[FOM] Librationist Closures of Paradoxes

Frode Bjørdal frode.bjordal at ifikk.uio.no
Wed Jul 25 14:45:09 EDT 2012

On the 13th of June last year I posted on librationism in reply to a
request by Harvey Friedman to have proponents of alternative foundational
points of view present such on the f.o.m. email list. A much more
comprehensive and detailed account is forthcoming, and a preprint is
available here: http://www.duo.uio.no/sok/work.html?WORKID=161995

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. PI(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: Bialethism, Burali-Forti's Paradox, Cantor's Theorem, Curry's
Paradox, Dialetheism, Foundations of Mathematics, Liar's Paradox,
Paraconsistency, Parasistency, Paradoxes, Reverse Mathematics, Russell's
Paradox, Second Order Arithmetic, Semantical paradoxes, Set Theoretic
Paradoxes, Set Theory, Theory of Truth.


Frode Bjørdal
Professor i filosofi
IFIKK, Universitetet i Oslowww.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
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