282 | Joel David Hamkins on Puzzles of Reality and Infinity

282 | Joel David Hamkins on Puzzles of Reality and Infinity

The philosophy of mathematics would be so much easier if it weren't for infinity. The concept seems natural, but taking it seriously opens the door to counterintuitive results. As mathematician and philosopher Joel David Hamkins says in this conversation, when we say that the natural numbers are "0, 1, 2, 3, and so on," that "and so on" is hopelessly vague. We talk about different ways to think about the puzzles of infinity, how they might be resolved, and implications for mathematical realism.

Blog post with transcript: https://www.preposterousuniverse.com/podcast/2024/07/15/282-joel-david-hamkins-on-puzzles-of-reality-and-infinity/

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Joel David Hamkins received his Ph.D. in mathematics from the University of California, Berkeley. He is currently the John Cardinal O'Hara Professor of Logic at the University of Notre Dame. He is a pioneer of the idea of the set theory multiverse. He is the top-rated user by reputation score on MathOverflow. He is currently working on The Book of Infinity, to be published by MIT Press.


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347 | Andrew Guthrie Ferguson on How Your Data Will Be Used Against You

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346 | Erica Cartmill on How Human and Animal Minds Think and Play

346 | Erica Cartmill on How Human and Animal Minds Think and Play

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AMA | March 2026

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345 | Adam Elga on Being Rational in a Very Large Universe

345 | Adam Elga on Being Rational in a Very Large Universe

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344 | Adam Gurri on Liberal Democracy and How to Fight For It

344 | Adam Gurri on Liberal Democracy and How to Fight For It

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343 | Tom Griffiths on The Laws of Thought

343 | Tom Griffiths on The Laws of Thought

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AMA | Feb 2026

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