YuTang Wu

In contemporary epistemology, fallibilism has become the universally presupposed stance. This trend is not confined to empirical knowledge; in recent years, it has also been extended to mathematical knowledge. In this paper, I argue against the fallibilist view on mathematical justification, and advocate infallibilism. Specifically, I examine the fallibilist account offered by De Toffoli (2021), which is the most developed version in the literature. This account proposes a distinctive characterisation of mathematical justification, which is fallibilistic. To counter this, I will demonstrate that De Toffoli’s argument is unsuccessful. From the objections emerges the positive view that I go on to develop and defend, which is a bi-level theory of mathematical epistemology. In my theory, I distinguish between first-level justification, which concerns mathematical beliefs, and second-level justification, which pertains to judgments about the justificational states of those mathematical beliefs. I will argue that while second-level justification is fallible, first-level justification is infallible, and it is this first-level justification that constitutes mathematical justification. Based on my picture, I then advocate an infallibilist view of mathematical justification.