  Given this, a number of critics have suggested that Skolemites face two explanatory burdens and that, so far, no Skolemite has managed to meet these burdens. First, the Skolemite needs to explain how we can identify sets across different models—i.e., why we should consider the various different objects which satisfy “x is the power set of ω” in different models of set theory to be “the same set.” Note that some such identification is essential if the Skolemite is going to start with a proof of the countability of one of these objects and then use this proof to argue for the absolute countability of all the others (Resnik 1966). Second, the Skolemite needs to explain his preference for countable sets. Even if the Skolemite can identify countable and uncountable “instances” of a given set, he needs to explain why this identification leads to the conclusion that all sets are “absolutely countable” rather than to the conclusion that all sets are “absolutely uncountable” (Resnik 1966; Benacerraf 1985).