, 30:17 | Cite as

If-Clauses and Probability Operators



Adams’ thesis is generally agreed to be linguistically compelling for simple conditionals with factual antecedent and consequent. We propose a derivation of Adams’ thesis from the Lewis-Kratzer analysis of if-clauses as domain restrictors, applied to probability operators. We argue that Lewis’s triviality result may be seen as a result of inexpressibility of the kind familiar in generalized quantifier theory. Some implications of the Lewis-Kratzer analysis are presented concerning the assignment of probabilities to compounds of conditionals.


Indicative conditionals If-clauses Probability Triviality Quantifier restriction Adams’ thesis Lewis-Kratzer analysis 


  1. Adams EW (1965) The logic of conditionals. Inquiry 8:166–197CrossRefGoogle Scholar
  2. Adams EW (1998) A primer of probability logic. CSLI, CAGoogle Scholar
  3. Barwise J, Cooper J (1981) Generalized quantifiers in natural language. Linguist Philos 4:159–219CrossRefGoogle Scholar
  4. Belnap N (1970) Conditional assertion and restricted quantification. Nous 4(1):1–12CrossRefGoogle Scholar
  5. Bradley R (2002) Indicative conditionals. Erkenntnis 56:345–378CrossRefGoogle Scholar
  6. Bradley R (2006) Adams conditionals and non-monotonic probabilities. J Logic Lang Inform 15:65–81CrossRefGoogle Scholar
  7. Douven I (2008) Kaufmann on the probability of conditionals. J Philos Logic 37(3):259–266CrossRefGoogle Scholar
  8. Edgington D (1995) On conditionals. Mind 104(414):235–329CrossRefGoogle Scholar
  9. Gibbard A (1981) Two recent theories of conditionals. In: Harper W, Stalnaker R, Pearce G (eds) Ifs: conditionals, belief, decision, chance and time. Reidel, Dordrecht, pp 211–247Google Scholar
  10. Grice P (1975) Logic and conversation. In: Studies in the way of words, Harvard University Press, Harvard, 1989Google Scholar
  11. Hajek A, Hall N (1994) The hypothesis of the conditional construal of conditional probability. In: Eells E, Skyrms B (eds) Probability and conditionals: belief revision and rational decision. Cambridge University Press, Cambridge, pp 75–111Google Scholar
  12. Jeffrey RC (1991) Matter-of-fact conditionals. Aristot Soc 65:161–183Google Scholar
  13. Kaufmann S (2005) Conditional predictions. Linguist Philos 28:181–231Google Scholar
  14. Kaufmann S (2004) Conditioning against the grain. J Philos Logic 33:583–606CrossRefGoogle Scholar
  15. Kaufmann S (2009) Conditionals right and left: probabilities for the whole family. J Philos Logic 38(1):1–53CrossRefGoogle Scholar
  16. Kratzer A (1991a) Modality. In Stechow A, Wunderlich D (eds) Semantik: Ein internationales Handbuch zeitgenoessischer Forschung. Gruyter, Berlin, pp 639–650Google Scholar
  17. Kratzer A (1991b) Conditionals. In: Stechow A, Wunderlich D (eds) Semantik: Ein internationales Handbuch zeitgenoessischer Forschung. Gruyter, Berlin, pp 651–56Google Scholar
  18. Kratzer A (2010) Papers on modals and conditionals. Available at:
  19. Leitgeb H (2007) Beliefs in conditionals vs. conditional beliefs. Topoi 26:115–132CrossRefGoogle Scholar
  20. Lewis D (1975) Adverbs of quantification. In: Keenan E (ed) Formal semantics of natural language. Cambridge University Press, repr. as Chap. 1 in Papers in Philosophical Logic, Cambridge, pp 5–20Google Scholar
  21. Lewis D (1976) Probabilities of conditionals and conditional probabilities, Chap. 20 in Philosophical Papers, vol. 2, Oxford, pp 133–56Google Scholar
  22. Lycan W (2001) Real conditionals. Clarendon Press, OxfordGoogle Scholar
  23. McDermott M (1996) On the truth-conditions of certain ‘If’-sentences. Philos Rev 105(1):1–37CrossRefGoogle Scholar
  24. McGee V (1989) Conditional probabilities and compounds of conditionals. Philos Rev 98(4):485–541CrossRefGoogle Scholar
  25. Peters S, Westerstahl S (2006) Quantifiers in language and logic. Oxford University Press, OxfordGoogle Scholar
  26. Rothschild D (forthcoming) Do indicative conditionals express propositions? NoûsGoogle Scholar
  27. Rothschild D (2009) Capturing the relationship between conditionals and probability with a trivalent semantics. Manuscript. OxfordGoogle Scholar
  28. Schlenker P (2004) Conditionals as definite descriptions (a referential analysis). Res Lang Comput 2(3):417–62CrossRefGoogle Scholar
  29. Schlenker P (2006) Ontological symmetry in language: a brief manifesto. Mind Lang 21:504–539Google Scholar
  30. Stalnaker R, Jeffrey R (1994) ‘Conditionals as Random Variables’. In Eells E, Skyrms B (eds) Probabilities and conditionals: belief revision and rational decision. Cambridge University Press, Cambridge, pp 31–46Google Scholar
  31. van Fraassen B (1976) Probabilities of conditionals. In: Harper WL, Hooker CA (eds) Foundations of probability, statistical inference and statistical theories of science 1, pp 261–301. Dordrecht.Google Scholar
  32. von Fintel K (1998) Quantifiers and if-clauses. Philos Q 48(1991):209–214CrossRefGoogle Scholar
  33. von Fintel K (2006) How ordinary are conditionals? Slides of the presentation given at the UConn conditional conference, April 08, 2006Google Scholar
  34. von Fintel K, Iatridou S (2002) If and when if-clauses can restrict quantifiers. Paper for the workshop at the university of MichiganGoogle Scholar
  35. Yalcin S (2007) Epistemic modals. Mind 116(464):983–1026CrossRefGoogle Scholar

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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institut Jean-Nicod (CNRS-ENS-EHESS), Département d’Etudes Cognitives de l’ENSParisFrance
  2. 2.Université Paris-Est Créteil, IHPST and Département d’Etudes Cognitives de l’ENSParisFrance

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