# Infinity Has a Story to Tell

Speaker: Joel David Hamkins
Course: Lectures on Infinity
Watch: https://ergo.org/videos/joel-david-hamkins-infinity-has-a-story-to-tell
Transcript: https://ergo.org/videos/joel-david-hamkins-infinity-has-a-story-to-tell/transcript/
YouTube: https://www.youtube.com/watch?v=6yWpSgD4y9Y

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In this opening lecture, Joel David Hamkins invites viewers into a wide-ranging exploration of infinity. He previews the major puzzles and paradoxes the series will tackle, from Zeno's paradox and supertasks to Galileo's paradox and the crucial distinction between the potentially infinite and the actually infinite. The series traces a historical arc from classical thinkers like Aristotle and Archimedes through Galileo, Frege, Dedekind, and Cantor, arriving at twentieth-century giants such as Gödel, Tarski, and Russell. Hamkins highlights Cantor's discovery of the difference between countable and uncountable infinity as a particularly profound turning point. At the heart of the lecture is an optimistic claim: the study of infinity represents a case of genuine intellectual progress. Ideas that once seemed hopelessly confusing have, over centuries of careful thought, yielded real insight. Hamkins makes the case that we now understand infinity far better than ever before, and he invites viewers to follow along as the story unfolds.

Hello. I'm Joel David Hamkins, and welcome to this series of lectures on infinity.

## Welcome to the Infinity Series

I want to show you all my favorite conundrums and paradoxes of infinity. We're going to see Zeno's paradox, and the paradox of supertasks, Galileo's paradox,

## Paradoxes and Conundrums of Infinity

## Potentially Infinite vs. Actually Infinite

The distinction between the potentially infinite and the actually infinite.

## Countable vs. Uncountable Infinity

Eventually, we'll find the distinction between the countably infinite and the uncountably infinite, a profound idea due to Cantor.

## From Zeno to Gödel: A Historical Journey

We'll start with Zeno and the classical ideas of Aristotle and Archimedes, but eventually, we'll move through Galileo, and then we'll see Frege, and Dedekind, and Cantor, and the 20th century thinkers of Gödel and Tarski, Russell, and so on, the contemporary ideas.

## Genuine Progress in Understanding Infinity

To my way of thinking, the study of infinity is a case where there has been genuine progress. We have come to understand these incredibly confusing, mystifying ideas to a state now where we can say that we understand things much better, actually. These ideas that were formerly confusing, now we think we have some insight about them.

## Join the Lecture Series

So please join me in these lectures and follow along.