Skip to main content Skip to main navigation menu Skip to site footer
  • Register
  • Login
  • Language
    • English
    • Język Polski
  • Menu
  • Home
  • Current
  • Archives
  • Online First Articles
  • About
    • About the Journal
    • Submissions
    • Editorial Team
    • Advisory Board
    • Peer Review Process
    • Logic and Logical Philosophy Committee
    • Open Access Policy
    • Privacy Statement
    • Contact
  • Register
  • Login
  • Language:
  • English
  • Język Polski

Logic and Logical Philosophy

Librationist closures of the paradoxes
  • Home
  • /
  • Librationist closures of the paradoxes
  1. Home /
  2. Archives /
  3. Vol. 21 No. 4 (2012): December /
  4. Articles

Librationist closures of the paradoxes

Authors

  • Frode Bjørdal The University of Oslo

DOI:

https://doi.org/10.12775/LLP.2012.016

Keywords

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,

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. 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.

Author Biography

Frode Bjørdal, The University of Oslo

Department of Philosophy, Classics, History of Art and Ideas

References

Beeson, Michael, Foundations of Constructive Mathematics, Metamathematical Studies, Springer, Berlin/Heidelberg/New York 1985.

Bjørdal, Frode, “Considerations Contra Cantorianism”, in: The Logica Yearbook 2010, M. Peliš, V. Punčochář (eds.), College Publications, London, 2011.

Bjørdal, Frode, “2+2=4” er misvisande, (“2+2=4” is misleading), pages 55–65 in: Enhet i mangfold, Festskrift i anledning Johan Arnt Myrstads 60-årsdag, Anita Leirfall & Thor Sandmel (eds.), Unipub, Oslo, 2009.

Bjørdal, Frode, “Minimalistic Liberalism”, in: The Logica Yearbook 2005, M.Bílková and O.Tomala (eds.), Filosofia, Prague, 2006.

Bjørdal, Frode, “There are Only Countably Many Objects”, pages 47–58 in: The Logica Yearbook 2004, Libour Behounek & Marta Bilková (eds.) Filosofia, Prague, 2005.

Burgess, John P., Philosophical Logic, Princeton University Press, Princeton and Oxford, 2009.

Cantini, Andrea, Logical Frameworks for Truth and Abstraction, Elsevier, Amsterdam, 1996.

Friedman, Harvey, and Michael Sheard, “An Axiomatic Approach to Self-Referential Truth”, Annals of Pure and Applied Logic 33, (1987): 1–21.

Gupta, Anil, “Truth and Paradox”, Journal of Philosophical Logic XI, 1 (1982): 1–60.

Hajek, Petr, On equality and natural numbers in Cantor-Łukasiewicz set theory (forthcoming).

Herzberger, Hans, Notes on Periodicity, unpublished and circulated, 1980.

Herzberger, Hans, “Notes on Naive Semantics”, Journal of Philosophical Logic XI, 1 (1982): 61–102.

Jensen, Ronald Björn, “The Fine Structure of the Constructible Hierarchy”, Annals of Mathematical Logic 4, (1972): 229–308.

McGee, Vann, “How Truthlike Can a Predicate Be?”, Journal of Philosophical Logic 14, (1985): 399–410.

Myhill, John, Paradoxes, Synthese 60, (1984): 129–143.

Simpson, Stephen G., Subsystems of Second Order Arithmetic, Perspectives in Mathematical Logic, Springer-Verlag, Berlin, Heidelberg, New York, 1999.

Smorynsky, Craig, “The Incompleteness Theorems”, pages 821–865 in: Handbook of Mathematical Logic, Jon Barwise (ed.), Elsevier Science Publishers B.V., Amsterdam, 1977.

Visser, Albert, Semantics and the Liar Paradox, pages 617–706 in: Handbook of Philosophical Logic. Vol. IV, Dov M. Gabbay & Franz Guenthner (eds.), Reidel, Dordrecht, 1989.

Welch, Philip D., “On Revision Operators”, Journal of Symbolic Logic 68, 3 (2003): 689–711.

Welch, Philip D., “On Gupta-Belnap revision theories of truth, Kripkean fixed-points and the next stable set”, Bulletin of Symbolic Logic 7, 3 (2001): 345–360.

Logic and Logical Philosophy

Downloads

  • PDF

Published

2012-12-20

How to Cite

1.
BJØRDAL, Frode. Librationist closures of the paradoxes. Logic and Logical Philosophy. Online. 20 December 2012. Vol. 21, no. 4, p. 323–361. [Accessed 2 July 2025]. DOI 10.12775/LLP.2012.016.
  • ISO 690
  • ACM
  • ACS
  • APA
  • ABNT
  • Chicago
  • Harvard
  • IEEE
  • MLA
  • Turabian
  • Vancouver
Download Citation
  • Endnote/Zotero/Mendeley (RIS)
  • BibTeX

Issue

Vol. 21 No. 4 (2012): December

Section

Articles

Stats

Number of views and downloads: 653
Number of citations: 0

Crossref
Scopus
Google Scholar
Europe PMC

Search

Search

Browse

  • Browse Author Index
  • Issue archive

User

User

Current Issue

  • Atom logo
  • RSS2 logo
  • RSS1 logo

Information

  • For Readers
  • For Authors
  • For Librarians

Newsletter

Subscribe Unsubscribe

Language

  • English
  • Język Polski

Tags

Search using one of provided tags:

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,
Up

Akademicka Platforma Czasopism

Najlepsze czasopisma naukowe i akademickie w jednym miejscu

apcz.umk.pl

Partners

  • Akademia Ignatianum w Krakowie
  • Akademickie Towarzystwo Andragogiczne
  • Fundacja Copernicus na rzecz Rozwoju Badań Naukowych
  • Instytut Historii im. Tadeusza Manteuffla Polskiej Akademii Nauk
  • Instytut Kultur Śródziemnomorskich i Orientalnych PAN
  • Instytut Tomistyczny
  • Karmelitański Instytut Duchowości w Krakowie
  • Ministerstwo Kultury i Dziedzictwa Narodowego
  • Państwowa Akademia Nauk Stosowanych w Krośnie
  • Państwowa Akademia Nauk Stosowanych we Włocławku
  • Państwowa Wyższa Szkoła Zawodowa im. Stanisława Pigonia w Krośnie
  • Polska Fundacja Przemysłu Kosmicznego
  • Polskie Towarzystwo Ekonomiczne
  • Polskie Towarzystwo Ludoznawcze
  • Towarzystwo Miłośników Torunia
  • Towarzystwo Naukowe w Toruniu
  • Uniwersytet im. Adama Mickiewicza w Poznaniu
  • Uniwersytet Komisji Edukacji Narodowej w Krakowie
  • Uniwersytet Mikołaja Kopernika
  • Uniwersytet w Białymstoku
  • Uniwersytet Warszawski
  • Wojewódzka Biblioteka Publiczna - Książnica Kopernikańska
  • Wyższe Seminarium Duchowne w Pelplinie / Wydawnictwo Diecezjalne „Bernardinum" w Pelplinie

© 2021- Nicolaus Copernicus University Accessibility statement Shop