Aristotle's Classification of Number
A T the beginning of Metaphysics M 6, Aristotle decides to examine the views of those who think that numbers are separate substances and the causes of existing things. l The rest of the chapter falls into two parts: a theoretical account of the different kinds of numbers that can be conceived (I080a15-bll), followed by a historical survey of the views of Aristotle's predecessors concerning the nature of number (1080bll-33), which ends with the contention that all the views outlined are
... tlined are impossible (I080b33-36). The classification Aristotle puts forward in I080a15-37 betrays misunderstanding of the concept of number and also of Plato's ideal numbers or ideas of numbers. Aristotle refers to this doctrine as that of acvILf3I\TJTOt aptOJLot, that is, incomparable or, even better, inasso-ciable numbers.2 These numbers, however, are not congeries of units, as Aristotle thinks they are, but merely the hypostatization of the universals which constitute the series of natural numbers.3 These points must be made at the outset in order to clarify that it is only because he considers number to be a congeries of abstract monads that Aristotle offers the following theoretical, a priori classification of number according to the nature of the units (1080a15-37): 1 This is the third question announced in the first chapter of M, cf 1076a29-32. The thinkers referred to are the Pythagoreans and the Platonisrs, cf W. D. Ross, Aristotle's Metaphysics II (repr. with corrections, Oxford 1953) 426-27. 8 As L. Robin says (La theorie platonicienne des idees et des nombres d' apres Aristote [Paris 1908, repro Hildesheim 1963] 272 n.