To answer these questions, we dive into Chapter 9 of Conjectures and Refutations: Why are the Calculi of Logic and Arithmetic Applicable to Reality?.

But before we get to that, we touch on some of the good stuff: evolutionary psychology, cunnilingus, and why Robin is better than Batman.

References:

• Conjectures and Refutations, Chapter 9: Why are the Calculi of Logic and Arithmetic Applicable to Reality? https://books.google.ca/books?id=iXp9AwAAQBAJ&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false
• Ben on Do Explain with Christofer Lovgren
• Debate between Spelke and Pinker
• Very Bad Wizards discussing the paper "Oral Sex as Infidelity detection" (episode, paper).
• Sturgeon's Law: https://en.wikipedia.org/wiki/Sturgeon%27s_law#:~:text=Sturgeon%27s%20law%20(or%20Sturgeon%27s%20revelation,science%20fiction%20author%20and%20critic.
• Eugene Wigner's paper The Unreasonable Effective of Mathematics in the Natural Sciences.
• Stoic versus Aristotelian logic. Here is a nice discussion of the differences between the two.
• Rob Wiblin's tweet that all probabilities are subjective probabilities (in an otherwise very good thread).
• Buhler's three functions of language: (i) Expressive, (ii) Signaling, and (iii) Descriptive. See the "Organon Model".
• Piece on Brett Weinstein and Ivermectin.
  

Quotes:

“The indescribable world I have in mind is, of course, the world I have ‘in my mind’—the world which most psychologists (except the behaviourists) attempt to describe, somewhat unsuccessfully, with the help of what is nothing but a host of metaphors taken from the languages of physics, of biology, and of social life.”

“In so far as a calculus is applied to reality, it loses the character of a logical calculus and becomes a descriptive theory which may be empirically refutable; and in so far as it is treated as irrefutable, i.e. as a system of logically true formulae, rather than a descriptive scientific theory, it is not applied to reality.”

Send us the most bizarre use of evolutionary psychology you've seen at incrementspodcast@gmail.com.

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• 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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