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. (shrink)

Aristotle’s classification of ideal number in Metaphysics M 6 has often been considered an unfair presentation of Plato’s actual views. I take another look at the passage and argue that Aristotle is a more careful critic than has been usually recognised. In particular, I argue that much of the scholarly discussion on the passage has failed to take account of Aristotle’s deeper concern, namely, the conditions necessary for numbers to be ordinal. I then set Aristotle’s critique within the broader context (...) of his concern to separate Form from Number, and thus to separate metaphysical questions from mathematical ones. The latter half of the article shows some of the consequences of mixing mathematics with metaphysics from a systematic and historical point of view. (shrink)