Skolem, the Skolem 'paradox' and informal mathematics

I discuss Skolem's own ideas on his 'paradox', some classical disputes between Skolemites and Antiskolemites, and the underlying notion of 'informal mathematics', from a point of view which I hope to be rather unusual. I argue that the Skolemite cannot maintain that from an absolute point of view everything is in fact denumerable; on the other hand, the Antiskolemite is left with the onus of explaining the notion of informal mathematical knowledge of the intended model of set theory. I conclude that one must take seriously the embodiment of the uncountable into countable languages, as a symptom of some specific features which characterize mathematical languages with respect to other languages.