Studia Logica

, Volume 94, Issue 1, pp 105–138 | Cite as

Associative Substitutional Semantics and Quantified Modal Logic

  • Bartosz WięckowskiEmail author


The paper presents an alternative substitutional semantics for first-order modal logic which, in contrast to traditional substitutional (or truth-value) semantics, allows for a fine-grained explanation of the semantical behavior of the terms from which atomic formulae are composed. In contrast to denotational semantics, which is inherently reference-guided, this semantics supports a non-referential conception of modal truth and does not give rise to the problems which pertain to the philosophical interpretation of objectual domains (concerning, e.g., possibilia or trans-world identity). The paper also proposes the notion of modality de nomine as an alternative to the denotational notion of modality de re.


first-order logic modal logic philosophy of quantified modal logic predication substitutional quantification truth-value semantics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Chihara, C.S., The Worlds of Possibility, Clarendon Press, 1998.Google Scholar
  2. 2.
    Copeland B.J.: ‘A note on the Barcan formula and substitutional quantification’. Logique et Analyse 25, 83–86 (1982)Google Scholar
  3. 3.
    Copeland B.J.: ‘Substitutional quantification and existence’. Analysis 45, 1–4 (1985)CrossRefGoogle Scholar
  4. 4.
    Divers, J., Possible Worlds, Routledge, 2002.Google Scholar
  5. 5.
    Dunn J.M., Belnap N.D. Jr.: ‘The substitution interpretation of the quantifiers’. Noûs 2, 177–185 (1968)CrossRefGoogle Scholar
  6. 6.
    Dunn, J. M., ‘A truth-value semantics for modal logic’. In [14] 87–100, 1973.Google Scholar
  7. 7.
    Fitting, M., Types, Tableaus and Gödel’s God, Kluwer Academic Publishers, 2002.Google Scholar
  8. 8.
    Hallnäs, L., and P. Schroeder-Heister, ‘A proof-theoretic approach to logic programming I: clauses as rules’, Journal of Logic and Computation 1:261–283, 1990/91. ‘A proof-theoretic approach to logic programming II: programs as definitions’, Journal of Logic and Computation 1:635–660, 1990/91.Google Scholar
  9. 9.
    Hughes, G.E., and M.J. Cresswell, A New Introduction to Modal Logic, Routledge, 1996.Google Scholar
  10. 10.
    Jager T.: ‘An actualistic semantics for quantified modal logic’. Notre Dame Journal of Formal Logic 23, 335–349 (1982)CrossRefGoogle Scholar
  11. 11.
    Kripke S.: ‘Outline of a theory of truth’. Journal of Philosophy 72, 690–716 (1975)CrossRefGoogle Scholar
  12. 12.
    Kripke, S., ‘Is there a problem about substitutional quantification?’, in G. Evans, and J. McDowell, Truth and Meaning: Essays in Semantics, Oxford University Press, 1976, pp. 325–419.Google Scholar
  13. 13.
    Leblanc H.: ‘Truth-value semantics for a logic of existence’. Notre Dame Journal of Formal Logic 12, 153–168 (1971)CrossRefGoogle Scholar
  14. 14.
    Leblanc, H. (ed.), Truth, Syntax and Modality. Proceedings of the Temple University Conference on Alternative Semantics, North-Holland, 1973.Google Scholar
  15. 15.
    Leblanc, H., ‘Semantic deviations’. In [14] 1–16, 1973.Google Scholar
  16. 16.
    Leblanc, H., ‘On dispensing with things and worlds’, in M. Munitz, (ed.), Logic and Ontology, New York University Press, 1973, pp. 241–259.Google Scholar
  17. 17.
    Leblanc, H., Truth-Value Semantics, North-Holland, 1976.Google Scholar
  18. 18.
    Leblanc, H., ‘Alternatives to standard first-order semantics’, in D. M. Gabbay, and F. Guenthner (eds.), Handbook of Philosophical Logic, 2nd Edition, Vol. II, Kluwer Academic Publishers, 2001, pp. 53–131.Google Scholar
  19. 19.
    Lewis, D., ‘Counterpart theory and quantified modal logic’, in D. Lewis, Philosophical Papers, Vol. I, Oxford University Press, 26–39 (postscripts, 39–46), 1983. First published in: Journal of Philosophy 65:113–126, 1968.Google Scholar
  20. 20.
    Lewis, D., On the Plurality of Worlds, Blackwell, 1986.Google Scholar
  21. 21.
    Linsky, B., and E. N. zalta, ‘In defense of the simplest quantified modal logic’, in J. Tomberlin (ed.), Philosophical Perspectives 8, Logic and Language, Ridgeview, 1994, pp. 431–458.Google Scholar
  22. 22.
    Marcus, R. Barcan, ‘Modalities and intensional languages’, [in] 26 3–23, 1993. First published in: Synthese 12:303–322, 1961.Google Scholar
  23. 23.
    Marcus R. Barcan: ‘Dispensing with possibilia’. Proceedings of the American Philosophical Association 49, 39–51 (1976)CrossRefGoogle Scholar
  24. 24.
    Marcus, R. Barcan, ‘Nominalism and the substitutional quantifier’, in [26] 111–124, 1993. First published in: Monist 61:351–362, 1978.Google Scholar
  25. 25.
    Marcus, R. Barcan, ‘Possibilia and possible worlds’, in [26] 189–213, 1993. First published in: Grazer Philosophische Studien 25/26:107–133, 1985/86.Google Scholar
  26. 26.
    Marcus, R. Barcan, Modalities: Philosophical Essays, Oxford University Press 1993.Google Scholar
  27. 27.
    Plantinga A.: ‘Actualism and possible worlds’. Theoria 42, 139–160 (1976)CrossRefGoogle Scholar
  28. 28.
    Quine, W. V., ‘Ontological relativity’, in W. V. Quine, Ontological Relativity and Other Essays, Columbia University Press, 1969, pp. 26–68. First published in: Journal of Philosophy 65:185–212, 1968.Google Scholar
  29. 29.
    Russell B.: ‘On denoting’. Mind 14, 479–493 (1905)CrossRefGoogle Scholar
  30. 30.
    Tarski, A., ‘The concept of truth in formalized languages’, in [33] 152–278, 1983. First published as: Pojęcie prawdy w językach nauk dedukcyjnych, Prace Towarzystwa Naukowego Warszawskiego, Wydział III Nauk Matematyczno-Fizycznych, nr 34, Warszawa 1933.Google Scholar
  31. 31.
    Tarski, A., ‘The establishment of scientific semantics’, in [33] 401–408, 1983. First published as: ‘O ugruntowaniu naukowej semantyki’, Przegląd Filozoficzny 39:50–57, 1936.Google Scholar
  32. 32.
    Tarski A.: ‘The semantic conception of truth and the foundations of semantics’. Philosophy and Phenomenological Research 4, 341–375 (1944)CrossRefGoogle Scholar
  33. 33.
    Tarski, A., Logic, Semantics, Metamathematics, translations by J. H. Woodger, J. Corcoran (ed.), 2nd Edition, Hackett Publishing Company, 1983.Google Scholar
  34. 34.
    Tichý P.: ‘On de dicto modalities in quantified S5’. Journal of Philosophical Logic 2, 687–692 (1973)CrossRefGoogle Scholar
  35. 35.
    Więckowski, B., Modality without Reference. An Alternative Semantics for Subsitutional Quantified Modal Logic and its Philosophical Significance, Dissertation, Universität Tübingen, 2007.Google Scholar
  36. 36.
    Więckowski, B., ‘Predication in fiction’, in M. Peliš (ed.), The Logica Yearbook 2007, Filosofia, 267–285, 2008.Google Scholar
  37. 37.
    Więckowski, B., ‘Substitution puzzles and substitutional semantics’, in A. Grønn (ed.), Proceedings of SuB 12, ILOS, 645–662, 2008.Google Scholar
  38. 38.
    Williamson T.: ‘Bare possibilia’. Erkenntnis 48, 257–273 (1998)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Wilhelm-Schickard-InstitutUniversität TübingenTübingenGermany

Personalised recommendations