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Towards a Probabilistic Analysis for Conditionals and Unconditionals

  • Stefan KaufmannEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10091)

Abstract

The thesis that the probability of a conditional Open image in new window is the corresponding conditional probability of C, given A, enjoys wide currency among philosophers and growing empirical support in psychology. In this paper I ask how a probabilisitic account of conditionals along these lines could be extended to unconditional sentences, i.e., conditionals with interrogative antecedents. Such sentences are typically interpreted as equivalent to conjunctions of conditionals. This raises a number of challenges for a probabilistic account, chief among them the question of what the probability of a conjunction of conditionals should be. I offer an analysis which addresses these issues by extending the interpretation of conditonals in Bernoulli models to the case of unconditionals.

Keywords

Conditionals Unconditionals Probability Bernoulli models 

Notes

Acknowledgments

I would like to thank the organizers of LENLS 12 for the opportunity to present this work. Parts of this material were previously presented at the “Work in Progress” seminar in the Philosophy Department at MIT. I am grateful to the audiences at both events for valuable feedback. Thanks also to Yukinori Takubo and Kyoto University for an invitation to a one-semester guest professorship in the fall of 2015, during which some of this work was carried out.

References

  1. 1.
    Adams, E.: The logic of conditionals. Inquiry 8, 166–197 (1965)CrossRefGoogle Scholar
  2. 2.
    Bennett, J.: A Philosophical Guide to Conditionals. Oxford University Press, Oxford (2003)CrossRefGoogle Scholar
  3. 3.
    Ciardelli, I., Roelofsen, F.: Generalized inquisitive semantics and logic (2009). http://sites.google.com/site/inquisitivesemantics/. Accessed Nov 2009
  4. 4.
    Edgington, D.: On conditionals. Mind 104(414), 235–329 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Eells, E., Skyrms, B. (eds.): Probabilities and Conditionals: Belief Revision and Rational Decision. Cambridge University Press, Cambridge (1994)zbMATHGoogle Scholar
  6. 6.
    Evans, J.S., Over, D.E.: If. Oxford University Press, Oxford (2004)Google Scholar
  7. 7.
    van Fraassen, B.C.: Probabilities of conditionals. In: Harper, W.L., Stalnaker, R., Pearce, G. (eds.) Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science. The University of Western Ontario Series in Philosophy of Science, vol. 1, pp. 261–308. D. Reidel, Dordrecht (1976)CrossRefGoogle Scholar
  8. 8.
    Groenendijk, J., Roelofsen, F.: Inquisitive semantics and pragmatics (2009). http://sites.google.com/site/inquisitivesemantics/. Accessed Nov 2009
  9. 9.
    Groenendijk, J., Stokhof, M.: Studies in the semantics of questions and the pragmatics of answers. Ph.D. thesis, University of Amsterdam (1984)Google Scholar
  10. 10.
    Hájek, A., Hall, N.: The hypothesis of the conditional construal of conditional probability. In: Eells and Skyrms [5], pp. 75–110Google Scholar
  11. 11.
    Hamblin, C.L.: Questions. Australas. J. Philos. 36(3), 159–168 (1958)CrossRefGoogle Scholar
  12. 12.
    Jeffrey, R.C.: If. J. Philos. 61, 702–703 (1964)Google Scholar
  13. 13.
    Karttunen, L.: Syntax and semantics of questions. Linguist. Philos. 1, 3–44 (1977)CrossRefzbMATHGoogle Scholar
  14. 14.
    Kaufmann, S.: Conditioning against the grain: abduction and indicative conditionals. J. Philos. Logic 33(6), 583–606 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Kaufmann, S.: Conditional predictions: a probabilistic account. Linguist. Philos. 28(2), 181–231 (2005)CrossRefGoogle Scholar
  16. 16.
    Kaufmann, S.: Conditionals right and left: probabilities for the whole family. J. Philos. Logic 38, 1–53 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Kaufmann, S.: Unconditionals are conditionals. Handout, DIP Colloquium, University of Amsterdam. http://stefan-kaufmann.uconn.edu/Papers/Amsterdam2010_hout.pdf
  18. 18.
    Kaufmann, S.: Conditionals, conditional probabilities, and conditionalization. In: Zeevat, H., Schmitz, H.-C. (eds.) Bayesian Natural Language Semantics and Pragmatics. LCM, vol. 2, pp. 71–94. Springer, Cham (2015). doi: 10.1007/978-3-319-17064-0_4 CrossRefGoogle Scholar
  19. 19.
    Khoo, J.: Probabilities of conditionals in context. Linguist. Philos. 39, 1–43 (2016)CrossRefGoogle Scholar
  20. 20.
    Lewis, D.: Probabilities of conditionals and conditional probabilities. Philos. Rev. 85, 297–315 (1976)CrossRefGoogle Scholar
  21. 21.
    Mellor, D.H. (ed.): Philosophical Papers: F. P. Ramsey. Cambridge University Press, New York (1990)Google Scholar
  22. 22.
    Oaksford, M., Chater, N.: Conditional probability and the cognitive science of conditional reasoning. Mind Lang. 18(4), 359–379 (2003)CrossRefGoogle Scholar
  23. 23.
    Oaksford, M., Chater, N.: Bayesian Rationality: The Probabilistic Approach to Human Reasoning. Oxford University Press, Oxford (2007)CrossRefGoogle Scholar
  24. 24.
    Ramsey, F.P.: General propositions and causality. Printed in [21], pp. 145–163 (1929)Google Scholar
  25. 25.
    Rawlins, K.: (Un)conditionals: an investigation in the syntax and semantics of conditional structures. Ph.D. thesis, UCSC (2008)Google Scholar
  26. 26.
    Rawlins, K.: (Un)conditionals. Nat. Lang. Seman. 21, 111–178 (2013)CrossRefGoogle Scholar
  27. 27.
    Stalnaker, R.C.: A theory of conditionals. In: Harper, W.L., Stalnaker, R., Pearce, G. (eds.) IFS. Conditionals, Belief, Decision, Chance and Time. The Western Ontario Series in Philosophy of Science, vol. 15, pp. 41–55. Blackwell, Oxford (1968). doi: 10.1007/978-94-009-9117-0_2 Google Scholar
  28. 28.
    Stalnaker, R., Jeffrey, R.: Conditionals as random variables. In: Eells and Skyrms [5], pp. 31–46Google Scholar
  29. 29.
    Zhao, M.: Intervention and the probabilities of indicative conditionals. J. Philos. 112, 477–503 (2016)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of LinguisticsUniversity of ConnecticutStorrs MansfieldUSA

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