  We should emphasize, here, that this algebraic conception of axiomatization would have been quite familiar to mathematicians working at the time Skolem wrote his 1922 paper. Skolem himself was trained in Schröder's algebraic school of logic, so this would have been the natural way for him to think about axioms. But even people who weren't trained in Schröder's school would have found the conception familiar. It's the conception which lay behind Hilbert's famous axiomatization of geometry (about which Hilbert reputedly claimed, somewhat notoriously, that we can replace points, lines, and planes with tables, chairs, and beer mugs as long as the latter objects stand in the right kinds of relations). It's also the conception which lay behind the 19th-century results that arithmetic and analysis can be given categorical (second-order) axiomatizations. Finally, and most importantly, it's the conception of axiomatization which Skolem attributes to Zermelo in the very paper that we're currently discussing, and so it's the conception of Zermelo's axioms that Skolem is primarily concerned with  criticizing.[32]