Aristotle and Number Theory

The standard gloss, 'Ancient Philosophy' tends to obscure that, in some respects, the definitive criticism of Platonism comes from Plato's most famous student himself, Aristotle. For sure, some aspects of Aristotelianism are Platonistic, especially its honoring of Contemplation as the highest state, and, more generally, the priority it accords Theory over Practice. But, Aristotle's contention that Unity is a Predicate cuts right to the heart of Platonistic Mathematics, by challenging the premise that Mathematical entities subsist in an eternal realm beyond the physical, i. e. it implies that e. g. ' a triangle' is a reification of 'is triangular'. Furthermore, since Mathematical entities are the archetypes of all Platonic Forms, the debunking applies to them as well--they are all reified Predicates. Hence, according to Aristotle, the entire realm of Platonic Forms is fictititous. But, this is no Nominalistic rejection of Platonism. For, Aristotle's own concept of One, "to be the first measure of a kind . . . the starting-point of number qua number", anticipates the Constructionism of Kant, or the Intuitionism of Brouwer, more than the Nominalistic Cardinalism of Russell. It also anticipates the Formaterial concept of One--that it is both an end and a beginning--that is the basis of the Evolvemental concept of Individual, more than it does the exclusively terminal concept of One implied by Aristotle's own Teleology.