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
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)
van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press (2011)
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)
van Benthem, J., Liu, F.: Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17(2), 157–182 (2007)
Board, O.: Dynamic interactive epistemology. Games and Economic Behavior 49, 49–80 (2004)
Chellas, B.F.: Modal Logic: An Introduction. Cambridge University Press (1980)
Cohen, S.: How to be a Fallibilist. Philosophical Perspectives 2, 91–123 (1988)
Cohen, S.: Basic Knowledge and the Problem of Easy Knowledge. Philosophy and Phenomenological Research 65(2), 309–329 (2002)
DeRose, K.: Solving the Skeptical Problem. The Philosophical Review 104(1), 1–52 (1995)
DeRose, K.: The Case for Contextualism. Oxford University Press (2009)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Springer (2008)
Dretske, F.: Epistemic Operators. The Journal of Philosophy 67(24), 1007–1023 (1970)
Dretske, F.: The Pragmatic Dimension of Knowledge. Philosophical Studies 40, 363–378 (1981)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press (1995)
Goldman, A.I.: Discrimination and Perceptual Knowledge. The Journal of Philosophy 73(20), 771–791 (1976)
Halpern, J.Y., Pucella, R.: Dealing with Logical Omniscience: Expressiveness and Pragmatics. Artificial Intelligence 175, 220–235 (2011)
Heller, M.: Relevant Alternatives and Closure. Australasian Journal of Philosophy 77(2), 196–208 (1999)
Heller, M.: Relevant Alternatives. Philosophical Studies 55, 23–40 (1989)
Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. College Publications (2005)
Holliday, W.H.: Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism (manuscript, 2012)
Holliday, W.H.: Knowing What Follows: Epistemic Closure and Epistemic Logic. PhD thesis. Stanford University (2012)
Lewis, D.: Completeness and Decidability of Three Logics of Counterfactual Conditionals. Theoria 37(1), 74–85 (1971)
Lewis, D.: Counterfactuals. Blackwell, Oxford (1973)
Lewis, D.: Scorekeeping in a Language Game. Journal of Philosophical Logic 8, 339–359 (1979)
Lewis, D.: Elusive Knowledge. Australasian Journal of Philosophy 74(4), 549–567 (1996)
Nozick, R.: Philosophical Explanations. Harvard University Press (1981)
Stalnaker, R.: The Problem of Logical Omniscience I. Synthese 89, 425–440 (1991)
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Holliday, W.H. (2012). Epistemic Logic, Relevant Alternatives, and the Dynamics of Context. In: Lassiter, D., Slavkovik, M. (eds) New Directions in Logic, Language and Computation. ESSLLI ESSLLI 2010 2011. Lecture Notes in Computer Science, vol 7415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31467-4_8
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DOI: https://doi.org/10.1007/978-3-642-31467-4_8
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