Epistemic Logic, Relevant Alternatives, and the Dynamics of Context

  • Wesley H. Holliday
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7415)

Abstract

According to the Relevant Alternatives (RA) Theory of knowledge, knowing that something is the case involves ruling out (only) the relevant alternatives. The conception of knowledge in epistemic logic also involves the elimination of possibilities, but without an explicit distinction, among the possibilities consistent with an agent’s information, between those relevant possibilities that an agent must rule out in order to know and those remote, far-fetched or otherwise irrelevant possibilities. In this article, I propose formalizations of two versions of the RA theory. Doing so clarifies a famous debate in epistemology, pitting Fred Dretske against David Lewis, about whether the RA theorist should accept the principle that knowledge is closed under known implication, familiar as the K axiom in epistemic logic. Dretske’s case against closure under known implication leads to a study of other closure principles, while Lewis’s defense of closure by appeal to the claimed context sensitivity of knowledge attributions leads to a study of the dynamics of context. Having followed the first lead at length in other work, here I focus more on the second, especially on logical issues associated with developing a dynamic epistemic logic of context change over models for the RA theory.

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References

  1. 1.
    Areces, C., ten Cate, B.: Hybrid Logics. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, pp. 821–868. Elsevier (2007)Google Scholar
  2. 2.
    van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press (2011)Google Scholar
  3. 3.
    van Benthem, J., Girard, P., Roy, O.: Everything else being equal: A modal logic for Ceteris Paribus preferences. Journal of Philosophical Logic 38, 83–125 (2009)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    van Benthem, J., Liu, F.: Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17(2), 157–182 (2007)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Board, O.: Dynamic interactive epistemology. Games and Economic Behavior 49, 49–80 (2004)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press (1980)Google Scholar
  7. 7.
    Cohen, S.: How to be a Fallibilist. Philosophical Perspectives 2, 91–123 (1988)CrossRefGoogle Scholar
  8. 8.
    Cohen, S.: Basic Knowledge and the Problem of Easy Knowledge. Philosophy and Phenomenological Research 65(2), 309–329 (2002)CrossRefGoogle Scholar
  9. 9.
    DeRose, K.: Solving the Skeptical Problem. The Philosophical Review 104(1), 1–52 (1995)MathSciNetCrossRefGoogle Scholar
  10. 10.
    DeRose, K.: The Case for Contextualism. Oxford University Press (2009)Google Scholar
  11. 11.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer (2008)Google Scholar
  12. 12.
    Dretske, F.: Epistemic Operators. The Journal of Philosophy 67(24), 1007–1023 (1970)CrossRefGoogle Scholar
  13. 13.
    Dretske, F.: The Pragmatic Dimension of Knowledge. Philosophical Studies 40, 363–378 (1981)CrossRefGoogle Scholar
  14. 14.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press (1995)Google Scholar
  15. 15.
    Goldman, A.I.: Discrimination and Perceptual Knowledge. The Journal of Philosophy 73(20), 771–791 (1976)CrossRefGoogle Scholar
  16. 16.
    Halpern, J.Y., Pucella, R.: Dealing with Logical Omniscience: Expressiveness and Pragmatics. Artificial Intelligence 175, 220–235 (2011)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Heller, M.: Relevant Alternatives and Closure. Australasian Journal of Philosophy 77(2), 196–208 (1999)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Heller, M.: Relevant Alternatives. Philosophical Studies 55, 23–40 (1989)CrossRefGoogle Scholar
  19. 19.
    Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. College Publications (2005)Google Scholar
  20. 20.
    Holliday, W.H.: Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism (manuscript, 2012)Google Scholar
  21. 21.
    Holliday, W.H.: Knowing What Follows: Epistemic Closure and Epistemic Logic. PhD thesis. Stanford University (2012)Google Scholar
  22. 22.
    Lewis, D.: Completeness and Decidability of Three Logics of Counterfactual Conditionals. Theoria 37(1), 74–85 (1971)MathSciNetMATHCrossRefGoogle Scholar
  23. 23.
    Lewis, D.: Counterfactuals. Blackwell, Oxford (1973)Google Scholar
  24. 24.
    Lewis, D.: Scorekeeping in a Language Game. Journal of Philosophical Logic 8, 339–359 (1979)CrossRefGoogle Scholar
  25. 25.
    Lewis, D.: Elusive Knowledge. Australasian Journal of Philosophy 74(4), 549–567 (1996)CrossRefGoogle Scholar
  26. 26.
    Nozick, R.: Philosophical Explanations. Harvard University Press (1981)Google Scholar
  27. 27.
    Stalnaker, R.: The Problem of Logical Omniscience I. Synthese 89, 425–440 (1991)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Wesley H. Holliday
    • 1
  1. 1.Department of PhilosophyStanford UniversityUSA

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