91–100 of 252 posts
G.E.B is hegelian philosophy without one mention to Hegel and more mechanic than organic Anyone read the Phenomenology of Spirit and notice the same ideas?
> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people p…
How can a statement that is unprovable be true? I always had the impression that unprovable means you could add either the statement or its negation as an axiom, and both resulting systems are as consistent as the system you started with
At 13:46 it gets into the "is there a way to prove every complete statement?" and furthermore goes into the Godel math for "there is no proof for the statement with Gödel number g" where that statement itself has a number "g".
The entire video is a good watch though.
And the related problem is that with Godel we don't know if math is consistent either.
> Gödel's Incompleteness Theorem: any sufficiently rich formal system, together with an interpretation, has strings which are true but unprovable. This is only half of it! Gödel's Incompleteness Theorem states that any sufficiently rich formal system, together with an interpretation, either has strings which are true but unprovable or has strings which are provable but untrue. Either is possible! In practice people p…
How can a statement that is unprovable be true? I always had the impression that unprovable means you could add either the statement or its negation as an axiom, and both resulting systems are as consistent as the system you started with
Goldbach's conjecture is that "every even number bigger than 2 is the sum of exactly two prime numbers", so 4 = 2 + 2, 6 = 3 + 3, 8 = 5 + 3, etc.
For this statement to be *true* it just means that every even number there must exist two primes that add to that number. This is a statement about infinitely many integers.
A *proof* of Goldbach's conjecture consists of a finite number of formal reasoning steps that start with some axioms and end up at the statement of the result.
To this day, it seems as though Goldbach's conjecture is true. It holds for every number we've been able to test. However, no one has proved it is true or false yet (or proved that it is unprovable).
The proof of Gödel's result's involves very carefully formalizing what statements and proofs mean so that they can be encoded as statements about arithmetic. He then shows there is a statement with encoding G that says "The statement with encoding G cannot be proved" – if it is true, then it cannot be proved.
It's kind of confusing at first, but there is an easier way to get an intuition why there might be true statements that cannot be proved. Think of each statement about the natural numbers as a subset where each number in the subset makes the statement true. There are uncountably many subsets of the natural numbers (by Cantor's diagonalization argument). Proofs are finite chains of finite statements so there are only countably infinitely many of these. Therefore there must be subsets/statements that are true that do not have a matching proof.
The approach that Gödel's proof takes is not too different to the above argument – it is essentially a diagonalization argument – the complexity is in making the encoding of statements are numbers very precise.
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The insult is the implication that thinking like this is somehow due to use of and exposure to psychedelics. Maybe some people need assistance in thinking deeply, Hofstadter certainly is not one of them.
Do you think that you feel better than others for not taking drugs, and that this superiority is assailed when people who take drugs find common ground with one of your favorite thinkers? Because that's the only explanation I can think of for this blatant assholeishness and gatekeeping. Hofstadter doesn't own thinking about consciousness, thinking deeply, or thinking philosophically. As a matter of fact these sorts o…
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I have no problems with psychedelics or their use. I took issue with the implication that they are needed in order to think in the way Hofstadter does - it's kind of like asking what flippers Michael Phelps uses when he swims in the olympics.
I didn't mean to imply that and certainly don't think it is required. My question had little to do with the content and much more to do with the style, and the author's intended effects upon the reader.
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Do you think that you feel better than others for not taking drugs, and that this superiority is assailed when people who take drugs find common ground with one of your favorite thinkers? Because that's the only explanation I can think of for this blatant assholeishness and gatekeeping. Hofstadter doesn't own thinking about consciousness, thinking deeply, or thinking philosophically. As a matter of fact these sorts o…
Oh, to be clear it has nothing to do with morality. Similar to someone elses comment above, having the experience of thinking you can salsa dance while drunk and actually being able to salsa dance are very different. In the same way, Someone might gain some understanding of H's thinking by taking psychedelics, but that does not lead to the same understanding as actually processing, imagining and writing the material…
So from my point of view, it devolved into flamebait the moment you said comparing GEB to psychedelics is insulting. Because to me, it makes sense on a lot of personal levels.
As I've said in another comment. If you think drinking alcohol and taking psychedelics have similar mental effects. Then I suggest you stop talking about what you don't know.
Just read the proofs. They're not that difficult. Their consequences are wonderful. Enjoy brilliance
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(upvoted!) can you say more about this sensibility of yours? I'm genuinely intrigued, as I haven't heard a take like that before :) At risk of asking a leading question: is it some idea that deep truth should come from reason rather than the noise and chaos of psychedelics? (I don't do them myself, but hold them in very high regard as a force in the world)
I have no problems with psychedelics or their use. I took issue with the implication that they are needed in order to think in the way Hofstadter does - it's kind of like asking what flippers Michael Phelps uses when he swims in the olympics.
i might feel a bit differently, but I think I hear where you're coming from: that it does a disservice to great people when we flippantly imply their greatness originates from simplistic things outside themselves (if I'm still way off, feel free to correct, but pls don't feel obligated to engage :) )
Earlier quoted context omitted.
Oh, to be clear it has nothing to do with morality. Similar to someone elses comment above, having the experience of thinking you can salsa dance while drunk and actually being able to salsa dance are very different. In the same way, Someone might gain some understanding of H's thinking by taking psychedelics, but that does not lead to the same understanding as actually processing, imagining and writing the material…
I took a lot of psychedelics in my life, and in that period I also read GEB quite religiously. And in my experience, I think it could have taken me a lot longer to empathize with the book than if I weren't taking psychedelics; not because of a false sense of understanding but because of a similarity in mental context. I felt like on LSD, I could look behind the curtain, so to speak. This isn't the same feeling as whe…
I did not struggle with 'looking behind the curtain' while reading GEB, nor did I find the concepts silly - I was rapt with curiosity the whole reading and came to many profound conclusions about the book and it's ideas - and I was not on LSD. Whatever helps you personally understand the world in a more meaningful light is wonderful, but it certainly was not needed for me and I doubt (based on what I know about the author) it was needed for him when writing this book.