Abstract
This chapter is concerned with the relation between the intuitive notions of truth and evidence or truth-recognition. While the intuitionists grant no space to the (intuitive) notion of truth of a mathematical sentence (Sect. 6.1), according to many supporters of anti-realist theories of meaning, in particular neo-verificationist ones, the intuitionistic attitude is unacceptable because, on the one hand, it is highly counterintuitive, and on the other hand some notion of truth, irreducible to proof possession, cannot be avoided even within an anti-realist conceptual framework. In Sect. 6.2 two arguments for the necessity of a distinction between truth and truth-recognition are analyzed and criticized: Dummett’s argument based on the Paradox of Inference, And Prawitz’s considerations concerning the content of assertions. Sect. 6.3 discusses the neo-verificationist debate between temporalist and atemporalist conceptions of truth.
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Notes
- 1.
- 2.
I am assuming here that what makes of a predicate a truth-predicate is the validity of Tarski’s equivalences “True(N) iff t’, where N is the name of a sentence of the object language and t the translation of that sentence into the metalanguage. I shall argue for this claim and discuss its significance in Chap. 9.
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- 4.
Actually, in Prawitz’s definition the clauses for the constants different from → and ∀ require that the subproofs are canonical; but, as Prawitz remarks (fn. 9), this requirement can be left out.
- 5.
Of course I am not speaking of hypothetical evidence, which is recognized by intuitionists, but of indirect evidence.
- 6.
With “conceptual necessity” I mean a principle whose validity can be extracted from the sole analysis of the concepts involved.
- 7.
This is not to say that a distinction on different grounds is not possible.
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- 9.
The problem consists in the fact, pointed out by Dummett himself, that, under the identification of truth with actual possession of a proof (or of a verification), α∨β may be sometimes true without either α being true or β being true, i.e. that temporal truth does not commute with disjunction. I shall come back to this point in Chap. 9.
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- 11.
See Chap. 2, (9).
- 12.
«Il serait erroné de dire que le principe du tiers exclu soit faux car cela signifierait qu’il impliquerait contradiction. Or il n’est pas contradictoire que [“Il existe un nombre exceptionnel” (g.u.)] ou [“Il n’existe pas de nombre exceptionnel” (g.u.)] soit vrai; nous avons seulement constaté qu’en l’état actuel de la science il n’y a aucune raison pour affirmer l’un ou l’autre. Cette constatation ne constitue pas un théorème de la logique, tout comme la constatation qu’un certain problème mathématique n’est pas résolu, ne constitue pas un théorème mathématique.» Heyting calls “exceptional” a number n such that n – 1, n is not prime and n is not the sum of two or three primes.
References
Brandom, R. (1976). Truth and assertibility. The Journal of Philosophy, 73(6), 137–149.
Brouwer, L. E. J. (1949). Consciousness, philosophy and mathematics. In Proceedings of 10th international congress on philosophy, Amsterdam, 1235–1249. (Now in Brouwer 1975, 480–494).
Brouwer, L. E. J. (1975). Collected works, vol. I: Philosophy and foundations of mathematics. In A. Heyting (Ed.). North Holland.
Cohen, M. R., & Nagel, E. (1934). An introduction to logic and scientific method. Routledge and Kegan Paul.
Dales, H. G. & Oliveri, G. (Eds.). (1998). Truth in mathematics. Oxford University Press.
Dummett, M. (1973). Frege: Philosophy of language. Duckworth.
Dummett, M. (1975). The justification of deduction. In Proceedings of the British Academy, LIX, 201–231, (pp. 290–318). (Now in Dummett (1978).)
Dummett, M. (1978). Truth and other enigmas. Duckworth.
Dummett, M. (1982). Realism. Synthese, 52(1), 55–112. (Reprinted in Dummett (1993) (pp. 230–276)).
Dummett, M. (1993). The seas of language. Oxford University Press.
Dummett, M. (1998). Truth from the constructive standpoint. Theoria, LXIV, 122–138.
Dummett, M. (2000). Elements of intuitionism, Clarendon Press. (First Edition 1977).
Frege, G. (1918). Thoughts. In Frege (1984) (pp. 351–372).
Frege, G. (1984). Collected papers on mathematics, logic, and philosophy. In B. Mc Guinness (Ed.). Blackwell.
Heyting, A. (1931). Die intuitionistische Grundlegung der Mathematik. Erkenntnis, 2, 106–15. (Engl. tr. The intuitionist foundations of mathematics. In P. Benacerraf & H. Putnam (Eds.), Philosophy of mathematics (pp. 52–61). Prentice-Hall, 19832.)
Heyting, A. (1956). La conception intuitionniste de la logique. Les Études Philosophiques, 2, 226–233.
Heyting, A. (1958). On truth in mathematics. Verslag van de plechtige viering van het honderdvijftigjarig bestaan der Koninklijke Nederlandse Akademie van Wetenschappen (pp. 277–279). North Holland.
Martin-Löf, P. (1985). On the meaning and justification of logical laws. In C. Bernardi & P. Pagli (Eds.), Atti degli incontri di logica matematica, vol. II (pp. 291–340). Università di Siena. (Reprinted in Nordic Journal of Philosophical Logic, 1(1), 1996, 11–60).
Martin-Löf, P. (1991). A path from logic to metaphysics. In G. Sambin & G. Corsi (Eds.), Atti del congresso Nuovi problemi della Logica e della Filosofia della Scienza, vol. 2 (pp. 141–149). CLUEB.
Martínez, C., Rivas, U., & Villegas-Forero, L. (Eds.). (1998). Truth in perspective. Ashgate.
Martino, E. & Usberti G. (1994). Temporal and atemporal truth in intuitionistic mathematics. Topoi, 13(2), 83–92. (Now in Martino (2018) (pp. 97–111)).
McGuinness, B. & Oliveri, G. (Eds.). (1994). The philosophy of Michael Dummett. Kluwer.
Prawitz, D. (1980). Intuitionistic logic: A philosophical challenge. In G. H. von Wright (Ed.), Logic and philosophy (pp. 1–10). Nijhoff.
Prawitz, D. (1987). Dummett on a theory of meaning and its impact on logic. In B. Taylor (Ed.), Michael Dummett: Contributions to philosophy (pp. 117–165). Nijhoff.
Prawitz, D. (1994). Meaning theory and anti-realism. In McGuinness & Oliveri (1994) (pp. 79–89).
Prawitz, D. (1998a). Truth and objectivity from a verificationist point of view. In Dales & Oliveri (1998) (pp. 41–51).
Prawitz, D. (1998b). Truth from a constructive perspective. In Martínez, Rivas & Villegas-Forero (1998) (pp. 23–35).
Prawitz, D. (1998c). Comments on the papers. Theoria, LXIV, 283–337.
Prawitz, D. (2005). Logical consequence from a constructivist point of view. In S. Shapiro (Ed.), The Oxford handbook of philosophy of mathematics and logic (pp. 671–695). Oxford University Press.
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Usberti, G. (2023). Truth and Truth-Recognition. In: Meaning and Justification. An Internalist Theory of Meaning. Logic, Epistemology, and the Unity of Science, vol 59. Springer, Cham. https://doi.org/10.1007/978-3-031-24605-0_6
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