Re: "Godel got it all wrong"


Peter_Smith wrote:
I can see how people can get confused about the supposed implications
of Gödel's First Incompleteness Theorem. What fazes me is the
seemingly perennial temptation to say that there is something wrong
with the Theorem itself. (When I was editing one of the philosophy
journals for twelve years, there'd be another "refutation" submitted
every four or five months.) The really odd thing is that the Theorem is
in fact *easy*.

Of course, if you want to prove it Gödel's way (and there's other ways
to choose from), there's work to be done, proving that primitive
recursive functions are representable in Peano Arithmetic (and it
requires a pretty bit of trickery with beta-functions to do that). But
once the spade-work is over, the Theorem is indeed easily demonstrated.
Which is not to belittle Gödel's achievement of course. As Kreisel
says in his memoir, it was in fact very important to Gödel that the
theorem was straightforward, *almost* obvious once one had got one's
head around the philosophical point that truth and provability in this
or that formal system are different concepts.

So why, I wonder, do people still get a bee in their bonnet about
this?! Very puzzling.

Maybe it comes from reading "Godel, Escher, Bach" while stoned. A
little knowledge is a dangerous thing...

(Not to take anything away from Hofstadter and his wonderful book, but
he convinced many people that speculating about Godel's theorem was
akin to shooting the breeze about Zen and the nature of the self. I
wouldn't be surprised if Godel-crankery had a measurable upsurge in the
years following G.E.B.)

-semiopen

.

Relevant Pages

  • "Godel got it all wrong"
    ... of Gödel's First Incompleteness Theorem. ... What fazes me is the ... seemingly perennial temptation to say that there is something wrong ... (When I was editing one of the philosophy ...
    (sci.logic)
  • Re: "Godel got it all wrong"
    ... What fazes me is the ... seemingly perennial temptation to say that there is something wrong ... (When I was editing one of the philosophy ... Not so puzzling, I think. ...
    (sci.logic)
  • Re: "Godel got it all wrong"
    ... What fazes me is the ... seemingly perennial temptation to say that there is something wrong ... (When I was editing one of the philosophy ... In the logic that I know; it is truth by another flavor. ...
    (sci.logic)