Dissertation, Umsl (
2013)
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Abstract
Inference to the best explanation (IBE) is the principle of inference according to which, when faced with a
set of competing hypotheses, where each hypothesis is empirically adequate for explaining the phenomena, we
should infer the truth of the hypothesis that best explains the phenomena. When our theories correctly display this
principle, we call them our ‘best’. In this paper, I examine the explanatory role of mathematics in our best scientific
theories. In particular, I will elucidate the enormous utility of mathematical structures. I argue from a reformed
indispensability argument that mathematical structures are explanatorily indispensable to our best scientific
theories. Therefore, IBE scientific realism entails mathematical realism. I develop a naturalistic, neo-Quinean
ontology, which grounds physical and mathematical entities in structures. Mathematical structures are the truthmakers for the entities of our quantificational discourse. I also develop an ‘ontic conception’ of explanation,
according to which explanations exist in the world, whether or not we discover and model them. I apply the ontic
account to mathematical structures, arguing that these structures are the explanations for particles, forces, and even
the conservation laws of physics. As such, mathematical structures provide the fundamental grounding for
ontological commitment. I conclude by reviewing the evidence from modern physics for the existence of
mathematical structures.