Lectures on the Philosophy of Mathematics

[bibtex key=”Hamkins2021:Lectures-on-the-philosophy-of-mathematics”]

From the Preface:

Philosophical conundrums pervade mathematics, from fundamental questions of mathematical ontology—What is a number? What is infinity?—to questions about the relations among truth, proof, and meaning. What is the role of figures in geometric argument? Do mathematical objects exist that we cannot construct? Can every mathematical question be solved in principle by computation? Is every truth of mathematics true for a reason? Can every mathematical truth be proved?

This book is an introduction to the philosophy of mathematics, in which we shall consider all these questions and more. I come to the subject from mathematics, and I have strived in this book for what I hope will be a fresh approach to the philosophy of mathematics—one grounded in mathematics, motivated by mathematical inquiry or mathematical practice. I have strived to treat philosophical issues as they arise organically in mathematics. Therefore, I have organized the book by mathematical themes, such as number, infinity, geometry, and computability, and I have included some mathematical arguments and elementary proofs when they bring philosophical issues to light.

9 thoughts on “Lectures on the Philosophy of Mathematics

  1. Pingback: Lectures on the Philosophy of Mathematics, Oxford Michaelmas Term 2020 | Joel David Hamkins

  2. Pingback: A model of set theory with a definable copy of the complex field in which the two roots of -1 are set-theoretically indiscernible | Joel David Hamkins

  3. Dear Joel –

    I bought myself a copy of the book for the holidays – I have just started reading it.

    I noticed a minor typo on the very last line of page 5 – the \qed box is at the end of the sentence, instead of at the end of the line. And it is the wrong size for some reason? (Compare the \qed box on line 6 of the same page.)



    • Thanks very much, Saul! I’ll fix this in the revision. It is an artifact of a workaround for the issues of using the wrapfigure environment with the proof environment—they do not play well together.

  4. Dear prof Hamkins,

    I’ve started reading your book. I learn a tremendous amount from it—it is great. Thank you!

    I’ve noticed a typo in the alternative proof of ‘Infinitude of primes’ in Section 1.9: it ends with “This contradiction our assumption” instead of “This contradicts our assumption”.

    Kind regards,

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