  In the 1922 paper where he originally presented Skolem's Paradox, Skolem used the paradox to argue for two philosophical conclusions: that set theory can't serve as a “foundation for mathematics” and that axiomatizing set theory leads to a “relativity of set theoretic notions” (Skolem 1922). These claims, and Skolem's arguments for them, have attracted considerable attention in the literature. Unfortunately, Skolem's paper is quite compressed, and so it's difficult to determine exactly what these claims were really supposed to amount to. At present, there are three interpretations of Skolem's paper which have some currency in the philosophical literature.