Abstract
This paper charts some early history of the possible worlds semantics for modal logic, starting with the pioneering work of Prior and Meredith. The contributions of Geach, Hintikka, Kanger, Kripke, Montague, and Smiley are also discussed.
Similar content being viewed by others
References
A. Bayart (1958) ArticleTitle‘Correction de la Logique Modale du Premier et du Second Ordre S5 [Soundness of First and Second Order S5 Modal Logic]’ Logique et Analyse 1 28–44
A. Bayart (1959) ArticleTitle‘Quasi-Adéquation de la Logique Modale du Second Ordre S5 et Adéquation de la Logique Modale du Premier Ordre S5 [Quasi-Completeness of Second-Order S5 Modal Logic and Completeness of First-Order S5 Modal Logic]’ Logique et Analyse 2 99–121
Borkowski, L. (ed.): 1970, Jan Łukasiewicz: Selected Works, North Holland, Amsterdam
R. Carnap (1946) ArticleTitle‘Modalities and Quantification’ Journal of Symbolic Logic 11 33–64 Occurrence Handle10.2307/2268610
B.J. Copeland (Eds) (1996) Logic and Reality: Essays on the Legacy of Arthur Prior Clarendon Press Oxford
B.J. Copeland (2002) ArticleTitle‘The Genesis of Possible Worlds Semantics’ Journal of Philosophical Logic 31 99–137 Occurrence Handle10.1023/A:1015273407895
J. Davis D. Hockney W. Wilson (Eds) (1969) Philosophical Logic D. Reidel Dordrecht
D. Føllesdal (1994) ‘Stig Kanger In Memoriam’ D. Prawitz B. Skyrms D. Westerståhl (Eds) Logic, Methodology and Philosophy of Science Elsevier Amsterdam
Hilbert, D. and W. Ackermann: 1928, Grundzüge der Theoretischen Logik [Principles of Mathematical Logic], Julius Springer, Berlin.
Hilpinen, R. (ed.): 1970, Deontic Logic: Introductory and Systematic Readings. Reidel, Dordrecht.
J. Hintikka (1955a) ArticleTitle‘Form and Content in Quantification Theory’ Acta Philosophica Fennica 8 7–55
Hintikka, J.: 1955b, ‘Notes on Quantification Theory’, Societas Scientiarum Fennica, Commentationes Physico-Mathematicae 17(12).
J. Hintikka (1957a) ArticleTitle‘Modality as Referential Multiplicity’ Ajatus 20 49–64
Hintikka J.: 1957b, ‘Quantifiers in Deontic Logic’, Societas Scientiarum Fennica, Commentationes Humanarum Litterarum 23(4).
J. Hintikka (1969) ArticleTitleReview of Kanger (1957a) Journal of Symbolic Logic 34 305–306
B. Jónsson A. Tarski (1948) ArticleTitle‘Boolean Algebras With Operators’ Bulletin of the American Mathematical Society 54 79–80
B. Jónsson A. Tarski (1951) ArticleTitle‘Boolean Algebras With Operators, Part I’ American Journal of Mathematics 73 891–939 Occurrence Handle10.2307/2372123
B. Jónsson A. Tarski (1952) ArticleTitle‘Boolean Algebras With Operators, Part II’ American Journal of Mathematics 74 127–162 Occurrence Handle10.2307/2372074
S. Kanger (1955) ArticleTitle‘A Note on Partial Postulate Sets for Propositional Logic’ Theoria 21 99–104 Occurrence Handle10.1111/j.1755-2567.1955.tb00250.x
S. Kanger (1957a) ArticleTitle‘The Morning Star Paradox’ Theoria 23 1–11 Occurrence Handle10.1111/j.1755-2567.1957.tb00263.x
Kanger, S.: 1957b, ‘New Foundations for Ethical Theory’, typescript, University of Stockholm, 1957. Reprinted with minor alterations in Hilpinen (1970).
Kanger, S.: 1957c, Provability in Logic, Almqvist and Wiksell, Stockholm.
Kaplan, D.: 1966, Review of Kripke (1963a), Journal of Symbolic Logic 31,120–122
S. Kripke (1959a) ArticleTitle‘A Completeness Theorem in Modal Logic’ Journal of Symbolic Logic 24 1–14 Occurrence Handle10.2307/2964568
S. Kripke (1959b) ArticleTitle‘Semantical Analysis of Modal Logic’ (abstract) Journal of Symbolic Logic 24 323–324
S. Kripke (1963a) ArticleTitle‘Semantical Analysis of Modal Logic I: Normal Modal Propositional Calculi’ Zeitschr. f. math. Logik und Grundlagen d. Math. 9 67–96
S. Kripke (1963b) ArticleTitle‘Semantical Considerations on Modal Logic’ Acta Philosophica Fennica 16 83–94
Kripke, S.: 1965, ‘Semantical Analysis of Modal Logic II: Non-Normal Modal Propositional Calculi’, In J. Addison, L. Henkin, and A. Tarski (eds.), The Theory of Models, North-Holland, Amsterdam.
Lemmon, E.J., C. Meredith, D. Meredith, A. Prior, and I. Thomas: 1957, ‘Calculi of Pure Strict Implication’, mimeograph, University of Canterbury Philosophy Department, 1957. Reprinted in Davis et al. (1969).
H. Leonard (1951) ‘Two-Valued Truth Tables for Modal Functions’ P. Henle H. Kallen S. Langer (Eds) Structure and Meaning: Essays in Honor of Henry M. Sheffer Liberal Arts Press New York
Lindström, S.: 1998, ‘An Exposition and Development of Kanger’s Early Semantics for Modal Logic’, in P. Humphreys and J. Fetzer (eds.), The New Theory of Reference, Kluwer, Amsterdam.
Łukasiewicz, J.: 1920, ‘On Three-Valued Logic’, Ruch Filozoficzny 5, 170–171. English translation in Borkowski 1970.
Łukasiewicz, J.: 1930, ‘Philosophical Remarks on Many-Valued Systems’, in Borkowski 1970.
R.B. Marcus (1946) ArticleTitle‘A Functional Calculus of First Order Based on Strict Implication’ Journal of Symbolic Logic 11 1–16 Occurrence Handle10.2307/2269159
R.B. Marcus (1962) ArticleTitle‘Interpreting Quantification’ Inquiry 5 252–259 Occurrence Handle10.1080/00201746208601353
J. McKinsey A. Tarski (1944) ArticleTitle‘The Algebra of Topology’ Annals of Mathematics 45 141–191 Occurrence Handle10.2307/1969080
J. McKinsey A. Tarski (1946) ArticleTitle‘On Closed Elements in Closure Algebras’ Annals of Mathematics 47 122–162 Occurrence Handle10.2307/1969038
J. McKinsey A. Tarski (1948) ArticleTitle‘Some Theorems about the Sentential Calculi of Lewis and Heyting’ Journal of Symbolic Logic 13 1–15 Occurrence Handle10.2307/2268135
Meredith, C.: 1951, ‘On an Extended System of the Propositional Calculus’, Proceedings of the Royal Irish Academy 54 (Sect. A), 37–47
C. Meredith (1953a) ArticleTitle‘A Single Axiom of Positive Logic’ Journal of Computing Systems 1 169–170
C. Meredith (1953b) ArticleTitle‘Single Axioms for the Systems (C, N), (C, 0), and (A, N) of the Two-Valued Propositional Calculus’ Journal of Computing Systems 1 155–164
Meredith, C. and A. Prior: 1956, ‘Interpretations of Different Modal Logics in the “Property Calculus” ’, mimeograph, University of Canterbury Philosophy Department, reprinted in Copeland 1996.
C. Meredith A. Prior (1965) ArticleTitle‘Modal Logic With Functorial Variables and a Contingent Constant’ Notre Dame Journal of Formal Logic 6 99–109 Occurrence Handle10.1305/ndjfl/1093958149
D. Meredith (1977) ArticleTitle‘In Memoriam: Carew Arthur Meredith (1904–1976)’ Notre Dame Journal of Formal Logic 18 513–516 Occurrence Handle10.1305/ndjfl/1093888116
Montague, R.: 1960, ‘Logical Necessity, Physical Necessity, Ethics, and Quantifiers’, Inquiry 3, 259–269, reprinted in Montague (1974).
R. Montague (1974) Formal Philosophy: Selected Papers of Richard Montague Yale University Press New Haven
P. Øhrstrøm P. Hasle (1993) ArticleTitle‘A. N. Prior’s Rediscovery of Tense Logic’ Erkenntnis 39 23–50 Occurrence Handle10.1007/BF01128202
A. Prior (1953) ArticleTitle‘Three-Valued Logic and Future Contingents’ Philosophical Quarterly 3 317–326
A. Prior (1955) Formal Logic Clarendon Press Oxford
A. Prior (1956a) ArticleTitle‘Logicians at Play; or Syll, Simp and Hilbert’ Australasian Journal of Philosophy 34 182–192
A. Prior (1956b) ArticleTitle‘Modality and Quantification in S5’ Journal of Symbolic Logic 21 60–62 Occurrence Handle10.2307/2268488
A. Prior (1957) Time and Modality Oxford University Press Oxford
Prior, A.: 1958, ‘The Syntax of Time-Distinctions’, Franciscan Studies 18,105–120.
Prior, A.: 1962a, ‘Logic in England Today’, typescript, translated into Polish and published as Prior 1962d.
A. Prior (1962b) ArticleTitle‘Possible Worlds’ Philosophical Quarterly 12 36–43
A. Prior (1962c) ArticleTitle‘Tense Logic and the Continuity of Time’ Studia Logica 13 133–148 Occurrence Handle10.1007/BF02317267
A. Prior (1962d) ArticleTitle‘Wspólczesna logika w Anglii Ruch Filozoficzny 21 251–256
Prior, A.: 1967a, ‘Logic, Modal’, in P. Edwards (ed.), The Encyclopedia of Philosophy, Vol. 4, Collier-Macmillan, London.
A. Prior (1967b) Past, Present and Future Clarendon Press Oxford
Prior, A.: 2003, Papers on Time and Tense, Oxford University Press, Oxford (second revised edition, edited by P. Hasle, P. Øhrstrøm, T. Braüner, and B. J. Copeland).
Segerberg, K. (ed.): 1977, An Introduction to Modal Logic: The ‘Lemmon Notes’. Monograph No. 11, American Philosophical Quarterly.
Smiley, T.: 1955, ‘Natural Systems of Logic’, dissertation submitted towards the Degree of Doctor of Philosophy in the University of Cambridge.
Smiley, T.: 1957, ‘Modal Logic’, lecture handout, Department of Philosophy, University of Cambridge.
M. Wajsberg (1933) ArticleTitle‘Ein erweiterter Klassenkalkül [An Extended Calculus of Classes]’ Monatshefte für Mathematik und Physik 40 113–126 Occurrence Handle10.1007/BF01708856
L. Wittgenstein (1922) Tractatus Logico-Philosophicus Routledge and Kegan Paul London
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Copeland, B.J. Meredith, Prior, and the History of Possible Worlds Semantics. Synthese 150, 373–397 (2006). https://doi.org/10.1007/s11229-005-5514-9
Issue Date:
DOI: https://doi.org/10.1007/s11229-005-5514-9