  These, then, are the main criticisms of the Skolemite position which have appeared in the literature. To treat them more thoroughly would, unfortunately, require us to dive pretty deeply into questions concerning, e.g., the status of our informal understanding of set-theoretic language, the legitimacy of second-order quantification, and the identity conditions associated with mathematical objects in structuralist philosophies of mathematics. Exploring these issues would take us pretty far away from Skolem's Paradox itself. For a recent survey of some of the relevant literature here, see Bellotti 2006.