Binghamton University The Open Repository @ Binghamton (The ORB) The Society for Ancient Greek Philosophy Newsletter 3-28-1991 Division and Explanation in Aristotle's Parts of Animals Allan Gotthelf The College of New Jersey Follow this and additional works at: https://orb.binghamton.edu/sagp Part of the Ancient History, Greek and Roman through Late Antiquity Commons, Ancient Philosophy Commons, and the History of Philosophy Commons Recommended Citation Gotthelf, Allan, "Division and Explanation in Aristotle's Parts of Animals" (1991). The Society for Ancient Greek Philosophy Newsletter. 241. https://orb.binghamton.edu/sagp/241 This Article is brought to you for free and open access by The Open Repository @ Binghamton (The ORB). It has been accepted for inclusion in The Society for Ancient Greek Philosophy Newsletter by an authorized administrator of The Open Repository @ Binghamton (The ORB). For more information, please contact [email protected]. SAGP, Pacific Division DRAFT March 28,1991 Ail&v\ Cx>ak&i-P (Version read) Division and Explanation in Aristotle’sParts of Animals L THE IMPORTANCE OF DIVISION IN ARISTOTLE The nature and proper methods of logical division, διαίρεσις, are important concerns in at least four of Plato’s later dialogues, and reflections on the process may even have led Plato to a revised conception of the very nature of a Form. The place of division in Aristotle’s Topics - both in the organization of some of its materials and as the method for seeking definitions which many of the topoi are designed to regulate - suggests the importance διαίρεσις must have had in the Academy,1 as does the Epicrates fragment and Aristotle’s criticism of alternative views of the nature or purpose of division in Prior Analytics 1.31, Posterior Analytics II.5 and 11.13, and Parts of Animals 1.2-3. But, as David Balme has argued,2 Aristotle criticizes these alternative views not in order to reject division but to reform it. When he criticizes those who think the production of a definition by division constitutes a deduction, or even demonstration, of that definition, he reminds us that division is nonetheless useful, in the establishment of definitions, and appears to devote most of a long chapter (APo. 11.13) to the central role of division in "huntpng] out what is predicated in what a thing is"(96a22), which m ay be a reference to the definitions that feature as first principles in demonstrations.3 And when Aristotle rejects dichotomous division as a way of defining είδη in PA 1.2-3, he replaces it with division by multiple differentiae simultaneously, and argues that that procedure successfully avoids the criticisms dichotomous division falls prey to. Finally, in Metaphysics Z.12, he indicates how one of his reforms of division - the rule that one must divide "by the differentia of a differentia",4 e.g .footed by split footed5 and not by feathered - allows at least a partial resolution of the problem of the unity of definition. Balme has even argued - controversially but not entirely implausibly - that definitions by division are involved in the solution to be found in M etaph. H.6 of the unity problem for the object of definition. And Pierre Fellegrin has insisted that the very concepts of γέι/ος, είδος and διαφορά which feature so centrally in the discussions of definitions and much else throughout the corpus, derive their precise logical relationships to each other from their place in the divisional process. These interpretative claims have been challenged, and alternative readings of some of the passages I’ve mentioned have been given, but these controversies, currently unresolved as they are, only underscore the fact that the topic of the place of division in Aristotle’s logic, metaphysics, and biology is an important one, and warrants more study. The biological case is perhaps the most perplexing. For the critique of dichotomous division in PA 1.2-3 ends, as I’ve said, with the firm endorsement of a method argued to work where dichotomous division does not. In seeking a definition of an ατομοι/ είδος (such as sparrow or crane), Aristotle instructs us to divide, not the γέι/οςA n im a l by one differentia at a time, but a commonly recognized γέι/ος of animals (in this case Bird), marked out by multiple differentiae, by dividing these differentiae simultaneously, each as many times as necessary to reach the definition sought. In PA 1.4 he even goes on to explain how to select the γέι/η from which to start the process. Thus the method, and now to work, one might think. But, as Balme put it in 1976: "The puzzle is, what happened to diaeresis after that? Aristotle makes no further use of it in biology; and no genos or eidos is 1Cf. Chemiss 1944 and Tarán 1981. 2Balme 1987; cf. Pellegrin 1988, ch. 1. 3Useful: APr. 1.31 46a31-2 9AP o. 11.13 96b25-26 (cf. II.5 91b28-32). In fact, it is "only" (96b35) with division that one can ensure completeness. Alternatively, 11.13 may be concerned with pre-causal definitions (cf. Ross ad loc.). 41038a9-10; cf. PA 1.3 643bl7, and Balme 1972:102-103,117 and 1987: 69, 73. actually defined." Or, to put the question more neutrally, does division have any role in the biology and, if so, is that role connected in any way with the reforms of division presented in PA 1.2-4, and more generally, with the discussions of division in the logical and metaphysical writings? Now, I don’t pretend to have the answers to the larger of these questions. I don’t think anyone does, yet. But work done since 1976, especially by Bahne, Pellegrin, and James Lennox, has moved us closer to solving the puzzle, and I would like, in this small paper, to add one more piece to that eventual solution. 2. SOME RECENT WORK In a recent essay on "The Reforms of Diaeresis",5 6 Bahne suggested that the reforms summarized in 1.2-4, with their focus on sameness, difference, and sub-division of differentiae, require a precise grasp of each of the differentiae that might appear in a divisional definition of animal είδη prior to the production of those definitions, and that the Historia Animalium (chronologically the last of the biological treatises) was conceived as the vehicle for achieving that grasp. HA would thus not itself contain definitions by division, but would make such definitions possible. Aristotle never reached the stage of providing such definitions, Bahne suggests, and "we may indeed doubt whether [he] maintained this aim when his experience as a naturalist increased", since he would have realized that "there is no end to the recognition of fresh significant differentiae". But the "unfinishable" character of the collection and analysis of differentiae would not preclude the use of "the correct identification and grouping" of differentiae collected, which would "[lead] directly to the fundamental causes of animals’ attributes and differences. This might well have seemed the best way towards a methodical apodebds of living nature" (80). But if Balme is right, it would seem that the reforms of division have now become useless - unless division so reformed plays a role in the search for and/or organization of scientific explanations. In two recent papers, James Lennox has argued that division indeed plays such a role, specifically in the pre-explanatory stage of Aristotelian science. In a paper significantly entitled "Divide and Explain" (1987), Lennox, as he summarized: develops Balme’s suggestion that APo. 11.14 is a key text in solving the puzzle of the relationship between division and demonstration in Aristotle’s scientific method. Central to the theory of the A P o. is the articulation of a distinction between incidental and unqualified understanding. Unqualified understanding requires locating the widest kinds to which differentiae belong universally: this allows explanations of why sub-kinds of these widest kinds have the differentiae in question, and identifies those features which are either essential to the kind, or explicable as consequences of its essence.7 To use an example from A P o. 1.5, isosceles triangles have an angle sum equal to that of two right angles because they are triangles; we understand the former connection fully only when we understand why triangles as such have that attribute. From that we explain why, say, isosceles triangles do. Thus APo. 11.14 instructs us to seek, for any differentia to be explained, the widest class to which it belongs, and to do so by "selecting from ... the divisions" (98al-2). This procedure, as Lennox puts it, "assumes a set of divisions of a subject domain ready at hand, and as the examples suggest, organized along Aristotelian lines" (1987: 98). Those divisions will be the source both of the predicates of the propositions to be demonstrated and of their subjects, as we look up and down the relevant divisions for the widest class to which each predicate applies universally. Division thus helps "direct, or redirect, inquiry to the appropriate level for...explanations of...primitive predications" (99). Division as such neither supplies the true propositions nor identifies the actual causes - empirical inquiry of specific sorts is required for that - but it organizes the former and facilitates the latter. Research into HA which Lennox and I did in collaboration, he goes on to argue, shows that this "downward division/correlation methodology" is much "like what we find in" that treatise (99).8 5"For split-footedness is a certain sort (τις) of footedness" (1038al5). 6Part I of Balme 1987. In a subsequent paper7 8 9 Lennox connects both the prescription of AP o.