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

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

Robinson's Podcast vor 3 Jahren

0:00

3:11:16

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

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

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