Extensionality and Restriction in Naive Set Theory

Abstract. The naive set theory problem is to begin with a full comprehension axiom, and to find a logic strong enough to prove theorems, but weak enough not to prove everything. This paper considers the sub-problem of expressing extensional identity and the subset relation in paraconsistent, relevant solutions, in light of a recent proposal from Beall, Brady, Hazen, Priest and Restall [4]. The main result is that the proposal, in the context of an independently motivated formalization of naive set theory, leads to triviality.

• Type: Journal
• Year: 2010
• Where: SLOGICA
• Authors: Zach Weber
• Keywords: Comprehension Axiom, Extensional Identity, SLOGICA 2010, Theory Problem