Re: what makes it true?

Torkel Franzen wrote:
> Timothy Little <tim-usenet@xxxxxxxxxxxxxxxxxx> writes:
>> Hence: if I make a claim that some property of the natural numbers is
>> true, I'm expected to back it up with at the least, an informal proof.
>> If the readers agree that it can in principle be formalized in a
>> suitable system, then they accept it as a true property.
>
> That's fine, but it in no way implies that there is no such thing
> as the natural numbers.

It does imply that the properties of "the" natural numbers depends
upon the system used to do the proofs. Which is what I was claiming
in the first place. You were claiming that some entity called "the
natural numbers" exists independently of such a system.

Going back to my original question, what happens if GC is undecidable
in that system? (Note: My knowledge of proof theory is incomplete, so
this may be a counterfactual question. If so, then replace "GC" by
any number theory conjecture that is not known to be decidable.)


- Tim
.