Hintikka and Cresswell on logical omniscience

Mark Jago

DOI: http://dx.doi.org/10.12775/LLP.2006.019


I discuss three ways of responding to the logical omniscience problems faced by traditional ‘possible worlds’ epistemic logics. Two of these responses were put forward by Hintikka and the third by Cresswell; all three have been influential in the literature on epistemic logic. I show that both of Hintikka’s responses fail and present some problems for Cresswell’s. Although Cresswell’s approach can be amended to avoid certain unpalatable consequences, the resulting formal framework collapses to a sentential model of knowledge, which defenders of the ‘possible worlds’ approach are frequently critical of.


logical omniscience; epistemic logic, nonclassical logics

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J.C. Beall, “From full blooded platonism to really full blooded platonism”, Philosophia Mathematica 7 (1999).

R. Brady, “The consistency of the axioms of abstraction and extensionality in a three-valued logic”, Notre Dame Journal of Formal Logic 12 (1971), 447–453.

R. Carnap, Meaning and Necessity, University of Chicago Press, 1947.

Roderick M. Chisholm, “The logic of knowing”, Journal of Philosophy 60(25) (1963), 773–795.

M.J. Cresswell, “Classical intensional logics”, Theoria 36 (1970), 347–72.

M.J. Cresswell, Logics and Languages, Methuen and Co., 1973.

N. da Costa, “On the theory of inconsistent formal systems”, Notre Dame Journal of Formal Logic 15(4) (1974), 497–510.

R. Fagin and J.Y. Halpern, “Belief, awareness and limited reasoning”, Artificial Intelligence 34 (1988), 39–76.

R. Fagin, J.Y. Halpern, Y. Moses, and M.Y. Vardi, Reasoning About Knowledge, MIT Press, 1995.

R. Fagin, J.Y. Halpern, and M.Y. Vardi, “A nonstandard approach to the logical omniscience problem”, in R. Parikh (ed.), Proceedings of the Third Conference on Theoretical Aspects of Reasoning about Knowledge, pages 41–55, Morgan Kaufmann, 1990.

Leon Henkin, “Some remarks on infinitely long formulas”, in Infinitistic Methods, pages 167–183, Pergamon Press, Oxford, 1961.

J. Hintikka, Knowledge and belief: an introduction to the logic of the two notions, Cornell University Press, Ithaca, N.Y., 1962.

J. Hintikka, Logic, Language-Games and Information: Kantian Themes in the Philosophy of Logic, Clarendon Press, Oxford, 1973.

J. Hintikka, “Surface semantics and its motivation”, in H. Leblanc (ed.), Truth, Syntax and Modality. North-Holland, Amsterdam, 1973.

J. Hintikka, “Impossible possible worlds vindicated”, Journal of Philosophical Logic 4 (1975), 475–484.

J. Hintikka, “A second generation epistemic logic and its general significance”, in V.F. Hendricks, S.A. Pedersen, and K.F. Jorgensen (eds.), Knowledge Contributors, number 322 in Synthese Library. Kluwer Academic, Dordrecht, 2003.

Max O. Hocutt, “Is epistemic logic possible?” Notre Dame Journal of Formal Logic 13(4) (1972), 433–453.

Mark Jago, “Imagine the possibilities: Information without overload”, Logique et Analyse 49(196) (2006), 345–370.

D. Kaplan, “Demonstratives”, in J. Almog, J. Perry, and H. Wettstein (eds.), Themes from Kaplan, chapter 17, pages 481–563, Oxford University Press, New York, 1989.

G. Lakemeyer, “Steps towards a first-order logic of explicit and implict belief”, in J. Y. Halpern (ed.), Proceedings of the First Conference on Theoretical Aspects of Reasoning About Knowledge, pages 325–340, Morgan Kaufmann, San Francisco, California, 1986.

G Lakemeyer, “A computationally attractive first-order logic of belief”, in Proceedings of JELIA 90, pages 333–347, Springer, Heidelberg, 1990.

H. J. Levesque, “A logic of implicit and explicit belief”, in National Conference on Artificial Intelligence, pages 198–202, 1984.

A. Meinong, “Über gegenstandstheorie”, in A. Meinong (ed.), Untersuchungen zur Gegenstadstheorie und Psychologie, Barth, Leipzig, 1904.

R. Montague, “Universal grammar”, Theoria 36 (1970), 373–98.

Charles Sanders Peirce, Reasoning and the Logic of Things: The Cambridge Conferences Lectures of 1898, Harvard University Press, Cambridge Mass., 1992.

G. Priest, In Contradiction: A Study of the Transconsistent, Martinus Nijhoff, Dordrecht, 1987.

G. Priest, Towards Non-Being, Clarendon Press, Oxford, 2005.

G. Priest, R. Routley, and J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, München, 1989.

V. Rantala, “Urn models”, Journal of Philosophical Logic 4 (1975), 455–474.

R. Routley, Exploring Meinong’s Jungle and Beyond, RSSS, Australian National University, Canberra, 1980.

R. Stalnaker, “The problem of logical omniscience I”, Synthese 89 (1991), 425–440.

R. Stalnaker, “On logics of knowledge and belief”, Philosophical Studies 128(1) (2006), 169–199.

W. van der Hoek, B. van Linder, and J.-J. Ch. Meyer, “An integrated modal approach to rational agents”, in M. Wooldridge and A. Rao (eds.), Foundations of Rational Agency, pages 133–168, Kluwer Academic, Dordrecht, 1999.

M.Y. Vardi, “On epistemic logic and logical omniscience”, in J.Y. Halpern (ed.), Theoretical Aspects of Reasoning about Knowledge: proceedings of the First Conference. Morgan Kaufman, 1986.

H. Wansing, “A general possible worlds framework for reasoning about knowledge and belief”, Studia Logica 49(4) (1990).

Timothy Williamson, “Conceptual truth”, The Aristotelian Society supplementary volume 80 (2006).

Ludwig Wittgenstein, Tractatus Logico-Philosophicus, Kegan Paul, 1922.

Edward N. Zalta, Abstract Objects: An Introduction to Axiomatic Metaphysics, D. Reidel, Dordrecht, 1983.

Edward N. Zalta, “A classically-based theory of impossible worlds”, Notre Dame Journal of Formal Logic 38(4) (1997), 640–660.

ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

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