Location: Savery Hall 264

Plato Was NOT A Mathematical Platonist

Elaine Landry
Professor
Department of Philosophy
UC Davis

In this paper, I will argue that Plato was not a mathematical Platonist. My arguments will be based primarily on the evidence found in the Republic’s Divided Line analogy and Book 7. Typically, the mathematical Platonist story is told on the basis of two realist components: a) that mathematical objects, like Platonic forms, exist independently of us in some metaphysical realm and the way things are in this realm fixes the truth of mathematical statements; and, b) we come to know such truths by, somehow or other, “recollecting” the way things are in the metaphysical realm. Against b), I have demonstrated, in Landry [2012], that recollection, in the Meno, is not offered as a method for mathematical knowledge. What is offered as the mathematician’s method for attaining knowledge is the hypothetical method. There I also argued, though mostly in footnotes, against Benson’s [2003; 2006; 2008; 2010] claim, that the mathematician’s hypothetical method cannot be part of the philosopher’s dialectical method. I now turn to reconsider, on the basis of what Plato says in the Republic and Book 7, why these methods must be taken as distinct and further consider what the ontological consequences of this distinction must be. Thus, my aim will be to argue that since both the method and the epistemological faculty used by the mathematician are distinct from those of the philosopher, then so too must be their objects, so mathematical objects cannot be Platonic forms.