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

[@joeldavidhamkins5484]

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

[@robinsonerhardt]

thank you for clarifying this!

[@Spacegraham]

Great lineup...great video!

[@robinsonerhardt]

thanks graham

[@romanbesel4759]

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

[@robinsonerhardt]

will get to work on that, then!

[@zeke4665]

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

[@robinsonerhardt]

I prefer the guests but am enjoying the mustache too

[@annesmith2400]

Discussion much appreciated TY gentlemen 💕

[@berick0176]

This is certainly one of the podcasts of all time

[@robinsonerhardt]

that’s precisely what I want to hear

[@bilgekoksal3537]

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?

[@MasterBoshan]

I saw this when it had

[@robinsonerhardt]

there’s a few billion people it hasn’t hit yet

[@pawarranger]

wow what a treat

[@robinsonerhardt]

🦢

[@timdion9527]

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

[@muhammadhanzlaqadri7229]

Wish you could’ve invited Hartry Field too.

[@mikhailfranco]

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

[@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.

[@ReflectiveJourney]

super hyped for this one.

[@robinsonerhardt]

me too and I’ve listened three times

[@johnschindler4152]

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.

[@joeldavidhamkins5484]

If the Yablo assertions assert "all later assertions are false," then your proposal wouldn't work. If they each merely assert "the next assertion is false", then your proposal is fine. It is the former situation, consequently, that is more paradoxical.

[@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?

[@pmcate2]

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

[@Erin-un3xp]

The electrons in that painting is definitely a responsive energy!

[@mkhex87]

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

[@BlakeErhardt-Ohren]

[@robinsonerhardt]

yes agreed

[@patrickwithee7625]

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.

[@Erin-un3xp]

This is great!

[@robinsonerhardt]

I'm so glad you like it :)

[@pairadeau]

this

[@annaclarafenyo8185]

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

[@jwp4016]

This the perfect youtube comment for the most renowned logician and set theorist lol

[@annaclarafenyo8185]

@@jwp4016 "Renowned". Joel Hamkins is a good set theorist, but he doesn't follow modern foundations, although he's a finitist when you compare him to other set theorists.

[@pmcate2]

@@annaclarafenyo8185 It's not clear how you came to the conclusion that Joel is more finitist than set theorists. Much of his work is infinitary.

[@annaclarafenyo8185]

@@pmcate2 He's a finitist compared to Woodin. Woodin still thinks the Continuum Hypothesis has an answer.

[@annaclarafenyo8185]

@@pmcate2 It is not easy to see when work in set theory is "infinitary". Likely the most finitist person in set theory was Cohen, the second in line is Solovay.

[@annesmith2400]

Eubulides the Megarian🏺😎 💞impredicativity💞