Abstract
Defined and formalized several decades ago, widely used in philosophy and game theory, the concept of common knowledge is still considered as problematic, although not always for the right reasons. I suggest that the epistemic status of a group of human agents in a state of common knowledge has not been thoroughly analyzed. In particular, every existing account of common knowledge, whether formal or not, is either too strong to fit cognitively limited individuals, or too weak to adequately describe their state. I provide a realistic definition of common knowledge, based on a formalization of David Lewis’ seminal account and show that it is formally equivalent to probabilistic common belief. This leads to a philosophical analysis of common knowledge which answers several common criticisms and sheds light on its nature.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aumann R. J. (1976) Agreeing to disagree. The Annals of Statistics 4(6): 1236–1239
Barwise, J. (1988). Three views of common knowledge. In M. Y. Vardi, (Ed.), Proceedings of the 2nd conference on theoretical aspects of reasoning about knowledge (pp. 365–379). Morgan Kaufmann Publihers Inc., San Francisco.
Bonnay D., Egré P. (2009) Inexact knowledge with introspection. Journal of Philosophical Logic 38: 179–227
Chwe M. S.-Y. (2001) Rational ritual culture. Coordination and common knowledge. Princeton University Press, Princeton
Clark H., Marshall C. (1981) Definite reference and mutual knowledge. In: Joshi A., Webber B., Sag I. (eds) Elements of discourse understanding. Cambridge University Press, Cambridge, pp 10–63
Cubitt R., Sugden R. (2003) Common knowledge, salience and convention: A reconstruction of David Lewis’s game theory. Economics and Philosophy 19: 175–210
Dokic J., Egré P. (2009) Margin for error and the transparency of knowledge. Synthese 166: 1–20
Dretske F. (1988) Explaining behavior. MIT Press, Cambridge MA
Fagin R., Halpern J. Y., Moses Y., Vardi M. Y. (1995) Reasoning about knowledge. MIT Press, Cambridge MA
Gilbert M. (1989) On social facts. Princeton University Press, Princeton
Godfrey-Smith P. (1992) Indication and evolution. Synthese 92: 283–312
Heal J. (1978) Common knowledge. Philosophical Quarterly 28: 116–131
Lewis D. (1969) Convention—A philosophical study. Harvard University Press, Cambridge
Lismont L. (1995) Common knowledge: Relating anti-founded situation semantics to modal logic neighbourhood semantics. Journal of Logic, Language, and Information 3(4): 285–302
Lismont L., Mongin P. (1995) Belief closure: A semantics of common knowledge for modal propositional logic. Mathematical Social Sciences 30: 127–153
Morris S. (1999) Approximate common knowledge revisited. International Journal of Game Theory 23: 385–408
Monderer D., Samet D. (1989) Approximating common knowledge with common beliefs. Games and Economic Behavior 1: 170–190
Morris S., Shin H. S. (1997) Approximate common knowledge and co-ordination: Recent lessons from game theory. Journal of Language, Logic and Information 6: 171–190
Osborne M., Rubinstein A. (1994) A course in game theory. MIT Press, Cambridge
Parikh, R. (2005). Logical omniscience and common knowledge: What do we know and what do WE know ? In R. van der Meyden (Ed.), Proceedings of the 10th conference on theoretical aspects of rationality and knowledge (pp. 62–77). National University of Singapore.
Peacocke C. (2005) Joint attention: Its nature, reflexivity and relation to common knowledge. In: Eilan N., Hoerl C., McCormack T., Roessler J. Joint attention: Communication and other minds. Clarendon Press, Oxford
Rubinstein A. (1989) The electronic mail game. Strategic behavior under ’Almost Common Knowledge’. The American Economic Review 79: 385–391
Schiffer S. R. (1972) Meaning. Oxford University Press, Oxford
Sillari G. (2005) A logical framework for convention. Synthese 147: 379–400
Sperber D., Wilson D. (1986) Relevance: Communication and cognition. Blackwell, Oxford
Tollefsen D. (2005) Let’s pretend! Children and joint action. Philosophy of the Social Sciences 35(1): 75–97
Wimmer H., Perner J. (1983) Beliefs about beliefs: Representation and constraining function of wrong beliefs in young children’s understanding of deception. Cognition 13(1): 103–128
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Paternotte, C. Being realistic about common knowledge: a Lewisian approach. Synthese 183, 249–276 (2011). https://doi.org/10.1007/s11229-010-9770-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-010-9770-y