The actual logical forms corresponding to the ten interpretations of the conditional
Abstract
This paper explores the idea of a syntax of thought proposed by theories such as the one of the mental logic. Taking into account that syntax as it is described by the mental logic theory can have some problems, this paper offers a possible alternative syntax based only on conjunctions, disjunctions, and negations. This alternative syntax is mainly studied here in the case of conditional reasoning and follows the mental models theory, a framework that considers semantics to be more relevant than syntax, and that hence is, in principle, incompatible with the mental logic theory.References
Braine, M. D. S. & O’Brien, D. P. (1998a). “How to investigate mental logic and the syntax of thought”, in M. D. S.
Braine & D. P. O’Brien (Eds.), Mental Logic. Mahwah, NJ: Lawrence Erlbaum Associates, Inc., Publishers, pp. 45-61.
(1998b). “The theory of mental-propositional logic: Description and illustra- tion”, in M. D. S. Braine & D. P. O’Brien (Eds.), Mental Logic. Mahwah, NJ: Lawrence Erlbaum Associates, Inc., Publishers, pp. 79-89.
(1998c). “A theory of if: A lexical entry, reasoning program, and pragmatic principles.” in M. D. S. Braine & D. P.
O’Brien (Eds.), Mental Logic. Mahwah, NJ: Lawrence Erlbaum Associates, Inc., Publishers, pp. 199-244.
Byrne, R. M. J. & Johnson-Laird, P. N. (2009). “«If» and the problems of conditional reasoning”, in Trends in Cognitive Science, vol. 13, n. 7, pp. 282-287.
Gentzen, G. (1934). “Untersuchungen über das logische Schließen I”, in Mathematis- che Zeitschrift, vol. 39, n. 2, pp. 176-210.
(1935). “Untersuchungen über das logische Schließen II”, in Mathematische Zeitschrift, vol. 39, n. 3, pp. 405-431.
Johnson-Laird, P. N. (2010). “Against logical form”, in Psychologica Belgica, vol. 5, nn. 3/4, pp. 193-221.
(2012). “Inference with mental models”, in K. J. Holyoak & R. G. Morrison (Eds.), The Oxford Handbook of Thinking and Reasoning. New York, NY: Oxford University Press, pp. 134-145.
Johnson-Laird, P. N. & Byrne, R. M. J. (2002). “Conditionals: A theory of meaning, pragmatics, and inference”, in Psychological Review, vol. 109, n. 4, pp. 646-678.
Johnson-Laird, P. N., Khemlani, Sangeet, & Goodwin, G. P. (2015). “Logic, proba- bility, and human reasoning”, in Trends in Cognitive Sciences, vol. 19, n. 4, pp. 201-214.
Khemlani, S., Hinterecker, T., & Johnson-Laird, P. N. (2017). “The provenance of modal inference”, in G.
Gunzelmann, A. Howes, T. Tenbrink, & E. J. Davelaar (Eds.), Proceedings of the 39th Annual Conference of the Cognitive Science Society. Austin, TX: Cognitive Science Society, pp. 259-264.
Kripke, S. A. (1959). “A completeness theorem in modal logic”, in Journal of Symbolic logic, vol. 24, n. 1, pp. 1-14.
(1962). “The undecidability of monadic modal quantification theory”, in Zeits- chrift für Mathematische Logik und Grundlagen der Mathematik, n. 8, pp. 113-116.
(1963a). “Semantical considerations in modal logic”, in Acta Philosophica Fenni- ca, n. 16, pp. 83-94.
(1963b). “Semantical analysis of modal logic I: Normal modal propositional calculi”, in Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, n. 9, pp. 67-96.
(1965). “Semantical analysis of modal logic II: Non-normal modal proposi- tional calculi”, in J. W. Addison, L. Henkin, & A. Tarski (Eds.), The Theory of Models: Proceedings of the 1963 International Symposium at Berkeley. Amsterdam, The Netherlands: North-Holland Publishing Co., pp. 206-220.
López-Astorga, M. (2016). “Logic, pragmatics, and types of conditionals”, in Frontiers of Philosophy in China, vol. 11, n. 2, pp. 279-297.
(2017a). “Mental models are compatible with logical forms”, in A. López- Varela Azcárate (Ed.), Interdisciplinary Approaches to Semiotics. Rijeka, Croatia: InTech., pp. 31-42.
(2017b). “An essentially syntactic and formal theory is still possible”, in Prag- malingüística, n. 25, pp. 330-344.
Orenes, I. & Johnson-Laird, P. N. (2012). “Logic, models, and paradoxical inferen- ces”, in Mind & Language, vol. 27, n. 4, pp. 357-377.
Quelhas, A. C., Johnson-Laird, P. N., & Juhos, Csongor. (2010). “The modulation of conditional assertions and its effects on reasoning”, in Quarterly Journal of Experimental Psychology, n. 63, pp. 1716-1739.