20000 Jillion + 12

General Aim of the Project

The general aim of my dissertation is to clarify the concept of ‘structure’ as it is used within mathematics and the philosophy of mathematics. There are currently a number of views within the philosophy of mathematics which can be described as ‘structuralist’. The common theme holding these widely divergent views together is the belief that mathematics is the science or study of structures. Where most of these views diverge is in their understanding of the concept of ‘structure’. Some of these views are realist in that they take structures to possess some sort of positive ontological content, while others are radically nominalist and treat structures merely as helpful ways of speaking. My aim is to contribute something novel to the structuralist debate within the philosophy of mathematics through a combination of historical analysis of the genesis of the concept of structure as well as a specifically ontological focus on this concept, which I believe has not yet been adequately pursued. My eventual position will be broadly ‘realist’ insofar as it takes structures seriously on an ontological level, but as will become clear below, the way in which I situate ‘structure’ within a broad ontological view is somewhat different than most extant realist structuralist positions. I hope that it becomes clearer below just how my ontological approach differs from most current positions within the philosophy of mathematics.