Abstract
This paper is a second half of a longer argument.1 In its predecessor,2 I argued that Kant saw the gist of the mathematical method in what essentially amounts to instantiation rules, i.e., what he himself characterized as arguing in terms of particular representatives of general concepts.3 But when can such an anticipatory introduction of representatives of general concepts yield synthetic knowledge a priori? Kant’s transcendental viewpoint commits him to answering: Only in so far as we have ourselves put the relations and properties we are arguing about into objects. Then our mathematical knowledge does not pertain to things, but only to the structure of our processes of coming to know them.
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Notes
This argument is presented in my paper, “Das Paradox transzendentaler Erkenntnis”, in W. Vossenkuhl and E. Schaper, (ed.), Die Bedingungen der Möglichkeit, Klett-Cotta Verlag, Stuttgart, 1984, pp. 123–149. The present paper is the English version of the second half of that paper.
This predecessor is “Kant’s Transcendental Turn and His Theory of Mathematics”, Topoi 3 (1984), pp. 99–108. It represents an English version of the first half of the paper mentioned in note 1.
See here my earlier work on Kant. Most of it is collected either in Logic, Language-Games, and Information, Clarendon Press, Oxford, 1973, and Knowledge and the Known, D. Reidel, Dordrecht, 1974 but see also “On Kant’s Notion of Intuition (Anschauung)”, in T. Penelhum and J. J. MacIntosh (eds.), Kant’s First Critique, Wadsworth, Belmont, CA, 1969, pp. 38–53, “Kantian Intuitions”, Inquiry 15 (1972), pp. 341–345, and “Kant’s Theory of Mathematics Revisited”, Philosophical Topics 12, 2 (1981), pp. 201–215.
Op. cit., note 2 above and “Semantical Games and Transcendental Arguments”, in E. M. Barth and J. L. Martens (eds.), Argumentation: Approaches to Theory Formation, Benjamins, Amsterdam, 1982, pp. 77–91.
For this theory, see Esa Saarinen (ed.), Game-Theoretical Semantics, D. Reidel, Dordrecht, 1979
Jaakko Hintikka, The Game of Language, D. Reidel, Dordrecht, 1983
Jaakko Hintikka and Jack Kulas, Anaphora and Definite Descriptions: Two Applications of Game-Theoretical Semantics, D. Reidel, Dordrecht, 1985.
On the subject of individuation and identification, see Jaakko Hintikka and Merrill B. Hintikka, “Towards a General Theory of Individuation and Identification,” in W. Leinfellner et al. (eds.), Language and Ontology: Proceedings of the Sixth International Wittgenstein Symposium, Hölder-Pichler-Tempsky, Vienna, 1982, pp. 137–151.
See Phänomenologie des Geistes, Introduction to Part I, sec. 73, pp. 3–5 of the 1807 edition; pp. 62–63 of the Hoffmeister edition, Felix Meiner, Hamburg, 1952.
See Juha Manninen, “Tietokyky mittauslaitteena” (in Finnish), in his book Dialektiikan ydin, Pohjoinen, Oulu, 1987.
See Jaakko Hintikka, “Wittgenstein’s Semantical Kantianism”, in Edgar Morscher and Rudolf Stranzinger (eds.), Proceedings of the Fifth International Wittgenstein Symposium, Hölder-Pichler-Tempsky, Vienna, 1981, pp. 375–390.
Note 10 above, and cf. also my paper, “Semantics: A Revolt Against Frege,” in G. Flöistad (ed.), Contemporary Philosophy: A New Survey, vol. 1, Martinus Nijhoff, The Hague, 1981, pp. 57–82.
Ludwig Wittgenstein, Vermischte Bemerkungen, Suhrkamp, Frankfurt am Main, 1977.
I have departed here from the translation of Peter Winch (see Ludwig Wittgenstein, Culture and Value, The University of Chicago Press, 1980, p. 10): “This has to do with the Kantian solution of the problem of philosophy”. This is far weaker than Wittgenstein’s point, which is not just that we are here dealing with Kant’s solution, but that we have the Kantian solution right here.
See his Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie, Halle, 1913, See. 144, p. 298 of the original, and cf. Sec. 149, p. 311 of the original.
Op. cit. Sec. 45, p. 84 of the original, and Sec. 47, pp. 88–89.
Bertrand Russell, “Introduction”, in Ludwig Wittgenstein, Tractatus Logico-Philosophicus, Kegan Paul, London, 1922.
Cf. Alfred Tarski, “Einige methodologische Untersuchungen uber die Definierbarkeit der Begriffe”, Erkenntnis 5 (1935–36), pp. 80–100
English translation in Alfred Tarski, Logic, Semantics, Metamathematics, Clarendon Press, Oxford, 1956, pp. 296–319.
Charles Scribner’s Sons, New York, 1929.
Cf. here Jaakko Hintikka, “Information, Deduction, and the ‘a prior’” in Logic, Language-Games, and Information (note 3 above).
Cf. Jaakko Hintikka, “Impossible Possible Worlds Vindicated”, in Saarinen (ed.), note 5 above.
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Hintikka, J. (1989). The Paradox of Transcendental Knowledge. In: Brown, J.R., Mittelstrass, J. (eds) An Intimate Relation. Boston Studies in the Philosophy of Science, vol 116. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2327-0_12
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