Investigations linking the philosophy and psychology of mathematics

[摘要] Recent progress in the field of cognitive science, specifically with respect to mathematical cognition, along with the turn in the philosophy of mathematics to a focus on mathematical practice, make for a great opportunity for interdisciplinary work that brings together the cognitive science of mathematics and philosophy of mathematics. This dissertation seeks to add to recent examples of such interdisciplinary work. I discuss three somewhat self-contained topics. In chapter two, I discuss some recent work in cognitive science on the topic of mental representation and show how we can shed light on a puzzle in the philosophy of mathematics by applying it to the issue of the mental representation of mathematics. In chapter three, I discuss a couple theories of the cognitive psychology of deduction and why some recent work in the philosophy of mathematics on diagrammatic reasoning in Euclidian proofs shows those theories have some shortcomings. Finally, in chapter four, I discuss how we can get at the question of what makes a system of representation, e.g. numeral systems or formal languages, good for doing mathematics, by considering how the cognitive system uses such things in the course of doing mathematics.

[效力级别] Mathematics

[关键词] Philosophy;Mathematics;Psychology;Deduction;Understanding;Representation;Cognitive;Practice;Mental;Proof, ,