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.

"Die Philosophie löst die Knoten in unserem Denken auf; daher muss ihr
Resultat einfach sein, ihre Tätigkeit aber so kompliziert wie die
Knoten, die sie auflöst."
(Wittgenstein)

"Philosophy undoes the knots in our thought; therefore its result must
be simple but its activity as complicated as the knots it undoes."
(my trans.)

#PH

.

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