Re: Fw: Something for Platonists]

From: Hal Finney <hal.domain.name.hidden>
Date: Mon, 16 Jun 2003 10:46:56 -0700

Jesse Mazer writes:
> Yes, a Platonist can feel as certain of the statement "the axioms of Peano
> arithmetic will never lead to a contradiction" as he is of 1+1=2, based on
> the model he has of what the axioms mean in terms of arithmetic. It's hard
> to see how non-Platonist could justify the same conviction, though, given
> Godel's results. Since many mathematicians probably would be willing to bet
> anything that the statement was true, this suggests a lot of them are at
> least closet Platonists.

What is the status of the possibility that a given formal system such as
the one for arithmetic is inconsistent? Godel's theorem only shows that
if consistent, it is incomplete, right? Are there any proofs that formal
systems specifying arithmetic are consistent (and hence incomplete)?

Hal Finney
Received on Mon Jun 16 2003 - 13:49:14 PDT