Inference to the best explanation as supporting the expansion of mathematicians’ ontological commitments

Abstract

This paper argues that in mathematical practice, conjectures are sometimes confirmed by “Inference to the Best Explanation” (IBE) as applied to some mathematical evidence. IBE operates in mathematics in the same way as IBE in science. When applied to empirical evidence, IBE sometimes helps to justify the expansion of scientists’ ontological commitments. Analogously, when applied to mathematical evidence, IBE sometimes helps to justify mathematicians' in expanding the range of their ontological commitments. IBE supplements other forms of non-deductive reasoning in mathematics, avoiding obstacles sometimes faced by enumerative induction or hypothetico-deductive reasoning. Both platonist and non-platonist interpretations of mathematics ought to accommodate explanation in mathematics and ought to recognize IBE in mathematics, though these interpretations disagree on the ontological commitments that mathematicians ought to have. This paper offers an inductive account of why mathematical IBE tends to lead to mathematical truths.