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A PROBABILISTIC SEMANTICS FOR COUNTERFACTUALS. PART A

Published online by Cambridge University Press:  17 November 2011

HANNES LEITGEB
HANNES LEITGEB*
Affiliation:
Ludwig-Maximilians-University Munich In memory of Horacio Arló-Costa
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Abstract

This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘if A then B’ to be true even in the presence of relevant ‘A and not B’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 1 , March 2012 , pp. 26 - 84
Copyright
Copyright © Association for Symbolic Logic 2011

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References

BIBLIOGRAPHY

Achinstein, P. (2001). The Book of Evidence. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Adams, E. W. (1965). On the logic of conditionals. Inquiry, 8, 166–197.CrossRefGoogle Scholar
Adams, E. W. (1975). The Logic of Conditionals: An Application of Probability to Deductive Logic. Synthese Library 86. Dordrecht, The Netherlands: Reidel.CrossRefGoogle Scholar
Adams, E. W. (1976). Prior probabilities and counterfactual conditionals. In Harper, W. L., and Hooker, C. A., editors. Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Dordrecht, The Netherlands: Reidel, pp. 1–21.Google Scholar
Albert, D. Z. (2000). Time and Chance. Cambridge, MA: Harvard University Press.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, 510–530.CrossRefGoogle Scholar
Arló-Costa, H. (2001). Bayesian epistemology and epistemic conditionals: On the status of the export-import laws. Journal of Philosophy, XCVIII, 555–598.Google Scholar
Arló-Costa, H., & Parikh, R. (2005). Conditional probability and defeasible inference. Journal of Philosophical Logic, 34, 97–119.CrossRefGoogle Scholar
Baltag, A., & Smets, S. (2008). Probabilistic dynamic belief revision. Synthese, 165, 179–202.CrossRefGoogle Scholar
Barker, S. (1999). Counterfactuals, probabilistic counterfactuals and causation. Mind, 108, 427–469.CrossRefGoogle Scholar
Bennett, J. (2003). A Philosophical Guide to Conditionals. Oxford, UK: Clarendon Press.CrossRefGoogle Scholar
Blackburn, S. (1986). How can we tell whether a commitment has a truth condition? In Travis, C., editors. Meaning and Interpretation. Oxford, UK: Basil Blackwell, pp. 201–232.Google Scholar
Bovens, L. (1998). Sequential counterfactuals, cotenability and temporal becoming. Philosophical Studies, 90, 79–101.CrossRefGoogle Scholar
Bratman, M. (1992). Practical reasoning and acceptance in a context. Mind, 101, 1–15.CrossRefGoogle Scholar
Easwaran, K. (2005). What conditional probability must (almost) be. Paper presented at the Formal Epistemology Workshop 05, Austin.Google Scholar
Edgington, D. (1995). On conditionals. Mind, 104, 235–329.CrossRefGoogle Scholar
Edgington, D. (1996). Vagueness by degrees. In Keefe, R., and Smith, P., editors. Vagueness. A Reader. Cambridge, MA: The MIT Press, pp. 294–316.Google Scholar
Edgington, D. (1997). Truth, objectivity, counterfactuals and Gibbard. Mind, 106, 107–116.CrossRefGoogle Scholar
Edgington, D. (2004). Counterfactuals and the benefit of hindsight. In Dowe, P., and Noordhof, P., editors. Cause and Chance: Causation in an Indeterministic World. London: Routledge, pp. 12–27.Google Scholar
Edgington, D. (2008). Counterfactuals. Proceedings of the Aristotelian Society, 108, 1–21.CrossRefGoogle Scholar
Eells, E., & Skyrms, B., editors. (1994). Probability and Conditionals. Belief Revision and Rational Decision. Cambridge, UK: Cambridge University Press.Google Scholar
Elga, A. (2000). Statistical mechanics and the asymmetry of counterfactuals. Philosophy of Science, 68, 313–324.CrossRefGoogle Scholar
Etlin, D. (unpublished). Modus ponens revisited. Unpublished draft.Google Scholar
Gärdenfors, P. (1986). “Belief Revisions and the Ramsey Test for Conditionals.” Philosophical Review, 95, 81–93.CrossRefGoogle Scholar
Gärdenfors, P. (1988). Knowledge in Flux. CambridgeMA: The MIT Press.Google Scholar
Gibbard, A. (1981). Two recent theories of conditionals. In Harper, W., Stalnaker, R., and Pearce, G., editors. Ifs. Conditionals, Belief, Decision, Chance, and Time. Dordrecht, The Netherlands: Reidel, pp. 211–247.Google Scholar
Gillies, T. (2007). Counterfactual scorekeeping. Linguistics and Philosophy, 30, 329–360.CrossRefGoogle Scholar
Grahne, G. (1991). Updates and counterfactuals. In Allen, J. A., Fikes, R., and Sandewall, E., editors. Principles of Knowledge Representation and Reasoning. San Mateo, CA: Morgan Kaufmann, pp. 269–276.Google Scholar
Hájek, A. (2003). What conditional probability could not be. Synthese, 137, 273–323.CrossRefGoogle Scholar
Hájek, A. (unpublished). Most counterfactuals are false. Unpublished draft.Google Scholar
Hájek, A., & Hall, N. (1994). The hypothesis of the conditional construal of conditional probability. In Eells, E., and Skyrms, B., editors. Probability and Conditionals. Belief Revision and Rational Decision. Cambridge, UK: Cambridge University Press, pp. 75–111.Google Scholar
Harper, W. L. (1975). Rational belief change, Popper functions and counterfactuals. Synthese, 30, 221–262. Reprinted in Harper & Hooker (1981, 73–112).CrossRefGoogle Scholar
Harper, W. L., & Hooker, C. A. (1976). Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Dordrecht, The Netherlands: Reidel.Google Scholar
Harper, W., Salnaker, R., & Pearce, G. (1981). Ifs. Conditionals, Belief, Decision, Chance, and Time. Dordrecht, The Netherlands: Reidel.Google Scholar
Hawthorne, J. (1996). On the logic of nonmonotonic conditionals and conditional probabilities. Journal of Philosophical Logic, 25, 185–218.CrossRefGoogle Scholar
Hawthorne, J. (2005). “Chance and Counterfactuals.” Philosophy and Phenomenological Research, 70, 396–405.CrossRefGoogle Scholar
Hawthorne, J. (2007). “Nonmonotonic Conditionals that Behave Like Conditional Probabilities Above a Threshold.” Journal of Applied Logic, 5, 625–637.CrossRefGoogle Scholar
Hawthorne, J., & Makinson, D. (2007). The quantitative/qualitative watershed for rules of uncertain inference. Studia Logica, 86, 247–297.CrossRefGoogle Scholar
Humphreys, P. (1985). Why propensities cannot be probabilities. Philosophical Review, 94, 557–570.CrossRefGoogle Scholar
Joyce, J. (1999). The Foundations of Causal Decision Theory. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Katsuno, H., & Mendelzon, A. (1992). On the difference between updating a knowledge base and revising it. In Gärdenfors, P., editor. Belief Revision. Cambridge, UK: Cambridge University Press, pp. 183–203.CrossRefGoogle Scholar
Kaufmann, S. (2005). Conditional predictions. Linguistics and Philosophy, 28, 181–231.CrossRefGoogle Scholar
Kratzer, A. (1981). Partition and revision: The semantics of counterfactuals. Journal of Philosophical Logic, 10, 201–216.CrossRefGoogle Scholar
Kratzer, A. (2009). Modals and conditionals again. Chapter 4 of unpublished book manuscript, to be published by Oxford University Press.Google Scholar
Kvart, I. (1986). A Theory of Counterfactuals. Indianapolis, IN: Hackett.Google Scholar
Kvart, I. (1992). Counterfactuals. Erkenntnis, 36, 1–41.CrossRefGoogle Scholar
Kvart, I. (2001). The counterfactual analysis of cause. Synthese, 127, 389–427.CrossRefGoogle Scholar
Kvart, I. (unpublished). The causal-process-chance-based analysis of counterfactuals.” Unpublished manuscript.Google Scholar
Levi, I. (1977). Subjunctives, dispositions and chances. Synthese, 34, 423–455.CrossRefGoogle Scholar
Levi, I. (1984). Decisions and Revisions. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Levi, I. (1996). For the Sake of the Argument. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Lewis, D. K. (1973a). Counterfactuals and comparative possibility. Journal of Philosophical Logic, 2, 418–446. Reprinted in Harper et al. (1981, pp. 57–85) and Lewis Lewis (1986, p. 3–31).CrossRefGoogle Scholar
Lewis, D. K. (1973b). Counterfactuals. Oxford, UK: Blackwell.Google Scholar
Lewis, D. K. (1976). Probabilities of conditionals and conditional probabilities. The Philosophical Review, 85, 297–315. Reprinted in Harper et al. (1981, pp. 129–147) and Lewis (1986, pp. 133–152).CrossRefGoogle Scholar
Lewis, D. K. (1980). A subjectivist’s guide to objective chance. In Jeffrey, R. C., editor. Studies in Inductive Logic and Probability, Vol. 2. Berkeley, CA: University of California Press, pp. 263–293. Reprinted in Harper et al. (1981, pp. 267–297) and Lewis (1986, pp. 83–113).CrossRefGoogle Scholar
Lewis, D. K. (1981). Ordering semantics and premise semantics for counterfactuals. Journal of Philosophical Logic, 10, 217–234.CrossRefGoogle Scholar
Lewis, D. K. (1986). Philosophical Papers, Vol. 2. Oxford, UK: Oxford University Press.Google Scholar
Loewer, B. (2007). Counterfactuals and the second law. In Price, H., and Corry, R., editors. Causation, Physics, and the Constitution of Reality: Russell’s Republic Revisited. Oxford, UK: Oxford University Press, pp. 293–326.CrossRefGoogle Scholar
MacFarlane, J. (2008). Truth in the garden of forking paths. In Kölbel, M., and García-Carpintero, M., editors. Relative Truth. Oxford, UK: Oxford University Press, pp. 81–102.CrossRefGoogle Scholar
Makinson, D. (unpublished). Conditional probability in the light of qualitative belief change. Unpublished manuscript.Google Scholar
McGee, V. (1989). Conditional probabilities and compounds of conditionals. The Philosophical Review, 98, 485–541.CrossRefGoogle Scholar
McGee, V. (1994). Learning the impossible. In Eells, E., and Skyrms, B., editors. Probability and Conditionals. Belief Revision and Rational Decision. Cambridge, UK: Cambridge University Press, pp. 177–199.Google Scholar
Paglieri, F. (2009). Acceptance as conditional disposition. In Hieke, A., and Leitgeb, H., editors. Reduction. Between the Mind and the Brain. Frankfurt a.m., Germany: Ontos Press, pp. 29–49.Google Scholar
Paris, J. B., & Simmonds, R. (2009). Review of Symbolic Logic, 2, 298–309.CrossRefGoogle Scholar
Pearl, J. (1988). Probabilistic Reasoning in Intelligence Systems. San Mateo, CA: Morgan Kaufmann.Google Scholar
Pearl, J. (1994). From Adams’ conditionals to default expressions, causal conditionals, and counterfactuals. In Eells, E., and Skyrms, B., editors. Probability and Conditionals. Belief Revision and Rational Decision. Cambridge, UK: Cambridge University Press, pp. 47–74.Google Scholar
Pearl, J. (1996). Causation, action and counterfactuals. In Shoham, Y., editor. TARK’96.Proceedings of the 6th conference on Theoretical Aspects Of Rationality And Knowledge. Los Angeles, CA: Morgan Kaufmann, pp. 51–73.Google Scholar
Pearl, J. (2000). Causality: Models, Reasoning, and Inference. New York, NY: Cambridge University Press.Google Scholar
Popper, K. R. (1968). The Logic of Scientific Discovery. Revised edition. London: Hutchinson.Google Scholar
Ramsey, F. P. (1929). General propositions and causality. In Braithwaite, R. B., editor. The Foundations of Mathematics and other Logical Essays. London: Kegan Paul, Trench & Trubner, pp. 237–255.Google Scholar
Resnik, D. B. (1992). Convergent realism and approximatetruth. In Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1. Contributed Papers. Chicago, IL: The University of Chicago Press, pp. 421–434.Google Scholar
Roeper, P., & Hugues, L. (1999). Probability Theory and Probability Logic. Toronto, Canada: University of Toronto Press.Google Scholar
Schaffer, J. (2004). Counterfactuals, causal independence and conceptual circularity. Analysis, 64, 299–309.CrossRefGoogle Scholar
Schurz, G. (1998). Probabilistic semantics for Delgrande’s conditional logic and a counterexample to his default logic. Artificial Intelligence, 102, 81–95.CrossRefGoogle Scholar
Schurz, G. (2001). What is ‘Normal’? An evolution-theoretic foundation of normic laws and their relation to statistical normality. Philosophy of Science, 68, 476–497.CrossRefGoogle Scholar
Schurz, G. (2005). Non-monotonic reasoning from an evolution-theoretic perspective: Ontic, logical and cognitive foundations. Synthese, 146, 37–51.CrossRefGoogle Scholar
Seidenfeld, T., Schervish, M. J., & Kadane, J. B. (2001). Improper regular conditional distributions. The Annals of Probability, 29, 1612–1624.Google Scholar
Smith, M. (2007). Ceteris paribus conditionals and comparative normalcy. Journal of Philosophical Logic, 36, 97–121.CrossRefGoogle Scholar
Skyrms, B. (1980a). The prior propensity account of subjunctive conditionals. In Harper, W., Stalnaker, R., and Pearce, G., editors. Ifs. Conditionals, Belief, Decision, Chance, and Time. Dordrecht, The Netherlands: Reidel, pp. 259–265.Google Scholar
Skyrms, B. (1980b). Causal Necessity. New Haven, CT: Yale University Press.Google Scholar
Skyrms, B. (1984). Pragmatics and Empiricism. New Haven, CT: Yale University Press.Google Scholar
Skyrms, B. (1994). Adams conditionals. In Eells, E., and Skyrms, B., editors. Probability and Conditionals. Belief Revision and Rational Decision. Cambridge, UK: Cambridge University Press, pp. 13–26.Google Scholar
Skyrms, B., Bell, G. D., & Woodruff, P. (1999). Theories of counter-factual and subjunctive conditionals in contexts of strategic interaction. Research in Economics, 53, 275–291.CrossRefGoogle Scholar
Spohn, W. (1988). Ordinal conditional functions. A dynamic theory of epistemic states. In Harper, W. L., and Skyrms, B., editors. Causation in Decision, Belief Change, and Statistics, Vol. 2. Dordrecht, The Netherlands: Kluwer, pp. 105–113.CrossRefGoogle Scholar
Stalnaker, R. C. (1968). A Theory of conditionals. In Studies in Logical Theory. American Philosophical Quarterly Monograph Series 2. Oxford, UK: Blackwell, pp. 98–112. Reprinted in Harper et al. (1981, pp. 41–55).Google Scholar
Stalnaker, R. C. (1970). Probability and conditionals. Philosophy of Science, 37, 64–80. Reprinted in Harper et al. (1981, pp. 107–128).CrossRefGoogle Scholar
Stalnaker, R. C. (1976). Letter to Harper. In Harper, W. L., and Hooker, C. A. (1976). Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. Dordrecht, The Netherlands: Reidel, pp. 113–116.Google Scholar
Stalnaker, R. C. (1984). Inquiry. Cambridge, MA: The MIT Press.Google Scholar
Stalnaker, R. C., & Jeffrey, R. C. (1994). Conditionals as random variables. In Eells, E., and Skyrms, B., editors. Probability and Conditionals. Belief Revision and Rational Decision. Cambridge, UK: Cambridge University Press, pp. 31–46.Google Scholar
Thomason, R., & Gupta, A. (1980). A theory of conditionals in the context of branching time. Philosophical Review, 89, 65–90. Reprinted in Harper et al. (1981, pp. 299–322).CrossRefGoogle Scholar
Unwin, N. (2007). Aiming at Truth. New York, NY: Palgrave Macmillan.CrossRefGoogle Scholar
van Benthem, J., Gerbrandy, J., & Kooi, B. (2009b). Dynamic update with probabilities. Studia Logica, 93, 67–96.CrossRefGoogle Scholar
van Benthem, J., Girard, P., & Roy, O. (2009a). Everything else being equal: A modal logic for ceteris paribus preferences. Journal of Philosophical Logic, 38, 83–125.CrossRefGoogle Scholar
van Fraassen, B. C. (1976). Representation of conditional probabilities. Journal of Philosophical Logic, 5, 417–430.CrossRefGoogle Scholar
van Fraassen, B. C. (1980). The Scientific Image. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Veltman, F. (2005). Making counterfactual assumptions. Journal of Semantics, 22, 159–180.CrossRefGoogle Scholar
von Fintel, K. (2001). Counterfactuals in a dynamic context. In Kenstowicz, M., editor. Ken Hale: A Life in Language. Cambridge, MA: The MIT Press, pp. 123–152.CrossRefGoogle Scholar
Woodruff, P. W. (1999). Partitions and conditionals. Journal of Philosophical Logic, 28, 113–128.CrossRefGoogle Scholar