Abstract
The possible-worlds semantics for modality says that a sentence is possibly true if it is true in some possible world. Given classical prepositional logic, one can easily prove that every consistent set of propositions can be embedded in a ‘maximal consistent set’, which in a sense represents a possible world. However the construction depends on the fact that standard modal logics are finitary, and it seems false that an infinite collection of sets of sentences each finite subset of which is intuitively ‘possible’ in natural language has the property that the whole set is possible. The argument of the paper is that the principles needed to shew that natural language possibility sentences involve quantification over worlds are analogous to those used in infinitary modal logic.
Similar content being viewed by others
References
Barwise, J., and J. Seligman, Information Flow: The Logic of Distributed Systems, Cambridge University Press, Cambridge, 1997.
Chisholm, R. M., Perceiving: A Philosophical Study Cornell University Press, New York, 1957.
Davidson, D., ‘Truth and meaning’, Synthese 17 (1967), 304–323.
Dunn, J. M., and G. M. Hardegree, Algebraic Methods in Philosophical Logic, Oxford University Press, Oxford, 2001.
Glanzberg, M., ‘Supervenience and infinitary logic’, Noûs 35 (2001), 419–439.
Goldblatt, R. I., Mathematics of Modality, CSLI publications, Stanford, 1993.
Humberstone, I. L., ‘From worlds to possibilities’, Journal of Philosophical Logic 10 (1981), 313–341.
Judson, L., ‘Eternity and Necessity in De Caelo I.12’, Oxford Studies in Ancient Philosophy 1 (1983), 217–55.
Kaplan, D., ‘A problem in possible world semantics’, in W. Sinnott-Armstrong et al., (eds.), Modality, Morality, and Belief Cambridge, 1995, pp. 41–52.
Lewis, D. K., Counterfactuals, Basil Blackwell, Oxford, 1973.
Lewis, D. K., On the Plurality of Worlds, Basil Blackwell, Oxford, 1986.
Lycan, W. G., Modality and Meaning, Kluwer, Dordrecht, 1994.
Prior, A. N., and K. Fine, Worlds, Times, and Selves, Duckworth, London, 1977.
Quine, W. V., From a logical point of view; 9 logico-philosophical essays, Cambridge Mass, Harvard University Press, 1953.
Rini, A. A., ‘When time is of the essence: Prior Analytics 1.15 and De Caelo 1.12’, Logique et Analyse 183–184 (2003), 419–440.
Segerberg, K., ‘A Model Existence Theorem in Infinitary Propositional Modal Logic’, Journal of Philosophical Logic 23 (4), (1994), 337–368.
Stalnaker, R. C., ‘Conceptual truth and metaphysical necessity’, in Ways a World Might be Clarendon Press, Oxford, 2003, pp. 201–215.
Wittgenstein, L., Philosophical Investigations translated by G.E.M. Anscombe, Macmillan, New York, 1953.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cresswell, M.J. From Modal Discourse to Possible Worlds. Stud Logica 82, 307–327 (2006). https://doi.org/10.1007/s11225-006-8099-5
Issue Date:
DOI: https://doi.org/10.1007/s11225-006-8099-5