“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? Wes Salmon was inclined to think that a Bayesian account of confirmation left 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 enliven my presentation with some (accessible and even amusing) examples from mathematics and I will derive inspiration at several points from Wes Salmon's important work on explanation and confirmation.
Wesley C. Salmon joined the Department of Philosophy as Professor and Chair in 1981. He held the rank of University Professor from 1983 until his retirement in 1999. He exerted a profound influence over philosophy of science as it was practiced in Pittsburgh and internationally. His investigations into scientific explanation, causality, probability and induction and the philosophy of space and time provide a model of insight and clarity, in both thought and word. He set an example personally through his unfailing integrity and kindness. He died in 2001. His memory survives through the scholars who study his work and the many who remember him personally, with respect and admiration. The Wesley C. Salmon Memorial Lecture Fund has been established to support an annual lecture by a prominent scholar in philosophy of science in honor of Wesley Salmon.
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