  Philosophical discussion of this paradox has tended to focus on three main questions. First, there's a purely mathematical question: why doesn't Skolem's Paradox introduce an outright contradiction into set theory? Second, there's a historical question. Skolem himself gave a pretty good explanation as to why Skolem's Paradox doesn't constitute a straightforward mathematical contradiction; why, then, did Skolem and his contemporaries continue to find the paradox so philosophically troubling? Finally there's a purely philosophical question: what, if anything, does Skolem's Paradox tell us about our understanding of set theory and/or about the semantics of set-theoretic language?