Extensionality and restriction in naive set theory

Studia Logica 94 (1):87 - 104 (2010)
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
Graham Priest (2008). Paraconsistent Logic. Stanford Encyclopedia of Philosophy.
Francesco Berto (2008). Adynaton and Material Exclusion. Australasian Journal of Philosophy 86 (2):165 – 190.

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Citations of this work BETA
Toby Meadows (2016). Sets and Supersets. Synthese 193 (6):1875-1907.
Tore Fjetland Øgaard (2016). Paths to Triviality. Journal of Philosophical Logic 45 (3):237-276.

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