Joel David Hamkins is the O’Hara Professor of Philosophy and Mathematics at the University of Notre Dame, where he recently moved from the University of Oxford. Joel is one of the world’s leading set theorists and philosophers of mathematics. Graham Priest is a Distinguished Professor in the philosophy department at the CUNY Graduate Center. He is one of the most influential philosophers of the past fifty years, and has done important work on a wide range of topics, ranging from the philosophy of mathematics (his doctorate is in mathematics from the London School of Economics) to logic and eastern philosophy. Robinson, Graham, and Joel discuss two topics—the liar paradox and the set-theoretic multiverse. More particularly, they address how solutions to the former revolve around questions of logical pluralism (is there more than one “correct” logic, and if so, how should we determine which to use in any given situation?), and regarding the latter, they address the metaphysics of the multiverse, how the multiverse theory squares with its monist alternative, and how it relates to the age-old question: Is mathematics created or discovered? Some resources for background information are included below. Check out Joel’s current project, The Book of Infinity, which is an accessible text on paradoxes and infinity. Joel has made the novel move of serializing it on Substack, so you can participate in its creation by checking out the link below, and otherwise see what he’s thinking about and working on through Twitter, MathOverflow, and his blog. You can keep up with Graham and his ever-growing, immense body of work through his website.

Graham’s Website: https://grahampriest.net

Joel’s Blog: http://jdh.hamkins.org

Joel's MathOverflow: https://mathoverflow.net/users/1946/joel-david-hamkins

Joel's Substack: https://joeldavidhamkins.substack.com

Joel's Twitter: https://twitter.com/JDHamkins

Background:

The Liar Paradox on the SEP: https://plato.stanford.edu/entries/liar-paradox/

Set Theory on the SEP: https://plato.stanford.edu/entries/set-theory/

Robinson's Website: http://robinsonerhardt.com

OUTLINE:

00:00 In This Episode…

1:12 Introduction

11:16 Graham’s History with the Liar Paradox

12:51 An Explication of the Liar

15:03 Paraconsistent Logic and the Liar

32:32 A Deflationary Account of Truth and the Liar

34:51 Joel’s Approach to the Liar

38:37 Hartry Field and the Liar

41:18 The Yablo Paradox

48:22 When to Change the Logic

56:24 A Difference in Opinion on Logic?

1:01:44 The Set-Theoretic Multiverse

1:14:43 Monism and Pluralism About the Set-Theoretic Universe

1:35:35 Philosophical Answers to Mathematical Questions

1:39:16 On Woodin’s Program

1:46:12 Logical Pluralism and the Set-Theoretic Multiverse

1:58:13 The Metaphysics of the Set-Theoretic Multiverse

2:09:42 Is Mathematics Created or Discovered?

2:16:59 The Continuity From Ancient To Contemporary Mathematics

Robinson Erhardt researches symbolic logic and the foundations of mathematics at Stanford University. Join him in conversations with philosophers, scientists, weightlifters, artists, and everyone in-between.