Extensionality and restriction in naive set theory

Studia Logica 94 (1):87 - 104 (2010)
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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References found in this work BETA
C. M. Asmus (2009). Restricted Arrow. Journal of Philosophical Logic 38 (4):405 - 431.
Francesco Berto (2008). Adynaton and Material Exclusion. Australasian Journal of Philosophy 86 (2):165 – 190.
Ross T. Brady (1989). The Non-Triviality of Dialectical Set Theory. In G. Priest, R. Routley & J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent. Philosophia Verlag. 437--470.

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