Teaching Theory of Knowledge
14. Epistemic Logic
Instruction in epistemic logic requires that students have a reasonable familiarity with symbolic logic and its semantics. It is possible to cover much of the field with only propositional logic, but some areas require knowledge of predicate logic.
Division of the field:
Epistemic Propositional Logic: Epistemic principles. This is the study of the formal relations holding between sentences with epistemic terms. The terms may be restricted to 'knows' and its cognates or extended to cover related notions such as 'believes', 'is justified', 'is true', etc. Some sample principles are:
if S knows (believes) that p, then S knows that S knows (believes that S believes) that p [KK or BB principle].
If S knows that p, then S believes that S knows that p.
If S knows that p, then S knows all p's logical consequences [logical omniscience].
Such principles can be formalized, and choice of appropriate principles is a rich topic of discussion.
Hilpinen, R. "Knowing that One Knows and the Classical Definition of Knowledge." Synthese 21 (1970), 109-32.Hintikka, J. "'Knowing That One Knows' Reviewed." Synthese 21 (1970), 141-62.
Hintikka, J. "Knowledge, Belief, and Logical Consequence." Ajatus 32 (1970), 32-47.
Hughes, G. E., and Cresswell, M. J. An Introduction to Modal Logic. London: Methuen, 1968.
Lemmon, E. J. "If I Know, Do I Know That I Know?" In Avrum Stroll (ed.), Epistemology: New Essays in the Theory of Knowledge. New York: Harper and Row, 1967, 54-82.
Lenzen, W. "Recent Work in Epistemic Logic." Acta Philosophica Fennica 30, 1-219, Sections 1-4.
Levi, I. The Enterprise of Knowledge. Cambridge, Mass.: MIT Press, 1980. Chapters 1-3.
McLane, E. "Is Epistemic Logic Possible?" Notre Dame Journal of Formal Logic 20 (1979), 559-74.
Rescher, N. "On Alternatives in Epistemic Logic." In Rescher, Studies in Modality. Oxford: American Philosophical Quarterly Monograph, 1974.
Schlesinger, G. The Range of Epistemic Logic. Aberdeen: Aberdeen University Press, 1985.
Epistemic Propositional Logic: Semantics. Kripke-style "possible worlds" semantics for modal logic can be straightforwardly applied to sentences containing 'knows' and 'believes'. The epistemic or doxastic terms are treated as non-truth-functional one-place operators on sentences. It can be easily shown how to determine the truth value of such sentences for a given interpretation. Discussion might center around the choice of the best semantics (which parallels the choice of epistemic principles). The question of the philosophical interpretation of possible worlds is also an interesting topic.
Hintikka, J. Knowledge and Belief: An Introduction to the Logic of the Two Notions. Ithaca: Cornell University Press, 1962. See especially chapters 1-5.Epistemic Predicate Logic: Semantics and Principles. The discussions in (1) can be extended to principles involving quantifiers. A particularly important problem is how to treat the interaction of quantifiers and epistemic operators.
Quine's treatment of propositional attitudes and responses to Quine are particularly important here.
Hintikka, J. Knowledge and Belief. Ibid. See especially chapter 6.Hintikka, J. "Quine on Quantifying in: A Dialogue." In Hintikka, The Intentions of Intentionality and Other New Models for Modalities. Dordrecht: Reidel, 1969, 87-111.
Lenzen. W. "Recent Work in Epistemic Logic". op. cit.. section 5.
Quine, W. V. ''Quantifiers and Propositional Attitudes." In Quine, The Ways of Paradox. New York: Random House, 1962.
'Knows' as a Predicate. Epistemic statements may be formalized in predicate logic with 'knows' represented as a relation between a person, a time and a sentence. Other terms ('believes', etc.) can be given the same kind of treatment.
Principles. Some epistemic principles, particularly those of Chisholm, have been formulated in this way.
Chisholm, R. and Keim, R. "A System of Epistemic Logic." Ratio 15 (1972), 99-115.Eberle, R. "A Logic of Believing, Knowing and Inferring." Synthese 26 (1974), 356-82.
Montague, R. "Syntactical Treatments of Modality, with Corollaries on Reflection Principles and Finite Axiomatizability." In Formal Philosophy, Selected Papers of Richard Montague, New Haven: Yale, 1974, 286-302.
Paradoxes. The combination of various epistemic principles in epistemic predicate logic leads to paradoxes. These are interesting in themselves, and they also shed interesting light on the principles.
Anderson, C. A. "The Paradox of the Knower." Journal of Philosophy 80 (1983), 338-55.Montague, R. and Kaplan, D. "A Paradox Regained." In Formal Philosophy, op. cit.
Thomason, R. "A Note on the Syntactical Treatment of Modality." Synthese 44 (1980), 391-95.
Tymoczko, T. "An Unsolved Puzzle about Knowledge." The Philosophical Quarterly 34 (1984), 437-58.