X-Message-Number: 4145 Date: Mon, 3 Apr 1995 20:39:47 -0700 From: John K Clark <> Subject: SCI.CRYONICS Godel -----BEGIN PGP SIGNED MESSAGE----- In #4131 Wrote : >John Clark (#4121) says Russell and I are both wrong because >Goedel did better. He also says I am talking about >Russell's Theory of Types; I am not. I am talking about >meaningfulness [...] The "paradox" of The Liar,in the form >above, is easily resolved by refusing to acknowledge that >the statement is a proposition That's exactly what Russell's discredited Theory of Types was talking about, meaningfulness. In a sense it was successful, it did eliminate all paradoxes by branding them as meaningless but it also branded a huge number of statements that I'm sure you would think perfectly reasonable ( anything with the word "I" or "this" in it among others) as meaningless as well. Godel's Theorem states that you can have a logical system that is totally consistent and free from paradox, but only by weakling it to such an extent that it becomes trivial and completely useless. >I suggest that a statement is meaningful only if IN >PRINCIPLE it can be tested or verified. According to your definition some things can be true but not be meaningful and other things can be false but be meaningful , also it still doesn't answer anything , it just kick the problem upstairs. When can a statement be tested or verified in a finite number of steps? The answer to this question is sometimes easy to find and sometimes it's far from obvious. The procedure for testing something in a finite number of steps is called a PROOF. For example take the Goldbach Conjecture, it states that every even number greater that 4 is the sum of two odd primes (all the primes except 1 and 2). Let's try it for some numbers: 6=3+3 8=5+5 10=3+7 12=5+7 14=3+11 16=3+13 18=7+11 20=3+17 22=5+17 24=7+17 26=7+19 28=11+17 30=11+19 This all looks very promising, but is it true for ALL even numbers? Leaving aside for the moment the question of whether it is true, is the Goldbach Conjecture even meaningful according to your definition? The meaning seems pretty straightforward to me, but checking all even numbers one by one would take an infinite number of steps, to test it in finite number of steps we need a proof, but I don't have one, nobody does. The Goldbach Conjecture was first proposed in 1742 ( 1742=1729+13) and since that time the top minds in mathematics have looked for a proof but have come up empty. Well, perhaps we can't prove it because it's not true, however modern computers have looked for a counterexample, they've gone up to a trillion or so and it works every time. Now a trillion is a big number but it's no closer to being infinite than the number 1 is, so perhaps The Goldbach Conjecture will fail at a trillion +2 or a trillion to the trillionth power. It's also possible that some brilliant mathematician will come up with a proof tomorrow as recently happened with Fermat's last theorem , but there is yet another possibility, it could be unprovable. The Goldbach Conjecture is either true or it's not, Godel never denied that, the question is if we will ever know if it's true or not? According to Godel some statements are unprovable, if The Goldbach Conjecture is one of these it means it's true so we'll never find a counterexample to prove it wrong and it means we'll never find a proof to show it's correct. A billion years from now, whatever hyper intelligent entities we will have become will still be deep in thought looking, unsuccessfully, for a proof and still grinding away at numbers looking, unsuccessfully, for a counterexample. >symbols and rules of formal logic and mathematics, instead >of ordinary words Ordinary words are also symbols and they have their own formal logic, grammar. >If it can't be proven, how do we know it's true? We can't , but remember Godel doesn't say you can't prove anything, he says you can't prove everything. >if something is undecidable, it has any practical importance. If something is undecidable you will never know it's undecidable, you'll just never find a proof or a counterexample. >Following is part of a draft of a chapter in one of my books >in progress[...] Goedel's Incompleteness Theorems are in >essence just as stupid as this. [...] I say the >incompleteness theorems are phony. I really hope you don't take this the wrong way but with the deepest respect I beg you, don't include this chapter in your new book. For some reason many respected scientists think that cryonics advocates are loony and probably members of the Flat Earth Society too, I guarantee you, calling the work of the greatest logician in two thousand years "stupid" and "phony" will not improve that perception. If you feel you absolutely positively must publish this anti intellectual chapter, please, please, PLEASE do it in a separate book that doesn't mention Cryonics. You might want to think about using a pseudonym as well, I don't think anybody on this list wants to see the father of Cryonics publicly humiliated and held up to scorn in the scientific community. John K Clark -----BEGIN PGP SIGNATURE----- Version: 2.6.i iQCzAgUBL39s8303wfSpid95AQHEMQTuPL0AviAHGGnfs7j0OmJ0sQwM0rh6Nbx7 1cRUau9NNC6Ph/4tyu4NhYdNZsbrMwaYFibqXD2iZ66dJY+UCahueOdhfPgN+8QL 4bmU//dbQqQvJMR1XzF9ChDGMSFx27uOlO3qDUfG5sv6+LA/jwLuicBCmvVsxPpY VJKNG69QKuieuNILFjglY69/NWhZdVAAGBSA3glWEr9HM/BD/Ug= =uV5U -----END PGP SIGNATURE----- Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=4145