Journal of Philosophical Logic

, Volume 44, Issue 1, pp 81–110 | Cite as

What Should I Believe About What Would Have Been the Case?

  • Franz Huber


The question I am addressing in this paper is the following: how is it possible to empirically test, or confirm, counterfactuals? After motivating this question in Section 1, I will look at two approaches to counterfactuals, and at how counterfactuals can be empirically tested, or confirmed, if at all, on these accounts in Section 2. I will then digress into the philosophy of probability in Section 3. The reason for this digression is that I want to use the way observable absolute and relative frequencies, two empirical notions, are used to empirically test, or confirm, hypotheses about objective chances, a metaphysical notion, as a role-model. Specifically, I want to use this probabilistic account of the testing of chance hypotheses as a role-model for the account of the testing of counterfactuals, another metaphysical notion, that I will present in Sections 4 to 8. I will conclude by comparing my proposal to one non-probabilistic and one probabilistic alternative in Section 9.


Counterfactuals Conditional belief Chance Credence Confirmation Probability measures Ranking functions 



I am very grateful to an anonymous referee, Alan Hájek, Christopher R. Hitchcock, Hannes Leitgeb, Timothy Williamson, and, especially, to Wolfgang Spohn for many most helpful comments and suggestions on several earlier versions of this paper


  1. 1.
    Adams, E.W. (1998). A Primer of Probability Logic. CLSI Publications: Stanford.Google Scholar
  2. 2.
    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
  3. 3.
    Baumgartner, M., & Glynn, L. (2013). Introduction to special issue on ‘Actual Causation’. Erkenntnis, 78, 1–8.CrossRefGoogle Scholar
  4. 4.
    Boutilier, C. (1996). Iterated revision and minimal change of belief. Journal of Philosophical Logic, 25, 263–305.CrossRefGoogle Scholar
  5. 5.
    Bradley, R. (2012). Multidimensional possible-world semantics for conditionals. Philosophical Review, 121, 539–571.CrossRefGoogle Scholar
  6. 6.
    Brössel, P., Eder, A.-M., Huber, F. (2013). Evidential support and instrumental rationality. Philosophy and Phenomenological Research, 87, 279–300.CrossRefGoogle Scholar
  7. 7.
    Briggs, R. (2009). The big bad bug bites anti-realists about chance. Synthese, 167, 81–92.CrossRefGoogle Scholar
  8. 8.
    Briggs, R. (2012). Interventionist counterfactuals. Synthese, 160, 139–166.Google Scholar
  9. 9.
    Carnap, R. (1980). A basic system of inductive logic, Part 2 In R. C. Jeffrey (Ed.) Studies in Inductive Logic and Probability (Vol. II, pp. 7–155). Berkeley: University of Berkeley Press.Google Scholar
  10. 10.
    Collins, J., Hall, N., Paul, L.A. (2004). Causation and Counterfactuals. Cambridge: MIT Press.Google Scholar
  11. 11.
    Darwiche, A., & Pearl, J. (1997). On the logic of iterated belief revision. Artificial Intelligence, 89, 1–29.CrossRefGoogle Scholar
  12. 12.
    Earman, J. (1992). Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. Cambridge: MIT Press.Google Scholar
  13. 13.
    Edgington, D. (2008). Counterfactuals. Proceedings of the Aristotelian Society, 108, 1–21.CrossRefGoogle Scholar
  14. 14.
    Fitelson, B., & Hájek, A (ms). Declarations of Independence.Google Scholar
  15. 15.
    Galles, D., & Pearl, J. (1998). An axiomatic characterization of causal counterfactuals. Foundations of Science, 1, 151–182.CrossRefGoogle Scholar
  16. 16.
    Halpern, J.Y. (2008). Defaults and normality in causal structures. In Proceedings of the Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2008) (pp 198–208).Google Scholar
  17. 17.
    Halpern, J.Y. (2013). From causal models to counterfactual structures. The Review of Symbolic Logic, 6, 305–322.CrossRefGoogle Scholar
  18. 18.
    Halpern, J.Y., & Hitchcock, C.R. (2010). Actual Causation and the Art of Modelling In R. Dechter, H. Geffner, J. Halpern (Eds.), Heuristics, Probability, and Causality (pp. 383–406). London: College Publications.Google Scholar
  19. 19.
    Halpern, J.Y., & Hitchcock, C.R. (2013). Compact representations of extended causal models. Cognitive Science, 37, 986–1010.CrossRefGoogle Scholar
  20. 20.
    Hild, M., & Spohn, W. (2008). The measurement of ranks and the laws of iterated contraction. Artificial Intelligence, 172, 1195–1218.CrossRefGoogle Scholar
  21. 21.
    Hintikka, J. (1961). Knowledge and Belief. An Introduction to the Logic of the Two Notions. Ithaca: Cornell University Press.Google Scholar
  22. 22.
    Huber, F. (2007). The consistency argument for ranking functions. Studia Logica, 86, 299–329.CrossRefGoogle Scholar
  23. 23.
    Huber, F. (2013a). Belief revision I: the AGM theory. Philosophy Compass, 8, 604–612.CrossRefGoogle Scholar
  24. 24.
    Huber, F. (2013b). Belief revision II: ranking theory. Philosophy Compass, 8, 613–621.CrossRefGoogle Scholar
  25. 25.
    Huber, F. (2013c). Structural equations and beyond. The Review of Symbolic Logic, 6, 709–732.Google Scholar
  26. 26.
    Huber, F. (2014). New foundations for counterfactuals. Synthese.Google Scholar
  27. 27.
    Jeffrey, R.C. (1970). Dracula meets Wolfman: acceptance vs. partial belief In M. Swain (Ed.), Induction, Acceptance, and Rational Belief (pp. 157–185). Dordrecht: D. Reidel.Google Scholar
  28. 28.
    Leitgeb, H. (2012a). A probabilistic semantics for counterfactuals. Part A. Review of Symbolic Logic, 5, 26–84.CrossRefGoogle Scholar
  29. 29.
    Leitgeb, H. (2012b). A probabilistic semantics for counterfactuals. Part B. Review of Symbolic Logic, 5, 85–121.CrossRefGoogle Scholar
  30. 30.
    Leitgeb, H. (2013). Reducing belief simpliciter to degrees of belief. Annals of Pure and Applied Logic, 164, 1338–1389.CrossRefGoogle Scholar
  31. 31.
    Lewis, D.K. (1973). Counterfactuals. Cambridge: Harvard University Press.Google Scholar
  32. 32.
    Lewis, D.K. (1979). Counterfactual dependence and time’s arrow. Noûs, 13, 455–476.CrossRefGoogle Scholar
  33. 33.
    Lewis, D.K. (1980). A subjectivist’s guide to objective chance In R. C. Jeffrey (Ed.) Studies in Inductive Logic and Probability (Vol. II, pp. 263–293). Berkeley: University of Berkeley Press.Google Scholar
  34. 34.
    Lin, H., & Kelly, K.T. (2012). Propositional reasoning that tracks probabilistic reasoning. Journal of Philosophical Logic, 41, 957–981.CrossRefGoogle Scholar
  35. 35.
    Mumford, S. (1998). Dispositions. Oxford: Oxford University Press.Google Scholar
  36. 36.
    Nozick, R. (1981). Philosophical Explanations. Oxford: Oxford University Press.Google Scholar
  37. 37.
    Paul, L.A. (2000). Aspect causation. Journal of Philosophy, XCVII, 235–256.CrossRefGoogle Scholar
  38. 38.
    Pearl, J. (2009). Causality: Models, Reasoning, and Inference (2nd edn.). Cambridge: Cambridge University Press.Google Scholar
  39. 39.
    Percival, P. (2002). Epistemic consequentialism. Proceedings of the Aristotelian Society, Supplementary 76, 121–151.Google Scholar
  40. 40.
    Popper, K.R. (1955). Two autonomous axiom systems for the calculus of probabilities. British Journal for the Philosophy of Science, 6, 51–57.CrossRefGoogle Scholar
  41. 41.
    Reichenbach, H. (1939). Experience and Prediction. An Analysis of the Foundations and the Structure of Knowledge. Chicago: University of Chicago Press.Google Scholar
  42. 42.
    Rényi, A. (1955). On a new axiomatic system for probability. Acta Mathematica Academiae Scientiarum Hungaricae, 6, 285–335.CrossRefGoogle Scholar
  43. 43.
    Rényi, A. (1970). Foundations of Probability. San Francisco: Holden-Day.Google Scholar
  44. 44.
    Spirtes, P., Glymour, C., Scheines, R. (2000). Causation, Prediction, and Search(2nd edn.). Cambridge: MIT Press.Google Scholar
  45. 45.
    Spohn, W. (1988). Ordinal conditional functions: a dynamic theory of epistemic states In W. L. Harper, & B. Skyrms (Eds.), Causation in Decision, Belief Change, and Statistics (Vol. II, pp. 105–134). Dordrecht: Kluwer.Google Scholar
  46. 46.
    Spohn, W. (2010). Chance and necessity: From humean supervenience to humean projection In E. Eells, & J. Fetzer (Eds.), The Place of Probability in Science. Boston Studies in the Philosophy of Science (Vol. 284, pp. 101–131). Dordrecht: Springer.Google Scholar
  47. 47.
    Spohn, W. (2012). The Laws of Belief. Ranking Theory and its Philosophical Applications. Oxford: Oxford University Press.Google Scholar
  48. 48.
    Spohn, W. (2013). A ranking-theoretic approach to conditionals. Cognitive Science, 37, 1074–1106.CrossRefGoogle Scholar
  49. 49.
    Stalnaker, R.C. (1968). A theory of conditionals In N. Rescher (Ed.), Studies in Logical Theory. American Philosophical Quarterly Monograph Series (Vol. 2, pp. 98–112). Oxford: Blackwell.Google Scholar
  50. 50.
    Stalnaker, R.C. (2002). Epistemic consequentialism. Proceedings of the Aristotelian Society, Supplementary 76, 153–168.CrossRefGoogle Scholar
  51. 51.
    Van Fraassen (1977). Relative frequencies. Synthese, 34, 133–166.CrossRefGoogle Scholar
  52. 52.
    Woodward, J.F. (2003). Making Things Happen. New York: Oxford University Press.Google Scholar
  53. 53.
    Zhang, J. (2013). A lewisian logic of causal counterfactuals. Minds and Machines, 23, 77–93.CrossRefGoogle Scholar
  54. 54.
    Zhang, J., Lam, W.-Y., De Clercq, R. (2013). A peculiarity in pearl’s logic of interventionist counterfactuals. Journal of Philosophical Logic, 42, 783–794.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of TorontoTorontoCanada

Personalised recommendations