Defending Classes
David Santamaría Legarda

Abstract:
In this work we describe a variety of formal theories that try to capture some of our pre-theoretical notions of collection, while being careful not to fall prey to paradox. We also present some considerations that a satisfactory theory of collections must take into account, focusing in self-instantiation and unrestricted quantification. We then offer a historical account of Cantor’s notion of set as a well asserting several differences between this notion and that of a Russellian class. We will also defend the use of classes in addition to sets in our theories of collections. Finally, we asses how the theories of collections surveyed fulfill the different requirements laid out for a theory to be considered satisfactory.