Re: A
Date: Mon, 11 Jul 2005 13:04:36 +0100
Message-ID: <42d26054$0$2890$ed2e19e4_at_ptn-nntp-reader04.plus.net>
Jan Hidders wrote:
>> Doesn't this only apply if you are considering the set of all relations
>> over all domains? What if you restrict yourself to a finite set of
>> domains? I can't see how Cantor's Paradox would apply in this case.
>
> It wouldn't. But the question at hand was whether the collection of all
> relations can be a domain. If you are going to postualte the set of
> domains a priori, then the set of relations over those domains will of
> course not be one of those postulated domains.
OK. but domains can be thought of as simply sets. So then the "collection of all domains" is like the "set of all sets" which, by Cantor's Paradox, isn't actually a well-defined set.
So we can't even get to the stage of considering the set of all
relations over all domains, because "all domains" is meaningless in set
theory! No wonder Cantor went insane... :)
Paul.