Daniele Molinini (University of Rome)
December 5 FRI — 14.30-16.30
Aula Seminari — Cortile Ghiacciaia, II floor (Via Festa del Perdono 7, Milano)
A reason for a mathematical reason?
The problem of mathematical explanation in science and in mathematics
Abstract: The philosophical problem of mathematical explanation steps from a very simple observation that we face when we are asked to account for (some bits of) scientific practice: there are cases in which the function of mathematics in science (i.e. the natural and social sciences, which we distinguish from mathematics), and in mathematics itself, is not simply to show that an empirical phenomenon (or a mathematical fact) occurs (or it’s true, in the case of mathematics), but it extends to that of shed light on why the empirical phenomenon (or the mathematical fact) occurs (or it’s true, in the case of mathematics). In other words, in these situations the mathematics we use seems to provide an answer to the question "Why does the empirical phenomenon F occur?" (or, in the case of pure mathematics, “Why is that particular mathematical fact M true?”). The problem amounts then to capture an adequate notion of mathematical explanation, i.e. a notion capable to account for those situations (in science and in mathematics itself) in which mathematics seems to have explanatory power.
In this talk I shall provide an introduction to the problem of mathematical explanation. I shall offer some examples of mathematical explanation and show how the recent interest in this topic can be traced back to Aristotle. Moreover, by focusing on two topics that are often discussed in relation to mathematical explanation (the new indispensability argument for mathematical realism and the applicability of mathematics in science), I shall show how the ongoing debate on mathematical explanation has important ramifications in different areas of philosophy of science and philosophy of mathematics.