Problems in philosophy of mathematics: A view from cognitive science

Abstract

I argue that many of the problems in mathematical ontology result from our use of natural language, a communication system that is imprecise. I discuss evidence from cognitive science illustrating the pervasive fuzziness of human conceptual and linguistic systems. When we use these systems to discuss the nature of reality, we often succumb to an illusion of conceptual precision that makes it very hard to realize that our mental tools are too imprecise to make useful progress on may questions that sound deep.