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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.
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. Received on Mon Jul 11 2005 - 07:04:36 CDT