Aristotle’s Numbers as Hylomorphic Compounds

Abstract One plausible approach to Aristotle’s philosophy of arithmetic is that he held numbers to be hylomorphic compounds. While research has been conducted to show the benefits of this theory, particularly in solving the problem of numbers’ unity, none has been extensively dedicated to justifying the initial hypothesis that numbers have hylomorphic structure. The absence of such an account is felt acutely due to Aristotle’s repetitive negation throughout Metaphysics M−N that numbers are not and could not be either forms or hylomorphic compounds. This paper argues that despite these explicit statements, Aristotle does, in a way, consider numbers to be hylomorphic without resorting to Platonic hypostatization. His thinking is grounded in the distinction between numbers’ ontological status in the natural world and their mental epistemological mode of being. In the natural world, numbers exist as quantitative properties of things, being numbers just potentially. However, in his understanding, the mathematician separates these properties and considers them as if they were individual entities possessing hylomorphic structure. This is how numbers mentally appear to be hylomorphic without actually being such. The paper further clarifies the epistemological procedure of abstraction which bridges the gap between numbers’ dual mode of existence and explores various aspects of numerical form and matter to strengthen the initial hypothesis and show that Aristotle indeed had a coherent understanding of the ontology of number.