From: Daniel Davies <[EMAIL PROTECTED]>
one way to think about this is that if you're saying that in a world without concrete entities there would also be no sets, then you (arguably) need some way of distinguishing between "the set of all sets" and "the set of all sets not members of themselves". If you're a Platonist, this is simple, because you just say that there existed an abstract, non-concrete entity called "the set of all sets", and there did not exist such an entity called "the set of all sets not members of themselves".
[I think a word of recognition is due to that concrete entity known as Bertrand Russell.]
Russell's Paradox
Russell's paradox is the most famous of the logical or set-theoretical paradoxes. The paradox arises within naive set theory by considering the set of all sets that are not members of themselves. Such a set appears to be a member of itself if and only if it is not a member of itself, hence the paradox. Some sets, such as the set of all teacups, are not members of themselves. Other sets, such as the set of all non-teacups, are members of themselves. Call the set of all sets that are not members of themselves "R." If R is a member of itself, then by definition it must not be a member of itself. Similarly, if R is not a member of itself, then by definition it must be a member of itself. Discovered by Bertrand Russell in 1901, the paradox has prompted much work in logic, set theory and the philosophy and foundations of mathematics....
(History, significance, bibliography, etc. at <http://plato.stanford.edu/entries/russell-paradox/>)
Carl
