> It's always worth recalling why we bother with set theory. Because we limit ourselves to First Order logic, which can quantify over only individuals. In ord

> It's always worth recalling why we bother with set theory. Because we limit ourselves to First Order logic, which can quantify over only individuals. In order to quantify over multitudes (sets, groups, whatever) you either need Second Order logic or else a First Order axiomatization of how these multitudes behave. We chose the latter rather than the former because Second Order logic has no Sound, Complete, and Decidable proof theory. First Order logic does. That is why we bother with set theory. https://en.m.wikipedia.org/wiki/Second-order_logic#Metalogical_results https://en.m.wikipedia.org/wiki/Second-order_logic#Metalogic...