Re: Fitch's paradox and OWA

Barb Knox says...
>
>In article
><a3f061ed-3838-4be9-b73a-836141dc640f_at_u7g2000yqm.googlegroups.com>,
> Marshall <marshall.spight_at_gmail.com> wrote:

>> I was more under the impression that Goedel showed there
>> was no complete finite theory of them, rather than no
>> way to define them. Are you saying those are equivalent?
>
>Yes, in this context. Since we are finite beings we need to use finite
>systems.

I don't agree. What Godel's theorem says is that we can't know all the truths about the natural numbers, but it doesn't imply that there is any fuzziness in what we mean by natural numbers.

All the nonstandard models of the naturals contain infinite objects. We're not likely to mistake such an object for an actual natural. As you say, we are finite beings, so any natural we can write down is finite.

--
Daryl McCullough
Ithaca, NY