Mathematical explanation has become a topic central to the philosophy of mathematics and category theory is an area of mathematics that has become increasingly applicable across mathematics. This dissertation bridges these two topics by arguing that category theory has explanatory value. Category theory has proven to be useful in many distinct areas of mathematics and the usefulness of this applicability is often a result of the fact that the category theoretic approach produces explanation. First, I demonstrate that existing accounts of mathematical explanation fall short and that these accounts can be improved by more closely considering features of mathematical practice. Second, I characterize the kind of structure inherent in category theory and illustrate that this structure often gives rise to explanatory generalizations and analogies. I then expand upon this point by considering a specific case study: the van Kampen theorem. This theorem serves as an illuminating example because it can formulated both category theoretically and non-category theoretically. The comparison of these two approaches highlights the explanatoriness of category theory. In total, these three chapters clarify some important features of mathematical explanation and shed philosophical light on the success of category theory within mathematics.
The Explanatory Value of Category TheoryDoctoral Dissertation
|Contributor||Curtis D. Franks, Research Director|
|Degree Level||Doctoral Dissertation|
|Degree Name||Doctor of Philosophy|
|Departments and Units|