4 - The Naïve Conception

Summary

The chapter discusses the naïve conception of set and criticizes attempts to rehabilitate it by modifying the logic of set theory. The focus is on the proposal that the Naïve Comprehension Schema – which formally captures the thesis that every condition determines a set – is to be saved by adopting a paraconsistent logic. Three strategies for doing so are distinguished: the material strategy, the relevant strategy and the model-theoretic strategy. It is shown that these strategies lead to set theories that are either too weak or ad hoc or give up on the idea that sets are genuinely extensional entities.