Logic and Logical Philosophy 21 (4):323-361 (2012)

Authors
Frode Bjørdal
University of Oslo
Abstract
We present a semi-formal foundational theory of sorts, akin to sets, named librationism because of its way of dealing with paradoxes. Its semantics is related to Herzberger’s semi inductive approach, it is negation complete and free variables (noemata) name sorts. Librationism deals with paradoxes in a novel way related to paraconsistent dialetheic approaches, but we think of it as bialethic and parasistent. Classical logical theorems are retained, and none contradicted. Novel inferential principles make recourse to theoremhood and failure of theoremhood. Identity is introduced à la Leibniz-Russell, and librationism is highly non-extensional. Π 1 1 -comprehension with ordinary Bar-Induction is accounted for (to be lifted). Power sorts are generally paradoxical, and Cantor’s Theorem is blocked as a camouflaged premise is naturally discarded
Keywords Parasistency  Second Order Arithmetic  Foundations of Mathematics  Paraconsistency  Burali-Forti Paradox  Liar’s Paradox  Curry’s Paradox  Bialethism  Russell’s Paradox  Dialetheism  Reverse Mathematics
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DOI 10.12775/LLP.2012.016
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References found in this work BETA

Truth and Paradox.Anil Gupta - 1982 - Journal of Philosophical Logic 11 (1):1-60.
The Incompleteness Theorems.Craig Smorynski - 1977 - In Jon Barwise (ed.), Handbook of Mathematical Logic. North-Holland. pp. 821 -- 865.
Notes on Naive Semantics.Hans G. Herzberger - 1982 - Journal of Philosophical Logic 11 (1):61 - 102.
An Axiomatic Approach to Self-Referential Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 33 (1):1--21.
Semantics and the Liar Paradox.Albert Visser - 1989 - Handbook of Philosophical Logic 4 (1):617--706.

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All Properties Are Divine or God Exists.Frode Bjørdal - 2018 - Logic and Logical Philosophy 3 (27):329-350.

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