Re: Cantor's Diagonal

From: Russell Standish <lists.domain.name.hidden>
Date: Mon, 24 Dec 2007 10:08:37 +1100

On Fri, Dec 21, 2007 at 01:08:38PM +0100, GŁnther Greindl wrote:
>
> Hi Russell,
>
> Russell Standish wrote:
>
> > In your first case, the number (1,1,1,1...) is not a natural number,
> > since it is infinite. In the second case, (0,0,0,...) is a natural
> > number, but is also on the list (at infinity).
>
> Why is (1,1,1,...) not in the list but (0,0,0,...) in the list at
> infinity? This seems very arbitrary to me.

Quentin replied correctly on the first point. On the second point, the
list is assumed to contain all natural numbers. If that is true, the
0, which maps to the sequence (0,0,0...) must lie at infinity on the
list. If you don't accept this, then the enumeration given is not an
enumeration of the naturals, since 0 is then not on the list. Either
way falsifies the argument.

>
> I am becoming more and more an ultra-finitist. Arguments with infinity
> seem to be very based on the assumptions you make (about platonia or
> whatever)
>
> Regards,
> GŁnther
>
>
> --
> GŁnther Greindl
> Department of Philosophy of Science
> University of Vienna
> guenther.greindl.domain.name.hidden
> http://www.univie.ac.at/Wissenschaftstheorie/
>
> Blog: http://dao.complexitystudies.org/
> Site: http://www.complexitystudies.org
>
>
-- 
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A/Prof Russell Standish                  Phone 0425 253119 (mobile)
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Received on Sun Dec 23 2007 - 18:08:57 PST

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