Metaphysical Implications Of Godel's Incompleteness Theorem - Part 1

Godel's Incompleteness Theorem - The philosophical implications of Godel's and Tarski's theorems that most logicians and mathematicians don't understand.

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[pugix]

I read Gödel, Escher, Bach in 1981. At the time I was completing a B.A. in Philosophy and taking an elective in Advanced Mathematical Logic, where our text "proved" the completeness and consistency of a particular system of symbols. When I raised the question of the incompleteness theorem of Gödel, the professor sort of glowered. He wasn't going there.

Recently, I went back to the book to see what sort of metaphysics Hofstadter himself held, at least at the time. It wasn't hard to find statements that indicated his physical materialist standpoint. So I agree with Leo that Hofstadter, despite his brilliance, did not fully see the implications.

I recommend Iain McGilchrist's book, The Matter With Things, for an in depth study of the imbalance of the rational and the intuitive side of the mind over the last several centuries. There is a chapter on paradox which argues that paradox is a result of over emphasis on rationality.

I disliked Leo Gura, after watching his interviews on Theories of Everything. But this lecture on Gödel was very good, a clear presentation exhibiting a knowledge of the history as well.

[DonWoschto]

What always keeps me skeptical about your content is the utter lack of people contradicting you in the comments. I would love to see more debate, discussion, questions. Most people seem to take what you say by faith and prefer writing "He made my girfriend squirt", "Leo here", "But Leo", "He put DMT up his donkey" etc..

[rv]

There's quite some sloppiness here. I suggest you read the book _Gödel's Theorem: An Incomplete Guide to Its Use and Abuse_ (2005) by logician Torkel Franzén.

[asura]

Uploads 2 hour long video and calls it part 1. Typical Leo move

[soip]

Beware of this content. There are interesting ideas here but you must be critical so you can tease out the valuable bits from the potentially detrimental. This topic is highly abstract and advanced so, unfortunately, in order for anyone to know if what he’s saying even makes sense they’d have to dig deeper into the details of the theorems. A lot of the ideas he expresses here display a sometimes deep misunderstanding of the concepts he’s referring to, and a lot of the arguments are fallacious. Of course, this does not mean that everything he says is false. Concluding that his conclusions are wrong from the observation that his arguments are fallacious would be itself a fallacious argument. It is quite possible that his statements about the enlightenment experience and the insights you obtain there are accurate. However, his ideas about mathematics, logic, and quantum physics, for example, often suggest that he understands them only at a superficial level. It is true that one does not need to have a PhD or any sort of arbitrary credential in order to talk about these topics, but one does need to at least understand them.

It is unfortunate and somewhat disturbing that he speaks from the position of an enlightened person but he seems intent in spreading misinformation about science and mathematics, perhaps unwittingly. This seems inconsistent with the idea of enlightenment and with a person who has no ego, but this may simply show my lack of understanding of the enlightening phenomenon.

Remember to use your critical mind, especially with assertions as profound and consequential as the ones he makes in his videos. How are we to tell if someone that comes and tells us all about enlightenment is actually legitimate? Without actually having had an enlightenment experience oneself one can only evaluate the legitimacy of their teachings by having a critical mind. For this reason it is possible that making all these inaccurate, and sometimes simply false, statements about science and mathematics will
be detrimental in terms of making enlightenment available to more people. The illegitimacy of some of his claims may push many people away and give this enlightenment enterprise a bad name. Be careful please!

If you want to learn more about paradoxes of self reference and are willing to get into some hardcore math there is one theorem that captures the essence of all the famous self referential paradoxes, it is known as Lawvere’s fixed point theorem. Look it up. You’ll see there that self reference does not necessarily lead to paradox, and in the cases in which it doesn’t it yields what is called a fixed point property. You can formulate your own conclusions from that.

[Lil_curious]

Funny our education system is called “university” when it doesn’t properly question and provide teachings about the Universe at all… is that a paradox lol

[RepoNut]

But are you qualified to tell me why you're qualified.... Let that sink in. Good discussion great video. Namaste

[ZakAmbrose]

Love the part on authority being full of it. We've seen a full breakdown of the scientific community as it's based on staying within the "cool" / authoritative crowd w/o having the creative risk aptitude to take risks & push boundaries.

[mateamatic]

You know when the thumbnail pic is not one of leo, the episode is going to be mindblowing

[astoma]

Phd from Caltech here again. I can attest to what Leo said about academia being a social hierarchy. It is. Most physicists i know couldnt care less about the meaning or the Truth. They care for publications and recognition.

[Wissenswert]

This is lovely. Most episodes I watch leave me contemplating for days - getting new perspectives, trying new things, changing my habits, having more or less significant insights. It's just great. Thanks you <3

[GamingUnleashed]

These episodes where you go through the mathematics are some of my favorites. It’s crazy how math has long since proved a lot of what you talk about. It’s very funny that in school everything we’re taught is put into a separate little box. School would be much better for everyone involved if a more holistic approach was used.

[travishunt]

I believe G. K. Chesterton said it best when he said, “You can only find truth with logic if you have already found truth without it.”

[georginaceri]

Hi Leo! Exceptional video! Reason is called "Logos" in Greek. Logos is synonymous with "Speech". The moment we speak, the word creates a world. So, when ancient Greeks used (still in use) the same word for Reason and Speech, the Loop is highlighted: our Mind creates the Reasoning and Reasoning feeds the Mind. Self-satisfaction produced by the existence of self-created correlations.

[lp]

Listening to this late at night half asleep is terrifying. This information is so damn fascinating

[bccybccy]

Just to sell himself. Comllyete waste of time

[aboubakramzil]

Great video. However I find that you have overcomplicated the Gödel discovery.
It's simply states that starting from any number of axioms to prove anything, then our axioms will either be incomplete or inconsistent, meaning their will always be a truth somewhere we can't prove from these axioms or we will prove a truth and it's contradiction. In that sense, truth cannot always be proven in the way of axioms.

[zholud]

It’s called proof of competence, not authority. And if you had a PhD in math you wouldn’t have made such logical mistakes. To be credible in this topic you must at least be either a mathematician and know some philosophy or a philosopher with some knowledge of mathematics, and ideally both.

[ronaldc]

Hey, I really like some of the things you say. Just got a couple of questions.
1. Do you really have to keep criticizing atheists for criticizing religious people? You are clearly not like other religious people, but the list of "smelly" ideas the average religious person has is beyond justification.

2. Also, just because he was a total genius and his theorem is flawless, doesn't mean we should take every word that Gödel says as fact, like the quote at 1:35:30.

3. Why are you assuming that Godel didn't reach enlightenment?

[idaho_rex]

What if the "idea" as hooves described at 1:11, is what you're teaching? It seems that since I've watched this video several years ago, I have zoomed out and can't zoom back in to normality.