Joel David Hamkins & Graham Priest: The Liar Paradox & The Set-Theoretic Multiverse | RP #60

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.

Background:

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.

[joeldavidhamkins]

Joan Bagaria, mentioned in the introduction, is staunchly Catalan, rather than Spanish, and based in Barcelona.

[berick]

This is certainly one of the podcasts of all time

[mkhex]

Priest and Hamkins is a dialogue I am only now realizing I needed

[StephenPaulKing]

Robinson, you might look into Non-well founded set theory. Jon Barwise, no longer with us, did a lot of work on its application in computer science.

[Erin-unxp]

The electrons in that painting is definitely a responsive energy!

[annesmith]

Discussion much appreciated
TY gentlemen 💕

[zeke]

Love both guests. And awesome dialogue. But I like the mustache even more

[romanbesel]

Those are two of my favorite thinkers. If you now bring Penelope Maddy on, I die a happy man.

[mikhailfranco]

I recommend the book:
_The Liar: An Essay on Truth and Circularity_
Barwise and Etchemendy

[bilgekoksal]

Great video! I wonder how the discussion at the end of the part Paraconsistent Logic and the Liar would go on. It seems reasonable that replacing the liar sentence with "this sentence is either false or not well-formed" should be giving rise to another paradox for Joel. Although he says he wouldn't recognize it as a well-formed proposition in the first place (which I am inclined to accept), then I am not so happy, because I can argue again what Graham said, and I feel like going back and forth between these is the liar all over again. Does anyone have any thoughts on this?

[muhammadhanzlaqadri]

Wish you could’ve invited Hartry Field too.

[MasterBoshan]

I saw this when it had <100 views. Few days later, everybody had a weekend and then the views came.

[StephenPaulKing]

Self-consistency of axioms seems to be the criteria of existence of a logical system. How is self-consistency proven internally in such cases?

[johnschindler]

If I understand Sorensen's setup of Yablo's paradox (46:25) correctly, can't we assign alternating truth-values consistently with the relevant instances of the T-Schema? That is, all odd-numbered people speak truly and all even-numbered people speak falsely, or vice versa.

[patrickwithee]

Isn’t the Liar’s Paradox a formal fallacy? That is, we can’t just define A=~A at the meta-level, but this seems to be exactly what the Liar’s Paradox is doing. Clearly, if you suppose A<—>~A, you’ll be able to get a contradiction and prove ~(A<—>~A). Those seem to be our two options: prove that an in-language formalization of the Paradox is just an inconsistency, or fallaciously define a formula as its negation.

In terms of natural language, I agree that “this sentence is false” seems to be saying something, but we know that a formal theory’s truth isn’t definable by that formal theory, a la Tarski. So, whatever it’s saying is either just absurdity in a different fashion, or it’s just a demonstration that semantic truth is logic/theory-specific.

[pmcate]

the poor audio on graham's end kinda makes this unlistenable.

[timdion]

All logicians are liars. It is the only solution to the Liar's Paradox... Alas, my statement is true but not provable.

[annaclarafenyo]

This discussion is pointless, as neither the mathematician or the philosopher understand computational foundations.

[annesmith]

Eubulides the Megarian🏺😎
💞impredicativity💞