HOW TO READ INTRA-MATHEMATICAL EXPLANATIONS? A DEFENSE FOR THE EPISTEMIC APPROACH

Abstract

Intra-mathematical explanations (IMEs) refer to mathematical facts that serve as expla- nations, such as explanatory mathematical proofs. In this paper, I apply the traditional ontic-epistemic division in philosophy of science to study IMEs and defend an epistemic approach. That being said, IMEs should be considered as cognitive achievements instead of mind-independent entities. These cognitive achievements refer to the enhancement of understanding of the target explanandum. I offer two arguments to show that if philosophers take mathematicians’ practices seriously, they should adopt an epistemic approach. The first argument focuses on mathematical disagreements, and the second concerns mathematical intuition. Later, I discuss what mathematical understanding means and propose that it should be understood as motivated procedural knowledge of mathematical practices. Lastly, I conclude the paper with brief discussions on how to adopt an epistemic approach, proposing two critical epistemic factors: mathematical ability and interests.