Syrianus on the Platonic Tradition of the Separate Existence of Numbers

This paper analyzes and explains certain parts of Syrianus’s Commentary on book M of Aristotle’s Metaphysics, which details Syrianus’s response to Aristotle’s attack against the Platonic position of the separate existence of numbers. Syrianus defends the separate existence not only of eidetic but also of mathematical numbers, following a line of argumentation which involves a hylomorphic approach to the latter. He proceeds with an analysis of the mathematical number into matter and form, but his interpretation entails that form is the constituent of number, which has the status and role of a Platonic Form. This solution allows him not only to explain and justify the unity of number, but also to apply the Platonic thesis of the separate existence of numbers, to the mathematical or monadic numbers themselves. It also betrays its tendency to combine theses of the Platonic Ontology with fundamental Aristotelian doctrines.