Marc Lange: 'Inference to the Best Explanation and the Confirmation of Mathematical Conjectures by Mathematical Evidence'
Non-deductive arguments for unproved mathematical hypotheses play crucial roles in mathematics. Some of these arguments operate by "inference to the best explanation" (IBE). To justify this interpretation, I will elaborate IBE in science and explanation in mathematics. I will then put these together to argue that sometimes mathematicians justly use IBE in confirming the truth of mathematical conjectures. I will give some examples of this reasoning from mathematical history and practice, give a Bayesian account of how IBE works, and briefly examine the concepts of mathematical coincidence and natural mathematical properties and kinds.
