Epistemic Value Pluralism in the Practice of Stochastic Analysis
Epistemic Value Pluralism in thePractice of Stochastic Analysis - Case study in the dynamic approach
IND's Studenterserie nr. 127, 2025, Speciale i Forsikrings Matematik
Mads Fencker
Vejledere: Mikkel Willum Johansen & Jesper Lund Pedersen
Abstract:
This thesis is a case study of the dynamic approach in stochastic analysis. As a response to rigor pluralism in Tanswell (2024), I present two proofs from the practice of mathematics to argue for epistemic value pluralism.
The contemporary discussion of mathematical rigor will be presented through advocates of opposing views. I argue that the standard view of rigor presents an operational conception that enables a clear demarcation of rigorous and unrigorous proofs. The success and failure in ascribing rigor present the possibility to address other valuable qualities of unrigorous proofs. Unlike rigor pluralism, which risks collapsing into semantic relativism, epistemic value pluralism better accommodates the diverse epistemic functions of proofs within mathematics.
The analysis and discussion are anchored in a case that presents two proofs of the same theorem in stochastic analysis: one by the dynamic approach and the other by the monotone class theorem. Although the proof by the monotone class theorem is rigorous, the proof by the dynamic approach, though unrigorous, demonstrates significant epistemic value by fostering intuition. I argue that such unrigorous proofs, although lacking precision, have an indispensable utility for mathematics.
Furthermore, I explore the ontological implications of semantic externalism, emphasizing how externalization of mathematical objects beyond their definitions allows complementary characterizations. By this, producing deeper familiarity with the concept.
In conclusion, epistemic value pluralism provides a robust framework for analyzing mathematical practice, demonstrating how unrigorous proofs, such as the one by the dynamic approach, offer indispensable utility by fostering intuition.