Logic and Foundations of Mathematics Commons^™

The Reasonable Effectiveness Of Mathematics In The Natural Sciences, Nicolas Fillion

Electronic Thesis and Dissertation Repository

One of the most unsettling problems in the history of philosophy examines how mathematics can be used to adequately represent the world. An influential thesis, stated by Eugene Wigner in his paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," claims that "the miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve." Contrary to this view, this thesis delineates and implements a strategy to show that the applicability of mathematics is very reasonable indeed.

I distinguish three forms of the …

Anti-Foundational Categorical Structuralism, Darren Mcdonald

Electronic Thesis and Dissertation Repository

The aim of this dissertation is to outline and defend the view here dubbed “anti-foundational categorical structuralism” (henceforth AFCS). The program put forth is intended to provide an answer the question “what is mathematics?”. The answer here on offer adopts the structuralist view of mathematics, in that mathematics is taken to be “the science of structure” expressed in the language of category theory, which is argued to accurately capture the notion of a “structural property”. In characterizing mathematical theorems as both conditional and schematic in form, the program is forced to give up claims to securing the truth of its …