Aucbvax.6568
net.math
utzoo!decvax!ucbvax!wildbill
Thu Mar 18 11:52:58 1982
Re: Set Theory Paradox
The catch is not that set theory doesn't explain the paradox. In fact, it
does so extremely well. The problem is that that object which you are so
blithely calling a "set" \\is not actually a set//. Loosely stated (and it
has been about 5 years since I sat in on a graduate-level logic/foundations
course in which you go through such contortions very rigorously), the
basic criterion for calling something a "set" is that it be possible to
determine for every object whether or not that object belongs to your
hypothetical set. Since this object (normally called a class) does not
have that property, it is not a set. For more details, check out any
standard reference on set theory. Be forewarned, though--such texts
can be extremely heavy going.