The intermediate character of mathematics and the ontological structure of its elements by Plato and Aristotle - Santos, Gilfranco Lucena dos (Revista Archai, 2025)
This article examines the ontological structure of mathematical “objects”, focusing on the opposing views of books VI-VII of Plato’s Republic and books XIII-XIV of Aris-totle’s Metaphysics. Plato understands Mathematics as a means or a path (method) of obtaining a philosophical education, and considers the “subject” of Mathematics as ὑποθέσει, rather than οὐσίαι (separate entities). In agreement with Plato, Aristotle seeks to describe the ontological structure of mathematical “ob-jects” not as οὐσίαι, but as quantity, quality or relation; which is to say, as the separable elemental properties (στοιχηῖαι) of entities. I will argue that while neither Plato nor Aristotle un-derstood the objects of Mathematics as separated entities, Aris-totle’s description is more effective by virtue of its consideration of an “object’s” separable elemental properties as the “subject” of mathematics.