Standard vs. Nonstandard Logic: Higher-Order, Modal, and First-Order Logics

  • Jaakko Hintikka
Part of the Synthese Library book series (SYLI, volume 149)


Model-theoretical (semantical) treatments of modal logic have enjoyed spec-tacular success ever since the pioneering work by Stig Kanger in 1957.1 Quine and others have admittedly proffered sundry philosophical objections to modal logic and its semantics but they have not impeded the overwhelming progress either of the semantical theory of intensional (modal) logics or of its applications.


Modal Logic Actual World Winning Strategy Standard Interpretation Tense Logic 
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  1. Marcel Guillaume, ‘Rapports entre calculs propositionels modaux et topologie impliques: par certaines extensions de la methode des tableaux: Systeme de Feys-von Wright’, Comptes rendus des seances de VAcademie des Science (Paris) 246 (1958), 1140–1142; ‘Systeme S4 de Lewis’, ibid., 2207–2210; ‘Systeme S5 de Lewis’, ibid., 247 (1958), 1282–1283; Jaakko Hintikka, ‘Quantifiers in Deontic Logic’, Societas Scientariarum Fennica, Commentationes humanarum litterarum, Vol. 23, 1957, No. 4; ‘Modality and Quantification’, Theoria 27 (1961), 119–128; ‘The Modes of Modality’, Acta Philosophica Fennica 16 (1963), 65–82.Google Scholar
  2. See Richmond Thomason (ed.), Formal Philosophy: Selected Papers of Richard Montague, Yale University Press, New Haven, 1974, Chapters 1–2.Google Scholar
  3. David Kaplan, UCLA dissertation, 1964.Google Scholar
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  5. Alfred Tarski and Bjarni Jonsson, Boolean Algebras with Operators I–II, American Journal of Mathematics 73 (1951), and 74 (1952).Google Scholar
  6. See Leon Henkin, ‘Completeness in the Theory of Types’, J. Symbolic Logic 15 (1950), 81–91. (Please note that Peter Andrews has discovered a flaw in Henkin’s original argument and has shown how to repair it.)Google Scholar
  7. See especially Jaakko Hintikka, ‘Quantifiers in Logic and Quantifiers in Natural Languages’, in S. Körner (ed.), Philosophy of Logic, Blackwell’s, Oxford, 1976, pp. 208-232; ‘Quantifiers vs. Quantification Theory’, Linguistic Inquiry 5 (1974), 153–177; Logic, Language-Games, and Information, Clarendon Press, Oxford, 1973. Much of the relevant literature has now been collected in Esa Saarinen (ed.), Game-Theoretical Semantics, D. Reidel, Dordrecht, 1978.Google Scholar
  8. Cf. here Jaakko Hintikka and Veikko Rantala, ‘A New Approach to Infinitary Languages’, Annals of Mathematical Logic 10 (1976), 95–115.Google Scholar
  9. For an explicit discussion of this idea see Jaakko Hintikka and Lauri Carlson, ‘Conditionals, Generic Quantifiers, and Other Applications of Subgames’, in A. Margalit (ed.), Meaning and Use, D. Reidel, Dordrecht, 1978.Google Scholar
  10. Cf. my paper ‘Language Games’, in Essays on Wittgenstein in Honour of G. H. von Wright (Acta Philosophica Fennica, Vol. 28, Nos. 1-3), North-Holland, Amsterdam, 1976, pp. 105–125.Google Scholar
  11. Quantifiers vs. Quantification Theory’, Linguistic Inquiry 5 (1974), 153–177.Google Scholar
  12. For backwards-looking operators, see Esa Saarinen, ‘Backwards-Looking Operators in Tense Logic and Natural Language’, in Jaakko Hintikka et. al (eds.), Essays on Mathematical and Philosophical Logic, D. Reidel, Dordrecht, 1978, pp. 341–367; and Esa Saarinen, ‘Intentional Identity Interpreted’, Linguistic and Philosophy 2 (1978), 151–223, with further references to the literature. The initiators of the diesa seem to have been Hans Kamp and David Kaplan.Google Scholar
  13. ‘Reductions in the Theory of Types’, Acta Philosophica Fennica 8 (1955), 56–115.Google Scholar
  14. See S. K. Thomason, ‘Semantic Analysis of Tense Logics’, J. Symbolic Logic 37 (1972), 150–158; ‘Noncompactness in Propositional Modal Logic’, ibid., 716–720; ‘An Incompleteness Theorem in Modal Logic’, Theoria 40 (1974), 30–34.Google Scholar
  15. Barbara Hall Partee (ed.), Montague Grammar, Academic Press, New York, 1976, and note 4 above.Google Scholar

Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • Jaakko Hintikka
    • 1
  1. 1.Florida State UniversityUSA

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