Infinitely More

Infinitely More is my ongoing collecton of essays on the mathematics and philosophy of the infinite. You’ll find paradox and fun—and all my favorite logic conundrums and puzzles. I like to reveal the quirky side of mathematics and logic, but with a keen eye open for when they happen to engage with philosophically deeper foundational matters.

The Book of Infinity

Throughout Spring 2023 I shall be serializing here the chapters of my forthcoming book, The Book of Infinity, a series of vignettes on infinity. I aim to cover a huge collection of topics—Zeno’s paradox, the coastline paradox, fractal dimension, supertasks, the paradox of the largest number contest, Galileo’s Salviati, Hilbert’s Grand Hotel, Cantor’s uncountable cardinals, Goodstein and the Hydra, counting in the ordinals, the infinitary Liar paradoxes, the continuum hypothesis, the axiom of choice, orders of infinity, infinitary utilitarianism, infinitary computability, indescribability, the sand reckoner, paradoxes of high dimension, the outer limits of reason via incompleteness, and more.

This substack is an experiment for me, publishing my book by serializing it this way, rather than in the usual manner. I see several benefits, chiefly the stronger connection with all of you, my readers. Please participate in the comment sections on the posts. I try to read everything there and I shall often respond to posts.

I am using this book as the main text for a new undergraduate course I have designed on infinity, which I am teaching this semester at the University of Notre Dame.

About myself

My name is Joel David Hamkins, and I am the O’Hara Professor of Philosophy and Mathematics at the University of Notre Dame. I just arrived here at Notre Dame from the University of Oxford, where until last year I was Professor of Logic, as well as the Sir Peter Strawson Fellow at University College, Oxford. Before Oxford, I was for many years at the City University of New York, where I was Distinguished Professor, on the graduate faculty at the CUNY Graduate Center in Mathematics, in Philosophy, and in Computer Science, and also in Mathematics at the College of Staten Island.

I am both mathematician and philosopher, conducting research in mathematical and philosophical logic, especially set theory and the philosophy of set theory, and the philosophy of mathematics.

My original training is in mathematics, PhD in mathematics 1994 from University of California at Berkeley, BS California Institute of Technology. Over the years my set-theoretic work became increasing engaged with philosophical issues in the foundations of mathematics and so I have turned myself also into a philosopher, although I suppose I have an identity crises as to whether I am a mathematician or philosopher.

You can find out more about me on my blog, on Twitter @JDHamkins, and my YouTube channel. I am the top-rated user on MathOverflow.

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Joel David Hamkins
The Mathematics and Philosophy of the Infinite