×

zbMATH — the first resource for mathematics

Intuitionistic truth. (English) Zbl 0574.03047
The paper considers formally slight variants of familiar logical laws that Kripke, Beth and others have related to intuitionistic truth. The author notes that they also hold for other kinds of ’epistemic accessibility’ (p. 210), for example, d-verifiability on p. 198. In the tradition of the socalled theory of meaning the author stresses, on p. 191, that ’the whole realm of truth’ is considered, and not merely mathematical statements. But he fails to stress that - as long as only familiar logical languages are considered, as in the present paper - this is a distinction without any difference (in validity).
Reviewer: G.Kreisel

MSC:
03F50 Metamathematics of constructive systems
PDF BibTeX Cite
Full Text: DOI
References:
[1] Beth, E. W., The Foundations of Mathematics, North-Holland, Amsterdam (1959). · Zbl 0085.24104
[2] Brouwer, L. E. J., Collected Works, vol. 1: Philosophy and Mathematics, ed. by A.Heyting, North-Holland, Amsterdam (1975). · Zbl 0311.01021
[3] Brouwer, L. E. J., Cambridge Lectures on Intuitionism, ed. by D.vanDalen, Cambridge Univ. Press, Cambridge (1981). · Zbl 0476.03056
[4] Dummett, M., Elements of Intuitionism, Oxford Univ. press, Oxford (1977). · Zbl 0358.02032
[5] Dummett, M., Truth and Other Enigmas, Duckworth, London (1978).
[6] Fitch, F. B., ?A logical analysis of some value concepts?, Journal of Symbolic Logic 28 (1963), 135-142. · Zbl 0943.03599
[7] Hart, W. D., ?Access and inference?, Proceedings of the Aristotelian Society, Supplementary vol. 53, pp. 153-165 (1979).
[8] Heyting, A., Intuitionism: An Introduction, North-Holland Publ. Co., Amsterdam (1956). · Zbl 0070.00801
[9] Kripke, S. A., ?Semantical analysis of intuitionistic logic I?. in J. N.Crossley and M. A. E.Dummett (eds.), Formal Systems and Recursive Functions, North-Holland, Amsterdam, pp. 92-130 (1965). · Zbl 0137.00702
[10] Mackie, J.L., ?Truth and knowability?, Analysis 40 (1980), 90-92.
[11] Prawitz, D., ?Meaning and proofs: on the conflict between classical and intuitionistic logic?, Theoria 43 (1977) 2-40. · Zbl 0361.02008
[12] Prawitz, D., ?Intuitionistic logic: a philosophical challenge?, in G. H. v.Wright (ed.), Logic and Philosophy, Martinus Nijhoff, The Hague, pp. 1-10 (1980).
[13] Williamson, T., ?Intuitionism disproved??, Analysis 42 (1982), 203-207.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.