Abstract
This chapter is an attempt to bury a problem, not to praise it. The problem is, as the title indicates, the possibility of quantified modal logic and, more generally, the possibility of using such referential notions as quantifiers and identity meaningfully in combination with modal notions in the narrow sense (necessity and possibility) and with the concepts known as propositional attitudes (e.g., knowledge, belief, memory, wishing, striving, hoping, etc.). Why such usage presents us with a problem will be explained later in this chapter.
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References
See Kurt Gödel, ‘Eine Interpretation des intuitionistischen Aussagenkalküls’, Ergebnisse eines mathematischen Kolloquiums, Vol. 4, Verlag Franz Deuticke, Vienna, 1933, pp. 39–40. Translated in The Philosophy of Mathematics, Jaakko Hintikka (ed.), Oxford University Press, London, 1969, pp. 128–129.
Richard Montague, ‘Syntactical Treatments of Modality, with Corollaries on Reflexion Principle and Finite Axiomatizability’, in the Proceedings of a Colloquium on Modal and Many-Valued Logics, Helsinki, 23–26 August, 1962, Acta Philosophica Fennica 16 (1963) 153–167.
Cf. Jaakko Hintikka, Knowledge and Belief, Cornell University Press, Ithaca, N.Y., 1962, Ch. 6, and (for important refinements of the view presented there) Jaakko Hintikka, The Semantics of Questions and the Questions of Semantics (forthcoming). Cf. also Chapter 7 below.
Cf., e. g., Wilfrid Sellars, ‘Some Problems About Belief’, in Words and Objections: Essays on the Work of W. V. Quine, Donald Davidson and Jaakko Hintikka (eds.), D. Reidel, Dordrecht, 1969, pp. 180–205;
Robert C. Sleigh, ‘Restricted Range in Epistemic Logic’, Journal of Philosophy 69 (1972) 67–77.
See Jaakko Hintikka, ‘Existential Presuppositions and Uniqueness Presuppositions’, in Models for Modalities, D. Reidel, Dordrecht, 1969, pp. 112–147, where these extra premisses required by EG are also generalized to more complex situations.
The reference is apparently to Jaakko Hintikka, ‘Questions about Questions’, in Semantics and Philosophy, Milton K. Munitz and Peter K. Unger (eds.), N.Y.U. Press, New York, 1974, pp. 103–158. See also the works referred to in note 17 above.
Cf. Jaakko Hintikka, Models for Modalities, D. Reidel, Dordrecht, 1969, pp. 97, 120–121, 141.
See Stig Kanger, Provability in Logic (Stockholm Studies in Philosophy, Vol. 1), Stockholm, 1957;
Stig Kanger, ‘The Morning Star Paradox’, Theoria 23 (1957) 1-11;
Stig Kanger, ‘A Note on Quantification and Modalities’, Theoria 23 (1957) 133–134;
Jaakko Hintikka, Quantifiers in Deontic Logic, Societas Scientiarum Fennica, Commentationes Humanarum Litterarum 23, no. 4, Helsinki, 1957;
Jaakko Hintikka, ‘Modality as Referential Multiplicity’, Ajatus 20 (1957) 49–64;
Marcel Guillaume, ‘Rapports entre calculs propositionnels modaux et topologie impliqués par certaines extensions de la méthode des tableaux sémantiques. Système de Feys - von Wright’, Comptes rendus des séances de l’Académie des Sciences (Paris) 246 (1958) 1140–1142;
Systeme S4 de Lewis’, ibid. 2207–2210;
Système S5 de Lewis’, ibid. 247 (1958) 1282–1283.
Cf. Quine’s review of Identity and Individuation, Milton K. Munitz (ed.), in The Journal of Philosophy 69 (1972) 488–497, especially 492–493.
See, e. g., Richard Montague, ‘Pragmatics and Intensional Logic’, Synthese 22 (1970–71) 68–94, especially p. 91; ‘On the Nature of Certain Philosophical Entities’, The Monist 53 (1969) 159–194, especially p. 164.
Jaakko Hintikka, ‘Carnap’s Semantics in Retrospect’, Synthese 25 (1973) 372–397, especially pp. 377–381, reprinted above as Chapter 5 of this volume.
Besides the papers already quoted, see Richard Montague, ‘Pragmatics’, in Contemporary Philosophy, Vol. 1, R. Klibansky (ed.), La Nuova Italia Editrice, Florence, 1968, ‘English as a Formal Language’, in Linguaggi nella società e nella technica, Edizioni de Comunità, Milan, 1970, pp. 189–223.
In case documentation is needed, the conventional strictures of textbooks and treatises against ‘the referential theory of meaning’ should be enough. Cf., e. g., William P. Alston, Philosophy of Language, Prentice-Hall, Englewood Cliffs, N.J., 1964, pp. 12–13.
Gottlob Frege, ‘Uber Sinn und Bedeutung’, Zeitschrift für Philosophie und Philosophische Kritik 100 (1892) 25–50, especially p. 26.
Cf., e. g., Quine’s use of ‘Nec’ as a “semantical” predicate in The Ways of Paradox, p. 166, or section iv of ‘Quantifiers and Propositional Attitudes’. The misleading idea that a difference in the referring expressions themselves suffices as the relevant difference between the ways in which their references are given is maintained explicitly in R. M. Martin, Logic, Language and Metaphysics, New York University Press, New York, 1971, pp. 59–60.
For instance, Frege acknowledges that two different arithmetical expressions for the same natural number, for instance 22 and 2 + 2, may have different Sinne, even though the identity of their references is of course for him a truth of logic. Cf., e. g., Gottlob Frege, Grundgesetze der Arithmetik, Vol. 1, Jena, 1893, pp. ix, 7.
See Dana Scott, ‘Advice on Modal Logic’, in Philosophical Problems in Logic, Karel Lambert (ed.), D. Reidel, Dordrecht. 1970, pp. 143–173;
cf. Richard Montague, ‘Pragmatics’, in Contemporary Philosophy La philosophie comtemporaine, R. Klibansky (ed.), La Nuova Italia Editrice, Florence. 1968, pp. 102 122;
Krister Segerberg, ‘Some Logics of Commitment and Obligation’, in Deontic Logic, Risto Hilpinen (ed.), D. Reidel, Dordrecht, 1971, pp. 148–158.
Jaakko Hintikka, ‘Surface Semantics: Definition and Its Motivation’, in Truth, Syntax, and Modality, Hugues Leblanc (ed.), North-Holland, Amsterdam, 1973, pp. 128–147;
Jaakko Hintikka and Ilkka Niiniluoto, ‘On the Surface Semantics of First-Order Proof Procedures’, Ajatus 35 (1973) 197–215. Cf. also Chapter 9 below.
Cf. Jaakko Hintikka, Models for Modalities, D. Reidel, Dordrecht, 1969, pp. 116–117;
Jaakko Hintikka, Knowledge and Belief, Cornell U.P., Ithaca, N.Y., 1962, pp. 132–136.
The reference is apparently to Jaakko Hintikka, ‘The Semantics of Modal Notions and the Indeterminacy of Ontology’, Synthese 21 (1970) 408–424: reprinted above as Chapter 2 of the present volume.
Cf. Jaakko Hintikka, Logic, Language-Games, and Information, Clarendon Press, Oxford, 1973, pp. 233–235.
Cf. David Lewis, ‘Counterpart Theory and Quantified Modal Logic’, The Journal of Philosophy 65 (1968) 113–126.
Richard C. Jeffrey, The Logic of Decision, McGraw-Hill, New York, 1965, p. 196.
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Hintikka, J. (1975). Quine on Quantifying In: A Dialogue. In: Hintikka, J. (eds) Rudolf Carnap, Logical Empiricist. Synthese Library, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1807-4_6
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