Hostname: page-component-7c8c6479df-995ml Total loading time: 0 Render date: 2024-03-27T18:07:43.297Z Has data issue: false hasContentIssue false

SENTENCES, BELIEF AND LOGICAL OMNISCIENCE, OR WHAT DOES DEDUCTION TELL US?

Published online by Cambridge University Press:  01 December 2008

ROHIT PARIKH*
Affiliation:
Departments of Computer Science, Mathematics, and Philosophy, CUNY
*
*DEPARTMENTS OF COMPUTER SCIENCE MATHEMATICS, AND PHILOSOPHY, CUNY NEW YORK, NY 10016 E-mail:rparikh@gc.cuny.edu

Abstract

We propose a model for belief which is free of presuppositions. Current models for belief suffer from two difficulties. One is the well known problem of logical omniscience which tends to follow from most models. But a more important one is the fact that most models do not even attempt to answer the question what it means for someone to believe something, and just what it is that is believed. We provide a flexible model which allows us to give meaning to beliefs in general contexts, including the context of animal belief (where action is usually our only clue to a belief), and of human belief which is expressed in language.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Alchourron, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: partial meet contraction and revision functions. Journal of Symbolic Logic, 50, 510530.CrossRefGoogle Scholar
Artemov, S., & Nogina, E. (2005). On epistemic logics with justifications. In Meyden, R., editor. Theoretical Aspects of Rationality and Knowledge. Singapore: University of Singapore Press, pp. 279294.Google Scholar
Aumann, R. (1976). Agreeing to disagree. Annals of Statistics, 4, 12361239.CrossRefGoogle Scholar
van Benthem, J. (1976). Modal correspondence theory. Doctoral dissertation, University of Amsterdam.Google Scholar
Bicchieri, C. (1997). Learning to co-operate. In Bicchieri, C., Jeffrey, R. C., and Skyrms, B., editors. The Dynamics of Norms. Cambridge, England: Cambridge University Press pp. 1746.Google Scholar
Brandom, R. (1994). Unsuccessful Semantics. Analysis, 54, 175178.CrossRefGoogle Scholar
Davidson, D. (1982). Rational animals. Dialectica, 36, 318327.CrossRefGoogle Scholar
Dennett, D. (1985). Brainstorms (second edition). Cambridge, MA: MIT Press, cf. p. 11.Google Scholar
Fagin, R., Halpern, J., Moses, Y., & Vardi, M. (1995). Reasoning About Knowledge. Cambridge, MA: MIT Press.Google Scholar
de Finetti, B. (1937). Foresight: its logical laws, its subjective sources. Annales de l'Institut Henri Poincare, 7. Translation by Henry Kyburg in Kyburg and Smokler, editors. (1980). Studies in Subjective Probability. Krieger Publishing Company, pp. 53–118.Google Scholar
Fitting, M. (2005). A logic of explicit knowledge, in The Logica Yearbook 2004, Behounek, Libor and Bilkova, Marta editors, pp. 1122, Filosofia, prague.Google Scholar
Gaifman, H. (2004). Reasoning with limited resources and assigning probabilities to arithmetical statements. Synthese, 140, 97119.CrossRefGoogle Scholar
Gettier, E. (1963). Is justified true belief knowledge? Analysis, 23, 121123.CrossRefGoogle Scholar
Gigerenzer, G. (1996) On narrow norms and vague heuristics: a reply to Kahneman and Tversky. Psychological Review, 103, 592596.CrossRefGoogle Scholar
Hayek, F. A. (1936). Individualism and Economic Order. Chicago: University of Chicago Press. See especially chapters II and IV.Google Scholar
Hintikka, J. (2004). A fallacious fallacy? Synthese, 140, 2535.CrossRefGoogle Scholar
Hume, D. (1978). A Treatise of Human Nature (Selby-Brigge, , editor). Oxford, UK: Oxford University Press, pp. 176179.Google Scholar
Kahneman, D. (2002). Maps of bounded rationality. Nobel prize lecture.Google Scholar
Kripke, S. (1979). A puzzle about belief. In Margalit, A., editor. Meaning and Use. Dordrecht, The Netherlands: Reidel.Google Scholar
Levi, I. (1997). Rationality and commitment. In his The Covenant of Reason. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Levi, I. (2004). Jaakko Hintikka. Synthese, 140, 3741.CrossRefGoogle Scholar
Marcus, R. (1990). Some revisionary proposals about belief and believing. Philosophy and Phenomenological Research, 50, 133153.CrossRefGoogle Scholar
Marcus, R. (1995). The anti-naturalism of some language centered accounts of belief. Dialectica, 49, 112129.Google Scholar
Millikan, R. (2006). Styles of rationality. In Nudds, M., and Hurley, S.Rationality in Animals. Oxford, UK: Oxford University Press, pp. 117126.CrossRefGoogle Scholar
Milner, R. (1989). Communication and Concurrency. Upper Saddle River: New Jersey Prentice Hall.Google Scholar
Moses, Y. (1988) Resource bounded knowledge. In Vardi, M., editor. Proceedings of the Theoretical Aspects of Reasoning About Knowledge. San Francisco, CA: Morgan Kaufmann, pp. 261276.Google Scholar
Parikh, R. (1987). Knowledge and the problem of logical omniscience. ISMIS-87 (International Symposium on Methodology for Intelligent Systems), North Holland, 432439.Google Scholar
Parikh, R. (1991). Finite and infinite dialogues. In Moschovakis, Y., editor. Proceedings of a Workshop on Logic from Computer Science. MSRI Publications, Heidelberg: Springer, pp. 481498.Google Scholar
Parikh, R. (1995). Logical omniscience. In Leivant, , editor. Logic and Computational Complexity, Springer Lecture Notes in Computer Science No. 960, pp. 2229.CrossRefGoogle Scholar
Parikh, R. (2001). Propositions, propositional attitudes and belief revision. In Segerberg, K., Zakharyaschev, M., de Rijke, M., and Wansing, H., editors. Advances in Modal Logic, vol. 2. Stanford, CA: CSLI Publications.Google Scholar
Parikh, R., & Ramanujam, R. (2003). A knowledge based semantics of messages. Journal of Logic, Language and Information, 12, 453467.CrossRefGoogle Scholar
Park, D. (1981). Concurrency and automata on infinite sequences. In Deussen, P., editor. Proceedings of the 5th GI-Conference Karlsruhe. Heidelberg: Springer-Verlag.Google Scholar
Pepperberg, I. (2004). Talking with Alex: logic and speech in parrots; exploring intelligence. Scientific American Mind, August.Google Scholar
Plato, . Meno, translation by Benjamin Jovett. Available online at http://classics.mit.edu//Plato/meno.htmlGoogle Scholar
Ramsey, F. P. (1931). Truth and probability. In The Foundations of Mathematics. London: Routledge and Kegan Paul, pp. 156198.Google Scholar
Ramsey, F. P. (1990). Facts and propositions. In Mellor, D. H., editor. Philosophical Papers. Cambridge, UK: Cambridge University Press, pp. 3451.Google Scholar
Savage, L. J. (1954). The Foundations of Statistics. Malden, MA: Wiley.Google Scholar
Searle, J. (1994). Animal minds. In French, and Wettstein, , editors. Philosophical Naturalism, Midwest Studies in Philosophy, XIX, Malden, MA: Wiley, pp. 206219.Google Scholar
Stalnaker, R. (1999). Context and Content. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
de Waal, F. (2005). Our Inner Ape. New York: Penguin.Google Scholar
Whyte, J. T. (1990). Success semantics. Analysis, 50, 149157.CrossRefGoogle Scholar
Wittgenstein, L. (1958). Philosophical Investigations. Oxford, UK: Blackwell.Google Scholar