Abstract
In this paper I shall sketch a system of modal logic in which modal operators are relativised to individuals or sets of individuals. This extension of modal logic is suggested by certain expressions in ordinary language. For example, under certain circumstances we may utter the sentence (A) John can catch the trainwhich may be taken to be equivalent to (A’) It is possible for John to catch the train.
I am indebted to Professor Jaakko Hintikka for his valuable suggestions and advice concerning this paper. This study has been facilitated by a Finnish State Fellowship (Valtion apuraha nuorille tieteenharjoittajille).
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Bibliography
Robert Feys, Modal Logics (ed. with some complements by J. Dopp), Gauthier-Villars, Paris, 1965.
Nelson Goodman, The Problem of Counterfactual Conditionals’, Journal of Philosophy 44 (1947) 113–128.
H. L. A. Hart, and A. M. Honoré, Causation in the Law, Oxford University Press, Oxford, 1959.
Jaakko Hintikka, ‘Quantifiers in Deontic Logic’, Commentat iones Humanum Litter arum 23, No. 4, Societas Scientiarum Fennica, Helsingfors, 1957.
Jaakko Hintikka, ‘Modality and Quantification’, Theoria 27 (1961) 119–128.
Jaakko Hintikka, ‘Studies in the Logic of Existence and Necessity, I: Existence’, Monist 50 (1966) 55–76.
Stig Kanger, Provability in Logic (Stockholm Studies in Philosophy, 1), Almqvist& Wiksell, Stockholm, 1957.
Saul Kripke, ‘Semantical Analysis of Modal Logic, I: Normal Propositional Calculi’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 9 (1963) 67–96.
Saul Kripke, ‘Semantical Considerations on Modal Logics’, Acta Philosophica Fennica 16 (1963), 83–94.
References
The modification is due to the condition concerning free individual symbols in (C.N*) (cf. also axiom (A2) on p. 187). It is, of course, irrelevant in propositional modal logic.
The syntactical proof of (5.11c) runs as follows: According to (A4), (5.1) implies N {d} (S(a, c)), and (5.14) implies by quantification theory, (A3), and (A2), N {d} (S(a, c)) ⊃ N {d} (S(c, d) ⊃ S (a, d)); hence (5.11c) follows by modus ponens.
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© 1969 D. Reidel Publishing Company, Dordrecht, Holland
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Hilpinen, R. (1969). An Analysis of Relativised Modalities. In: Davis, J.W., Hockney, D.J., Wilson, W.K. (eds) Philosophical Logic. Synthese Library, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9614-0_15
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