Re: Fitch's paradox and OWA
From: Nam Nguyen <namducnguyen_at_shaw.ca>
Date: Thu, 31 Dec 2009 21:44:06 -0700
Message-ID: <t4f%m.10975$0U1.10631_at_newsfe16.iad>
>
>
> 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.
Date: Thu, 31 Dec 2009 21:44:06 -0700
Message-ID: <t4f%m.10975$0U1.10631_at_newsfe16.iad>
Daryl McCullough wrote:
> 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.
For what it's worth, in mathematics the truths about the natural numbers is what we mean we mean by the natural numbers, not what they existentially are!
>
> 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.
But there's no such thing as finite natural numbers. Natural numbers are natural numbers, infinite or not. Received on Fri Jan 01 2010 - 05:44:06 CET