Re: THIS STATEMENT HAS NO PROOF IN ANY SYSTEM = true or false?

From: Torkel Franzen (torkel_at_sm.luth.se)
Date: 01/12/05 

Date: 12 Jan 2005 13:18:39 +0100

daryl@atc-nycorp.com (Daryl McCullough) writes:

> I think you're making it more mysterious than it actually is. There
> really are only a handful of tricks that mathematicians use to
> try to determine the truth of a mathematical statement, and they
> seem to be pretty much captured by ZFC, together with reflection-type
> principles ("I believe ZFC, so Con(ZFC) is not much of a stretch".

  So by "the set of possible truths recognizable to mathematicians"
you mean "the set of truths provable in ZFC or in a reflection-type
extension of ZFC". Two questions naturally arise. First, why should
we adopt this stipulation of what "recognizable truth" means? Second,
even given this stipulation, you haven't actually defined any set
for which it makes any sense to ask whether or not it is recursively
enumerable. "ZFC plus reflection-type principles" is too vague for
this.

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