Abstract
In this paper, I shall discuss one singularly important problem. It is a generalization of the question I am using as the title of the paper. It has probably played a more important role in the philosophy of language and philosophical analysis in general in the last hundred-odd years than any other single issue. It is a problem which would have delighted Hegel. For it has remained almost completely implicit in the actual philosophical literature. Its general significance still is virtually unacknowledged. Only now, in the evening twilight of its career, has this problem followed the example of Minerva’s owl and begun to rise to the consciousness of philosophers. One does not have to be a Hegelian, however, to believe that this tacit role of my theme problem testifies to its fundamental significance for twentieth-century philosophy. Another variety of idealistic philosophers might, for instance, compare it to a Collingwoodian “absolute presupposition” characteristic of the period in philosophy which began with Frege — or perhaps with Kant — and which is only now ending.1 Or perhaps the philosophy of this period is, rather, returning to its own ultimate sources in Kant’s transcendental method.
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Notes
Cf. R.G. Collingwood, Essays on Metaphysics (Oxford: Clarendon Press, 1940), pp. 21–48 and passim.
This contrast was introduced into recent discussion by Jean van Heijenoort in his paper, “Logic as Language and Logic as Calculus,” Synthese 17 (1967) 324–30. Because of its nature as an unspoken presupposition, the contrast has not received much conscious attention. Perhaps the most extended discussions of the distinction are Chapter 1 of Merrill B. Hintikka and Jaakko Hintikka, Investigating Wittgenstein (Oxford: Basil Blackwell, 1986); and Jaakko Hintikka, “On the Development of the Model-Theoretical Tradition in Logical Theory,” Synthese (forthcoming). Recently, the role of the contrast in the phenomenological-hermeneutical tradition has also begun to be recognized; see Martin Kusch, Sign vs. Picture (forthcoming), Martin Kusch, Language Is the Universal Medium: Gadamer’s Philosophy of Language (Oulu: Oulun yliopiston historian laitos, 1987); and Martin Kusch, “Husserl and Heidegger on Meaning,” forthcoming.
Cf. R.G. Collingwood, pp. 23–33; Autobiography (Oxford: Clarendon Press, 1939), pp. 29–43.
See van Heijenoort, pp. 32430.
See Peter Hylton, “Russell’s Substitutional Theory,” Synthese 45 (1980): 1–31.
See Hintikka and Hintikka, chap. 1.
Cf. Jaakko Hintikka, “Ludwig’s Apple Tree: Evidence Concerning the Philosophical Relations of Wittgenstein and the Vienna Circle” (forthcoming).
Cf. my contribution to the 1988 Symposium on W.V. Quine (St. Louis), forthcoming.
On the development of the model-theoretical (“language as calculus”) tradition, see Jaakko Hintikka, “On the Development of the Model-Theoretical Tradition in Logical Theory,” and Warren Goldfarb, “Logic in the Twenties: the Nature of the Quantifier,” Journal of Symbolic Logic 44 (1979): 351–68.
Cf. here van Heijenoort, pp. 324–30.
MS no. 109 (von Wright), p. 1%.
The quote is from Ludwig Wittgenstein, Culture and Value (Oxford: Basil Blackwell, 1980), p. 10. I have modified Peter Winch’s translation which waters down Wittgenstein’s point.
Gottlob Frege, “Logik,” in Schriften zur Logik und Sprachphilosphie (Hamburg: Felix Meiner, 1971), P. 39.
Gottlob Frege, p. 35.
Cf. Hintikka and Hintikka, Chap. 1, sec. 5.
Cf. Hintikka and Hintikka, Chap. 4, sec. 9.
This assumption or its rejection may have important implications for the prospects of developing formal systems of alethic modal logic in the first place. See here Jaakko Hintikka, “Is Alethic Modal Logic Possible?” Acta Philosophica Fennica 35 (1982): 89–105.
Cf. Jaakko Hintikka, “`Is,’ Semantical Games and Semantical Relativity,” Journal of Philosophical Logic 8 (1979): 433–68.
Hintikka and Hintikka, chap. 1.
Letter to Schlick, dated August 8, 1932. Cf. Jaakko Hintikka, “Ludwig’s Apple Tree,” sec. 11.
Cf. especially W.V. Quine, Word and Object (Cambridge, MA: MIT Press, 1960) and Ontological Relativity and Other Essays (NY: Columbia University Press, 1969).
Cf. Jerry A. Fodor, The Language of Thought (NY: Thomas Y. Crowell Co., 1975).
See, e.g., Martin Heidegger, Sein and Zeit, passim, and Unterwegs zur Sprache (Günther Neske, 1959); and cf. Martin Kusch’s book mentioned in note 2 above.
Cf. Jaakko Hintikka, “On the Development of the Model-Theoretical Tradition.”
Interestingly, although Tarski used model-theoretical conceptualizations freely in his studies of the semantics of formal languages including the concept of truth, he believed that the semantics of our actual ordinary (colloquial) language is ineffable. See Alfred Tarski, Logic,Semantics, Metamathematics (Oxford: Clarendon Press, 1956), pp. 164–5.
Gnindlagen der Geometrie, originally 1899, many subsequent editions.
Bertrand Russell, Introduction to Mathematical Philosophy (London: Allen & Unwin, 1919), p. 169.
Cf. Kurt Gödel, Collected Papers, Vol. 1 (Oxford: Clarendon Press, 1986); John W. Dawson, Jr., “The Reception of Gödel’s Incompleteness Theorems,” in PSA 1984, Vol. 2 (East Lansing, MI: Philosophy of Science Association, 1985).
Alfred Tarski, “Der Wahrheitsbegriff in den formalisierten Sprachen,” Studia Philosophica 1 (1936): 261–405; included in English translation in Tarski, Logic, Semantics,Metamathematics, pp. 152–278.
The earliest work in this direction included Stig Kanger, Provability in Logic (Stockholm; Almqvist and Wiksell, 1957), and Jaakko Hintikka, “Quantifiers in Deontic LoBe” Societas Scientianun Fennica, Commentationes Humananun Litterarum, Vol. 23 (1958), No. 4. (Appeared in 1957.)
The most fully worked-out version of possible-worlds semantics in Montague semantics; see Richmond Thomason, ed., Formal Philosophy: Selected Papers of Richard Montague (New Haven: Yale University Press, 1974), and cf. Barbara H. Partee, ed., Montague Grammar (NY: Academic Press, 1976).
Veikko Rantala, “Urn Models: A New Kind of Non-Standard Model for First-Order Logic,” Journal of Philosophical Logic 4 (1975): 455–74. Cf. also Jaakko Hintikka, “Impossible Possible Worlds Vindicated,” Journal of Philosophical Logic 4 (1975): 475–84.
This is, e.g., in effect what happens in the so-called relevance logic.
My work in this direction is still in progress. For an indication of its philosophical motivation, see, “Is There Completeness in Mathematics After Gödel?” in Philosophical Topics 17 (1989): 69–90.
See W.V. Quine, “On What There Is,” in From a Logical Point of View (Cambridge, MA: Harvard University Press, 1953). Cf. Warren Goldfarb, 351–68.
For the following, cf. also Jaakko Hintikka, “On the Development of the Model-Theoretical Tradition.”
See Jaakko Hintikka, The Game of Language (Dordrecht: D. Reidel, 1983); Jaakko Hintikka and Jack Kulas,Anaphora and Definite Descriptions: Two Applications of Game-Theoretical Semantics (Dordrecht: D. Reidel, 1985); Esa Saarinen, ed., Game-Theoretical Semantics (Dordrecht: D. Reidel, 1979).
Leon Henkin, “Completeness in the Theory of Types,” Journal of Symbolic Logic 15 (1950): 81–91. (For a correction, see Peter Andrews, “General Models and Extensionality,” Journal of Symbolic Logic 37 (1972): 395–97.) Cf. also Jaakko Hintikka, “Is Alethic Modal Logic Possible?” 89–105.
Cf. Jean van Heijenoort, ed., From Frege to Gödel: Source Book in Mathematical Logic (Cambridge, MA: Harvard University Press, 1967), chapter on Lowenheim.
Kurt Gödel, “Úber eine bisher noch nicht benützte Erweiterung des finiten Standpunktes,” Logica. Studia Paul Bemays dedicata (Neuchâtel: Editions Griffon, 1959), pp. 76–83; in English in the Journal of Philosophical Logic 9 (1980): 133–42.
There are, however, other kinds of constructivistic interpretations of elementary logic and arithmetic which make the axiom of choice false.
Bertrand Russell, “Knowledge by Acquaintance and Knowledge by Description,” in Mysticism and Logic (London: Longmans, London, 1918). Cf. Jaakko Hintikka, “Knowledge by Acquaintance,” in Bertrand Russell: A Collection of Critical Essays, ed. David Pears (Garden City, NJ: Doubleday, 1972), pp. 52–79.
This judgment is undoubtedly too harsh for one can find in Wittgenstein’s philosophy of mathematics several ideas which could be developed and related to developments in actual logical and foundational theorizing. Cf. Jaakko Hintikka, “’Die Wende der Philosophie’: Wittgenstein’s New Logic of 1928,” Proceedings of the 12th International Wittgenstein Symposium, eds. Ota Weinberger et al. (Wien: Hölder-Pichler-Tempsky, 1988): 380–396.
Alfred Tarski, “Der Wahrheitsbegriff,” 261–405.
Cf. Jaakko Hintikka, “Is Alethic Modal Logic Possible?” 85–105.
Cf. Jaakko Hintikka, “Das Paradox transzendentaler Erkenntnis”, in Bedingungen der Möglichkeit: `Transcendental Arguments’ und transzendentales Denken, eds. E. Schaper and W. Vossenkuhl (1984), pp. 12349; and “Wittgenstein’s Semantical Kantianism,” in Ethics: Proceedings of the Fifth International Wittgenstein Symposium, eds. E. Morscher and R. Stranzinger, (Vienna: Hölder-Pichler-Tempsky, 1981), pp. 375–90.
The semantical games which give our sentences their meanings are of the character of “games” of verification and falsification. Cf. note 37 above.
Cf. “Das Paradox,” pp. 123–49, and “Information, Deduction, and the A Priori,” Nous 4 (1970): pp. 135–52.
This was called one of the “main theses” of logical empiricism by G.H. von Wright in Den logiska empirismen (Helsingfors, 1944). Cf. here Jaakko Hintikka, “G.H. von Wright on Logical Truth,” in The Philosophy of G. H. von Wright, eds. P. A. Schilpp and L. E. Hahn (La Salle, IU.: Open Court, 1989): 517–537.
Cf. the works referred to in notes 46 and 49 above.
Cf. “’Is,’ Semantical Games and Semantical Relativity,” 433–68, and The Game of Language.
Hilary Putnam, “Models and Reality,” Journal of Symbolic Logic Vol. 45 (1980): pp. 464–82.
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Hintikka, J. (1997). Is Truth Ineffable?. In: Lingua Universalis vs. Calculus Ratiocinator. Jaakko Hintikka Selected Papers, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8601-6_2
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