a problem lies at the heart of Aristotle’s theory of definition. On the one hand, Aristotle says in Topics VI.4 that “the one who defines well must define by means of genus1 and differentia” (141b25–7); indeed his view of definition most often seems to be confined to its role of picking out the definiendum by indicating the class it belongs to—what can be called its “class definition.”2 But on the other hand, in Posterior Analytics II.2 he makes the pronouncement that “knowing what something is ” is the same as knowing why it is ” (90a31–2), and then goes on in II.2 and 8 to argue that definition is an , “explanation” or “explanatory principle.” How can these two notions of definition be reconciled?
Short of giving the full Aristotelian solution to this problem, I hope here to suggest one way in which Aristotle’s notion of class definition—especially the reformed version presented in De Partibus Animalium I.2–4—can be shown to relate to his notion of explanatory definition in APo II. The link is his notion of scientific , “problems,” as discussed in APo II. 14 and elsewhere.3 It will turn out that a class definition in effect presents a scientific problem to the scientist which can best be solved by an explanation—ultimately by an “explanatory definition”—accounting for the attributes that form the basis of [End Page 487] class membership. Or more succinctly: the class definition presents a problem that the explanatory definition solves. Further, although the discussion in PA I is meant to be a reform of the simpler but unworkable method of arriving at the genus-differentia formula based upon , “division,” I intend to argue that an important ancillary benefit of the reformed method is that it is capable of articulating scientific problems in a much clearer way than division can. In fact, it seems very well suited to the task of presenting problems and hence to the task of searching for explanatory definitions.
2. scientific problems
In APo II. 14, Aristotle begins to outline the proper procedure for formulating scientific problems. We are told that “in order to obtain problems, we must pick out the sections 4 and divisions” of the subject we are investigating, about which we are formulating a problem (98a1–3). That is, we must learn to pick out each genus in the hierarchy of genera the subject belongs to by learning to identify the attributes associated with each of these genera. This will enable us to account for each attribute we find in the subject under investigation in terms of the genus the attribute is primarily associated with. As Aristotle explains: “Let A stand for animal, B for [an attribute] of every animal, and C, D, and E some particular animal [species]; it is clear why B belongs to D—because of A” (98a9–11).
This, in a sense, shows one way a scientific problem—Why does attribute B belong to D?—can be “solved”: by finding the right “division” of D that accounts for its having B. But what is important to note here is that, in fact, our investigation only begins with this process of finding the right genus. This is simply how we “obtain” the problem, strictly speaking, not the means for ultimately solving it. Indeed the problem of accounting for why an attribute belongs to a given subject is not even completely formulated until we are able to determine the proper “division,” or genus, the attribute universally belongs to. Then we can ask the more fundamental question of why the attribute belongs to this genus, i.e., why B belongs to genus A. Now this question can be analyzed further, in terms of the other attributes of the genus. Any genus (or infima species) is, in effect, designated by a regular concomitance of the many attributes that identify it—i.e., attributes that universally co-occur in it. So the scientific problem we are formulating, regarding why a certain attribute belongs to a certain subject, ultimately should be reformulated in this way: Why does the attribute in question always accompany the other attributes...