IBE, Bayesianism, and the Confirmation of Mathematical Conjectures
Title: IBE, Bayesianism, and the Confirmation of Mathematical Conjectures Abstract: Are mathematical conjectures confirmed by mathematical evidence in much the same way as scientific hypotheses are confirmed by empirical evidence? Perhaps, but in what way is that? Some philosophers think that a Bayesian account of confirmation leaves no work for "inference to the best explanation" (IBE) to do. I will suggest that IBE (suitably interpreted) can be incorporated within a Bayesian framework and is useful in understanding the confirmation of mathematical conjectures. But this approach requires both some grasp of explanatory proofs in mathematical practice and some way to apply the Bayesian framework to the confirmation of mathematically necessary truths. I will attempt to address both of these requirements.