The philosophy of mathematics has a large number of open questions. How do we single out a particular number to refer to? How do we acquire knowledge about numbers? In what way do we acquire the concepts used in mathematical thought? The purpose of this project is to investigate the relevance of empirical results for such questions. The aim is to demonstrate that empirical results are highly relevant for answering the questions above.
This work is important because it shows that empirical results are relevant for developing a philosophy of mathematics that captures how we actually use mathematics, in a way that is both more extensive and more detailed than can be found anywhere in the current literature. It is also expected to lead to improvements in mathematics education.