  In this section, we isolate the key idea behind some classical developments of these Skolemite claims, and we then consider some of the responses to them which have appeared in the recent literature. (In section 3.3,  we consider an interesting new approach to the Skolemite position.)  We start with the Skolemite argument itself. Very roughly, this argument comes in three steps. First, it argues that the algebraic conception of set theory is the only respectable conception for contemporary mathematicians and philosophers to adopt. Second, it follows Skolem in arguing that the algebraic conception of set theory leads to a relativity of set-theoretic notions. Finally, it extends Skolem's argument to defend the strong form of relativity mentioned at the end of the last paragraph—i.e., the one under which every set turns out to be countable when it's considered from an “absolute” perspective.