Mathematical Actualism: An Alternative Realist Philosophy of Mathematics

Abstract

The present thesis argues for a philosophy of mathematics, herein dubbed Actualism, which is contrasted with several existing views on the philosophy of mathematics. It begins with a brief introduction to the classical (Platonist) view on the philosophy of mathematics and examines some of the major problems with the account. Thereafter, two alternative philosophies of mathematics (mathematical Constructivism and mathematical Finitism) are examined. Constructivism is detailed in the first chapter through the work of Brouwer and Dummett and, in the second chapter, a description of Finitism is provided through the work of Dantzig and Mayberry. In the final chapter of the thesis, the underpinnings of mathematical Actualism are articulated. The central motivation behind Actualism as an alternative philosophy of mathematics arises from the desire to restore a realist thesis to mathematics that is consistent with the semantics of our modern scientific discourse, or else, with a naturalistic worldview.