We often talk of explanation in the context of empirical sciences, but what about explanation in logic and mathematics? Is there such a thing? If so, what does it look like and what are the consequences? In this episode we sit down with professor of philosophy Mark Colyvan and explore
- How mathematical explanation differs from explanation in the natural sciences
- Counterfactual reasoning in mathematics
- Intra versus extra mathematical explanation
- Alternate logics
- Mathematical thought experiments
- The use of probability in the courtroom
- The Unreasonable Effectiveness of Mathematics in the Natural Sciences by Eugene Wigner.
- Proofs and Refutations by Imre Lakatos.
Mark Colyvan is a professor of philosophy at the University of Sydney, and a visiting professor (and, previously, Humboldt fellow) at Ludwig-Maximilians University in Munich. He has a wide array of research interests, including the philosophy of mathematics, philosophy of logic, decision theory, environmental philosophy, and ecology. He has authored three books: The Indispensability of Mathematics (Oxford University Press, 2001), Ecological Orbits: How Planets Move and Populations Grow (Oxford University Press, 2004, co-authored with Lev Ginzburg), and An Introduction to the Philosophy of Mathematics (Cambridge University Press, 2012).