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New Yearbook for Phenomenology and Phenomenological Philosophy

Volume 11, 2011

Edward C. Halper
Pages 271-281

Klein on Aristotle on Number

Jacob Klein raises two important questions about Aristotle’s account of number: (1) How does the intellect come to grasp a sensible as an intelligible unit? (2) What makes a collection of these intelligible units into one number? His answer to both questions is “abstraction.” First, we abstract (or, better, disregard) a thing’s sensible characteristics to grasp it as a noetic unit. Second, after counting like things, we again disregard their other characteristics and grasp the group as a noetic entity composed of “pure” units. As Klein explains them, Aristotle’s numbers are each “heaps” of counted units; in contrast, each of Plato’s numbers is one. This paper argues that Klein is right to understand a noetic unit existing in the sensible entity, but that his answer to the second question is not consonant with Aristotle’s insistence that Plato cannot account for the unity of a number, whereas he can. Slightly modifying Klein’s analysis, I show that Aristotle’s numbers are each one.