Abstract: 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.

Keywords: unity of units in a number; abstraction; Jacob Klein; counting; Aristotle's account of number; Plato's account of number.

Let me begin with a story. The year was 1976, and I was writing a dissertation on Aristotle's Metaphysics. For reasons I can no longer recall, I decided to spend the summer in London working at the British Library, then still located in the British Museum. After some weeks on my own, I began to look around for people who were working in my area.