Aristotle's mathematical objects as the intermediates

Abstract

In his “Metaphysics” Aristotle often claims plainly that Plato believed in a third class of entities, which are identical neither with Forms nor with physical objects – these are the so-called intermediates (ta metaxu). But although there are passages in Plato where similar ideas seem to be indicated, nowhere does he accept this important and rather unexpected doctrine in a straightforward way. Since the intermediates are identified with mathematical objects, the very concept of the former helps us to understand the features of the latter. But why should the intermediates be exactly and only the objects of mathematics? Can't we postulate the same form of intermediate objects for every other science? In this article I also tackle different approaches to understanding Aristotle's reading of Plato: is the existence of intermediates something claimed by Plato, by Aristotle only or a kind of modification of Plato's concepts in Aristotle's work in order to overcome his own difficulties within the philosophy of mathematics?