The aim of this paper is to explore and elaborate a puzzle about definition that Aristotle raises in a variety of forms in APo. 2.6, in Metaph. Ζ.12, and again in Metaph. Η.6. My focus will be on the puzzle itself and its relevance to an inquiry into substance, but I will also touch on some issues pertaining to his proposed solution (or solutions) to it. One version of the puzzle is formulated in the aporetic section of Posterior Analytics as follows:

Here he is considering accounts that purport to define a thing by mentioning both a genus to which it belongs and one or more differentiae. The object of definition is not a word or expression such as “man,” but it is rather some entity picked out or signified by that expression. What is at stake is the unity of the thing, that entity. Accounts constructed out of genera and differentiae may be arrived at as the end results of a method of division, and he further indicates that they may be arrived at as conclusions of syllogisms.