131–140 of 252 posts
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commitment to the material in that depth is not the product of drugs
He doesn't say it was written while high. He is wondering if H knew the effects of psychedelics and maybe tried to replicate the feeling in the reader.
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"This statement is false". GEB is a marvellous work that is accessible to anyone with reasonably good school grade maths. I chanced upon it by accident in the school library one day and was hooked after a few pages. Anyway the crux of the matter is that you can very carefully construct a statement about a system that can't be either proven or disproven by that system! I don't have anything like the formal knowledge t…
> "This statement is false" My take on that statement is that it is not saying anything about the world. It only refers to itself, making it a self-contained mini-universe with no relation to the real world. So, since it's not saying anything, it's neither true nor false. Only something confusing that feels like it should have some meaning.
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Note that I said "profound change" not "arbitrary change". What a faithful argument you've blessed us with. If you think drinking alcohol or taking cocaine has the same mental effects as psychedelics, then, I guess all I can say is don't talk about what you don't know.
For someone who is complaining about someone supposedly not reading the exact words you wrote - you're awfully quick in putting words in their mouth. I don't see "alcohol" or "cocaine" mentioned, and yes, the public does put psychedelics in the generic term 'drugs'.
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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
It might be easiest to give a sense of what "unprovable but true" means by way of an imagined example. 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 integer…
Is there a good book that is similar in spirit, but doesn't require the maturity of GEB? I know an 8th grader that would be a great target, but I don't know if they have the mathematical/logical maturity to get through it.
Penrose's The Emperor's New Mind Timothy Ferris Coming of Age in the Milky Way and the Zen and the Art of Motorcycle Maintenance, previously mentioned.
Maybe not the most current thinking (but perfectly fine as an introduction), but the writing is more accessible than GED.
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I don't find that insulting. It's wonderful for you. What I find insulting is saying that calling GEB trippy is an insult. It's genuinely trippy and there's nothing wrong with that.
You explicitly "wondered" if H was "experienced" with psychedelics, implying that you thought so since you found it "trippy". Go back and read your original comment. No one here is saying psychedelics are morally suspect, they're saying that your explicit suggestion that H was "experienced" is insulting. Because it is. And your trying to move the goalposts after the fact is just digging that hole deeper.
The suggestion that Hofstadter has tripped isn't insulting because GEB is a trippy book. Even if it weren't it wouldn't be insulting, only confusing, unless you think that trippy is a bad quality. Examine that.
GEB is whimsical, fun and mind-bending. If it were written any other way it wouldn't be trippy. There is nothing wrong with that.
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what if the proofs cannot be described as finite or countable sets that does not render a straightforward application of diagonalization? What happens to Goedel’s theorem then?
What's an example of an uncountably infinite proof?
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?
Can you elaborate? I've had some friends talk about Hegel with me but I never understood much of it
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It's not an insult. Psychedelics can profoundly change how someone perceives things. GEB has that sort profound shift in POV that many would associate with psychedelics.
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.
> 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…
Somewhat oddly, this is actually technically correct - a "sufficiently rich" system is one that can distinguish true versus false statements of Peano Arithmetic, and a inconsistent system, by the principle of explosion, can prove any statement, so cannot distinguish statements of Peano Arithmetic (eg, 1+1=2 and 1+1=3 are both provable), and hence is not sufficiently rich.
That's a somewhat unintuitive way of looking at it in practice, though.