Pluralism in the philosophy of mathematics : Can Pluralism give a satisfactory solution to the foundational crisis in mathematics?

Sammanfattning

Over the last decade, the demand for a unifying and foundational theoryof mathematics has become more critical. This is referred to as ”thefoundational crisis in Mathematics”. In this paper I will present a newposition in the philosophy of mathematics called Pluralism. Pluralismquestions the demand for a foundational theory that can encompass all ofmathematics, and consider the possibility of having opposing mathematicaltheories that are all veracious. I will argue for Pluralism being themost advantageous theory in the philosophy of mathematics in responseto the foundational crisis of mathematics. I will argue for this by discussingthe three major themes in philosophy of mathematics: Realism,Anti-realism, and Nihilism, and show that none of them are suitable asa foundational theory. I will further argue that Pluralism gives us thebest account of mathematics as it is practiced and gives the best possibleoutset for future mathematical research and creativity.