Frode Alfson Bjørdal

English version of this page
Treffetider By appointment
Besøksadresse Blindernveien 31 Georg Morgenstiernes hus 0313 OSLO
"The test of a first-rate intelligence is
the ability to hold two opposing ideas
in the mind at the same time and still
retain the ability to function."
F. Scott Fitzgerald
I was born and raised in Ørsta. When I was ten we moved to Ålesund. This is some towns and countries ago.

In Aasen by! I attempted to name a new city resulting from a merger of Ørsta and Volda in honour of Ivar Aasen, whose life work was instrumental in giving the Norwegian language much deeper roots in and forms from its old Norse tradition than what prevailed in the superceded Danicized versions.

A description of interests, as well as some online papers and lists of publications and talks are found below. You can also look me up in Cristin or in Orcid.


I am a Professor emeritus of Philosophy at the Department of Philosophy and Classics and the History of Art and Ideas at the University of Oslo and a CAPES researcher at Programa de Pós-Graduação em Filosofia at Universidade Federal do Rio Grande do Norte in Natal in Brazil.


Doctor of Philosophy (PhD) in Philosophy at the University of California, Santa Barbara, 1993. Advisor: Anthony Brueckner. Committee: Anthony Brueckner, Nathan Salmon and William Forgie.

Candidate in Philosophy (C.Phil) in Philosophy at the University of California, Santa Barbara, 1990.

I studied Philosophy and Logic as a Deutscher Akademischer Austauschdienst Stipendiat at the Johann Wolfgang von Goethe Universität in Frankfurt am Main, 1985/86. At the time I planned on taking a doctorate there, and I was accepted as a Doktorand (doctoral student), just as those with a German Magister Artium degree, on the basis of my Norwegian education, written work and an oral Zwischenprüfung.

Candidatus magisterii (cand.mag) from the University of Bergen, 1985. I double majored in Philosophy and Economics, and had Logic, Mathematics and Social Science as minors.

Examen artium (reallinjen) at Ålesund Gymnas, 1976/79.

Some of my teachers:

At the University of Bergen I had seminars by Erik Brown, Nile Gilje, Arild Haaland, Kåre Johnsen, Vigdis Songe-Møller and Hans Skjervheim. In Frankfurt I followed seminars by Jürgen Habermas, Karl Otto Apel and Wolfgang Kuhlmann. At UCSB I had seminars from all my committe members as well as by Peter Hylton, Noel Fleming and Charlotte Stough. At UCLA I followed a seminar by David Kaplan and took a gradute seminar in logic by Alonzo Church (with an oral exam) in the spring of 1989.

Former positions:

Associate professor of Philosophy at the University of Tromsø, 1994/96.

University lecturer in Philosophy at the University of Trondheim (now the Norwegian University of Science and Technology), 1992/94.

Teaching Assistant at the University of Calfornia, Santa Barbara, 1989/92.

High-School teacher in Mathematics and Economics at Ålesund Videregående Skole avd. Langhaugen (now Spjelkavik Videregående Skole), 1987/88.

My civil service was for the Wittgenstein Archives at the University of Bergen, 1986/87.


Member of the advisory board for philosophy, Norwegian Research Council, 1994-97.

Referee for Journal of Symbolic Logic

Referee for The Review of Symbolic logic

Referee for Mathematical Reviews

Referee for Notre Dame Journal of Philosophical Reviews 

Referee for Princípios: Revista de Filosofia

Referee for Nordic Journal of Philosophical Logic

Guest position:

During the 2001/02 academic year I was a visitor at the pontifical University of Malta. In the fall of 2001 former university rector professor Fr. Peter Serracino Inglott and I had a seminar on the Problem of Evil for graduate Philosohy and Theology students.

Scholarships awarded:

When a student in Bergen I was twice awarded a scholarship from the L. Melzers Høyskolefond. As mentioned above, I was a DAAD scholar in Frankfurt am Main, 1985/86. The first year of my studies in California, 1988/89, was supported by the Education Abroad Program of the University of California and by Norge Amerika Foreningen through the John D. Archbold scholarship of its Nansen Fund. The following three years of my Californian sojourn was, in addition to my employment as a Teaching Assistant, supported by tuition and fee waivers from the Department of Philosophy through its endowed Ralph W. Church Fund.

Scientific and philosophical interests:

My interests in philosophy and beyond are quite broad; but one must focus. Since before my promotion in 1993 I have primarily been preoccupied with foundational issues in mathematics and semantics. This has resulted in the theory librationism (until recently I used the term "liberalism"), which is inter alia geared to deal with semantical and set theoretical paradoxes. Librationism offers a way to deal with paradoxes that is related to paraconsistent ones, though without giving up on or contradicting any theorems of classical logic. The semantics of librationism has an ancestry in Hans Herzberger's semi inductive approach to deal with semantical paradoxes, and related ones. Unlike paraconsistent approaches, the mathematical strength of librationism is immense (and in an important sense full) though yet to be precisely gauged. A cornucopia of important issues are potentially shed light upon in new and distinct manners by librationism. Many fields of exploration are opened up here, and they are all related to the deeper question as to precisely what mathematics librationism supports.

I have a strong interest in many topics in the philosophy of religion. To those who know their history of philosophy, it should come as no surprise that there is often a strong affinity between mathematical meditation and theological thinking.


Emneord: Filosofi, Logikk, Grunnlagsproblem i matematikk, Semantiske og Mengdeteoretiske Paradoks, Religionsfilosofi




Librationist Closures of the Paradoxes was published in Logic and Logical Philosophy Volume 21 (4), p. 323-361, 2012.

Librationist Closures of Paradox and other Mathematical Phenomena is the preprint of the abstract for the talk I held at the Logic Colloquium 2011 held under the auspices of the Association of Symbolic Logic. The final version will be published in the Bulletin of Symbolic Logic.

Introducing Librationism was published on the professionally moderated Foundations of Mathematics emaillist on the 13th of June 2011. Moderator in chief, Martin Davis.

The Evaluation Semantics - A Short Introduction was published in The LOGICA Yearbook 2011, College Publications 2012. The Evaluation Semantics for Modal Logics is the abstract for my precedent talk at LOGICA 2011.Librationist closures is one of the announcements of a talk I held at Universidade Estadual de Campinas (02.03.2011) and at Universidade Federal do Rio Grande do Norte (25.02.2011), Brasil.

The Arithmetical Program - An Addendum, posted on The Foundations of Mathematics email list on February 23, 2011.

The Arithmetical Program, posted on the The Foundations of Mathematics email list on February 22, 2011.

Considerations Contra Cantorianism was published in The LOGICA Yearbook 2010, College Publications 2011.

The Inadequacy of a Proposed Paraconsistent Set Theory was published in The Review of Symbolic Logic Vol. IV No. 1, 2011. The link to a preprint in DUO is available here.

"2+2=4" er misvisande ("2+2=4" is misleading) came in Anita Leirfall and Tor Sandmel (red.): Enhet i mangfold - festkrift til Johan Arnt Myrstad i anledning 60-årsdagen, Unipub 2009, pp. 55-65. (In Norwegian.)

Bør naturen ødelegges? Nihilisme, partialisme, ameliorisme eller optimisme? Det apokalyptiske argument came in Anita Leirfall (red) Non Plus Ultra: Festskrift til Stein Erik Johansen i anledning 50-årsdagen, Tapir 2004, ISBN 82-303-0231-6. pp. 211- 224. (In Norwegian.)

Ateistisk Etikk - Anmeldelse av Finngeir Hiorths Etikk for Ateister (publisher: Oslo Fylkeslag av Human-Etisk Forbund, 1998), Opuscula, Examen Philosophicums småskriftserie. 1999 (1):77-79. (This is a review of a book by Finngeir Hiorth - Ethics for Atheists. In Norwegian.)

En Metrisk Feil - med Følgesetninger om Barmhjertighetsprinsipp, Opuscula, Examen Philosophicums småskriftserie 1999 (1):44-49. (This is a criticism of Ludwig Wittgenstein's point of view concerning the standard meter rod in Paris. In Norwegian)

In Understanding Gödel's Ontological Argument, published in The Logica Yearbook 1998, I show how C. Anthony Andersion's rectified version of Kurt Gödel's ontological argument for the existence of a deity can be simplified by presupposing a second order modal logic including S4 and taking the property of being God-like as primitive; as a result we only need two plausible premises for the argument to go through whereas Gödel and Anderson presupposed five distinct premises (including versions of the two I presuppose).

Er denne druen laget av det den er laget av?  (Is this grape made of what it is made of?) was published in Anniken Greve and Sigmund Nesset (red.): Filosofi i et nordlig landskap - Jakob Meløe 70 år, Ravnetrykk Tromsø 1997, pp. 172-175. In Norwegian.

Bør vi gjøre så godt vi kan? in Festskrift til Johan Arnt Myrstad i anledning 50-års dagen. : Tapir Forlag, Trondheim 1997 ISBN 82-519-1367-5. p. 1-2. (In Norwegian)

On Beliefs came in Nordic Journal of Philosophical Logic, Vol. 1 No. 1, 1996.

My book Kritisk Tenkning, Cappelen Akademisk Forlag 1996, is available from The National Library of Norway.

My dissertation A Theory of Knowledge is available from the UMI Dissertation Services Ann Arbor, Michigan, order number 9335093.

See also Cristin and Orcid.

  • Bjørdal, Frode Alfson (2019). Humean cum Counterfactual Skepticism and Epistemological Deontologism, In Tiegue Vieira Rodrigues (ed.),  Epistemologia Analítica, Vol .1: debates contemporâneos.  Editora Fi.  ISBN 978-85-5696-665-0.  Independent chapter.  s 47 - 54 Vis sammendrag
  • Bjørdal, Frode Alfson (2019). Review of "Fujimoto, Kentaro Truths, inductive definitions, and Kripke-Platek systems over set theory. J. Symb. Log. 83 (2018), no. 3, 868--898.". Mathematical Reviews.  ISSN 0025-5629.
  • Bjørdal, Frode Alfson (2019). Review of "Sochański, Michał What is diagrammatic reasoning in mathematics? Log. Log. Philos. 27 (2018), no. 4, 567--581.". Mathematical Reviews.  ISSN 0025-5629.
  • Bjørdal, Frode Alfson (2018). All Properties are Divine or God Exists - The Sacred Thesis and its Ontological Argument. Logic and Logical Philosophy.  ISSN 1425-3305.  27(3), s 329- 350 . doi: 10.12775/LLP.2017.027
  • Bjørdal, Frode Alfson (2018). Review of Sy-David Friedman`s Evidence for set-theoretic truth and the Hyperuniverse Programme. The hyperuniverse project and maximality, 75–107, Birkhäuser/Springer, Cham, 2018.. Mathematical Reviews.  ISSN 0025-5629.
  • Bjørdal, Frode Alfson (2017). Review of Field, Hartry; Lederman, Harvey; Øgaard, Tore Fjetland Prospects for a naive theory of classes. Notre Dame J. Form. Log. 58 (2017), no. 4, 461–506.. Mathematical Reviews.  ISSN 0025-5629.
  • Bjørdal, Frode Alfson (2017). Skolem Satisfied: On £ and ₽, In Massoud Pourmadhian & Ali Sadegh Daghighi (ed.),  Logic around the World.  Andisheh & Farhang-e Javidan.  ISBN 9786006386997.  Kap.  s 31 - 42
  • Bjørdal, Frode (2016). Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability. Logica Universalis.  ISSN 1661-8297.  10(2-3), s 373- 376 . doi: 10.1007/s11787-016-0149-9 Vis sammendrag
  • Bjørdal, Frode Alfson (2016). Review of Hamkins, Joel David; Kikuchi, Makoto Set-theoretic mereology. Log. Log. Philos. 25 (2016), no. 3, 285–308.. Mathematical Reviews.  ISSN 0025-5629.
  • Bjørdal, Frode Alfson (2016). Review of Jago, Mark Alethic undecidability doesn't solve the liar. Analysis (Oxford) 76 (2016), no. 3, 278–283.. Mathematical Reviews.  ISSN 0025-5629.
  • Bjørdal, Frode Alfson (2016). Review of Sheridan, Flash A variant of Church's set theory with a universal set in which the singleton function is a set. Log. Anal. (N.S.) 59 (2016), no. 233, 81–131.. Mathematical Reviews.  ISSN 0025-5629.
  • Bjørdal, Frode Alfson (2015). On the Type-Free Paracoherent Foundation of Mathematics with the Sedate Extension of Classical Logic by the Librationist Set Theory £, and Specifically on Why £ Is Neither Inconsistent nor Contradictory nor Paraconsistent, In J.-Y. Béziau; M. K. Chakraborty & S Dutta (ed.),  New Directions in Paraconsistent Logic.  Springer.  ISBN 9788132227199.  Kapittel 23.  s 509 - 515
  • Bjørdal, Frode Alfson (2015). Review of (the book) Metaphysics of Logic. Notre Dame Philosophical Reviews.  ISSN 1538-1617.
  • Bjørdal, Frode (2012). Librationist Closures of the Paradoxes. Logic and Logical Philosophy.  ISSN 1425-3305.  21(4), s 323- 361
  • Bjørdal, Frode (2012). The Evaluation Semantics - A Short Introduction, In Michael Pelis & Vit Punchochar (ed.),  The Logica Yearbook 2011.  College Publications.  ISBN 978-1848900714.  Scientific article.  s 31 - 36 Vis sammendrag
  • Bjørdal, Frode (2011). Considerations Contra Cantorianism, In Vit Puncochar & Michael Pelis (ed.),  The Logica Yearbook 2010.  College Publications.  ISBN 978-1-84890-038-7.  Independent scientific article.  s 43 - 52 Vis sammendrag
  • Bjørdal, Frode (2011). The Inadequacy of a Proposed Paraconsistent Set Theory. The Review of Symbolic Logic.  ISSN 1755-0203.  4(1), s 106- 108 . doi: 10.1017/S1755020310000171 Fulltekst i vitenarkiv. Vis sammendrag
  • Bjørdal, Frode (2008). "2+2=4" er misvisande, I: Thor Sandmel & Anita Leirfall (red.),  Enhet i mangfold. Festskrift for Johan Arnt Myrstad i anledning 60-årsdagen.  Unipub forlag.  ISBN 978-82-303-1179-0.  Independent article.  s 55 - 66
  • Bjørdal, Frode (2006). Minimalistic Liberalism. An adequate, Acceptable, Consistent and Contradictory Foundation, In Marta Bilková & Ondrej Tomala (ed.),  The LOGICA Yearbook 2005.  Filosofia.  ISBN 80-7007-229-6.  Artikkel.  s 39 - 50
  • Bjørdal, Frode (2005). There are Only Countably Many Objects, In Libour Behounek & Marta Bilková (ed.),  The LOGICA Yearbook 2004.  Filosofia Yearbook.  ISBN 8070-07-2083.  kapittel.  s 47 - 58
  • Bjørdal, Frode (2004). Bør naturen ødelegges? Nihilisme, partialisme, ameliorisme eller optimisme? Det apokalyptiske argument, I: Anita Leirfall (red.),  Non Plus Ultra: Festskrift til Stein Erik Johansen i anledning 50-årsdagen.  Tapir Akademisk Forlag.  ISBN 82-303-0231-6.  Frittstående artikkel.  s 211 - 225 Fulltekst i vitenarkiv.
  • Bjørdal, Frode (1999). Ateistisk Etikk - Anmeldelse av Finngeir Hiorths Etikk for Ateister (utgiver: Oslo Fylkeslag av Human-Etisk Forbund, 1998). Opuscula, Examen Philosophicums småskriftserie.  ISSN 0806-3656.  (1), s 77- 81 Fulltekst i vitenarkiv.
  • Bjørdal, Frode (1999). En Metrisk Feil - med Følgesetninger om Barmhjertighetsprinsipp. Opuscula, Examen Philosophicums småskriftserie.  ISSN 0806-3656.  (1), s 44- 49 Fulltekst i vitenarkiv.
  • Bjørdal, Frode (1999). Understanding Gödel's Ontological Argument, In Timothy Childers (ed.),  The Logica Yearbook (1998).  Filosofia.  ISBN 8070071230.  Kapittel.  s 214 - 217
  • Bjørdal, Frode (1998). Towards a Foundation for Type free Reasoning, In Timothy Childers (ed.),  The Logica Yearbook (1997).  Filosofia.  ISBN 8070071095.  Kapittel.  s 259 - 273
  • Bjørdal, Frode (1997). Bør vi gjøre så godt vi kan?, I: Anita Leirfall & Thor Sandmel (red.),  Festskrift til Johan Arnt Myrstad i anledning 50-års dagen.  Tapir Forlag, Trondheim.  ISBN 82-519-1367-5.  Artikkel.  s 1 - 2 Fulltekst i vitenarkiv.
  • Bjørdal, Frode (1997). Er denne druen laget av det den er laget av?, I: Greve Anniken & Sigmund Nesset (red.),  Filosofi i et nordlig landskap.  Ravnetrykk : Universitetsbiblioteket i Tromsøs skriftserie.  ISBN 82-91378-13-4.  Kapittel.  s 172 - 175
  • Bjørdal, Frode (1997). Om Gyldighet. Opuscula, Examen Philosophicums småskriftserie.  ISSN 0806-3656.  (3), s 99- 106
  • Bjørdal, Frode (1996). Når blir et menneske til?. Omsorg: Nordisk tidsskrift for Palliativ Medisin.  ISSN 0800-7489.  (1), s 41- 42
  • Bjørdal, Frode (1996). On Beliefs. Nordic Journal of Philosophical Logic.  ISSN 0806-6205.  1(1), s 79- 94
  • Bjørdal, Frode (1995). Kontra Asheim om Vaghet. Agora : Journal for metafysisk spekulasjon.  ISSN 0800-7136.  (2), s 140- 143
  • Bjørdal, Frode (1994). Om Asheim om Vaghet. Agora : Journal for metafysisk spekulasjon.  ISSN 0800-7136.  (1), s 250- 255

Se alle arbeider i Cristin

  • Bjørdal, Frode (1996). Kritisk Tenkning. Cappelen Damm Akademisk.  ISBN 82-456-0050-4.  156 s.

Se alle arbeider i Cristin

  • Bjørdal, Frode Alfson (2018). Cartesian Skepticism and Epistemic Deontologism.
  • Bjørdal, Frode Alfson (2018). Humean Skepticism and Epistemic Deontologism.
  • Bjørdal, Frode Alfson (2017). All Properties are Divine or God Exists.
  • Bjørdal, Frode Alfson (2017). Volutionary Considerations.
  • Bjørdal, Frode Alfson (2017). Volutionary Reflections.
  • Bjørdal, Frode Alfson (2017). Volutionary foundational ruminations: paradox, provability, truth and irrefutability.
  • Bjørdal, Frode Alfson (2016). Reciprocity in Infinite Dimensional Hyper Cubes. Vis sammendrag
  • Bjørdal, Frode Alfson (2016). Todas as Propriedades são Divinas ou Deus Existe.
  • Bjørdal, Frode Alfson (2016). Volutionary Foundational Visions. Vis sammendrag
  • Bjørdal, Frode Alfson (2016). Volutionism.
  • Bjørdal, Frode Alfson (2016). Volutionísmo.
  • Bjørdal, Frode Alfson (2015). All Properties are Divine or God Exists.
  • Bjørdal, Frode Alfson (2015). Librationist Capture and Domination of Definable Real Numbers.
  • Bjørdal, Frode Alfson (2015). Librationist motives and perspectives.
  • Bjørdal, Frode Alfson (2015). Modelling Librationist Set Theory £ with a Sigma-3 Admissible Ordinal.
  • Bjørdal, Frode Alfson (2015). The Isolation of the Definable Real Numbers with Domination and Capture in Librationist Set Theory.
  • Bjørdal, Frode Alfson (2015). The Librationist Domination of Second Order Arithmetic.
  • Bjørdal, Frode Alfson (2014). Capture, Collecton, Choice and Domination.
  • Bjørdal, Frode Alfson (2014). Definable Real Numbers with Librationist Capture and Domination.
  • Bjørdal, Frode Alfson (2014). Deontic Logic without Perfect Possible Worlds.
  • Bjørdal, Frode Alfson (2014). Evaluationist Necessitism, Revivalism, Anti-Essentialism and Fictional Realism.
  • Bjørdal, Frode Alfson (2014). Necessitarianismo Evaluationistica e Escatologia Confidentialista.
  • Bjørdal, Frode Alfson (2014). On the Librationist Foundational System.
  • Bjørdal, Frode Alfson (2014). The Cube of Opposition for Agentual Directives.
  • Bjørdal, Frode Alfson (2014). Things as Individuals, Queues, Crowds and Sets.
  • Bjørdal, Frode Alfson (2014). Truth degrees in the interval [-1,1] for the librationist system £.
  • Bjørdal, Frode Alfson (2014). With Librationism from Paraconsistency to Contrasistency, Incoherency and Complementarity.
  • Bjørdal, Frode Alfson (2013). A Sober Librationist Interpretation of ZF.
  • Bjørdal, Frode Alfson (2013). Librationist Farewells to Modus Ponens and Truth Functionality.
  • Bjørdal, Frode Alfson (2013). Nominist things and librationist world views.
  • Bjørdal, Frode Alfson (2012). Bør verda vere der?.
  • Bjørdal, Frode Alfson (2012). Negation, Contradiction, Contravalence and Complementarity.
  • Bjørdal, Frode Alfson (2012). Should the world be there?.
  • Bjørdal, Frode (2011). Bør verda vere tilstades?.
  • Bjørdal, Frode (2011). Er det bra at verda er til stade?.
  • Bjørdal, Frode (2011). Librationist Closures. Vis sammendrag
  • Bjørdal, Frode (2011). Librationist Closures. Vis sammendrag
  • Bjørdal, Frode (2011). Librationist Closures of Paradox and other Mathematical Phenomena - Lecture Abstract for LC2011. Fulltekst i vitenarkiv.
  • Bjørdal, Frode (2011). The Arithmetical Program. Vis sammendrag
  • Bjørdal, Frode (2011). The Arithmetical Program - An Addendum. Vis sammendrag
  • Bjørdal, Frode (2011). The Evaluation Semantics for Modal Logics. Fulltekst i vitenarkiv.
  • Bjørdal, Frode (2011). Til spørsmålet om eit liv etter døden er mogeleg: alle objekt er evige og naudsynelege.
  • Bjørdal, Frode Alfson (2011). A Librationist Quest for Strength.
  • Bjørdal, Frode (2010). Lecture in Ghent: Mathematical Librationism Contra Cantorianism.
  • Bjørdal, Frode (2010). Lecture in Hejnice Monastery: Considerations Contra Cantorianism.
  • Bjørdal, Frode (2010). Lecture in Lisbon: Minimalistic Liberalism - A Complementary Semi-Formal Set Theory that Respects Classical Logic, and with Mathematical Power beyond PI(1,1)-CA(0).
  • Bjørdal, Frode (2010). Lecture in Lisbon: Minimalistic Liberalism - a complementary semi-formal resolution that respects classical logic.
  • Bjørdal, Frode (2010). Lecture in Oslo: Minimalistisk liberalisme - ein kontradiktorisk grunnlagsteori som respekterer klassisk logikk.
  • Bjørdal, Frode (2009). Lecture in Hejnice Monastery: Paraconsistency with Classical Logic.
  • Bjørdal, Frode (2008). Lecture in Melbourne: Resisting Cantor's Arguments.
  • Bjørdal, Frode (2006). Lecture in Villa Lanna: On the Limits of Vague Identity.
  • Bjørdal, Frode (2005). Lecture in Hejnice Monastery: The Banach-Tarski Paradox in the Bialethic Framework of Caption and Its Theory of Sorts.
  • Bjørdal, Frode (2004). Lecture in Hejnice Monastery: Bialethism, Sorts, ZFC and Countability.
  • Bjørdal, Frode (2002). Lecture in Malta: Standard Theism and Egalitarian Optimism.
  • Bjørdal, Frode (2001). Contemporary Arguments for the Existence of God. Vis sammendrag
  • Bjørdal, Frode (2000). Lecture in Bergen: On the Reality of the Future. Vis sammendrag
  • Bjørdal, Frode (1999). Lecture in Villa Lanna: An Alternative Semantics for Deontic Logic.
  • Bjørdal, Frode (1998). A Theodicy.
  • Bjørdal, Frode (1998). Lecture at Liblice Chateau: Understanding Gödel's Ontological Argument. Vis sammendrag
  • Bjørdal, Frode (1997). Lecture in Villa Lanna: Towards a Foundation for Type-Free Reasoning.
  • Bjørdal, Frode (1996). Truth in Perspectives.
  • Bjørdal, Frode (1993). PhD-dissertation: A Theory of Knowledge.

Se alle arbeider i Cristin

Publisert 2. juni 2010 11:56 - Sist endret 23. mars 2020 11:46