  Note, here, that these initial points seem to tell against using any completely general criticism of mathematical realism to push people towards the algebraic conception of axioms. On the surface, after all, any sufficiently general criticism of realism would apply to the Skolemite's own model theory as much as it does to classical set theory. It's doubtful, therefore, whether the Skolemite can really appeal to, say, simple worries about “platonism” or about our epistemic access to mathematical objects to motivate a full-blown Skolemite position. In short: the very fact that Skolemite arguments turn on substantial mathematical theorems seems to force the Skolemite into accepting that some parts of mathematics are not subject to Skolemite relativity. (In addition to the references in the last paragraph, see Bays 2001; Bellotti 2005; and Bays 2007b for discussion of this kind of point in the context of Putnam's model-theoretic argument.)