What is a genuine intuitionistic notion of falsity?
DOI:
https://doi.org/10.12775/LLP.2012.001Keywords
intuitionism, truth, falsity, negationAbstract
I highlight the importance of the notion of falsity for a semantical consideration of intuitionistic logic. One can find two principal (and non-equivalent) versions of such a notion in the literature, namely, falsity as non-truth and falsity as truth of a negative proposition. I argue in favor of the first version as the genuine intuitionistic notion of falsity.
References
Brouwer, L.E.J., “The effect of intuitionism on classical algebra of logic”, Proceedings of the Royal Irish Academy Section A 57 (1955): 113–116.
Dummett, M., Elements of Intuitionism, Oxford: Clarendon Press, 1977.
Dunn, J.M., “Intuitive semantics for first-degree entailment and “coupled trees””, Philosophical Studies 29 (1976): 149–168.
Frege, G., “Logik”, pages 35–73 in: Frege, G., Schriften zur Logik und Sprachphilosophie, Hamburg: Felix Meiner Verlag, 1990.
Gödel, K., “Zum intuitionistischen Aussagenkalkul”, Anzeiger Akademie der Wissenschaften Wien (Math.-naturwiss. Klasse) 69 (1932): 65–66.
Gottwald, S., A Treatise on Many-valued Logic, Baldock: Research Studies Press, 2001.
Gottwald, S., “Many-valued logic”, The Stanford Encyclopedia of Philosophy (Spring 2010 Edition), E.N. Zalta (ed.). http://plato.stanford.edu/archives/spr2010/entries/logic-manyvalued
Grzegorczyk, A., “A philosophically plausible formal interpretation of intuitionistic logic”, Indagationes Mathematicae 26 (1964): 596–601.
Heyting, A., “Sur la logique intuitionniste”, Acadèmie Royale de Belgique, Bulletin de la Classe des Sciences 16 (1930): 957–963. English translation in [13, p. 306–310].
Heyting, A., Intuitionism: An Introduction, Amsterdam: North-Holland, 1956.
Jaśkowski, S., “Recherches sur le système de la logique intuitioniste”, Actes du Congrès Internationale de Philosophie Scientifique 1936, 6: 58–61. Englich translation: Studia Logica 34 (1975): 117–120.
Kripke, S., “Semantical analysis of intuitionistic logic I”, pages 92–130 in: Formal Systems and Recursive Functions, ed. by J.N. Crossley and M.A. Dummett, Amsterdam: North-Holland, 1965.
Mancosu, P., From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s, Oxford: Oxford University Press, 1998.
Martin-Löf, P., “A path from logic to metaphysics”, pages 141–149 in: Atti del Congresso ’Nuovi problemi della logica e della filosofia della scienza’, G. Sambin, G. Corsi (eds.), Viareggio, 8–13 gennaio 1990, vol. II, CLUEB, Bologna, 1991.
Martino, E., and G. Usberti, “Temporal and atemporal truth in intuitionistic mathematics”, Topoi 13 (1994): 83–92.
Nelson, D., “Constructible falsity”, Journal of Symbolic Logic 14 (1949): 16–26.
Prawitz, D., “Intuitionistic logic: a philosophical challenge”, pagess 1–10 in: Logic and Philosophy, G.H.v. Wright (ed.), Martinus Nijhoff, The Hague, 1980.
Raatikainen, P., “Conceptions of truth in intuitionism”, History and Philosophy of Logic 25 (2004): 131–145.
Rabinowicz, W., “Intuitionistic truth”, Journal of Philosophical Logic 14, (1985): 191–228.
Routley, R., “The American plan completed: Alternative classical-style semantics, without stars, for relevant and paraconsistent logics”, Studia Logica 43 (1984): 131–158.
Shramko, Y., “A philosophicallyplausible modified Grzegorczyk semantics for first-degree intuitionistic entailment”, Logique et Analyse 161–162–163 (1998): 167–188.
Shramko, Y., Intuitionismus und Relevanz, Berlin: Logos-Verlag, 1999.
Shramko, Y., “American plan for intuitionistic logic 1: an intuitive background”, The Logica Yearbook 1999, Timothy Childers (ed.), Prague: Filosophia, 2000.
Shramko, Y., “American plan for intuitionistic logic 2: generalized intuitionistic models” (in Russian), Logical Studies (Online Journal) 5 (2000). http://logic.ru/en/node/160
Shramko, Y., J.M. Dunn, and T. Takenaka, “The trilaticce of constructive truth values”, Journal of Logic and Computation 11 (2001): 761–788.
Shramko, Y., and H. Wansing, “Truth values”, The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), E.N. Zalta (ed.). http://plato.stanford.edu/archives/sum2010/entries/truth-values
Suszko, R., “The Fregean axiom and Polish mathematical logic in the 1920’s”, Studia Logica 36 (1977): 373–380.
Thomason, R., “A semantical study of constructive falsity”, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 15 (1969): 247–257.
Topoi. An International Review of Philosophy, vol. 13, no. 2, 1994.
Wansing, H., “A non-inferentialist, anti-realistic conception of logical truth and falsity”, to appear in: Topoi, 2011.
Wansing, H., and Y. Shramko, “Suszko’s Thesis, inferential many-valuedness, and the notion of a logical system”, Studia Logica 88 (2008): 405–429.
Wansing H., Shramko, Y., “Harmonious many-valued propositional logics and the logic of computer networks”, pages 491–516 in: Dialogues, Logics and Other Strange Things. Essays in Honour of Shahid Rahman, C. Degremont, L. Keiff and H. Rueckert (eds.), College Publications, 2008.
Downloads
Published
How to Cite
Issue
Section
Stats
Number of views and downloads: 330
Number of citations: 3
