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Jan Hidders wrote:
>>> In some sense you might say that is is "too large" to be a set. The >>> collection of all relations has the same problem. >> >> I'm skeptical to this, but if it is too difficult to explain (or to >> give an example of a problem), I'll let it be for the moment.
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.
So rather than having a domain of "the set of all relations", which can't exist, you could have a domain of "the set of all relations over a specified finite set of domains". Or even an infinite set of domains, I suppose, providing it's still a well-defined set.
So the "size explosion" problem here is with the domains rather than the relations?
Paul. Received on Sun Jul 10 2005 - 06:08:32 CDT