[FOM] Is Godel's Theorem surprising?
auerbach at unity.ncsu.edu
Sun Dec 10 19:56:55 EST 2006
On Dec 10, at 3:53 PM, Harvey Friedman wrote:
> On 12/10/06 9:19 AM, "Charles Silver" <silver_1 at mindspring.com> wrote:
>> First, thanks very much for all the interesting and enlightening
>> responses to my question. A couple of comments:
>> Diagonalization is not central to Godel's (first) theorem, as shown
>> by Kripke's proof of G's theorem that was published by Putnam, which
>> does not *require* diagonalization.
>> I believe this proof also shows--please correct me if I'm wrong--
>> that a specifically *mathematical* proposition (though an unusual
>> one) cannot be proved nor can its negation.
> It would be helpful to the FOM readership for you to give us a
> reference to
> this paper by Putnam. I have serious doubts about the claims you are
> Harvey Friedman
There's a "semantic" proof due to Kripke that involves enumerating
the formulas with x as the sole free variable, adding c(i) whose
interpretation is the ith such formula with c(i) replacing x. The
diagonal lemma becomes trivial, but it is still there. (the 2nd
theorem then needs extra work to establish that the standard numerals
are provably identical to the corresponding constants...) But this
can't be Putnam's Kripke's proof?
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