Mathematics, Meaning, and Commitment
Smith, Mark Charles Reginald
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This thesis offers a defence of realism in mathematics, principally through an a priori re-construal of the indispensability argument as revelatory of the commitments of mathematical thought. Following the articulation and defence of that argument—called the ‘argument from constraint’—in the first chapter, I address semantic and metaphysical consequences and objections in turn. The second chapter broaches the value of Fregean semantics for arithmetical language, and the indispensability of semantic considerations in accounting for mathematical thought. The third chapter assesses and responds to objections from the fictionalist account of mathematical thought and meaning, and the final chapter articulates a programmatic proposal for mathematical epistemology.