  This, then, gives us the basic structure of the various Skolemite arguments. Before turning to some responses to these arguments which have appeared in the recent literature, it is important to be clear about the role that Skolem's Paradox itself can and cannot play in these arguments. At times, it appears as though some Skolemites think that the Löwenheim-Skolem theorems by themselves show that there's a problem with our ordinary conception of sets: so, the theorems show that set-theoretic notions are relative, relativity is incompatible with our ordinary conception of sets, and so our ordinary conception of sets has to be abandoned (Kneale and Kneale 1962; Goodstein 1963). It should be clear from section 2, however, that this line of argument has no chance of succeeding. The analysis in section 2 shows that those of us who are willing to take a naively realistic attitude towards set theory—or, for that matter, those who take more sophisticated stances which rest on the iterative conception of sets and/or some form of second-order structuralism—will have no problems with Skolem's Paradox. Hence, the paradox itself cannot force us to abandon our ordinary conception of sets.