Re: what makes it true?


>> 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).


I see, and partly agree with, your point. The main area of disagreement
would be that I simply would consider such undecidable properties
as undecidable properties of the natural numbers. In any case, I'd
consider ZFC to be the arbiter unless another axiom system is adopted.

--Dan Grubb
.