Date: 11 Jul 2005 09:01:20 -0700
> 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... :)
Received on Mon Jul 11 2005 - 18:01:20 CEST