  These, then, are the three main interpretations of Skolem's paper in the literature. Without taking a stand on which of these interpretations best captures Skolem's own intentions, we note that most of Skolem's contemporaries interpreted him as giving something like the “traditional” argument described above and that their responses to Skolem's Paradox reflected this interpretation. Zermelo himself came to accept the algebraic conception of his axioms, but he then insisted that these axioms should be interpreted in second-order terms and that, so interpreted, they do not fall prey to Skolem's Paradox (Zermelo 1930; Taylor 1993; Ebbinghaus 2003). Similarly, Tarski suggested that Skolem's Paradox could be defused by treating “∈” as a logical constant in some version of type theory (see the remarks published at the end of Skolem 1958). But, while both of these suggestions would allow mathematicians to avoid Skolem's Paradox, they both depend on accepting pieces of powerful mathematical machinery which Skolem—on any reading of his paper—would almost certainly have wanted to reject. Given Skolem's philosophical purposes, therefore, these contemporary responses to his paradox would not have seemed very threatening (see Skolem 1955 and Skolem 1958 for some of Skolem's own reflections on these kinds of responses).