Zermelo and the Skolem Paradox

Abstract

On October 4, 1937 Zermelo wrote down a hitherto unpublished manuscript entitled "Der Relativismus in der Mengenlehre and der sogenannte Skolemsche Satz" ("Relativism in Set Theory and the so-called Theorem of Skolem" ) in which he gives a refutation of "Skolem's paradox", i.e., the fact that Zermelo- Fraenkel set theory - guaranteeing the existence of uncountably many sets - has a countable model. Compared with what he wished to disprove, the argument fails. However, at a second glance, it strongly documents his view of mathematics as based on a world of intuitively given objects that could only be grasped adequately by infinitary means.