42 - Joel David Hamkins: Paradox, Infinity, & The Foundations of Mathematics

Joel David Hamkins is the O’Hara Professor of Philosophy and Mathematics at the University of Notre Dame, where he recently moved from the University of Oxford. Joel is one of the leading set theorists and philosophers of mathematics in the world, and he and Robinson discuss a lot—Hilbert’s Hotel, the continuum hypothesis, the set-theoretic multiverse, and even Joel’s dapper hat collection—but the main subject is his upcoming book, The Book of the Infinite, which is an accessible text on paradoxes and infinity. Joel has made the novel move of serializing it on Substack, so you can participate in its creation by checking out the link below, and otherwise see what he’s thinking about and working on through Twitter, MathOverflow, and his blog. The conversation grows technical from 1:10:26-2:00:25, but for those to whom that doesn’t appeal there are timestamps to navigate around this portion of the show.

Substack: https://joeldavidhamkins.substack.com

Twitter: https://twitter.com/JDHamkins

MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins

Joel’s Blog: http://jdh.hamkins.org

OUTLINE:

00:00 Introduction

2:52 Is Joel a Mathematician or a Philosopher?

6:13 The Philosophical Influence of Hugh Woodin

10:29 The Intersection of Set Theory and Philosophy of Math

16:29 Serializing the Book of the Infinite

20:05 Zeno of Elea, Continuity, and Geometric Series

39:39 Infinite Games and the Chocolatier

53:35 Hilbert's Hotel

1:10:26 Cantor's Theorem

1:31:37 The Continuum Hypothesis

1:43:02 The Set-Theoretic Multiverse

2:00:25 Berry's Paradox and Large Numbers

2:16:15 Skolem's Paradox and Indescribable Numbers

2:28:41 Pascal's Wager and Reasoning Around Remote Events

2:49:35 MathOverflow

3:04:40 Joel's Impeccable Fashion Sense

Linktree: https://linktr.ee/robinsonerhardt

Twitter: https://twitter.com/robinsonerhardt

Instagram: https://www.instagram.com/robinsonerhardt/

Twitch (Robinson Eats): https://www.twitch.tv/robinsonerhardt

YouTube (Robinson Eats): youtube.com/@robinsoneats

TikTok: https://www.tiktok.com/@robinsonerhardt