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.
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?
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: ruclips.net/video/WIrdyu9WquQ/видео.html One day I'll do one explaining how these two connect, but not yet.
This is very similar, Tarski is talking about Truth predicates, while Godel is talking about completeness and incompleteness, but the process is very similar.
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.
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.
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?
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: ruclips.net/video/WIrdyu9WquQ/видео.html One day I'll do one explaining how these two connect, but not yet.
nice work
Wait, this is how godel proved the incompleteness theorem, right? How is Tarky's proof different?
This is very similar, Tarski is talking about Truth predicates, while Godel is talking about completeness and incompleteness, but the process is very similar.
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.
So they could have been any arbitrary symbols right? And not arbitrary numbers?
Ok but who says its the only way out of this paradox
Why do you pronounce gödel as grdel?
I am famously bad at pronouncing names, My video on Peano Arithmetic is a testament to this issue.
Idk what he does here, probably an equivalent of the Fixed Point Lemma. But he does it in an annoying way.
Honestly your channel's presentation delivery needs help.