Philip Kitcher has proposed an account of mathematical truth which he hopes avoids platonistic commitment to abstract mathematical objects. His idea is that the truth-conditions of mathematical statements consist in certain general structural features of physical reality. He codifies these structural features by reference to various operations which are performable on objects: the world is structured in such a way that these operations are possible. Which operations are performable cannot be known a priori; rather, we hypothesize, conjecture, idealize, and eventually wind up with theories which are true of the world (taking into account our idealizations), just as we do in the sciences. Kitcher argues that mathematical and physical knowledge are continuous, in that they concern the same subject matter (the physical world) and are subject to the same epistemological and methodological constraints.
