Talk (Work in Progress): Mohammed Maarefi (IUSS Pavia)

Title:

What is a Mathematical Explanation?

Abstract:

Mathematics plays a significant role in natural as well as social sciences. In particular, there is an explanatory role that mathematics plays when it comes to accounting for physical, as well as social phenomena. This role was and is a central issue in philosophy of science. But the question ‘does mathematics have an explanatory role when accounting for mathematical facts?’ has not been addressed officially in the literature until recently. Mancosu addresses five questions about mathematical explanation. The fourth and fifth of the list are ‘what are the philosophical accounts of mathematical explanation?’ and ‘what is the relationship between mathematical explanation and scientific explanation?’. This paper aims to provide mathematical explanation with an account that is motivated by explanations in physical sciences. I'll argue that a separatist theory of grounding relation is the natural proposal for solving the questions about mathematical explanation. To do that, I'll first make a few natural assumptions about grounding relation, i.e. a form of non-causal determination (referred to as determinism_{G}) that ‘backs’ an explanation. Then, I put forward my dependency argument, claiming that this version of grounding results in a dependency notion that, unless proven guilty, is a natural proposal for mathematical explanation.