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AN EXPRESSIVIST ANALYSIS OF THE INDICATIVE CONDITIONAL WITH A RESTRICTOR SEMANTICS

Part of: Philosophical aspects of logic and foundations General and miscellaneous specific topics

Published online by Cambridge University Press:  29 June 2020

JOHN CANTWELL
JOHN CANTWELL*
Affiliation:
DIVISION OF PHILOSOPHY ROYAL INSTITUTE OF TECHNOLOGY (KTH) TEKNIKRINGEN 76 100 44STOCKHOLM, SWEDENE-mail: [email protected]
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Abstract

A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of ‘global’ expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic (negation, disjunction, etc.) and so allows the conditional to embed in arbitrarily complex sentences (thus avoiding the Frege–Geach problem). The expressivist framework is semantically characterized in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed ICL (‘Indicative Conditional Logic’). The expressivist framework extends the AGM (after Alchourron, Gärdenfors, Makinson) framework for belief revision and so provides a categorical (‘yes’–‘no’) epistemology for conditionals that complements McGee’s probabilistic framework while drawing on the same semantics. The result is an account of the semantics and acceptability conditions of the indicative conditional that fits well with the linguistic data (as pooled by linguists and from psychological experiments) while integrating both expressivist and semanticist perspectives.

Keywords

global expressivismconditionalsindicative conditionalsdynamic semanticsrestrictor semantics

MSC classification

Primary: 03A05: Philosophical and critical
Secondary: 00A30: Philosophy of mathematics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 14 , Issue 2 , June 2021 , pp. 487 - 530
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Copyright
© Association for Symbolic Logic, 2020

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References

BIBLIOGRAPHY

Adams, E. W. (1975). The Logic of Conditionals. Dordrecht: Reidel.CrossRefGoogle Scholar
Alchourrón, C., Gärdenfors, P., & Makinson, D.. (1985). On the logic of theory change: partial meet functions for contraction and revision. Journal of Symbolic Logic, 50, 510–530.CrossRefGoogle Scholar
Arló-Costa, H. (1999a). Belief revision conditionals. Annals of Pure and Applied Logic, 96, 3–28.CrossRefGoogle Scholar
Arló-Costa, H. (1999b). Belief revision conditionals: basic iterated systems. Annals of Pure and Applied Logic, 96, 3–28.CrossRefGoogle Scholar
Arló-Costa, H. & Levi, I.. (1996). Two notions of epistemic validity. Synthese, 109, 217–262.CrossRefGoogle Scholar
Barrouillet, P. & Gauffroy, C.. (2008). Mental models and the suppositional account of conditionals. Psychological Review, 115(3), 760–772.CrossRefGoogle ScholarPubMed
Barrouillet, P., Grosset, N., & Lecas, J.. (2000). Conditional reasoning by mental models: chronometric and developmental evidence. Cognition, 75, 237–266.CrossRefGoogle ScholarPubMed
Bendall, K. (1979). Negation as a sign of negative judgement. Notre Dame Journal of Formal Logic, 20, 68–76.CrossRefGoogle Scholar
Bennett, J. F. (2003). A Philosophical Guide to Conditionals. Oxford: Oxford University press.CrossRefGoogle Scholar
Brandom, R. (1994). Making it Explicit. Cambridge, MA: Harvard University Press.Google Scholar
Cantwell, J. (2008). Changing the modal context. Theoria, 74(4), 331–347.CrossRefGoogle Scholar
Cantwell, J. (2014). Unity and autonomy in expressivist logic. Dialectica, 68(3), 443–457.CrossRefGoogle Scholar
Cantwell, J. (2015). An expressivist bilateral meaning-is-use analysis of classical propositional logic. Journal of Logic, Language and Information, 24(1), 27–51.CrossRefGoogle Scholar
Dickie, I. (2010). Negation, anti-realism and the denial defence. Philosophical Studies, 60(24), 508–531.Google Scholar
Douven, I. (2015). The Epistemology of Indicative Conditionals. Cambridge: Cambridge University Press.Google Scholar
Douven, I. & Dietz, R.. (2011). A puzzle about Stalnaker’s hypothesis. Topoi, 30, 31–37.CrossRefGoogle Scholar
Douven, I. & Verbrugge, S.. (2010). The Adams family. Cognition, 117, 302–318.CrossRefGoogle ScholarPubMed
Edgington, D. (1995). On conditionals. Mind, 104, 235–329.CrossRefGoogle Scholar
Evans, J., Over, D., & Handley, S.. (2003). A theory of hypothetical thinking. In Hardman, D. & Maachi, L., editors. Thinking: Psychological Perspectives on Reasoning and Decision Making. Chichester: Wiley, pp. 3–22.Google Scholar
Fitelson, B. (2015). The strongest possible Lewisian triviality result. Thought, 4(2), 69–74.Google Scholar
Gärdenfors, P. (1986). Belief revision and the Ramsey Test for conditionals. Philosophical Review, 95, 81–93.CrossRefGoogle Scholar
Gärdenfors, P. (1988). Knowledge In Flux. Cambridge, MA: MIT press.Google Scholar
Gibbard, A. (1981). Two recent theories of conditionals. In Harper, S. & Pearce, S., editors. Ifs. Dordrecht: Reidel, pp. 211–247.Google Scholar
Gillies, A. (2009). On truth-conditions for If (but not quite only if). Philosophical Review, 118, 325–249.CrossRefGoogle Scholar
Gillies, A. S. (2018). Updating data semantics. Mind, 129, 1.CrossRefGoogle Scholar
Giordano, L., Gliozzi, V., & Olivetti, N.. (2005). Weak AGM postulates and strong Ramsey Test: a logical formalization. Artificial Intelligence, 168, 1–37.CrossRefGoogle Scholar
Grice, P. (1989). Studies in the Way of Words. Cambridge, MA: Harvard University Press.Google Scholar
Groenendijk, J. & Stockhof, M.. (1991). Dynamic predicate logic. Linguistics and Philosophy, 14(1), 39–100.CrossRefGoogle Scholar
Handley, S. J., Evans, J. S. B. T., & Thompson, V. A.. (2006). The negated conditional: a litmus test for the suppositional conditional?. Journal of Experimental Psychology: Learning, Memory, and Cognition, 32(3), 559–569.Google ScholarPubMed
Hansson, B. (1968). An analysis of some deontic logics. Nous, 3, 373–398.CrossRefGoogle Scholar
Hansson, S. O. (1992). In defense of the Ramsey Test. Journal of Philosophy, 89, 499–521.CrossRefGoogle Scholar
Incurvati, L. & Schlöder, J. J.. (2019). Weak assertion. The Philosophical Quarterly, 69(277), 741–770.CrossRefGoogle Scholar
Jackson, F. (1979). On assertion and indicative conditionals. Philosophical Review, 88, 565–589.CrossRefGoogle Scholar
Johnson-Laird, P. N. (1983). Mental Models: Toward a Cognitive Science of Language, Inference and Consciousness. Cambridge, MA: Harvard University Press.Google Scholar
Johnson-Laird, P. N. (2006). How We Reason. Oxford: Oxford University Press.Google Scholar
Johnson-Laird, P. N. & Byrne, R. M. J.. (2002). Conditionals: a theory of meaning, pragmatics and inference. Psychological Review, 109(4), 646–678.CrossRefGoogle ScholarPubMed
Kamp, H. (1981). A theory of truth and semantic representation. In Groenendijk, J., Janssen, T., & Stokhof, M., editors. Formal Methods in the Study of Language. Amsterdam: Matematisch Centrum, pp. 277–322.Google Scholar
Kaufmann, S. (2009). Conditionals right and left: probabilities for the whole family. Journal of Philosophical Logic, 38, 1–53.CrossRefGoogle Scholar
Kern-Isberner, G. (1999). Following conditional structures of knowledge. In Burgard, W., Christaller, T., & Cremers, A., editors. KI-99, LNAI, Vol. 1701. Berlin Heidelberg: Springer-Verlag, pp. 125–136.Google Scholar
Khoo, J. & Mandelkern, M.. (2019). Triviality results and the relationship between logical and natural languages. Mind, 128, 485–526.CrossRefGoogle Scholar
Kolodny, N. & MacFarlane, J.. (2010). Ifs and oughts. Journal of Philosophy, 107(3), 115–143.CrossRefGoogle Scholar
Kratzer, A. (1977). What ‘must’ and ‘can’ must and can mean. Linguistics and Philosophy, 1(3), 337–356.CrossRefGoogle Scholar
Kratzer, A. (1979). Conditional necessity and possibility. In Bäuerle, R., Egli, U., & von Stechow, A., editors. Semantics from Different Points of View. Berlin: Springer-Verlag, pp. 117–147.CrossRefGoogle Scholar
Kratzer, A. (1991). Modality. In von Stechow, A. & Wunderlich, D., editors. Semantics: An International Handbook of Contemporary Research. Berlin: de Guyter, pp. 639–650.Google Scholar
Kratzer, A. (2012). Modals and Conditionals: New and Revised Perspectives. Oxford: Oxford University Press.CrossRefGoogle Scholar
Krzyżanowska, K. (2015). Between “If” and “Then”: towards an empirically informed philosophy of conditionals. PhD Thesis, Groningen University.Google Scholar
Lance, M. (1991). Probabilistic dependence among Conditionals. Philosophical Review, 100, 269–275.CrossRefGoogle Scholar
Levi, I. (1988). Iteration of conditionals and the Ramsey Test. Synthese, 76, 49–81.CrossRefGoogle Scholar
Levi, I. (1996). For the Sake of the Argument. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Lewis, D. (1976). Probabilities of conditionals and conditional probabilities. Philosophical Review, 85, 297–315.CrossRefGoogle Scholar
MacFarlane, J. (2014). Assessment Sensitivity: Relative Truth and its Applications. Oxford: Oxford University Press.CrossRefGoogle Scholar
Mandelkern, M. (2019). Bounded modality. The Philosophical Review, 128(1), 1–61.CrossRefGoogle Scholar
McGee, V. (1985). A counterexample to modus ponens. Journal of Philosophy, 82, 462–471.CrossRefGoogle Scholar
McGee, V. (1989). Conditional probabilities and compounds of conditionals. Philosophical Review, 98, 485–542.CrossRefGoogle Scholar
McGee, V. (2018). The Adams Two-Switch Example. Available from http://fitelson.org/few/few_10/mcgee.pdf.Google Scholar
Oberauer, K. (2006). Reasoning with conditionals: A test of formal models of four theories. Cognitive Psychology, 53(3), 238–283.CrossRefGoogle ScholarPubMed
Over, D., Douven, I., & Verbrugge, S.. (2013). Scope ambiguities and conditionals. Thinking & Reasoning, 19(3–4), 284–307.CrossRefGoogle Scholar
Over, D. E. & Evans, J. S. B. T.. (2003). The probability of conditionals: the psychological evidence. Mind & Language, 18(4), 340–358.CrossRefGoogle Scholar
Pfeifer, N. (2012). Experiments on Aristotle’s thesis: towards an experimental philosophy of conditionals. The Monist, 95(2), 223–240.CrossRefGoogle Scholar
Rott, H. (2004). A counterexample to six fundamental principles of belief formation. Synthese, 139, 225–240.CrossRefGoogle Scholar
Rott, H. (2011). Reapproaching Ramsey: conditionals and iterated belief change in the spirit of AGM. Journal of Philosophical Logic, 40(2), 155–191.CrossRefGoogle Scholar
Rumfitt, I. (2000). Yes and no. Mind, 109, 781–823.CrossRefGoogle Scholar
Russell, J. S. & Hawthorne, J.. (2016). General dynamic triviality theorems. The Philosophical Review, 125(3), 307–339.CrossRefGoogle Scholar
Schulz, M. (2018). Modus ponens under the restrictor view. Journal of Philosophical Logic, 47(6), 1001–1028.CrossRefGoogle Scholar
Segerberg, K. (1998). Irrevocable belief revision in dynamic doxastic logic. Notre Dame Journal of Formal Logic, 39, 287–306.CrossRefGoogle Scholar
Skovgaard-Olsen, N. (2016). Motivating the relevance approach to conditionals. Mind & Language, 31(5), 555–579.CrossRefGoogle Scholar
Skovgaard-Olsen, N., Singmann, H., & Klauer, K. C.. (2016). The relevance effect and conditionals. Cognition, 150, 26–36.CrossRefGoogle ScholarPubMed
Smiley, T. (1996). Rejection. Analysis, 56, 1–9.CrossRefGoogle Scholar
Stalnaker, R. (1968). A theory of conditionals. In Studies in Logical Theory. Oxford: Blackwell.Google Scholar
Starr, W. (2014a). Indicative conditionals, strictly. Unpublished manuscript.Google Scholar
Starr, W. B. (2014b). A uniform theory of conditionals. Journal of Philosophical Logic, 43(6), 1019–1064.CrossRefGoogle Scholar
Thomason, R. (2012). The semantics of conditional modality. Unpublished manuscript. Available from http://www.eecs.umich.edu/rthomaso/.Google Scholar
van Fraassen, B. (1976). Probabilities of conditionals. In Harper, W. L. & Hooker, C. A., editors. Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Dordrecht: Reidel, pp. 261–300.CrossRefGoogle Scholar
van Wijnbergen-Huitink, J., Elqayam, S., & Over, D. E.. (2014). The probability of iterated conditionals. Cognitive Science, 39(4), 788–803.CrossRefGoogle ScholarPubMed
Veltman, F. (1985). Logics for conditionals. PhD Thesis, University of Amsterdam, Amsterdam.Google Scholar
Veltman, F. (1996). Defaults in update semantics. Journal of Philosophical Logic, 25, 221–261.CrossRefGoogle Scholar
Vermuelen, C. (1993). Sequence semantics for dynamic predicate logic. Journal of Logic, Language and Information, 2, 217–254.CrossRefGoogle Scholar
Vidal, M. & Baratgin, J.. (2017). A psychological study of unconnected conditionals. Journal of Cognitive Psychology, 29, 769–781.CrossRefGoogle Scholar
Yalcin, S. (2007). Epistemic modals. Mind, 116, 983–1026.CrossRefGoogle Scholar
Yalcin, S. (2012). A counterexample to modus tollens. Journal of Philosophical Logic, 41(6), 1001–1024.CrossRefGoogle Scholar