Aristotle's Critique of Platonist Mathematical Objects: Two Test Cases from Metaphysics M 2

Books M and N of Aristotle's Metaphysics receive relatively little careful attention. Even the scholars who do give detailed analyses of the arguments in M-N dismiss many of them as hopelessly flawed and biased, and find Aristotle's critique to be riddled with mistakes and question-begging. This assessment of the quality of Aristotle's critique of his predecessors ( and of the Platonists in particular), is quite widespread. The series of arguments in M 2 (1077a14-b11) that targets separate mathematical objects is the subject of particularly strong criticism by Annas and Ross. Two related arguments in this series (1077a14-20 and 1077a24-31) will serve as cases in point. The principal charges made against these arguments (that Aristotle misunderstands or misrepresents his opponents' views, and that he engages in question-begging because he presupposes his own metaphysical views) are frequently made against Aristotle's critique of Platonist positions more generally. Thus if, as I argue, these charges are false for our two test case arguments, then there is good reason to think that they might also be false when they are leveled against the other arguments in this M 2 series. And, although presenting an argument for this is beyond the scope of this paper, I would suggest that these two charges are more often than not false when applied to Aristotle's critique of Platonist mathematical views in M-N and beyond.