An epistemology of practice: from knowledge-that to knowledge-how in mathematics
An epistemology of practice: from knowledge-that to knowledge-how in mathematics

Summary/Abstract: Philosophical problems of mathematics are closely tied to how we understand mathematical knowledge. This paper explores two major philosophical perspectives that offer substantially different views on its nature. According to the traditional view, mathematical knowledge consists primarily in knowing what one might call “mathematical truths” or “mathematical facts” - it is comprised of a body of theorems and definitions central to the given field. This perspective places the problem of justification at the core of mathematical epistemology: How do we explain and justify our access to these truths? As we will argue, this focus, which characterizes most traditional epistemology of mathematics, stems from what Ryle called the intellectualist legend - a tendency to treat propositional knowledge as central, while regarding knowledge how as secondary and unworthy of philosophical attention. Some authors felt that the traditional approach overlooked important epistemological aspects of mathematics, which prompted them to offer an alternative perspective based on mathematical practice. This trend marks a shift from metaphysically charged foundational questions to inquiries centered on actual mathematical research and methods, framing mathematical knowledge as a form of knowledge how. In this paper, we contrast the two traditions and explore how the new approach to mathematical knowledge can help us better understand the role and significance of concepts in mathematics.

• Details
• Contents