Platonism about Mathematical Objects

Platonism about mathematical objects holds that numbers, sets, functions, and other mathematical entities exist mind-independently, as abstract objects outside space and time, and that mathematical statements are objectively true or false in virtue of facts about this timeless realm, regardless of whether any human mind ever grasps them. The view's historical origin lies in Plato's theory of Forms: in the Republic (Books VI–VII), the divided-line simile distinguishes "the mathematicals" as intermediate objects, more real than sensible diagrams but dependent on the higher Forms, while in the Meno, the slave-boy geometry demonstration illustrates Plato's doctrine of anamnesis, recollection of eternal truths the soul supposedly knew before birth. Aristotle rejected this separate existence in Metaphysics Books M and N, arguing that mathematical objects are abstracted from, and exist only within, sensible substances rather than in a separate realm.