Journal of Philosophical Logic

, Volume 47, Issue 4, pp 649–671 | Cite as

Higher-Order Contingentism, Part 3: Expressive Limitations

  • Peter FritzEmail author


Two expressive limitations of an infinitary higher-order modal language interpreted on models for higher-order contingentism – the thesis that it is contingent what propositions, properties and relations there are – are established: First, the inexpressibility of certain relations, which leads to the fact that certain model-theoretic existence conditions for relations cannot equivalently be reformulated in terms of being expressible in such a language. Second, the inexpressibility of certain modalized cardinality claims, which shows that in such a language, higher-order contingentists cannot express what is communicated using various instances of talk of ‘possible things’, such as ‘there are uncountably many possible stars’.


Contingentism Higher-order modal logic Expressivity 



In addition to those thanked in the acknowledgements of Part 1, I would like to thank a reviewer for comments on Part 3, and the editor, Frank Veltman, for all his help with the publication of the three parts.


  1. 1.
    Adams, R.M. (1979). Primitive thisness and primitive identity. The Journal of Philosophy, 76(1), 5–26.CrossRefGoogle Scholar
  2. 2.
    Blackburn, P., de Rijke, M., & Venema, Y. (2001). Modal logic. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  3. 3.
    Fine, K. (1977). Postscript to worlds, times and selves (with A. N. Prior). London: Duckworth.Google Scholar
  4. 4.
    Fine, K. (1977). Properties, propositions and sets. Journal of Philosophical Logic, 6(1), 135–191.CrossRefGoogle Scholar
  5. 5.
    Fine, K. (2003). The problem of possibilia. In Loux, M.J., & Zimmerman, D.W. (Eds.) The Oxford handbook of metaphysics (pp. 161–179). Oxford: Oxford University Press.Google Scholar
  6. 6.
    Fraïssé, R. (1958). Sur une extension de la polyrelation et des parentés tirant son origine du calcul logiques du k-ème échelon. In Le raisonnement en mathématiques et en sciences expérimentales, volume 70 of Colloques Internationaux du CNRS, pages 45–50. Paris: Editions du Centre National de la Recherche Scientifique.Google Scholar
  7. 7.
    Fritz, P. (2013). Modal ontology and generalized quantifiers. Journal of Philosophical Logic, 42(4), 643–678.Google Scholar
  8. 8.
    Fritz, P. Higher-order contingentism, part 2: Patterns of indistinguishability. Journal of Philosophical Logic, forthcoming.Google Scholar
  9. 9.
    Fritz, P., & Goodman, J. (2016). Higher-order contingentism part 1: Closure and generation. Journal of Philosophical Logic, 45(6), 645–695.CrossRefGoogle Scholar
  10. 10.
    Fritz, P., & Goodman, J. Counting incompossibles. Mind, forthcoming.Google Scholar
  11. 11.
    Hintikka, J., & Rantala, V. (1976). A new approach to infinitary languages. Annals of Mathematical Logic, 10(1), 95–115.CrossRefGoogle Scholar
  12. 12.
    Hodges, W. (1997). A shorter model theory. Cambridge: Cambridge University Press.Google Scholar
  13. 13.
    Leuenberger, S. (2006). A new problem of descriptive power. The Journal of Philosophy, 103(3), 145–162.CrossRefGoogle Scholar
  14. 14.
    Lewis, D. (1986). On the plurality of worlds. Oxford: Basil Blackwell.Google Scholar
  15. 15.
    Stalnaker, R. (2012). Mere possibilities. Princeton: Princeton University Press.Google Scholar
  16. 16.
    Williamson, T. (2013). Modal logic as metaphysics. Oxford: Oxford University Press.CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Philosophy, Classics, History of Art and IdeasUniversity of OsloOsloNorway

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