Leon Horsten

Professor for Theoretical Philosophy with special emphasis on Metaphysics, Epistemology and Logic

Leon Horsten lächelt vor einem Bücherregal

After my studies in Leuven, Belgium, and Minnesota, USA, I finished my PhD in philosophy in 1993. Afterwards I worked as a PostDoc (1993-1999 National Fund for Scientific Research Belgium and 1999-2003 Katholieke Universiteit Leuven), and as Professor of Philosophy (2003-2008 KU Leuven) in Belgium. In 2007 I started working at the University of Bristol, first as a lecturer (2007-2008), and later as a professor of philosophy (2008-2019). In October 2019 I joined the philosophy department at the University of Konstanz where I am now a full professor for theoretical philosophy with special emphasis on metaphysics, epistemology and logic.

In my research I often bring formal methods to bear on philosophical problems. The formal methods involved are drawn not only from philosophical and mathematical logic, graph theory, but also from other parts of mathematics and probability theory. I apply these methods to problems in many sub-disciplines of theoretical philosophy (philosophy of mathematics, metaphysics, epistemology, philosophy of language, philosophy of logic). My research strength lies in a capacity to discern formal structure behind philosophical problems, being able to solve the formal problems involved, and shedding new light on the original philosophical problems.

I am also a core member of the Luxemburger Zirkel.

Current Courses (Winter 2023-2024)

Courses Taught (previous semesters)


Academic Journal Articles

  1. Horsten, L. Boolean-valued sets as arbitrary objects. Mind 133 (2024), p. 143–166. 
  2. Brickhill, H. & Horsten, L. Sets and Probability. Erkenntnis, Online first, 2023.
  3. Cieśliński, C., Horsten, L., & Leitgeb, H., Axioms for typefree subjective probability. Review for Symbolic Logic, Online first, 2023.
  4. Zhang, L. & Horsten, L., The minimalist theory of truth and the generalisation problem. Dialectica, accepted for publication.
  5. Schuster, D. & Horsten, L. On the pure logic of justified belief. Synthese, Online first, 2022.
  6. Heylen, J. & Horsten, L. Strict conditionals: Replies to Lowe and Tsai, Croation Journal of Philosophy 64 (2022), p. 123-131.
  7. Horsten, L. On reflection. The Philosophical Quarterly. 71 (2021), p. 738-757.
  8. Fischer, M., Horsten, L. & Nicolai, C. Hypatia’s silence. Truth, justification, and entitlement. Noûs 55 (2021), p. 62-85.
  9. Horsten L. Generic structures. Philosophia Mathematica 27 (2019), p. 362–380.
  10. Horsten, L. & Speranski, S. Reasoning about arbitrary natural numbers from a Carnapian perspective. Journal of Philosophical Logic 48 (2019), p. 685–707.
  11. Campbell-Moore, C., Horsten, L. & Leitgeb, H. Probability in the revision theory of truth. Journal of Philosophical Logic 48 (2019), p. 87–112.
  12. Antonutti Marfori, M. & Horsten, L. Human-effective computability. Philosophia Mathematica 27 (2019), p. 61–87.
  13. Brickhill, H. & Horsten, L. Triangulating non-Archimedean probability. Review of Symbolic Logic 11 (2018), p. 519–546.
  14. Benci, V., Horsten, L. & Wenmackers, S. Infinitesimal probabilities. British Journal for Philosophy of Science 69 (2018), p. 509–552.
  15. Fischer, M., Horsten, L. & Nicolai, C. Iterated reflection over full disquotational truth. Journal of Logic and Computation 27 (2017), p. 2631–2651.
  16. Heylen, J. & Horsten, L. Truth and existence. Thought 6 (2017), p. 106–114.
  17. Horsten, L. & Leigh, G. Truth is simple. Mind 126 (2017), p. 195–232.
  18. Welch, P. & Horsten, L. Reflecting on absolute infinity. Journal of Philosophy 113 (2016), p. 89–111.
  19. Linnebo, Ø. & Horsten, L. Term models for abstraction principles. Journal of Philosophical Logic 45 (2016), p. 1–23.
  20. Horsten L. One hundred years of semantic paradox. Journal of Philosophical Logic 44 (2015), p. 681–695.
  21. Horsten L. The influence of the Polish school in logic on mathematical philosophy. European Review 23 (2015), p. 150–158.
  22. Fischer, M. & Horsten, L. The expressive power of truth. Review of Symbolic Logic 8 (2015), p. 345–369.
  23. Horsten, L. Angst and the empty set. Nautilus 16 (2014).
  24. van der Veen, J. & Horsten, L. Cantorian infinity and philosophical concepts of God. The European Journal for Philosophy of Religion 5 (2013), p. 117–138.
  25. Benci, V., Horsten, L. & Wenmackers, S. Non-Archimedean probability. Milan Journal of Mathematics 81 (2013), p. 121–151.
  26. Horsten, L. & Welch, P. The aftermath. Mathematical Intelligencer 35 (2013), p. 16–20.
  27. Wenmackers, S. & Horsten, L. Fair infinite lotteries. Synthese 190 (2013), p. 37–61.
  28. Horsten, L., Leigh, G., Leitgeb, H. & Welch, P. Revision revisited. Review of Symbolic Logic 5 (2012), p. 642–666.
  29. Horsten, L. Vom Zählen zu den Zahlen: On the relation between computation and arithmetical structuralism. Philosophia Mathematica 20 (2012), p. 275–288.
  30. Horsten, L. Having an intepretation. Philosophical Studies 150 (2010), p. 449–459.
  31. Horsten, L. Impredicative identity criteria. Philosophy and Phenomenological Research 80 (2010), p. 411–439.
  32. Douven, I., Horsten, L. & Romeijn, J.-W. Probabilist anti-realism. Pacific Philosophical Quarterly 91 (2010), p. 38–63.
  33. Horsten, L. Levity. Mind 118 (2009), p. 555–581.
  34. Horsten, L. An argument concerning the unknowable. Analysis 69 (2009), p. 240– 242.
  35. Horsten, L. & Douven, I. Formal methods in the philosophy of science. Studia Logica 89 (2008), p. 151–162.
  36. Horsten, L. & Welch, P. The undecidability of propositional adaptive logic. Synthese 158 (2007), p. 41–60.
  37. Halbach, V. & Horsten, L. Axiomatizing Kripke’s theory of truth. Journal of Symbolic Logic 71 (2006), p. 677–712.
  38. Heylen, J. & Horsten, L. Strict conditionals: A negative result. Philosophical Quarterly 56 (2006), p. 536–549.
  39. Halbach, V. & Horsten, L. Computational structuralism. Philosophia Mathematica 13 (2005), p. 174–186.
  40. Horsten L. Canonical naming systems. Minds and Machines 15 (2005), p. 229–257.
  41. De Clercq, R. & Horsten, L. Closer. Synthese 146 (2005), p. 371–393.
  42. Verhoeven, L. & Horsten, L. On the exclusivity implicature of ‘Or’ or on the meaning of eating strawberries. Studia Logica 81 (2005), p. 19–42.
  43. Horsten, L. On the quantitative scalar Or-implicature. Synthese 146 (2005), p. 111– 127.
  44. Horsten, L. Remarks on the content and extension of the notion of provability. Logique et Analyse 48 (2005), p. 15–32.
  45. Horsten, L. A note concerning the notion of satisfiability. Logique et Analyse 47 (2004), p. 463–468.
  46. Delvaux, S. & Horsten, L. On best transitive approximations to simple graphs. Acta Informatica 40 (2004), p. 637–655.
  47. De Clercq, R. & Horsten, L. Perceptual indiscriminability: in defence of Wright’s proof. Philosophical Quarterly 54 (2004), p. 439–444.
  48. Van Belle, W., Horsten, L., Schaeken, W. Redeneren met conditionele zinnen (“Reasoning with conditional sentences.”). Tijdschrift voor Taalbeheersing 24 (2002), p. 106–119.
  49. Horsten, L. Platonistic formalism. Erkenntnis 54 (2001), p. 173–194.
  50. Horsten, L. & Leitgeb, H. No Future. Journal of Philosophical Logic 30 (2001), p. 259–265.
  51. Ladyman, J., Douven, I., Horsten, L. & van Fraassen, B. Uma defesa da crítica de van Fraassen à inferência abdutiva: uma réplica a Psillos., Critica 6 (2000), p. 63–88.
    [Portugese translation of: Ladyman, J., Douven, I., Horsten, L. & van Fraassen, B. A defense of van Fraassen’s critique of abductive inference: reply to Psillos.]
  52. Horsten, L. Models for the logic of possible proofs. Pacific Philosophical Quarterly 81 (2000), p. 49–60.
  53. Halbach, V. & Horsten, L. Two proof-theoretic remarks on EA+ECT. Mathematical Logic Quarterly 46 (2000), p. 461–465.
  54. Horsten, L. A Kripkean approach to knowability and truth. Notre Dame Journal of Formal Logic 39 (1998), p. 389–405.
  55. Douven, I. & Horsten, L. Earman on underdetermination and empirical indistinguishability. Erkenntnis 49 (1998), p. 303–320.
  56. Horsten, L. In defense of Epistemic Arithmetic. Synthese 116 (1998), p. 1–25.
  57. Horsten, L. Provability in principle and controversial constructivistic principles. Journal of Philosophical Logic 26 (1997), p. 635–660.
  58. Ladyman, J., Douven, I., Horsten, L. & van Fraassen, B. A defense of van Fraassen’s critique of abductive inference: reply to Psillos. The Philosophical Quarterly 47 (1997), p. 305–321.
  59. Horsten, L. Reflecting in Epistemic Arithmetic. Journal of Symbolic Logic 61 (1996), p. 788–801.
  60. Horsten, L. & Roelants, H. The Church-Turing thesis and effective mundane procedures. Minds and Machines 5 (1995), p. 1–8.
  61. Horsten, L. On modal-epistemic variants of Shapiro’s system of Epistemic Arithmetic. Notre Dame Journal of Formal Logic 35 (1994), p. 284–291.
  62. Horsten, L. Scope and rigidity. Communication and Cognition 25 (1992), p. 353–372.
  63. Horsten, L. Two problems concerning Frege’s distinction between concepts and objects. Logique et Analyse 32 (1989), p. 267–284.

Authored Books

  1. Horsten, L. The metaphysics and mathematics of arbitrary objects. Cambridge University Press (2019) xviii + 232 p.
  2. Horsten, L. Eindig, Oneindig, Meer Dan Oneindig. Grondslagen van de wiskundige wetenschappen. (“Finite, Infinite, More than Infinite. Foundations of the Mathematical Sciences”) Epsilon Uitgaven, no.56, Utrecht (2004) xii + 204 p. (second edition in 2018)
  3. Horsten, L. The Tarskian Turn. Deflationism and Axiomatic Truth. MIT Press, Cambridge (MA) & London (2011) xii + 165 p.
  4. Horsten, L.; Douven, I.; Weber, E. Wetenschapsfilosofie. Een grondige inleiding. (“Philosophy of Science. An Introduction”) Van Gorcum, Assen (2007) vii + 238 p.

Edited books

  1. Horsten, L. & Welch, P. (eds.) Gödel’s Disjunction. The scope and limits of mathematical knowledge. Oxford University Press (2016) 288 p.
  2. Horsten, L. & Pettigrew R. (eds.) The Bloomsbury Companion to Philosophical Logic Bloomsbury, London & New York (2014) 637 p. [This is the second edition of Horsten & Pettigrew 2011.]
  3. Horsten, L. & Pettigrew R. (eds.) The Continuum Companion to Philosophical Logic. Continuum Publishing Group, London & New York (2011) viii + 637 p.
  4. Halbach, V. & Horsten, L. (eds.) Principles of Truth. Second edition. Ontos Verlag, Frankfurt / Lancaster (2004) 245 p.
  5. Halbach, V. & Horsten, L. (eds.) Principles of Truth. (Deutsche Hochschulschriften: Epistemische Studien; Bd. 1) Hänsel-Hohenhausen, Frankfurt (2002) 245 p. (This book is reviewed by Gabriel Uzquiano in: Notre Dame Philosophical Reviews 2003.04.03.)
  6. Decock, L. & Horsten, L. (eds.) Quine. Naturalised Epistemology, Perceptual Knowledge, Ontology. Poznan Studies in the Philosophy of Science and the Humanities, volume 70, Rodopi, Amsterdam (2000) 225 p.
  7. Douven, I. & Horsten, L. (eds.) Realism in the Sciences. Proceedings of the Ernan McMullin symposium Leuven 1995. Louvain Philosophical Studies 10, Leuven University Press, Leuven (1996) 216 p.

Conference or Book Contributions

  1. Horsten, L. Quantity has a quality all its own. In: M. Szatkowski (ed) Ontology of divinity. Routledge, forthcoming.
  2. Hallbach, V. & Horsten, L. Self-referential Gettier sentences. In: Venturi,G. & Petrolo, M. (eds.) Paradoxes between truth and proof. Synthese Library, to appear.
  3. Horsten, L. & Ito, R. Russell and Fine on variable objects. In: Faroldi, F. & Van De Putte, F. (eds.) Outstanding contributions to logic: Kit Fine. Springer (2023) p. 691–704.
  4. Horsten, L. & Zicchetti, M. Truth, reflection, and commitment. In: Nicolai, C. & Stern, J. (eds.) The unified approach to truth, modality, and paradox. Routledge (2021) p. 69-87.
  5. Antonutti, M. & Horsten, L. Epistemic Church’s Thesis and Absolute Undecidability. In: Horsten, L. & Welch, P. (eds.) Gödel’s Disjunction. The scope and limits of mathematical knowledge. Oxford University Press (2016) p. 254–271.
  6. Horsten, L. Absolute infinity in class theory and in theology. In: Boccuni, F. & Sereni, A. (eds.) Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Boston Studies in the Philosophy of Science 318. Springer (2016) p. 103–122.
  7. Halbach, V. & Horsten, L. Norms for theories of reflexive truth. In: Achourioti, T., Galinon, H., Fernandez, J.M. & Fujimoto K. (eds.) Unifying the philosophy of truth. Springer (2015) p. 263–280.
  8. Horsten, L. Mathematical Philosophy? In: Andersen, H. et al (eds.) The Philosophy of Science in a European Perspective 4. Springer (2013) p. 73–86.
  9. Horsten, L. & Pettigrew, R. Mathematical methods in philosophy. In: Horsten, L. & Pettigrew, R. (eds.) The Continuum Companion to Philosophical Logic. Continuum Press (2011) p. 14–26.
  10. Horsten, L. & Halbach, V. Truth and paradox. In: Horsten, L. & Pettigrew, R. (eds.) The Continuum Companion to Philosophical Logic. Continuum Press (2011) p. 351–382.
  11. Horsten, L. Perceptual indiscriminability and the concept of a color shade. In: Dietz, R. & Moruzzi, S. (eds.) Cuts & Clouds. Vagueness, its nature, and its logic. Oxford University Press (2010) p. 209–227.
  12. Horsten, L. On a necessary use of truth in epistemology. In: Czarnecki, T. et al (eds.) The Analytical Way. Studies in Logic Series, College Publications (2010) bp. 371–376.
  13. Horsten, L. & Leitgeb, H. How abstraction works. In: Hieke, A. & Leitgeb, H. (eds.) Reduction, Abstraction, Analysis. Ontos Verlag (2009) p. 217–226.
  14. Horsten, L. Formalizing Church’s Thesis. In: Olszewski, A., Wolenski, J. & R. Janusz (eds.) Church’s Thesis After 70 Years. Ontos Mathematical Logic, Ontos Verlag (2006) p. 253–268.
  15. Halbach, V. & Horsten, L. The Deflationist’s Axioms for Truth. In: Beall, J.C. & Armour-Garb, B. (eds.) Deflationism and Paradox. Clarendon Press (2005) p. 203–217.
  16. Dieussaert, K., Ford, M. & Horsten, L. Influencing nonmonotonic reasoning by modifier strength manipulation. In: Forbus, K. et al (eds.) Proceedings of the 26th Annual Conference of the Cognitive Science Society, Cognitive Science Society (2004) p. 315–320.
  17. Horsten, L. The logic of intensional predicates. In: Löwe, B., Malzkorn, W. & Räsch, T. (eds.) Foundations of the Formal Sciences II: Applications of Mathematical Logic in Philosophy and Linguistics. Trends in Logic: Studia Logica Library Volume 17, Kluwer Academic Publishers (2003) p. 89–111.
  18. Horsten, L. An Axiomatic Investigation of Provability as a Primitive Predicate. In: Halbach, V. & Horsten, L. (eds.) Principles of Truth. Deutsche Hochschulschriften (2002) p. 203-233
  19. Horsten, L. On our ability to fix intended structures. In: Derksen, T. (ed.) Moving Ahead: Philosophy of Mind and Realism. Studies in the General Philosophy of Science Vol. 7, Dutch University Press (2001) p. 121–134.
  20. Horsten, L. Enkele opmerkingen over recursieve omega-rijen (“Some remarks on recursive omega-sequences”). In: Filosofie in het tijdperk van ICT. Acta van de 22e Nederlands-Vlaamse Filosofiedag. Leiden, 28 oktober 2000.
  21. Horsten, L. The semantical paradoxes, the neutrality of truth, and the neutrality of the minimalist theory of truth. In: Cortois, P. (ed.) The many problems of realism. Studies in General Philosophy of Science 3. Tilburg University Press (1995) p. 173–187.
  22. Horsten, L. De modaal-structuralistische interpretatie en de verklaring van rekenkundige kennis (“The modal-structural interpretation and explanation of scientific knowledge”). In: Raymaekers, B. (ed.) Gehelen en Fragmenten. De vele gezichten van de filosofie. Acta van de 14de filosofendag te Leuven. Universitaire Pers Leuven (1993) p. 46–50.
  23. Horsten, L. Note on an objection of Lifschitz against Shapiro’s ‘Epistemic Arithmetic’. In: Czermak, J. (ed.) Proceedings of the 15th International Wittgenstein-Symposium. Part 1: Philosophy of Mathematics, Verlag Holder-Pichler-Tempsky (1993) p. 289–296.

ArXiv papers (not yet published in journals)

  1. Cieslinski, C., Horsten, L. & Leitgeb, H. Axioms for typefree subjective probability (2022). ArXiv:2203.04879.
  2. Horsten, L. Boolean-valued sets as arbitrary objects (2022). ArXiv:2002.02181v2.
  3.  Brickhill, H. & Horsten, L. Sets and probability (2019). ArXiv:1903.08361.

Review Articles

  1. Horsten, L. De gelaagde structuur van de natuurkundige praktijk volgens Peter Galison (“The layered structure of physics according to Peter Galison.”). Tijdschrift voor Filosofie 61 (1999), p. 747–778.
  2. Horsten, L. Gödels disjunctie (“Gödel’s disjunction"). Tijdschrift voor Filosofie 60 (1998), p. 83–105.

Short articles, comments, and introductions

  1. Horsten, L. & Welch, P. Introduction. In: Horsten, L. & Welch, P. (eds.) Gödel’s Disjunction. The scope and limits of mathematical knowledge. Oxford University Press (2016), p. 1–15.
  2. Horsten, L. & Pettigrew, R. Introduction. In: Horsten, L. & Welch, P. (eds.) The Continuum Companion to Philosophical Logic. Continuum Press (2011), p. 1–13.
  3. Horsten, L. & Starikova, I. Mathematical knowledge: Intuition, visualization, and understanding. Topoi 29 (2010), p. 1–2.
  4. Horsten L. Apofatisch finitisme? [“Apophatic finitism?”] Algemeen Nederlands Tijdschrift voor Wijsbegeerte 102 (2010), p. 184–187.
  5. Horsten L. Paradoxen (“Paradoxes”). Preface for a special issue on the subject of paradoxes, Algemeen Nederlands Tijdschrift voor Wijsbegeerte 97 (2005), p. 1–2.
  6. Halbach, V. & Horsten, L. Contemporary methods for investigating the concept of truth: an introduction. In: Halbach, V. & Horsten, L. (eds.) Principles of Truth  (2002) p. 11–35.
  7. Decock, L. & Horsten, L. Introduction. In: Decock L. & Horsten, L. (eds.) Quine. Naturalised epistemology, Perceptual Knowledge, Ontology. Poznan Studies in the Philosophy of Science and the Humanities 70, Rodopi, Amsterdam (2000) p. 7–12.
  8. Horsten L. Waarheid en semantische paradoxen (“Truth and semantic paradox.”). Onze Alma Mater 96 (1996), p. 239–268.
  9. Douven, I. & Horsten, L. Introduction. In: I. Douven & L. Horsten (eds.) Realism in the sciences. Proceedings of the Ernan McMullin symposium Leuven 1995. Louvain Philosophical Studies 10, Leuven University Press, Leuven (1996) p. 7–12.

Other Publications

  1. Horsten, L. & Zhang, L. (in Chinese) Philosophy of mathematics. Chinese translation of the Stanford Encyclopedia article on Philosophy of Mathematics,  Modern Foreign Philosophy 2(2022), p. 77-113
  2. Horsten L. Philosophy of Mathematics. Entry in the Stanford Encyclopedia of Philosophy, 2007 (substantially revised in 2012, 2017, 2022), 40p.
  3. Horsten, L. & Weber, E. INUS Conditions. In: Everitt, Brian S., & Howell, David C. (eds) Encyclopedia of Statistics in Behavioral Science. Volume 2. John Wiley & Sons, Ltd, Chichester, 2005, p. 955–958.