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DIFFERENCE-MAKING CONDITIONALS AND THE RELEVANT RAMSEY TEST

Part of: General logic

Published online by Cambridge University Press:  12 December 2019

HANS ROTT
HANS ROTT*
Affiliation:
DEPARTMENT OF PHILOSOPHY UNIVERSITY OF REGENSBURG93040REGENSBURGGERMANYE-mail: [email protected]
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Abstract

This article explores conditionals expressing that the antecedent makes a difference for the consequent. A ‘relevantised’ version of the Ramsey Test for conditionals is employed in the context of the classical theory of belief revision. The idea of this test is that the antecedent is relevant to the consequent in the following sense: a conditional is accepted just in case (i) the consequent is accepted if the belief state is revised by the antecedent and (ii) the consequent fails to be accepted if the belief state is revised by the antecedent’s negation. The connective thus defined violates almost all of the traditional principles of conditional logic, but it obeys an interesting logic of its own. The article also gives the logic of an alternative version, the ‘Dependent Ramsey Test,’ according to which a conditional is accepted just in case (i) the consequent is accepted if the belief state is revised by the antecedent and (ii) the consequent is rejected (e.g., its negation is accepted) if the belief state is revised by the antecedent’s negation. This conditional is closely related to David Lewis’s counterfactual analysis of causation.

Keywords

conditionalsrelevancedependenceRamsey Testbelief revision

MSC classification

Primary: 03B42: Logics of knowledge and belief (including belief change) 03B45: Modal logic (including the logic of norms)
Type
Research Article
Information
The Review of Symbolic Logic , Volume 15 , Issue 1 , March 2022 , pp. 133 - 164
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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. E., Gärdenfors, P., & Makinson, D. (1985). On the logic of theory change: Partial meet contraction and revision functions. Journal of Symbolic Logic, 50(2), 510–530.CrossRefGoogle Scholar
Andreas, H. & Günther, M. (2019). On the Ramsey Test analysis of ‘because’. Erkenntnis, 84(6), 1229–1262.CrossRefGoogle Scholar
Bradley, R. (2007). A defence of the Ramsey Test. Mind, 116(461), 1–21.CrossRefGoogle Scholar
Burgess, J. P. (1981). Quick completeness proofs for some logics of conditionals. Notre Dame Journal of Formal Logic, 22, 76–84.CrossRefGoogle Scholar
Chandler, J. (2013). Transmission failure, AGM-style. Erkenntnis, 78(2), 383–398.CrossRefGoogle Scholar
Crupi, V. & Iacona, A. (2018). Three ways of being non-material. Manuscript.Google Scholar
Douven, I. (2008). The evidential support theory of conditionals. Synthese, 164(1), 19–44.CrossRefGoogle Scholar
Douven, I. (2016). The Epistemology of Indicative Conditionals: Formal and Empirical Approaches. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Evans, J. & Over, D. (2004). If – Supposition, Pragmatics, and Dual Processes. Oxford: Oxford University Press.Google Scholar
Fariñas del Cerro, L. & Herzig, A. (1996). Belief change and dependence. In Shoham, Y., editor. Proceedings of the Sixth Conference on Theoretical Aspects of Rationality and Knowledge. San Francisco, CA: Morgan Kaufmann, pp. 147–161.Google Scholar
Fuhrmann, A. & Levi, I. (1994). Undercutting and the Ramsey Test for conditionals. Synthese, 101(2), 157–169.CrossRefGoogle Scholar
Gärdenfors, P. (1978). Conditionals and changes of belief. In Niiniluoto, I. and Tuomela, R., editors. The Logic and Epistemology of Scientific Change. Acta Philosophica Fennica. Amsterdam: North Holland, pp. 381–404.Google Scholar
Gärdenfors, P. (1986). Belief revisions and the Ramsey Test for conditionals. Philosophical Review, 95(1), 81–93.CrossRefGoogle Scholar
Gärdenfors, P. (1987). Variations on the Ramsey Test: More triviality results. Studia Logica, 46(4), 321–327.CrossRefGoogle Scholar
Giordano, L., Gliozzi, V., & Olivetti, N. (2005). Weak AGM postulates and strong Ramsey Test: A logical formalization. Artificial Intelligence, 168(1–2), 1–37.CrossRefGoogle Scholar
Godden, D. & Zenker, F. (2015). Denying antecedents and affirming consequents: The state of the art. Informal Logic, 35(1), 88–134.CrossRefGoogle Scholar
Goodman, N. (1947). The problem of counterfactual conditionals. Journal of Philosophy, 44, 113–128.CrossRefGoogle Scholar
Grove, A. (1988). Two modellings for theory change. Journal of Philosophical Logic, 17(2), 157–170.CrossRefGoogle Scholar
Hawthorne, J. & Makinson, D. (2007). The quantitative/qualitative watershed for rules of uncertain inference. Studia Logica, 86(2), 247–297.CrossRefGoogle Scholar
Ismail, H. O. (2010). A reason maintenance perspective on relevant Ramsey conditionals. Logic Journal of the IGPL, 18(4), 508–529.CrossRefGoogle Scholar
Keenan, E. L. & Stavi, J. (1986). A semantic characterization of natural language determiners. Linguistics and Philosophy, 9, 253–326.CrossRefGoogle Scholar
Kraus, S., Lehmann, D., & Magidor, M. (1990). Nonmonotonic reasoning, preferential models and cumulative logics. Artificial Intelligence, 44, 167–207.CrossRefGoogle Scholar
Krzyżanowska, K., Collins, P., & Hahn, U. (2017). The puzzle of conditionals with true clauses: Against the Gricean account. In Gunzelman, G., Howes, A., Tenbrink, T., and Davelaar, E. J., editors. Proceedings of the 39th Annual Meeting of the Cognitive Science Society (COGSCI 2017). London, pp. 2476–2481.Google Scholar
Lehmann, D. & Magidor, M. (1992). What does a conditional knowledge base entail? Artificial Intelligence, 55, 1–60.CrossRefGoogle Scholar
Lewis, D. (1973a). Causation. Journal of Philosophy, 70(17), 556–567. Reprinted in Lewis, Philosophical Papers, Vol. 2. Oxford: Oxford University Press, 1986, pp. 159–172. Postscripts pp. 172–213.Google Scholar
Lewis, D. (1973b). Counterfactuals (second edition, 1986). Oxford: Blackwell.Google Scholar
Lindström, S. & Rabinowicz, W. (1998). Conditionals and the Ramsey Test. In Gabbay, D. M. and Smets, P., editors. Handbook of Defeasible Reasoning and Uncertainty Management Systems. Belief Change, Vol. 3. Dordrecht: Kluwer, pp. 147–188.Google Scholar
Makinson, D. (1989). General theory of cumulative inference. In Reinfrank, M., de Kleer, J., Ginsberg, M. L., and Sandewall, E., editors. Non-Monotonic Reasoning: Proceedings of the 2nd International Workshop 1988. Lecture Notes in Artificial Intelligence, Vol. 346. Berlin: Springer, pp. 1–18.CrossRefGoogle Scholar
Martin, C. J. (1987). Embarrassing arguments and surprising conclusions in the development of theories of the conditional in the twelfth century. In Jolivet, J. and de Libera, A., editors. Gilbert de Poitiers et ses contemporains. Naples: Bibliopolis, pp. 377–400.Google Scholar
McCall, S. (2012). A history of connexivity. In Gabbay, D. M., Pelletier, F. J., and Woods, J., editors. Handbook of the History of Logic. Logic – A History of its Central Concepts, Vol. 11. Amsterdam: North Holland, pp. 415–449.Google Scholar
Oaksford, M. & Chater, N. (2007). Bayesian Rationality: The Probabilistic Approach to Human Reasoning. Oxford: Oxford University Press.CrossRefGoogle Scholar
Pearl, J. (1989). Probabilistic semantics for nonmonotonic reasoning: A survey. In Brachman, R. J., Levesque, H. J., and Reiter, R., editors. Proceedings First International Conference on Principles of Knowledge Representation and Reasoning (KR 1989). Morgan Kaufmann, pp. 505–516.Google Scholar
Raidl, E. (2018). Ranking semantics for doxastic necessities and conditionals. In Arazim, P. and Lávička, T., editors. Logica Yearbook 2017. London: College Publications, pp. 223–238.Google Scholar
Ramsey, F. P. (1931). General propositions and causality. In Braithwaite, J. B., editor. The Foundations of Mathematics and Other Logical Essays. London: Kegan Paul, pp. 237–255.Google Scholar
Rott, H. (1986). Ifs, though and because. Erkenntnis, 25(3), 345–370.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
Skovgaard-Olsen, N. (2016). Motivating the relevance approach to conditionals. Mind and Language, 31(5), 555–579.CrossRefGoogle Scholar
Skovgaard-Olsen, N., Collins, P., Krzyżanowska, K., Hahn, U., & Klauer, K. C. (2019). Cancellation, negation, and rejection. Cognitive Psychology, 108, 42–71.CrossRefGoogle ScholarPubMed
Spohn, W. (2012). The Laws of Belief. Oxford: Oxford University Press.CrossRefGoogle Scholar
Spohn, W. (2015). Conditionals: A unifying ranking-theoretic perspective. Philosophers’ Imprint, 15(1), 1–30.Google Scholar
Stalnaker, R. (1968). A theory of conditionals. In Rescher, N., editor. Studies in Logical Theory. APQ Monograph Series, Vol. 2. Oxford: Blackwell, pp. 98–112.Google Scholar
van Benthem, J. (1986). Essays in Logical Semantics. Dordrecht: Reidel.CrossRefGoogle Scholar
van der Auwera, J. (1997). Conditional perfection. In Athanasiadou, A. & Dirven, R., editors. On Conditionals Again. Amsterdam: John Benjamins, pp. 169–190.CrossRefGoogle Scholar
van Rooij, R. & Schulz, K. (2019). Conditionals, causality and conditional probability. Journal of Logic, Language and Information, 28(1), 55–71.CrossRefGoogle Scholar
Veltman, F. (1985). Logics for Conditionals. Ph.D. Thesis, University of Amsterdam.Google Scholar
Walters, L. & Williams, J. R. G. (2013). An argument for conjunction conditionalization. Review of Symbolic Logic, 6(4), 573–588.CrossRefGoogle Scholar