Graduation Year
2016
Document Type
Open Access Senior Thesis
Degree Name
Bachelor of Arts
Department
Mathematics
Second Department
Philosophy
Reader 1
Yuval Avnur
Reader 2
Gizem Karaali
Rights Information
© 2016 Hannah C. Thornhill
Abstract
This thesis examines possible philosophies to account for the practice of mathematics, exploring the metaphysical, ontological, and epistemological outcomes of each possible theory. Through a study of the two most probable ideas, mathematical platonism and fictionalism, I focus on the compelling argument for platonism given by an appeal to the sciences. The Indispensability Argument establishes the power of explanation seen in the relationship between mathematics and empirical science. Cases of this explanatory power illustrate how we might have reason to believe in the existence of mathematical entities present within our best scientific theories. The second half of this discussion surveys Newtonian Cosmology and other inconsistent theories as they pose issues that have received insignificant attention within the philosophy of mathematics. The application of these inconsistent theories raises questions about the effectiveness of mathematics to model physical systems.
Recommended Citation
Thornhill, Hannah C., "The Philosophy of Mathematics: A Study of Indispensability and Inconsistency" (2016). Scripps Senior Theses. 894.
https://scholarship.claremont.edu/scripps_theses/894
