Sentences, Belief and Logical Omniscience, or What Does Deduction Tell Us?

  • Rohit ParikhEmail author
Part of the Springer Graduate Texts in Philosophy book series (SGTP, volume 1)


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.


Belief State Recursive Call Kripke Structure Dutch Book Conjunction Fallacy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Sergei Artemov, Can Başkent, Samir Chopra, Horacio Arló Costa, Juliet Floyd, Haim Gaifman, Isaac Levi, Mike Levin, Larry Moss, Eric Pacuit, Catherine Wilson, and Andreas Witzel for comments. The information about chess came from Danny Kopec. This research was supported by a grant from the PSC-CUNY faculty research assistance program. Earlier versions of this paper were given at TARK-05, ESSLLI-2006, at the Jean Nicod Institute, at a seminar in the philosophy department at Bristol University, and at the Philosophy Colloquium at the City University Graduate Center. Some of the research for this paper was done when the author was visiting Boston University and the Netherlands Institute for Advanced Study. A very preliminary version of some of the ideas was presented at Amsterdam, and published as Parikh (2001). This research was partially supported by grants from the PSC-CUNY program at the City university of New York.


  1. Alchourron, C., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. The Journal of Symbolic Logic, 50, 510–530.CrossRefGoogle Scholar
  2. Artemov, S., & Nogina, E. (2005). On epistemic logics with justifications. In R. Meyden (Ed.), Theoretical aspecits of rationality and knowledge (pp. 279–294). Singapore: University of Singapore press.Google Scholar
  3. Aumann, R. (1976). Agreeing to disagree. Annals of Statistics, 4, 1236–1239.CrossRefGoogle Scholar
  4. van Benthem, J. (1976). Modal correspondence theory. Doctoral dissertation, University of Amsterdam.Google Scholar
  5. Bicchieri, C. (1997). Learning to co-operate. In C. Biccheri, R. C. Jeffrey, & B. Skyrms (Eds.), The dynamics of norms (pp. 17–46). Cambridge: Cambridge University Press.Google Scholar
  6. Brandom, R. (1994). Unsuccessful seminatics. Analysis, 54, 175–178.CrossRefGoogle Scholar
  7. Davidson, D. (1982). Rational animals. Dialectica, 36, 318–327.CrossRefGoogle Scholar
  8. Dennett, D. (1985). Brainstorms (2nd ed.). MIT, cf. page 11. Singapore.Google Scholar
  9. Dennett, D. (1996). The Intentional Stance (6th printing), Cambridge, Massachusetts: The MIT Press.Google Scholar
  10. Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. (1995). Reasoning about knowledge. Cambridge: MIT.Google Scholar
  11. de Finetti, B. (1937). Foresight: Its logical laws, its subjective sources. Annales de l’Institut Henri Poincare, 7. (Trans.: Kyburg, H. (1980). Studies in subjective probability, Kyburg and Smokler (Eds.), (pp. 53–118). Krieger Publishing.)Google Scholar
  12. Fitting, M. (2004). A logic of explicit knowledge. Logica Yearbook, 11–22.Google Scholar
  13. Gaifman, H. (2004). Reasoning with limited resources and assigning probabilities to arithmetical statements. Synthese, 140, 97–119.CrossRefGoogle Scholar
  14. Gettier, E. (1963). Is justified true belief knowledge? Analysis, 23, 121–123.CrossRefGoogle Scholar
  15. Gigerenzer, G. (1996). On narrow norms and vague heuristics: A reply to Kahneman and Tversky (1996). Psychological Review, 103, 592–596.CrossRefGoogle Scholar
  16. Hayek, F. A. (1948). Individualism and economic order (See especially chapters II and IV). Chicago: University of Chicago Press.Google Scholar
  17. Hintikka, J. (2004). A fallacious fallacy? Synthese, 140, 25–35.CrossRefGoogle Scholar
  18. Hume, D. (1988). A treatise of human nature, (L. A. Selby-Brigge (Ed.), pp. 176–179). New York: Oxford University Press.Google Scholar
  19. Kahneman, D. (2002). Maps of Bounded Rationality, Nobel prize lecture.Google Scholar
  20. Kripke, S. (1979). A puzzle about belief. In A. Margalit (Ed.), Meaning and use. Dordrecht/Boston: ReidelGoogle Scholar
  21. Levi, I. (1997). Rationality and commitment. In The covenant of reason. Cambridge/New York: Cambridge University Press.Google Scholar
  22. Levi, I. (2004). Jaakko Hintikka. Synthese, 140, 37–41.CrossRefGoogle Scholar
  23. Marcus, R. (1990). Some revisionary proposals about belief and believing. Philosophy and Phenomenological Research, 50, 133–153.CrossRefGoogle Scholar
  24. Marcus, R. (1995). The anti-naturalism of some language centere accounts of belief. Dialectica, 49, 112–129.Google Scholar
  25. Millikan, R. (2006). Styles of rationality. In M. Nudds & S. Hurley (Eds.), Rationality in animals (pp. 117–126). Oxford: Oxford University Press.CrossRefGoogle Scholar
  26. Milner, R. (1989). Communication and concurrency. New York: Prentice Hall.Google Scholar
  27. Moses, Y. (1988). Resource bounded knowledge. In M. Vardi (Ed.), Proceedings of the 2nd Conference on Theorectical Aspects of Reasoning About Knowledge (pp. 261–276). San Francisco: Morgan Kaufmann.Google Scholar
  28. Parikh, R. (1987). Knowledge and the problem of logical omniscience. In International symposium on methodology for intelligent systems (ISMIS- 87), Charlotte (pp. 432–439). North Holland.Google Scholar
  29. Parikh, R. (1991). Finite and infinite dialogues. In Moschovakis (Ed.) Proceedings of a Workshop on Logic from Computer Science (pp. 481–498). Berlin: Springer/MSRI Publications.Google Scholar
  30. Parikh, R. (2001). Propositions, propositional attitudes and belief revision. In K. Segerberg, M. Zakharyaschev, M. de Rijke, & H. Wansing (Eds.), Advances in modal logic (Vol. 2). Stanford: CSLI Publications.Google Scholar
  31. Parikh, R. (1995). Logical omniscience. In Leivant (Ed.), Logic and computational complexity (Lecture notes in computer science, Vol. 960, pp. 22–29). Berlin/New York: Springer.Google Scholar
  32. Parikh, R., & Ramanujam, R. (2003). A knowledge based semantics of messages. Journal of Logic, Language and Information, 12, 453–467.CrossRefGoogle Scholar
  33. Park, D. (1981). Concurrency and automata on infinite sequences. In P. Deussen (Ed.), Proceedings of the 5th GI-Conference Karlsruhe. Berlin/Heidelberg: Springer.Google Scholar
  34. Pepperberg, I. (2004). Talking with Alex: Logic and speech in parrots; exploring intelligence. Scientific American Mind, August 2004.Google Scholar
  35. Plato. Meno. (380 BC). (trans. Benjamin Jowett). Available online at
  36. Ramsey, F. P. (1990). Facts and propositions. In D. H. Mellor (Ed.), Philosophical papers (pp. 34–51). Cambridge/New York: Cambridge University Press.Google Scholar
  37. Ramsey, F. P. (1931). Truth and probability. In The foundations of mathematics (pp. 156–198). London: Routledge and Kegan Paul.Google Scholar
  38. Savage, L. J. (1954). The foundations of statistics. New York: Wiley.Google Scholar
  39. Schwitzgebel, E. (2002). A phenomenal, dispositional account of belief. Nous, 36:2, 249–275.Google Scholar
  40. Schwitzgebel, E. (2006, Fall). Belief. In E. N. Zalta (Ed.), The stanford encyclopedia of philosophy (Fall 2006 ed.).
  41. Searle, J. (1994). Animal minds. In P. French & H. Wettstein (Eds.), Philosophical naturalism, midwest studies in philosophy (XIX, pp. 206–219). Notre Dame: University of Notre Dame Press.Google Scholar
  42. Stalnaker, R. (1999). Context and content. Oxford/New York: Oxford University Press.CrossRefGoogle Scholar
  43. de Waal, F. (2005). Our inner ape. Penguin. Singapore.Google Scholar
  44. Whyte, J. T. (1990). Success semantics. Analysis, 50, 149–157.CrossRefGoogle Scholar
  45. Wittgenstein, L. (1958). Philosophical investigations. New York: MacMillan.Google Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.City University of New YorkNew YorkUSA

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