TOWARDS A CRITICAL EPISTEMOLOGY OF MATHEMATICS

Abstract

This essay addresses a critical epistemology of mathematics as an investigation into the epistemic limitations of mathematical thinking. After arguing for the relevance of a critical epistemology of mathematics, I discuss assumptions underlying standard arithmetic and assumptions underlying standard logic as examples for such epistemic limitations of mathematical thinking. Looking into the work of philosophically interested scholars in mathematics education such as Alan Bishop and Ole Skovsmose, I discuss some early insights for a critical epistemology of mathematics. I conclude that these insights can only be the beginning, that we are yet far away from a proper understanding of the epistemic limitations of mathematics, and that more research is needed.