Re: what makes it true?

Daniel Grubb wrote:
[ Definition of The natural numbers ]
> In ZFC, the smallest inductive set. I could turn that into a purely
> formal definition if desired. Someone who doesn't know what is meant
> by the set of natural numbers, yet has an intution about them would
> probably agree that this set gives a good rendition of their
> intuition, at least initially. It also nails down exactly what is
> meant by the term 'natural numbers'. That is what a definition in
> mathematics is for.

I disagree that it nails down exactly what is meant by the natural
numbers. There will be properties that remain undefined since their
corresponding propositions will be undecidable (though I don't happen
to have any examples).


- Tim
.