Talk (Work in Progress): Nata Yang (MCMP)

Title:

Virtue Theory of Mathematical Understanding

Abstract:

Ernest Sosa's reliabilist virtue epistemology explains the possibility of what we know by showing how we should know -- our cognitive process should rely on the virtuous intellectual competencies to constitute our knowledge. An optimistic anticipation is that Sosa's reliabilist virtue epistemology brings epistemological insight into the epistemic role of mathematical practice in advancing mathematics. The idea is straightforward: normative mathematical practice discerns mathematical truths, propelling the evolution of mathematics as more truths are identified. However, real-world mathematical practices do not always result in knowledge, though they still contribute to mathematics' evolution. Regarding this, this talk questions whether only knowledge counts epistemic success. Adopting a pluralistic response to this question, the study shifts focus to mathematical understanding, examining how it is constituted through truth-driven mathematical practices. This approach represents an adaptation of Sosa's theory within the framework of internalist epistemology. Accordingly, it proposes a normative theory of mathematical understanding.