Godel, Turing and Truth

John K Clark (johnkc@well.com)
Thu, 16 Jan 1997 10:24:43 -0800 (PST)


On Wed, 15 Jan 1997 "Lee Daniel Crocker" <lcrocker@calweb.com> Wrote:

>How about "Godel has no implications about the limits of our
>knowledge of reality."?

No reason we couldn't have an infinite amount of knowledge, but there would
still be an infinite number of things we didn't know.

>I reject your postulation that "The Goldbach Conjecture is
>either true or false", except within the definitions of
>"true" and "false" postulated by the system in which it is

There is nothing esoteric about my computer, I have programmed it to do
nothing more sophisticated than arithmetic, the same sort they teach in grade
school. If my computer were not hooked up to a H Bomb there would be nothing
unusual about it at all. My computer takes an even number and then tries to
find 2 prime numbers that add up to it. If it can find two such prime numbers
it adds 2 to the even number and tries again. If it can not find two such
prime numbers the H Bomb goes off. Will the bomb go off? I don't think the
bomb is interested in logical systems and I don't think any of them will
protect me from the blast.

>There is no fundamental connection between the mathematical,
>human-made concept of "true theorem" (i.e., theorem logically
>consistent with axioms) and the metaphysical "truth" as in
>"consistent with reality".

You have said, and I certainly agree, that according to Godel a system can be
complete or consistent but not both. Consistent just means you can't have a
proof that something is true and a proof that the same thing is not true,
but if complete does not mean complete with respect to the truth what does it

>Godel's result is simply a fact about the way we manipulate

Yes, and thinking is "simply" the way the brain manipulates symbols.

John K Clark johnkc@well.com

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