#25 - Mathematical Explanation with Mark Colyvan
from Increments Hosted by Ben Chugg and Vaden Masrani
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 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). Special Guest: Mark Colyvan.
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Chapters
- 0:00 Cold open and intro music
- 0:12 Guest introduction: Mark Colyvan
- 12:30 Main segment: what is mathematical explanation?
- 19:07 Counterfactuals and mathematics
- 35:02 Impossible worlds and counter-possibles
- 45:21 Consistency and Godel's incompleteness
- 1:01:22 Intra vs extra mathematical explanation
- 1:03:35 Mathematical realism and indispensability
- 1:11:50 Honeycomb theorem: math explains biology
- 1:16:51 Alternate logics and paraconsistent logic
- 1:37:27 Thought experiments: uses and misuses
- 1:40:51 Statistical evidence in the courtroom
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