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I prefer the 2nd theorem which states "A system cannot demonstrate its own consistency" ! It's so powerful and poignant ! I can't but ask myself "can a system be (perfectly) consistent ?" and then "can a system demonstrates its own in-consistency ? But I can't fathom by which end to grab these questions...

Sorry to be frank: This is by no means an "explanation" of GT. On this level the liar paradox (ie. 10 seconds) are sufficient. To add the Penrose-Lucas 'argument' is misleading. I would really recommend the following video: czcams.com/video/qSiLjXlFlYE/video.html (German professor of mathematics)

Say what you want: Joe Rogan had Roger Penrose on his show. Who else does that? Didn't see anyone else interviewing one of the brightest minds in human history. We all look like Cro Magnons next to Sir Roger.

meathead joe mustve walked away thinking that this just meant facts and scientific provability arent worth anything and thats what informed his choice in guests to platform for the rest of the show

The language and the mathematics are not compatible.

Making fun of Joe Rogan because what Penrose is explaining clearly slides upon his bald head is unfair. He has the humility and intelligence to shut up and give the listeners a pleasant experience, which is his job. Much wiser than most of you arrogant pricks who believe are much smarter than you actually are. Just saying.

WONDERFUL!!

Sir. You’re saying a bunch of nothing

Simple, it means we will never know if math is actually right or was BS all along.

Thanks

it is kind of redeeming to learn that wittgenstein did not wanted to accept godel and penrose don't know how to explain it concisely

Penrose is a good example of what can go horribly wrong. As one of the mathematicians who invaded Einstein's theory of relativity, he made up his own rules and satisfied himself that his incorrect "proofs" were valid. It earnt him a very ill-deserved Nobel Prize during a pandemic he himself helped to trigger, because his comprehension of gravity was so sadly lacking.

This is a lie

why are all the videos on advanced set theory by the most insufferable people alive. MUST I LEARN ABOUT SET THEORY FROM JOE ROGAN????

Ha, tell me something I don't know... again...

He is must smarter than Hawking

This is exactly how my long conversation about why not to drink out of the toilet bowl with my dog goes.

Penrose will throw down with anybody; he was a boxer in the 50s!

🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣 And philosophers are smirking like ya’ll just figuring this out? That reason can’t itself justify why reason works to justify reason? Any monkey familiar with the Prolegomena to any Future Metaphysics could’ve told Gödel this. In fact Kant did. That why the man called it the Prolegomena to Any Any Future Metaphysics.

In other words: Start with a set of operations and rules for applying them (such as arithmetic). Godel showed, (1) it is possible to combine the operations according to the rules in ways that cannot be satisfyingly explained by the existing operations & rules. However, (2) To explain those inexplicable things, you will simply, cleverly, invent at least one new operation/rule. Invent an "innovation" and voila, (3) Thanks to the new operation/rule, you can now explain everything that "cannot be satisfactorily explained" (from step 1). However, （4）As it happens, while the addition of the new rule (step 2) did indeed successfully achieve our aim (step 3), there are now ALSO some fresh things that are possible (thanks to the new operations/rule in step 2) and SOME of those fresh things cannot be satisfactorily explained (seems like be are back at step 1, but these new things are fresh; they were impossible without the new rule that was invented in step 2). Go to step 5 to see how to deal with these "fresh things". (5) To deal with these fresh things, we just need to "repeat" step 2 but with a fresh innovation. Our clever, fresh innovation will succeed to get us to step 3 ( all the fresh things will now be satisfactorily explained), but it will also lead us to a fresh case of step 4. This sounds like an endless loop, but it's more like a tower that is built higher and higher. Sometimes, people say that Godel's theorem "breaks" mathematics. Quite the opposite. Without Godel's theorem, Math would eventually die -- at step3! But, as Godel has shown, every time we succeed in solving every (or, generally, almost any) existing set of math puzzles, we will also create a fresh set puzzles never before seen (step 4) to which we can turn our attention. Mathematics has no end. Godel proved that mathematics is infinite; it will never end. Math will only be increasingly interesting. It appears that we have every reason to believe the same might be true of Physics, too: There will never be an ultimate "theory of everything" in Physics just as there will never be a "complete" mathematics. Every time we create a new theory of Physics, we can use it to create new ways to look at Physical reality (new kinds of telescopes for example, eg LIGO) and we'll use the new tools to discover new things that will themselves need to be explained. Math and Science are both unending projects that will keep us and our descendents endlessly engaged. There is likely every reason to suppose that this might also be true of every other interesting human endeavour. For example, Justice: We strive to create a perfect system of justice; but while we might be able to bring justice to every existing problem, as we create new rules and laws and procedures to address existing injustices, we create new situations in which fresh injustices may arise; fresh injustices which we'll be able to address with new proceedings and laws. People may be able to continuously improve our situation because we can always find a way to solve any significant problem in Math, Science, the Law, etc, etc, but in doing so we will not come to a "final" answer because each improvement we make will bring to our attention new issues to which our attention will be drawn and which we'll strive to improve. Godel's theorem is a profound insight into mathematics but perhaps also into every other interesting facet of our universe and ourselves.

I have a bachelors in math. After I graduated I read Godel’s incompleteness theorem. What a bunch of gobbledygook crap. All of that to “prove” that yeah, math (a system of logic designed within a larger system of reality) might not be able to prove everything in reality. Ya think?

Proof itself unprovable.

All this time I was waiting for Joe to interrupt and ask if Roger saw last UFC fight.

Penrose said: "If you trust the algorithm for proofing mathematical things, then you can see by the way it's constructed that it's true but you can also see (by the way it's constructed) that it cannot be proven by this procedure." What exactly are the "it"s referring to? To the algorithm for proofing? Or to a statement the algorithm was used on?

The idea of someone like Roger Penrose going on Joe Rogan’s podcast lol. I don’t get why he’d want to be associated with that

“Jamie, pull up that video of the bear fighting Gödel.”

The dumb trite comments signal the end of our Empire.

Joe Rogan, thank you for the brilliant conversation with the brilliant Roger Penrose!❤ I am sure Roger Penrose is assured that when he has to deal with thugs, you are watching his back!

Explanation incomplete. I look forward to Rogan dumbing that down for me.

To me, Godel's Essential Incompleteness Theorem simply means there is no finite set of axioms that can encompass all the truthful things that can be said about infinite sets... which confirms what my naive intuitions about infinite sets would say.

P is false = P . Then by sub. P is false is false. But P is still present. An infinite regress.

Joe was waiting for him to finish so he could ask him if he's ever done DMT.

I'd never believed the day would come that someone would want to swap a Porsche for a yaris, and I'd agree. That yaris looks like a great car.

Kant.

Do we really have a philosophy that explains the internet? Surely this is what Godel is talking about. Systems are just that, systems, which are reproducible, like computer language.. But meaningless in epistemological terms. We have produced an idiot, even autistic, universe.