Aristotle’s Problem

Platonism is traditionally defined as the view that there are abstract mathematical objects, and that those objects are independent of human beings and their thoughts, language, and practices. This paper has two goals. First, to show that this definition fails to distinguish platonism from various forms of aristotelianism in the philosophy of mathematics, according to which mathematical objects depend for their existence and properties on non-mathematical ones. Second, to argue that platonism is best defined in terms of metaphysical fundamentality, as the view that there are fundamental mathematical entities. I finally distinguish between different varieties of mathematical aristotelianism.