Aristotle, Speusippus, and the method of division

Abstract

IntroductionAs Aristotle himself says,A.Po.2.13 is an attempt to provide some rules to hunt out the items predicated in what something is, namely to discover definitions. Since most of this chapter is devoted to the discussion of some rules of division(diairesis), it may be inferred that somehow division plays a central role in the discovery of definitions. However, in the following pages I shall not discuss what this role is. Nor shall I discuss what place division has in the wider discussion of definition and explanation as it emerges fromA.Po. 2.1 shall rather focus on the argument that Aristotle reports and discusses inA.Po.2.13.97a6–22, and which our extant sources ascribe to Speusippus. As will become clear later on, this argument undermines the possibility of giving any definition, and Aristotle deals with it here because he can block it by exploiting some properties of the method of division.

On What Ontology is and Not-is

“…II.13,, in a chapter that deals with diairesis and the discovery of definitions, about "some" who claim that, on order to know the differentia of A, one has to know the differentia of B, C, D,... It is generally assumed that this argument undermines the possibility of giving any definition (Falcon 2000). Tradition ascribes this view to Speusippus, Plato's student and successor in the Academy (Tarán 1981).…”

On what Ontology Is and not-Is

“…It is generally assumed that this argument undermines the possibility of giving any definition. 60 Tradition ascribes this view to Speusippus, Plato's student and successor in the Academy. 61 I am not sufficiently familiar with the extant sources concerning Speusippus, but it seems clear to me that it is not recommendable to deny, as Falcon does, that Speusippus builds his system an absolute or universal diairetic tree.…”