A Question of Numbers: Aristotle's Critique of Platonic Mathematical Objects, Form-Numbers, and First Principles in "Metaphysics" M-N

Defense Date


Graduation Date

Spring 1-1-2008



Submission Type


Degree Name





McAnulty College and Graduate School of Liberal Arts

Committee Chair

Ronald Polanksy

Committee Member

James Lennox

Committee Member

Therese Bonin


Aristotle, critique, mathematics, metaphysics, number, Plato


Many Aristotelian commentators have noted the difficult, dense, and generally baffling nature of Metaphysics M-N. The challenge of interpreting these books is increased because while many of the arguments they contain seem to be directed against Platonic views, scholars have been unable to locate the corresponding doctrines in Plato's writings. This difficulty has elicited three main responses. (1) Aristotle is attacking unwritten Platonic doctrines (2) The positions that Aristotle attacks are his own misinterpretations of the dialogues. (3) The "unwritten" doctrines are actually written--but only in Plato's so-called later dialogues.

I argue that all three of these responses contain serious misconceptions. In particular, scholars have assumed that thinkers should aim to give historically accurate reports of their predecessors' positions, so that any strange account must either be due to reporting unfamiliar doctrines or to incompetence. Nor have they recognized that Aristotle is often critiquing a deliberately modified version of Plato's ideas because this is an effective way of responding to their obscurity. This is an approach that Aristotle recommends, in the Topics, for a questioner who wishes to refute an ambiguous position. Finally, commentators have not noticed that Aristotle often approaches his opponent by eliminating all the positions to which he could retreat, including positions his opponent has not actually supported.

I argue that the discrepancies between Plato's dialogues and the views Aristotle critiques disappear once we recognize that Aristotle does not try to give a full exposition of Plato's ideas and then attack them in all their complexity. Rather, as part of a deliberate critical strategy, he attacks possible (and usually literal) interpretations of Plato's views.

I defend my position by examining passages in Topics, Sophistical Refutations, and other works that explain Aristotle's response to the use of obscure language in his opponents' positions. I demonstrate that my understanding of Aristotle's critical strategy allows us to achieve coherent interpretations of formerly perplexing passages in Metaphysics M-N. I also show that although Aristotle does not give verbatim reports of Plato's views, his literal interpretive approach sheds light on ideas that are adumbrated but not plainly expressed in Plato's dialogues.





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