Abstract

Necessitists about set theory think that the pure sets exists, and are the way they are, as a matter of necessity. They cannot explain why the sets (de rebus) are all the sets. This constitutes the Ur-Objection against necessitism; it is the primary motivation cited by potentialists about set theory. At least three families of potentialism draw motivation from the Ur-Objection. Contingentists think that any things could form a set even if they actually did not. Prioritists think that sets hyperintensionally depend upon their members. Structural-potentialists think that any possible set-hierarchy could be extended. However, once we have disentangled these three versions of potentialism, we see that the Ur-Objection should not motivate anyone.