Description

• Title:
  Librationist closures of the paradoxes
• Creator:
  Bjørdal, Frode
• Description:
  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. Π11-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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Date:
  2012.12.20
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 21 No. 4 (2012): December; 323–361;
  Logic and Logical Philosophy; Tom 21 Nr 4 (2012): December; 323–361;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2012.016/773
• Subject:
  Bialethism;
  Burali-Forti 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
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2012.016
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text