Philosophy of Mathematics

If we have any clear and distinct knowledge, then it's knowledge about mathematical facts. This knowledge is about abstract entities, and yet it plays a crucial role in our scientific endeavors. How is mathematical knowledge at all possible? What is it about the practice of mathematics that enables it to produce such apparently certain knowledge? We investigate the development of mathematical thought, focusing in particular on the early 20th century debates about the foundations of mathematics. We also consider issues emerging from the practice of mathematics, such as the legitimacy of using diagrams in proofs.