The intermediate character of mathematics and the ontological structure of its elements by Plato and Aristotle - Santos, Gilfranco Lucena dos (Revista Archai, 2016)
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 Aristotle’s Metaphysics. Plato understands Mathematics as a means or a path (method) of obtaining a philosophical education, and considers the “subject” of Mathematics as á½‘Ï€Î¿Î¸ÎÏƒÎµÎ¹, rather than Î¿á½ÏƒÎ¯Î±Î¹ (separate entities). In agreement with Plato, Aristotle seeks to describe the ontological structure of mathematical “objects” not as Î¿á½ÏƒÎ¯Î±Î¹, but as quantity, quality or relation; which is to say, as the separable elemental properties (ÏƒÏ„Î¿Î¹Ï‡Î·á¿–Î±Î¹) of entities. I will argue that while neither Plato nor Aristotle understood the objects of Mathematics as separated entities, Aristotle’s description is more effective by virtue of its consideration of an “object’s” separable elemental properties as the “subject” of mathematics.