“Mathematical Gettier Cases"
Abstract: Are Gettier cases possible in mathematics? At first sight we might think not: The standard for mathematical justification is proof, and since proof is bound at the hip with truth, so there is no possibility of having an epistemically lucky justification of a true proposition. In this paper, we argue that Gettier cases are possible (and very likely actual) in mathematical reasoning. We do this via arguing that abductive inference and auxiliary assumptions are essential to mathematical practice. This results in the following two argumentative strands: (1.) We dispute the claim that the standard of mathematical justification is the production of an actual formal proof, and (2.) We argue that even if we do accept that the standard of justification is formal proof, there is still the possibility of luck resulting in true belief. We'll do this by considering several examples from the history of mathematics, contemporary mathematics, and some (hopefully not too distant) possible worlds. We also discuss how these examples relate to the traditional responses to Gettier-like problems.