Speaker: SARAH FREDERICKS (University of North Texas)

Title: Mathematical Objects: Really Existing, Useful Fictions, or Something in Between?

Abstract: For hundreds of years scholars have debated whether mathematical objects exist in and of themselves and thus are discovered by humans or whether they are useful fictions, devices invented by humans for pleasure or use as tools to make predictions about the world. In the twentieth century one of the largest and most controversial developments in this ancient argument is the Quine-Putnam indispensability argument. It maintains that scientific theories refer to real entities in the world (quarks, stars, black holes, etc.) and that the elements which are indispensable to these theories including mathematical entities should also be understood as real. By investigating the Quine-Putnam indispensability argument we will explore questions about the reality of mathematical entities and the role of scientific and philosophical criteria in such discussions.