Studia Logica

, Volume 94, Issue 1, pp 87–104 | Cite as

Extensionality and Restriction in Naive Set Theory



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.


Naive set theory paraconsistency relevant logic restricted quantification 


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© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.School of Philosophical and Historical InquiryUniversity of SydneySydneyAustralia

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