Set theory, pluralism, and the multiverse view—About Logic #13

A sweeping conversation on the philosophy of mathematics and set theory, including a few core disagreements, on the About Logic series with Deniz Sarikaya and Thorsten Altenkirch.

Recently I was invited by Deniz Sarikaya and Thorsten Altenkirch to appear on their podcast About Logic to talk about logic, the philosophy of mathematics, and set theory. The episode has now been released, so please take a look—I think you will enjoy it.

We discussed a sweeping selection of topics—the nature of mathematical truth, proof, platonism, fictionalism, the roles of set theory in mathematics, pluralism in the foundations of mathematics, the multiverse view, the continuum hypothesis, the junk-theorem phenomenon, the dispute between classical logic and constructive mathematics, and much more.

I should confess that one of my hosts and I are known to disagree on a few core philosophical matters—there are some Twitter exchanges to prove it—and our conversation here did not shy away from these points of contention. In a friendly spirit of constructive philosophical exchange, there were probing questions, challenges, and witty counterpoints. What an enjoyable and fruitful meeting of the minds it was. On which side of these questions do you find yourself? Post your views in the comments.

Please enjoy!

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Learn more at these links:

• Deniz and Thorston’s About Logic YouTube channel, where you’ll find numerous interviews with prominent logicians, mathematicians, and philosophers. Highly recommended.

• Joel David Hamkins YouTube channel

• My book, Lectures on the Philosophy of Mathematics

• My new book, The Book of Infinity

• Joel David Hamkins, “How the continuum hypothesis could have been a fundamental axiom,” Journal for the Philosophy of Mathematics (2024), DOI:10.36253/jpm-2936, arxiv:2407.02463.