in the WP table . There was asyet no consideration of cause or demonstration. But it is precisely thesecorrespondences and similarities that must either be explained or serveas explanations in demonstrations, and it is precisely these that, whenthey arise, are treated as common. We noticed the underdeveloped stateof analogies of function in the PA. Though Aristotle recognizes them intheory and occasionally uses them in practice, he tends to treat functions ascommon. In fact, this tendency is a manifestation of a widespread featureof Aristotle's general methodology, which starts with the material, thespeCific, and the familiar and moves to investigate the common cause (d.KOLV~ aiTia MA 1 698a4). Analogy appears especially clearly at a precausalstage of investigation. But once causes are brought to bear on the subjects,the common begins to prevail, both in the material cause, which oftenextends more widely than the specific explanandum, and in the final cause,which is expressed as a general function.We have already seen in Aristotle's study of animal movement thetransition from the material, the specific, and familiar fact to the formal,generic, and abstract cause. The various aspects of animal movement (e.g.,wings, joints, hearts, desire) are best treated at different qua-levels, becausethey have different extensions. And yet these qua-levels cannot be entirely18 Again, at GA 11 .3 737a36-b4, I All bodies are held together by the glutinous; this quality,as the embryo develops and increases in size, is acquired by the sinewy substance,which holds togeth er the parts of animals, being actual sinew in some and its analoguein others.' Sinew and its analogue are both glutinous, a material feature necessitated bytheir common function. As such they share a power, and therefore differ by the moreand the less in a weak sense. And yet they remain analogues.

109 Analogy and Demonstrationcausally isolated from one another, the latter being causes for the former.Likewise, we see in APo II.19 that in some cases the search for the causeand the search for the universal is one and the same: the search for theimmediate connections of demonstration is the search for the universal. Byallowing specific subject matters to be subsumed under more general andabstract subject matters, the assimilation of the cause and the universalproduces that scientific unification through hierarchy which is so characteristicallyAristotelian. But at the same time it creates a tension with therules of demonstration, which require that the cause be treated at the samequa-level as the fact.The tendency to introduce the universal cause is especially strong whenthe analogy on the phenomenal level is not matched by a terminology ofcause at the same level. This is especially prevalent with nameless analogues.So underdeveloped is Aristotle's vocabulary that often an analogouspart is nameless; so much more likely is it, then, that the function of thatpart, which already tends in Aristotle's conception towards the universal,will have no special name. It is not surp~ising, then, that the vast majorityof cases involving demonstrative analogy of the third kind involve partswith nameless analogues.Analogies arise in a demonstrative context when the subjects we aretreating are generically different. According to the rules of the APo, theterms of the demonstrations must be adapted to the subject-genus. Theterms of analogous demonstrations, though they are adapted to their genus,can be abstracted and generalized, but in so doing, the terms no longerremain the same, and the subject matter changes and a different scienceemerges. In cases where Aristotle does not follow this strict model, thetendency to generalize the cause is usually matched by the unavailabilityin the common language of specific causal terms. The language of facts ismore specific than the language of causes.Analogy and the Scala NaturaeThere is another form of explanation operative in the biological works thatis often confused with analogy. At the widest level, spanning the wholerange of animal kinds, Aristotle has established sweeping continuities,which constitute what is traditionally known as the scala naturae. The scalaadmits two different theoretical interpretations. It may either be consideredsolely as a scale of difference with no normative implications, like that ofcartilage and bone, or it may also involve value, one end of the scale beingbetter than the other. It is clear from what we have said that various partsof animals have different extensions, and some attributes, for example,

110 Aristotle's Theory of the Unity of Sciencemouth, extend to all animals and vary by differences of degree. Mouthsare different because they serve different functions, and not because onemouth is better than another mouth. In the same way, all animals havevital heat, but some have more and others less. Furthermore, the scaleof heat may correspond to or be covariant with other attributes, like themodes of reproduction and so on. Such scales, since they connect all thegenera of animals together, have threatened to erase generic distinctionsby representing animal kinds as a smear of variation rather than as discretegroups. Dualizers (f7raJloTEpi("oVTES), like dolphins, are doubly challengingin this regard: because they stand between two great groups, they aredifficult to place in either one of the groups, but because they can equallybe placed in either, they make the great groups themselves indistinct andindefinite. These scales when treated non-normatively present the sameproblem as we faced with bone and cartilage. Because the essential featuresof the two parts differ by more and less, it is difficult to place an exact lineof demarcation between them and distinguish them exactly.But the scala may also be a normative system, in which one end ofthe scale is positively valorized, and all other points fall short of it forvarious reasons. As a result, two objects on a scale are not just different,one is better than the other, and we explain features of one kind of animalin terms of its proximity to a different, but normative, kind. Indeed, thechallenge of the scala arises not so much within the first interpretation, butrather when it is conceived as a hierarchical tool of explanation, in whichanimals and their parts are explained as deficiencies from one primary type,usually man. For on this view the usual injunction against metabasis breaksdown, and principles proper to one genus are used in the explanation of adifferent genus. Indeed Pellegrin has asserted that analo~l has the purposeof joining together animals in an intelligible hierarchy:[I]n the History of Animals (8.1.588a25), Aristotle explains that psychologicalfaculties differ between man and various other animals either by the more and theless or analogically. And this example helps us to understand the truly fundamentalfunction of the analogical relationship in biology. It does not serve so much toset apart natural families of living things as to relate one group of animals toanother by some point of reference, and ultimately to relate all living things toone unique being, taken as a model of intelligibility, man ... Thus, in a sense,all the 'anatomical' parts of the History of Animals. really do not constitute,19 1986a, 90--2. He cites Leblond's attempt to tie analogy to taxonomy by supposing thatanalogy allows comparison of parallel and independent genera, and as such is a kind ofcomparative morphology within a taxonomy (LeBlond 1945, 41-2).

111 Analogy and Demonstrationdespite what some have mistakenly said, a comparative anatomy, but are rather ananthropocentric anatomy and ethology, and that thanks to the employment, explicitor not, of analogy ... Animals are, as it were, sketches of the human animalAristotle declares that, in relation to man, they are like dwarves, that is, badlyproportioned and badly constructed men.Pellegrin's argument here is an extension of his claim that there is nonatural distinction between genus and analogy, and that analogues areinterchangeable with genera. Here the more and less, analogues, and hierarchyall aim at one grand purpose. But, in fact, series arguments, whichare the basis of the scala naturae, presuppose a norm with respect tothe shared attributes in that scale, and that norm provides an explanatoryprinciple?O Analogical arguments/_by contrast, make no such presupposition.Because they maintain their generic autonomy foremost, analoguesdo not as such show any tendency to priority and posteriority. Althoughthere is indisputable evidence in general for a scala naturae, it does notthreaten to obliterate generic distinctions that are the basis of analogy.Any attempt to construct a purely scalar arrangement of the parts andtheir attributes would result in an overly simple scheme of explanationincapable of accounting for the phenomena. 21Although the non-normative interpretation of the scala has been discussedelsewhere,22 it is useful to clear up some confusions in what hasbecome a standard interpretation. The classic passage at the beginning ofHA VIII suggests in the Revised Oxford Translation that Aristotle thoughtit difficult to make distinctions between genera:Nature proceeds little by little from things lifeless to animal life in such a waythat it is impossible to determine the exact line of demarcation, nor on which sidethereof an intermediate form should lie.23 Thus, next after lifeless things comesthe plant, and of plants one will differ from another as to its amount of apparentvitality; and, in a word, the whole genus of plants, whilst it is devoid of life ascompared with an animal, is endowed with life as compared with other corporealentities. Indeed, as we just remarked, there is observed in plants a continuous scaleof ascent towards the animal. So, in the sea, there are certain objects concerning20 See Preus 1983 for this and other normative aspects of Aristotle's biological definitions.21 See Lovejoy's judicious comments on Aristotle's use of scalar arguments, 1964, 55-9;also Coles 1997.22 These issues have been effectively discussed by Granger 1985.23 OVTW l)' EK TWV a'/tvxwv Et~ TO. (0a IJ.ETaj3atvn KaTo. IJ.tl

112 Aristotle's Theory of the Unity of Sciencewhich one would be at a loss to determine whether they be animal or vegetable.(588b4-13)This passage does not claim that demarcations are impossible to determine.In the first sentence the subordinate clause is constructed with WfJT€ andthe infinitive of natural result, and as such does not affirm that it isimpossible to determine the exact line of demarcation, but only that itis something that would naturally escape our notice 24 Obviously Aristotledoes not think that it has escaped his notice. Indeed, comparison of otherpassages with WaTE plus Auv8civftv clearly shows that what escapes noticenevertheless unequivocally exists." It is also seldom observed that thispassage is situated in the midst of Aristotle's introduction to the psychologicaltraits of animals, and that throughout he is remarking not onthe difficulty of distinguishing the external forms of the various genera ofplants and animals, but of locating demarcations in psychological capacities.It is difficult to tell, for example, whether certain animals sleep or havesensation. This passage, then, cannot be used to suggest that Aristotlethought his generic distinctions based on parts could be reduced to scalesof more and less. In spite of their own peculiar ambiguities, the physicalforms of the genera are clearer than the differences in functional capacities,which can be associated with wider variety of external form.We see the same kind of issue at stake in the other oft-cited passage,PA IV.5 681a9-15:The ascidians differ but slightly from plants, and yet have more of an animalnature than the sponges, which are plants and nothing more. For nature passesfrom lifeless objects to animals in such unbroken sequence, interposing betweenthem beings which live and yet are not animals, that scarcely any difference seemsto exist betWeen two neighbouring groups owing to their dose proximity?6Again we see the same tentative natural-purpose clause with a verb whichdistinguishes appearance from reality, and which states that the distinction,though obscure, nevertheless exists. 27 Again, Aristotle seems to be24 Smyth 1956, 507-10.25 Cf. HA 11.15 506a15; 11.17 508a16; and GA III.5 756032.26 ~ yap cptxn

113 Analogy and Demonstrationperfectly able to distinguish ascidians from sponges, and presumably thesetwo groups from algae and the various kinds of terrestrial plants. That is,while the demarcation between animal and plant is difficult to observe, thesub-groups are clear enough, and they do not blend into one another. Thereason, again, is that the demarcation between animal and plant is not somuch structural and based on parts as it is psychological and functional.Sensation and movement are considered to be essential features of animals,and yet some animals are sessile. Sponges, when pulled off from theirattachments die just like plants (681aI5- 17). Sponges and sea cucumbershave no sensation (681aI9-20). Ascidians are sessile like plants, but theyare fleshy like animals and therefore probably are capable of sensation ofa kind (681a25-28). The loci classici do not support the interpretation thatthe scala is so continuous as to erase the distinctions between genera. 28In fact, dualizers, far from destroying the distinctions between groups, area strategy employed to preserve the essential natures of the genera. Theproblem of dualizers occurs not because there are no generic differences,but precisely because there are and those differences are set by the systemof internally defined multiple differentiae. Only in a system of dichotomousdivision could we ensure that there are no dualizers.There is also clearly a normative component to the scala naturae. 29 Onepassage, for example (PA IV.I0 686a24-687a2), places man first among theanimals because of his upright posture. Man stands erect because he is godlike,and so must think and be wise. This hypothetically necessitates hisbeing not earthy, since earthiness impedes thought. Man has the naturaland normative posture (what we might call the default posture that occursif nothing prevents), and increased earthiness causes an animal to tenddownward and so require four legs for support:Dwarf-like again is the race of the birds and fishes; and so in fact, as already hasbeen said, is every animal that has blood ... The explanation, as already stated,is that in many their psychical principle is corporeal and impeded in its motions.Let now a further decrease occur in the elevating heat, and further increase inthe earthy matter, and the animals become smaller in bulk, and their feet morenumerous, until at a later stage they become footless and extend full length on theground. (PA IV.l0 686b20-31)28 Herein I concur with Granger 1985.29 Lennox 1985, 313-15, has argued briefly that the normativity of Aristotle's biology isoverrated. Coles 1997 has collected the data and argued more fully and persuasivelythan anyone that Aristotle had in mind a single and coherent scala. He, however, didnot directly address the possible conflict with analogical explanation.

114 Aristotle's Theory of the Unity of ScienceOther blooded animals are like dwarves having their upper parts larger thantheir lower; this presses them down, makes them quadrupeds (or worse)and incapable of thought. Such an argument has important implications forgeneric unity. For it can prove that viviparous quadrupeds are quadrupedswithout invoking the principle that quadrupeds have four legs; instead ituses man as a principle and demonstrates quadrupediry as a conclusion.For one of the premisses must state that quadrupeds are dwarf humans,and as such quadrupeds will be related per se to humans. This is either aclear case of Jlfj(J./3acns or it genuinely erases generic distinctions.Scalar arguments of this sort depend upon the highest member of thescale to provide a principle for all the members. But it is evident by the factthat Aristotle introduces many more specific principles to explain groups ofnarrower extension that he did not consider the broad scalar attributes fullyexplanatory. The subsequent changes from humans through quadrupedsand testacea to plants cannot all. be explained on the principle of increasingweight and dwarfishness. In fact, no single set of principles starting fromman can explain the variery of animals and their parts, and Aristotle clearlydoes not suppose that they all can be completely explained as deficienthumans.The normative status of the human is also undercut by the fact that thispassage explicitly states that thinking is in man's logos. For this impliesthat thinking is a specific element in the definition of man, and as such isnot present in the logos of other animals. The series argument, by_contrast,suggests that 'human' will be a per se predicate of other animals inasmuchas they are deficient humans. That is, if they were not impeded by theirearthy nature and defiCiency of heat they would be humans as well. Butthe denial of thinking as a part of their essence indicates that they are notprincipally to be defined as deformed (7I'E7I''1pwjJ.Eva), in spite of the factthat certain resemblances in their nature suggest as much. In fact, Aristotle.makes it just as easy to view man as a deviation from quadrupeds throughthe addition of his thinking faculry. His intellect makes him capable ofusing hands (PA IV.I0 687a8-23), and if he is to have hands, he must goon two legs, and so must be upright, and be less earthy than quadrupeds.On this view quadrupeds are causally primary and man is explained on thebasis of them. It is unclear which order of explanation Aristotle thoughtcorrect. Ultimately the explanatory factors are so numerous and so complexthat any attempt to create a single scala can only capture a few closelyrelated genera of animals, and explain their attributes only in the roughestway. The posture scala would seem to treat birds as closer to man thanquadrupeds, and yet the reproduction scala treats them as further removed.Although Aristotle clearly thought that vital heat was the common element

US Analogy and Demonstrationin these various scala, the accompanying attributes are not consistentlycovariant. As a result, each genus must still be treated independently.Aristotle does not introduce analogy in the biological context in orderto facilitate and ground scalar arguments, but in order to complement theirdeficiencies. The need for analogues as stafting points cannot be eliminatedby the occasional presence of arguments of scale or more and less. Withoutdenying that analogues exhibit structural and material similarities and thatsometimes these are scalar, they cannot fully explain the variation anddistribution we find. Some aspects of apart's nature can be explained byscalar arguments, but other aspects are sui generis, and can be explainedonly within the genus.

4The Structure of Focality'Focal meaning' is a term that was coined by G.E.L. Owen to translatethe phrase Trpo) €V A.eyOjlEVOV,1 !t is used in several Aristotelian contexts,and provides an explanation for why a word is applied to a variety ofobjects that are neither specifically or generically identical nor completelyunrelated:[E]ssence will belong, just as the 'what' does, primarily and in the simple sense tosubstance, and in a secondary way to the other categories also, - not essence simply,but the essence of a quality or of a quantity. For it must be either homonymouslythat we say these are, or by making qualifications and abstractions (7J'po(J"nBivrasKal. dcpaLpovvTas) (in the way in which that which is not known may be said to beknown), - the truth being that we use the word neither homonymously nor in thesame sense, but just as we apply the word 'medical' when there is a reference toone and the same thing, not meaning one and the same thing, nor yet speakinghomonymously; for a patient and an operation and an instrument are called medicalneither homonymously nor in virtue of one thing, but with reference to one thing.(Met. 2 .4 l030a29-b3)1 Earlier discussions of focality have tended to concentrate on issues of meaning, includingG.E.L. Owen's (1960, 184), who called it 'focal meaning: Leszl, who has also treatedthes~ issues extensively, presented them largely in terms of synonymy, homonymy,and meaning, and, unable to see how 'being' could apply to non·substance within thisframework, supposed that it applied metaphOrically from its application to substance.See Hamlyn 19n-s for a critique of Leszl. For a new study in tenns of homonymy seeShields 1999. The debate is now emerging from the confusions of linguistic philosophy,and some attempts have been made to place focality and issues of meaning within theframework of demonstrative science, e.g., Ferejohn 1980 and Bolton 1995. For otherattempts to remove Aristotle from the grip of conceptual analysis, see Irwin 1981 and1982.

117 The Structure of FocalityThere must, then, be three kinds of friendship, not all being so named for onething or as species of one genus, nor yet having the same name quite by mereaccident. For all the senses are related to one which is the primary, just as is thecase with the word 'medic~l'; for we speak of a medical soul, body, instrument,or act, but properly the name belongs to that primarily so called. The primary isthat of which the definition is contained in the definition of all (Bonitz's 7rU(Tt forMSS r,J.llV); -e.g. a medical instrument is one that a medical man would use, butthe definition of the contained is not implied in that of 'medical man.' (EE VII.21236a15- 22)So, too, there are many senses in which a thing is said to be, but all refer toone. starting-point; some things are said to be because they are substances, othersbecause they are affections of substance, others because they are a process towardssubstance, or destructions or privations or qualities of substance, or productive orgenerative of substance or of things which are relative to substance, or negationsof some of these things or of substance itself. It is for this reason that we say evenof non-being that it is non-being. As, then, there is one science which deals withall healthy things, the same applies in the other cases also. For not only in thecase of things which have one common notion does the investigation belong to onescience, but also in the case of things which are related to one common nature.(Met. r.2 1003b5-14)We can draw a number of preliminary and tentative conclusions fromthese passages:1. In a certain sense focally related items share a name, for instance,medical skill and medical instrument; substantial being and qualitativebeing. However, focally derivative objects also have their own propernames (scalpel, quality, etc. ), and the common focal term is predicatedof them in addition to this name. Properly speaking, then, they do notshare a name, but have the same term predicated of them.2. There is a focus or primary term whose definition or whose name ispresent in the definitions of the derivative terms, for example, medicalinstrument is by definition a tool useful for the medical man.' We get2 For the substitution of a name for a formula in focality, see Ferejohn 1980, 118-19.Also, Met. Z.5 1030b23- 26: 'And such attributes [per se attributes1 are those in whichis involved either the formula or the name of the subject of the particular attribute, andwhich cannot be explained without this; e.g. white can be explained apart from man,but not female apart from animal: On the replacement of the name for the definition,see Owen 1965, 262, who cites D1 21a29-32, APr 49b3-5; and Top. 101b39-102a1,130,39, 142b2-4, 147b13-14, 149a1-3.

118 Aristotle's Theory of the Unity of Sciencedefinitions of primary items from definitions of secondary items andvice versa by addition (7rpo0"8«m) and abstraction (acf>aipEO"L

119 The Structure of Focalityand its species may then form subject-genera for demonstrations. Thisrelationship implies that a single subject-genus will be composed of asingle kind of object. For example, when beaks are divided into straightbeaks and hooked beaks, and hooked beaks are treated as a subject-genus,hooked beaks are all the same kind of thing. Confusion, however, ariseswhen we try to treat as a subject-genus objects that do not form asingle kind of thing, and that are not species derived from a divisionof a single genus, for example, hooked beak and being predatory. Thisconfusion becomes especially acute when these objects are all describedby the same term, and so appear to be species of a common divisionarygenus and treatable as instances of the same kind of thing. Now, suchconfusion does not usually occur among objects that share the same nameby accident. The attempt to treat capes (the article of clothing and thegeographical feature) as a single subject-genus is too obvious a mistaketo cause trouble. Serious difficulties, however, arise among homonymsthat are related to one another essentially, but not as species of a genus.Medical instruments (scalpels) and medical people (doctors) are not speciesof the same divisionary genus, but they can be considered to belong inthe same subject-genus, since there is an essential relationship betweenthem. In fact, between every focal term and its derivatives there is a perse relation. Not only is the definitional inclusion criterion a guarantorfor the essential relationship between the terms, Aristotle's list of focalrelations also recalls the array of relations typical of normal demonstrations.Processes towards a focus and things productive of a focus, thingsnaturally adapted to or functions of a focus are all explanatory causesof a focus, and so are descriptive of the immediate per se connectionsof demonstrative premisses. Symptoms are attributes of a focus and aredescriptive of per se accidents or conclusions of demonstrations. Indeed,with the exception of the accidental predications (affections, qualities, etc.,to be dealt with in the next chapter), all the focal relationships mentionedby Aristotle correspond to the causal explanations in normal sciences, andare described in the same way as the relationships between terms in normaldemonstrative sciences.In fact, Aristotle himself draws the parallel between focal and nonnaldemonstrative science in the Met. r.2 passage, where he explains thestructure of the science of Being through a comparison to the structureof medicine. No one would dispute the fact that medicine is a science ofthe normal sort, and by showing that the science of Being has a structurecorresponding to this science, Aristotle can argue that the science of Beingis of the same basic kind. Just as the terms of medical science are not alldrawn from the same divisionary genus, so it is also with the science ofBeing. It is only because medicine is uncontroversially a normal science

120 Aristotle's Theory of the Unity of Sciencethat Aristotle can assimilate the science of Being to it, and argue that Beingforms a subject-genus.Yet there are a number of important objections to the view that thefocal relation is the same as the per se relation characteristic of normaldemonstrative science. At the most obvious level, focally related itemsshare a name, whereas this is not explicitly the case among the terms ofa normal science. And even if we are willing to dismiss that objection asa relatively trivial issue and concentrate instead on the logical and definitionalrelations, we still face problems with the criterion of definitionalinclusion. Let us take these questions up in turn.It is important to be clear what focal homonymy consists in. Sincescalpel, patient, and so on are different names and refer to different things,there is clearly no homonymy among them. Likewise, there is no homonymybetween quality, quantity, and substance. Homonymy arises onlywhen a common term, medical or Being, is predicated of them, but eachin a different sense. This way of viewing the matter gives the appearanceof a one-over-many structure, and this is why Aristotle says that in somesense the focal term is predicated univocally (we' EV r.2 1003bl4-15):medicalis predicated ofpatient scalpel operation doctorin virtue of the relation ofundergoing instrument means havingThe issue of homonymy, then, which results in an apparently universalpredication, is the problem to be solved, and when Aristotle solves it byinvoking definitional inclusion, he effectively dismisses the issue of names.For if names and the definitions of these names signify the same thing,then we can replace all the names with definitions and thereby eliminatethe homonymy. For example, it does not change the structure of the scienceof health if we just talk about food, climate, exercise, and disease, withoutexplicitly saying that they are all healthy. The fact that they are all healthythings results from their being related to the primary item, not from theircommon name. That is, their focality does not arise from their being calledhealthy climate, healthy exercise, or any other name, but from the factthat their definitions contain 'health' in them. s Focal homonymy causesdifficulties only if we fail to make the distinction between the primary and5 So also Bolton 1995, 428.

121 The Structure of Focalityderivative terms. If we suppose that there is no difference between them, ifwe suppose 'health' is predicated of bodies in the same way it is predicatedof climates, we make the typical Platonic mistake.To take a biological example, bone is focally related to flesh, sincebone is defined as 'support of flesh.' Flesh is contained in the definition ofbone, because flesh is a final cause for bone in animals that have it. Wemight say, then, that flesh is the primary fleshy thing, and bone is calledfleshy, not because it has the attributes that flesh has, but in virtue ofits relationship to flesh. But, of course, Aristotle never calls bone fleshy,because focality is not a strategy for creating homonymy, but for resolvinghomonymy by appealing to the per se connections characteristic of normalscience; and the talk about a common predicate need only be made explicitwhen the homonymy is in current usage. Since it is obvious in what wayflesh is related to bone, and we do not call bone fleshy, there is no needto make explicit the definitional inclusion latent in these terms. It is onlyin especially abstract cases, like Being, where the nature of the object isso difficult to determine, that such confusions arise. The fact that normaldemonstrations in the natural sciences do not regularly make their focalitymanifest is irrelevant to the fact that these sciences are focal sciences andare focal sciences precisely because they are based on the causal connectionsof normal science.The per se relation gives us important information about the natureof focality. For focality is an application of the per se relations of ordinaryscience to solve a problem that arises from the confusion between thetwo senses of genus. Objects that because of their common name seemto be, but are not, members of a common divisionary genus, may fallwithin the same subject-genus. Since these objects are not specifically orgenerically identical, the only remaining way to include them in a singlescience is by relation. At the same time, focality and especially the examplesof health and medicine provide important clues about the structure ofordinary science and the interpretation of the per se relation in that context.The definitional inclusion criterion suggests that whenever some item isused in a science, it must have the definition of the focal item in it. Becauseof this strict criterion for focal inclusion in a science, focality provides ananswer to a question we faced in the last chapter, namely, whether commonterms mean different things when used in different sciences. To judge bythe focal relationship, the answer is yes, since the relation of the item tothe subject matter must be specified in the definition of the derivative item.So, for example, in medicine the knife is medical and contains medicine inits definition, but in cookery the knife is culinary and contains cookery inits definition.

122 Aristotle's Theory of the Unity of ScienceFocality and Per Se PredicationI would like now to address in more detail the question whether focalityis amenable to an analysis in terms of per se predicates and demon~stration. There are good reasons why it should be. First, Aristotle announcesat the beginning of Met. r that there is a science of Beingqua Being and the attributes that belong to it per se (ov y, OV Kat TaTOVTI!' lJ7rapX{'VTa

123 The Structure of Focalitythe demonstration seems to explain a linguistic fact, namely, why it is thatwe call drugs healthy, rather than the natural causal relationship betweendrug and health. In order to show the linguistic fact of focality (i.e., that wecall drug healthy), the derivative term (i.e., drug) will appear as the minor,the focus term (i.e., healthy) will appear as the major, and the definitionof the minor as the middle. These two features suggest that this is not aproper demonstration, and for this reason it is a poor candidate on whichto base the structure of a focal science.We can instead formulate genuine demonstrations that make use ofthe focally related terms and that reflect the natural causal relationshipsof normal scientific demonstrations. Whereas the improper demonstrationthat proves the linguistic fact consistently places the focal term in the majorposition, the demonstrations of natural connections are much more flexible,and in fact place it in any of the three positions. Using as a model the causaldemonstrations discussed in APo II.ll and the rather loose way in whichAristotle connects terms there, we can arrange the focally connected termsin a variety of ways:healthy IPO material restoring the uniform state of the bodymaterial restoring the uniform state of the body IPO drughealthy IPO drugBy substituting 'health' in the middle term with a definition of health,'uniform state of the body,' we provide an explanation, not of the linguisticfact anymore, but of the natural fact. Now, the explanation given here isthe formal cause, and indeed, this sort of substitution will in every casechange a demonstration of the focal linguistic fact into a demonstrationthrough the formal cause. Obviously, too, in this case, the arrangementof the terms and the premisses will remain the same as in the linguisticdemonstration. But when we provide other causes, we must often rearrangeor change the terms of the demonstration:taking drugs IPO restoring healthrestoring health IPO patienttaking drugs IPO patientIn this case the focus is contained in the middle term and provides the finalcause. Middle and major can also be interchanged, thus changing the finalinto an efficient explanation. The focus will appear as the major, as in thelinguistic explanations, but here the explanation is not of the term, but ofthe fact:

124 Aristotle's Theory of the Unity of Sciencerestoring health IPO taking drugstaking drugs IPO patientrestoring health IPO patientExamples in which health occupies the minor position are rare, becausehealth is a state of the body, and is generally predicated of man or patient.Moreover, objects that are predicated of health (e.g., good, desirable, useful,pleasant, harmony) seem to be poor candidates for focality, since we donot usually call any of these things healthy. The reason for this is that allthese predicates are generic and extend more widely than the focus subject.But at least one seems amenable to this scheme:pleasant IPO having a uniform state of the bodyhaving a uniform state of the body IPO healthpleasant IPO healthSo the arrangement of the terms in demonstrations of natural facts isdifferent from and more flexible than demonstrations of linguistic (focal)facts' More important, according to this scheme the focally related termscan be arranged into demonstrations, and so actually pass muster as ascience. It seems, then, that focally related terms must be arranged in thisnormal manner if there is to be a focal science. Moreover, as we saw, thelinguistic demonstrations are dependent on the natural causal connections,6 When we manipulate the focal tenn$ to produce scientific (rather than linguistic)demonstrations, we change the nature of the per se connections among the terms. Now,Aristot.le leaves us in no doubt as to whether the causal definition passes muster asan immediate and ne

125 The Structure of Focalityand without these there would be no grounds for the focal relationship.Focal science, then, to the extent that it is science, depends upon the naturalcausal connections of nonnal science. The demonstration of the linguisticfact is only an apparent demonstration. Because the focal relationship is(usually) an immediate per se relationship, the syllogisms that show thisare not strictly demonstrations.There are two principal problems in identifying focal and normaldemonstrative science that have to do with the per se criterion. The firstis that focality forces us to provide a single unified subject for a science,which all related terms must contain in their definitions. This is a demandingrequirement, and one that we have already considered. While itis certainly true that in a normal science all the tenns are connected to oneanother through a series of per se relations, it seems impossible for themall to be connected directly to one single term through per se relations.After all, th~ conclusion of a demonstration states a connection that is notcontained in the definition of its subject, and for this reason we mightsuppose that the major term is not focally related to the minor. As we sawin chapter 1, Aristotle recognized the conclusion as a per se connection,but not one that required immediate definitional inclusion. But if focallyrelated terms are to appear in demonstrations, the conclusion must alsohave an immediate definitional connection. This, however, would destroythe nature of demonstration.There are two solutions for this problem. First, it may be that, after all,the definitional inclusion at work in focality is not the same as the per seconnection, but instead may be something looser, like a relevance criterionthat marks the derivative item as broadly related to the central subject ofthe science. This is an interesting possibility, since it would make the unityof a subject-genus dependent on something other than per se connections.Alternatively, immediate definitional inclusion may not be essential to thefocal relationship. Instead, two terms may be focally related even if one isonly the per se accident of the other. That is, the focal relationship maybe transitive. There are two considerations which suggest that this latterpossibility is the more likely. First, Aristotle does not draw the distinctionbetween the two kinds of connection postulated in the first solution. Herecognizes only per se connections made explicitly in definitions. Second,he clearly explicates the focal relationship in terms of per se connections,and these connections may be used to prove remoter connections. Thepossibility that focality is a transitive relationship is strongly suggested bysome examples in r.2: things that are 'productive or generative of substanceor of things which are relative to substance, or negations of some of theseor of substance itself' are said to be (I003b8-10). To take an extreme case,

126 Aristotle's Theory of the Unity of Scienceit seems quite likely that even that which is productive of a negation of aquality of a substance will be said to be and so be included in the scienceof Being. Since these linguistic facts must be backed by natural causes, thetransitivity of the linguistic facts will be matched by transitivity of the perse relations. For one term to be focally related to another does not, then,entail immediate definitional inclusion.There is a second problem in interpreting the focal science as a normaldemonstrative science, a problem that will lead us to a reconsideration ofthe nature of the subject-genus. We might expect the focus term to serveinvariably as the ultimate subject of predication in the minor position.After all, a science studies a genus and its per se attributes, and APo I.775a42- b2 implies that the genus is that of which the attributes are proved,and this can only be the minor term. And yet it is clear that among thefocally related terms the focus will frequently, and in the specific case ofhealth most often, not be found in the minor or subject position. Not onlywill the focus not be the subject, but there will be a variety of differentsubjects and therefore a variety of different sciences. For if we accept theclaim that the identity of a science is determined by the minor term, theneither there will be many sciences where there should only be one (in thedemonstrations given above, a science of patient, of health, of drug, etc.), orall these demonstrations must ultimately be attached to some basic subject,which will be the true genus of the science. An obvious candidate for sucha genus is patient or man qua healthy. The latter is especially appealing,because it points to the two-fold answer to the question. The subject-genusis determined by the qua expression, but the subject of predication is whatappears before the qua expression? This is Aristotle's practice in the PA.The ultimate subjects of predication are the animals, which have parts andattributes, but in each demonstration they are treated qua having somepart or other, and this is the genus. So, for example, having lungs is thecause of having necks in animals that have necks (IlI.3 664a12-36). Thesubject of predication is animal, but not animal universally. In this passageAristotle is talking about necks, so the subject-genus and minor term ofdemonstration is animals qua having necks:having a neck IPO having a larynxhaving a larynx IPO having a lunghaving a lung IPO animals qua neckedhaving a neck IPO animals qua necked7 There is some evidence to suggest that the subject lenn must be a substance. APo 1.2283,2-17; Met. Z.9 1034.30-32. Cf. Lewis 1991, 57.

127 The Structure of FocalityLikewise in his discussion of cause as substance in Met. HA, Aristotlementions two cases in which an attribute belongs to a substance, but notstraightforwardly in virtue of that subject. When we seek the cause forthings, we must beware what we are seeking the cause of:Nor does matter belong to those things which exist by nature but are not substances;their substratum is the substance. E.g. what is the cause of an eclipse?What is its matter? There is none; the moon is that which suffers eclipse ... In thecase of sleep it is not clear what it is that proximately has this affection. Surelythe animal, it will be said. Yes, but the animal in virtue of what, i.e. what is theproximate subject? The heart or some other part. Next, by what is it produced?Next, what is the affection - that of the proximate subject, not of the whole animal?Shall we say that it is immobility of such and such a kind? Yes, but to what processin the proximate subject is this due? (1044b8-20)The subject of predication in the case of eclipse is moon, a substance.And since asking what an eclipse is is the same as asking why darkne~s ispredicated of the full moon (Z.17), the subject of predication is a substance,moon, but not moon without qualification, since the eclipse occurs onlywhen the moon is full. Similarly sleep is an affection of animals, andanimal is the subject of which it is predicated, but it is in virtue of somepart of the essence of animal that sleep belongs to it, namely, the heart.To return to the case of health, under this interpretation we wouldmodify the minor term so that it is not the focus, but is itself a derivativeterm, that is, not health, but that ·which has health as such, for ultimatelywe need as a subject a recipient of the state of health. With that in placeit may be possible to discuss the entire science of health as both a focalscience and one with the subject of health as such as the subject of thescience, for the minor term is considered only insofar as it is the recipientof the focus term. In the first two demonstrations we provided above, wecan easily substitute 'patient' for 'that which has health as such.' In thesingle case we considered in which the subject was health, we can againeasily reformulate it so that pleasure is predicated of the healthy subjectas such. In sum, the focal science can be interpreted as normal science, thefocal term being the genus of the science, and its substrate, if it has one,being the subject of predication or minor term of the demonstrations. 88 This also distinguishes focality from paronymy to which it is often likened. Forthe paronymy relationship exists between a substantive noun and its correspondingadjective, e.g., courage and courageous (tivopda and avep€tos-). Paronymy makes nocommitments regarding the categorial status of the paronyms: the word from which-------------------------

128 Aristotle's Theory of the Unity of ScienceThe final and most important challenge to the view that focal scienceis logically identical with normal science argues that I have simply misinterpretedAristotle's basic intentions. Aristotle, the objection contends,did not think of the focally derivative terms as the per se accidents andcauses of the focally primary term, and did not intend to force them intoa demonstrative mould. Instead he was concerned to show how varioussubject-genera each with its own causes and per se attributes might heconsidered as parts of a single science. My solution may solve the problemof unity but at the price of destroying the architecture of focal sciencethat Aristotle wanted to account for. The 'normal science' solution simplydoes away with the derivative terms as subject-genera, and makes theminstead into causes and attributes in demonstrations concerning the focalsubject-genus.This challenge is important because the answer to it opens up a newand wider conception of subject-genus and clarifies the connections betweenfocality on the one side and analogy and semi-abstraction on theother. Focality is the meeting-point of two conceptions of subject-genus.The narrow subject-genus, now very familiar, is proper to the realm ofdemonstration. It is the subject of the demonstration, and attributes andcauses are predicated of it. Since these attributes and causes do not belongin the same divisionary genus as their subject-genus, they are includedin the subject-genus by focality. This focal inclusion of other terms isuncontroversial, and indeed a necessary condition for demonstrative proofas we saw in chapter l.But there is a wider sense of subject-genus, beyond that of both the minorterm of a demonstration and the whole demonstration together. Manyof the terms that are used in a demonstration, and that are therefore boundto the specific subject-genus per se and universally, may be abstracted tosome degree from that subject-genus and treated as subject-genera in theirown right. In many cases, and in all cases of natural substances, perfectconceptual abstraction will be impossible. The semi-abstracts maintain theirper se - though not their universal- connections to the genus from whichthey are abstracted. When there is a variety of terms that are abstractedin this manner and treated as semi-autonomous subject-genera, they maybe drawn back together in virtue of their remaining per se relations intoa single focal science. This view of focal science does not attempt to fitthe paronym is derived need not be a substance, though it must be a noun. By contrast,the focus must be that of which attributes may be predicated, even if the subject neednot be a substa nce as such. The subject of health does not have to be man, but onlythat subject which admits of health.

129 The Structure of Focalityfocally related terms into a single demonstrative syllogism; it is rather ameans for organizing semi-autonomous subject-genera.There is no doubt that this is a great organizing principle of Aristotelianscience. In Aristotle's lists of the focal relations we can virtually read off thetreatises of his biological works: the affections of animals are the subject ofthe HA, generations of animals are the subject of the GA, the preservationand destruction of animals are the subject of Juv., instruments of animalsare the subject of the PA and lA, the various activities of animals are thesubject of the MA, PN, and DA . Since the focal term is animal, we mightlook for a subject-genus of animal apart from all the derivative sciences. Ofcourse, it does not exist separately,9 Animal is always the ultimate subjectof predication, but it is always qualified by some qua expression.This system of organization is not peculiar to the biological or even tothe theoretical works. The ethics too manifests all the traits of a wide focalscience. It studies. eudaimonia, which is defined as activity in accordancewith virtue. Accordingly, EN III and IV discuss the various species ofvirtue, courage, liberality, and so on. They also study the things focallyrelated to virtue, the negations of virtue, vice, and later those things, likefriendship, that contribute to virtue.So once again, focal science turns out to be normal science, though thiswider view describes new aspects of scientific organization. The wide andthe narrow view of focal science are hardly exclusive, indeed they form atwo-stage organization related through the nexus of semi-abstraction. Aterm that is a focal member of a narrow genus may be semi-abstractedfrom that narrow genus to become a subject-genus of a new science. Butsince it has been only semi-abstracted, this new subject-genus remainsfocally related within the wider focal science.An important corollary of this connection between wide and narrowfocal science is that the subject of predication of the narrow science is thesame as the focus of the wide science. In the zoological works it is alwaysanimal. In the narrow science the subject of predication is animal withoutqualification, while the several biological treatises themselves are focusedon animal qua this or that feature.The Limits of Focality in the Biological WorksBefore turning to the metaphysical focalities, I want to discuss an aspectof biological focality in the demonstrative mode. Focality is a means of9 Aristotle suggests that it can exist, but that it is too cumbersome to treat animal s inthat way (PA 1.1 639alS- 29).

130 Aristotle's Theory of the Unity of Sciencetreating generically different terms as belonging to the same genus. Howfar outside the divisionary genus can one go, and still remain within thesubject-genus? Can or does Aristotle use the techniques of focality todevelop a logic of interdisciplinarity? Just as scalpels are part of the medicalscience through focalization, so we might expect nests to be included inthe study of birds (because they are the shelter for birds), or even antelopeto be included in the study of lions (because they are the prey of lions). Infact, Aristotle generally remains within quite narrow limits in the biologicalsciences. His procedure may be contrasted with evolutionary theory, whichfinds sources of explanation both in the internal nature of the animal and inthe external environment. The genetic code proposes and the environmentdisposes; the environment poses a problem that the genetic code must solveon pain of extinction. Evolutionary biologists explain features of animalsas adaptations to the environment, and so make the environment (e.g.,niches) a source of explanation for the animal. The study of ecology, theway species are affected by one another and by inorganic factors, is anatural development of this mode of explanation. Aristotle for the mostpart avoids explanatory factors that come from outside of the animal, andwhen avoidance is impossible, he redescrihes them so as to make theminternal to the animal's nature itself. So, for example, the environment isdescribed as a way of life or {3ios internal to the animal. Marsh birdsare well adapted to marshes, not because the marsh environment hasexerted evolutionary pressures, but because it is the internal nature ofmarsh birds to live in marshes, and if they are to do so, they must havesuch and such features. This is consistent with Aristotle's general systemof explanation in the PA, which provides the causes of parts of animalsfrom within the essential functions and activities each animal perfonns.The reason why Aristotle chooses this method is fairly clear: his methodprivileges unity of definition, while the evolutionary account makes a largepart of the cause and therefore the essence of an animal external" to theanimal. Obvious difficulties arise if we make antelope focally related tolions because they are prey for lions. For in the definition of the antelopewould be found the fact that they are essentially food for lions.The problem here is not that this would represent a constraint on naturalteleology, but rather that those constraints would come from the outsiderather than, as Aristotle invariably presents them, from within, either asmaterial limitations or as limitations imposed by the need to fulfil otherfunctions.Aristotle does, however, discuss some cases where environment, livingand non-living, plays a role. The terrestrial and marine environmentsprovide sources of explanation, but they have been focalized and are

131 The Structure of Focalityrepresented as land animals and water animals.lO These definitory factsof their {3io, explain the different kinds of limbs and modes of respiration.Habitat may also have a more specific influence: the hot and dry environmentof Libya seems to grow large animals (PA II.9 655aS-1O). Man hasthe hairiest head because hair shelters the head from excessive cold andheat (PA II.14 65Sb2- 7). Among the living environmental factors, someanimals are related to other animals by the f3{or; of being- carnivorous. Bonesof carnivores, for example, are hard because they have to fight for theirfood (PA II.9 655a12-17). We also find adaptations designed for defenceor preservation (aAK~ and O'wT'/Pia). But only rarely (as with eyebrowsand eyelashes, PA II.l5 65Sbl4-15) does Aristotle state explicitly whatexternal threat these parts provide defence against. Now, Aristotle does notprovide a hypothetical deduction for the existence of parts instrumental fordefence, but if he had, his clear inclination would be towards explainingthem as hypothetically necessitated by the life of the animal, rather thanas means to avoid being injured by something external. This tendencytowards exploiting internal principles of explanation has some effects onhis selection of facts for which he provides explanations. In explaining whysome animals lack certain modes of defence, he never cites lack of externalthreats but only notes that the animal's own nature prevents such defencefrom being useful.The major source of external causation, however, is in the explanationsfor sensation. For the organ of sensation is potentially what the sensibleobject is actually, and the nature of the sense organ must correspond to thenature of the sensible and the medium for the sensible. Since the actualis prior in knowledge to the potential (Met. 0.S), external sensible objectswill have a causal role in animals ll So since the organ of touch deals withmore than one kind of sense-object, it must have several oppositions in it,even though it is a uniform part (PA II.l 647al4-19). Likewise, the ears areplaced on man halfway around the head because they have to hear soundsfrom all directions (PA 11.10 656b26-29). Environment also clearly playsa role in the explanation of why fish have fluid eyes (PA 11.13 65Sa3- 10):10 Cf. Top . VI.6 144b31-145al: 'See, too, if he has rendered being in something as thedifferentia of a thing's substance, for it seems that locality cannot differentiate betweenone substance and another. Hence, too, people condemn those who divide animals bymeans of the terms terrestrial and aquatic, on the ground that terrestrial and aquaticindicate locality. Or possibly in this case the censure is undeserved; for aquatic does notmean "in" anything; nor does it denote locality, but a certain quality; for even if thething is on the dry land, still it is aquatic - and likewise a land animal, even though itis in the water, will still be a land animal and not aquatic.'11 See Cleary 1988, 57.

132 Aristotle's Theory of the Unity of ScienceFor animals that move much about have to use their vision at considerable distances.For land animals, the air is transparent enough. But the water in which fishes live isa hindrance to sharp sight, though it has this advantage over the air, that it does notcontain so many objects to knock against the eyes. For this reason, nature, whichmakes nothing in vain, has given no eyelids to fishes while to counterbalance theopacity of the water they have eyes of fluid consistency. (modified ROT)Sense perception is not only an external cause; it is also the ultimate finalcause of animals, and all other parts and functions are in one way oranother instrumental towards this end. In fact, all the major soul facultiesand their objects (nutrition, sensation, and intellection) provide explanatorygrounds outside of the animal in the wider world, and in all three cases. Aristotle provides this connection with a theoretical basis in potentialityand actuality. So the material in the environment that animals ingest isgiven a functional description as a potentiality and is consistently calledfood (TpO~) (e.g., PA II.3 650a2-8). Only rarely does Aristotle describefood in independent per se terms. For example, in his discussion of beaks,the kind of food each bird eats provides an explanation for the shape of itsbeak. Crooked-taloned birds have hooked beaks because they feed on flesh;their beaks are useful for them to master their prey and for the exertionof force. Conversely, some birds have finely constructed beaks, becausethey pick up seeds and minute insects. Swimming birds have broad beaksbecause they dig for roots, and sometimes they have a sharp point at theend of the beak by means of which they may easily deal with herbaceousfoods (III.l 662a33-b16).There is one notorious case of environmentalism (PA IY.13 696b24-31):[In] the dolphin and the Solachia, [the mouth] is placed on the under surface [of thebody]; so that these fishes turn on the back in order to take their food. The purposeof nature in this was appar~ntly not merely to provide a means of salvation forother animals, by allowing them opportunity of escape . . . but also to prevent thesefishes from giving way too much to their gluttonous ravening after food.If we are to follow the strict criteria of APo, 'preserving other animals fromthem' must be per se related to dolphins and selachia and therefore part oftheir definitions. It is probably for this reason that Aristotle provides analternative internal explanation for their mode of eating, which he seems toconsider more likely, namely avoiding the dangers inherent in the naturalgluttony of sharks.

133 The Structure of FocalityThe extent to which Aristotle has restricted his use of external explanationsis dear through a brief comparison with some of the explanationsPlato provides in the Timaeus. Throughout the description of the structureand composition of man, we find theological and moral principles invoked:the head would have survived much longer if it were fleshy, but it wouldhave been less sensitive, and since it is better to live a short but good life,rather than a long but inferior one, the gods ordained the former (75b-c).The final cause of the liver is said to be the means for receiving propheticdreams (71d-72b). All other animals are food for humans (77a-c). Evengeometry provides principles: weaker triangles from which food is madeare overcome by the triangles of the body, which break them down for use(81c--

5Metaphysical FocalityOur study of the definitional inclusion criterion and Aristotle's examplesof health and medicine have led us to interpret focal science as structurallyidentical with normal science. We must now apply this interpretation to thescience of Being and consider whether metaphysics fits the model of normalscience. The importance of medicine and health as examples of sciences hasbeen largely ignored or denied. Most commentators have been content tofocus on the issue of homonymy and its logical form without consideringthe scientific implications of the examples' Owen, however, related focalityto the issue of the autonomy of sciences and argued that focality providedAristotle with the means to unify the science of Being, and thereby toestablish a qualified return to Platonic universalism.' Ferejohn has extendedthis observation and attempted to provide a sketch of what the focal scienceof Being would look like.' He confined his remarks to Met. r .2 and evenwithin that chapter dealt only with the relation between substance and thenon-substantial categories. But he made the important advance of treatingthe science of Being as a demonstrative science. He interpreted the scienceof substance as a superordinate science over the subordinate sciences ofnon-substances. The theorems to be proved in the subordinate scienceswere proofs of the existence of some of the objects in those sciences.On the grounds that science A is superordinate to science B if some of1 E.g., Owens 1978, 119; Ross 1924, i, 256. Kirwan 1993, 81, comments only on theinadequacy of the illustrations to vindicate the possibility of metaphysics. Burnyeat eta1. 1979, 25-8, do not mention these cases at all. Ferejohn 1980 and Bolton 1995 arenotable exceptions.2 Owen 1960, 1965. See Shields 1999, 225-36, for a criticism of Owen's position.3 Ferejohn 1980.

135 Metaphysical Focalitythe principles of science B are proved within science A, Ferejohn arguedthat the existence of quality can be proved from the principles proper tothe science of quality. One of the principles of the science of quality isthe statement that translates 'quality exists' into 'quality is predicated ofsubstance.' But that translation principle contains 'quality is predicated ofsubstance,' and Ferejohn claimed that if this statement is provable at all,it must be provable in a science whose genus is composed of substances,that is, in the superordinate science. 4Ferejohn made only modest claims for this attempt to relate focal Beingto the theory of science. He did not try to extend the interpretation to coverthe other focal relations mentioned even in r.2, nor did he deal with thediscussion of categorial focality that arises in the early chapters of Z. Butapart from the fact that Ferejohn did not provide a comprehensive theory,there are reasons for rejecting his suggestion that we should interpret therelation of substance and non-substance as a superordinate-subordinaterelationship. Although there are some hints in the text that point in thisdirection, Aristotle makes no mention of the paradigm case of superordinateand subordinate sciences, geometry and optics, in connection with thefocality of BeingS And yet we would expect him to call upon this examplerather than develop the new, or at least seldom used, example of medicinewhich makes no pretense of illustrating the superordinate-subordinate relationshipat all.There are philosophical objections as well. A superordinate science iscapable of being formulated in complete abstraction from the genus ofthe subordinate science. Geometry qua geometry has no per se relationsto optical rays. If it had, it would not be a superordinate and differentscience. If the science of substance qua substance were superordinate, thenwe would expect it to have no per se connections with the non-substance.But in fact this is not so. One of the essential functions of substance isto be a substrate, that of which other things are predicated but which isitself not predicated of anything else. In virtue of this nature, substance isper se related to predications of non-substance. Ferejohn admits this factfreely, indeed, it is necessaty for his argument that' quality is predicated ofsubstance' be proved within the science of substance. But it is impossible fora superordinate science to have such per se relations with the subordinatescience, and for this reason the superordinate-subordinate model must fail.4 Ibid., 126.5 Aristotle says that the focus is called a principle, and the other things are said onaccount of it (l003b5-6; lOO3b16-17); he also says that these parts of the science ofBeing may be arranged like universal and special mathematics (1004a6-9).

136 Aristotle's Theory of the Unity of ScienceYet Ferejohn has pointed the way towards interesting possibilities, sinceAristotle himself extends the promise that the science of Being will be ademonstrative science.' In this chapter I want to explore a group of relatedissues concerning the science of Being. This exploration is not intended tobe a systematic exposition of Aristotle's doctrine, because in many respectsAristotle allows us only the most tentative and sketchy conclusions. This isnowhere more true than at our starting point, Aristotle's avowed reasonsfor denying a genus of Being. In fact, I shall conclude rather reluctantlythat the reasons for his denial are relevant to the focal solution he proposesonly in the most general way. I shall then go on to consider focality in thecontext of the categories of Being, and finally broaden the discussion byconsidering the rather neglected focal relation between the One and Being.On all these issues the difficult and ambiguous texts require both c.autionand speculation.The Genus of BeingThe reason that focal analysis has to be applied to Being is that Beingdoes not form a genus. Under the conventional understanding, therefore,it cannot form a single subject-matter for a single science. Although Aristotlerepeatedly stresses that Being cannot form a genus, he usually treatsthis as an assumption, and argues the thesis only in one brief passagein the aporetic book B of the Metaphysics.' It would stand to reasonthat this argument should shed light on the focal science of Being thatAristotle introduces. However, the context of the passage iS ,an argumentagainst the Platonists, who hold that the highest genus is the highestprinciple. Since Aristotle merely needs to refute the Platonists, he need notintroduce a full-blown theory concerning the categories. Nevertheless, the6 Met. B.2 997a25-33: 'Further, does our investigation deal with substances alone or alsowith their attributes? I mean for instance, if the solid is a substance and so are lines andplanes, is it the business of the same science to know these and to know the attributesof each of these classes (the attributes which the mathematical sciences prove), or of adifferent science 7 If of the same, the science of substance also must be a demonstrativescience; but it is thought that there is no demonstration of the essence of things. Andif of another, what will be the science that investigates the attributes of substance?'7 There is a brief recapimlation of this argument at K.1 1059b31-34. For Being beingsaid in many ways: DA I.5 410a13, Met. E.2 1026a33, Z.l 1028a10, Z.4 l030bll, H.21042b25, 8.10 1051a34, 1.2 1054a14. Being falls immediately into genera: r.2 1004a5,1\.4 1070bl-2. For a recent treatment of this argument see Shields 1999, 247--60, whoargues against its relevance to the categories. His book was published too late for me totake proper account of his argument.

137 Metaphysical Focalityargument is important since it supports a position that Aristotle clearlyheld and without which there would be no need for a solution of anykind at all.Aristotle argues that there is no genus of Being because a genus termcannot be predicated of the differentia taken by itself apart from the species:But it is not possible that either unity or being should be a genus of things; for thedifferentiae of any genus must each of them both have being and be one, but it isnot possible for the genus to be predicated of the differentiae taken apart from thespecies (any more than for the species of the genus to be predicated of the properdifferentiae of the genus) (B.3 998b22-26)The argument consists of two premisses: no genus can be predicated of itsdifferentiae, and Being must be predicable of all differentiae. of course,from these premisses Aristotle is only permitted to conclude that Beingas a genus is not predicated of its differentiae. But since Being is such apredicate that it must be a generic term and express the essence of whateverit is predicated of, Being can only be predicated as a genus. For details ofthe reasons why a genus cannot be predicated of its differentiae, we mustturn to Topics VI.6 144a31-b3: 8Again see if the genus is predicated of the differentiae; for it seems that the genusis predicated, not of the differentia, but of the objects of which the differentia ispredicated. Animal (e.g.) is predicated of man and ox and other terrestrial animals,not of the differentia itself, which we predicate of the species. (a) For if animal isto be predicated of each of its differentiae, then many animals will be predicated ofthe species (Eioovs"); for the differentiae are predicated of the species. (b) Moreover,the differentiae will be all either species or individuals, if they are animals; forevery animal is either a species or an individual.In spite of the specific example Aristotle has chosen, this argument seemsto be of general application, and there does not appear to be anythingpreventing our applying it to Being. We may best begin with Aristotle's8 Ross 1924, i, 235, cites this passage as an explanation of the Metaphysics passage, andprovides the following interpretation: '(a) If Igenus were predicated of the differentia],the genus would be predicated of the species many times over, since it would bepredicated of each of the successive differentiae which constitute the species. (b) If"animal" is predicable of each of its differentiae, each of them will be either a speciesor an individual, since "an animal" always means one or the other.' There is no reasonto suppose with Ross that Aristotle has successive differentiae in mind. As in 2.12, theiteration of the predicate is not impossible, just redundant.

138 Aristotle's Theory of the Unity of Sciencesecond objection (b), which is clearer and more cogent. Like the Metaphysicspassage this argument depends on the presupposition that a genusterm by its very nature as a genus term can be predicated only of species,and whatever a genus is predicated of must for that reason be a species. Theclause 'if they are animals' (Er7fEp (0a 144b2), implies that the genus mustbe predicated as the what-is-it (TL fUTL) of the differentiae, and so if animalis the genus term predicated of the differentiae, then the differentiae mustbe species (or individuals) of animal. Since biped is obviously not a speciesof animal, the genus cannot be predicated of differentiae. This argumentprompts us to think of the genus as a pile of objects to be divided up. If thispile is to be divided by differentiae, the differentiae cannot be members ofthe pile, since the differentiae function quite differently from a species ofthe genus. And so if we place the differentiae in the genus, we would haveto include both the items in the pile and the criteria used to distinguishone sub-pile from another.The first objection is less obvious and less cogent, but it probablyinvolves the issue of babbling ("OO'\EOX"")' a dialectical misdemeanour(SE 3 165b12- 17) perpetrated when someone repeats himself (usuallyimplicitly) a number of times. Strictly speaking, babbling occurs in thecontext of relative terms (SE 13 173bl-11) and so is not properly applicableto this situation. Notwithstanding, Aristotle probably has in mind a lessvicious form of babbling, in which the same information is given twice,once explicitly through the genus of the species and once again implicitlythrough the genus of the differentia. If there are multiple differentiae forone species the genus will be given many times. 9 Now, Aristotle claimsthat both the differentia and the logos of the differentia are predicable ofthe species (Cat. 5 3a22-28). If that logos contains a genus term, then thegenus of the differentia will also be predicable of the species. So man, whois a biped animal, may have two genera predicated of him, animal andlegged, if legged is the genus of biped. Aristotle requires this conclusion inorder for the babbling charge to hold. And yet this same conclusion opensup the possibility of a genus being predicated of a species, but not as agenus of the species (legged is not the genus of man), and this seems to9 So Ross 1924, if 235. Alexander objects that these arguments are tOO dialectical(206.12-13) and provides a couple of counter-examples. First, if all differentiae arequalities (7Tot6v), then the differentiae of quality will be qualities, and so in the categoryof quality, the genus will in fact be predicated of the differentiae. Second, even if theimmediate genus is not predicated of the differentia of a substance as, for example,biped taken by itself is not animal, yet at a higher level biped is ollsill. Alexander's twoobjections arise out of the unclear categorial status of the differentia.

139 Metaphysical Focalityundermine Aristotle's argument against the genus of Being. For if we arenot saying the same univocal thing twice, then we cannot be babbling. Evenapart from this difficulty, babbling is at worst a venial sin, one that anyonetalking about the physical realm is bound to commit. The definitions ofsnub nose and all natural substances also entail babbling (Met. 2.5), butthis does not immediately exclude their being defined. They may still bedefined with a qualification.We face further problems when we apply the general argument of theTopics to the specific case of Being. According to Aristotle's objection (a),if we admit a genus of Being, we are forced to babble, since all definitionswill take the form, 'x is a Being differentiated by y whiCh is a Being.'According to objection (b), a species is a Being with a differentia, whichis itself a Being. This species, then, would be many Beings, whereas infact it is just one. Again, the predication of the genus is to be taken inthe strictest sense: the genus is always predicated of species and whenpredicated always creates species. Under this interpretation, a species likeman will not just be many Beings (which hardly seems problematic if weunderstand animal and biped as two Beings), but he will be many species.Since a man is essentially his differentiae, if his differentiae are species ofhis genus, he will be several species of the same genus, and the unity ofman will clearly be lost.This strict interpretation of the genus predication reveals further presuppositionsof the argument. It is not possible for one object to be twospecies, and the what-is-it question must have a unique answer for everywell-formed object. This presupposition becomes clear when the correctgenus is predicated of the differentia, for though the object will havetwo different genus terms predicated of it, if its differentia is part of thewhat-is-it of the species, it will not belong to two genera, since the genusof the differentia is not the genus of the species (e.g., man is legged, butlegged is not his genus). By contrast, when we attempt to predicate thegenus univocally of its differentiae, the differentiae become species of thegenus in the same sense as the species (e.g., man) themselves.Aristotle also presupposes that if the genus is predicated of a differentia,then that genus cannot create species that will stand alongside (i.e., becogeneric with) the species of which the differentia is predicated. This istantamount to saying that the genus and the differentia play different rolesin definition and classification. If we try to predicate a term like Being ofboth the species and the differentia, then we are assuming that, if Being isunivocal, it is being predicated in the same way, whereas in fact it is not.To be a genus, then, implies among other things that its species are of thesame logical and predicational type.

140 Aristotle's Theory of the Unity of ScienceIf we insist on a unified genus of Being, Aristotle argues, the individualand species will become many and lose their unity. We must thereforesacrifice unity at the highest level of generality in order to achieve unityat the lower levels. Genus and differentia will be different kinds of Being,but the species will be a single thing, a unity of genus and differentiaand not two species. Given Aristotle's prejudice towards the species andthe individual, this is a reasonable response. Uniry at the lower levelis maintained by distinguishing different kinds of predication. Plato, bychampioning the unity of the genus in the theory of the Forms, did notallow for the unity of the species or individual, and as a result a thingbecomes many by participation. All the forms exist equally and have acommon nature to the extent that they are forms, and each species fallsunder many kinds. Aristotle alludes to the Platonic origin of this problemin a different context, Metaphysics H.6 1045al4-17:What then is it that makes man one; and why is he one and not many, e.g.,animal and biped, especially if there are, as some say, animal itself and bipeditself> (modified ROT)There are a number of ways of interpreting the claim that Being is nota genus. Drawing on the class model, we may suppose that the differentia,since it is Being, will be a member of the pile of Beings; but since it isa differentia, it must be the criterion by which the piles are divided. Ifa differentia is a criterion, it cannot be a member, and so cannot haveBeing. Conversely, if it is a member, we shall need a new criterion bywhich to divide the pile. Nothing on this view prevents all existing thingsfrom forming a pile, but this pile cannot be divided and therefore cannotbe a genus. It must remain one pile, indeterminate and indeterminable,an inchoate unintelligible AIL Not only can it not be divided, but nothingpositive can be said of it at alL Certainly no predicate can be applied to it,since that predicate is Being, and therefore must be applied to all Beingsand itself. Since the predicate is a Being, we must still find somethingpredicable of all Beings, and so we must look for a further predicate, andso on to infinity, In this way the genus of Being falls victim' to a third-manargument.Again, Aristotle assumes as a premiss of his argument that all differentiaeare Beings and, as such, have Being predicated of them. 1O As a result,10 B.3 998b23-24; at Top. JV.6 128a26-29 they are nOta.

l41 Metaphysical FocalityBeing cannot be predicated of them as a genus. But as 1.2 l 053b20- 21says, Being is the most universal of predicates, and so Aristotle seems tobe canvassing the possibility that even if Being is not predicated as a genus,still it is a univocal universal predicate. But none of the other predicables -definition, property, or accident - seems to be a possibility. In saying thatdifferentiae are, what else are we saying than that Being is their genus /"Since Being is predicated of all Beings, but is neither a single genus norany other predicate, it follows that Being must predicated as more thanone genus: the Signification of Being must be different for the species andits differentia. Being, therefore, is not a general predicate.Even if Aristotle had something like this interpretation in mind, itnevertheless fails as a problem that the categories solve. His argumentmerely requires that differentiae and species not be in the same sense, asthe pile analogy makes clear. It does not require the ten categories as asolution. In fa ct, it does not require any of the canonical categories at all.How does he intend to bridge the gap / He does not explicitly provide anargument, but he may. have had something like the following in mind.There is no genus of Being, that is, of everything. But let us accept thatthere are some genera, if only, say, low-level genera, like animal, thatare divisible into species. Animals, then, form a genus in the heap ofBeing. Now we ask whether there is anything that prevents animal frombeing a member of a higher genus, living things. If nothing prevents, wemay proceed to form a higher genus and continue the procedure up to thehighest level possible, that of the categories. At this point we are preventedfrom going further. The categories are genera, but they are not species of11 According to Loux 1973, while Aristotle's argument that there is no genus of Beingis valid, it does not entail that Being is equivocal. He is not satisfied with Aristode'sindirect method of es tablishing that there is no genus of Being, and accordingly heprovides his own argument, which is predicated on his understanding of genus. ForLoux a genus is an answer to the what-is-it question. And for there to be such ananswer, 'there must be competing, incorrect answers,' that is, other genera (230). Agenus, therefore, must have a place in a classification system. Loux then goes on toargue that 'one can make sense of the claim that T-words [transcendental tenns likebeing and one] are ambiguous on ly if he grants implicitly that the claim is false' (236).For the categories are, according to Loux, a classification of things that are, and tospeak of 'things that are' is to assume an unambiguous sense of the term. Loux'sunderstanding of genus is mistaken. In fact, his description applies not to a genus, butto a speci es, which is what it is by being differentiated from another species. A genus isdetermined internally, without reference to differences from other thi ngs, as we havealready seen in the biological works. See Loux's retraction (1991, 27n29). For anotherview of the argument see Wein 1983.- ------ -------

142 Aristotle's Theory of the Unity of Scienceany further genus. 12 The determination that Being is ambiguous along thelines of the categories is the result of a closing in on these highest generafrom two sides. The first argument establishes that Being is not a genus,but rather a heap, and then since there are genera, there must be highestgenera, and these must constitute the ultimate groups or parts of the heap.But as Alexar:tder observes, the introduction of the categories createsmore problems than it solves B If all differentiae are ?TOt", as Aristotleclaims at Topics IV.6 128a26-29, then the genus of a quality will bepredicated of its differentia. And even if we defend Aristotle on the groundsthat he distinguishes ?TOt" as differentiae (a 'sort of' or determination ofa genus) from categorial quality, then 'we must still answer the questionabout the categorial status of the differentia. 14 If it is not to be placed inany category at all, then there will be no reason to worry that the genuswill be predicated of the differentia and there will be no argument againsta genus comprising the rest of categorial Being.Since this is the only argument Aristotle provides for his claim thatBeing does not form a genus, it is important to ask how it is related tothe solution Aristotle apparently developed for it, focality. The argumentagainst the genus of Being involves a fundmental distinction betweengenus and differentia, and the categories seem at best secondary in thisscheme. If we assume that genus and differentia are the principal kindsof Being, then we should expect these to enter into the focal relationship.On this interpretation genus would be ·the primary and differentiathe derivative Being, containing in itself the focal term, genus. This is aplausible interpretation of the relationship, since differentia is arguably aper se (2) predicate of genus. There is a focal solution that corresponds tothis problem, precisely that which solves the aporia quoted above in thepassage from H.6 1045al4-17. The genus animal is potentially man, andthe differentia biped is man in actualiry. They form a single thing justbecause they are focally and per se related to one another, as we shall seemore clearly in chapter 6. Genus and differentia, then, cannot be in thesame genus of Being, but they can be studied by the same focal science of12 So Met . 6.28 l 024b9-16: 'Those things are said to be other in kind (TeP )'fllH) whoseultimate substratum is different, and which are not analysed the one into the other norboth into the same thing ... and things which belong to different categories of being;for some of the things that are said to be signify essence, others a quality, others the. other categories we have before distinguished; these also are not analysed either intoone another or into some one thing:13 In Metaphysica, 206.13-22.14 Cf. Met. Ll.14, which distinguishes the senses of 7TOWV (differentiae from the ·attributesof natural bodies); K.12 l068b18-20.

143 Metaphysical FocalityBeing. All the same, this is not a solution that applies to the categories.Substance is primary, and categorial Being, not differentia, is derivative.In fact, since differentia is part of substance, it too will be primary, notderivative. 15 So clearly the problem of Being in Metaphysics B is not aproblem solved by the form of categorial focality we find in Z.Now, one might point to Met. H.2 and its assimilation of the differentiaeand Beings in non-substantial categories. If differentiae of substanceare predicated in all the non-substantial categories, then the argument maypoint the direction towards the genera of the categories. However, nothingprevents OUf substituting accident into the argument in place of differentiaand arriving at the same conclusion. If the genus of man is predicated ofhis accidents, in the same man Being will be predicated many times. overand there will be many Beings. But accidents clearly are, and thereforeBeing must be of a different kind in the case of accident and what theaccident is predicated of. This version of the argument seems as valid asthe differentia form, and moreover, it will come closer to generating thecanonical categories. At least it fits the description of the categories wefind at Topics I.9. For there the ti esti corresponds to genus, and the othercategories are in the first instance non-ti esti predications, that is, accidents.So the accident version of the argument rather than the differentia versionis more suitable to the generation of the categories. It also avoids someof Alexander's criticisms, since a thing and its accident are not in thesame category. Aristotle did not make use of this version presumablybecause the context of the B passage is an argument against the Platonists,and he does not require the theory of the categories for his immediatepurposes.Nevertheless, the argument of B.3 suggests that Aristotle's basic objectionto a genus of Bein& whether that objection is described in terms ofdifferentia and genus or in some other way, consists in his observation thatdifferent Beings have different logical functions, and that discourse itselfdepends on the difference in these functions. To treat all things as speciesof a genus will destroy discourse as surely as the sophists destroy discourseby replacing all essence with accident. If this is the fundamental insight, itis one that focality can address. For focality is precisely intended to providewithin a single study a treatment of items that are functionally related toone another without being species of a genus. It is ideally situated to dealwith the problem of the unity of genus and differentia just because itsobjects are relatives rather than congeners.15 On this interpretation we shall face the problem that once again the same genus wlll bepredicated of both species and differentia; Top. VI.6 143a29-32; Met. Z.12 1038aI8- 21.

144 Aristotle's Theory of the Unity of ScienceCategorial Focality in Metaphysics ZWhatever the deficiencies of Aristotle's arguments against the genus ofBeing, it is clear that he held that position, conceived of the problemprimarily in terms of categories, and sought to solve it by means of focality.I shall argue that Aristotle lays out a focal science of Being that matchesthe pattern described in the previous chapter. This science consists of twoclosely related parts, corresponding to the focus term, namely substance,and the derivative terms, namely the non-substantial categories, One, potentiality,and so on. As we have seen, this conception corresponds to themodel of health and ordinary science generally. The core science studiessubstance and its functions, being a substrate and essence. But just as healthdoes not exist without a body or an animal without activities, so substancedoes not exist without non-substance. Indeed, the most characteristic featureof substance, its being a substrate, requires that it be a substratefor something. As such, substance in its designation as substrate cannotbe completely abstracted from that of which it is the substrate. In thisway the core notion of substrate points to the more expansive science ofBeing, a science that includes non-substance. In addition to being substrate,substance is also essence, and in a similar manner substantial essence willnecessarily imply non-substantial essence. For example, in the study ofnose (which is a substance or part of a substance) we must consider snub(presumably, a quality), and in the study of animal, we must consider maleand female (an affection). Again, this view is in accordance with the modelof health: we can hardly have grasped much of the essence of the focushealth, if we do not know that it is the body that has health, or much ofmedicine, if we do not know that it aims at the medical goal health 1 6 I aimto show, then, that by taking seriously Aristotle's models of focality wecan construct a coherent interpretation of categorial focality and maintainthat in its broad outlines metaphysics is a normal science.But first a couple of preliminary issues and observations. The claimthat the focus implies the derivative or network terms seems to be indirect contradiction with the statement that the focus does not containthe derivative objects in its definition (EE VII.2 1236a21- 22). But, simplereflection on the cases involved shows that the situation cannot be sostraightforward. Some of the focally derivative items, as we have already16 It is clear that the two examples of focality, medicine and health, are themselves focallyrelated, presumably with health as the core, since medicine contains health in itsdefinition, but not vice versa. This fact serves as a further indication that derivativetenns can form semi-abstract subject matters on their own. Cf. EE VII.15 1249b9-13.

145 Metaphysical Focalitynoted, must be present in the definition of the focus. So, for example, thegoal (,pyov r.2 l003b3) of medicine is essential to the art of medicine,if anything is. Others, while not specifically mentioned in the definitionof the focus, must be implied in some way. For example, intelligent anddextrous people are medically talented «VCPUE, 7fPO, aVT~v l003b2-3). Butthough being talented is not present in the definition of the medical art,talent is certainly implied through necessary connections: an art necessarilyhas practitioners, who necessarily are more or less talented. In this waya derivative term need not be related to a core term by direct definitionalinclusion in order to be implied in the network. Likewise, substance in itsrole as substrate does not contain in its definition quality, quantity, andso on, but rather it implies a predicate being predicated of it, and thatpredicate necessarily must be either a quality or a quantity and so on.This may seem rather pat, but in fact, definitional inclusion is oftenmade to fit demonstrative convenience. Indeed, the focal criterion oftenmeans little more than that the focus is the subject of the science andthe derivative terms are useful and adapted to it. For this reason, onescience's focus is another science's derivative, as Aristotle's own examplesmake clear. So, for example, the art of medicine is the focus for operation,patient, and knife, because the art is contained in their definitions. But theart of medicine can also be called healthy, and serve as a derivative term inthe genus of health. Moreover, the connections among terms can becomemultilateral without ever being confused. We may call medicine human fortwo quite different reasons and include it in two quite different sciences.Since health is a state of the human body, it can be called human andbe included in the genus of the substance man. For this reason, medicine,too, can be human, in virtue of the transitivity of focal relations throughhealth. But in addition, medicine, since it is a cognitive state of the humansoul, can be called rational, and so be focally dependent on human in adifferent way. For all the versatility of these focal relationships, there isnever any reason to confuse them, and it is always clear why medicine,insofar as it heals our bodies, should be treated by a different science fromthat which considers it as a cognitive state ·of the soul.The focal science of categorial Being is constructed on an ambiguity inthe treatment of the non-substantial items, which arises as a result of theirbeing considered both strictly as predicates of substance as well as in theirown right. From the first perspective, they serve solely as non-essential,sometimes accidental, predicates of substance (e.g., man is white); but as perse Beings they themselves are treated as subjects of further predication, andthis predication is essential (e.g., white is the measure of colour). These twoperspectives give rise respectively to the core science of Being (substance)

146 Aristotle's Theory of the Unity of Scienceand the extended science that includes the other categories. This ambiguitymakes it necessary to consider the nature of the categories, especially thenon-substantial categories. Unfortunately, Aristotle's statements on thisissue are almost perversely obscure. In various contexts and with confusingexamples he conceives of the non-substantial items as accidents ofsubstances, as per se predicates of substances, and as objects that haveessences predicated of them. 17Nevertheless, there is clear evidence, even before the Metaphysics, thatthe non-substantial categories are treated both as accidents and as per seBeings. 18 Topics 1.9 provides the clearest account of how the two views arerelated and provides much of the framework for the focal science of Beingthat emerges in the Metaphysics:Next then we must distinguish between the categories of predication in which thefour above-mentioned [predicables] are found. These are ten in number: What athing is (ri €OTt), Quantity, Quality, Relation, Place, Time, Position, State, Activity,Passivity. For the accident and genus and property and definition of anything will17 A less serious difficulty concerns what is being focalized in metaphysics. Are categorialitems, like quality, being made focally dependent on substance, or are more specificgenera within each non-substance category, like snub and odd, made focally dependenton specific genera of substance? Aristotle's statements and examples point towards boththe categorial and the generic interpretation of metaphysical focality. But inasmuchas Aristotle is outlining a science of Being qua Being, his concern cannot be with thegenera that constitute the subject matters of the special sciences. When the science ofBeing is focused narrowly on substance, the non-substances are predicated of substanceand no distinction is made as to whether they are per se or accidental; they are not partof the what-is-it of the subject under consideration (substance) and, therefore, theiressence is irrelevant. They are merely properties or accidents of substance. However,these same Beings can be semi-abstracted and treated as per SI! subjects. As such theyhave essences (in a qualified way). This distinction holds whether we consider substanceand quality, etc., as categories or whether we consider particular kinds of substance andquality, like nose and snub.18 In the Cafegories the non-substantial categories are often treated as subjects withessences in their own right. Chapters 5-8 form an incomplete study of the natureof each category, starting with substance. We learn the basic sub-classes of eachcategory (for quantity [chap. 6], e.g., that some are continuous, other discrete), andtheir properties (e.g., quantity does not admit of opposites or more and less; that theyare equal or unequal). In this incomplete survey the categories are considered not aspredicates of substance but as subjects, i.e., they are the kinds of things that exist,rather than the way substance is qualified, quantified, etc. At the same time, the essenceof non-substance seems to be rather limited. For example, among the non-substantialcategories there is no mention of species, genus, or differentia in the appropriate senses.The genus-species relationship in the Categories seems restricted to substance (Fredeand Patzig 1988, 66).

147 Metaphysical Focalityalways be in one of these predications; for all the propositions found through thesesignify either what something is or its quality or quantity or some one of the othertypes of predicate. It is clear, too, from them (€~ avrwv) that the man who signifieswhat something is signifies sometimes a substance, sometimes a quality, sometimessome one of the other types of predicate. For when a man is set before him and hesays that what is set there is a man or an animal, he states what it is and signifiesa substance; but when a white colour is set before him and he says that what is setthere is white or is a colour, he states what it is and signifies a quality. Likewise,also, if a magnitude of a cubit be set before him and he says that what is set thereis a cubit or a magnitude, he will be describing what it is and signifying a quantity.Likewise, also, in the other cases; for each of these kinds of predicate, if either itbe asserted of itself, or its genus be asserted of it, signifies what something is; if,on the other hand, one kind of predicate is asserted of another kind, it does notsignify what something is, but a quantity or a quality or one of the other kinds ofpredicate. (Topics 1.9 l03b2Q.-39; modified ROT)In this passage Aristotle first enumerates the categories, commentingbriefly on their relation to the four predicables (definition, property, genus,and accident) and their place in propositions before drawing a further conclusionfrom them (ft aiiTwv). In the first step of this argument, Aristotlethinks of the T{ €(J'n predication primarily as substance and the non-T{fun predications as accidents (necessary or not). Once this scheme is laiddown (it aUTwv), Ti fO"TL can secondarily apply to the other categoriesas well. 19 This two-step procedure shows how the same non-substantialpredicate can be treated both as an accidental predicate of substance andas a subject admitting of essential predication. It suggests that though onestep comes before the other, non-substance can be treated in both ways,and that they need not be confused. One item may be predicated as qualityonly or as what-is-it and quality, depending on whether it is property oraccident on the one hand or a genus or definition on the other. It is animportant consequence of this scheme that when a quality is predicated asa quality alone, it may be predicated either as a property or as an accident,and the categorial scheme does not distinguish between the two forms ofpredication. 2o19 Though the categories play only a very minor role in the Topics, Aristotle is verygenerous in providing definitions of non-substances and treats them as uncontroversial.It is clear that his treatment of non-substance as essential is not confined to I.9.20 See Frede 1987a and Malcolm 1981 for promising attempts to provide an essentialistreading for Topics 1.9. I do not, of course, follow Frede in his contention that substanceis not a category in the Topics.

148 Aristotle's Theory of the Unity of ScienceMetaphysics Z provides a more searching investigation of the relationshipbetween the categories and the centrality of substance in thatrelationship. Focality among the categories of Being is featured in threeearly chapters (1, 4, and 5), and in each chapter non-substantial Beingis per se. 21 Aristotle discusses the problem of categorial Being before heever comes to a definite conclusion regarding the nature of substanceitself, and so it is clear that the question of the focality of categorialBeing can be satisfactorily addressed without entering into a discussionof form and matter. Z.l, as we shall see, considers Being as per se (3),a self-subsistent subject of predication in its own right. Aristotle asks towhat extent non-substances have this 'sort of per se Being. Both Z.4 and5 consider Being as essence, which is predicated as a per se (1) predicate,that is, what can be predicated essentially of something. Substance hasessence primarily and -the non-substance categories have it by an addition(7Tpo(J'8w'''). Z.5 also takes up per se (2) Being, in which categorial Beingis treated as belonging to its primary recipient.Z.l begins with a recapitulation of the ambiguity of Being:There are several senses in which a thing may be said to be, as we pointed outpreviously in our book on the various senses of words; for in one sense it meanswhat a thing is or a 'this' (Ti fern Kal T(}OE TL), and in another sense it means thata thing is of a certain quality or quantity or has some such predicate asserted of it.While 'being' has all these senses, obviously that which is primarily is the 'what,'(r{ EUTL) which indicates the substance of the thing. (Met. Z.1 l028a10-15)21 Mctaphysics 11.7 also seems to provide a per se analysis of the non-substantialcategories. It enumerates and describes four of the major senses of av, accidental, persc, true I false, actual! potential:Those things are said in their own right (per se) to be that are indicated by the figuresof predication; for the senses of 'being' are just as many as these figures. Since somepredicates (rwv KanrYOpOVjJ.EVWV) indicate what the subject is, others its quality, othersquantity, others relation, others activity or passivity, others its place, others its time,'being' has a meaning answering to each of these. For there is no difference between'the man is recovering' and 'the man recovers', nor between 'the man is walking' or'cutting' and 'the man walks' or 'cuts'; and Similarly in all other cases. (11.71017a22-30)But there are many features that suggest the predicational approach. The emphasis in thepassage is on predication, as indicated by the partitive genitive (rwv KarllyopoVjJ.EVWV),which introduces the enumeration of the kinds of predication. Furthermore, theexamples cited at the end of the passage, man recovers, man walks, man cuts, allseem to be accidental rather than pcr se predicates. See Ross 1924, i, 307-8. Met. B.2996b14-22 makes th"e same distinction that the Topics makes.

149 Metaphysical FocalityThis passage commences with an allusion to t..7, and because Aristotlehad joined the issue of categorial Being with per se Being in t..7, it isreasonable to suppose that the discussion in Z.l will likewise be centredon per se categorial Being.We notice that the first category has changed, and in place of the simplewhat-is-it (rt €a-n) that we saw in the Topics we find rL tOIL Kat roo€ n .This does not, however, prevent the what-is-it from being applied to nonsubstanceslater in the chapter (1028bl-2) and again at Z.4 (1030a17-23).It merely implies, as in the Topics, that the what-is-it is applied first andforemost to substance. The this (ToIiE Tt) is the subject of predications, andit itself is not predicated of anything else. Because of the identificationof the what-is-it with the this, subjecthood and essence belong primarilyto substance. Now, there has never been a doubt that substance serves assubject, but the question becomes whether non-substances can also serveas subjects. This question is addressed in a passage starting Z.11028a20:And 50 one might raise the question whether 'to walk' and 'to be healthy' and'to sit' signify in each case something that is, and similarly in any other caseof this sort; for none of them is either self-subsistent (Kat)' aim)) or capable ofbeing separated from substance, but rather, if anything, it is that which walks or isseated or is healthy that is an existent thing. Now these are seen to be more realbecause there is something definite which underlies them; and this is the substanceor individual, which is implied in such a predicate; for 'good' or 'sitting' are notused without this. Clearly then it is in virtue of this category that each of theothers is. Therefore that which is primarily and is simply (not is something) mustbe substance. (1028a20-31)The distinction in this aporia between that which walks (TO /3alii(ov) andto walk (f3a/ii(ELv) lies in the fact that the latter is not per se (3) (i.e.,self-subsistent) or capable of being separated from substance. By contrast,there is something underlying that which walks, and therefore it involvessomething self-subsistent. It is clear, then, that the sense of per se used inthis passage does not refer to a per se predicate, but rather to per se Being,and it is described by the same example of walking that we find at APo1.4.22 It is Aristotle's point in Z.l that although 'that which walks' is nota per se Being, it is more like one than 'to walk' is. While such a Being22 'What is not said of some other underlying subject - as what is walking is somethingdifferent walking (and white), while a substance, and whatever signifies some "this"(T(~bE n) is just what it is without being something else.' (73b6-8).

150 Aristotle's Theory of the Unity of Scienceis explicitly called accidental in APo (73b9-10) and Z.5 (1030b20- 21), it isgranted in Z .I, rather paradoxically, a dependent per se status. By contrast,'to walk' has no per se (3) Being, because it does not have a substrate. Sinceper se (3) Being is the Being of the individual subject (TO KaB' EKarrTOV,1028a27), non-substantial Being of the 'to walk' kind seems to have per se(3) Being least of all, since it is a subject least of all. That which walks' atleast implies in itself a subject of the appropriate kind, and identifies sucha subject, even if accidentally.In Z.1 Aristotle recognizes the possibility that entities like 'that whichwalks' may have a qualified per se (3) Being. The innovation in this chapterlies in the introduction of focality and the language of causal and definitionalpriority of substance over the other categories to describe how thisis possible:23And all other things are said to be because they are, some of them, quantities ofthat which is in this primary sense, others qualities of it, others affections of it,and others some other determination of it. (1028a18- 20)And in formula also {substance} is primary; for in the formula of each term theformula of its substance must he present. (1028a3S- 36)24Derivative Beings are said to be in a very qualified and attenuated sense.Only because the subject is implied in predications of the kind 'that whichwalks,' do such things have per se existence. Since the non-substancecontributes nothing per se in itself, substance in such compounds is theonly Being in this sense. It is only because such tags as 'that which walks'pick out individual substantial subjects that 'that which walks' qualifiesas per se (3) Being. In this case focality provides a redescription of thenatural and ontological dependence of non-substance on substance. 25 Infact, Aristotle draws this conclusion at 1028a29-30 when he says that it is23 It has long been noted that the paronymy relationship of Cat. 1 1a12-1S is a precursorto the focal relationship. It differs from focality, however, in that.it makes thenon-substantial category the focus, rather than the substance (the grammatical containsgrammar in its definition). Moreover, paronymy, for all its similarity with focality,simply is not invoked as a means of scientific unification. See Owen 1960 and Patzig1961.24 Cf. the recapitulation at 0.1 1045b27-32: 'We have treated of that which is primarilyand to which all the other categories of being are referred - i.e., of substance. For itis in virtue of the formula of substance that the others are said to be - quantity andquality and the like; for all will be found to contain the formula of substance.'25 So Ferejohn 1980, 122-3.

151 Metaphysical Focalityon account of substance that each of the non-substances is. He clearly doesnot mean to say that the non-substances make no contribution in any wayto the compound, but only that they do not contribute to its per se (3)Being, its subjecthood, and without subjecthood there is no Being at all.What precisely is the focal connection between predicate and subject?How is substance implied in the definition of its predicate in these cases?This question is of the first importance because the answer tells us howAristotle intends the science of categorial Being to form a unity. It is clearfrom the examples that that which walks implies substance as a category,and does not imply something specifically adapted to the predicate, likelegged animals. Aristotle makes no use of examples like the snub to suggestthat the subject must be per se related to the predicate in a speCificallyadapted way. More importantly, accidents no less than essential featuresand properties require a subject. 26 The non-substantial categories, as wesaw, frequently pick out accidents predicated of a subject, and their chieffunction is to identify features that are not the what-is-it of the subject. 27Since being a subject is the roo£ n function of substance, and the T()OE n isan individual subject, the focus term is not conceived of as an essence. Theupshot is that, even though substance must be included in non-substancein order for non-substance to be a subject, the essence of some specificsubstance need not be included. For example, the essence of nose need notbe included in snub in order for 'the snub' to be a subject. Likewise, for 'thatwhich walks' to be a subject is for walking to be predicated even accidentallyof a substance in its subject function. More than any of the others in Z,this form of dependence seems to be a recapitulation of the natural priorityof the Categories, and in fact Aristotle uses some of the same tags. 28In Z.4 Aristotle turns from the self-subsistent to a discussion of substanceas essence (ro rl ryv ELVat). Here too the notion of essence involveswhat is per se. However, the sense of per se is not that of per se (3) Being,but what is predicated per se (5 A'YETat Kae' auro 1029b14). It is clear,26 The fact that the subject is 70 Ka8' (KarrrOV (1028a27) does not have any Significanteffect on the nature of the definitional inclusion. Both the categorial and the genericrelationship can be expressed individually (white is predicated of this/these individualsubstance[s]; white is predicated of this/these individual surfacers]) or universally(white is predicated of substance; white is predicated of surface). .27 It may be objected that Aristotle's fonnulations 'the healthy,' 'the sitting' do notinvoke accidental relations. However, they are part of an aporia that explicitly (ota1028a20) grows out of the categorial distinction that dearly treats non-substantial itemsas accidents.28 For example, that 'good' or 'Sitting' are not said without substance (1028a28-29); d.Cat. 5 2a34--b5.

152 Aristotle's Theory of the Unity of Scienceor at least assumed for the time being, that essence belongs primarily tosubstance. In Z.4 Aristotle considers whether essence can be extended tothe same sort of entities that were treated in Z.l, compounds of substanceand accident.The central problem of this chapter concerns white man, an obviouslyaccidental compound, and Aristotle explicitly asks whether there is a logosof the essence of such compounds (1029b22-27). The mention of the accidentalat 1030a14 further indicates that accidents are the subject of thischapter. However, the focal solution beginning 1030a17, if it is a solution,makes no mention of white man, and instead argues that there is someway in which non-substances, like the qualified (TO ?TOL6v) can be defined.The difference between the two formulations can be exaggerated, however,and I think that white man and the white can be treated as much thesame for the purposes of extending essence to non-substantial categories. 29In spite of the fact that the chapter concludes with a statement that theproblem has been resolved and that accidental compounds, like white man,have definitions, but in a different way from that which is white, thedifference between the two is clear and not very significant. For in bothcases the essence will have to embrace an accidental compound that includessubstance. The difference between the two is that, in the case of the white,the substance will remain unspecified, whereas in the case of white man,the essence of man will be included in the definition of the compound.1029b22 introduces the major problem of the chapter, whether there isan account of the essence of compounds of substances and non-substances(O'VVeETa), like white man, which Aristotle then denominates 'mantle,:30But after all, 'definition,' like 'what a thing is,' has several meanings; 'what athing is' in one sense means substance and a 'this,' in another one or other of thepredicates, quantity, quality, and the like. For as 'is' is predicable of all things, nothowever in the same sense, but of one sort of thing primarily and of others ina secondary way, so too the 'what' belongs simply to substance, but in a limitedsense to the other categories. For even of a quality we might ask what it is, so thata quality also is a 'what: - not simply, however, but just as, in the case of thatwhich is not, some say, in the abstract, that that which is not is - not is simply,but is non-existent. So too with a quality. (Met. Z.4 1030a17-27)29 So Frede and Patzig 1988, 64-5.30 There does not seem to be any necessity to rename this object, but Aristotle doesso perhaps to indicate that many of our words, including mantle itself in its normaldesignation, denote accidental compounds just like white man, and that if white mandoes not admit of definition, many other objects that are commonly named also willnot.

153 Metaphysical FocalityAlluding to Top. 1.9 and Met. Z.l 1028bl-2, Aristotle says that the nonsubstantialcategories also admit of the what-is-it. But within this passagehe does not explain how they do, nor does he invoke definitional inclusion,except in the cryptic remark about the non-existent. For the dear use offocality we must look to the immediately following passage:[EJssence will belong. just as the 'what' does, primarily and in the simple sense tosubstance, and in a secondary way to the other categories also, - not essence simply,but the"essence of a quality or of a quantity. For it must be either homonymouslythat we say these are, or by making qualifications and abstractions (TrpOunf3EvTosKat acpa.~pofjvTas) (in the way in which that which is not known may be said to beknown), - the truth being that we use the word neither homonymously nor in thesame sense, but just as we apply the word 'medical' when there is a reference toone and the same thing. not meaning one and the same thing, nor yet speakinghomonymously; for a patient and an operation and an instrument are called medicalneither homonymously nor in virtue of one thing. but with reference to one thing.(Met. Z .4 l030a29-b3)Essence can be extended to white man and the white in much the same way.White man and the white will have essences because in their definitionswill be found respectively man (or its definition) and substance (or itsdefinition). The inclusion of non-substance in the science of essence isbased on the same inclusion of substance in a quality and quantity as wesaw in Z.l. Such inclusions extend to accidental relationships and are notrestricted to per se relationships such as that between female and animalor snub and nose. It is because a quality, whether it is an accident ornot, must be predicated of a substance, that its definition and essence willcontain substance.Aristotle seems also to express the focal relation in terms of additionand abstraction, and it is probable that he had in mind the same logicaloperations we have discussed in the first chapter. For in both cases whatis abstracted is part of the essential nature of some more concrete entity.Now, it is easy to see how we can get -rrpo,; fV definitions by addition: wesimply add the definition of the primary entiry in the proper logical relationto the other elements of the derivative's definition. But it is more difficultto see how abstraction works, and there has been some dispute. 31 In view31 Ross 1924, ii, 171, reports Ps.-Alexander's view, hut disagrees and offers 'If we saythat they [non-substances} are OUTa we add a qualificati on to, and deduct from the fullmeaning of, Oll.' (Owens 1978, 350, agrees.) Bumyeat et al. (1979, 27-9) considered thisquestion twice. They are unhappy with Ross's suggestion because it means that differenttypes of things are being added and subtracted. If linguistic items are subtracted, then

154 Aristotle's Theory of the Unity of Scie"ceof the similarity with DC III.1 299a13-17, which says that mathematicalsare said it aa

155 Metaphysical Focalitypredications like white being predicated of Callias or man with a description(1030b18-24) that matches the one at APo 1.4. He further distinguishes thetwo kinds of predication by stating (1030b25-26) that white can be madeclear without man, whereas snub cannot be made clear without nose.However, Aristotle seems to assimilate these per se (2) cases to categorialpredications in a claim at 1031al-3 that there is definition of substanceonly, 'for if the other categories are definable (El yap Kat TWV aA.A.WVKaTT/yopLWV), it must be by an addition, e.g. the odd, for it cannot bedefined apart from number.' He does not explain just how such predicateswill be definable, if indeed they are definable, though he does remarkthat they will be defined in the same sort of way as other predicatednon-substances (1031a7-11). Snub and odd are clearly considered to bein categories different from substances, but it is equally clear that theyare related to their subjects in quite a different way from the way whiteis related to man, which was the case examined in Z.l and 4. For thesecontain specific kinds of substrates in their definitions: snub contains nose,odd contains number. The focality here depends on the essence functionof substance rather than the subject function.The significance of these kinds of predicates lies in the different mannerin which they and the predicates of Z.1 and 4 are focalized. We have tracedthrough the Topics and Metaphysics what amount to two subject mattersinvolved in the science of categorial Being. These manifest different per seand accidental relations. The first and central subject matter is substance.Concerning substance Aristotle's basic distinction is between the what-is-itand the other predications. The non-substantial items may be predicatedeither as property or as accident, and there is no distinction drawn betweenthese two modes. Because at this stage they are not answers tothe what-is-it question and because they are predicates, not subjects, thenon-substantial items are not part of the core science of Being except bynegative inclusion. That is, just as the not-known can be said to be known,so non-substance is Being because it does not fulfil the functions of Being. 3333 In order for there to be a science, its terms must be essentially related. "For this reason,the science of Being too must treat essence, and cannOt treat accidental cases. This iswhy Aristotle rejects a science of accident in E.2. But accidents may be included in thescience of Being through the rule of negative inclusion, which Aristotle describes as theinclusion of that which is not, because it is not. Accident is included in the science ofBeing, because science concerns that which is per se related, and accident is not per serelated, it is the opposite of being per se related. Accident is whatever occurs neitheralways nor for the most part (1026b27-33). For this reason he speaks approvingly ofPlato's identification of non.being with the accidental (E.2 l026bl4-21). This methodallows for the inclusion of accident as such, and gains further support from the text at

156 Aristotle's Theory of the Unity of ScienceIt provides the limits of the study of Being, and helps us make sense ofthe distinction between subject and non-subject, essence and non-essence.But non-substantial items can also be treated in another way. Theymay be treated in their per se nature both as subjects and as essences.Aristotle's thoughts on this issue are far from clear, and many factorsare involved that are not altogether consonant. Z.1 suggests hownon-substances may have subjecthood. This form of subjecthood is opento accidental as well as necessary attributes. Accidents are included nowin the wider focal science, not merely by negative inclusion, but in virtueof the fact that their accounts include substance as subject. Essence too isextended from substance to non-substance, but this extension takes twoforms. Z.4 treats the essence that corresponds precisely to non-substantialsubjecthood, a form of essence that can cover accidents. And within thisrype of essence there appear to be two further sub-types, the fully specifiedaccidental compound, like white man, and the unspecified accidentalcompound, the white. Such compounds have essences because the essenceof substance or the essence of a specific substance is included in theirdefinitions.The second main form of non-substantial essence is the special concernof Z.5. Snub is predicated of nose, male and female are predicated ofanimaL These predications are not and cannot be accidentaL By contrast,white is an accident of man, and there are no focal relations betweenwhite qua white and man qua man. Not only are the predications ofthe snub type not accidental, the per se relations are more varied anddo not adhere strictly to the substance/non-substance relations of thecategorial level. A non-substantial item does not have to be immediatelypredicated of a substance. Although it is true that nose and animal aresubstances or parts of substances, other substrates that Aristotle mentionsare not substantial. So, odd is predicated per se of number, but numberis not substance (Z.5 1031a2-5). White is predicated per se of surface,but surface is not substance. Now this peculiarity is problematic, becauseAristotle does connect the odd-number predication closely with the categorialpredication. It is supposed to serve as an example that there isdefinition only of substance, and that of the rest of the categories thereis definition only by addition. In fact, this difficulty is only apparent.Such items will still have essence and belong in the science of Being invirtue of a mediated focal relationship to substance. Odd, for example,2 .4 l030a23-27. This interpretation could account unproblematically for the example ofwhite man, a genuine accidental compound with no per se connections between whiteand man. It is considered by the science as that which is not a per se thing.

157 Metaphysical Focalityis predicated per se of number, which in turn is predicated per se ofsubstance. 34 Aristotle recognizes such mediated relationships in r.2, wherehe includes in the science of Being things that are destructions and privationsand qualities both of substance and 'of things which are relative tosubstance' (1003b8-9).Nevertheless, the fact remains that the logic of odd and snub is differentfrom that of accidents, and their importance for the science of Being isindisputable. For the definition and existence of such objects form the firstprinciples of demonstrative sciences (APo 1.10), and metaphysics in someway provides these first principles (r.l). If Aristotle cannot account forthe Being of such entities, then his theory of science is in grave peril.For such predications are the bulwark of the special sciences. We need,therefore, some account of the essence of objects that are not substancesand whose Being is not merely to be accidentally predicated of substance(as white man or the white is). In fact, the very model of focal scienceitself, health, is in danger of lacking an essence for exactly this reason,Health is a state of a living body, not a substance itself, and yet Aristotlet~eats it as the focus of its genus, upon which other objects are dependent.In order for it to do its work as the subject of a science, its Being andessence cannot be merely an accident of some substance, since accident isnot the subject of any science. It is for this reason that the coupled termsare so important. For whereas the Being of accidents and its correspondingscience is questionable at best, the Being of necessary attributes (per 5e (2))dearly comes under the purview of the science of Being (for this sciencestudies Being qua Being and its per se attributes 1003a21- 22), and if Beingmeans in the first instance substance, such per se (2) attributes of substanceare also a part of the science.The focal science of Being, then, consists of two parts. The first is thecore study of substance. The science of Being is the science of substance(Z.l 1028b2-4), because substance is the focal term to which all otherterms of the science are related. Of substance in general, some thingscan be said and perhaps even proved, for instance, that it is species formor individual form; that some substance is enmattered, and therefore issensible; that because substance is a subject, it has attributes, both necessaryand accidental. These and similar propositions and proofs constitute thecore science of substance. 35In addition, the derivative items may themselves act as parts of a morediffuse focal science and may be treated in different sections of that science.34 So Loux 1991, 84.35 See Bolton 1995 for an attempt to flesh out some aspectS of this core science.

158 Aristotle's Theory of the Unity of ScienceQuality qua quality can be semi-abstracted and studied as a per se entity."As such it is similar or dissimilar to other qualities; it has potentiality,actuality, unity, plurality, substrate, and so on. It is in virtue of thissemi-abstraction that all the generic qualities and non-substantial items,like snub, odd, and health can serve as subjects with essences in theirown right. Aristotle alludes to this in a passage concerning the nature ofmathematicals at M.3 1078a5-8:Many properties attach to things in virtue of their own nature as possessed ofsome such property; e.g. there are attributes peculiar to the animal qua female orqua male, yet there is no female nor male separate from animals.Aristotle here exaggerates the conceptual separability of female and male,but it is clear nevertheless that he recognizes some way in which maleand female can be provided with a qualified essence, and be a subject ofstudy in their own right. It is important also to note that though femalecannot be separated from animal, it is not coextensive with animal or anykind of animal. As a result there are properties that can only be treatedas belonging to female and not as belonging to animal in general. Theclear implication is that subjects within the wider focal science will haveextensions different from that of the core science, and yet this will notcompromise the unity of the science.Demonstration in the Science of BeingWe can now hazard some suggestions as to the demonstrative structureof the science of categorial Being. But first some caveats. There is littleevidence of a richly developed demonstrative science here. 37 Thoughdemonstrations are common in the PA, they are very· rare in the M etaphysics,in spite of the fact that in his discussion of the aporiai Aristotleseems to consider the science of substance demonstrative. 38 The obvious36 At APo H.l3 96a34-37 and 96b5--6 Aristotle extends the tenn ovrrla to the definition oftriad (which is dearly not a substance).37 The degree to which metaphysics is amenable to demonstrative analysis continues tobe debated. See Bolton's (1994) arguments against Code concerning demonstrativemetaphysics in r and Bolton 1995 for a different view on Z.38 B.2 997a25-32: if the .science of substance concerned both substance and its per seaccidents, then the science will be demonstrative, since the per se accidents will beproved from the essence and definitions of substance. Bolton (1995) discusses thispassage in his model of metaphysics as a demonstrative science. He argues that Met. Zis laid out according to the canons of APo II, and in a manner familiar from PA. i.e.,

159 Metaphysical Focalityreason for this difference is that metaphysics is the science of principles(A.1 982al-3), and to this extent the focal science of categorial Beingwill not be similar to any ordinary demonstrative science. For the specialsciences make no study of the what-is-it. Rather they make it clear byperception or assumption, and they prove the properties from their assumptions(Met. E.1 1025b7-13). Even so, special sciences do not haveto be richly demonstrative in order to be scientific. After all, the Physics,like the Metaphysics, clarifies and discusses principles, but provides littlein the way of demonstration. The principles that the Physics proVides arescientific, because they are based on necessary connections. So, the perse relations characteristic of focal sciences are the same per se relationscharacteristic of ordinary science, even if those relations are not strungtogether into long chains of deductions.All the same, there seems to be some scope for demonstration in thescience of categorial Being. There is at least one demonstration in Z.l whichproves that non-substances have per se (3) Being, but confusion arises whenwe try to prOVide a specific formulation of it: 'Clearly then it is in virtueof this category [substance] that each of the others is.' Substance is saidto be a cause of Being (3

160 Aristotle's Theory of the Unity of Sciencepredicated of both substance and non-substance. This form of predicationis to all appearances universaL but in fact it is based on the focal predication,and ultimately on the natural predication. The distinction between focaland universal discourse is mentioned by Aristotle at 2.4 1030a27-32 and1030b3-4. In these passages he discusses various ways of talking aboutthe essences of substance and non-substance and draws the distinctionbetween a dialectical mode of expression (AOYLKW, 1030a25), which stateshow one should speak about them (7TW, /l" AiYEL" a27) and how thingsreally are (7TW, EXEL a28).39 The dialectical or universal mode of expressionpredicates Being of quality and even of non-Being without considering thegrounds on which the predication is made. Aristotle says that it does notmatter which mode of expression we wish to use; it does not matter, thatis, whether we treat the Beings as homonymous, or as a single universaltype, or focally, just so long as we keep the facts straight. It is importantto keep this distinction in mind in order to avoid the confusion that ariseson account of the fact that the terms involved in focal predications arethemselves natural predications.We may begin solving the problem of constructing the demonstrationby turning again to the demonstration concerning the model of medicineand health:medicine (medical) IPa instrument of medicineinstrument of medicine IPa scalpelmedicine (medical) IPa scalpelThis demonstration expresses the argument that scalpel is called medicalbecause it is an instrument of medicine. The common focal term, 'medical,'does not in itself explain why the various medical things are treated by thesame science; rather 'instrument of' and similar relational terms explainthe application of the focal term to the derivative items. For this reas'on,when we consider our demonstration in the science of Being, the proposalBeing IPa substancesubstance IPa qualityBeing IPa qualityhardly seems satisfactory. Although substance is clearly in the middle positionas befits its role as cause of the Being of non-substance, nevertheless39 Following the interpretation of Frede and Patzig 1988, 68.

161 Metaphysical Focalitysubstance alone by itself does not express the relation in virtue of whichquality is called Being. Instead, we might reorganize the terms startingwith:substance (Being) IPO ?? IPO qualityThis more closely follows the medical example by placing the focal term inthe major position, but it is unclear what relation can explain why qualityshould be treated by the same science as substance. Accordingly we mustalter the example:substance (Being) IPO quality predicationquality predication IPO redsubstance (Being) IPO redOr more universally:substance (Being) IPO quality predicationquality predication IPO a quality itemsubstance (Being) IPO a quality itemA quality item is called Being because it is predicated as quality of asubstance. We make use here of the distinction Frede has clarified, thatbetween the predicate and the predication, that is, between the item predicatedand the mode or relation in which it is predicated. 40 The predicationrelation (e.g., predicated as a quality of) must always be in the middleposition, and the item that is predicated must be in the minor position.This scheme reveals that the cause of Being is not just substance, butthe predication relation to substance. It is clear that the modes of predicationprovide the explanation for the existence of the items predicated.Under this interpretation we must distinguish the subject of ontologicalpredication (substance) and the subject of demonstrative predication (thenon-substantial item of which existence is predicated).It is precisely this ontological dependence characteristic of nonsubstantialcategorial Being that proVides the most powerful challengethat metaphysics does not follow the pattern of the science of medicineor health. Ontological dependence is not an issue in the case of medicine.40 Frede 1987a.

162 Aristotle's Theory of the Unity of ScienceScalpel is not predicated of medicine in the same way that quality ispredicated of substance. It is certainly true that if medicine did not exist atall, neither would scalpels exist, but a scalpel is at least physically separablefrom the state of the doctor's soul (the medical art). This is not trueof quality and substance. In fact, it is clear that the ontological priorityof substance over quality, quantity, and so on, is the very basis of thecategorial focality. For if qualiry were not dependent on substance forits existence, then there would be no reason to suppose that substance isincluded in the definition of quality. For since a quality can be predicated asan accident, there is no other reason than ontological dependence to includesubstance in the definition of the accident. If this is the case, then categorialmetaphysics, contrary to what Aristotle avers, is focal in a different wayfrom medicine. It is focal for ontological (dependency of existence) reasons.This means that its subject matter is special and importantly different fromthat of medicine or health.There are a number of answers to this challenge at a couple of levels.First, even if the challenge is cogent, nevertheless the ontological basis offocality applies only to the categorial form of Being, and not generallythroughout all the areas of metaphysics. Processes towards Being, mentionedin r.2, for example, are not predicated of substances in the sameway as qualities arc, and therefore arc not focally related to substance onthe basis of ontological priority. For this reason, the ontological predicationinvolved in categorial Being cannot be the grounds for focalizing the wholescience of Being, since the same ontological conditions do not obtain in theother parts of this science. Nothing, then, prevents most of the science ofBeing from following the pattern of medicine.Moreover, there are reasons to suppose that the challenge itself doesnot hit the mark. While the ontological dependency certainly grounds andprovides the cause for the definitional inclusion, ontological dependencyis not identical with the focal relationship. The distinction we drew abovebetween natural, focal, and universal forms of predication makes this clear.The demonstration,per se (3) Being IPO what is predicated in the category of quality of a perse (3) Beingwhat is predicated in the category of quality of a per se (3) Being IPOqualified thingper se (3) Being IPO qualified thingmanifests and distinguishes all three levels of discourse. The conclusion ofthe demonstration displays a connection that applies universally (Ku8' EV)

163 Metaphysical Focalityto all non-substances, and as such it is couched in the universal discourse.The terms in the premisses of the argument are bound to one anotherby per se connections, which display the focal relationship between thequalified thing and substance. In the minor premiss 'what is predicatedin the category of quality ofa per se (3) Being' is a definition or partialdefinition of 'qualified thing.' And in the major premiss the relationshipbetween 'per se (3) Being' and 'what is predicated in the category ofquality of a per se (3) Being' is a per se (1) predication. It is this firstpremiss that expresses the focal relationship. Finally, natural predicationis exhibited in the terms themselves. The natural fact that substance is notpredicated of anything else is manifested in its being a per se (3) Being.The natural fact that quality is predicated of substance is manifested inits being what is predicated in the category of quality of a per se (3)Being. Thus this one demonstration, which proves that non-substances aresubjects, involves all three forms of predication and displays the dependencyrelationship, according to which the universal conclusion is provedfrom focalizing premisses constructed out of terms that express the naturalrelations.If these predication relations are distinguished, there is no reason tosuppose that the science of categorial Being is extraordinary. Although thenatural relations have to do with ontological dependence and predication,these relations are just as amenable to being expressed in focal terms as anyother per se relationship. In fact, they are mentioned in r.2 alongside otherquite different focal relationships. Along with privations of substance andthings that generate substance, we find qualities and affections of substance(lO03b6- 1O). The ontological dependence of non-substance on substance isjust one of the many focal relations. And just like all focal relations, itcan be expressed in terms of per se predication. It is strictly irrelevant tofocality that the item being focalized is itself a predication relation. Thus,though the natural priority of substance over quality is the basis of thedefinition of quality and the inclusion of substance in that definition, itis the per se relations that ground the focality of categorial metaphysics.Metaphysics is indeed unusual in that most sciences do not take predicationrelations as such for their subject matter, but there is no reason to supposethat the focal structure invoked in metaphysics is in any significant waydifferent from the focality we find in a normal science like the science ofmedicine. .In fact, the normalcy of the science can be seen when we alter the focaldemonstration so that the conclusion no longer expresses the universal factthat quality is a per se (3) Being, but rather expresses the natural fact thatquality is predicated of substance:

164 Aristotle's Theory of the Unity of Sciencea quality item IPO quality predication of substancequality predication of substance IPO substancequality item IPO substanceA quality item is predicated of substance because substance is of such anature that it admits a predication in the category of quality. Here theconclusion reflects the natural order of predication, and the middle termexpresses something of the nature of substance. Such demonstrations areparallel to the natural demonstrations concerning health that we saw inthe last chapter:pleasant IPO having a uniform state of the bodyhaving a uniform state of the body IPO healthpleasant IPO healthAgain categorial metaphysics is unique in taking as its subject matterpredication relations, but its logical form is common. To the extent thatthe content of categorial metaphysics is demonstrable, we may expect it totake this form.Demonstrations concerning essence can be formulated in the same wayas those concerning subjecthood. 'Essence' is a universal predicate thatbelongs to all non-substance categorials in virtue of the middle term, 'logoscontaining substance in it':essence IPq logos of quality containing essence of substance in itlogos of quality containing essence of substance in it IPO qualityessence IPO qualityThe universal conclusion (essence IPO quality) is proved through premissesfocally related (,essence' is a per se (1) predicate of 'logos of quality containingessence of substance in it') and consisting of terms that expressthe natural relationship between the essence of quality and the essenceof substance (quality logos containing substance). The especial ground forconfusion in dealing with the focality of essence is that the natural and thefocal relationship are expressed by exactly the same per se relations. Atthe natural level, the essence of quality implies that it will have a naturalrelation to a substance, and this is precisely captured by the definitionalinclusion criterion characteristic of focality.41 It is for this reason that41 For a similar distinction between essence used as a predicate and the natural predicationthat backs it up, see APo 11.4 91bl-7.

165. Metaphysical Focalirynon-substance is included in the science of Being, not just because it isrelated to substance, but also because it stands alongside substance as asubsidiary subject. For snub naturally contains nose in its definition, andthis makes it part of the science of nose; but at the same time, the essenceof nose contained in the definition of snub provides snub with its claim toessence and per se Being.The Wider Focal Science of BeingCategorial focality is only one part of the science of Being. Focality showsits unifying power, not only by joining substance and non-substantialcategories, but also by joining a host of other items. First, the scienceof Being treats substance and its essential attributes:We must inquire ... whether OUf investigation is concerned only with substancesor also with the essential attributes of substances. Further, with regard to the sameand other and like and unlike and contrariety, and with regard to prior and posteriorand all other such terms, about which the dialecticians try to inquire. (Met. B .1995b18-24)Aristotle then goes on to include qualiry as well as the things that belong toquality per se. This will naturally include substance (since substance is perse related to quality) but also other things, for example, 'it is in virtue ofqualities only that things are called similar and dissimilar' (Cat. 8 11a15).42In focal terms, the statement 'qualified things are similar' forms part of thescience of Being, because similar is per se (2) predicated of a qualified thing,and qualified thing, of course, is per se related to substance inasmuch as itimplies substance as its subject. Thus, this statement in the science (stillnot adapted to a specific demonstration) is about the attributes of quality,but at the same time maintains the dependence on substance necessary forunified focal science. In this way the science of Being is articulated andramified.r .2 presents an outline of the elements and architecture of the scienceof Being. In general Aristotle's task is to show that a number of differentsubjects fall under the same science. Focaliry is one, but only one, of themeans used to accomplish this task. The two great parts of the science,TO DV and TO iv, for example, are joined in a different manner. Their42 Cf. also Met. B .1 995b26-27, where Aristotle considers the possibility that the scienceshould treat not only the what~is-it of the accidents, but also whether each has a Singleopposite:

166 Aristotle's Theory of the Unity of Scienceconnection is more intimate though less clear than focality: they are of onenature (cpvem), though they are not made clear by one "oyo< (1003b22-25).Minimally, they are coextensive, but they also imply one another, andimply one another necessarily, since Aristotle says that the substance ofeach thing is one not by accident (ov KaT" uv!'-(3,(3'1KO< b32-33). For thisreason they belong in the same science. If we can describe them in focalterms at all, they must be 'bifocally' related. Aristotle, in any case, doesnot use the focal technique to unify them. Their being of one nature issufficient to warrant their inclusion in the same science.There is in addition a third technique of inclusion, the rule accordingto which the same science treats opposites. Again, Aristotle invokes thisrule without any mention of focality, although, since one of the pair ofopposites is explainable by the presence or absence of the other (Met. Z.71032b2-5; Phys. 1.7 191a6-7), and presence or absence is a focal relation(Met. r.2 lO03b8), the rule of opposites can be subsumed under focality.These, then, are the three techniques Aristotle uses to unify the scienceof metaphysics. Other information is provided in Met. i, but from r .2 alonewe can construct an already quite elaborate scheme, as illustrated in theaccompanying figure.Within r the science of One is represented as a large part of the scienceof Being. I wish to discuss it in some detail, because the connection betweenBeing and One is not entirely clear and has been largely ignored. [ shallargue that the most promising candidate for the connection between Beingand One is the notion of measure, which is the Single nature (cpvu«) thatreceives different logoi according to whether it is treated as Being or asOne. It is the difference in these logoi that accounts for the structuraldifferences in the two parts of the science.Aristotle's claim that One is said in as many ways as Being leads us toexpect that the ambiguity of One will be isomorphic with Being and willbe overcome by the same focal strategy.43 He encourages this expectationin r.2.44 He argues that One is studied by the same science as Being(1003b33-36), and that One and Being are the same and have a singlenature (1003b22-25) and follow one another (i.e., are coextensive), thoughthey do not have the same logos's Aristotle even goes so far as to say that43 2.4 1030b8-12; 2,16 1040b16; 1.2 1053b22-24; r.2 1003b33-34.44 [n a passage that Jaeger in his ocr (following Alexander) thinks breaks the argumentand is out of place (lOO3b22-1004a2). I tend to agree, though it certainly belongssomewhere nearby, since it discusses what the subject matter of metaphysics is.45 For how they can have the same nature but not the same logos, see 1.1 1052b1-19; d.teeth and bone in GA 11.6 745b2-9.

167 Metaphysica! Focalitydenial (not Being)Iqualificationsengenderingsproductionsroad toaffections of~ /'-,,-------_ substance _______ --'IBeing (species of)!,-------------__ on< ______________ -,similar same equal[privation / denial}Idissimilar other unequal~many ________ +_ difference _Amakinghaving -------'oppositionScience of Being qua Being according to r.2 lOO3b5-1004a31we may suppose that the logoi are similar, since the phrases 'one manand 'man being' and 'man' do not refer to anything different from oneanother. His argument is intended to show that the species of One are asmany as the species of Being (l003b33-34), and that the reason why Beingforms its species applies to the One with analogous results.We are led to expect, then, that the articulations of the science ofBeing (categoria! Being, potentiality, etc.) will be mirrored in the scienceof One. Moreover, if One is ambiguous in the same way as Being is,

168 Aristotle's Theory of the Unity of Sciencewe would expect the resolution of the ambiguity to occur in the sameway, with a focus on substantial unity. In fact, Aristotle does considerthe possibility that substantial unity is the primary kind of unity (

169 Metaphysical Focalitythat which has one form, like the shoe assembled from its parts is one(1'>.6). Likewise, that which is continuous (O"vv'X~,) is one in this sense,because it is one thing, not twO. 47 Aristotle holds out a fleeting promisethat both senses of One may be unified with the science of Being in a waythat mirrors the dependence of non-substantial categories on substance.But in the end he leaves both schemes undeveloped and takes up insteadthe notion of measure.It is the internal sense of unity that promises the closest connectionbetween One and the categories of Being. Aristotle argued in Z that adefinition can apply to a substance and cannot apply properly to anythingwith an addition. The addition clearly takes away from the definability ofthe object and also from its unity. Substance is prior in definition, because itcan be defined without reference to anything else. Items in other categoriescannot be independently defined. Unity and substance, therefore, coincidein essence and definability. For this reason he says that the cause of theunity of substance is the first unity (1.11052a33-34). At H.6 essence 'is byits nature essentially a kind of unity, as it is essentially a kind of being -a this, a quality or a quantity ... This is why none of these has any reasonoutside itself for being one, nor for being a kind of being' (1045a36-b5).The connection between One and Being through the unified essenceextends the promise that One will be explicated along categoriallines, justas Being was in Z, and in one short passage Aristotle does seem to relateOne to the categories:Now most things are called one because they do or have or suffer or are related tosomething else that is one, but the things that are primarily called one are thosewhose substance is one, - and one either in continuity or in form or in formula; forwe count as more than one either things that are not continuous, or those whoseform is not one, or those whose formula is not one. (.6. .6 l016b6-11)48At first glance this appears to be a reference to the focality of One: therewill be a Single primary substantial Unity to which all the derivative non-47 There are differences between the presentations in 6.6 and 1.1. 6.6 is primarilyconcerned with the relational sense: of the seven uses I count, four are relational. BycOntrast, in 1.1 all uses besides measure are internal. Aristotle starts by leaving peraccidens uses out of account, and for this reason his interest in relational similaritymay retreat to the background.48 Cf. 1.4: 'the other contraries must be called so with reference to these, some becausethey possess these, others because they produce or lend to produce them, others becausethey are acquisitions or losses of these or other contraries' (1055a35-38). The samekind of focal arrangement for One is mentioned at r.2 1004a28-31.,------- -

170 Aristotle's Theory of the Unity of Sciencesubstantial Unities (activity, state, passivity) are related. 4Y But to interpretthis as a focality focused on substance would be a mistake. For while wefind definitional inclusion, there is no primary focal One to which all thederivative Ones are related. It seems rather to be a recipe for accidentalunities. If a thing is one if it does one thing, then for example a baker isone thing because he doe; one thing, namely, baking. The odd feature ofthis relationship, then, is that it reverses the usual priority in the realmof Being: according to this passage an accidental compound is called onein virtue of the accident that is predicated of a substance: the accidentalunity of the man performing the baking activity is a unity in virtue of thebaking activity, rather than in virtue of the unity of the substance, man. Assuch it is reminiscent of the paronymy relationship of Cat. 1, which alsonames an accidental compound. 50 If this is what the passage intends, thenOne and Being are not focalized in a parallel manner, since the unity ofaccidental compounds is dependent on the unity of the accidental addition.Nevertheless, we can see how this order of priority would be useful in thespecial sciences, which depend on the ability to abstract a unified accidentalfeature of substance and treat it as essence, while letting the substance fallinto the scientific background.Even if this passage makes accident prior to substance, that does notimply that the orthodox priority of substance over accident in unity doesnot also apply. In fact, t..6 (on One) and 7 (on Being) treat the accidentalforms in a similar manner, and it is clear in this context that the accidentalunity is a unity because accidents inhere in one thing, the substance.Substance is the cause of the unity of the compound.In the end, there does not seem to be a contradiction between theview that the substance is the cause of unity and the view that the accidentis the cause of unity. In fact, the distinction between them seems. 49 The predominant interpretation of the passage, however, which stems from Alexanderand is accepted by Ross (1924, i, 303-4) and Kirwan (1993, 138) views the One hereas relational: honey is one with honey because it affects things similarly, musician isone with musician (having), the heated with the heated (suffering). This interpretationis, however, almost certainly wrong. Kirwan finds the passage intrusive and strange,bur, in fact, the immediate context (starting 1016b1) shifts from the relational to thedefinitional sense of unity. That passage argues that those things, of which the thoughtof the essence 'is one, are one. If man qua man does not admit of division, it is one.Substances most of all are one in this way. Whatever does not admit of division in thissense is one. It is at this point that Aristotle adds his focal qualification: most thingsare called one because they do things that are one, etc. The immediate context gives noindication that Aristotle is considering relational unity.50 Cf. Lewis 1991, 88-90.

171 Metaphysical Focalityto correspond to the two parts of the science of Being in Z, the narrowscience of substance in which non-substance is viewed strictly as somethingpredicated of substance, and the wider science in which non-substance istreated as per se Being. It is interesting and important for the unity ofmetaphysics that these two ways of treating One correspond to ways oftreating Being. But for all its interesting consequences, Aristotle leaves thisstrategy undeveloped.There is also some evidence of categorial focality in the context ofthe second, relational, form of unity. r.2 lists as kinds of One, the Same,Similar, and such like (1003b35-36), which suggests that he has catogorialspecies or forms (cLOry) in mind. The Same means oneness in substance,Similar means oneness in quality, and so on. However, there is no attemptto arrange these relational predicates in focal order, and rightly so, sinceSimilar does not seem definitionally dependent on Same. Moreover, whenAristotle elaborates the ambiguity of these terms in 1.3, he does not observethe strict categorial correspondences. So the Same is used to denote what isnumerically the same, what is the same both in form and number, and whatis the same in the definition of the primary essence. For the latter Aristotleprovides the example, equal straight lines are the same, and so makes clearthat 'same' does not refer solely to substances. Likewise, Similar is notrestricted to quality: 'Things are similar if, not being absolutely the same,nor without difference in their concrete substance, they are the same inform, e.g., the larger square is similar to the smaller' (modified ROT;1054b3-6). It is clear, then, that relational unity is not focally organizedin a way parallel to categorial Being.We have considered two possibilities of focal ordering within the fieldof One, the first concerning internal unity, the second concerning relationalunity. In both cases we see that Aristotle does not develop these schemesfully or consistently. This result leads us to approach the question froma different angle and to consider whether the study of relational unityhas anything to do with the study of internal unity, or whether they areindependent of one another. The answer to this question in turn will leadus to a more satisfactory answer to the problem concerning the relation ofOne and Being.What is the connection between relational and internal unity? Twoheaps of objects may be identical either numerically or in descriptionwithout either heap forming an internally coherent unity. Heaps have noessential unity, and yet two heaps can be identical with one another. So itseems clear that internal unity is not a necessary condition for relationalunity (and it hardly need be said that relational unity is not a necessarycondition for internal unity).---- --

172 Aristotle's Theory of the Unity of ScienceAristotle intends to unify the science of One through the primarydesignation of One, measure, in such a way that measure will be a focusfor both internal and relational unity. Measure provides the criterion ofsameness. One thing, whether quantity or quality or substance, is thesame as another thing with respect to measure. At the same time, measureprovides internal unity: to be one is to be the first measure of a kind (genus)(1.1 1052bl8-20). This measure is indivisible and one (1052b31-32). Itis true that measures are often arbitrary, as in the case of measures ofweight and so on, which occur in the genus of continuous quantity, butin the category of substance, where the object measured is not continuousquantity, measure will be based on the essences of substances. The viewthat the reconciliation of the forms of One is to be found in measure isconfirmed by Aristotle in 1.1 where he distinguishes the things said to beOne from the essence (T{ ~v etVaL) of One, and says that measure is theessence of One. If measure is the essence of One, all uses of One should beexplicable with reference to it. So although internal and relational unityare not mutually explicable, measure will, nevertheless, be the focus ofboth kinds of One.This is one possible strategy for unifying the science of One, accordingto which measure provides the focus for both relational and internal unity.But there is also a more direct way of establishing the connection, andat the same time establishing a connection with Being. Essence is thecommon term. It takes little effort to show that essence is fundamentalto measure. Outside of continuous magnitude, the unit will be determinedby some essence or quasi-essence, depending on the category of the genusmeasured. Nor is it difficult to establish that internal unity is dependenton essence, since it is precisely essence that is the cause of unity of anobject. T~e distinction between essence and accident is just the distinctionbetween internal unity and internal plurality. A substance together withan accident is not a unity, at least not in the same privileged way as asubstance alone is. Difficulties by all means arise if we demand a metaphysicalstructure identical to that of Being, one that sets substance inthe preeminent position. For measure is found primarily in the categoryof quantity. Nevertheless, to the extent that there is an internal unity tomeasure, that unity will be based on essence.It is somewhat more complicated to establish the nature of the connectionbetween essence and relational identity. As we noted, there seems tobe no reason to suppose that identity depends on essence. One man maybe identical with another man, one heap with another, and the degree ofinternal coherence of the objects being compared is irrelevant to the issueof identity. And yet it is clear that all identity is identity in some respect;

173 Metaphysical Focalityso two objects are identical in number or in form. Similarly, two objectsmay be accidentally the same, as the white and the musical are, if they areboth this man. Two objects may be identical, of course, in one respect, forinstance, in form, without being numerically or accidentally identical. Asa result, the notion of identity is incomplete without further specification,and that specification must make the distinction between essence and accident.In order to identify two objects, there must be identity conditions.Even if the objects being compared are heaps, we must know the essenceof a heap, to the extent that a heap has an essence. Even a heap has unityof position, and this will be its essence to the extent that it has one. Now,relational unity is posterior to internal unity. Internal unity is of variousdegrees, that of the heap, of the accidental compound, of the substance.We need to detennine the degree of internal unity we are interested inbefore we can make an evaluation of relational unity. In order to determinewhether two objects are identical in essence, we must know what essenceis in general and what their particular essences are, and this is tantamountto knowing their internal unity. Though Aristotle does not provide thisanalysis of unity, the unification of the science of One is clearly one ofhis goals. This interpretation provides a unification scheme consistent withAristotelian doctrine, and is constructed out of the major components ofhis focal theory of One and Being.More important for Aristotle than the focalization of the ambiguities ofOne is the relation between One and the other objects included in the samescience, the many, same, different, and the other, opposite, and privation.The One in its primary designation is measure, and it is explicated in termsof genus: 'but [to be One] is especially to be the first measure of a kind, andabove all of quantity' (1.1 1052b18-19). Thus measure and One have perse relations with genus, and continuing in this way Aristotle increases thescope of the science. The measure is of importance in knowledge, because itis the principle of number, and number is that by which we know quantity.The measure also is one and indivisible, and necessarily indivisible, and soagain indivisibility joins the list of terms of the science. Now, oppositesare included in the same science, not only because of the old sophistic rule,but also because that rule can be subsumed under the focal scheme. Foropposites are relative, and relatives by their definitions are defined in termsof one another, and are therefore focally related. The opposite of One isMany, and so Many too is included in the science of the One.5151 This is not the only way of connecting One and Plurality. Without a lot of fanfare,Aristotle introduces plurality in 1.3: 'that which is divided or divisible is called aplurality.' In this case the order of priority is reversed: 'the one gets its meaning and

174 Aristotle's Theory of the Unity of ScienceOf course, the interesting feature of the passage above is the claim thatmeasure is found first and foremost in the category of quantiry, rather thanin substance. This is peculiar, and shows the extent to which Aristotle wasunconcerned to maintain isomorphy between Being and One. It may beargued that the whole discussion in I is less dependent on r than I havesupposed, but r clearly mentions as focally related precisely the subjectsthat Aristotle discusses in J. The significance of the One lies in the factthat the internal organization of the terms of this part of metaphysicsdoes not follow the organization of the terms concerning Being. Just asnon-substantial categories can be semi-abstracted and treated as per seBeings with their own per se attributes, so too One has a nature of itsown, however logically dependent that nature is on Being. Measure, for allits connections with essence, means something different from essence andoperates differently from Being. Focality, as a flexible strategy of genericunification, can both explain the unity of a subject matter and provide foran articulated study of the disti~ct elements within that subject matter.explanation from its contrary .. so that in formula, plurality is prior to the indivisible:It is clear that the divisible must be de6nitionally prior to the indivisible, so that ifthis is what we mean by One, then it will be posterior to plurality. The oddity of thisreversal of priority is increased by Aristotle's statement that 'plurality and {he divisibleis more perceptible than the indivisible' (l.3 1054a26-29). This is obviously unusualfor Aristotle. Perception ·cannot ground definition in this way, and it is impossible thatplurality should be prior to one, for in order for there to be plurality, there must be ameasure, and the measure is the unity. So the measure must be prior to the pluralitymeasured. Moreover measure, the principle of number, is that by which quantity isknown: plurality cannot be prior to one. This difficulty points to the problems involvedin establishing the appropriate priority relations. If we define the One as the indivisiblewe may not be defining it in terms more intelligible without qualification, and if wedefine in this way, as Aristotle makes dear in Topics V1.4, we cannot show the essenceof the definiendum (141b15-18). Such a definition is intended only to lead a lessscientific mind to some understanding of the subject.

6Mixed Usesof Analogy and FocalityBecause the categories constitute the irreducible genera of Being, and everythingthat exists is predicated in one of these categories, it is reasonableto suppose that relational similarities among them will best be expressedby analogy. However, as we saw in the biological context, analogies areresolved into identities by choosing a new common subject, which, thoughnot their genus, is nevertheless pe"r se related to them. Among the categories,by contrast, there is no common Being that is not already a Being inone of the categories, and so analogies at this level cannot be resolved intoa more abstract identity. For this reason analogy in metaphysical contextshas sometimes been viewed as significantly different. 1 For since no absoluteidentity can be found, analogy is the only form of commonality available.I want to argue, however, that this difference between categorial analogyand analogy in the special sciences has been exaggerated. We often findthat these metaphysical analogies, like potentiality and good, are not in factbased on the categories, but rather on lower and abstractable genera. Butmore importantly, we invariably find that they are based on a commonality,not of course on the absolute generic commonality of the biologicalanalogies, but on some kind of natural or focal relationship among thesubject-genera. Whereas wings and fins share common principles of locomotion,potentialities are found in categories, like substance and qualitythat are focally and naturally related. In no instance, however, is analogya fundamental and independent form of similarity; there is always somerelationship besides analogy that exists between the· subject-genera. Now,this issue has had a controversial history. G.E.L. Owen, because of his1 Hesse 1965.

176 Aristotle's Theory of the Unity of Sciencedevelopmental view, conceived of focaliry and analogy largely as competingprinciples of organization, and though he recognized that the developmentof focality did not eliminate the usefulness of analogy, he saw them asalternative solutions to the same problem.' So, for example, he (rightly)observed that Aristotle does not mention focality in his discussion of theprinciples in the supposedly early Met. A, and omits analogy from r infavour of focality. From this observation (and others) he concluded that theanalogical presentation of A was an inadequate unification of the scienceof Being and was superseded by r's focality.Though Owen's view has been influential and provocative, it has notbecome the received opinion. Most scholars, whatever their views on thegeneral question of philosophical development, agree that many groups ofobjects are amenable to both analogical and focal analysis. j. Owens maybe taken as the vox consensus in pronouncing that 'the two types thoughclearly distinct are not mutually exclusive.,3 On this view A does not aimat unifying the subject-genera of the science of Being, as r does, but atdrawing to our attention the differences and identities among the principlesof various kinds of Being. Different problems, even if they involve someof the same objects, will naturally require different solutions.The arguments in favour of this consensus are compelling, but a strongerclaim should also be made. Whether or not focality was explicitlyarticulated at a later stage of Aristotle's development, in its logical natureit is prior to analogy in two ways.4 At a general level it is a logicalprecondition for all analogy, and as a result one might say that analogyis a focal derivative of focality. For in order for there to be analogy, theremust be different genera, each one constituted out of elements per serelated to its core subject in the focal manner. So, while focality can existindependently of analogy, analogy cannot exist independently of focality.Since th~ focal connection is identical with the normal per se connection,this focal precondition has generally escaped notice, in spite of the factthat it is common to all analogies. It is most apparent in the case ofpotentialities: they are analogously the same, but each is homonymous2 1960,193 and n. 39.3 1978, 125; so also Berti 1971; Rist 1989, 276; Menn 1992; Code 1996; for recentcontributions on the question of development see Wians 1996.4 Cf. M. ~ D. Philippe 1969, 46-7: 'These various ways of considering unity in diversity[analogy and focality] do not necessarily exclude one another; on the contrary, theycan complete one another, yet remain distinct, each having its own proper character.'However, Philippe holds that analogy has precedence over focality: 'unity according toanalogy is surely ultimate, since it is achieved within the greatest variety and reducesthis diversity to a certain unity.'

177 Mixed Uses of Analogy and Focalitywith its corresponding actuality (e.g., the potentially and the actually hot)and includes its actuality in its definition.There is, in addition, a special use of focality that, together with thenatural priority relation, provides the framework for some metaphysicalanalogies. As we have seen, analogues must share some abstractable andessential feature. Among metaphysical analogues, however, there is noabsolutely common feature to be abstracted, because the analogues arefound in several or all of the categories of Being. Nevertheless, analogues,if they are to avoid the metaphorical and unscientific quality Aristotlecriticized in Plato, must be bound by some essential connections, even if acommon abstractable is not available. For otherwise the analogies will beaccidental. Among the metaphysical analogies the necessary connection isprovided by natural or focal priority. Sometimes the categories of Beingprovide this framework, but more often they do not.Two cases reveal the interaction of analogy and focality especiallyclearly, potentiality and the good. The discussion of potentiality is dominatedby analogy, but throughout focality (or natural priority) providesthe framework for the analogues in more or less explicitly developed ways.Good, by contrast, is dominated by focality, and since focality is logicallyprior to analogy, analogy's role becomes ultimately inconsequential.Matler and PotentialityIn three separate passages (Met. A.4-S, Phys. 1.7, Met. 0.6) Aristotlediscusses two pairs of principles: actuality and potentiality, and form andmatter. There are good superficial reasons for considering these passagesand pairs together. The passages are among the few in which Aristotlediscusses the most general principles in terms of analogy and, becausehe often elides the two pairs, he is clearly talking about closely relatedelements and principles. A close examination of the contexts of the passages,however, reveals a multiplicity of purpose. Let us first considerwhy Aristotle treats these principles as analogous, and then ask how theirunderlying subject-genera are related to one another.Aristotle has two basic reasons for treating the principles as analogous,corresponding to the relativist (formalist) and realist (orthodox) view ofbiological analogy, which we saw in chapter 2. According to the relativistaccount, prevalent in Met. 1\.4-5, potentiality and the other principles areanalogous, because they are principles of sciences, and as such are boundto their subject-genera. The various potentialities and other principles willbe analogous at any level of generality we choose to examine: the potentialitiesassociated with light and sound are analogous, and likewise the

178 Aristotle's Theory of the Unity of Sciencepotentialities of substance and quantity (A.S 1071a26). On this interpretationpotentialiry and the other principles are analogous solely becauseof their use and function in various subject-genera, and there is nothingpeculiar about their natures themselves that makes them capable of onlyanalogical identity. As we shall see, the subject-genera themselves areconnected by natural priority.The second, realist view, found in Phys. 1.7 and Met. 0.6, appliesspecifically to potentiality or matter and looks to the kinds of potentialitiesor matters in each case: potentialities are analogous because they are differentkinds of potentiality. The potentialities function differently in eachcase: one is associated with change and another with activity, or one isassociated with artefacts and another with substance. They are differentconceptions of what it is to be potentiality. These different conceptions arerelated by focality and the logic of abstraction and addition. Specifically,Aristotle leads us from a more familiar to a less familiar conception ofpotentiality by a process of induction (E7TaywY'i). This induction is nota path to a universal definition of potentiality, but rather a movementbetween different but logically related conceptions.The strongest evidence for the relativist interpretation of analogy andits underlying scheme of natural priority is found in A.4-S. Because Aristotleis concerned here not only with matter, but also with the othercauses, principles, and elements of things, including form, privation, andthe moving cause, it is clear that the multiplicity of subject-genera is thereason for the analogy. The principles are analogical because they are usedin different genera:These things then have the same elements and principles, but different thingshave different elements; and if we put the matter thus, all things have not thesame elements, but analogically (Tee avaAoyov) they have; Le. one might say thatthere are three principles - the form, the privation, and the matter. But each ofthese is different for each class [my italics; YEvos-I, e.g. in colour they are white,black and surface. Again, there is light, darkness, and air; and out of these areproduced day and night. (A.4 l070b16-21)Aristotle explicitly connects analogy with the fact that the principles arefound in different genera; and this difference in the genera certainly providesthe reason why they can be treated as only analogically identical. Itis also dear that analogy holds equally among the categories and amongthe more specific genera. The passage above cites specific genera, but thequestion concerning the identity of principles is first taken up in-the context

179 Mixed Uses of Analogy and Focalityof the categories (1070a33-b10), and the analogical solution that immediatelyfollows seems to be directed to that question. Moreover, categoriesare explicitly mentioned and included among more specific genera in thecontext of analogy later in A.S (1071a26). The fact that Aristotle treatsspecial genera and categories as equivalent for the purposes of analogyshows that the justification for the analogical identity of the principles doesnot reside in the nature of the things that are called principles, but rather intheir function as principles of different genera. For while arguments mightbe produced to show that the kinds of things that are potentialities in substanceand in quality should be analogous, it is very difficult subsequentlyto extend this argument to specific genera. For if the substantial and qualitativepotentialities are analogous to one another, then we have assumedthat the substantial potentiality forms a genus and that the qualitativepotentiality likewise forms a genus. We cannot then argue that the potentialitiesamong the various genera of substances are analogous. If we do, wehave clearly already supposed that all the analogies are purely formal. Andif analogy applies to potentiality for this reason, it applies equally to allthe other principles merely because they are principles of several genera.In corroboration of the relativist interpretation is the fact that Aristotleis explicitly discussing the principles of things, and talk about the principlesof things is distinct from talk about things in their own right. We can,for example, talk about earth, its nature and transformations, in whichcase earth is the subject-genus and receives predications. But once we caUearth a potentiality, we treat it as relative to something else, say wood.Earth now explains something about wood, namely its material nature. sThis distinction between subject and principle is made clear in a differentcontext at Met. 1.1 (10S2b7-16):This [that there is sometimes a difference between what a thing is called and theessence of the thing so denominated] is also true of 'element' or 'cause', if one hadboth to specify the things of which it is predicable and to give the definition of theword. For in a sense fire is an element (and doubtless 'the indefinite' or somethingelse of the sort is by its own nature the element), but in a sense it is noti for it isnot the same thing to be fire and to be an element, but while as a particular thingwith a nature of its own fire is an element, the name 'element' means that it hasthis attribute, that there is something which is made of it as a primary constituent.And so with 'cause' and 'one' and all such terms.5 See eill 1997 for similar observations in the context of Mete. IV.l2.--------------------- -

180 Aristotle's Theory of the Unity of ScienceAristotle makes this claim of all terms that describe relative functionsrather than things. Fire has a nature in its own right, but relative to someother subject it performs a certain function. To say that fire is an elementis to include this relative function in its definition. All causes and elementsas such will be definitionally related to that of which they are the causesand principles.This very distinction provides a reason why matter and potentialityespecially should be considered analogous: matter is said to be that whichis potentially form or privation directly and per se (1fpwrov Ka8' aim) A.41070b12-13). This fact about matter and potentiality clearly impressedAristotle, since he mentions it on several occasions. 6 Potentiality or matteris not like any other term that happens to be useful in a specific genus;rather in its own nature it is adapted to that of which it is the potentiality.Unlike earth, which can be both a per se thing and a principle,for something to be a potentiality, it must be defined in terms relative toits actuality, and as a result it cannot even be logically abstracted fromwhat it is the potentiality for without ceasing to be a potentiality. Thisseems to be less the case with a principle like form or actuality, becauseform and actuality are not what they are relative to something else. Thereis no difference between being something and actually being something,and this is certainly why Aristotle pays more attention to the analogy ofpotentiality than to the analogy of actuality.This interpretation is attractive, but there are some reasons to supposethat it is not an adequate basis for the analogy of potentiality. Whenwe say that two things are analogically the same, we say, among otherthings, that they do not have a wholly common definition. And yet Phys.1.9 (192a31-32), for instance, provides the following general account ofmatter:by matter I mean the primary substratum of each thing (€KaO"Tce), from which itcomes to be, and which persists in the result non-accidentally. (modified ROT)There is no mention here of specific actualities of which matter is thepotentiality. The definition seems perfectly general and unadapted to anyspecific subject matter? Potentiality can, it seems, be treated as a genus.6 In reference to privation Phys. 1.8 191b15-16; Met. Z.3 1029a20-26; DA 11.1 412a7-8.7 Cook 1989, 117-18, argues that we understand through analogy not what theunderlying nature is in general, but rather what it is in particular cases, but shesuggests that Aristotle can nevertheless give a general account of it.

181 Mixed Uses of Analogy and FocalityThis 'general' definition, however, exhibits a characteristic that we seein several other I definitions,' an ambiguous term, 'of each thing,' whichmakes dear that the account must be adapted to each use. This same kind offormulation is used for friendship (NE VIII.2 1156a3-5) and motion (phys.III.1 200b32-201a1), both being genera that contain a latent plurality. It isclear that Aristotle does not consider the plurality to be trivial:To be friends, then, they must be mutually recognized as bearing goodwill andwishing well to each other for one of the aforesaid reasons [pleasure, utility, virtue;my italics].There is no such thing as motion over and above the things. It is always withrespect to substance or to quantity or to quality or to place that what changes,changes. But it is impossible, as we assert, to find anything common to thesewhich is neither 'this' nor quantity nor quality nor any of the other predicates.Hence neither will motion and change have reference to something over and abovethe things mentioned; for there is nothing over and above them.The matter or underlying nature (il'7rOKHJ.tEY7) -0,,«), just like friendshipand change, cannot be defined without adapting it to some specific application,and there is no formulation that is abstracted from any of thesespecific kinds.'All the same, we can grant that a potentiality cannot be a potentialitywithout being a potentiality for some specific thing, and still claim thatthat very fact, namely that potentiality is a relative term, is common topotentialities in general and might be included in the account in order torender a legitimate general definition. This feature of potentiality, after all,arises from the fact that it is a relative term (TWY 7rpo< n Phys. IL2 194b9),and yet Aristotle does not suggest in the Categories that relatives are anyless amendable to general definition than any other non-substance term(Cat. 7 6a36-37): 'we call relatives all such things as are said to be justwhat they are, of or than other things, or in some other way in relationto something else.'It is, however, precisely because potentiality is a relative that a commondefinition is impossible. For at Topics VL8 146a36-b1, Aristotle recommendsthat 'if the term is relative, either in itself or in respect of itsgenus, see whether the definition fails to mention that to which the term,8 For a similar point see Owen 1978-9, 283; and Kung 1986, 11.- ~ -- --------- --

182 Aristotle's Theory of the Unity of Scienceeither in itself or in respect of its genus, is relative: 9 The specification ofthe relata is an essential part of the definition of the relative.While these considerations reveal a plurality in potentiality, they donot explain why that plurality cannot be included in a definition. A finalanswer may be provided by noting that a potential something is a Being,and its Being and essence is to be potentially some Being. Since Being isnot a genus, potentiality, since it necessarily is defined relative to someactual Being, will be predicated in all the categories. The analogy of potentialityarises from the fact that definitions in the proper sense can onlybe provided for existent Beings. To be susceptible of real definition (andnot merely a nominal definition), something must be a Being, primarilya substance, secondarily some non-substance. A potential Being can bedefined, and a general definition can be given to the extent that its relativecan be generalized and still remain a Being, that is, to the level of thecategories. By contrast, potentiality abstracted from anything that is aBeing is not a Being and cannot be defined. While it is possible to providea general account of the meaning of the word 'potentiality,' this cannot bethe definition of any existent thing. This interpretation would explain therelativity of analogy and the various levels of analogy we find in A.4-S,categories and particular genera. For at whatever level of generality theBeing is determined, at that level will the analogy be found.Granted that analogy in A is of the relative sort, we must now askhow the genera and categories in which the principles operate here areconnected to one another. Though the principles may be analogously related,it is an important fact that, properly speaking, the categories of Beingthemselves can never be analogously related IO Quality cannot be analogousto substance, since an analogy requires at least four terms. Only somethingrelated to quality, like a principle of quality, can be analogous to somethingrelated to substance. Met. H .2 comes the closest to claiming the analogyof Being, but even here it is clear that what is analogous is the cause oft hB e emg ·(" atnov TOV A'). €LVat In eac h case. 119 At Top. V .B 13Bb23-26 Aristotle sa ys that simple iden tity of relation is revealed byanalogy: 'The rule based on things that are in a like relation differs from the rulebased on attributes that belong in a like degree, because the fanner point is securedby analogy, not from reflection on the belonging of any attribute, while the latter isjudged by a comparison based on the fact that an attribu te belongs:10 In spi te of Owen 1960, 193n38: 'beings are the same by analogy because as one use of"being" is to substance so another is to quantity, etc.'11 H.2 1043a2-7: 'It is dear then from th!!se facts that if its subs tance is the cause of eachthing's being, we must seek in these differentiae the cause of the being of each of thesethings. Now none of these differentiae is substance, even when coupled with matter,

183 Mixed Uses of Analogy and FocalityWe are accustomed from biological analogy to find some abstractable orsemi-abstractable commonality that provides the necessary connections betweenthe analogues. The commonality extends further than each analogue,but not further than the group of analogues. This commonality preventsthe analogues from being incidentally or metaphorically connected; it preventsthe introduction of inappropriate analogies, like sail:boat::wing:bird,into biological science. Minimally, the analogies must occur at the samelevel of generality, categories with categories, genera with genera, and inselected contrast sets, and minimally the relata must be essentially of sucha nature as to admit of that relation.Where are we to look for a similar commonality among the analoguesof potentiality? One obvious answer is that since these analogies are pursuedat the highest level of generality, there is no danger of metaphoricalanalogy, since there is nothing outside of the genera in which the analogiesoccur that could ·be irrelevant and non-scientific. There is nothing thatcould be a metaphorical analogy to potentiality in the way a sail couldbe a metaphorical analogy of a biological wing or a fin. Such an answermakes the defensible assumption that the categories of Being are exhaustiveof reality (APa 1.22 83b13-l?). But because we may be comparing oneirrelevant heap with another, we should look to other, more rigorous,means by which the various genera are related. In A, the obvious candidateis natural priority. Aristotle opens chapter 4 by asking whether the causesand principles are the same for all things, and begins with the answer thatthere are a couple of ways of looking at the issue:The causes and the principles of different things are in a sense different, but in asense, if one speaks universally and analogically, they are the same for all. (1\.41070.31- 33)The expression 'universally and analogically' (Ka86Aov ... Kat KaT' dvaAo~yiav) is initially surprising, but as Aristotle goes on, he makes clear whatkinds of sameness and difference he has in mind. 12 In a way the causesof substance are the causes of all things because if they are destroyed, theother things are destroyed (A.5 1071a34-35). This expression of naturalyet in each there is something analogous to substance; and as in substances that whichis predicated of the matter is the actuality itself, in all other definitions also it is whatmost resembles full actuality.'12 There is no reason to suppose that the Kat is not epexegetic. For another use of Ka8dholJthat does not mean 'univocal universal,' see Phys. 1.1 184a23-25. Cf. r.2 l003bl4--15,where focally related Beings are said to be Ka8' fV.-.- ---- ---------------~~~~

184 Aristotle's Theory of the Unity of Sciencepriority establishes the causes of substance as universal principles. Aristotlemakes clear that this is not a contradictory but merely an alternative andperhaps complementary way of looking at the question (1071a29-35). Ifthe members of non-substance categories like light and colour are viewedas subjects in their own right, they must have their own principles, butin another sense substance is the principle of everything, because it isnaturally primary.Aristotle nowhere says that the analogies hold because some otherrelation holds. Nevertheless we have seen reasons why analogues shouldbe fixed in a framework avoidance of metaphor and, what is essentiallythe same thing, the need for the parts of a science to be bound by per5e relations. Of the connection between the analogy of principles and theunderlying connections among their subject-genera, Aristotle has little tosay. His comments opening A..5 are the clearest:Some things can exist apart and some cannot, and it is the fanner that are substances.And therefore all things have the same causes, because, without substance,affections and movements do not exist. Further, these causes will probably be souland body, or reason and desire and body.Aristotle is hardly clear in his expression, and he could be implying severalthings:1. Substance is the cause of all, because it is the cause of itself and thecause of non-substances.2. The causes of substance are the causes of all, because they are thecauses of substance, and they provide the substrate for non-substance.3. The causes of substance are the causes of alL because the causes of substanceare identical with the causes of non-substance (i.e., potentialityfor substance is potentiality for quality, etc.).The third interpretation is attractive inasmuch as it provides the greatestunity among the principles, but it is also the least likely since Aristotleholds that the causes are different for different things (though analogouslythe same). It is clear that the causes of substance are limited in theirexplanatory power, just as the oblique course of the sun is a limited movingcause (1071a15- 17): they do not explain all the essential features of theBeings.The first interpretation is recommended by the fact that Aristotle at thebeginning of A.5 draws the distinction between what is separable and whatis not. This distinction seems to be important in explaining why substance

185 Mixed Uses of Analogy and Focalityfunctions as a general cause. But separability is a feature of substance, notof its causes, least of all matter and privation.The statement at the end of A.5 that 'the causes of substances are thecauses of all things, in this sense when they are destroyed all things aredestroyed' (modified ROT; 1071a34-35) supports the second interpretation.Indeed, in 0.7 Aristotle presents a way of understanding the causes ofsubstance, at least matter and form, as the causes of all other things.Aristotle says there that man, both body and soul, is the substrate for hisaffections, the affections being the white and the musical (1049a29-30).13It is clear that musical is an affection of the soul and white is an affectionof the body. If we understand the issue in this way, then the causes ofsubstance, both matter and form, serve as substrates, potentialities, andexistential preconditions for non-substance. 14Although this natural priority does not proVide as tight a form of unityas foca lity and definitional inclusion, it does provide a sufficient frameworkfor treating the principles as an analogical unity. The non-substantial generaare dependent on substance for their existence, and they are dependentin a specific way, not as I am dependent on the sun, but because theyare inseparable (0,) xwp'O'T

186 Aristotle's Theory of the Unity of Sciencecommonality among non-substances. This commonality is the basis uponwhich the various categories and genera can also be treated analogously.At the same time, in substances as well as non-substances there are properprinciples that discharge the function of form, privation and moving cause.The passage at Phys. 1.7 191a7-12, though it manifests superficialsimilarities to A, does not invoke the genus argument, and so leads usaway from the relativist towards the realist account. 15 We find that hereand at Met. 0.6 Aristotle treats as analogous different senses of what it isto be potentiality:The underlying nature (V7TO/cELJlEV1J CPl)(Tts) can be known (E7HOTl1T?j) by analogy.For as the bronze is to the statue, the wood to the bed, or the matter and theformless before receiving form to anything which has form, so is the underlyingnature to substance, i.e. the 'this' or existent.The motivation for introducing analogy here is different from A, in spite ofthe fact that the principles of sensible bodies are at issue in both passages. Inorder to discover what this motivation is, we may most profitably start withthe grouping of examples: on the one hand, statue, bed, and other thingsthat have form are contrasted with bronze, wood, and the unformed beforeit gets form (7Tpiv !l.a{3.lv T~V !-,opcp~v); on the other side of the analogy, theunderlying nature is contrasted with substance (overia) and the particularthing (T66. n) and the being (TO ov). The grouping within the analogysuggests that the first three pairs illustrate some common relation. If so,Aristotle is not interested in shOWing the analogy of potentiality across allgenera as he was in A. Instead he is pointing to two sets of differencesin the very notion of potentiality. First, craft production (though a!-'opcpovis certainly ambiguous in this respect), in which there is, a pre-existingsubstrate, is contrasted with substances (like animals) in which there isno pre-existing substrate, but only a coexisting one. Second, there is a15 Charlton (1970, 78-9) mentions the two standard interpretations: a traditionalinterpretation has connected this passage closely with Met. Z.3 and claimed thatAristotle is trying to arrive at a conception of prime matter. On this view theanalogy involves a series of inductive steps whereby properties are stripped away untilprime matter is reached. Alternatively, 'underlying thing' is a generic name for therelationship that exists between the members of the proportion (the position Charltonaccepts). There is a further interpretation, by which the heuristic analogy induces notto a concept of prime matter, but to the matter underlying substance. AccordinglyAristotle is trying to grasp the nature of substantial change, having dealt with thegeneral principles of change earlier in 1.7 (Witt 1989, 67). See also Hesse 1965 andCook 1989, for further references.

187 Mixed Uses of Analogy and Focalitycontrast between coming-to-be and being. The wider context of Physics J,however, makes the coming-to-be/persistent Being interpretation somewhatout of place. As Aristotle says just after this passage, there hadbeen a move among his predecessors from positing just the opposites asprinciples towards including a third principle, the underlying thing. Ourpassage is introduced as part of the proposal that these three principlesmay be considered in a way as two in number: the underlying thing canbe considered numerically identical with one of the contraries, privation.This identification will serve as the key to the paradox of change, whichearlier philosophers had engendered (1.8), a solution already alluded to in1.7 190b17-27 16 By reducing the contraries to presence and absence in asubstrate, and insisting that the substrate changes in a way per se related toitself (e.g., it is the patient, not the man, that is healed), there comes to be alogical unity, which had not been present before, between the substrate andthe element changed. As Aristotle says, this solution can also be expressedin the two-term contrast between actuality and potentialiry (191b27-29).Rather than just the contraries being related (a situation in which change isstill difficult to explain), the substrate and form will now be per se related.It is this context that motivates our analogy. Aristotle needs to show howthe two different conceptions of the principles (their being two or three innumber) are related. The generalizing description 'as the matter and theformless before receiving form to anything which has form' representsthe three-principle view, involVing the matter (,)1..1]),17 privation (ap.opq,ov.7rP'V 1..a{3fLv T~V p.opq,ryv ), and the form (TOW 'XDVTWV p.opq,ryv), while thelast pair, 'so the underlying nature is to substance, i.e. the this or existent,'represents the two-principle view, which Aristotle is moving towards asa solution to the problem of change. The examples of the three-principleview come from the realm of artefacts, because artefacts have an ambiguousstatus between the three- and the two-principle view. With respect totheir names they behave like substances (wood:bed::f1esh:man), but theircategoriallogic is closer to that of an accidental compound, since the q,UG ...of bed is not bed, but wood, and bed is an accidental arrangement of wood.According to the logic, therefore, artefacts follow the three-principle structure:wood is what exists before it takes on the form; it is formless, thenit takes on a form. The analogy, then, is not primarily about a comparisonbetween artefact and natural substance, since it is clear that the generalformulation in the first half of the analogy is applicable to cases other thanartefacts (e.g., substance-accident relations). Nevertheless, artefacts setve16 50 Charlton 1970, 80; see Waterlow 1982, 14nll.17 Keeping the reading of the M5S against Diels ~nd Ross 1936, 494.

188 Aristotle's Theory of the Unity of Scienceboth as a paradigm case of the three-principle view and as a station alongthe way towards understanding the two-principle structure, which is bestadapted to natural substances.Why, then, on this interpretation is the analogy necessary? It is noteworthythat Aristotle does not explicitly state that a general definition ofthe underlying thing is impossible. Although induction is not explicitlymentioned, the fact that the underlying nature is known (E7ftaT'IT~) byanalogy recommends the inductive view, and this in turn may suggest thatwe are supposed to arrive at a universal account. Moreover, there is a clearmovement of discovery in the chapter as Aristotle approaches a solutionto the paradox of change using the pre-existing philosophical material athis disposal and setting the pieces in a new arrangement. But the inductivecontext of analogy does not entail the move to a universal account. Quitethe opposite. Aristotle rarely uses analogy in an inductive context, anddoes so in fact only in this passage, 0.6, H.2 (1042a4-5) (all passagesconcerning principles), and in the discussion about excerpting problems inAPo 11.14 (98a20--23). In all these passages Aristotle carefully distinguishesbetween what belongs universally and what belongs according to analogy.It is clear, then, that universal connections are treated differently fromanalogical connections, and that even in an inductive context the standardconsiderations of analogy are still relevant.The fact that Aristotle is working with different views of potentiality,based on three and two principles, recommends a realist view of analogy.The three-principle view, especially in the realm of artefacts, makes a cleardistinction between matter, privation, and form, just because the mattercan exist separately from the form. Indeed, that which is the matter forthe form has itself a per se existence, as wood and bronze do, and onlyincidentally does it lack or have the specific form. By contrast, in thetwo-principle view the matter exists only insofar as it is related to the form,and its being is to have that form potentially. Aristotle makes this clearwhen he says that the potentiality-actuality distinction is an alternativesolution (1.8 191b27-29). As a result, the principles have different per 5erelations in each case, and therefore belong in different genera.At the same time, the constituent genera of the analogy are not incidentallyrelated. Artefacts provide more than merely metaphorical understandingof the underlying principle in substances. The three-principlegenus is related to the two-prinCiple genus in virtue of the fact that onlyin the latter is the matter directly and per se related to its form. That is,a per se relation is added to the three-principle genus in order to generatethe two-principle genus. Equally, a principle, privation, is subtracted. Thatis to say, a relation of subtraction and addition, similar to that in Met. Z.4,

189 Mixed Uses of Analogy and Focalitybinds together the two genera between which the analogy arises. For thenotion of capacity for a form is added to the notion of persistent substrateof change. At the same time, the addition entails the subtraction of theprinciple of privation conceived independently from the substrate. The factthat they are related by addition and subtraction ensures that the principleswill be of different genera, but it also ensures that they will be per screlated. And this in turn provides a reason why the two genera shouldbe treated together and why we may legitimately move in the processof understanding from one to the other. Although this structure is onlyimplicit in the Phys., Aristotle develops it further and more explicitly,though with different emphases, in Met. 0.6 18The discussion of potentiality in e is most interesting for our purposebecause of the explicit interaction between focality and analogy in a realistaccount. Aristotle distinguishes two kinds of livval'm. The first kind, whichhe treats in 0.1; 2 and 5, is concerned with change (Kivry

190 Aristotle's Theory of the Unity of Science·m the context of change, have a different significance from the OWal''''when considered in the context of persistence. Just as non-substance canbe treated as per se Being only if the focal relationship between accidentand substance is broken, so here too the OVVa.,uH~ of persistence can onlyemerge, if the focal connection characteristic of change is dissolved.Aristotle begins his discussion of DVVal't< with a focal scheme in thecontext of change. In 8.1 he takes up the sense of 'active capacity,' anddefines DVVal't< as a 'principle of change in another or in itself qua other'(1046a10--11). This sense he designates as primary, and explicitly builds afocal scheme of derivative tenns around it. One of the derivatives is thepassive capacity, the principle of being affected in change by somethingelse (im' a""au) or by itself qua other (1046a11-13). Owen proposes forthe focally derivative formulation 'source in patient of change effected byanother or (by itself) qua other, viz. by a source of change (somethingwhich is/has dunamis [in the primary senseD,19When we come to 0.6 Aristotle reiterates the important methodologicalclaim he made in 0.1, saying that he will introduce EV

191 Mixed Uses of Analogy and Focalityis not the only one. We may come to know this new form of 3VvaJ.L'S byanalogy:Actuality means the existence of the thin& not in the way which we express by'potentially'; we say that potentially, for instance, a statue of Hermes is in theblock of wood and the half-line is in the whole, because it might be separated out,and even the man who is not studying we call a man of science, if he is capableof studying. Otherwise, actually. OUf meaning can be seen in the particular cases(E7Tt TC;JV /CaB' g/CQOTa) by induction (i.'rraywyfi), and we must not seek a definitionof everything (7TQVTOS' opov) but be content to grasp the analogy, - that as thatwhich is building is to that which is capable of building, so is the waking to thesleeping, and that which is seeing to that which has its eyes shut but has sight, andthat which is shaped out of matter to the matter, and that which has been wroughtto the unwrought. Let actuality be defined by one member of this antithesis, andthe potential by the other. But all things are not said in the same sense to existactually, but only by analogy - as A is in B or to S, C is in D or to 0; for someare as movement to potentiality, and others as substance to some sort of matter.(1048a30- b9)We note some immediate similarities with the Physics passage: induction isexplicitly mentioned (E7TaywY'i); the statement that the potential is knownas different from the form or actualiry (fOT' a~ EV€py"a TO V7Tapx"v TO7TpdYJ.La J.L~ OVTWS wrnrEp A€yoJ.L'" BvvaJ.L" 1048a30-32; J.Lia J.LEV ouv iipX~aVTl1. ouX ovrw jJ.ia ova-a Ou~€ ovrws- OV WS TO r6~£ n 191a12-13). Inaddition, it is clear that Aristotle is engaged in a process of discovery,since he begins from the more familiar senses of Suva/.us- and moves to theless familiar and technical senses; moreover, he is investigating the familiarsense for the purpose of arriving at the technical sense (B,o ('1ToilVTfS Kat7TEpt TOVTWV a,~A80J.LEV 1048a30). This process is linked with induction andanalogy in the passage above (1048a35-37). Nevertheless, even in the contextof induction the rigours of per se connections apply. The language ofdefinition and the distinction between universal and particular are present(opos, TWV Kae' EKaOTa, 7TavTos). In this passage the use of analogy is anexplicit indication that no universal definition of BVvaJ.Lts can be attained.The scheme introduced in the first chapter of 0 in its simplest formhad consisted in the focal relationship, active BVvaJ.L'..-passive BVvaJ.L's, Accordingto this scheme the application of the first element to the secondproduces change. It is reasonable to suppose that when EV€PYELa is introducedit will be paired with each BVvaJ.L'S, and that by this pairing a newsense of BvvaJ.L's will emerge. Aristotle does not make explicitly clear how

192 Aristotle's Theory of the Unity of Sciencehe intends the introduction of EVEpYfLa, but he seems to have the followingscheme in mind:active ~UVa.J..LL~(building art)Iactive fvepYELa(building activity)passive Bvva/-LLS(buildable material)Ipassive fvepy€ta(a building being built/ having been built)The examples provided here are still suitable for and adapted to bVVa}LLS inthe context of change, and as a result the conception of the scheme has notmoved significantly beyond 0.1. But a new sense of OVVa}LLS emerges whenthe focal relation bet~een active and passive 5vva,u.Ls is set aside, and thesignificance of the OVVci,uHS' are no longer seen in relation to one another,but each in a new relation with its corresponding form of Evipyf.w. Thisnew relationship is described at 0.8 1049b12- 17 in terms of definitionalinclusion, and so has the logical form of focality, even though the items donot share a name: EvePYHa is prior in definition to ovvap.ts. By setting asidethe primary focal relation between active and passive OVVajlLS, Aristotle is atthe same time setting aside the EV aAA1p-{nr' aAAov relations characteristicof change that bound them in the first scheme 20 Change is now no longerbeing considered as an essential feature of ovva}u~, and is abstracted fromthe definitions of the terms. The new scheme contains the same terms asthe original (but now expanded) scheme, but those terms are understood ina new set of per se relations, and therefore take on a new significanceY Thesenses of ovva}LL< and EVEpYHa are now apprehended by analogy, since thefocal arrangement based on change (EV aAA'f'-inr' aAAov) that kept activeand passive capacity linked has been set aside, and the BVVG.}LEL< are beingtreated in relation to their actualities.The chief difficulty in understanding the import of the analogy hasbeen interpreting the examples provided. The clearest (though still hardlylucid) contrast is provided at the end of the quoted passage: EVEPYHa is notthe same in all cases but is analogical; as KiV17GU is to ovvaJlt~, so ovuLa is tosome vA'I (1048b6-9). This in some ways seems to recapitulate the Physicsanalogy. The· first pair seems to imply change, the second pair persistence.It has been often pointed out that the distinction between the OVVa}LLSof 0.1- 5, ovva}L'~ for change, and the ovva}LL< of 0.6, ovva}LL< in stable20 Charles 1994, 97, discusses the significance of this distinction between the two schemes.2] This seems to be Frede's (1994) basic point, though he seems to extend the focal sensefrom the first scheme to the second (190 and passim).

193 Mixed Uses of Analogy and Focalitybeing, seems to fit the purpose of the Metaphysics insofar as it aims at anunderstanding of being qua being and not qua moving and changing. 22But the examples provided at 1048a37- b4 do not fit this pattern well:waking/ sleeping and seeing/having eyes shut do not suit either side ofthe analogy. I follow Gill, therefore, in interpreting all the examplesas belonging to the conception that has been abstracted from change:building, waking, and seeing are active €V€PY€laL that correspond to theactive owaf"«' ability to build, sleeping, and being able to see but havingone's eyes shut. No doubt the activity of building usually implies change,but strictly within the pair as Aristotle has provided it - building andthe ability to build - there is no change in another thing or even inoneself as other. 23 It is merely the actualization of the internal learnedcapacity. The last two examples of ivipYHa, that which has been separatedfrom the matter (a7ToK'Kp(f'ivov) and that which has been worked up(o:TrHpyaap.€vov), co.rrespond to the passive QvvafJ.EL>, matter and what isnot worked up. As Gill points out, the fact that perfect participles are usedin both cases suggests that the persistent state, not change, is at issue. 24 Onthis interpretation, then, active ovvaj.w; is a capacity for an activity, passiveovvaf'« a potentiality for a form. The KtV'1CT«-ovvaf'« pair (1048b8) mustaccordingly be interpreted as ivipYHa- OVVaf'«.25What is the relationship between the original focality and the analogythat arises between the OVVcljJ.H) in the context of persistence? Whenactuality is added to the original focal scheme, nothing prevents the expandedscheme from being applicable to change. In fact, the example ofbuilding provides a complete range of terms to fill up a scheme associatedwith change. In this case, the original focality and the original range and22 Gill 1989, 172ft and 214ff. distinguishes the first scheme concerning change from thesecond scheme concerning persistence; d. Ide 1992, 3-4 and Burnyeat et al. 1984, 48,who advert to the use of SVVaI-'LS' and fVfpYHa in H.6.23 Gill 1989, 21Snll cites DA II.S 417b8-9 for building as pure activity.24 Gill 1989, 215. But how are we to interpret the first set of examples? The first tworepresenting MVUI-'LS' are the Hermes in the wood and the half in the whole. Theyare potentially, because they could be taken out of what they are in (d. the almostidentical example at Phys. 1.7 190b7-8 in the context of coming*to.be). The third isthe knower who is not actively studying/ contemplating. The first two, then, seem toimply change, and the third does not. I suggest that since at this point Aristotle hasnot yet introduced analogy or the induction, we should not be too concerned aboutfinding consistency in this set of examples. Their purpose here is merely to give anoutline of the distinction between actuality and potentiality, and to introduce actualityas a kind of Being not like potentiality. Aristotle then goes on (in accordance with hisstated purpose) to distinguish the senses and draw the analogy.2S See Gill 1989, 217 and Ross 1924, ii, 251.

194 Aristotle's Theory of the Unity of Sciencesignificance of 5vva,."tr; remain in place, and the focality is based on theEV aA.ACf-inr' Q.AAOV relation. But in order to extend the sense of ovva}lt'lbeyond change, the EV aAAcp-tm' al\i\ov relation must be set aside, and ananalogy rather than a focality will take its place. The focality will ceaseto exist, because the necessary relations concerning change no longer holduniversally. It is dear that the first pair at least (e.g., active thinking, seeing,etc.), when it is considered complete in itself, extends beyond sources ofchange in another and encompasses activities that do not result in anyproducts or any changes in other objects.The relationship between the two conceptions of bVva!"t< (change andpersistence) is similar to what we saw in Z between non-substance consideredas an accident of substance and non-substance considered as per seBeing. For in order to arrive at the per se conception of non-substance, wehad to break the accidental relationship between white and man and setwhite into a new per se relationship with surface. The function of white isquite different in the two relations. In a similar manner, the relationshipbetween the active and the passive owa!"". is broken in order that eachmay enter into a new per se relationship with their respective EVEpy€ta;and the function of ovva!"L> is quite different in these two relations.Aristotle, then, makes two very different uses of analogy in the contextof potentiality and matter. One is a relativist use appropriate for the studyof principles, the other a realist view intended to lead us to a new conceptionof matter and potentiality. In all cases, however, we find a relationship ofnatural priority or focality connecting the genera of the analogies, whicheither allows us to treat the principles as a single group or allows us tomove from one conception of the principles to another by addition orabstraction.The GoodThe good has traditionally been treated alongside other transcategorialterms, like Being, One, and potentiality, in discussions of analogy andfocality. 26 It seems especially promising for our purposes, because Aristotle'sdiscussion of the good in EN 1.6 1096b26-29 contains the onlypassage in the corpus that mentions analogy and foeality immediatelytogether. OUf discussion begins again with Owen: since the EE lacks apassage parallel to EN's discussion of analogy and focality, Owen arguedfor the ea rly dating of the EE. He supposed that Aristotle had not yet26 E.g., Alexander on Met. r. ,242.5-6..--~- '"'-

195 Mixed Uses of Analogy and Focalitythought to use focality in the context of transcategorials, and so had not yetdeveloped the focal solution that is fully revealed in Met. r.2. But Owenwas misled by EN 1.6 1096a23-29 (where good is said to be predicatedin all the categories) into supposing that the 1.6 1096b26- 29 passage wasrelevant to the categories, and his misreading seems to persist in somerecent accounts." Interpretation of the passages is further bedevilled bythe fact that the context throughout is a critique of the Platonic idea ofthe Good. Aristotle adduces arguments in both the EE 1.8 and EN 1.6 onlyto the extent that they are useful for his critical task, and where he doesmake positive comments (1096b26-29) he explicitly recognizes that theyare strictly speaking out of place (1096b30-31).In response to Owen's claims concerning the EE, Berti has argued -I think successfully - that Aristotle implicitly recognizes the basis of afocal arrangement in the EE. This arrangement consists in the means-endsrelationship, and it fulfils both of the formal criteria of focality. Both meansand ends are called 'good,' and the definition of the end is contained in thedefinition of the means.28 Robinson, while agreeing with Berti about theEE, urged that a focality based solely on ends and means would result ina single ultimate good, which the EN with its multiplicity of per se endsdenies (1096b16-25).29 In this state, more or less, the controversy hasrested. There is, however, more to be said about the scope for focality andanalogy among the goods and the role of categories in these arrangements.Both the EE and the EN offer further evidence for a focal arrangementamong means and ends, and this becomes apparent in light of the intimaterelationship between focality and demonstration. For a passage at EE 1.81218b16-24 expressly discusses the final good as T

196 Aristotle's Theory of the Unity of ScienceA series of means and ends, which are connected in hypothetically necessarypremisses (civaYK'11218bI9), can be displayed in a syllogism. The endsare causes (bI6, 18) and principles (24), and as such take the middle position.The per se relations, which underlie focal relations, are clearly presentand at issue here. The use of the relative "'po, is a further indication ofthe focal arrangement (avciYK17 rODE Eiva~ TO crV}J.cpEpOV npos aVT7JV). We seethe familiar distinction between the natural and the focal demonstration.The natural final-cause syllogismexercise IPO healthhealth IPO manexercise IPQ mandoes not contain the term 'good,' though it is implicit through our understandingof the relations between the terms. The good can be made moreevident through a linguistic, focal demonstration,healthy IPO conducive to healthconducive to health IPO exercisehealthy IPO exercise,in which 'conducive to' implies the relationship of means to ends. Bysubstituting 'conducive to' and 'exercise' for other terms we can fill outthe terms of the science of health. Finally, if we substitute 'health' and'exercise' for the general 'good,' we shall have the desired focal demonstration:good IPO conducive to the final goodconducive to the final good IPO means (specifically exercise)good IPO means (specifically exercise)It is easy, then, to see how ends and means fit into the wider focal science.The derivative good, means, has a different significance and different propertiesfrom a good in some other derivative sense, for example, evil, which,by the I'~ ov rule of focal inclusion, can also be called 'good.' Means, thoughthey qualify as focally derivative because they are homonymous with thefocus and imply the focus in their definition, are also peculiar in that theyactually share some properties with the focus. For the final good and thederivative good are both objects of desire and both are pursued. This isobViously one of the reasons that Plato was led to the idea of the Good,and it is preCisely this fact that allows goods to be treated analogically as

197 Mixed Uses of Analogy and Focalitywell as focally. It is an arrangement closely akin to cumulative series, aswe shall see in the next chapter.In the EN as well, Aristotle maintains the focality of ends and means(1.6 1096b8-14), and although he does not use the 7TPO< iiv expressionin this context (perhaps because he is arguing in this section that themeans are not related 7TPO< iiv but 7TPO< 7ToMa) the language of focalityis unmistakable. The means are described as 'those which tend to produce(7TOL'lnKa) or preserve (q,vAaKnKa) these [ends] somehow or to preventtheir contraries' and they 'are called so [good] by reference to these (BLD.ravra Aiy«reaL) and in a different sense.' These are the standard formulaeof Met. r.2 30But the EN also moves beyond ends-means focality. The further developmentcomes at 1096bl4-26, where Aristotle calls on us to set aside themeans and consider whether the ends themselves are goods in accordancewith a single form (KaTD. /liav 1biav). He claims that the definitions ofhonour, prudence, and pleasure are different and distinct qua goods (iiTEpOLKa, BLaq,ipoVTE> 01 A6yOL ralJTy/ V ayaea). Since they are not related as endsand means and do not share a common definition qua goods, we are forcedto consider whether they are chance homonyms (1096b26-31):But then in what way are things called good? They do not seem to be like thethings that only chance to have the same name. Are goods one, then, by beingderived from one good or by all contributing to one good or are they rather one byanalogy? (a.hA' ct.pa.)'f TCp clq,' EVo) fivQt 17 7rpo) Ell a7rQVTQ UVVTfAE1v 17 p.O.AAOV Kar'civaAoyiav;) Certainly as sight is in the body, so is reason in the soul, and so onin other cases. But perhaps these subjects had better be dismissed for the present;for perfect precision about them would be more appropriate to another branch ofphilosophy.Since Aristotle does not provide a solution to this question here, weshould not immediately take the disjunction, ~ , to imply that only oneor another of the techniques of unification is correct, nor even that thet;are exclusive.31 Certainly to look for three distinct techniques is hopeless. 2The first two disjuncts are to be treated as a unit, T~ acp' €vO~ ElvaL r, 7TPO~ €Va:rravTa CTVVTEhELV. Granted, the diction, as Fortenbaugh has pointed out,30 Met . r .2 1003a35-36: CPVNiTHIV, 7fOl£lV; 1003b17: ~l ' 0 AEYOVTal .31 Berti 1971, 170, claims that the goods can he both analogically and focally related. Soalso Menn 1992, 551n11.32 Ross 1914, 291, distinguishes acp' EVOS as the efficient cause, 7fPOS fV as the final cause.This is not an Aristotelian usage.,-------------------- .-

198 Aristotle's Theory of the Unity of Sciencedoes not correspond to the technical expression for focality,33 and thereare hints towards a means-ends interpretation: (T1)VTEA£tV is chosen in partbecause of the root TfA-; and it is connected with usefulness at GA 1.18725a5. Nevertheless, a passage at PA IlL5 667b21-26, though in a quitedifferent context, contains similar diction and suggests that act>' €VOs and"'pos fV represent two ways of looking at the same phenomenon. 34 And amore relevant use for CTVVTfAE'V is found at SE 1 165a35-37. Concerningsophistical arguments, Aristotle says that he will discuss how many kindsthere are, the number of their elements and parts, and the other things thatcontribute to this art (7T€pl. TWV aAAwv TWV CTVVTEAOVVTCOV ELS T1JV T€xvrJVTavT~v).35 He provides some indication of what he thinks the CTVVTfAOVVTaare at the beginning of SE 34: the appropriate order of questions, how tosolve arguments and solecisms, and so on, both of which go beyond a mereenumeration and description of the parts and elements. This passage is theclosest parallel to the EN, since it deals with the logical organization ofan investigation. 36 As the order of questions contributes, but is not necessarilyan element, so the per se goods contribute to a single good withoutnecessarily being elements of that good. The traditional interpretation thatreads this phrase as a reference to focality, then, is not likely to be far offthe mark. 37 .If this is correct, can Aristotle provide a focal arrangement for theseper se goods 1 38 He lists four: intelligence, sight, certain pleasures, and honours(1096b17-18), to which we might add virtue generally (from 1097b2;Aristotle already provides p6V~CT"). Unfortunately, Aristotle provides noexample of what he has in mind and expressly dismisses the question as tooexact for his study. Moreover, in the remainder of book I he leaves asidethe relations among these per se goods, because he has already assertedthat they are also desired for the sake of something else, and it is this33 Fortenbaugh 1966, 188-9.34 'The reason why these two vessels [the aorta and the great vessel] coalesce into onesource and from one source ((is' ",ia.I1 apxi]v a-vVT£A.t"tv leal cina ,tuas) is that the sensorysoul is in aU animals actually one, so that the part in which it primarily abides mustalso be one' (modified ROT).35 TWV ci.v..wv TWV cTVlITEAovlITWV means 'the other things, I mean the ones contributory':the parridple 'is emphatically attributive.36 This tells against Fortenbaugh's generic interpretation, since Eta77 TWV Ao)'wv (165a34)are dearly distinguished from the contributory factors.37 E.g., Owens 1978, 116-17.38 Fortenbaugh has tried to show that the phrase clef {vat Eivcu 11 1TpOt iv Q'l'T(U)TCl O'lWTEAEivdoes not refer to focality, but to generic affiliation through means and ends. This is, ofcourse, impossible since Aristotle has already set this possibility aside at 1096bl4-16and b24-25.

199 Mixed Uses of Analogy and Focalitysomething else that he pursues in 1.7 through the methodology of themeans-ends scheme. This obviously does not preclude other relationshipsalluded to in the 7rPO, EV ITVVTfAElv phrase, for how can we exclude someother relationship to €VOaLMOvia if we do not yet know what EvoaLMovlais? What that relationship might be, we are left to speculate, and yet,our understanding of focality provides a clear direction for the search.We should look beyond the confines of EN I to the later books, andseek Aristotle's final word on the focal relationship in the host of perse relationships that bind together the central terms of his ethical theory.Each of the per se goods is not just a means to EVOaLj.wv{a in some vaguesense, but also enters into a very precise relationship with EVaaLJ1-0vla andwith the terms in which Ev~a'Jlovia is defined. 39 A brief survey of thesereveals that their relationship to EvoaLfLov{a is not the same in all cases.f:voaLjlOv{a, the human good, is the activity of the soul in accordance withvirtue, and if the virtues are severaL then in accordance with the bestand the most complete of them (1098al6-17). Virtue, then, is obviouslya central part of the theory, because it is per se (1) related to happiness.It is a state of the soul concerned with choice, lying in the mean relativeto us, this being determined by reason and in the way in which the manof practical wisdom would determine it (11.6 1l06b36-1107a2). Virtue isgood because it is the activity in accordance with this state that is good.Accordingly, q,povryIT" too is part of the theory, because it is a virtue,indeed in many ways it is the most complete virtue. For C/>POVTfa"LS is notonly a virtue (whose activity constitutes the human good), but it is thevirtue that determines the mean states that constitute the other virtues(whose activities in turn constitute the human good). It is therefore botha species of virtue, and related to ethical virtu~. Honour turns out to havea plurality of roles in Evoa'Jlovia. Ev~a'Jlovia itself is honoured (1102al;1178b31-32). But honour is also that with which the state of pride isconcerned. In this sense it is not a good at ali, but rather it is how weact and react relative to it that is a good; and honours and dishonours arethe object with respect to which the proud man is as he should be (thatis, has the human good) (IV.3 1123b20). Pleasure has the most interestingrelationship to EVOaLfJ.OVta. In a general way, all ethical virtue is concernedwith pleasure and pain (7rEPL ~~ovas yap KaL Alma, 'ITn ~ ~elK~ apET~ 11.21l04bS-9; d. X.l), since virtue concerns action and reaction, and pleasureand pain attend every action and reaction. But pleasure enters the theorythrough another relation, and thereby has a different significance: pleasure39 See Tuozzo 1995 for some similar conclusions, though from a different perspective.------------ ---

200 Aristotle's Theory of the Unity of Sciencecompletes the (best) activity not as the inherent state does, but as an endthat supervenes (X.4 1174b31- 33). We do not have to determine the exactnature of this form of pleasure to see that it has a different significancefrom the more general form. Finally, of sight Aristotle has little relevantto say in the ethical treatises, but the outlines may be filled in from thefirst chapter of the Metaphysics. In general, then, the per se goods may besaid to contribute to a single end through a variety of focal relationshipswithout being means to that end.Although Aristotle left us to speculate about the focal relationship, hedoes provide an example of the analogy of the goods: as sight is in the body,so reason is in the soul. Sight is the good for the body, in that the bodygenerally (the instrumental parts) is to be explained with reference to it.Though sight may also contribute to the welfare of the body, we enjoy sightmost of all for its own sake, since it is the purest (EN X.51175b36-1176a1).The genera, body and soul, are obviously related as matter and form. Sightand reason will be the goods of the two parts of the substance. Moreover,we have here a continuous analogy (A:B::B:C), since sight is an activityof the soul, and soul is for the sake of reason. This analogy is obViouslycomplete as it stands, and it is difficult to see how pleasure or honour canbe fit into the scheme. For this reason the analogy should only be takenexempli gratia. A much more promising field for analogy is found amongthe crafts. After all, tradesmen need only know the good of their own craft(1097a3- 8), and the good of each activity and craft is different (a16-18).But Aristotle also makes clear that the analogy is not sufficient in itself,or at least that it must be framed by some further form of commonality.For all the crafts derive their ends from the political craft, connected byends-means focality. Similarly among the per se goods, a simple analogywithout some framework would result in incommensurability of ends, andwould be no guide for a rational life. We might think back to exchangevalue, which though it was analogically distributed among the varioustrade goods, nevertheless was made somehow commensurable by beingtreated in terms of need through money. If we want to avoid completeincommensurability among the per se goods within the analogical scheme,we could try to commensurate between them in some way, seeking somuch honour and expending so much intelligence for it, trading as it wereamong the ends 50 as to achieve a certain balance in life. This is, of course,not Aristotle's solution. Focal unity is the ultimate unity among the goods.The mention of voils as a per se good and the fact that analogy is foundamong terms associated with the categories has encouraged the assimilationof this passage with the passage at 1096a23- 29, which also discusses theambiguity of the term good. In the context of refuting the Platonic idea

201 Mixed Uses of Analogy and Focalityof the Good, Aristotle asserts that the good is not one thing, because it issaid in as many ways as Being. Essentially the same argument is found inthe EN and EE with only minor modifications:[S]ince good is said in as many ways as being is said (for it is said 40 both in thecategory of substance, as God and reason, and in quality, e.g. the virtues, and inquantity, e.g. that which is moderate, and in relation, e.g. the useful, and in time,e.g. the right opportunity, and in place, e.g. the right locality and the like), dearlythe good cannot he something universally present in all cases and single; for thenit would not have been predicated in all the categories hut in only one. (EN 1.61096.23-29)[T]he good has many senses, as numerous as those of being. For being, as we havedivided it in other works, signifies now what a thing is, now quality, now quantity,now time, and again some of it consists in being changed and in changing; and thegood is found in each of these modes, in substance as mind and God, in quality asjustice, in quantity as moderation, in time as opportunity, and concerning changethat which teaches and that which is being taught. As then being is not one in allthat we have just mentioned, so neither is good, nor is there one science regardingBeing or the Good. (modified ROT; EE 1.8 1217b25-34)The key to the correct interpretation of these passages comes from Topics1.15 107a3-17: terms, like AfVKOV, when they are applied to subjects, likebody and sound, have different significance, and indeed refer to predicatesin different categories·1 For a body to be AfVKOV is for that body to be40 A slight alteration from the Oxford translation, which reads 'since things are said tohe good in as many ways as they are said to be {for things are called good both inthe category .. .' The Oxford translation inclines towards the correct interpretation, hutwithout indication from the Greek.41 lowe this interpretation to Ackrill 1978, who noticed the significance of the Topicspassage: 'Look also at the classes of the predicates signified by the tenn, and see ifthey are the same in all cases. For if they are not the same, then clearly the term ishomonymous; e.g. good in the case of food is what is productive of pleasure, and inthe case of medicine what is productive of health, whereas as applied to the soul itis to be of a certain quality, e.g. temperate or courageous or just; and likewise also,as applied to a man. Sometimes it signifies what happens at a certain time, e.g. whathappens at the right time; for what happens at the right time is called good. Oftenit signifies what is of a certain quantity, e.g. as applied to the proper amount; for theproper amount too is called good. So then good is homonymous. In the same way alsohUlK"" as applied to a body, signifies a color, but in regard to a sound it denotes whatis easy to hear.' Notice that this tapas does not consider the possibility of ambiguitybetween the good in the area of food and good in the area of medicine {a shock for a

202 Aristotle's Theory of the Unity of Sciencesomehow qualified; for a sound to be A.evKov is for that sound to causesome effect. Since the Topics treats the cases of good and II.€VKOV as parallel,the term good, when predicated of various objects, will likewise fall intodifferent categories. For a man to be good is for that man to be virtuous,to have virtue predicated of him (Le., to be somehow qualified). Similarly,for the weather to be good is for it to be neither too hot nor too cold,to be moderate (i.e., somehow quantified). For a delivery to be good isfor it to arrive before 5:00 pm, at the right time (i.e., sometime). Thisinterpretation fits the examples provided by both the EE and the ENversions. For it is clear that the examples are essentially goods in theircategory, but it is equally clear that the predicate, that which teaches, isnot the only good in the category of change. Virtue, moderation, and so onare predicates that signify 'good' for various things, and these predicatesfall under different categories. Within some categories, doubtless, 'good'has several significations, for others it has not only just one significationbut one object of which it is predicated. 42In view of the proximity of the EN passage to the passage later inthe same chapter that proposes a logical organization among per se goods,it has been suggested that good in our present passages is amenable tobeing expressed as an analogical or a focal unity·3 It is true that there isno explicit mention of analogy in these passages, and, in fact, it wouldprobably be inappropriate in the context of Aristotle's critique of theplatonic doctrine of the unity of the good, but the claim that the goodis said in as many ways as Being encourages an analogical view alongthe same lines as potentiality.44 However, analogy among the goods at acategorial level, while possible, is not especially useful for Aristotle, andfor this reason he makes no mention of it.The examples of the Topics passage do provide some superfiCial encouragementfor an analogical arrangement of the good along categoriallines: asfood is good because it is productive, so man is good because he is qualified(TO 7TOlo'V e1'vat). But a brief examination of these examples reveals that thereader of the Gorgias), since the first is 1TOU7TlKOV of pleasure, the second 1I"OUITUCOV ofhealth. Since both goods are 1J'Otl1TIICOV, no ambiguity can be detected· by this topos. Theambiguity of the good is treated solely on a categorial level. For a different view seeShields 1999, 202-4.42 For the problem of god and mind, see Ackrill1978, 23, and more recently, Menn 1992.43 So Owen 1960, 193n38, and to some extent Menn 1992, 550-1 and n. 11. Broadie hasli nked the passages for the purposes of focality (1991, 28-9).44 As Rist points out (1989, 276), we should not expect to see Aristotle saving the Platonistposition by introdUCing focality in the midst of an anti-Platonist polemic.

203 Mixed Uses of Analogy and Focality .category of the subject and the category of the predicate do not have to bethe same. Only in the case of substance, where self-predication is the onlylogical possibility, are the subject and predicate necessarily of the samecategory: for god to be good is for god to be reason (ie., a substance).Since the categories of the goods do not consistently correspond to thecategories of the subjects of the goods, it is clear that the Topics examplescannot provide a model for the analogy of the good along categorial lines.If we look, not at the predicate-subject relation, but instead at the relationshipbetween the good predicated and the category in which it is predicated,we find a more promising candidate, virtue:quality::god:suhstance,and so on. In this analogy, the goods are clearly not the goods for acategory, in the sense that Aristotle develops his analogies of the goodelsewhere. While in some sense substance is for the sake of god, clearlyquality is not for the sake of virtue. If these goods were the goods fortheir categories, then all and only the members of the category would beinstrumentally good for the good of that category. Vice would then bean instrumental good for virtue. Moreover, as we saw, the goods by nomeans have to be in the same category as that of which they are goods, sothere is no reason to suppose that the good for a quality will be a virtue.Again, if the good for a category falls into several categories, then therecan hardly be one good that is the good for that category. This seemsto happen in many cases: the good of an express delivery (a 7TO"'V) is a7TOT

204 Aristotle's Theory of the Unity of Scienceso on are the terms given in each category to the things that are aimed ator chosen. This is not, however, a very interesting or revealing analogy,because it is the 'for the sake of' relation that does the real explanatorywork. This may be one of the reasons why the good is not treated extensivelyin the Metaphysics (with the exception of god, whose essence isto be good), and with that exception does not belong in a study of beingqua being: good is an accident and is best understood in the context ofaction and in the analogical and focal arrangements that relate one goodto another rather than to Being. Their categorial status, which is the basisof the science of Being qua Being, is largely irrelevant 4 'In thi~ respect the good is significantly different from potentiality,for which the categorial analogy is genuinely significant. For potentialitydischarges its function as potentiality in the category for which it is thepotentiality. Good does not. Potential substance does not exist in severalcategories, but if in any category, in substance. 47 The categorial status ofnon-substantial potentialities is arguably twofold. For non-substance thesubstrate is always the same, substance (Z.3 1029a23-24). Of course, thesubstrate is actually a substance, but it is potentially the non-substance itmay become (in a different sense of is, of course). So air is actually air,but potentially transparent (so as to be light). However, since the privationis in the same category as the form, and since the substrate is consideredonly insofar as it is relevant to the form (Phys. 1.8 191b4-10), Aristotlemakes the matter essentially adapted to take on that form. Inasmuch asthe matter is potentially, say, transparent, it is potentially qualified and sois in the category of quality.If a categorial analogy of the good is an unpromising arrangement,Aristotle extends even less of an invitation to interpret the categorial goodsfocally, in spite of the attractive suggestion that god as substantial good canbe viewed as the focus 4s It is true that god is the ultimate final cause andend (DA 11.4 41Sa23-b7), the goal towards which all things strive, and thatfor the sake of which they do whatsoever their natures render possible.At the end of EE (VII.IS 1249a21-b2S) god and the ruling principle inus are likened to health and medicine respectively: it is with an eye to46 Shields 1999, chap. 8, comes to a slmilar conclusion from a very different argument.47 As 6.7 says, per SI! being is said in the categorial ways (1017a22-27; d. 2.3 1029a20-23),so potentiality, since it is not a per se being, may be thought not to be in a category. ButA.4-5 presents matter as associated with categories, and matter is one sense of Ol/sin(e.g., Z.10 1035a2; H.2 1043a19-21), and so would seem to be categorially detennined.48 As Berti rightly points out (1971, 166), Aristotle's positive thesis about the organizationof the goods does not depend on the doctrine of the categories.

205 Mixed Uses of Analogy and Focalitygod that the ruling principle directs the part of us that takes commands.And just as there is a focal relationship between health and medicine, it isnot unreasonable to posit a focal relationship between god and the rulingprinciple: the ruling principle is called good, because it aims at attaining, tothe extent possible, the primary good (god). And since the ruling principledefines virtue and virtue defines EvbaL!,ovia and the human good, in thedefinition of the human good will ultimately be found, by one or more stepsof focal inclusion, the term god, or its definition, and since its definition isto be the good substance, substance, too, will be included in the definition ofthe human good. Mutatis mutandis, the same situation applies to the goodof all other things. We can and should accept this form of focal inclusionas important for Aristotle's ethical theory, since he argues that god is adeterminative cause in the human good, and as such must be included inthe theory.That inclusion, however, does not depend on substance and its relationsto the other categories of Being. The fact that good falls into all thecategories is not relevant to Aristotle's theory of the good, alid he onlyalludes to it in these passages because he is criticizing the Platonic idea ofthe Good. The dependence of the good does not follow the dependence ofBeing. For virtue (as good quality) includes in its definition a substance, notgod, but man, or whatever substance of which it is the quality. And thecase is similar with all the other non-substantial categories. Moreover,the proposed focality is peculiar in that the non-substantial goods aredependent on god rather than on substance generally, as is the case withthe focality of categorial Being. Since there is no substantial good exceptgod, non-substantial goods must be directly dependent on god for theirgoodness. This is clearly not the way that Aristotle chose to develop thefocal relations among the goods in his ethical theory. Aristotle made theimportant and anti-Platonic discovery that, though it is a transcategorial,good does not follow Being per se. As such the categorial organizationof good does not reveal the nature and function of the term, and in factdisrupts the fundamental relation of means and ends. To pursue the goodthrough categorial Being and essence is to resign oneself to a second sailingand to ignore the winds blOwing towards the o~ fV€Ka.Analogy and focality, then, are not merely compatible means of providingnecessary scientific relations among terms; rather, they bear a fixedand determinate relation to one another. In the cases we have studied,analogy is posterior to focality (or some similar logical arrangement suchas natural priority or subtraction/ addition). Potentiality is dominated bythe analogical structure, but is framed by focality. Because it is a relativeterm, its primary affiliation is to the genus in which it functions;

206 Aristotle's Theory of the Unity of Sciencebut if potentiality is to form a single subject, and if we are to pass inunderstanding from one form of potentiality to another, there must besome per se relations between them or their subject-genera. The good, bycontrast, is dominated by focaliry, and as a result of the prioriry of focalityover analogy, largely dispenses with analogy. The concept of good is bestadapted to the unification provided by focality.

7CumulationFinally, we turn to a fusion of analogy and focality, an Aristotelian techniqueI shall distinguish by the term 'cumulation.' According to this techniqueobjects from the same categoty form a series of priority and posteriority,each member of which potentially contains in its definition theantecedent term. We have already seen similar techniques in the scalanaturae and the ends-means relationship among the goods. It is due tothis similarity that cumulation is sometimes supposed to be a focal relationship,but I hope to show that this is not accurate 1 In spite of the factthat focality and ' cumulation share the definitional inclusion criterion andmanifest an order of priority and posteriority, they have very differentlogical properties and involve different kinds of objects. Whereas focallyderivative objects have a single subject to which they are causally related,each cumulative object is first and foremost a subject in its own right,though it may also exhibit certain causal relations with other objects inthe series. It is not the purpose of cumulation to form one genus. Incontrast to focal objects, Aristotle takes pains to show why cumulativeobjects cannot form a single genus. Although these objects are the samebasic type of thing at a certain level of generality, they show less coherencewith one another than do focally related objects.The difference between cumulative objects and other serial objects, likethe scala naturae and the goods, is more subtle. The latter series mightbe called series of perfection, because the first members are the perfectinstances, and the subsequent members are qualifications and diminutions1 E.g., Owen 1960, 187, who notes that there are differences between foeality andcumulation without discussing them. Shields 1999 most recently con£lates them as'core-dependent homonymies.'

208 Aristotle's Theory of the Unity of Scienceof the first. In such series the focal aspect predominates, and as a resultthe genus is strong. Means are good, for example, because of their relationshipto the end, and they are intelligible as goods only in virtue ofthat relationship. By contrast, in cumulative series, where the membersare not primarily viewed in causal relationship with each other, the genusis weaker: the sensitive soul is a soul in its own right and not because itrequires the nutritive souL Because perfective series are best understoodas a variation on focality, my main attention will be on cumulative series.Two cases are of especial interest to us, souls and friendships. Aristotle'streatment of souls is a paradigm case of cumulation and allows us todetermine the pattern. The discussion of friendship provides variationson the theme and allows us to compare a focal arrangement (in the EE)with a hybrid account that contains elements of cumulation and elementsof similarity (in the EN). We shall, however, return at the end to a series,which Aristotle seems to understand as perfective, but which may be moreamenable to a cumulative interpretation, the series that locates theologyin the science of Being qua Being.SoulsIn turning to Aristotle's treatment of the soul in the de Anima we arecompleting the task of chapter 3 by considering the affiliations among thefunctions of animals at the most abstract level (KaT' aKpif3ELav 402a2).For this treatise deals with the highest functions of animals, nutrition,sensation, locomotion, and intellect, and these constitute the final causesof all of the instrumental parts. These highest functions are, however, notindependent of one another. In an intricate analysis Aristotle considers inturn whether they are universally (KaB' fV), or analogically, or cumulativelyrelated.Aristotle's analysis in DA 11.1-3 of the kinds of souls and their relationshipsto one another is framed as an answer to three problems that hehas introduced in 1.1. As he solves these problems he calls upon the universal(

209 Cumulationwe define them in terms of their final cause or in terms of their materialconditions (403a3-b19)?Each of these problems presents a contrast between abstract and concreteapproaches to the subject. While we must look for the most generallegitimate explanation, if we focus too narrowly on abstractions, we runa risk of committing one of three related errors corresponding to each ofthese three problems: defining a genus where there is none, providing adefinition that explains nothing about how living things live, and assertingthat the entire soul is separable from the body.Aristotle devotes DA II.1-3 to solving these three problems in a preliminaryway. As he solves each problem, he moves in turn towards afuller account of soul. Since voil, does not easily fit into the organizationalformat he is constructing, he leaves it conspicuously on the side. 2 He takesthe problems in reverse order, declaring that the faculties of the soul are forthe most part not separable from the body. The reason he gives constitutesthe first' definition' of the soul: the soul is the first actuality of a naturalorganic body potentially having life (Il.1 412b4-9). Since the soul is theactuality of a body, it is as inseparable from the body as the impression ofa signet ring is from the wax that bears it.Without completely solving this problem (Il.1 413a8-9), he moves onto the second aporia, which is the subject of the second chapter and halfof the third (to 414b19). The quick answer is that we simply cannot studythe whole soul, since soul is said in many ways. We must distinguishthe faculties, since each is a sufficient condition for calling a thing living(413a22-23). Later at II.3 414b6-14 (and again at II.4 415al4-23) AristotleimpliCitly accepts the need to consider the objects of the senses as well asthe individual faculties, and so answers both parts of the second problem.Again he promises further investigation (414b14).In the last half of II.3 he takes up the first problem, and concludesthat we must consider the individual kinds of souls, since there is nosingle kind (414b32- 33). The tendency in all three solutions is to drive theinvestigation away from the general account towards the particular, andaway from the separate soul towards the composite. The three solutions areset in a discussion that moves from the most common and familiar accountof the soul to the most sophisticated and explanatory. Each of the threesuccessive accounts of the soul explains and grounds the preceding account,and is contained in the next. They are respectively universal, analogical,and cumulative. Let us consider them in more detail.2 IU 413,8-9; IL2 413,31-32; 413b24--27; II.3 414b16-19; 415,11-12. Cf. Me'. E.11025b34--1026,6.

210 Aristotle's Theory of the Unity of Science1. The Analogical AccountThe first, universaL account presents the soul as the first actuality of anatural organic body potentially having life (11.1 412b4-5). Before introducinghis second account of the soul at 11.2, Aristotle says that this firstaccount is more evident to us (tK cpaV€PWTEpWV) rather than more familiarin account (KllTa TOV AOyov yvwP'/,-WT€pov), and that it plays the role ofthe conclusion of a demonstration rather than the middle, as a definitionshould (413a11-20). The first definition is too general to deduce all the perse accidents of the soul from it. Though it tells us something about souls, itdoes not tell us what soul is, since soul is not a Single general thing. In theTopics (V1.10 148a25-26) Aristotle had already cast this problem in termsof homonymy: '[IJf the definition applies in a like manner to the wholerange of the homonym, it does not define any of the objects described bythe term. ,3 Life is homonymous, he goes on to say, and there is no singledefinition that holds good for both animals and plants. Dionysius' accountof life, which Aristotle quotes in the Topics passage as 'movement of acreature sustained by nutriment, congenitally present in it,' is common toplants and animals, but is not the definition of either because (W'I namesparticular kinds of life, not an abstracted and general concept of life 4 In3 There is no mention here of ordered series, or what kind of homonyms we are dealingwith, and Aristotle does not suggest that some kind of homonyms can be gatheredtogether under one definition. Owen (1960, 187) notes the Topics position as a stagealong the path to the final position in the DA. Comparing the use of 'focal meaning'in metaphysics and psychology, he remarks, '[Alt the same time there are largedifferences in the two uses of focal meaninSt and we are not concerned with thepsychology.' A more thorough study of the DA forrilUlation could well have alteredsome of his conclusions, especially his depreciation of the role of analogy (192-3): hedenies that analogy engages in studying 'a particular connexion between the definitionsof a polychrestic word ... [I]t is merely to arrange certain tenns in a (supposedly)self-evident scheme of proportion.'4 We find a similar test for homonymy in APo II .13 (97b7-15):We should look at what are similar and undifferentiated, and seek, first, what they allhave that is the same; next, we should do this again for other things which are of thesame genus as the first set and of the same species as one another but of a differentspecies from those. And when we have grasped what all these have that is the same,and similarly for the others, then we muSt again inquire if what we have grasped haveanything that is the same - until we come to a single account; for this will be thedefinition of the obje

211 Cumulationthe DA Aristotle elaborates this argument by introducing the language ofdemonstration as a way of explaining the homonymy of the objects. AtII.2 he sets aside the common 'definition,' and turns to the species of soul.We can deduce from the definitions of the species both their specific per seaccidents and the general account, which is posterior (414a17-28). This isnot to say that Aristotle considers the conclusion of the first chapter false,but its status is down-graded from that of a first principle to a theoremof psychology. He can prove the first' definition' by means of the secondusing the same scheme as we used for longevity;first actuality of a certain body IPQ that in virtue of which things live(414a12-19)that in virtue of which things live IPO nutrition, sensation, intellect(413a22-25; bl-2)nutrition, sensation, intellect IPQ soul (413bl1-13)first actuality of a certain body IPQ soul (414a27-28)From the conclusion we can further deduce that the soul is not separablefrom the body, since inseparability from the body is predicated of the firstactuality of a certain body. Since soul is homonymous in the sense thatmany values can be substituted for it, the conclusion must be proved foreach of the homonyms S Although Aristotle's argument is not so neatlylaid out as this, it is clear that he reaches this conclusion at the endof 11.2.When Aristotle claims that living (TO 07v) is homonymous (413a22),he is not denying that plant and animal life have something in common.What he denies is that the definition in accordance with the name is thesame in each case. When we answer the question 'What is it for this plantto be alive?', we say that it absorbs nutriment and grows. When we answerof which they are called high-minded, but two, unwillingness to brook insult andindifference to misfortune. If there is some attribute common to both, say self-respect,it is secondary and explained by the two kinds of states of the soul. The fact thatunwillingness to brook insult is manifested in different actions, withdrawing from thefight (Achilles), committing suicide (Ajax), and making· war (Alcibiades), does not meanthe 'unwillingness to brook insult' itself is homonymous. These actions are not kindsof high-mindedness, but rather the results of high-mindedness. Unwillingness to brookinsult is not part of the concept of committing suicide, even though it may be a resultof it in particular cases. Such cases are contrasted with animal, which, at least in theCategories, is predicated of man and ox in virtue of the same account of substance.S Bolton (1978) has proposed that the definitions of the soul in Il.1 (he counts four) areindeed proved by the definition of Il.2, but they are proved generically.

212 Aristotle's Theory of the Unity of Sciencethe question for animals, we say 'It moves and has sense perception.' If wegive the most general account that will cover all the cases, it will make nomention of any faculties in virtue of which we sayan animal is alive. Sincewe say something is alive in virtue of its thinkin~ perception, nutrition,growth, and so on, we say that so long as there is one of these facultiespresent, a thing is alive (413a22-25). There is not a single set of necessaryand sufficient conditions for life; there are many sufficient conditions orcauses. For a plant to be alive, it must have nutrition. For an animal tobe alive, it must have sensation, and what it is for animal to be and to bealive are the same thing. But as we saw in APo Jl.l7, there cannot be twodifferent causes of things that are the same in species; so where there aretwo causes, the things caused must be different, and so the actuality of thebody potentially having life in it will be different in each case.There are several other reasons why Aristotle should adopt the analogicalstrategy in the case of the souls. As a result of the analogy, inseparabilitycannot be proved universally for all the kinds of souls, but onlyspecifically for each kind. This fact is of advantage when Aristotle comes todeal with voi), 6 For the fact that there is no general proof for inseparabilirymakes it easier to accept the possibility that there may be an instance ofsoul that is not the actuality of some body. If we admit a case of separabiliry.- and Aristotle must prepare for it, even if he does not immediately dealwith it - the universal/definition' of soul is incorrect. If vovs is a faculty ofsoul and is separable, it cannot fall under the common definition provided,and must be related to soul, or be soul, in some other way. The analogicalaccount of soul provides a solution both to the separation problem and thesecond, parts / whole problem.Moreover, the fact that the general account is couched in terms ofactuality and potentiality without a specification of a particular actualityand potentiality should remind us of the warnings Aristotle issues regardingthe analogy of principles in Metaphysics A. Moreover, as we haveseen, definitions as well as terms can be ambiguous (e.g., the definitionof 'quick' in Phys. VII.4), and the general account of soul contains anambiguous term, 'life.' Thus, the actualities and potentialities mentioned6 Bolton 1978 deals more extensively with this feature. I think he is generally right insaying that there is no fundamental contradiction between the hylomorphic view of thesoul in the VA and the unembodied soul of the unmoved mover. Aristotle is almostcompletely consistent in his resolve to deal with soul only among 8v'T/TCt. I disagree withBolton, however, that there is a generic definition of soul. Like Hicks, he assimilates theserial problem to the nonnal dependency of the genus on the species. More recently,G. Matthews (1992, 190-1) has also tried to discover a generic definition of life.

213 Cumulationare of different sorts of things, and this is sufficient to eliminate the generalaccount as a universal definition.Finally, the analogical strategy also suits the basic Greek conceptionsof the soul. It is among humans primarily and, through theories of transmigrationof sout among other animals too, that the traditional Greeknotion of tvx~ is most at home? For Greeks it is an extension of theterm to apply it to plants. Aristotle complains that previous thinkers hadconfined their discussions to human soul (1.1 402b3-5), but in fact theywere doing nothing more than following common conceptions. But thecommon conceptions are also the source of the homonymy. Since "'VX~ isa term that applies first and best to humans and to what human beings are,Aristotle and the Greeks in general find it more natural than we do to saythat man lives by virtue of his intellectual soul. It would be for Aristotlean abuse of the term to say that human "'vX~ is a "'VX~ in virtue of itsvegetative functions. Moreover, the higher faculties are in some way thepurpose of the lower faculties, and thus are the most important part of thedefinition of higher living things. When Aristotle extends "'vX~ to otheranimals and plants, they must be alive in virtue of some other faculty thanintellect. For all these reasons, the analogical strategy seems more suitablethan the universal.But the analogical account does not do full justice to the phenomena.Whereas among the biological analogues there was some common essentialfeature to which all the analogues were related, but that was not theirgenus, Aristotle has not yet provided any common feature among thesouls, which would serve as the framework for drawing analogies.' It isclear that it cannot be a common function, since the souls are themselvesfunctions and are fundamentally different from one another. What, then,prevents the homonymy among the souls from being chance homonymyor the analogy between them from being pure metaphor? Aristotle has twoanswers. First, from the definition of each subject separately we can deduceat least one shared property that only those subjects have. But that sharedproperty, to be an actuality of a natural organic body, is defined in termsof the matter rather than the form, and so hardly provides an adequateconnection among the souls themselves. The second and more compellinganswer is that the souls are related among themselves by a variety of per se7 For some of the limited evidence on animal and especially plant souls, see Bremmer1983, 125£f.8 Hamlyn (1968, 94), who rightly subscribes to the 'empty' theory of the generaldefinition, suggests that the general definition will be uninformative because it willleave out the crucial fact that the species are serially ordered.

214 Aristotle's Theory of the Unity of Sciencerelations, which have the effect of gathering together the several subjectsof study. The souls fonn a group because of their serial order and theirdefinitional inclusion relations. This does not make them a Ka8' EV genus,but it does legitimate their being treated under the same study.2. The Cumulative AccountThe second half of DA 11.3 answers the first aporia, concluding that thereis no genus soul, and explaining how instead the souls are related to oneanother. Here Aristotle considers the serial nature of the faculties and itsimplications: the faculties of the soul are cumulatively organized. While itis true that any faculty of the soul is a sufficient condition for life, in fact,only the vegetative soul can be found apart from the other faculties. Thisfact complicates but does not nullify the analogical relationship betweenthe faculties. It shows that the causes, which have been so far treated onlyas analogical, are related in some more intimate way. Aristotle explainsthe implications of the serial order of the soul faculties in a difficult andcontroversial passage:It is now evident that a single definition might be given of soul in the same senseas one might be given of figure. For, as in that case there is no figure apart fromtriangle and those that follow in order, so here there is no soul apart from theforms of soul just enumerated. There might be a common definition given forthe figures which will fit them all, but it will not be the peculiar definition ofany figure. So here in the case of the aforementioned souls. Hence it is absurd inthis and similar cases to look for a common definition which will not express thepeculiar nature of anything that is and will not apply to the appropriate indivisiblespecies, while at the same time omitting to look for an account which will. Thecases of figure and soul are exactly parallel; for in both the case of figures andliving beings the predecessor is potentially contained in each successive term, e.g.the triangle in the square, the nutritive in the sensory power. Hence we must askin each case, What is its soul, i.e. What is the soul of plant, man, beast? (modifiedROT; 11.3 414b19- 33)The two basic features of cumulation are clear from this passage. First,souls and figures form series by adding some factor to a prior memberin order to form a posterior member. Second, the addition does not alterthe category or basic type of the object, that is, the addition of a triangleto a triangle creates another figure, and the addition of sensitive facultiesto nutritive faculties creates another kind of soul. This is in contrast tofocality, where the addition of 'operation of' to 'doctor' creates an object

215 Cumulationof a different category from that of the focus term, 'doctor.' Yet in spite ofthe explicit comparison between figures and souls, there are several waysin which the likeness is inept. Since this passage is the locus classicus forcumulation, it is important to examine in detail how the example of figuresis inappropriate for Aristotle's purpose. I shall subsequently argue that adifferent example concerning types of citizenship found in the Politics ismore apposite.There are some important differences between figures and souls.Whereas the figures form a potentially infinite se ries, the souls form afinite series; and whereas the figures are generated by the same additionat each step, the generation of the souls requires a different addition. 9 Forthis reason sensitive and intellectual soul cannot be analysed into vegetativesoul, as if three digestive systems connected together could make a mind.Furthermore, if this passage is taken as a denial of a genus of figure,then Aristotle ·is not entirely consistent with himself. For at Met. 6.28(1024a36-b3) he says that plane is the genus of plane figures and thateach figure is a plane of such and such a kind (€"i"dlov TOLOVOi) .There are also difficulties in understanding the nature of the seriesitself. Though Aristotle says that the predecessor in the series is potentiallycontained in each successive term (a Et yap EV T'i' Ecpefr, !> irmipX€L l>vvaf-L€L TO"ponpov), he does not explain what he means by potential containment.In view of the fact that he is looking for a definition, it is reasonable tosuppose that the containment is logical, if nothing else besides. However,it is clear from the term l>vVaf-LEL that this containment is not explicitdefinitional containment. This is also clear from the examples: the squareis not defined in terms of triangle, though it necessarily contains twotriangles in it; the sensory power is not defined by nutrition, though itpresupposes nutrition. Natural priority also seems to be at issue, at least inthese examples. The prior member can exist independently of the posterior,but the posterior cannot exist without the prior (415al - 11). In the contextof psychological faculties this natural priority can also be described ashypothetical necessity: if an animal is to have sensation, it must have thenutritive faculty to sustain it (d. PA I.l 640a34-35). Nutrition, therefore,is not present in the essence of sensation, but is necessitated by it. In thegeometri cal context, the triangle is naturally prior, since if there were notriangle, quadrilateral could not exist.Most important for our purposes is determining the role of the generalaccount of the series, for Aristotle says, ' [T]here might be a common9 Cf. Met. 1.2 l054a3-4, where the triangle is the uni t measure of rectilinear figures.--- ------ - ~

216 Aristotle's Theory of the Unity of Sciencedefinition given for the figures which will fit them all, but it will notbe the peculiar definition of any figure.' Concerning this difficulty thereare two interpretations. First, by drawing on parallel passages at EE 1.81218al-9, EN 1.6 1096a17-23, and Met. B.3 999a6-14,'0 one can arguethat it is impossible for objects arranged in a series to form a genus.Aristotle provides a dialectical and ultimately unsatisfying argument forthis position. Although these passages use series of mathematical objects,including figures, and so support the contention that Aristotle intendedto deny a genus of soul in our passage, they are all polemic argumentsagainst the Platonists, and rely on premisses granted by them to refutetheir own position. For this reason the denial of a genus over a series neednever have been an Aristotelian doctrine. This interpretation, however,has become orthodoxy, and whether or not it has been viewed as a validargument, most scholars agree that Aristotle intended to apply it to hisseries of souls. It will be necessary, in consequence, to spend some time inits refutation and to argue that although it is valid for a Platonic contextand a Platonic understanding of genus, Aristotle could not have used theargument in his own voice. The second interpretation of the difficultybegins by comparing a different form of the series argument found atPol. III.1 1275a34-b5 concerning forms of citizenship, and argues thatAristotle did not intend to reject a genus of souls on purely logical, butrather on pragmatic, grounds. That is, when objects are arranged in aseries, their genus contains so little of causal significance as to be negligible.This second interpretation seems to be better adapted to the DApassage, and relies on peculiarly Aristotelian doctrines of demonstrationand explanation.The first, dialectical interpretation receives its clearest expression in thecontext of the refutation of the platonic idea of the Good in EE 1.8:[I]n things having an earlier and a later, there is no common element beyond, and,further, separable (xwPW"Tov) from, them, for then there would be something priorto the first; for the common and separable element would be prior, because with itsdestruction the first would be destroyed as well; e.g. if the double is the first of themultiples, then the universal multiple cannot be separable, for it would be prior tothe double ll ... if the common element turns out to be the Idea, as it would be ifone made the common element separable.10 The Metaphysics argument intends to do away with separate genera altogether,showing that they are secondary in every case, and not just among series of prior andposterior.11 There seems to be a lacuna here in the text. See Woods 1992, 72.

217 CumulationEN 1.6 1096a17-23 assures us that this argument had a Platonic origin, andwas used to deny Forms over Form numbers and over any other series inwhich there was prior and posterior. Aristotle turns the argument againstthe Platonists by showing that trans-categorials like the good, among whichsubstance is prior, cannot have a genus.Even in its Platonic contex~ the motivation for the argument is notundisputed. There are those who hold, contrary to Aristotle's express statement,that the argument is directed specifically and solely against Formsof Form number. Their position can be outlined as follows. Plato identifiedthree kinds of numbers, sensible, mathematical, and Form numbers. Themathematical numbers (we can ignore sensible numbers) are combinablewith one another and subject to all manner of ordinary mathematicaloperations. They are eternal and without matter, but there is a multitudeof each kind so that, for example, two can be combined with another twoso as to make four. Of Form number, by contrast, there is only one ofeach kind, Oneness, Twoness, and so on. These numbers, being Forms,cannot change or undergo operations. They cannot be divided so .as tobecome other numbers, for in that case they would admit of becoming andnot-being. Unlike mathematical numbers, Form numbers exhibit an orderof priority and posteriority, since their unchanging Oneness, Twoness, etc.make them well suited to staying in their appointed order.Cook Wilson, the champion of this view, asserted that there is noForm of Form numbers because Form numbers are aa1;M{3A:TlTO~, incomparablewith one another, and therefore uncombinable; and because thenumbers are incombinable, they form series of prior and posterior overwhich there is no Form or genus. This uncombinability stems from theirbeing Forms, since no Forms can be combined with one another. 'Theyare entirely outside one another, in the sense that none is part of another.Thus they form a series of different terms, which have a definite order.'l2This interpretation does go some way towards explaining why they areuncombinable: if the Two and the Three were combinable so as to makeup the Five, then the Three will be part of the Five. But it does not explainwhy their uncombinability entails their forming a series of priority andposteriority. After all, in order to be related as prior and posterior, Formnumbers must be related to one another, even if they are not part ofone another. Making them uncombinable and incomparable is precisely totake away the grounds upon which they may be compared as prior andposterior. The Two cannot be prior to the Three in generation, since Form12 Cook Wilson 1904, 253; d. Cherniss 1944, 513- 14.

218 Aristotle's Theory of the Unity of Sciencenumbers are not generated; nor can it be prior ontologically, since oneForm does not depend on another for its existence; nor logically, since inthe realm of the Forms logical priority is identical to ontological priority.What makes the Two prior to the Three, if not the fact that the Three isOne more than the Two? Form numbers must either be combinable or theycannot form a series. Contrary to Cook Wilson, then, the uncombinabilityof the Form numbers, far from providing a sound reason for priority andposteriority, destroys any possibility of there being a series among thernYNot only is the Form number interpretation of the argument suspecton its own grounds, but Aristotle also states that Platonists considered theargument valid in all series of prior and posterior, and not just among Formnumbers.14 Michael Woods, while adduCing reasons why such an argumentcould not be held by Platonists at all, suggests a different approach to thePlatonic argument, one that neither relies on the uncombinability of Formnumbers to ensure their serial order, nor restricts the series argumentsolely to Form number. In the main issue he is correct. Woods's interpretationrelies on seriality to show that there can be no genus, and assuch has the virtue of being consistent with Aristotle's claims about theargument. He points out that the Form of the Form numbers will be priorto the Form numbers, and because of the self-predication of the Forms, theForm of Form numbers will also share in the essential features of Formnumbers. But he argues that the Form of Form number will be prior in adifferent sense from that in which the first member is prior to the second:'[TJhere seems no good reason why a holder of the theory of Forms shouldretain the premiss that the number two is, without qualification, the firstnumber. It may be the first number in the number series, but there seems13 For variations on the Cook Wilson thesis, see Burnyeat 1987, who claims thatincomparability is the Aristotelian incomparability of the constituent units of eachForm number.14 Cherniss charged that Aristotle misunderstood Plato's argument in a way that affectshis own prior-posterior arguments. He argued that the Platonist argument was intendedonly for application among Form numbers, that the priority and posteriority hereis numerical order and not ontological priority and posteriority (1944, 522); thatAristotle's criticisms, which imply that the Platonists did not distinguish between thetwO senses of priority (first in the sense of ideal and first in the sense of first term of aseries), is belied by the fact that the Platonic 'first one' and 'first twO' etc. (mentionedMet. 1081b8-10) did not imply a series of ones and twos, etc. (520). Cherniss contendsthat when Aristotle extends the prior-posterior argument beyond mathematicals bygeneralizing the argument and making it hold good in every case of ontological priority(to which, citing Met. 1019a11- 12, Cherniss claims Aristotle reduced all other forms ofpriority), the argument that had been inappropriate against the Platonists suffices forhis purposes to show that there cannot be a genus of things arranged in a series.

219 Cumulationno reason why a holder of the theory of Forms should continue to holdthat it is the first number in every sense, if he holds that each Form is priorto its particulars and is itself a possessor of the character it represents. TheForm of number will itself be a number, and in an appropriate sense priorto any member of the number series. /1S Contrary to Woods's assertion,however, there is no reason to suppose that the Platonists did not acceptthe full implications of their own argument, and admit that the Form ofForm number will become the first member in the number series. For thepower of self-predication entails the Form's inclusion in the series, andtherefore makes the Platonic argument valid for (Aristotle's interpretationof) Platonic metaphysics: since it is an essential characteristic of the Formnumbers to be members of the series of Form numbers, the Form of Formnumber must also share this characteristic, that is, it must be in the seriesof Form numbers, and since it is also prior to all Form numbers, it willbe prior to the first in the series. If we emend Woods's interpretation inthis way, the argument does what Aristotle says it is meant to do. Forhe says that the Platonists denied Forms over series of prior and posteriorthings generally, and not only over Form numbers. This argument holdsgood in all cases where members of series are essentially serial, and forthe Platonists that will occur wherever Forms are serially ordered. It alsoshows how being a series prevents there being a genus of it, and does notrely on the obscure argument from uncombinability.Problems arise, however, when we suppose that Aristotle accepts theargument as his own and applies it to the soul series. To create an Aris~totelian metaphysical framework for the argument we need only changethe meaning of XWPLrrTOV from 'separable' to 'logically or conceptuallydistinct.'16 The denial of the genus is established by two sub-arguments.First, it is a fact about series that the first element is a member of the series,a subject alongside all the others, for all that it may also be the principleof the series. If it were to serve as the genus of the series, the membersof the series, including the first member, would become its species. Theidentical thing, the first member, would have to be both a species and itsown genus; and this is impossible, since a species is distinct from its genus.This argument is sufficient to eliminate the first member of the series as acandidate for genus. Second, it is necessary to argue that there is nothing15 Woods 1992, 71.16 Bonitz's Index (1961, 86Oal1-21) identifies a use of XWpKHV meaning 'ratione et notionedistinguere: used principally for the function that the differentia discharges: Tau WlOVT17~ oixrias £.occlOTO'U '\o)'ou Ta,~ 7f€pl E.ocaOTou oua:ia,~ lllacpopatr XWpi(HU dWOalJ.(U (Top. 1.18l08b6). According to this use XWptOTOU means 'distinct.'

220 Aristotle's Theory of the Unity of Sciencecommon to and distinct from all members of the series including the first.Such a thing would be an element in the logos of all the members of theseries. Aristotle's argument at a very dialectical level might be that suchan element would be prior to the first member (TOi) 7rPWTOV 7rpOTEpOV), andnothing can be prior to the first. This argument is based on the implausibleassumption, as Woods points out, that priority is univocal and that the firstmember of the series cannot be preceded in some other way; for we cangrant that a genus will be prior without admitting that it must be the firstmember of the series.For this reason, Aristotle might make the stronger claim that theprospective genus must become the first member in the series displacing thepreviously first member. He describes this prospective genus as common,distinct, and naturally prior. But the prior members of the series are alsodescribed as common, distinct, and naturally prior to the posterior members(d. t..ll1019a3ff.). By describing the genus in such a way that it has allthe same logical characteristics as a prior member, Aristotle might arguethat the genus will become the new first member of the series. And ifthis occurs, then the genus is identical with one of the species, and this isimpossible.Such an interpretation provides a fine description for a Platonic genus,but does some violence to Aristotle's notion of genus and consequentlyfaces serious difficulties in explaining why this argument would apply tothe souls17 The Platonic genus is naturally prior to the first member of theseries, is common and separable, and this will make it into the new firstmember of a Platonic series. 18 But this does not fit Aristotelian doctrine. Forif the common element were an Aristotelian genus, the difference betweenit and the original first member would have to be the specific differentia ofthe original first member, and since we are supposing that all. the membersof our new series have the same logical relationship to one another, thegenus-species relationship, which holds between the new first member andthe original first member, will hold between all the subsequent membersof the series. The result will be that the series is merely an extendedgenus-species string. 19 Since the series will form a string, each successivespecies will be differentiated by the differentia of the preceding differentia,in the manner of Met. 2.12's footed, cloven-footed model. But Aristotle'sargument never explicitly assumed that series create genus-species strings,and a consideration of the applications of the argument amply shows that17 Chemiss 1944, 513ff.18 For these characteristics of a Platonic genus, see Met. B.3 999a16-23.19 This position is defended by A.c. Lloyd (1962) .

221 Cumulationthe assumption is absurd: a quadrilateral is not a species of triangle nor asensitive soul a species of nutritive SQu1. 20 Posterior members are not 7TOtaof prior members. On logical grounds also it is impossible: there cannot beonly one species of a genus, but this is what this argument entails. 21 TheEE argument against the genus of series, then, seems to be better adaptedto Platonic than to Aristotelian logic and metaphysics.So far, then, the dialectical interpretation of the DA passage providesonly unAristotelian reasons for denying a genus over a series. There is,however, an alternative interpretation. There are two contexts in whichAristotle uses the prior / posterior argument in his own voice, our DApassage and in the Politics, and in neither passage do we find the dialecticalformulation for the rejection of genera of ordered series. Instead, other,pragmatic reasons are offered. At Pol. III.1 1275a34-b2 Aristotle discussesthe definition of the citizen:But we must not forget that things of which the underlying things (imoIH:i,uwa)differ in kind (njJ Ei'OH), one of them being first, another second, another third,have, when regarded in this relation (Y TOtaVra), nothing, or hardly anything,worth mentioning in common. Now we see that governments differ in kind, andthat some of them are prior and that others are posterior; those which are faultyor perverted are necessarily posterior to those which are perfect. (modified ROT)The passage itself seems clear as far as it goes. Unlike the previouslyconsidered passages, Aristotle does not deny that there may be some commonalityamong the citizenships, only that this commonality is negligible.This is quite a different objection from arguing on dialectical grounds thatper impossibile the genus will become the first member of the series. Thepassage suggests that, when the objects are arranged in a series en TOLaiha),the first member is contained in all the others, and therefore by treatingit, one not only treats something that is explanatory, but also everythingthat is common to the series. Accordingly, he leaves open the possibilitythat there may be some arrangement other than a series in which there issignificant generic commonality.This is borne out in Aristotle'·s discussion of the citizen. The definitionof the first citizen is provided immediately prior to this passage, a definitionthat he says is most adapted to all those who are called citizens (}.ta)u(1T'au Ecpapp.oCTa~ OPLCTP.O~ E7T1. 7T(iUTa~ TOV~ A€yOP.€UOV~ 7TOAtTar; 1275a33- 34):20 Cf. Me t. A.9 992a18- 19 for a similar series; ' [TJhe broad is not a genus which includesthe deep, for then the solid would have been a species of plane.'21 So Top. 1.5 102a31· b3.

222 Aristotle's Theory of the Unity of Sciencethe citizen is one who shares in the indefinite offices (deliberation andjudicial administration) of the state (1275a30-33). For the real power ofthe state resides in these offices, which have no fixed tenure. As it turnsout, however, some bona fide citizens do not fit this definition. For hesays (1275b5-6) that the definition is best adapted to the citizen of thedemocracy, which is only one of the perfect constitutions (aristocracy andkingship being the others). In Sparta and Carthage, by contrast, it is onlythe holders of the definite offices who are admitted to deliberative andjudicial offices, and therefore they are not indefinite officers. That is, theyhold executive offices for determinate lengths of time, and they judge anddeliberate ex officio. Aristotle is unwilling to emend the definition so asto make any office-holder a citizen, because he thinks that the citizenis the one who has the power in the state, and the power is exercisedthrough deliberative and judicial function, and not, say, through being anoverseer (a Spartan ephor). For this reason, Aristotle treats the Spartancitizen as a perversion of the perfect citizen. Accordingly, he provides asecond definition, 'whoever has the power (itovCTia) to have a share indeliberation and judicial administration' (1275b18-19)." This definitionpotentially contains perfect citizenship insofar as it covers perfect citizenship,but it does not define it in the strict sense that the first definitiondoes. The difference between the two definitions seems to consist in this:the democratic citizen, who holds the indefinite offices, is a citizen mostof all, since he has a penn anent hold on these offices and exercises themthroughout his life. The Spartan citizen, who holds definite offices, haslimited opportunity to be a citizen; and limited in two ways: limited in timebecause of the definite tenure of the office, and limited in extent, since thedeliberative and judicial job is split up among the various definite offices.The second definition is more generaL in the sense that it will include thedemocratic as well as the oligarchic citizen, but it is also defective becausein the addition of the itovCTia clause is contained the notion that the exofficio potential for citizenship activity is sufficient to qualify as a citizen.In those respects in which the second kind of citizen is similar to thefirst, it is similar because it is related to the first, that is, it is a perversionof the first. The first member, then, will appear in explanations concerningthe second, but not vice versa. In the investigation of the citizen we should22 Irwin 1990, 82, has sensibly argued that the first definition is not annulled by thesecond, but that they are serially ordered. He provides a different reason for the order:the first definition is first because it accounts for the fact thaI in order for the citizento be good, he must rule as well as be ruled, and this is not ensured by the Spartan orCa rthaginian constitution.

223 Cumulationexpect the majority of the attention to be paid to the judicial and legislativefunctions of indefinite tenure and only secondarily to the definite executivefunctions. It is clear that citizenship can be studied in its most commonform, but to treat it as a set of differences within a genus would ignore thefact that the second form is a perversion of the first. The genus arrangementwould neither capture citizenship in its fullest sense, nor would it call uponthe explanatory principles central to understanding the deficient citizenshipas deficient.Now, the series of citizenships is in some important respects differentfrom the series of souls. It is a perfective series: the definition of the firstform of citizenship is logically prior and is somehow contained in the definitionof the second on the basis of the 'better and worse' relationship (ef.Met. B.3 999a13-14). Moreover, the citizenships are not arranged by ontologicaladdition, nor by natural priority; rather Spartan and Carthaginiancitizens are included as citizens on the basis of a qualification to the firstform of citizenship. In spite of these differences, the common account ofthe souls is vacuous for the same reasons. Though the second account ofcitizenship will cover all cases, we should first explain democratic citizenshipand its legislative and judicial functions, since that is where the realcitizenship power resides, then turn to the executive functions of Spartancitizenship and their relationship to the authoritative functions. Similarly,Aristotle does not deny that there is a general account of the soul, he onlysays that it is absurd to overlook an account that will treat the peculiarnature of the serial objects. Though 'the actuality of the potentially livingbody' is common to all the souls, it only explains inseparability of the souland body. What are most important for explanations are the particularfaculties of the soul and their per se relations among one another.If the members of the series do not form a strong generic unity, whatmakes them a Single group, that is, what are the principles of extendingand limiting the series? First, each requires a non-nindom addition to themember before it. The prior member is the precondition for the posteriormember. DA III.12 provides a more detailed account of the faculties in theseries: nutritive soul is first, because it is necessary for all living embodiedthings. As such, it can be treated as an independent and per se subject. Tasteis a sort of touch and is relative to nutriment, which is tangible body. Forthis reason, taste and touch presuppose nutrition (which is now relativeto them) and are next in the series, first among the senses. Imaginationdoes not occur without sensation, nor thought without imagination. Inthis way a prior faculty can be treated both per se and as related toa posterior through hypothetical necessity: the relations of hypotheticalnecessity establish the order and explain the reasons for that order.

224 Aristotle's Theory of the Unity of ScienceSecond, we need something that will limit the series at the beginningand the end. After all, what prevents something causally significant andlogically prior to the first member from being included in the soul series?For example, just as nutritive soul is prior to sensitive soul, so the naturalchange of simple bodies is prior to the nutritive soul. Why should thenatural change of simple bodies not be such a member? To say that thisnatural change is not life is to beg the question, since life is said in manyways and the only thing binding homonyms together is their serial order,in which natural change also participates. It is clear that the series isgenerated, but not limited, by logical potential containment. The limits ofthe series come from the posterior commonality that the members of theseries generate, specifically from the material component. Natural changeof simple bodies cannot be included in the series, because simple bodiesare not organic. Every faculty of the soul per se must be in an organicbody. The common account, then, provides a common feature that limitsthe series both at the beginning and at the end. For there is no activitythat is logically prior to nutrition that requires an organic body, and thereis no activity logically posterior to embodied intellect that in its own rightrequires an organic body. Nevertheless, 'having an organic body' cannotbe the genus of soul, because the genus must be the genus of the form,not the matter. 'Having an organic body' is not what the soul is.The cumulative soul series, then, introduces us to a new form of organizationamong subject matters. The subjects are generated by a seriesof additions. The additions are ontological, in the sense that one faculty isadded to another faculty, but the relationship between the members is oneof natural priority and hypothetical necessity, that is, the posterior facultyrequires the existence of the prior. The members of the series share acommon account that is not the account of their genus, but rather of theirmaterial correlate. Nothing prevents such subjects from having a genus,but it is unlikely that the genus will explain much that the first memberof the series does not.FriendshipAristotle trears friendship both in the Eudemian Ethics and the NicomacheanEthics. In both works he distinguishes three kinds of friendship,those based on virtue, pleasure, and utility. In the Eudemian Ethics Aristotlecharacterizes the relationship between these three kinds as focal, butin the Nicomachean version he speaks in terms of similarity (op.oiwp.aand Ka(J' O,uoLoT17Ta). The Ka8' o,umoT11Ta solution is characteristic of manydiscussions in the EN, and has close affinities to cumulation and analogy.

225 CumulationThere has been much discussion as to whether Aristotle changed his mindabout the relationship between the kinds of friendship. I think he did,but not in the way or for the reasons often attributed to him. I interpretthe shift not in terms of a general chronological development away fromfocality, but as a realization that the focal analysis of friendship does notdo justice to the phenomena. 231. Eudemian Ethics and the Problems of Focal FriendshipIn the Eudemian version Aristotle argues at length for a focal arrangementof the ends of friendship and, therefore, of the friendships themselves.24The argument we are concerned with appears in EE VII. 1-3, of which thefollowing is part:[W}e must attempt to .gain clear distinctions, starting from the following principle.The desired (OP€KT()V) and the wished for (f3ovA71TOV) is either the good or theapparent good. Now this is why the pleasant is desired, for it is an apparent good;for some think it such (OOKt:L), and to some it appears such (~aiVf.TaL), though theydo not think so (om,V) . For appearance and opinion do not reside in the same partof the soul. It is clear, then, that we love both the good and the pleasant. (VII.21235b24-30)Before this passage Aristotle discussed the opinions of others (ooKOvvm)and the aporiai; now he lays down a principle that states that the objectof desire (OpEKTOV) and wish (f3ovl\~TOV) is either a good or an apparentgood. From this principle and the fact that the pleasant is an apparentgood, Aristotle concludes that both the good and the pleasant are objectsof desire.23 So also the conclusion of Price 1989, 148: '[WJhile the EHdemian Etllies offers anexplicit statement (of focality) that is clearly less than successful and satisfactory,the Nicomaellean offers a less explicit analysis that seems much more apt to thesubject-matter ... ' See his chap. 5 for a significantly different analysis of the focalrelationship.24 The details of the argument have not been carefully studied by those who havebeen concerned with the question of focality. Owens (1989) makes no mentionof this section, and speaks of the focal relationship in terms of imitation (136-7).Berti sees the Significance of the argument, but treats it only briefly (1971,176). Moreover, he says that just because a focal relationship holds benveen thethree objects of friendship, there must also be a focal relationship between thefriendships themselves. Rowe (1971, 57-60) sees no difference in purpose betweenthe nvo passages, but considers the EN presentation a misleading version ofthe EE.

226 Aristotle's Theory of the Unity of ScienceHe next introduces a second principle: some goods are good withoutqualification, others are good to somebody (1235b30-32). Throughan induction he argues (1235b33-1236a7) that what is pleasant withoutqualification is good without qualification." And since he has already laiddown in the first principle that what is pleasant to someone is good to thatperson, he can conclude that there are two kinds of pleasant things, ~bva7rAw< and ~M ny"~ of which the first is identical with the a.yaeov a7rAw and aya80v cbr'\'wS', and especially that thereare psychic as well as physical pleasures that fall into this category. He argues from theobvious case that what is advantageous to a healthy body is aya8ov, to what is pleasantto a health body is pleasant without qualification, and finally to what is pleasant toa healthy soul is pleasant without qualification. There is no explicit connection madebetween the pleasant and the good until the end of the passage, and this is stated as aconclusion: 'To [sensible and good adults] that which suits their habit is pleasant, andthat is the good and noble' (1236a5-7).

227 Cumulationbecause it is apparently good." Although both the pleasant and the goodare objects of desire, they are not coordinate species of desirables. The goodis prior, while the pleasant is posterior and dependent on the good.By establishing a focal relationship between the objects of friendshipAristotle prepares the way for a focal interpretation of the friendshipsthemselves. Since pleasure is definable in terms of the good - for it is theapparent good, if it is not the good itself - pleasure is said to be focallyrelated to the good (VII.2 1236a15- 33):There must, then, be three kinds of friendship, not all being so named for one thingor as species of one genus, nor yet having the same name quite by mere accident.For all the senses are related to one which is the primary, just as is the case withthe word 'medical'; for we speak of a medical soul, body, instrument, or act, butproperly the name belongs to that primarily so-called. The primary is that of whichthe definition is contained in the definition of all/ 7 e.g. a medical instrument is onethat a medical man would use, but the definition of the contained is not impliedin that of 'medical man.' Everywhere, then, we seek for the primary. But becausethe universal is primary, they also take the primary to be universal, and this is anerror. And so they are not able to do justice to all the phenomena of friendship;for since one definition will not suit all, they think there are no other friendships;but the others are friendships, only not similarly 50. But they, finding the primaryfriendship wiJI not suit, assuming it would be universal if really primary, denythat the other friendships even are friendships; whereas there are many species offriendship; this was part of what we have already said, since we have distinguishedthe three senses of friendship - one due to excellence, another to usefulness, athird to pleasantness.Later he explains further (VIl.2 1236b17-26):But those whose love is based on pleasure do not seem to be friends, when we lookcarefully, because their friendship is not of the primary kind, being unstable, whilethat is stable; it is, however, as has been said, a friendship, only not the primarykind but derived from it. To speak, then, of friendship in the primary sense onlyis to do violence to the phenomena, and makes one assert paradoxes; but it isimpossible for all friendships to come under one definition. The only alternativeleft is that in a sense there is only one friendship, the primary; but in a sense all26 Although apparent x's are not regularly listed as focal terms, we can compare the focalway in which that which is not known may be said to be known, Met. Z.4 1030a33-34.27 This is to accept Bonitz's emendation of 1fucn for ~J.Ltv .

228 Aristotle's Theory of the Unity of Sciencekinds are friendship, not as possessing a common name accidentally without beingspecifically related to one another, nor yet as falling under one species, but ratheras in relation to one and the same thing.It is clear here why the medical things are not one species or species ofone genus. In spite of their per se relations, they are different kinds ofthings, substance (man) and non-substances (actions, events, etc.). But theapplication of the principle here to friendship is much more problematic,and has been used to support the theory that the EE is earlier than theEN, which rejects the focal relationship in favour of mB' Ol'-o

229 Cumulationchildren or brutes, but to the adult is really pleasant; at least, when we rememberboth we choose the latter. And as the child or brute is to the adult man, so are thebad and foolish to the good and sensible. (VII.2 1235b33-1236a2)Aristotle implies a division into two kinds of desirables: those goods andpleasures that are natural and not peculiar to an individual in aberrantcondition, and those that are both cpaLVO/lEVa aya86. (apparently good) andaya86. TLV' (good to someone). The examples provided imply that cpavTaIT{aincorrectly affirms the not-good object to be good. Thus, an immatureperson will mistake the pleasant for the good. He must mistake his pleasurefriend for a virtue friend. Now, if the pleasant is to be focally related tothe good, pleasure must contain the definition of good in it. But equallythere are many pleasure friends who can accurately identify the basis oftheir friendship. There is no reason to suppose that every person mustsay of his pleasure friend that he thought he was a virtue friend andintend by 'virtue' what the word is defined to mean. We do not have tobe deluded or bad to have a pleasant friend whom we do not think to bevirtuous. If this is so, the focal relationship between pleasure and goodbreaks down.Aristotle is not wholly unaware of this problem. He treats virtue andpleasure friendship together and makes it clear that bad men are not capableof virtue friendship. Owing to their debility the pleasure they derive isperverted:Nothing prevents [bad men's] loving with the other kinds [0£ friendship]; forowing to pleasure they put up with each other's injury since they are incontinent.(modified ROT; VII.2 1236b15-17)The harm they do one another is a result of their perversion. Such a view,however, makes it impossible for a good man to pursue a purely pleasurefriendship, something Aristotle makes room for at the end of the chapter:For the bad may be pleasant to one another, not qua bad or qua neither good norbad, but (say) as both being musicians, or the one fond of music and the othera musician, and inasmuch as all have some good in them, and in this way theyharmonize with one another. (VIL2 1238a35-38)The pleasure friendship that a good man enters into cannot be for merelythe apparent good, for he would not in that case be good. Conversely,the pleasure friendship that the bad man shares with the good man is

230 Aristotle's Theory of the Unity of Sciencenot merely an apparent good, since 'all have something of the good'(1238b13-14). In order to save the phenomena, then, Aristotle assimilatespleasure friendships that are not actually perverted to virtue friendshipsby identifying the grounds of pleasure in some limited virtue.What is the result if we reject the focal principle in its present fonn?If we treat good and pleasure as independent ends but preserve the relative/absolute distinction for each in its own right, we eliminate the basis ofthe focal relationship. And, as we shall see, this is precisely what happensin the EN account.Clearly, though, Aristotle intended this argument to be the basis of hisclaim that the friendships are focally related. In order for the argument tosucceed, the cpawoJ.Lwou aya80v must appear to the bad man to be virtue,but in fact be pleasure; he must mistake pleasure for virtue. Since virtueis pleasurable, Aristotle may have supposed that the mistake would not beinfrequent.The characterization of the useful friendship also presents a problem forthe focal relationship. The EE seems to take the dependency of the usefulon the good as obvious, but it is clearly not the same kind of dependency asthat of the pleasant. For, as we saw, pleasure friendship was construed as akind of sick virtue friendship. A friendship is useful, however, because it isa means to other ends, like pleasure and virtue. Now, utility friendship isuseful for many things, among them virtue and pleasure friendships. Bututility friendship is useful for other goods and pleasures besides friendship,since friendship is not the only locus of virtue or pleasure. Although onecan easily argue that the useful is focally related to the pleasant and thevirtuous (and if the pleasant is itself focally related to the virtuous, thenthe useful is always ultimately focally related to the virtuous), the utilityfriendship is not focally related to the pleasure or virtue friendship. For thedefinition of utility friendship does not potentially contain the definitionof pleasure or virtue friendship, even though it may potentially containthe definition of pleasure or virtue. In spite of Aristotle's attempts, neitherutility friendship nor pleasure friendship can convincingly be brought intoa dependency relationship with virtue friendship.'o Pleasure friendshipscan be made focally dependent only if they are perversions of virtuefriendships, and utility friendships cannot be subordinated focally to virtuefriendships at all.30 Even the pleasure associated with virtue is different from the pleasure pursued asan end. So, for example, Aristotle asks (1.5 1216a33-37) whether for the good lifeit will be necessary to add pleasures, or whether it will be pleasurable in anotherway.

231 Cumulation2. The Nicomachean VersionIn the EN Aristotle makes no explicit mention of analogy or focality offriendship. But, just as in the EE, EN VII/'2 says that the problem of friendshipcan be solved if we first come to know the purposes of friendships, andby knowing the purposes we shall be able to make the distinctions. Sincethe purposes of friendship differ in species, so do the friendships differ inspecies (VIII.3 1156a6-8)31The most notable feature of EN VIII.2 is Aristotle's dismissal of thefocal relationship between the ends of friendship (1155b17-27):The kinds of friendship may perhaps be cleared up if we first come to know theobject of love. For not everything seems to be loved but only the lovable, and thisis good, pleasant, or useful; but it would seem to be that by which some good orpleasure is produced that is useful, so that it is the good and the pleasant that arelovable as ends. Do men love, then, the good, or what is good for them? Thesesometimes clash. So too with regard to the pleasant. Now it is thought that eachloves what is good for himself, and that the good is without qualification lovable,and what is good for each man is lovable for him; but each man loves not whatis good for him but what seems good, This however will make no difference; weshall just have to say that this is that which seems lovable.Aristotle assumes from the beginning that there are three ends of friendship,the good, the pleasant, and the useful, and asks whether one lovesthe good or what is good for oneself. Although his analysis of the problemconsiders only the good, the pleasant could be easily substituted. He impliesthat the ends are to be treated ,eparately for the purpose of his analysis,and makes no attempt to connect or relate the pleasant and the good. Inthis way he treats the good and the pleasant as independent objects oflove and, as a result, eliminates the basis for the focal arrangement. As forutility friendship, it is almost brushed aside, this time not because it is easyto fit into a focal arrangement (although it is), but because it is not an endin itself. This separate treatment for the three objects of love is picked upagain in chapter 3, where Aristotle considers the three kinds of friendshipin terms of their ends. Virtue friends love each other for themselves, butpleasure and utility friends abstract some feature from their friend that isof interest to them. The pleasant aspects of another person are abstractedfrom the whole person, and are not considered as logically dependent on31 bta

232 Aristotle's Theory of the Unity of Sciencethe whole person or on virtue friendship, which has as its object the wholecharacter of the other (1156a10-16). Pleasure and utility friendships areconsidered as abstractable parts of complete friendship. Thus, Aristotle'sefforts in the EE to construe pleasure as dependent on the good are overturned,and pleasure is treated as an independent end alongside virtue. Afocal arrangement on this basis is no longer possible. 32In the place of a focal analysis Aristotle arranges the friendships in amanner that in several respects is similar to the cumulative arrangementof the souls. First, he provides a general account that covers all the cases(me' EmITTOV, 1156a8-10) but that fails to be a definition:[W]ith respect to each of the aforementioned objects there is a mutual and recognizedlove, and those who love each other wish each other well in that respect inwhich they love one another (ad apa d)VOE~V clAi\~i\O~S' KUL f3ovAf.(J"ea~ Taya8a /J.r,Aav8avovTuS' at' Ell n TWV Elprfl.LEvwV). VIII.2 1156a3-5In spite of the fact that he is able to give a general account, he clearlysays that pleasure and utility friendships are only incidentally friendships(1156a16-17).33 They are incidental because one wants the friends' good,not for their own sake but in order that they may continue to be a sourceof profit or pleasure to oneself. That is not to say that pleasure friendsdo not wish each other well, but they do so insofar as they are pleasantto each other. The friend's good, then, may either be defined in terms ofoneself Oust as one is a friend to wine, in order that it may be preserved foroneself), in which case it is the friend's good only incidentally, or it maybe defined in terms of one's friend, for his own sake. 34 This distinctionmakes clear that the general definition contains at least one -ambiguousterm, en' EV TL TWV €ip1JJ1.€vWV and this casts doubts on the generic statusof the definition. 35Second, in the EN Aristotle both reverses and alters the dependencywe found in the EE, so that pleasure and utility friendship will be priorto virtue friendship in the series. No longer is virtue friendship containedin pleasure friendship, instead pleasure friendship is contained in virtue32 Gauthier and lolif (1959, ii, 686) quOte the EE passage on. focal meaning withoutmentioning the differences between the two presentations. They suppose that thesimilarity mentioned at 1157a32 (V yap aya.8olJ n Kat O},wtOlJ n. TaUT!! $ii\m) is the kindof similarity discussed in EE, which is certainly incorrect.33 KaTa (J"V}J.f3Ej37JK6~ TE 01) at $!ALa! aUral ELn-W.34 This is contrary to the opinion of Walker, who holds that the definition states thenecessary and sufficient conditions for all kinds of friendship (1979, 185).35 Cf. Phys. VIl.4 248b17-19 and the discussion above on the soul.

233 Cumulationfriendship. The nature of the containment has also changed. The term'pleasure friendship' is not contained in the definition of virtue friendship,but pleasure friendship is nevertheless implied in virtue friendship, and canbe proved to belong to virtue friendship because of the essential attributesof virtue friendship. So at EN VIII.3 1156b12- 17, Aristotle says:And each [virtue friend] is good without qualification and to his friend, for thegood are both good without qualification and useful to each other. So they arepleasant; for the good are pleasant both without qualification and to each other,since to each his own activities and others like them are pleasurable, and the actionsof the good are the same or like.Whether or not this argument is sufficiently articulated to constitute aproof, it is clear that virtue friendship is pleasant and useful because of itsown nature. The virtue friendship is not a pleasure friendship in the waya pleasure friendship is a pleasure friendship, since a virtue friendship isnot pursued for pleasure, but it is nonetheless pleasant, and presumablymore pleasant than a pleasure friendship. In a similar way, the definition ofthe sensitive soul does not explicitly contain the definition of the nutritivesoul, though it implies the existence of the nutritive souL Likewise, too,the nutritive soul is not the final cause of the animaL as it was for theplant, but rather is set in some causal relation, namely necessary condition,to the sensitive soul.Third, the series are also similar with respect to ontological priority andposteriority. Just as the nutritive soul can exist without the sensitive soul,but the sensitive soul cannot exist without the nutritive souL so there canbe a pleasure friendship without it being a virtue friendship, but a virtuefriendship must be a pleasure friendship.At the same time, there are features of the friendship series that aremore difficult to assimilate to cumulation of the soul type. Clearly, theutility and pleasure friendship are not serially related to one another,but only to virtue friendship. Again, Similarity (0I"0'OT'1< 1156b33- 1157a4)figures largely in Aristotle's description of the relationship between perfect(virtue) friendship and pleasure friendship, and this would be moreappropriate within a perfective series:This kind of friendship, then is complete both in respect of duration and in all otherrespects, and in it each gets from each in all respects the same as, or somethinglike what, he gives; which is what ought to happen between friends. Friendship forthe sake of pleasure bears a resemblance (of.LoiwJ.W.) to this kind; for good peopletoo are pleasant to each other. So too does friendship for the sake of utility; for. -----

234 Aristotle's Theory of the Unity of Sciencethe good are also useful to each other. Among men of these sorts too, friendshipsare most permanent when the friends get the same thing from each other.VIII.6 (1158b5- 11) gives a similar description:II]t is from their likeness and their unlikeness to the same thing that they arethought both to be and not to be friendships. It is by their likeness to the friendshi pof excellence that they seem to be friendships (for one of them involves pleasureand the other utility, and these characteristics belong to the friendship of virtueas well); while it is because the friendship of virtue is proof against slander andlasting, while these quickly change (besides differing from the former in manyother respects), that they appear not to be friendshipsi Le. it is because of theirunlikeness to the friendship of virtue. (modified ROT)The likeness and unlikeness are based on three sets of factors that serveto determine friendships: the general account, the purposes of friendship,and the characteristics (Tp07TO< ) of the complete friendship.'6 The generalaccount establishes their common claim to the title, while their purposesdiffer. The purposes, in turn, entail certain characteristics that the completefriendship has most completely and others share more or less." The friendshipsare even described as differing by the more and the less, in spite of thefact that they are speCifically different (VIII .11155b13-16). The Similarityamong the characteristics of friendships, then, is a deduced result of the36 These three sets fonn a SOrt of tree. The general definition contains three factors: 1.IlEt EVVOEtii aA'\~'\otS' Kat !3ovAE(!"8aL TayaOci 2. J.l.~ Aav8civoVTa~ 3. OL' ill TL TooV Elp1JJ.l.f.vwv.The last is divided into 1. virtue; 2. pleasure; 3. utility. Virtue friendship is thencharacterized by (i) durability, (ii) age-group considerations, (iii) living together,(iv) needing a long time to fonn, (v) getting the same thing from one another, (vi)unsusceptibility to slander, (vii) between people who are similar, and (viii) who trusteach other.37 The Magna Momfia ILll (1209a19-35) gives an explanation that combines elements ofthe EE and the EN accounts:And these forms of friendship, that of the good, the pleasant, and the useful ... hangin a way from the same point. JUSt so we call a knife surgical, a man surgical, andknowledge surgical ... Similarly ... the fri endship of the good which is based on thegood, the friendship depending on pleasure, and that depending on utility ... while theyare nm actually the same, they have still in a way the same sphere and the same origin... [TJhe friendship of the virtuous ... is a compound of all these, of the good and thepleasant and the useful.Clearly, the author of the MM combines the definitional inclusion (from the medicalexample) and association by accumulation. There is no reason why they can not applyto the same objects, but they do not explain one another.

235 Cumulationpurposes. For this reason, these similarities are secondary and need not bethought to establish any sort of rival order among the friendships: they areposterior to the purposes. They are discussed at length, because Aristotleis interested in explaining why pleasure and utility friendships are calledfriendships (1157a25-32), in spite of the fact that he considers them to beincidentally friendships.On balance, then, Aristotle's analysis of friendship in the EN hasstrongest affiliations with cumulation. He is able to give an account ofwhy one friendship is more, another less, like friendship properly so calledon the basis of the logically prior purposes, and these purposes most closelyresemble the order of inclusion among the souls. By these organizationalmeans Aristotle is able to provide a more convincing and plausible accountof the nature of friendship than he had in the EE.Series in which there are prior and posterior members manifest avariety of forms . The souls and the friendships, when viewed serially, aregenerated through logical and ontological additions and they progress inorder of perfection. As such, they are basically cumulative series. For theirlogical additions are not diminutions or perversions of the first member,but rather completions. In other series, like that of citizenship, the orderis based on logical but not ontological inclusion: the first member is notontologically prior to the second member. Instead, the terms of the seriesare related by the addition of an element that represents a qualification anddiminution of the first member. In all cases, though, it is the additions thatgive the series their distinctive scientific form. For each member individuallyserves as a principle of explanation for analogically common features,and the first member serves as the causal explanation for all the propertiesthat derive from it and that all the other members share in because of theirpossessing that member.The Place of Theology in the Science of BeingOur findings concerning cumulation may help clarify a famous problemin metaphysics, the place of theology in the science of Being. Metaphysicsr discusses general metaphysics but does not include any consideration oftheology. E .1, by contrast, makes theology the centrepiece of the science ofBeing qua Being. 38 The question 'arises, then, whether these are compatiblepositions. If Aristotle meant what he clearly appears to mean in E.l, thenhe is probably overestimating the perfective aspects of the series of Being38 For a brief summary of the controversy see Patzig 1960-61, 185- 7, and Frede 1987b,84.

236 Aristotle's Theory of the Unity of Scienceand is granting too large a role to theology. There is no question that inK1 he intends theology to have the central place in the science of Being(1026a23-32):One might indeed raise the question whether first philosophy is universal, or dealswith one genus; i.e. some one kind of being; for not even the mathematical sciencesare all like in this respect, - geometry and as tronomy deal with a certain particularkind of thing, while universal mathematics applies alike to all. We answer that ifthere is no substance other than those which are formed by nature, natural sciencewill be the first science; but if there is an immovable substance, the science of thismust be prior and must be first philosophy, and universal in this way, because itis first. And it will belong to this to consider being qua being - both what it is andthe attributes which belong to it qua being.Both Frede and Patzig view the relationship between sensible substanceand god (non-sensible substance) as focal; Patzig, insofar as god is thecause, that is, the prime mover, for sensible substance, and Frede becausegod is form and pure actuality, and therefore more abstract than sensiblesubstance, though containing that feature which is substance first andforemost. 39 What is said of it qua Being will, therefore, apply as well toconcrete sensible substance, which in turn will be treated as a subordinatescience. 'Why would it be the task of the theologian to consider thesematters [i.e., general metaphysics]?' Frede asks. 'There are two possibleexplanations. The first is that since these matters have to be discussedsomewhere, and since they are most naturally discussed in the context ofontology, it will be the task of the theologian to deal with them, sinceit is his task to do ontology. But there is another possible explanationwhich ties this fact to Aristotle's claim that first philosophy is universal,because it is first. Since it is first, and since these principles and notionsare universal, first philosophy will be the first place where they are used.Hence, it will be the task of the theologian to introduce them: 40There are important distinctions between these views, and each is opento particular objections. Patzig's view that god is cause, the prime moverof all things, implies that god is useful in the explanations of sensiblesubstances and is adapted to these substances, just as Aristotle suggestsin A.4-S. Accordingly, the definition of god will contain the definition ofsensible substance, and god will be secondary to sensible substance. This39 So also Owens 1978, 298: 'In studying thi s definite nature, one studies the Being foundin everything else.'40 Frede 1987b, 93.

237 Cumulationis not to say that god cannot be focally primary in some relation, but asprime mover god will be derivative.Frede, by contrast, claims that god, being pure form and actuality,will be treated prior to sensible substance in the order of the science.All those attributes that belong to Being qua Being will be treated firstwhen god as form is treated. For this reason the science of form as wellas the principle of non-contradiction (PNC) and principles such as unitywill be treated under theology. Frede notes the parallel Aristotle adducesbetween metaphysics and mathematics to support his claim. But there aresome problems with Aristotle's parallel. The study of proportion, universalmathematics, considers attributes that are common to all magnitudes andcan be abstracted in conception. When theorems of proportion are proved,they are proved of the genus, general magnitude, and can be applied tothe specific instances of magnitude, geometry and astronomy. God, bycontrast, is a separate substance and not just the sum of common attributesof sensible substance. God has peculiar attributes, pure actuality, thoughtthinking itself eternally, and so on, that are discussed in /\, and thatsensible substances do not share. Similar difficulties arise for Frede's claimthat theology will consider the principle of non-contradiction. For PNCdoes not hold of god as such, nor even of actuality as such.Now, there is no question that Aristotle claims that theology is thescience of Being qua Being, and universal because it is first . But it is equallyclear that he must be overstating the case, and may be assimilating theologyto the role of the primary member of a strong perfective series, like endsand means, in which the good of the means is defined in terms of the goodend. 41 If this is so, there are a couple of respects in which his account in E.lis off the mark. There is no question that the substances form a series ofprior and posterior - god, sensible substances; and that god is the most abstract,lacking matter and change (the Metaphysics for the most part treatssubstance with matter, but not with change). I suggest, though, that forthe purposes of the science of Being qua Being this series should be likenedto the cumulative soul series, vegetative, sensitive, intellectual, in whichconceptual and ontological additions are made to each member in order togenerate a series of objects that share the same category. As we saw, what issaid commonly of all living things, namely, that the soul is the actuality ofthe potentially living organic body, is not said just of vegetative soul onlynor is it said of the other kinds of soul in virtue of vegetative soul. Rather41 Compare also Aristotle's comment in the EE's discussion of friendship: 'But because theuniversal is primary, they also take the primary to be universal, and this is an error'(VII. 2 1236a23-25).

238 Aristotle's Theory of the Unity of Scienceit is said of all souls in virtue of each kind of soul, and it is a conclusionderived equally from the nature of the vegetative, sensitive, and intellectualsouls. We may interpret the kinds of Being and the general attributes ofBeing, like PNC, in a similar manner. In the series god, sensible substance,conceptual and ontological additions are made, but the general attributePNC does not belong to sensible substance in virtue of god, but ratherit belongs in virtue of the nature of sensible substance. Now it may beargued that the order of excellence is reversed in the two series: the seriesvegetative, sensitive, intellectual increases in order of excellence while theseries god, sensible substance decreases. But in fact, this just strengthensthe point. For god is separate and unchanging essence and actuality. Asa result, PNC will belong to god if it belongs to anything. But PNC alsobelongs to Beings that do not meet the stringent qualifications of god. Infact, it applies to anything definite, substance or non-substance, in virtueof whatever their definition is. Aristotle's favourite example in r, man asa biped animal, indicates that PNC will hold even of. definition expressedin terms of the matter of a substance. Moreover, Aristotle nowhere claimsthat PNC holds in virtue of god or pure actuality; rather he makes clearin APo 1.10 and r.3 (1005.22- 29), that PNC is common by analogy, justas the common definition of soul is common by analogy.The example of general and special mathematics mentioned at theend of E.1 is .lso relevant, though not in the way Aristotle appears touse it. The study of PNC belongs to the science of Being at the generaland universal level, and so corresponds to universal mathematics. But thespecific branches of mathematics (geometry and astronomy) are based onontological principles that form a series. Geometry considers the plane orsolid, astronomy adds motion. Correspondingly, god and sensible substanceform an ontological series, god concerning form alone, sensible substanceconcerning form together with matter. Just as general mathematics (theoryof proportion) does not hold generally in virtue of its holding specificallyof geometry (for there can be proportion in locomotion), so general metaphysics(PNC) holds of all Beings qua what they are and not in virtue ofgod or pure actuality.42 PNC holds of Being in an even more abstract sensethan god.There is another respect in which Aristotle's E.l account differs fromhis usual doctrine. He claims that if separate and unchanging substancedoes not exist, physics will be the first science. But this does not followfrom what he says about abstraction elsewhere. For if there were only42 The fact would be especially dear in the series arithmetic and geometry, since generalmathematics holds for both rational and irrational quantity.

239 Cumulationisosceles triangles or even bronze isosceles triangles, 2R would still notbelong to them in virtue of bronze or isosceles (APo 1.5 74a16). Aristotleclearly has ways of talking about sensible substance abstracted conceptuallyfrom change even if it is not actually separated, as he says at Met. M.31077b17-30. Likewise, god need not exist in order for PNC and generalmetaphysics not to be included in physics. For these reasons Aristotlewould have been better off organizing Being in accordance with the cumulativepattern rather than the focal and perfective pattern that Patzig andFrede envision.Conclusion: Analogy, Focality, and CumulationAristotle once accused Speusippus of representing nature like an episodictragedy, on the grounds that he had made each hypostasis independentand isolated from every other (Met. N.3 1090b19-20). His own theoryof the subject-genus, however, was perhaps even more vulnerable to thischarge. Accordingly, Aristotle developed the doctrine of abstraction togetherwith analogy, focality, and cumulation to provide a set of interlockingand mutually dependent techniques for overcoming the isolationof the subject-genus. In spite of the fact that these techniques receive littleattention within the formal presentation of the APo, it is clear that theycan be expressed best within that theory and especially within the fundamentalnotions of genus and essential connections. Without sacrificingthe integrity of the autonomous genus, these techniques allow for theinclusion of the relevant and necessary external objects and causes withina science as the well as the connections between autonomous genera.Focality is, of course, the primary relation, being identical with per sepredication. It provides a flexible description of normal science in both itscore and extended aspects. Focally derivative items, which surround a coresubject-genus, both reveal the nature of the core subject and may also besemi-abstracted so as to become subjects in their own right. These newsubjects, nevertheless, remain part of the science of the core. Any per se(2) predicate, for example, male and female which belong to animal, mayhave properties proved of them per se, and these proofs will form a partof the extended science of animal. Focality, then is the primary means ofunifying a science and displaying the unity of the components of a science.Analogy allows Aristotle to remain within the limitations of thequa-requirement, and yet consider commonalities between different butrelated genera. Analogy resolves the tension between qua and per serequirements within the same science, since the genera in which analogiesoccur must be related in virtue of some abstractable commonality. The

240 Aristotle's Theory of the Unity of Sciencenature of this commonality varies. In lower ge'nera, the commonality isoften some aspect of form, and is related to each genus by a commonrelation, as, for example, the functions in the biological works are commonamong various parts. Among higher genera, where no genuine commonalityis available, some sort of serial order supplies the per se relationsnecessary for the unity of science. Focality provides one such series. Theanalogy of potentiality in A.4-S is arguably backed by such a focality. Thefocal relations take many different forms, including the causal relationscharacteristic of normal science and the medical example; but we also findthe relations of imitation and deficiency, which are especially useful inbacking analogies. For objects so related are of the same basic kind andtherefore amenable to analogical comparisons. Such is the basis of thescala naturae in which one genus, man, forms a normative kind in termsof which other genera are explained. The imitation and deficiency relationis not, as I have argued, an essential feature of analogy, but only one ofthe means by which two analogous genera can be related.Owen suggested that the relationship between the souls is focal, on thegrounds that the definitions of the souls exhibit definitional inclusion andare related by 7fporr$f(n< and acpaipErr«.43 He is certainly right that cumulationexhibits some focal characteristics. We find, besides these additions,relations of hypothetical necessity among the souls discussed in DA III.l2.But the cumulative soul series is not focal insofar as the primary purpose ofcumulation is not to bring one object into an explanatory relationship withthe primary object, in spite of the fact that this is a necessary conditionfor cumulation. Although the souls do exhibit definitional inclusion, then+ 1 th member of a series does not include the nth member for the purposeof explaining the nth member. Nor are cumulative objects included in thescience only to the extent to which they are useful for the primary term,as focally derivative objects are; each member of the series is treated as asubject in its own right with its own per se predicates.Again, an important criterion of a focal science is that all membershave their shared name in virtue of the first member. This may also betrue of imitative or perfective series, but since the kinds of souls are calledsoul in virtue of the highest faculty they possess, this series cannot becalled focal in the proper sense. 44 Ontological and logical priority aloneare not enough to create a focal term. The first term must also be that in43 Owen 1960, 192n37.44 Because cumulation is a fusion of analogy and focahty, Rodier (1900, 218) was partlycorrect to say that the kinds of soul are analogically related, and Owen (1960) partlycorrect to say that they are focally related.

241 Cumulationvirtue of which all subsequent terms are called by the same name. Whenthese three criteria are taken together, it becomes impossible for a seriesof the soul type to be focally related.Cumulation also has some analogical characteristics. Like analogues,cumulative subjects are all in the same category; focally related subjectsare not; and all share some per se attribute and not just by relation.Souls are all actualities of organic bodies, friendships are mutual andrecognized bonds of affection. The result of the cumulative TrpoO"$'O"t< isnot the creation of a genus network around a subject, but a proliferationof parallel subjects, which share attributes analogically and in virtue ofcommon essential elements, for instance, the assimilation of the nutritive,sensitive, and intelligible by that which has the capacity to receive them.Souls are per se things and are treated in their own right and not as relativeto the first member of the series.Cumulation differs from biological analogy because in biological analogythere must be some absolutely common element to which the analoguesare all per se related, and which is semi-abstractable, but which,given the concrete subject matter is not abstracted. This semi-abstractableelement is causally significant and distinct. In cumulation, by contrast, .there is not a single common cause to which the members are all related;their commonality is posterior and proved from different and specificcauses. Like metaphysical analogues, members of cumulative series aregathered together because of their mutual focal relations of definitionalinclusion. Since members of cumulative series are not per se related tosome common and logically prior item, they do not need to be related toanything more abstract than themselves in order to be analogically related.For this reason they are well adapted to operate at the most general andabstract levels of Aristotle's ontology. Indeed, analogues, precisely becausethey require a distinct abstract can never be the ultimate form of scientificunification, but instead always rely on focality or cumulative series.Finally, these three techniques themselves can be seen to form a sortof cumulative series: focality, analogy, cumulation. A new qualification isadded at each stage in order to create an additional form of unification.To the per se relation between genera that is characteristic of focalitywe add a proportional identity in order to create analogy, and the perse relation among analogical genera is further qualified by progressiveontological and logical additions in order to create cumulation. Togetherthese techniques contribute to a style of philosophy and science that isdistinctively Aristotelian. For Aristotle combines that rigour so admiredamong us moderns, that isolates a subject matter for study and seeksto understand it in its own right together with the synoptic vision of

242 Aristotle's Theory of the Unity of Sciencecosmic unity through hierarchical and progressive abstraction. From thesetechniques also emerges a certain flexibility, according to which severalmodes of unification can be used on the same group of objects to differenteffects. Aristotle, with his interest in explaining the phenomena and solvingaporiai, maximizes thereby his ability to explain. These techniques aremost properly expressed in the formal language of essential relations anddemonstration, and for this reason Aristotle can provide a unified view ofthe world while avoiding the nebulous and metaphorical expression of thePlatonists.

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INDEX LOCORUMCat. 1.4 73b9-10 1501 1.12- 15 150n23 1.4 73b10-16 163 1b16 62n18 1.4 73b26-32 17n45 2.34--b5 151n28 1.4 73b32-33 17n45 3.22-28 138 1.5 74.12-13 17n46 5.38-b10 41n40 1.5 74.16-17 18, 2396 6.19- 25 38n36 1.5 74.17-25 247 6.36-37 181 1.5 74.35-b4 308 11.15 165 1.6 74b8-10 16n21.6 75.28-29 30D1 1.7 75.38-39 21- 211 21.29-32 117n2 1.7 75.39-b2 201.7 75a42-b1 18n7,APr 1261.39 49b3--5 117n2 1.7 75b10--11 21,901.7 75b12-20 21-22APo 1.7 75bl4--17 33n261.2 72.14--24 80 1.7 75b37-76.2 221.2 72.16- 17 26 1.9 75b37-38 211.4 73.24--25 19n8 1.9 76.4--7 181.4 73.24--27 15 1.9 76.9-15 32-31.4 73.34--b16 16 1.10 157, 2381.4 73.34--37 16 1.10 76.37- b2 26, 911.4 73.37-b3 16 1.10 76b16-19 811.4 73b4--5 21 1.11 77.26-35 261.4 73b5-10 16 1.12 77.40--b6 33n261.4 73b6-8 149n22 1.13 78b32-79.16 33n26

256 Index Locorum1.22 83a2-17 126n7 VI.6 144,31-b3 137- 81.22 83b13-17 183 VI.6 144b31- 145al 131nl01.22 83b19-20 19n7 VI.8 146,36- bl 1811.28 21 VI.9 147b13-14 117n2128 87a38 31 VUO 148,25- 26 21011.4 91,18- 21 19n8 VI.11 149al-3 117n211.4 91bl-7 164n4111.11 123 SE11.13 96b5--6 158n36 1 165.35- 37 19811.13 97.6-19 6n1 3 165b12-17 13811.13 97.34-37 158n36 13 173bl-11 13811.13 97b7-15 210 31 181b37-182a2 3211.14 98a20--23 83, 84, 34 19891,99,188 Phys.IU7 212 U 184a23- 25 183n1211.17 99.1-16 93 1.7 177-811.17 99.8- 10 28 1.7 190b7-8 193n2411.17 99a15- 16 83,91 1.7 191,6--7 16611.17 99.16--37 94 1.7 191.7- 12 18611.17 99.37- b7 94 1.7 191a12- 13 19111.18 97 1.7 191a17- 27 18711.19 109 1.7 191a27-29 1871.8 187Top. 1.8 191b4-10 2041.5 101b39- 1.8 191b15- 16 180n6102.1 117n2 1.8 191b27-29 1881.5 102.31-b3 221n21 1.9 192a31- 32 1801.9 143, 153 11.2 193b22-1.9 103b20--39 146-7 194.12 30U5 107.3-17 201 11.2 193b26--32 19n71.15 107b13- 18 40n38 11.2 193b32-33 30n221.15 107b19 62n18 11.2 193b34 301.18 108b6 219 11.2 194al-12 35IV.6 128a26-29 140nl0, II.2 194.7-15 31142 11.2 194b9 181V.2 130.39 117n2 lll.1 2OOb32-201a3 40n37,V.8 138b23-26 182 181VI.4 141b15-18 174n51 IV.l 209,9 101n12VI.4 142b2--4 117n2 IV.8 214b22- 23 101n12VI.6 143a29-32 143n15 V.2 226,26- 29 79n42

257 Index LocorumVnA 39-41, n.3 414b19-33 214212 n.3 414b19 209VnA 24Sb17-19 40,49, 11.3 414b32-33 209232n35 n.3 415al-11 215Vn.4 249.21-25 40 11.3 415a11-12 209nVn.4 249a29-b26 41 nA 415,14-23 20911.4 415a23-b7 204DC 1I.5 417bS-9 193n231.2 26Sb17-19 23n14 11.8 420a30-b4 104IIJ.I 299,13-17 31, 154 n.s 420bl-4 82n4611.9 421,16-20 S2n46GC 11.9 421,17-bl 10411.6 333a20-34 46n49 11.11 423,12-15 69n291II.l0 433b19-21 50Mete. 1IJ.12 223,III.3 372b34-240373,5 34III.3 373,6-16 35 Sens.III.3 373,16-19 35 5 443b3-12 104DASomn.1.1 402,6-7 51 1 454bl4-23 72I.l 402bl-8 208 2 455b32-33 721.1 402b3-5 213I.l 402b9-403,2 208 Long.I.l 403,3-b19 209 6 467a6-S 96I.l 403,25-b19 31n231.5 410a13 136n7 Juv.11.1 412.7-8 180n6 1 468,9-12 6S,7211.1 412a4-5 210 2 468a13-17 6711.1 412b4-9 209 3 468b28-30 75II.l 413a8-9 209, 5 469b21-22 95209n2 6 470.19-20 9511.1 413a11-20 21011.2 413a22-23 209, Resp.211-12 17 478b32-33 9511.2 413a31-32 209n 20 479b19-26 9511.2 413b24-27 209n 21 480.23-b20 10111.2 414.12-28 21111.3 41416-14 209 HAn.3 414b16-19 209n 1.1 486.5-14 80

258 Index Locorum1.1 486.14- VI.12 566b12-13 64n20487.10 81 VII(VIII).l 588.25-31 731.1 486.14-b22 53-4, VII(VIII).1 588b4-13 111-1255n4, VII(VIII).2 589b1S-19 10162n181.1 486.20-21 60 PA1.1 486.21-23 38 1.1 7n11.1 486b5 38,79 1.1 639.15-29 129n91.1 486b14-16 61 1.1 639.15-19 19n71.1 486b17 65n21 1.1 639.29-b3 48n531.1 486b20 70 1.1 639b5-10 36n331.1 486b21-22 102 1.1 640.10-19 761.1 486b24-487.1 60n13 1.1 640.34-35 2151.2 488b29-32 55n4, 1.2-4 7468 1.4 644.12-23 781.4 489.19-22 71 1.4 644.14-16 691.4 489.23-26 67 1.4 644.1~23 55n4,1.6 490b10-12 93 65n211.6 491.14-19 55n4 1.4 644.22-23 63n191.6 491.19 79n42 1.4 644.23-27 67n261.12 493.12-16 67n27 1.5 645b6 10111.1 497b6-12 62 1.5 645bS-10 71n3411.1 497b1S-20 70 1.5 645b20-28 55n4, 7211.1 497b26-27 70 11.1 646.13-24 8011.1 497b33-498.2 67 11.1 646b20-22 8511.12 503b29-32 67 11.1 646b30-34 107n1711.15 506.15 112n25 11.1 647.14-21 106n1511.17 508.16 112n25 11.1 647.14-19 131I1I.1 510.21-23 112n25 11.1 647.24-33 105111.9 517.6-10 66n24 11.2 647b29-35 59I1I.11 517b21-26 66n24 112 648.2-7 103111.16 519b26-30 67 11.2 648.4-8 73II1.19 520b1S-19 71n33 112 648.4-5 71n34III.19 520b25-33 69 11.2 648b2-8 95n5IY.1 523b27-29 64n20 11.3 650.34-35 71n34IV.3 527b22-24 112n27 11.3 650.2-8 132IV.5 530b31-33 68 11.4 651.17-18 69IV.8 533.28-30 112n27 11.7 652b23-25 72IV.8 534b12-15 64n20 11.7 653.10-12 72IV.11 538b8-9 103 11.8 653b35-V.4 540bl-3 112n27 654.19 84

259 Index Locorum11.8 653b35 65n21, IV.5 678331-34 10083 IV.5 679315-23 8311.8 653b36 57 IV.5 679b15 56n711.8 65435-9 102 IY.5 680315 55n611 .9 65538-10 131 IV.5 68139-15 11211.9 655312-17 131, IV.5 681315-28 11384 IV.5 681b28-30 7111.9 655317-28 83 IY.5 681b33-34 7111.9 655323-34 69 IV.8 683b28 56n711.9 655332 57, IV.8 684333-35 10065n23, IV.10 686324--68732 11384 IV.10 686325-28 10011.9 655333 65n21 IV.10 686b2D-31 11311.9 655b2--4 69, IV.10 686b31-68731 72107n17 IV.10 68738-23 11411.9 655b2 65n21, IV.10 687b6 55n666n24 IV.10 68832--4 7011.9 655b4--15 71 IV.ll 690bl4--16 48n5211.9 655b4--5 70 IV.ll 691316 7011.9 655b8 66 IV.ll 691317-19 10211.9 655bll 65n21 IV.12 692b3-9 61-211.10 656b26-29 131 IV.12 692b13 55n611.12 657318-23 101 IV.12 693b4--13 10011.13 65833-10 131 IVJ2 693b1D-13 4811.14 65836-7 102 IV.12 693b13-14 9011.14 658b2- 7 131 IV.12 693b26-11.15 658bl4--15 131 694312 4811.16 658b35-36 70 IV.13 10111.16 659b23-27 59 IV.13 695b17-19 100I1I .1 661b3--

260 Index Locorum1 704b9-11 49 f.2 1003.35- 36 197n3018 714b3- 7 70n31 f.2 1003b2-3 14519 714b20-23 49 f.2 1003b5- 14 117f.2 1003b5-6 135n5GA f.2 1003b6-10 1631.2 716b5- 9 112n27 f.2 1003b8-10 125, 1571.2 717.4-6 112n27 f .2 1003b8 166Ll8 725.5 198 f.2 1003bl4-15 120,Ll9 726bl-5 107 183nILl 735.16-26 106 f.2 1003b16- 17 135n511.3 737.36- b4 108 f.2 1003b17 197n3011.4 739.18-20 68 f.2 1003b22-11.5 741b11-15 75n37 1004.2 166n4411.6 742.18-b17 75 f .2 1003b22-25 16611.6 743bl8-25 75 f .2 1003b32-36 166,11.6 745b2-9 166n45 166n43lll.2 753b35- 754.3 68,72 f.2 1003b33- 34 167111.5 756.32 112n25 f.2 1003b35-36 168, 171IIL11 76la24-32 60n14 f.2 1004.5 136n7V.l 779.2-4 73 f.2 1004.6-9 135n5V.3 782.14-20 103 f.3 1005.22- 29 238V.3 783b2-8 69, 103 f .3 1005.26-27 26n206.2 1014.1-3 20n10Met. 6.6 170A.l 982.1- 3 159 6.6 1016bl- 3 168A.2 982.25-28 31n24 6.6 1016b1 170n49AA 985blO-13 79n42 6.6 1016b6-11 169A.9 992.18-19 221n20 6.7 170B.l 995b18- 24 165 6.7 1017.22-30 148n21,B.1 995b26-27 165 204n47B.2 996bl4-22 148n21 6.8 16n1B.2 997.21-22 18n7 6.11 1019.3 220B.2 997.25-33 136n6, 6.11 1019.11-12 218158n38 6.14 142n14B.3 998b9- 21 6 6.18 1022.31-32 19n8B.3 998b22-28 6, 137 6.21 1022b15-18 79n42B.3 998b23-24 140n10 6.28 1024.36-b3 215B.3 999.6-14 216 6.28 1024b6-9 74n35B.3 999.13-14 223 6.28 1024b9-16 142n12B.3 999.16-23 220n18 6.30 1025.30-32 18, 18n7f. 1003.21-22 122, 157 £.1 1025b7-13 159

261 Index LocorumE.1 1025b3G-- 2.4 1030b11 136n71026.6 31n23 2.5 139E.1 1025b34- 2.5 1030b18-24 1551026.6 209n 2.5 1030b2G--21 150E.2 1026.23-32 236 2.5 1030b23-26 117n2,E.2 1026.33 136n7 155E.2 1026bl4-21 155n33 2.5 103101- 3 155E.2 1026b27-33 155n33 2.5 1031.2-5 1562 .1 185n14 2.5 1031.7-11 1552.1 1028.1G--15 148 2.7 1032b2- 5 1662.1 1028.10 136n7 2.9 1034.30-32 126n72 .1 1028.18-20 150 2 .10 1035.2 204n472.1 1028.20 151n27 2.10 1035bl4-22 82n452.1 1028.20-31 149 2.10 1035bl6-18 118n32.1 1028.27 150, 2.11 1036.26-b3 18n6151n26 2 .11 1036b3G--32 118n32 .1 1028.28-29 151n28 2.12 74,2.1 1028.29-30 150, 159 137n8,2.1 1028.35-36 150 2202 .1 1028bl-2 149, 153 2.12 1038.3-9 74n352.1 1028b2-4 157 2.12 1038.18-21 143n152.3 1029.20-26 180n6, 2.16 1040b16 166n43204n23 H .2 1432.3 1029.23-24 185n13, H.2 1042.4-5 188204 H.2 1042b25 136n72.4 189 H.2 1043.2-7 1822.4 1029b14 151 H.2 1043.19-21 204n472.4 1029bl6-18 154n32 H.3 1043.29-b4 190n192.4 1029b22-27 152 H.3 1043.34-37 51n572.4 1029b22 152 H.4 1044.25-31 107n172.4 1030.14 152 H.4 1044b8-20 1272.4 1030.17-27 152 H.6 1045.14-25 74n352 .4 1030.17-23 149 H.6 1045.14-17 140,1422.4 1030.17 152 H.6 1045.36- b5 1692.4 1030.23-27 156n33 8.1 1045b27-32 150n242.4 1030.25-28 160 8.1 1045b36-2.4 1030.27-32 160 1046.1 1892.4 1030.29-b3 116, 153 8.1 1046.11-13 1902.4 1030.33-34 227n26 8.1 1046.17-19 190n192 .4 1030b3-4 160 8.6 177-8,2.4 1030b8-12 166n43 188

262 Index Locorum8.6 1048a30-b9 191 M.2 1077b4-11 31n248.6 1048.37- b4 193 M.3 1077b17-30 29, 2398.6 1048b6-9 192 M.3 1078.5-8 19n7,8 .6 1048b8 193 1588.7 1049.29-30 185 M.3 1078.14-16 368.8 131 M.3 1078.31-b5 23n158 .8 1049b12- 17 192 M.7 1081b8-10 218n148.8 1050.21-23 118n3 N.3 1090b19-20 2398.10 1051.34 136n7L1 1052.31-34 168 ENL1 1052.33-34 169 1.6 1096.17-23 216, 217L1 1052bl- 19 166n45 1.6 1096.23-29 195, 200,L1 1052b7- 16 179 201L1 1052bl8-20 172, 173 1.6 1096.31-34 203L1 1052b31-32 172 1.6 1096b8-14 197L2 1053b20-21 141 1.6 1096bl4-16 198n381.2 1053b22-24 166n43 1.6 1096b16-25 195, 197L2 1054.3-4 215n9 1.6 1096bI7- 18 1981.2 1054.14 136n7 1.6 1096b24-25 198n38L3 1054.26-29 174n51 1.6 1096b26-31 197L3 1054b3-6 171 1.6 1096b26-29 194-51.4 61n16 1.6 1096b30-31 1951.4 1055a6-7 38 1.6 1097.3-8 2001.4 1055.35-38 169n48 1.7 1097al6-18 2001.8 1058.21-26 74n35 1.7 1097b2 198K.l 1059b31-34 136n6 I.7 1098a7-17 203K.12 1068b18- 20 142n14 1.7 1098al6-17 1991\.4-5 177, 1.12 1102.1 199204n47, 11.2 1104b8-9 199240 11.6 1106b36-1\.4 1070.31-33 183 1107.2 1991\.4 1070.33-b10 179 IV.3 1123b20 1991\ .4 1070bl-2 136n7 V.5 1133.7-29 431\.4 1070b12-13 180 V.5 1133al6-18 45n471\.4 1070bl6-21 178 V.5 1133b7 451\.5 1071.2-3 185 V.5 1133b18-23 431\.5 1071.15-17 184 V.5 1133bI8-20 43n43,1\.5 1071.26 178, 179 44n461\.5 1071.29-35 184 V.5 1133b23-26 451\.5 1071.34-35 183, 185 V.ll 1138.4-b14 51\.10 1075.14-15 51n56 VIL3 1147a5-6 95

263 Index LocorumVIII.1 1155b13- 16 234 VII.2 1235b33-VIII.2 1155b17-27 231 1236a2 229VIIl.2 1156a3-5 181, 232 VII.2 1236a5-7 226VlIl.3 1156a6-8 231 VIL2 1236a15-33 227VIIL3 1156a1G-16 232 VII.2 1236a15-22 117VIIL3 1156al6-17 232 VII.2 1236a21-22 144VIIL3 1156b12-17 233 VII.2 1236a23-25 237n41VIIL3 1156b33- VII.2 1236b15- 17 2291157a4 233 VII.2 1236b17-26 227VIllA 1157a25- 32 235 VII.2 1238a35- 38 229VIII .4 1157a32 232n32 VII.2 1238b13-14 230VIIl.6 1158b5- 11 234 VII.10 1243b30- 35 45n47X.1 199 VIL13 1246a26-31 43n42X.4 1174b31- 33 200 VII .15 1249a21-b25 204X.5 1175b36- VII.15 1249b9- 13 1441176a1 200X.8 1178b31-32 199 Pol.L9 1257a6- 18 41- 2MM L9 1257al4-17 4211.11 1209a19- 35 234n37 L9 1257b35 47LlO 1258a38-b8 47EE 11.5 1264b4-6 5L5 1216a33- 37 230n30 IILl 1275a30- 33 222L8 1217b25-34 201 IILl 1275a33-34 101n12L8 1218al- 9 216 IILl 1275a34-b5 216, 221L8 1218b16-24 195-6 IILl 1275b5-6 222VII.2 1235b24-30 225 IILl 1275b18-19 222VII.2 1235b27-29 228 IV.1 1288b12 101n12VII.2 1235b30- V.3 1302b33-1236a7 226 1303a2 59n12

GENERAL INDEXabstraction 30, 239; addition and 31,154, 178, 188, 240; in biology 82;from change 193-4; degrees of 15,38 (see also semi-abstraction); amongfriendships 231; general cause and47, 51; genus-species chain vs., 87;inappropriate 47, 105; mathematical10, 29, 154; outside mathematics 30;other views of 30021; per se/qua and29, 39, 51; pure 14; among souls209; from substances 154Academy 5- 6, 13accident 8; good as 203; per se 19;science of 143,151, 155n33activity 193actuali ty, absence of analogy amongkinds of 180. See also potentialityadaptation of terms to subject-genus26, 90, 92addition, ontological 224, 235. See alsoabstraction; cumulationaffection (mii17)f'aj, 79, 83, 85Alexander Aphrodisiensis 138n9, 154,194n26alternating proportion, theoremof 24-9. Sec also mathematics;universalambiguity. See homonymyanalogy 10,53-115,239; absence in Cat.and Top. 77; biological demonstrationand 89-115; common cause among88,95- 7, 101- 8; continuous 200; demarcationof genus and 56- 8,91, 183;flexibility and fixity in 60, 67-8, 86,183; focality and 12,175,189, 240 (secalso focality); function in 10 (see alsofunction); of goods 200-3; betweengreatest kinds 61; in imperceptiblecases 71; in lower genera 239; otherviews of 56-9 (sec also realist view;relativist view); place in speciesgenus-analogyand wholes-partssystems 77-86, 108; relative positionand 69; role in APo 89-99; semiabstractionand 128; among subjectgenera26-8, 88; ubiquity in biologicalworks 53, 53n1; among wholeanimals 60. See also Being; commoncause; good; potentiality; soulappetite 50application argument 19, 35, 106;adaptation and 26, 106; metabasisand 23; mixed science and 33Aquinas, Thomas 12

266 General Indexartefact 186ascidian 113auditory passages 100autonomy 8, 33axiom 9, 26, 91babbling 138balding 103Balme, D. 55, 92barter 42Being: difficulties in interpreting thescience of 136; and foeality 12,142-3; genus of 136-43; internalunity of 169; One and 166-71,174; prior to genesis 76. See alsodemonstration, in the science ofBeing; metaphysicsBerti, E. 195bifocality 166, 190n19. See also focalitybiological works, organization of48n51, 81, 108, 129{3ios. Sec way of lifeblood 69, 71, 100, 103, 107blood-vessel 71, 100bone 69, 83, 93brain 71breast 67bronze triangle 239capitalism 47carnivore 131cartilage. Sec bonecategories: analogy among 175, 182;among goods 202-4; One and 171;in the science of Being 141-2,144--65, 183coextension. See extension; noocoextensioncommensurability 15, 38, 40-4, 46n49,49common cause 49-50composition of parts 80-2, 108. Seealso wholes-parts systemconclusion, demonstrative 18connatural spirit 50connection, techniques of 4, 239-42.See also analogy; cumulation; focalityCook Wilson, J. 217core science 144-5; of Being 155-7,171; extended and 155,189, 194 (seealso extended science)coupled terms 156- 7crafts, analogy among the 200cumulation 13,214-24,240-1; analogyand 13, 241; focality and 13, 207,240-1; of friendship 232; of god235-9; at high levels of abstraction241; means and ends and 207; scalanaturae and 207; of soul 214-24dating of EN and EE 225defence, parts for 131definition: in accordance with thename 211; empty 223; in Euclid 27;generic 180, 191, 209-12, 221, 223,232; matter in the 213, 224; nominaland real 182; of relative terms 181;unity of 130, 140definitional inclusion 117, 240; inaccidental compounds 151-3; withends and means 195; in focalconclusions 125; and homonymy120; potential 215, 222, 233;problems with 145demonstration 7, 15, 34; accidental22; analogy in 90-2, 100; in thebiological works 90; conclusionsof 18, 210; Euclidean 34; of focalfacts 123, 196 (see also linguisticpredication); and focality 195; atgeneral and specific levels 25-8;of natural facts 123, 196 (see also

267 General Indexnatural predication); parts of 34;in the science of Being 136, 158,164difference and otherness 78Dionysius 210division: dichotomous 74, 220; genusas subject to 9n7, 11, 21; bymultiple differentiae 74. See alsospecies-genus-analogy systemdoctor. See medicine as exampledualizer lID, 113dunamis. See potentialityear 131eggshell 72embedded terms 32-6embryology 58, 75ends 230. See also means and endsessence 151-5Euclid 24-9, 33-7eudaimonia 129, 199evolution, theory of 130exchange 43-5explanation: asymmetry in 97; externaland internal 130-1; flexibility in114; generic and specific 105 (seealso demonstration, at general andspecific levels). See also middle termextended science 144-6, 156-7; ofBeing 165, 171. See also core scienceextension 158; of animal parts 61; indemonstration 91; as part of definition98. See also non-coextensioneye 131familiarity (yvwP'fWV) 108, 191, 210feather 69, 102Ferejohn, M. 134figures, series of 214. See also series;soulflesh 67focality, 11, 116-74; analogy and12, 176, 193, 200, 205, 239 (seealso analogy); in biology 129;demonstrations and 122; in EE225-31; in EN 197, 231; homonymyand 120, 240; perfective seriesand 208; predications in 159-64;relation of, broken 192; relationsof 118, 145, 197; in the science ofBeing 12, 134-74, 177; subordinatescience and 135; transitivity of125, 157; as two-step process 144;various cases of 44, 148, 194,230-1. See also bifocality; normalsciencefood 132formal cause 98formalist view of analogy. See relativistviewForm Numbers 217form as substrate 185. See alsosubstrateFrede, M. 161, 236friendship 224-35; accidental 232;complete 234; non-cumulativefeatures of 233; objects of 225, 231function(s): analogy among 72-4,213;general and specific 44; similarity,difference, and 82functionalist view of analogy. Seerealist viewgeneral account. See definition, genericGeneration of Animals, role of 48n5l.See also biological worksgeneration of parts, order of 75genus: ambiguity in term 54-5, 78;Aristotelian vs. Platonic 216-20;of Being, see Being, genus of; andcommensurability 38; demarcationof analogy and, see analogy,

268 General Indexdemarcation of genus and; anddifference 79, 142; of series 215-16;and species 138, 220. Sec alsodivision; focality; subject-genusgill 101Gill, M.L. 193god 204, 235-9good 194-206; " accident 203;apparent 225-9; and categories204-5; foeality of 195, 206; god asfocus of 204; independence of 231;potentiality and 204Gotthelf. A . 56greatest kind (}liyWTO/.l yivos) 61hair 69-70, 102, 131halo 34happiness. Sec eudaimoniahealth 157heap 183; Being as 138-40; unity of171hearing 104heart 71homonymy 5, 40, 94, 160, 195-{;,210-12; of Being 148, 201; indefinitions 40, 181, 212, 232; andfoeality 119-20, 134; of good 201;of potentiality 190honour 199hoof 69-70horn 107hylomorphism 80-6; and abstraction47ichor 69incidental. Sec accidentincommensurable number 217incomplete abstraction. See semiabstractioninduction 188, 191instrumental parts of locomotion 48intelligence 73, 103interdisciplinarity 130, 145internal unity 168, 172-3interpretation of Aristotle's corpus asunity 4irrational quantities 27joint 50kind-crossing. See metabasisknowledge, relational 5-6Kullmann, W. 56land animal 131linguistic predication 118,124. See a/sonatural predicationlocomotion, animal 39, 47-8, 73;abstraction in 47; four-point theoryof 48longevity 94-7, 211; and analogy 97lung 101manufactured goods 39many 173. See a/so Onematerial cause 98mathematics, universal 10, 237-8. Seealso alternating proportionmatter: definition in terms of 213;genus as 58, 74; logical vs. physical76; as substrate 185. Sec alsopotentialityme,ming 98, 121means and ends 205, 237; as focallyrelated 196-7measure 166, 172-4; and essence 172medicine as example 11, 119, 144metabasis 9-10, 21-2, 32-3, 87; andapplication argument 23; betweenclosely related genera 22-4; andscala naturae 110-14metaphor 177, 184

269 General Indexmetaphysics: general 236; as normalscience 161-2; and predicationrelations 163. See also Beingmiddle term 94--5, 159mind. See nousminor term, focus as 126mixed science 31-7money 47more and less 58, 69, 79, 84, 101-2;and scala naturae 110mouth 72Muskens, G.L 56nail 70names 117; generic 24, 32; lack of 68,84, 93, 109natural dependence 150natural predication 159,162-4; identityof focal and 164necessity 8, 20, 157, 159need lxPEia) 43- 5non-coextension of terms 107non-contradiction, principle of 237- 8.See also axiom; principlenon-substance 145, 156. See alsoaccident; category; substancenormal science 118-19, 144. See alsofoealitynormativity 109, 113nous 200, 209, 212offices, indefinite 222One 166- 74; categories of 169 (seealso categories); as divisible 173n51;internal and relational 168, 171;measure as essence of 172 (see alsomeasure); science of 166. See alsoBeingopposites 166orthodox view of analogy. See realistviewotherness 78; and animal composition81Owen, G.E.L 116, 134, 175, 190, 194Owens, j. 176packing 36paronymy 8n5, 127n8, 170particulars 7parts of animals: corresponding towhole animals 61, 76, 84; asessential 100; order of generation of75Patzig, G. 236Pellegrin, P. 55, 63- 6, 73-4, 92, 110perfective series. See series, perfectiveper se 4, 8, 11, 41, 45, 81, 188;accident 19; goods 198; predicationand abstraction 15, 31; predicationand analogy 86-7; predication andconfusion of terms 42; predicationand focality 119-22, 124, 146-8,192, 196; predication and metabasis22-3; predication and qua 40,90, 98, 107, 135; predication andsubordinate science 135; specific,predications 16-17, 149, 154, 161;tension between qua and 32, 37, 53,109, 128, 239. See also quaperversion 228-9, 235Plato 5,136,140,143,177,195- 6,200,202, 205, 218-19, 242pleasure 199, 226-32Posterior Anaiytics, importance of 4potentiality 177-94; analogy and 191,205; compared with good 204;different kinds of 178; focality and191; in persistence and change 190;as a principle 177, 180; and thescience of Being 194pounce. See bonepractical syllogism 50

270 General Indexpractical wisdom 199precausal stage of inquiry 108predicables, four 147predication, vs. predicate 161. Seealso linguistic predication; naturalpredication, per Sf, qu.aprinciple 7, 80, 159, 178-9priority 150, 218, 220; in friendshipseries 232; natural 183, 185, 215,220, 223, 233; ontological 161-2,232Proclus 25n18proper (OiKEtOV) 41proportional analogy 43. See alsoalternating proportionqua 4, 8, 81, 86; abstraction and29-30; analogy and 11, 86; localityand 122, 126; metabasis and 22-3;tension between per se and 32, 37,53, 109, 128, 239. See also per serealist view of analogy 56, 92; inpotentiality 177-8, 186; resolutionwith relativists 98. See also relativistviewrecursive unification 13n13. See alsocumulationrelational unity 168, 171relative terms, definition of 181relativist view of analogy 57, 59, 82,92, 177, 179; resolution with realists98. See also Balme; Pellegrin; realistviewrelevance criterion, focal relation as125rest, point of 50restriction of demonstrative terms 92.See also adaptationRobinson, D. 195root 72Same 168, 171scala naturae 109-15, 240; analogyand 58, 111; lack 01 explanatorypower Ill, 114; more and less and112, 115; psychological capacities and112scales 69-70, 102Selachia 132self-predication 218-19semen 107semi-abstraction 10, 14, 38, 51-2, 158,183, 241; and core and extendedscience 129; and subject genus 51-2.See also abstractionsensation 131separability 185, 211series: first member of 220; and focality207-8, 214; 01 locality, an~logy , andcumulation 241; of Form Numbers217; genus of 216, 221; kinds 01235; limiting the 224; perfective207-8, 222, 235; species in 221; 01substances 237sight 200Similar 168, 171similarity 208, 224, 233. See also moreand lesssleep 73snub 154, 156; ambiguities of 38; andbandy 32; distinct from accidentalpredication 155; and focality 144;and mathematical abstraction 31;and mixed science 35; and per se31soul 208-24; analogical account of208, 210-14; compared with figures214-15; cumulative account of 208,214-24; defined by actualiry andpotentiality 212; as primarily intellectual213; problems concerning208; relations among faculties of 223;, .......................... ......

271 General Indexserial order of 214; traditionalconcept of 213; universal account of208. See also seriesspecies-genus-analogy (SGA) system77-86, 108; different from dichotomy78; hierarchy of 77; reasons for thesystem 86; relation to wholes-parts(WP) system 81-2Speusippus 5, 239sponges 113subject-genus, 14, 20-1, 30, 239;absence of species in 54; and analogy10; core and extended 128; differentfrom divisionary genus 54, 118;different from substrate 127; andexplanation 7; identity conditions of14, 20-1; Euclid and 25; isolation of3, 9; multiplicity of, in mixed science33; principles in 26, 50; problemswith 3. See also genussubordinate science 9, 37. See alsomixed sciencessubstance 151, 170, 184. See alsoBeing; metaphysics; non-substancesubstrate 149, 185-7; form and matteras 185; of non-substance 150;pre-existing and coexisting 186subtraction. See abstractionUlJVn-At:'iV 198superordinate science. See subordinatescience; mixed sciencesyllogistic 107. See also demonstrationtalons 69taxonomy 55, 57teeth 68teleology, universal 133theology 235-9. See also godtheorem 211, 233. See also demonstration,conclusions ofthird-man argument 140Ti. E(rn. See what-is-itTimaeus 133touch 104trade, retail 42, 47traditional language 78, 107traditional view of analogy. See realistviewtransitivity. See focality, transitivity oftrunk 70underlying thing. See substrateuniversal: and cause 7, 97; and focality120; and qua 17; science 3, 6, 7, 13unity: accidental 170; within greatestkind 61; internal and relational 168,172- 3. See also Oneuniversal predication 159, 162, 164. Seealso natural predication; linguisticpredicationusury 47value 41, 200. See also exchange; tradevirtue 109; friendship 228-30, 231-5water animals 131way of life (/3io,) 48, l30wealth 42; and abstraction 43what-is-it (Ti. fun) 147, 149whole animals 60. See also parts ofanimalswholes-parts system 80, 107; and cause86; and function 81; and position81; relation to species-genus-analogysystem 81. See also species-genusanalogysystemwomb 68,72Woods, M. 218

PHOENIX SUPPLEMENTARY VOLUMES1 Studies in Honour of Gilbert Norwood edited by Mary E. White2 ArbitH of Elegance: A Study of the Life and Works of C. PetroniusGilbert Bagnani3 Sop hocles the Playwright S.M. Adams4 A Greek Critic: Demetrius on Style C,M.A. Grube5 Coastal Demes of Attica: A Study of the Policies of Kleisthcncs C.W.]. Eliot6 Eros and Psyche: Studies in Plato, Piotinu5, and Origen John M. Rist7 Pythagoras and Early Pythagorean ism l.A. Philip8 Plato's Psychology T.M. Robinson9 Greek Fortifications F.E. Winter10 Comparative Studies in Republican Latin Imagery Elaine Fantham11 The Orators in Cicero's 'Brutus'; Prosopography and Chronology G.V. Sumner12 'Caput' and C%nate: Towards a History of Latc Roman TaxationWalter GoHart13 A Concordance to the Works of Amrnianus Marcellinus Geoffrey Archbold14 Faffax opus: Poet and Reader in the Elegies of Propertius John Warden15 Pindar's 'Olympian One': A Commentary Douglas E. Gerber16 Greek and Roman Mechanical Water-Lifting Devices: The History of aTechnology John Peter Oleson

17 The Manuscript Tradition of Propertius James L. Butrica18 Pannenides of Elea Fragments: A Text and Translation with an Introductionedited by David Gallop19 The Phonological Interpretation of Ancient Greek: A Pandialectal AnalysisVit Bubenfk20 Studies in the Textual Tradition o/Terence John N. Grant21 The Nature 0/ Early Greek Lyric: Three Preliminary Studies R.t. Fowler22 Heraclitus Fragments: A Text and Translation with a Commentary edited byT.M. Robinson23 Th e Historical Method of Herodotus Donald Lateiner24 Near Eastern Royalty and Rome, 100-30 Be Richard D. Sullivan25 The Mind of Aristotle: A Study in Philosophical Growth John M. Rist26 Trials in the Late Roman Republic, 149 BC to 50 BC Michael Alexander27 Monumental Tombs of the Hellenistic Age: A Study of Selected Tombs from thePre-Classical to the Early Imperial Era Janos Fedak28 The Local Magistrates of Roman Spain Leonard A. Curchin29 Empedocles The Poem of Empedocles: A Text and Tran slation with anIntroduction edited by Brad Inwood30 Xenophanes of Colophon Fragments: A Text and Translation with aCommentary J.H. Lesher31 Festivals and Legends: The Formation of Greek Cities in the Light of PublicRitual Noel Robertson32 Reading and Variant in Petronius: Studies in the French Humanists and TheirManuscript Sources Wade Richardson33 Th e Excavations of San Giovanni di Ruoti, Volume 1 Alastair M. Small andRobert J. Buck34 Catullus Edited with a Textual and Interpretative Commentary by D.ES.Thomson35 The Excavations 0/ San Giovanni di Ruoti, Volume 2: The Small Finds c.J .Simpson, with contributions by R. Reece and J.J. Rossiter

36 The Atomists: Leucippus and Democritus Fragments: A Text and Translationwith a Commentary by c.C.W. Taylor37 Imagination of a Monarchy: Studies in Ptolemaic Propaganda KA Hazzard38 Aristotle's Theory of the Unity of Science Malcolm Wilson