Date of Award

Spring 6-15-2025

Document Type

Thesis (Senior Honors)

Department

Philosophy

First Advisor

Kenneth Walden

Abstract

This thesis examines whether the indispensability argument justifies belief in the existence of mathematical entities. I adopt ontological naturalism, arguing that we should believe in entities that feature in our best scientific theories, which are determined through inference to the best explanation. The indispensability argument contends that because mathematical entities are explanatorily indispensable to our best scientific theories – as demonstrated by examples like the prime number explanation of cicada life cycles – we should believe they exist just as we believe in electrons and stars.

However, I identify a challenge: our scientific explanations are inherently parochial, shaped by human cognitive interests, abilities, and limitations. Using Bradford Skow's distinction between first-level and higher-level reasons why, I explore whether mathematical explanations could be segregated as merely accommodating human limitations. I argue that this approach fails because first-level and higher-level reasons are fundamentally entangled – we cannot identify causes without appealing to broader theoretical frameworks that include mathematical patterns.

This entanglement reveals that explanation is unavoidably parochial, meaning our ontology will necessarily reflect pragmatic considerations. Rather than undermining the indispensability argument, I contend this shows we should accept a pragmatic approach to ontology. I defend this position by comparing it with Rudolf Carnap's linguistic frameworks approach, arguing that the indispensability argument's use of a single total theory provides a more unified and valuable method for determining what exists. The thesis concludes that while our belief in mathematical entities has an ineliminable pragmatic dimension, the indispensability argument remains a compelling justification for mathematical anti-nominalism.

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