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
References:
- The Unreasonable Effectiveness of Mathematics in the Natural Sciences (https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf) by Eugene Wigner.
- Proofs and Refutations (https://en.wikipedia.org/wiki/Proofs_and_Refutations#:~:text=Proofs%20and%20Refutations%3A%20The%20Logic,characteristic%20defined%20for%20the%20polyhedron.) by Imre Lakatos.
Mark Colyvan (http://www.colyvan.com/) 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).
Special Guest: Mark Colyvan.
