Studia Logica

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

Extensionality and Restriction in Naive Set Theory

Article

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.

Keywords

Naive set theory paraconsistency relevant logic restricted quantification 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

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

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