Øystein Linnebo

• Thin Objects: An Abstractionist Account, Oxford University Press (2018)
• "Actual and Potential Infinity" (with Stewart Shapiro), Noûs (2018)
• Philosophy of Mathematics, Princeton University Press (2017) 
• “On the Innocence and Determinacy of Plural Quantification” (with Salvatore Florio), Noûs 53 (2016), 65-83
• “Two Types of Abstraction for Structuralism” (with Richard Pettigrew), Philosophical Quarterly 64 (2014), 267-83
• “The Potential Hierarchy of Sets”, Review of Symbolic Logic 6:2 (2013), 205-28
• “Hierarchies Ontological and Ideological” (with Agustín Rayo), Mind 121 (2012): 269-308
• “Pluralities and Sets,” Journal of Philosophy 107:3 (2010), 144-164
• “Platonism in the Philosophy of Mathematics,” in Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy (2009)
• “Superplurals in English” (with David Nicolas), Analysis 68:3 (2008), 186-97
• “Structuralism and the Notion of Dependence,” Philosophical Quarterly 58 (2008), 59-79
• “Epistemological Challenges to Mathematical Platonism,” Philosophical Studies 129:3 (2006), 545-574
• “Predicative Fragments of Frege Arithmetic,” Bulletin of Symbolic Logic 10:2 (2004), 153-174
• “Plural Quantification,” in Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy (2004)
• “Plural Quantification Exposed,” Noûs 37:1 (2003), 71-92

• Linnebo, Øystein (2020). Peacocke on numbers and magnitudes. Philosophical Studies.  ISSN 0031-8116. . doi: https://doi.org/10.1007/s11098-020-01542-8 Full text in Research Archive.
• Linnebo, Øystein (2020). Riemann’s Scale: A Puzzle About Infinity. Erkenntnis: An International Journal of Scientific Philosophy.  ISSN 0165-0106. . doi: 10.1007/s10670-020-00345-x
• Linnebo, Øystein & Florio, Salvatore (2020). Critical Plural Logic. Philosophia Mathematica.  ISSN 0031-8019.  28(2), s 172- 203 . doi: 10.1093/philmat/nkaa020 Full text in Research Archive.
• Linnebo, Øystein & Hale, Bob (2020). Ontological Categories and the Problem of Expressibility, In Bob Hale (ed.),  Essence and existence: Selected Essays.  Oxford University Press.  ISBN 9780198712084.  ch. 5.  s 73 - 103 Full text in Research Archive.
• Linnebo, Øystein & Shapiro, Stewart (2020). Potentiality and Indeterminacy in Mathematics. Journal of Applied Logics: The IfCoLog Journal of Logics and their Applications.  ISSN 2055-3706.  7(7), s 1199- 1219
• Hamkins, Joel David & Linnebo, Øystein (2019). THE MODAL LOGIC of SET-THEORETIC POTENTIALISM and the POTENTIALIST MAXIMALITY PRINCIPLES. The Review of Symbolic Logic.  ISSN 1755-0203. . doi: 10.1017/S1755020318000242 Full text in Research Archive.
• Linnebo, Øystein (2019). The Context Principle in Frege’s Grundgesetze, In Philip Ebert & Marcus Rossberg (ed.),  Essays on Frege's Basic Laws of Arithmetic.  Oxford University Press.  ISBN 9780198712084.  ch. 4. Full text in Research Archive.
• Linnebo, Øystein & Shapiro, Stewart (2019). Actual and potential infinity. Noûs.  ISSN 0029-4624.  53(1), s 160- 191 . doi: 10.1111/nous.12208 Full text in Research Archive.
• Linnebo, Øystein & Shapiro, Stewart (2019). Realizability as a Kind of Truthmaking, In Miroslaw Szatkowski (ed.),  Quo Vadis, Metaphysics.  Walter de Gruyter.  ISBN 3110662493.  chapter.
• Cook, Roy & Linnebo, Øystein (2018). Cardinality and Acceptable Abstraction. Notre Dame Journal of Formal Logic.  ISSN 0029-4527.  59(1), s 61- 74 . doi: 10.1215/00294527-2017-0012 Full text in Research Archive.
• Linnebo, Øystein (2018). DUMMETT ON INDEFINITE EXTENSIBILITY. Philosophical Issues.  ISSN 1533-6077.  28(1), s 196- 220 . doi: 10.1111/phis.12122 Full text in Research Archive.
• Linnebo, Øystein (2018). On the Permissibility of Impredicative Comprehension, In Jessica Leech (ed.),  Being Necessary Themes of Ontology and Modality from the Work of Bob Hale.  Oxford University Press.  ISBN 9780198792161.  kapittel 9.  s 170 - 189 Full text in Research Archive.
• Linnebo, Øystein (2018). Putnam on Mathematics as Modal Logic, In Roy Cook & Geoffrey Hellman (ed.),  Hilary Putnam on Logic and Mathematics.  Springer.  ISBN 978-3-319-96274-0.  chapter 14.  s 249 - 267
• Linnebo, Øystein (2018). Rumfitt on the logic of set theory. Inquiry (Oslo).  ISSN 0020-174X.  62(7), s 826- 841 . doi: 10.1080/0020174X.2018.1530832 Full text in Research Archive.
• Linnebo, Øystein (2018). Truth in Mathematics, In Michael Glanzberg (ed.),  Oxford Companion to Truth.  Oxford University Press.  ISBN 9780199557929.  kapittel 24.  s 648 - 665 Full text in Research Archive.
• Linnebo, Øystein & Florio, Salvatore (2017). Logic and Plurals, In Kirk Ludwig (ed.),  The Routledge Handbook of Collective Intentionality.  Routledge.  ISBN 9781138783638.  34.  s 451 - 463 Full text in Research Archive.
• Linnebo, Øystein (2016). How to Harness Basic Law V, In Massimiliano Carrara; Alexandra Arapinis & Friederike Moltmann (ed.),  Unity and Plurality: Logic, Philosophy, and Linguistics.  Oxford University Press.  ISBN 9780198716327.  kapittel 2.  s 19 - 32
• Linnebo, Øystein (2016). Impredicativity in the Neo-Fregean Program, In Ebert Philip & Marcus Rossberg (ed.),  Abstractionism: Essays in the Philosophy of Mathematics.  Oxford University Press.  ISBN 9780199645268.  kapittel 12.  s 247 - 268
• Linnebo, Øystein (2016). Plurals and Modals. Canadian Journal of Philosophy.  ISSN 0045-5091.  46(4-5), s 654- 676 . doi: 10.1080/00455091.2015.1132975
• Linnebo, Øystein & Florio, Salvatore (2016). On the Innocence and Determinacy of Plural Quantification. Noûs.  ISSN 0029-4624.  50(3), s 565- 583 . doi: 10.1111/nous.12091
• Linnebo, Øystein; Shapiro, Stewart & Hellman, Geoffrey (2016). Aristotelian Continua. Philosophia Mathematica.  ISSN 0031-8019.  24(2), s 214- 246 . doi: 10.1093/philmat/nkv024
• Horsten, Leon & Linnebo, Øystein (2015). Term Models for Abstraction Principles. Journal of Philosophical Logic.  ISSN 0022-3611.  s 1- 23 . doi: 10.1007/s10992-015-9344-z
• Linnebo, Øystein; Florio, Salvatore; Welch, Philip & Walsh, Sean (2015). Set Theory and Higher-Order Logic: Foundational Issues and Philosophical Developments. Notre Dame Journal of Formal Logic.  ISSN 0029-4527.  56, s 1- 2
• Linnebo, Øystein & Shapiro, Stewart (2015). Frege Meets Brouwer (or Heyting, or Dummett). The Review of Symbolic Logic.  ISSN 1755-0203.  8(3), s 540- 552 . doi: 10.1017/s1755020315000039
• Linnebo, Øystein (2014). 'Just is'-Statements as Generalized Identities. Inquiry (Oslo).  ISSN 0020-174X.  57(4), s 466- 482 . doi: 10.1080/0020174X.2014.905037
• Linnebo, Øystein & Pettigrew, Richard (2014). Two Types of Abstraction for Structuralism. The Philosophical Quarterly.  ISSN 0031-8094.  64, s 267- 283 . doi: 10.1093/pq/pqt044
• Linnebo, Øystein & Rayo, Agustin (2014). Response to Florio and Shapiro. Mind.  ISSN 0026-4423.  123, s 175- 181
• Shapiro, Stewart & Linnebo, Øystein (2014). Frege Meets Brouwer (or Heyting or Dummett). The Review of Symbolic Logic.  ISSN 1755-0203.  8(3), s 540- 552 . doi: 10.1017/S1755020315000039
• Ladyman, James; Linnebo, Øystein & Bigaj, Tomasz (2013). Entanglement and non-factorizability. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics.  ISSN 1355-2198.  44(3), s 215- 221 . doi: 10.1016/j.shpsb.2013.02.004
• Linnebo, Øystein (2013). Freges oppfatning av logikk: Fra Kant til Grundgesetze. Norsk Filosofisk tidsskrift.  ISSN 0029-1943.  48(3-4), s 219- 229
• Linnebo, Øystein (2013). Føllesdal and Frege on Reference, In Michael Frauchiger (ed.),  Reference, Rationality, and Phenomenology. Themes from Føllesdal.  Ontos Verlag.  ISBN 978-3-86838-182-5.  part V.  s 259 - 279
• Linnebo, Øystein (2013). THE POTENTIAL HIERARCHY OF SETS. The Review of Symbolic Logic.  ISSN 1755-0203.  6(2), s 205- 228 . doi: 10.1017/S1755020313000014
• Muller, F.A. & Linnebo, Øystein (2013). On Witness-Discernibility of Elementary Particles. Erkenntnis: An International Journal of Scientific Philosophy.  ISSN 0165-0106.  78, s 1133- 1142 . doi: 10.1007/s10670-012-9385-4
• Linnebo, Øystein (2012). Hierarchies Ontological and Ideological. Mind.  ISSN 0026-4423.  121, s 269- 308 . doi: 10.1093/mind/fzs050
• Linnebo, Øystein (2005). Epistemological challenges to mathematical platonism. Philosophical Studies.  ISSN 0031-8116.
• Linnebo, Øystein (2005). To Be Is to Be an F. Dialectica.  ISSN 0012-2017.  59
• Linnebo, Øystein (2004). Frege's Proof of Referentiality. Notre Dame Journal of Formal Logic.  ISSN 0029-4527.  45(2), s 73- 98 Show summary

  I present a novel interpretation of Frege's famous attempt at Grundgesetze I §§29-31 to prove that every expression of his language has a unique reference. I argue that Frege's proof is based on a contextual account of reference, similar to but more sophisticated than that enshrined in his famous Context Principle. Although Frege's proof is incorrect, I argue that the account of reference on which it is based is of potential philosophical value, and I analyze the class of cases to which it may successfully be applied.

• Linnebo, Øystein (2004). Predicative fragments of Frege Arithmetic. Bulletin of Symbolic Logic.  ISSN 1079-8986.  10, s 153- 174 Show summary

  Frege Arithmetic (FA) is the second-order theory whose sole non-logical axiom is Hume's Principle. According to Frege's Theorem, FA and some natural definitions imply all of second-order Peano Arithmetic. This paper distinguishes two dimensions of impredicativity involved in FA--one having to do with Hume's Principle, the other, with the underlying second-order logic--and investigates how much of Frege's Theorem goes through in various partially predicative fragments of FA. Theorem 1 shows that almost everything goes through, the most important exception being the axiom that every natural number has a successor. Theorem 2 shows that this axiom cannot be proved in the theories that are predicative in either dimension.

• Linnebo, Øystein (2003). Frege's Conception of Logic: From Kant to Grundgesetze. Manuscrito - Revista Internacional de Filosofia.  ISSN 0100-6045.  26(2), s 235- 252 Show summary

  I first argue that Frege started out with a conception of logic closer to Kant's than is generally recognized. Then I analyze Frege's reasons for gradually rejecting this view. Although I concede that the demands imposed by Frege's logicism played some role, I argue that his increasingly vehement anti-psychologism provides a deeper and more interesting reason for rejecting his earlier view.

• Linnebo, Øystein (2003). Critical Study of Stewart Shapiro, Philosophy of Mathematics: Structure and Ontology. Philosophia Mathematica.  ISSN 0031-8019.  11(1), s 92- 104 Show summary

  Jeg gjør en kritisk analyse av Stewart Shapiros nye bok i matematikkens filosofi og kommer med et positivt forlag om hvordan matematisk strukturalisme bør forstås.

• Linnebo, Øystein (2003). Plural Quantification Exposed. Noûs.  ISSN 0029-4624.  37(1), s 71- 92 Show summary

  Jeg gir en fremstilling av George Boolos sin teori om plural-kvantifikasjon og kritiserer påstanden hans om at denne teorien er en rent logisk teori sterk nok til å tolke full annen-ordens logikk.

View all works in Cristin

• Linnebo, Øystein (2018). Thin Objects: An Abstractionist Account. Oxford University Press.  ISBN 9780199641314.  256 s.
• Linnebo, Øystein (2017). Philosophy of Mathematics. Princeton University Press.  ISBN 9780691161402.  216 s.

View all works in Cristin

• Linnebo, Øystein (2020). Review of John Bell, The Continuous, the Discrete. American Mathematical Society Mathematical Reviews.  ISSN 2167-5163.
• Linnebo, Øystein (2020). The Paradox of the Largest Number: From Aristotle to Cantor, In Frode Kjosavik & Camilla Serck-Hanssen (ed.),  Metametaphysics and the Sciences. Historical and Philosophical Perspectives.  Routledge.  ISBN 978-0-367-26369-0.  ch. 12.
• Linnebo, Øystein & Bøhn, Einar Duenger (2020). Interview with Dagfinn Føllesdal. Norsk Filosofisk tidsskrift.  ISSN 0029-1943.  55(1), s 46- 79
• Linnebo, Øystein (2019). DORA-erklæringen og vår vurdering av forskningskvalitet. Khrono.no.  ISSN 1894-8995.
• Linnebo, Øystein (2017). Bokmelding: Frege – Utvalgte Tekster. Norsk Filosofisk tidsskrift.  ISSN 0029-1943.  52(4), s 187- 192
• Maliks, Reidar; Linnebo, Øystein & Strand, Arne (2017). Den viktige uenigheten. Klassekampen.  ISSN 0805-3839.
• Linnebo, Øystein (2016). Identity and two conceptions of ontology. Filosofisk supplement.  ISSN 0809-8220.  s 44- 47
• Linnebo, Øystein (2013). Review of Patricia Blanchette, Frege’s Conception of Logic. Notre Dame Philosophical Reviews.  ISSN 1538-1617.
• Linnebo, Øystein (2013). “What is the Infinite and Is It Real?”. Philosophers' magazine.  ISSN 1354-814X.  (61), s 42- 47
• Linnebo, Øystein (2004). Kant and Frege on Formal Logic.
• Linnebo, Øystein (2004). Plural Quantification, In Ed Zalta (ed.),  Stanford Encyclopedia of Philosophy.  Stanford Encyclopedia of Philosophy.  http://plato.stanford.edu/entries/plural-quant/. Show summary

  Ordinary English contains two sorts of object quantifiers. In addition to the usual singular quantifiers, as in 'There is an apple on the table', there are plural quantifiers, as in 'There are some apples on the table'. This article provides a survey of recent discussions of the logic, semantics, and metaphysics of plural quantification, as well as of its various philosophical applications.

• Linnebo, Øystein (2004). Reference and Frege's Context Principle.
• Linnebo, Øystein (2004). Reference and Frege's Context Principle.
• Linnebo, Øystein (2004). Review of Kit Fine, The Limits of Abstraction. Australasian Journal of Philosophy.  ISSN 0004-8402.  82(4), s 653- 656
• Linnebo, Øystein (2003). Mathematical Structuralism.
• Linnebo, Øystein (2003). Neo-Logicism and Impredicativity.
• Linnebo, Øystein (2003). Predicative Fragments of Frege Arithmetic.
• Linnebo, Øystein & Parsons, Charles (2003). Introductory Note to Correspondence with Walter Pitts, In Solomon Feferman (ed.),  Kurt Gödel: Collected Works, Vol. V.  Clarendon.  ISBN 0198500750.  s 157 - 159
• Linnebo, Øystein (2002). Naturalistic Challenges: On the Possibility of Non-Scientific Knowledge. Show summary

  Jeg diskuterer filosofisk naturalisme og noen av de utfordringer denne posisjonen gir opphav til, spesielt angående matematikk og etikk. Etter å ha avvist de tradisjonelle utfordringene av denne typen ved å skille mellom minimal- og scientistisk naturalisme, argumenterer jeg for at naturalisme likevel gir opphav til visse utfordringer.

View all works in Cristin