Difference between revisions of "Russell's Paradox"
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Revision as of 06:52, 4 August 2007
This paradox, due to Bertrand Russell, was one of those which forced the axiomatization of set theory. We start with the property : ( does not belong to ). We define to be the collection of all with the property . Now comes the question: does have the property ? Assuming it does, it cannot be in itself, in spite of satisfying its own membership criterion, a contradiction. Assuming it doesn't, it must be in itself, in spite of not satisfying its own membership criterion. This is the paradox.