Librationist Closures

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Date(s) - 25 Feb 2011
2:00 PM - 3:00 PM

Auditório do CCET-UFRN

Category(ies) No Categories

Speaker: Frode Bjørdal (**)

Abstract: Librationism’s name is coined from”libration”, and so baptized because of shifts in perspectives associated with its treatment of paradoxes.  It’s a semiformal theory of sorts, and reminds of paraconsistent approaches.  But librationism fully respects classical logic in that all its theorems are retained, and none of them contradicted.  For paradoxical sentences such as the one stating that Russell’s sort (of all and only sorts that are not self-membered) is a member of itself, librationism proves it, while it also proves its negation.  Inference rules are novel, so librationism doesn’t prove the conjunction.  The semantics is based on a semi inductive Herzbergerian process, and focuses on one designated model.  So librationism is negation complete; this also facilitates an evasion of Curry’s paradox.  Librationism is strong. A fixed point construction shows it’s fully impredicative.  Recent progress suggests that an arithmetical program may be viable in such a way that one may show that librationism contains countable models of theories much stronger than ZFC; nevertheless, and somewhat surprisingly, Cantor’s entirely valid arguments for uncountable infinites do not hold librationistically, but only serve to show that the premise that certain sorts are not paradoxical must be given up.

(**) Professor of the Department of the Department of Philosophy, Classics, History of Art and Ideas, University of Oslo, Norway.

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