Description | 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. |
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