Colloquium: December 5th

Title: Plato Was NOT A Mathematical Platonist

Speaker: Dr. Elaine Landry (University of California, Davis)

Friday, Dec 5th at 2:30pm in CLE A203  


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 in 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, so that b) we come to know such truths by, somehow or other, “recollecting” how things are in the metaphysical realm. Against b), I have shown in another paper (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 knowledge, in the Meno and in the Republic, is the hypothetical method. There I also argued, against Benson’s [2006; 2012] claims, that the mathematician’s hypothetical method cannot be part of the philosopher’s dialectical method.

Here I will further show that both the method and the epistemology of the mathematician are distinct from those of the philosopher. 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. Taking my evidence from the Divided Line analogy and Book 7, I will argue that mathematical objects are not forms, and so, against a), they do not either exist independently of us in some metaphysical realm or fix the truth of mathematical statements.

Why does this new reading of Plato matter for current practitioners of philosophy of mathematics? Because it shows that we would do well to keep the requirements for mathematical knowledge distinct from those of philosophical knowledge. It is only the philosopher's method that requires a first-principled account, and so requires a metaphysics of forms. And, more generally, it shows that, for both considerations of mathematical epistemology and ontology, we would do well to place more focus on mathematical methodology than we do on mathematical metaphysics. Thus, we would do well to place more focus on the mathematician’s method, and so on mathematical practice, then we do on mathematical philosophy.