Confirming Mathematical Conjectures by Analogy

Abstract

AbstractAnalogy has received attention as a form of inductive reasoning in the empirical sciences. Its role in mathematics has, instead, received less consideration. This paper provides a novel account of how an analogy with a more familiar mathematical domain can contribute to the confirmation of a mathematical conjecture. By reference to case-studies, we propose a distinction between an incremental and a non-incremental form of confirmation by mathematical analogy. We offer an account of the former within the popular framework of Bayesian confirmation theory. As for the non-incremental notion, we defend its role in rationally informing the prior credences of mathematicians in those circumstances in which no new mathematical evidence is introduced. The resulting framework captures many important aspects of the use of analogical inference in the domain of pure mathematics.