Metavaluations, Naïve Set Theory and Inconsistency
Ross Brady

May 4, 2012, 12:00pm - 2:00pm
Department of Philosophy, University of Melbourne

Common Room, Old Quad
University of Melbourne (Parkville)
Melbourne
Australia

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This paper proves the non-triviality of inconsistent naïve set theory using metavaluations. The proof is based on a 4-valued logic rather than the 3-valued logics previously used, and metavaluations are, for the first time, used without a completeness theorem, thus disassociating themselves somewhat from the proof theory. Further, it is shown that some axioms and a rule can be added to the logic, which could not be included in earlier model-theoretic approaches.

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