Gödel's Incompleteness Theorem. Primitive Recursion.

The real heart of the theorem is primitive recursion and how it can be used to guarantee that Godel sentence exists in the first place. But for some reason so many channels just focus on the Godel encoding.

[danzigvssartre]

Giving the technical details of Godel theorem in 16 minutes while not skipping the technical details. Good work.

[academyofuselessideas]

Cool... I find Godel theorem very deep. One of the best presentations of the general idea of the theorem was given by Smullyan in Forever Undecidable. In that book, Smullyan presents a modal logic for provability, and he proves that in any "self aware" reasoner (or deductive system) will have to be incomplete. The godel numbering becomes the a technical step to prove that PA is "self aware". Great book!

[nukeeverything]

I'm so glad there is at least some vids on Youtube which give a proper discussion on Godel's Incompleteness theorem. The real heart of the theorem is primitive recursion and how it can be used to guarantee that Godel sentence exists in the first place. But for some reason so many channels (even very big channels like Veritasium) just focus on the Godel encoding.

[benheideveld]

A computer reading the text makes it a lot harder to understand, because the requisite intonation from understanding is lacking…
Also putting music under reading a proof shows a complete lack of understanding of the kind of listening required.

[ai_serf]

I love the video and community, GJ!

the PA axioms listed here are wrong. where is, "0 is an element of the natural numbers, or 0 is a natural number?". The whole point of formal systems is to be rigorous. The PA presented here is meaningless. I assume the rest of the video will just be more music and spectacle without meaning?

also the rules come from FOL and PL, they aren't PA specific....

[metinelitas]

Your style resembles of Eugene Khutoryansky.