Abstract

An insight, Central to platonism, That the objects of pure mathematics exist "in some sense" is probably essential to any adequate account of mathematical truth, Mathematical language, And the objectivity of the mathematical enterprise. Yet a platonistic ontology makes how we can come to know anything about mathematical objects and how we use them a dark mystery. In this paper I propose a framework for reconciling a representation-Relative provability theory of mathematical truth with platonism's valid insights. Besides helping to clarify the ontology of pure mathematics, I think this approach suggests a novel philosophical interpretation of some central results of modern mathematics, Including godel's incompleteness theorems and the independence theorems for the continuum hypothesis