Disimplicature

Speranza

According to the iterative conception of sets, standardly formalized by ZFC, there is no set of all sets. 

And Grice liked to say that he was the class of philosophers who had no class.

But why is there no set of all sets? A simple-minded, though unpopular, “minimal” explanation for why there is no set of all sets is that the supposition that there is contradicts some axioms of ZFC. In this paper, I first explain the core complaint against the minimal explanation, and then argue against the two main alternative answers to the guiding question. I conclude the paper by outlining a close alternative to the minimal explanation, the conception-based explanation, that avoids the core complaint against the minimal explanation.