Introduction to Abstractionism

First paragraph: Abstractionism in philosophy of mathematics has its origins in Gottlob Frege’s logicism—a position Frege developed in the late nineteenth and early twentieth century. Frege’s main aim was to reduce arithmetic and analysis to logic in order to provide a secure foundation for mathematical knowledge. As is well known, Frege’s development of logicism failed. The infamous Basic Law V— one of the six basic laws of logic Frege proposed in his magnum opus Grundgesetze der Arithmetik—is subject to Russell’s Paradox. The striking feature of Frege’s Basic Law V is that it takes the form of an abstraction principle

Categories and Constructs

University of Minnesota Ph.D. dissertation. August 2015. Major: Philosophy. Advisors: Geoffrey Hellman, Roy Cook. 1 computer file (PDF); vii, 97 pages.The essays in this collection concern two subjects, each of which falls within the purview of the philosophy of mathematics. The first three essays concern the philosophical status of category theory. The last essay concerns the possibility of a social constructivism regarding mathematicalia