Inference to the Best Explanation as a Form of Non-Deductive Reasoning in Mathematics.

The article discusses how mathematicians utilize Inference to the Best Explanation (IBE) to confirm their conjectures, positing that the best explanation for mathematical evidence is often a proof that supports the conjecture. It argues that non-deductive reasoning plays a crucial role in mathematics, particularly in the context of experimental mathematics, where computational evidence can lend support to conjectures even before formal proofs are established. The paper further explores the relationship between IBE in mathematics and scientific reasoning, suggesting that explanatory considerations can enhance the confirmation of mathematical hypotheses, particularly when mathematicians anticipate the existence of unified proofs that explain observed patterns in their evidence. The author also addresses the challenges of applying Bayesian confirmation theory to mathematical conjectures, proposing a framework that accommodates the unique aspects of mathematical reasoning. [Extracted from the article]