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
• “What is the Infinite?” The Philosophers' Magazine 2nd quarter (2013), 42-47
• “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
• “Plural Quantification,” in Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy (2004)
• “Plural Quantification Exposed,” Noûs 37:1 (2003), 71-92

• Brauer, Ethan; Linnebo, Øystein & Shapiro, Stewart (2022). Divergent Potentialism: A Modal Analysis with an Application to Choice Sequences. Philosophia Mathematica. ISSN 0031-8019. 30(2), p. 143–172. doi: 10.1093/philmat/nkab031.
• Linnebo, Øystein (2022). Aristotelian Aspirations, Fregean Fears: Hossack on Numbers as Magnitudes. In Kürbis, Nils; Assadian, Bahram & Nassim, Jonathan (Ed.), Knowledge, Number and Reality: Encounters with the Work of Keith Hossack. Bloomsbury Academic. ISSN 9781350186439. p. 189–201. Full text in Research Archive
• Hartimo, Mirja; Kjosavik, Frode & Linnebo, Øystein (2022). Introduction to special issue on ‘critical views of logic’. Inquiry (Oslo). ISSN 0020-174X. 65(6), p. 631–637. doi: 10.1080/0020174X.2019.1651077. Show summary

  Critical views of logic are presented. These are views that are critical of logic in a sense akin to the way in which Kant is critical rather than dogmatic about traditional metaphysics. Such approaches differ from the Fregean ‘logic-first’ view. In accordance with the latter, logic is often regarded as epistemologically and methodologically fundamental. Hence, all disciplines – including mathematics – are considered as answerable to logic, rather than vice versa. In critical views of logic, by contrast, the logical principles that govern some subject matter may depend on the metaphysics of this subject matter or on the semantics of our discourse about it. Space is thereby carved out between a Fregean position on the one hand and thoroughgoing holism à la Quine on the other.

• Linnebo, Øystein & Shapiro, Stewart (2021). Modality in Mathematics. In Bueno, Otávio & Shalkowski, Scott A. (Ed.), The Routledge Handbook of Modality. Routledge. ISSN 9781138823310. p. 281–291. Full text in Research Archive
• Linnebo, Øystein & Shapiro, Stewart (2020). Potentiality and indeterminacy in mathematics. Journal of Applied Logics (JAL-FLAP). ISSN 2631-9810. 7(6), p. 1201–1221.
• 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 & 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), p. 1201–1221. Full text in Research Archive
• Linnebo, Øystein & Hale, Bob (2020). Ontological Categories and the Problem of Expressibility. In Hale, Bob (Eds.), Essence and existence: Selected Essays. Oxford University Press. ISSN 9780198712084. p. 73–103. Full text in Research Archive
• Linnebo, Øystein (2020). Peacocke on numbers and magnitudes. Philosophical Studies. ISSN 0031-8116. 178, p. 2717–2729. doi: 10.1007/s11098-020-01542-8. Full text in Research Archive
• Linnebo, Øystein & Florio, Salvatore (2020). Critical Plural Logic. Philosophia Mathematica. ISSN 0031-8019. 28(2), p. 172–203. doi: 10.1093/philmat/nkaa020. Full text in Research Archive
• 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 & Shapiro, Stewart (2019). Realizability as a Kind of Truthmaking. In Szatkowski, Miroslaw (Eds.), Quo Vadis, Metaphysics . Walter de Gruyter (De Gruyter). ISSN 3110662493. Full text in Research Archive
• Linnebo, Øystein (2019). The Context Principle in Frege’s Grundgesetze. In Ebert, Philip & Rossberg, Marcus (Ed.), Essays on Frege's Basic Laws of Arithmetic. Oxford University Press. ISSN 9780198712084. doi: 10.1093/oso/9780198712084.003.0004. Full text in Research Archive
• Linnebo, Øystein & Shapiro, Stewart (2019). Actual and potential infinity. Noûs. ISSN 0029-4624. 53(1), p. 160–191. doi: 10.1111/nous.12208. Full text in Research Archive
• Linnebo, Øystein (2018). Putnam on Mathematics as Modal Logic. In Cook, Roy & Hellman, Geoffrey (Ed.), Hilary Putnam on Logic and Mathematics. Springer. ISSN 978-3-319-96274-0. p. 249–267. doi: 10.1007/978-3-319-96274-0_14.
• Linnebo, Øystein (2018). Rumfitt on the logic of set theory. Inquiry (Oslo). ISSN 0020-174X. 62(7), p. 826–841. doi: 10.1080/0020174X.2018.1530832. Full text in Research Archive
• Linnebo, Øystein (2018). On the Permissibility of Impredicative Comprehension. In Leech, Jessica (Eds.), Being Necessary Themes of Ontology and Modality from the Work of Bob Hale. Oxford University Press. ISSN 9780198792161. p. 170–189. doi: 10.1093/oso/9780198792161.003.0009. Full text in Research Archive
• Linnebo, Øystein (2018). Truth in Mathematics. In Glanzberg, Michael (Eds.), Oxford Companion to Truth. Oxford University Press. ISSN 9780199557929. p. 648–665. doi: 10.1093/oxfordhb/9780199557929.013.24. Full text in Research Archive
• Linnebo, Øystein (2018). DUMMETT ON INDEFINITE EXTENSIBILITY. Philosophical Issues. ISSN 1533-6077. 28(1), p. 196–220. doi: 10.1111/phis.12122. Full text in Research Archive
• Cook, Roy & Linnebo, Øystein (2018). Cardinality and Acceptable Abstraction. Notre Dame Journal of Formal Logic. ISSN 0029-4527. 59(1), p. 61–74. doi: 10.1215/00294527-2017-0012. Full text in Research Archive
• Linnebo, Øystein & Florio, Salvatore (2017). Logic and Plurals. In Ludwig, Kirk (Eds.), The Routledge Handbook of Collective Intentionality. Routledge. ISSN 9781138783638. p. 451–463. Full text in Research Archive
• Linnebo, Øystein (2016). Impredicativity in the Neo-Fregean Program. In Philip, Ebert & Rossberg, Marcus (Ed.), Abstractionism: Essays in the Philosophy of Mathematics. Oxford University Press. ISSN 9780199645268. p. 247–268. doi: 10.1093/acprof%3Aoso/9780199645268.003.0012.
• Linnebo, Øystein (2016). How to Harness Basic Law V. In Carrara, Massimiliano; Arapinis, Alexandra & Moltmann, Friederike (Ed.), Unity and Plurality: Logic, Philosophy, and Linguistics. Oxford University Press. ISSN 9780198716327. p. 19–32. doi: 10.1093/acprof%3Aoso/9780198716327.003.0002.
• Linnebo, Øystein & Florio, Salvatore (2016). On the Innocence and Determinacy of Plural Quantification. Noûs. ISSN 0029-4624. 50(3), p. 565–583. doi: 10.1111/nous.12091.
• Linnebo, Øystein (2016). Plurals and Modals. Canadian Journal of Philosophy. ISSN 0045-5091. 46(4-5), p. 654–676. doi: 10.1080/00455091.2015.1132975.
• Linnebo, Øystein; Shapiro, Stewart & Hellman, Geoffrey (2016). Aristotelian Continua. Philosophia Mathematica. ISSN 0031-8019. 24(2), p. 214–246. doi: 10.1093/philmat/nkv024.
• Horsten, Leon & Linnebo, Øystein (2015). Term Models for Abstraction Principles. Journal of Philosophical Logic. ISSN 0022-3611. p. 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, p. 1–2.
• Linnebo, Øystein & Shapiro, Stewart (2015). Frege Meets Brouwer (or Heyting, or Dummett). The Review of Symbolic Logic. ISSN 1755-0203. 8(3), p. 540–552. doi: 10.1017/s1755020315000039.
• Shapiro, Stewart & Linnebo, Øystein (2014). Frege Meets Brouwer (or Heyting or Dummett). The Review of Symbolic Logic. ISSN 1755-0203. 8(3), p. 540–552. doi: 10.1017/S1755020315000039.
• Linnebo, Øystein & Rayo, Agustin (2014). Response to Florio and Shapiro. Mind. ISSN 0026-4423. 123, p. 175–181.
• Linnebo, Øystein & Pettigrew, Richard (2014). Two Types of Abstraction for Structuralism. The Philosophical Quarterly. ISSN 0031-8094. 64, p. 267–283. doi: 10.1093/pq/pqt044.
• Linnebo, Øystein (2014). 'Just is'-Statements as Generalized Identities. Inquiry (Oslo). ISSN 0020-174X. 57(4), p. 466–482. doi: 10.1080/0020174X.2014.905037.
• Linnebo, Øystein (2013). What is the infinite? . Philosophers' magazine. ISSN 1354-814X. p. 42–47.
• Linnebo, Øystein (2013). Freges oppfatning av logikk: Fra Kant til Grundgesetze. Norsk Filosofisk tidsskrift. ISSN 0029-1943. 48(3-4), p. 219–229.
• Muller, F.A. & Linnebo, Øystein (2013). On Witness-Discernibility of Elementary Particles. Erkenntnis: An International Journal of Scientific Philosophy. ISSN 0165-0106. 78, p. 1133–1142. doi: 10.1007/s10670-012-9385-4.
• Linnebo, Øystein (2013). Føllesdal and Frege on Reference. In Frauchiger, Michael (Eds.), Reference, Rationality, and Phenomenology. Themes from Føllesdal. Ontos Verlag. ISSN 978-3-86838-182-5. p. 259–279. doi: 10.1515/9783110323542.259.
• 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), p. 215–221. doi: 10.1016/j.shpsb.2013.02.004.
• Linnebo, Øystein (2013). THE POTENTIAL HIERARCHY OF SETS. The Review of Symbolic Logic. ISSN 1755-0203. 6(2), p. 205–228. doi: 10.1017/S1755020313000014.
• Linnebo, Øystein (2012). Hierarchies Ontological and Ideological. Mind. ISSN 0026-4423. 121, p. 269–308. doi: 10.1093/mind/fzs050.
• Linnebo, Øystein (2005). To Be Is to Be an F. Dialectica. ISSN 0012-2017. 59.
• Linnebo, Øystein (2005). Epistemological challenges to mathematical platonism. Philosophical Studies. ISSN 0031-8116.
• Linnebo, Øystein (2004). Frege's Proof of Referentiality. Notre Dame Journal of Formal Logic. ISSN 0029-4527. 45(2), p. 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, p. 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). Plural Quantification Exposed. Noûs. ISSN 0029-4624. 37(1), p. 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.

• Linnebo, Øystein (2003). Critical Study of Stewart Shapiro, Philosophy of Mathematics: Structure and Ontology. Philosophia Mathematica. ISSN 0031-8019. 11(1), p. 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). Frege's Conception of Logic: From Kant to Grundgesetze. Manuscrito - Revista Internacional de Filosofia. ISSN 0100-6045. 26(2), p. 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.

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• Linnebo, Øystein & Florio, Salvatore (2021). The Many and the One: A Philosophical Study . Oxford University Press. ISBN 9780198791522. 336 p. Full text in Research Archive
• Linnebo, Øystein (2018). Thin Objects: An Abstractionist Account. Oxford University Press. ISBN 9780199641314. 256 p.
• Linnebo, Øystein (2017). Philosophy of Mathematics. Princeton University Press. ISBN 9780691161402. 216 p.

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• Linnebo, Øystein (2021). Har bevisstheten en plass i en fysisk verden?
• Linnebo, Øystein & Torgersen, Eivind (2021). Hvilken nytte kan historikere, filosofer og språkforskere ha av algoritmer?
• Linnebo, Øystein (2021). Critical Study of Bob Hale, Essence and Existence: Selected Essays. Philosophia Mathematica. ISSN 0031-8019. 29(3), p. 420–427.
• Linnebo, Øystein (2021). Finnes universets begynnelse? [Internet]. https://www.uio.no/om/aktuelt/universitetsplassen/nyheter/20.
• Linnebo, Øystein (2021). Tiden som filosofisk problem.
• Linnebo, Øystein (2020). Review of John Bell, The Continuous, the Discrete. American Mathematical Society Mathematical Reviews. ISSN 2167-5163.
• Linnebo, Øystein & Bøhn, Einar Duenger (2020). Interview with Dagfinn Føllesdal. Norsk Filosofisk tidsskrift. ISSN 0029-1943. 55(1), p. 46–79.
• Linnebo, Øystein (2020). The Paradox of the Largest Number: From Aristotle to Cantor. In Kjosavik, Frode & Serck-Hanssen, Camilla (Ed.), Metametaphysics and the Sciences. Historical and Philosophical Perspectives. Routledge. ISSN 978-0-367-26369-0.
• Linnebo, Øystein (2019). DORA-erklæringen og vår vurdering av forskningskvalitet. Khrono.no. ISSN 1894-8995.
• Maliks, Reidar; Linnebo, Øystein & Strand, Arne (2017). Den viktige uenigheten. Klassekampen. ISSN 0805-3839.
• Linnebo, Øystein (2017). Bokmelding: Frege – Utvalgte Tekster. Norsk Filosofisk tidsskrift. ISSN 0029-1943. 52(4), p. 187–192.
• Linnebo, Øystein (2016). Identity and two conceptions of ontology. Filosofisk supplement. ISSN 0809-8220. p. 44–47.
• Linnebo, Øystein (2013). “What is the Infinite and Is It Real?”. Philosophers' magazine. ISSN 1354-814X. p. 42–47.
• Linnebo, Øystein (2013). Review of Patricia Blanchette, Frege’s Conception of Logic. Notre Dame Philosophical Reviews. ISSN 1538-1617.
• Linnebo, Øystein (2004). Plural Quantification. In Zalta, Ed (Eds.), Stanford Encyclopedia of Philosophy. Stanford Encyclopedia of Philosophy.
• Linnebo, Øystein (2004). Review of Kit Fine, The Limits of Abstraction. Australasian Journal of Philosophy. ISSN 0004-8402. 82(4), p. 653–656.
• Linnebo, Øystein (2004). Reference and Frege's Context Principle.
• Linnebo, Øystein (2004). Kant and Frege on Formal Logic.
• Linnebo, Øystein (2004). Reference and Frege's Context Principle.
• Linnebo, Øystein & Parsons, Charles (2003). Introductory Note to Correspondence with Walter Pitts. In Feferman, Solomon (Eds.), Kurt Gödel: Collected Works, Vol. V. Clarendon. ISSN 0198500750. p. 157–159.
• Linnebo, Øystein (2003). Neo-Logicism and Impredicativity.
• Linnebo, Øystein (2003). Predicative Fragments of Frege Arithmetic.
• Linnebo, Øystein (2003). Mathematical Structuralism.
• 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.

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