Skip to main content
Log in

The Many Faces of Closure and Introspection

An Interactive Perspective

  • Published:
Journal of Philosophical Logic Aims and scope Submit manuscript

Abstract

In this paper I present a more refined analysis of the principles of deductive closure and positive introspection. This analysis uses the expressive resources of logics for different types of group knowledge, and discriminates between aspects of closure and computation that are often conflated. The resulting model also yields a more fine-grained distinction between implicit and explicit knowledge, and places Hintikka’s original argument for positive introspection in a new perspective.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Abramsky, S. (2008). Information, processes and games. In J. Van Benthem & P. Adriaans (Eds.), Handbook on the philosophy of information (pp. 483–550). Amsterdam: Elsevier.

    Chapter  Google Scholar 

  2. Balbiani, P., Baltag, A., van Ditmarsch, H., Herzig, A., Hoshi, T., & De Lima, T. (2008). Knowable as known after an announcement. The Review of Symbolic Logic, 1(3), 305–334.

    Article  Google Scholar 

  3. Baltag, A., & Moss L. S. (2004). Logics for epistemic programs. Synthese, 139(2), 165–224.

    Article  Google Scholar 

  4. Barwise, J. (1988). Three views of common knowledge, TARK II. Pacific Grove, California.

    Google Scholar 

  5. Bonnay, D., & Egré, P. (2009). Inexact knowledge with introspection. Journal of Philosophical Logic, 38(2), 179–227.

    Article  Google Scholar 

  6. Brogaard, B., & Salerno, J. (2009). Fitch’s Paradox of Knowability. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy.

  7. Chellas, B. F. (1980). Modal logic: An introduction. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  8. Danto, A. C. (1967). On knowing that we know. In A. Stroll (Ed.), Epistemology. New essays on the theory of knowledge (pp. 32–53). New York: Harper and Row.

    Google Scholar 

  9. Dretske, F. (1970). Epistemic operators. The Journal of Philosophy, 76(24), 1007–1023.

    Article  Google Scholar 

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

    Article  Google Scholar 

  11. Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about knowledge. Cambridge/London: MIT Press.

    Google Scholar 

  12. Gochet, P., & Gribomont, P. (2006). Epistemic logic. In D. M. Gabbay & J. Woods (Eds.), Handbook of the history of logic (Vol. 6, pp. 99–195). Elsevier.

  13. Halpern, J. Y. (1996). Should knowledge entail belief? Journal of Philosophical Logic, 25(5), 483–494.

    Article  Google Scholar 

  14. Halpern, J. Y., & Moses, Y. (1985). A guide to the modal logics of knowledge and belief. In Proceedings of IJCAI- 85 (pp. 480–490). Los Angeles, CA.

  15. Halpern, J. Y., & Moses, Y. (1990). Knowledge and common knowledge in a distributed system. Journal of the Association for Computing Machinery, 37(3), 549–587.

    Article  Google Scholar 

  16. Harman, G. (1986). Change in view. Principles of reasoning. Cambridge: MIT.

    Google Scholar 

  17. Hawthorne, J. (2004). Knowledge and lotteries. Oxford: Oxford University Press.

    Google Scholar 

  18. Hendricks, V. (2006). Mainstream and formal epistemology. Cambridge: Cambridge University Press.

    Google Scholar 

  19. Hilpinen, R. (1970). Knowing that one knows and the classical definition of knowledge. Synthese, 21(2), 109–132.

    Article  Google Scholar 

  20. Hintikka, J. (1962). Knowledge and belief. An introduction to the logic of the two notions. Ithaca: Cornell University Press.

    Google Scholar 

  21. Hintikka, J. (1970). Knowing that one knows, reviewed. Synthese, 21(2), 141–162.

    Article  Google Scholar 

  22. Lemmon, E. J. (1967). If I know, do I know that i know? In A. Stroll (Ed.), Epistemology. New essays on the theory of knowledge (pp. 54–82). New York: Harper and Row.

    Google Scholar 

  23. Levesque, H. J. (1984). A logic of implicit and explicit belief. National conference on artificial intelligence. Houston, Texas.

  24. Lewis, D. (1969). Convention. A philosophical study. Cambridge: Harvard University Press.

    Google Scholar 

  25. Minsky, M. (1987). The society of mind. London: Willian Heineman.

    Google Scholar 

  26. Nozick, R. (1981). Philosophical explanations. Cambridge: Harvard University Press.

    Google Scholar 

  27. Palczewski, R. (2007). Distributed knowability and Fitch’s paradox. Studia Logica, 86(3), 455–478.

    Article  Google Scholar 

  28. Parikh, R. (2008). Sentences, belief and logical omniscience, or what does deduction tell us? The Review of Symbolic Logic, 1(4), 459–76.

    Article  Google Scholar 

  29. Plaza, J. (2007). Logics of public communications. Synthese, 158(2), 165–179.

    Article  Google Scholar 

  30. Restall, G. (1997). Ways things can’t be. Notre Dame Journal of Formal Logic, 38(4), 583–596.

    Article  Google Scholar 

  31. Roelofsen, F. (2006). Distributed knowledge. Journal of Applied Non-classical Logics, 16(2), 255–273.

    Google Scholar 

  32. Sequoiah-Grayson, S. (2011). Epistemic closure and commutative, nonassociative residuated structures. Synthese. doi:10.1007/s11229-010-9834-z.

    Google Scholar 

  33. Stalnaker, R. (1984). Inquiry. Cambridge: MIT Press.

    Google Scholar 

  34. Stalnaker, R. (1991). The problem of logical omniscience, I. Synthese, 89(3), 425–440.

    Article  Google Scholar 

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

    Article  Google Scholar 

  36. van Benthem, J. (2004). What one may come to know. Analysis, 64(282), 95–105.

    Article  Google Scholar 

  37. van Benthem, J. (2006). Epistemic logic and epistemology: The state of their affairs. Philosophical Studies, 128(1), 49–76.

    Article  Google Scholar 

  38. van Benthem, J. (2008). Logical dynamics meets logical pluralism? Australasian Journal of Logic, 6, 182–209.

    Google Scholar 

  39. van Benthem, J. (2009). Actions that make us know. In J. Salerno (Ed.), New essays on the knowability paradox (pp. 129–146). Oxford: Oxford University Press.

    Chapter  Google Scholar 

  40. van der Hoek, W., van Linder, B., & Meyer, J. J .C. (1999). Group knowledge is not always distributed (neither is it always implicit). Mathematical Social Sciences, 38, 215–240.

    Article  Google Scholar 

  41. Van Ditmarsch, H., & Kooi, B. (2006). The secret of my success. Synthese, 151(2), 201–232.

    Article  Google Scholar 

  42. Van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic epistemic logic. Dordrecht: Springer.

    Google Scholar 

  43. van Ditmarsch, H., van Eijck J., & Verbrugge, R. (2009). Common knowledge and common belief. In J. van Eijck, & R. Verbrugge, (Ed.), Discourses on social software (pp. 107–32). Amsterdam: Amsterdam University Press.

    Google Scholar 

  44. van Eijck, J., & Wang, Y. (2008). Propositional dynamic logic as a logic of belief revision. Logic, language, information and computation (pp. 136–148).

  45. Van Linder, B., van der Hoek, W., & Meyer, J. J. Ch. (1994). Communicating rational agents. In B. Nebel & L. Dreschler-Fischer (Eds.), KI-94: Advances in artificial intelligence (pp. 202–213). New York: Springer.

    Chapter  Google Scholar 

  46. Williamson, T. (2000). Knowledge and its limits. Oxford: Oxford University Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Patrick Allo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Allo, P. The Many Faces of Closure and Introspection. J Philos Logic 42, 91–124 (2013). https://doi.org/10.1007/s10992-011-9214-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10992-011-9214-2

Keywords

Navigation