Infinitely More

What is infinity? —Lectures on Infinity (lecture 7)

What is infinity? What does it mean exactly to be infinite? Or to be finite?

Oct 28 • Joel David Hamkins

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Every game of chess ends prematurely

Why do we play chess for checkmate instead of playing more naturally to capture the enemy king? Would it be game-theoretically equivalent? Surprisingly…

Oct 15 • Joel David Hamkins

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September 2026

Galileo’s Paradox of Infinity—Lectures on Infinity (lecture 6)

Galileo recognized that some infinite collections can be placed into one-to-one correspondence with a proper subcollection. How are we thus to make…

Sep 30 • Joel David Hamkins

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Ordinal definability—how did Gödel do it?

Gödel proposed the concept of ordinal definability well before the reflection theorem of Lévy and Montague existed. How did he do it?

Sep 20 • Joel David Hamkins

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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

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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

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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

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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

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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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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

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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

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Lectures on Infinity

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

Jul 9 • Joel David Hamkins

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