The Aristotelian Plato

Source abstract

Abstract The purpose of this paper is to point out that some mathematical doctrines attributed by Aristotle to Plato find their origin in a threefold order of problems: first, in some allusions contained in the dialogues, which might create ambiguities within the so-called standard model of ideas; second, in the Aristotelian interpretation of ideal entities as universals or predicates, an interpretation in turn partly authorized by Plato himself; third, in the tendency not to emphasize the possibility of understanding participation and the whole-part relationship from a non-quantitative point of view. In this paper I will disregard the complex debate about whether or not to attribute the unwritten doctrines of the Aristotelian account to Plato, but I will appraise in what sense some Aristotelian objections to participation may arise from the fact of conceiving of numbers and magnitudes as ideas.