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.
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Weber, Z. Extensionality and Restriction in Naive Set Theory. Stud Logica 94, 87–104 (2010). https://doi.org/10.1007/s11225-010-9225-y
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DOI: https://doi.org/10.1007/s11225-010-9225-y