Infinitely More

Potential versus Actual Infinity—Lectures on Infinity (lecture 5)

Two radically different conceptions of the infinite—potentialism versus actualism. Disputed for millennia, then a sea change in views. Contemporary…

Sep 9 • Joel David Hamkins

10

3

August 2026

Ordinal definability is definable

Why is the notion of ordinal definability definable in set theory, when the underlying notion of definability, we know, is not definable? How do we…

Aug 31 • Joel David Hamkins

14

2

Is Infinity Even or Odd?

The question is naturally taken in a variety of ways—About the ordinals? Specifically ω? But are we dividing into pairs or cutting in half? Standard or…

Aug 24 • Joel David Hamkins

15

3

The Largest Tweetable Number—Lectures on Infinity (lecture 4)

The paradox of the largest tweetable number. What is the largest number you can tweet?

Aug 12 • Joel David Hamkins

34

12

7

July 2026

The Paradox of Giants: Strange Consequences in High Dimension—Lectures on Infinity (lecture 3)

The paradox of giants, the paradox of Gabriel's horn, the painter's paradox, and further paradoxes of dimension.

Jul 23 • Joel David Hamkins

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4

5

Supertasks: Doing Infinitely Many Things — Lectures on Infinity (Lecture 2)

Let us explore several paradoxical supertasks—the deal with the Devil, balls in a sack, the Chocolatier's game, and more.

Jul 16 • Joel David Hamkins

26

6

Zeno's Paradox and Infinite Sums—Lectures on Infinity (lecture 1)

An ancient puzzle leads ultimately to a remarkable observation on the malleable nature of infinite sums.

Jul 10 • Joel David Hamkins

21

1

4

Lectures on Infinity

A series of lectures on infinity, with all my favorite paradoxes and conundrums.

Jul 9 • Joel David Hamkins

24

3

6

June 2026

The Natural Field of Ordinals

Which numbers are transcendental over the ordinals? Which are irrational? Let us introduce the natural field of ordinals and consider the status of √2…

Jun 25 • Joel David Hamkins

9

2

6

Fermat’s last theorem in the natural ring of ordinals

Are there any nontrivial solutions of the famous Fermat equation in the natural ring of ordinals?

Jun 13 • Joel David Hamkins

11

3

5

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…

Jun 3 • Joel David Hamkins

17

3

3

May 2026

Regrettable Failures in the Natural Ring of Ordinals

The natural ring of ordinals has unique prime factorization, but other natural features go awry—there are consecutive odd numbers, entire intervals of…

May 24 • Joel David Hamkins

13

9

5