The Indefinability of Truth (Tarski's Theorem)

[@liammcooper]

Excellent work. I think it's pretty simple to comprehend, the statement says there's a number that's not true (p) that can be arithmatized as n, and then also says there's a function that gives you p if you plug in something for m. Which would mean that it's true, but the statement says it's not true, hence you're proving something untrue is true, which is a contradiction.

[@LonleyBoy1105]

One question: I think I watched all the videos on Tarski, but I never ran into the so called "diagonalization lemma", which in other sources I used to understand Tarski and Godel, this lemma was always mentioned. It serves as a stepping stone to prove their theorems. It enables self-reference within a system, I presume. So, am i wrong or you did include it in another video?

[@CarneadesOfCyrene]

I do not have a particular video explaining the diagonalization lemma. Basically it is a proof that self referential statements exist in all languages that do some basic arithmetic. For more on diagonalization itself, check out my video on Cantor: kzbin.info/www/bejne/jXrVlayrbrykq7M One day I'll do one explaining how these two connect, but not yet.

[@Nicoder6884]

7:00 Hold on, plugging that big number into (∃n)(~T(n) & Q(m,n)) will give you (∃n)(~T(n) & Q([big number],n)), which is the original statement. However, that still contains the number and therefore leads to an infinite regress.

[@CarlosLlosa1]

Wait, this is how godel proved the incompleteness theorem, right? How is Tarky's proof different?

[@CarneadesOfCyrene]

This is very similar, Tarski is talking about Truth predicates, while Godel is talking about completeness and incompleteness, but the process is very similar.

[@fluxpistol3608]

So they could have been any arbitrary symbols right? And not arbitrary numbers?

[@yahavitah2791]

Ok but who says its the only way out of this paradox

[@rafaelo6198]

nice work

[@alexandros6433]

Why do you pronounce gödel as grdel?

[@CarneadesOfCyrene]

I am famously bad at pronouncing names, My video on Peano Arithmetic is a testament to this issue.

[@BelegaerTheGreat]

Idk what he does here, probably an equivalent of the Fixed Point Lemma. But he does it in an annoying way.

[@ahmedmahmud4238]

Honestly your channel's presentation delivery needs help.