Abstract
The main vehicle of speaking and reasoning about knowledge in philosophy has recently been epistemic logic.1 Even though epistemic logic is not the only relevant language-game in town, it offers a useful perspective here, for certain other approaches can be thought of as improvements on epistemic logic. In its axiomatic-deductive forms, epistemic logic is normally considered a branch of modal logic, and its semantics is usually subsumed under the misleading heading of “possible-worlds semantics”. I will not attempt here a survey of the existing literature on epistemic logic.2 Most of this literature is focused on syntactical (e.g., deductive and axiomatic) methods of dealing with knowledge representation and reasoning about knowledge. This is in my view a serious defect in much of the current work on epistemic logic. For typically the most interesting problems and solutions are found by considering the model-theoretical (semantical) situation. For this reason, I will not attempt here a survey of existing literature, but a review of some of the central conceptual problems arising in epistemic logic.
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Notes
The idea of epistemic logic goes back at least to G.H. von Wright: 1951, An Essay in Modal Logic, North-Holland, Amsterdam. The first book-length treatment was my: 1962, Knowledge and Belief: An Introduction to the Logic of the Two Notions, Cornell U.P., Ithaca.
For a partial survey of earlier work, see Wolfgang Lenzen: 1978, Recent Work in Epistemic Logic (Acta Philosophica Fennica 30, no. 1), Societas Philosophica Fennica, Helsinki.
See here, e.g., Melvin Fitting: 1969, Intuitionistic Logic, Model Theory, and Forcing, North-Holland, Amsterdam;
Kenneth A. Bowen: 1979, Model Theory for Modal Logic, D. Reidel, Dordrecht. These treatises are not addressed to the specific problems of epistemic logic, however.
In the earlier literature, the knower used to be indicated by a subscript. This is misleading, however, for the term referring to the knower is not within the scope of the epistemic operator.
Some philosophers have tried to find a difference in principle between the two kinds of applications. It is nevertheless clearer in epistemic logic than in some of the parallel theories that the intended applications have always been to “small worlds”, to use L.J. Savage’s phrase.
See Jon Barwise and John Perry: 1983, Situations and Attitudes, MIT Press, Cambridge, Mass..
See here Jaakko Hintikka: 1976, The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, 28, no. 4), Societas Philosophica Fennica, Helsinki.
The question here is under what conditions existential generalization is valid in epistemic logic. The conditions are of course the same as the conditions on valid universal instantiation dealt with in sec. 2, part ii, below.
Cf. here chapter 1 of my book: 1974, The Intentions of Intentionality, D. Reidel, Dordrecht.
I am assuming that a distinction is made between those name-like free singular terms which pick out the same individual from different worlds and those that might refer to different individuals in different worlds. Here “z” is assumed to be of the former kind.
This matter will be dealt with in a greater detail in a projected monograph of mine.
See here chapters 3–4 of my book: 1974, The Intentions of Intentionality, D. Reidel, Dordrecht.
Bertrand Russell: 1917, ‘Knowledge by Acquaintance and Knowledge by Description’, in Mysticism and Logic, George Allen & Unwin, London;
chapter 5 of: 1912, The Problems of Philosophy, Home University Library, London, and cf. Jaakko Hintikka, Knowledge by Acquaintance - Individuation by Acquaintance, in D.F. Pears (ed.): 1972, Bertrand Russell (Modern Studies in Philosophy), Doubleday, Garden City, N.J., 52–79.
See Endel Tulving: 1983, Elements of Episodic Memory, Clarendon Press, Oxford.
See Lucia Vaina, From Vision to Cognition: A Computational Theory of Higher-Level Visual Functions, Kluwer, Dordrecht, forthcoming.
Cf., e.g., Noam Chomsky: 1982, The Generative Enterprise, Foris, Dordrecht. From what is reported in the rest of this section, this objection against possible-worlds analysis of knowledge was effectively disposed of more than ten years ago.
See Jaakko Hintikka: 1973, Logic, Language-Games, and Information, Clarendon Press, Oxford.
See Jaakko Hintikka: 1986, ‘Mental Models, Semantical Games, and Varieties of Intelligence’, in Lucia Vaina, ed., Varieties of Intelligence, D. Reidel, Dordrecht.
The so-called paraconsistent logics have never been given any realistic model-theoretical and pragmatic interpretation, and hence have in their present form little interest. Cf. here Nicholas Rescher and Robert Brandom: 1979, The Logic of Inconsistency, Basil Blackwell, Oxford.
See Veikko Rantala: 1975, ‘Urn Models: A New Kind of Non-Standard Model for First-Order Logic’, Journal of Philosophical Logic, 4, 455–474, reprinted in Esa Saarinen (ed): 1979, Game-Theoretical Semantics, D. Reidel, Dordrecht.
The first time this interesting phenomenon was pointed out in the literature is in Lauri Carlson and Alice ter Meulen: 1972, ‘Informational Independence in Intensional Context’, in Esa Saarinen et al., (eds.): 1979, Essays in Honour of Jaakko Hintikka, D. Reidel, Dordrecht, 61–72.
See here Esa Saarinen (ed.), Game-Theoretical Semantics,
Jaakko Hintikka and Jack Kulas: 1983, The Game of Language, D. Reidel, Dordrecht.
For branching quantifier structures, there exists a growing body of studies. For references, see the bibliography of Jaakko Hintikka and Jack Kulas: op. cit. Independences between other kinds of concepts have scarcely been studied, except for the papers referred to here.
See here Jaakko Hintikka: 1982, ‘Questions with Outside Quantifiers’, in R. Schneider, K. Tuite and R. Chametzky (eds.), Papers from the Parasession on Nondeclaratives, Chicago Linguistic Society, Chicago, 83–92.
See here Jaakko Hintikka: 1974, ‘Quantifiers vs. Quantification Theory’, Linguistic Inquiry, 5, 153–77, reprinted in Esa Saarinen (ed).:1979, Game-Theoretical Semantics, D. Reidel, Dordrecht, 367–379.
See, e.g., Danny Dolev, Joseph Y. Halpern and Yoram Moses: 1985, ‘Cheating Husbands and Other Stories: A Case Study of Knowledge, Action and Communication’, preprint.
The model sketched here has been studied in a number of papers of mine. See, e.g., Jaakko Hintikka and Merrill B. Hintikka: 1982,‘Sherlock Holmes Encounters Modern Logic: Towards a Theory of Information-Seeking by Questioning’, in E.M. Barth and J.L. Martens, Argumentation: Approaches to Theory Formation, Benjamins, Amsterdam, 55–76; ‘The Logic of Science as a Model-Oriented Logic’, in RD. Asquith and P. Kitcher (eds.): 1984, PSA 1984, 1, Philosophy of Science Association, East Lansing, MI, 177–85.
As a book-keeping device we can use a Beth-type semantical tableau. (For them, see W. Beth: 1955, ‘Semantic Entailment and Formal Derivability’, Mededelingen van de Koninklijke Nederlandse Akademie van Wetenschappen, Afd. Letterkunde, N.R. 18, no. 13, Amsterdam, 309–42.) Then we can use all the usual terminology of the tableau method, and the deductive “moves” will be simply tableau-building rules. (We shall minimize movements between the left and the right column, however, and restrict the rules to those in keeping with the subformula principle.) Each application of the game rules is then relative to a given stage of some one subtableau. As is well known, the tableau method is simply the mirror image of a Gentzen-type sequent calculus. The only novelty here is that Nature’s answers are centered into the left column of a subtableau as additional premises.
For the concept of presupposition presupposed here, see Jaakko Hintikka: 1976, The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, 28, no. 4), Societas Philosophica Fennica, Helsinki.
An excellent example of what can be done in this direction is Lauri Carlson: 1982, Dialogue Games, D. Reidel, Dordrecht.
This observation has important consequences for the contemporary philosophy of science, where it has generally been assumed that only questions concerning the truth of falsity of atomic sentences are answered by Nature. In reality, the logic of experimental inquiry is an AE logic, not the logic of the atomistic case.
The notions of subformula principle, cut elimination, Gentzen’s Hauptsatz, etc. are explained in any decent introduction to proof theory. For Gentzen’s classical papers, see M.E. Szabo (ed.): 1969, The Collected Paper of Gerhard Gentzen, North-Holland, Amsterdam.
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Hintikka, J., Hintikka, M.B. (1989). Reasoning about Knowledge in Philosophy: The Paradigm of Epistemic Logic. In: The Logic of Epistemology and the Epistemology of Logic. Synthese Library, vol 200. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2647-9_2
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