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

Frode Bjørdal
University of Oslo
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
Categories (categorize this paper)
DOI 10.12775/LLP.2012.016
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 62,242
Through your library

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.

View all 12 references / Add more references

Citations of this work BETA

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

Add more citations

Similar books and articles


Added to PP index

Total views
19 ( #558,280 of 2,444,785 )

Recent downloads (6 months)
1 ( #457,287 of 2,444,785 )

How can I increase my downloads?


My notes