Linguistics and Philosophy

, Volume 28, Issue 2, pp 181–231 | Cite as

Conditional Predictions

A probabilistic account
Article

ABSTRACT

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey’s conditional, but also opens up the possibility of a uni?ed probabilistic account of indicative and counterfactual conditionals.

Keywords

conditionals counterfactuals probability causality 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, E. 1965’The Logic of Conditionals’Injury8166197Google Scholar
  2. Adams, E. 1970’Subjunctive and Indicative Conditionals’Foundations of Language68994Google Scholar
  3. Adams, E. 1975The Logic of ConditionalsReidelDordrechtGoogle Scholar
  4. Adams, E.: 1976, ’Prior Probabilities and Counterfactual Conditionals’, in W. L. Harper and C. A. Hooker (1976), pp. 1– 21.Google Scholar
  5. Adams, E. 1998A Primer of Probability LogicCSLI PublicationsStanfordGoogle Scholar
  6. Anderson, A.R. 1951’A Note on Subjunctive and Counterfactual Conditionals’Analysis123538Google Scholar
  7. Aristotelian Society: 1991, ’The Symposia Read at the Joint Session of the Aristotelian Society and the Mind Association at the University of Durham’, The Aristotelian Society, Supplementary Volume 65.Google Scholar
  8. Aristotelian Society: 1995, ’Proceedings of the Aristotelian Society’, The Aristotelian Society, Supplementary Volume 69.Google Scholar
  9. Athanasiadou, A. and R. Dirven (eds.): 1997, On Conditionals Again, Vol. 143 of Amsterdam Studies in the Theory and History of Linguistic Science, John Benjamins, Amsterdam/Philadelphia.Google Scholar
  10. Barker, J.S. 1998’Predetermination and Tense Probabilism’Analysis58290296CrossRefGoogle Scholar
  11. Barwise, J.: 1986, ’Conditionals and Conditional Information’, in E. C. Traugott et al. (1986), pp. 21– 54.Google Scholar
  12. Bennett, J. 1984’Counterfactuals and Temporal Direction’The Philosophical Review935791Google Scholar
  13. Bennett, J. 1988’Farewell to the Phlogiston Theory of Conditionals’Mind97509527Google Scholar
  14. Bennett, J. 2003A Philosophical Guide to ConditionalsOxford University PressOxfordGoogle Scholar
  15. Braithwaite, R. B. (ed.): 1931, The Foundations of Mathematics and other Logical Essays, Routledge and Kegan Paul, London.Google Scholar
  16. Burgess, J.P. 1979’Logic and Time’The Journal of Symbolic Logic44566582Google Scholar
  17. Cohen, A. 2003

    ’Probabilistic Approaches to Semantics’

    Bod, R.Hay, J.Jannedy, S. eds. Probabilistic Linguistics, Chap. 9MIT PressCambridge, MA343379
    Google Scholar
  18. Comrie, B. 1985TenseCambridge University PressCambridgeGoogle Scholar
  19. Comrie, B.: 1986, ’Conditionals: A Typology’, in E. C. Traugott et al. (1986), pp. 77–99.Google Scholar
  20. Cowell, R.G., Dawid, A.P., Lauritzen, S.L., Spiegelhalter, D.J. 1999Probabilistic Networks and Expert SystemsSpringerNew YorkGoogle Scholar
  21. Dahl, O.: 1997, ’The Relation between Past Time Reference and Counterfactuality: A New Look’, in A. Athanasiadou and R. Dirven (1997), pp. 97–112.Google Scholar
  22. Dancygier, B. 1998Conditionals and PredictionCambridge University PressCambridgeGoogle Scholar
  23. Davis, W. A. 1988, ’Probabilistic Theories of Causation’, in J. H. Fetzer (1988), pp. 133 – 160.Google Scholar
  24. Downing, P.B. 1959’Subjunctive Conditionals, Time Order, and Causation’Proceedings of the Aristotelian Society59125140Google Scholar
  25. Dudman, V.H. 1984’Conditional Interpretations of If-sentences’Australian Journal of Linguistics4143204Google Scholar
  26. Dudman, V.H. 1988’Indicative and Subjunctive’Analysis48113122Google Scholar
  27. Dudman, V.H. 1994’On Conditionals’Journal of Philosophy91113128Google Scholar
  28. Edgington, D. 1986’Do Conditionals Have Truth Conditions?’Critica18320Google Scholar
  29. Edgington, D.: 1991, ’The Mystery of the Missing Matter of Fact’, in Aristotelian Society (1991), Supplementary Volume 65, pp. 185–209.Google Scholar
  30. Edgington, D. 1995’On Conditionals’Mind104235329Google Scholar
  31. Eells, E. and B. Skyrms (eds.): 1994, Probabilities and Conditionals: Belief Revision and Rational Decision, Cambridge University Press, Cambridge.Google Scholar
  32. Ellis, B. 1978’A Unified Theory of Conditionals’Journal of Philosophical Logic7107124CrossRefGoogle Scholar
  33. Fetzer, J. H. (ed.): 1988, Probability and Causality, Vol. 192 of Studies in Epistemology, Logic, Methodology, and Philosophy of Science, Reidel, Dordrecht.Google Scholar
  34. Fine, K. 1975’Review of Lewis (1973)’Mind84451458Google Scholar
  35. Fintel, K. 1998

    ’The Presupposition of Subjunctive Conditionals’

    Sauerland, U.Percus, O. eds. The Interpretive Tract,Vol.25 of MIT Working Papers in LinguisticsMIT PressCambridge
    Google Scholar
  36. Fleischman, S. 1989’Temporal Distance: A Basic Linguistic Metaphor’Studies in Language13150Google Scholar
  37. van Frassen, B. C.: 1976, ’Probabilities of Conditionals’, in W. L. Harper and C. A. Hooker (1976), pp. 261 – 308.Google Scholar
  38. van Fraassen, B. C.: 1981, ’A Temporal Framework for Conditionals and Chance’, in W.L. Harper et al. (1981), pp. 365 – 414.Google Scholar
  39. Funk, W.-P. 1985’On a Semantic Typology of Conditional Sentences’Folia Linguistics19365414Google Scholar
  40. Gabbay, D. and F. Guenthner (eds.): 1984, Extensions of Classical Logic, Vol. 2 of Handbook of Philosophical Logic, Reidel, Dordrecht.Google Scholar
  41. Galavotti, M. C., P. Suppes, and D. Costantini (eds.): 2001, Stochastic Causality,CSLI Publications, Stanford.Google Scholar
  42. Gärdenfors, P. 1982’Imaging and Conditionalization’Journal of Philosophy79747760Google Scholar
  43. Gärdenfors, P. 1988Knowledge in Flux: Modeling the Dynamics of Epistemic StatesMIT PressCambridgeGoogle Scholar
  44. Gibbard, A.: 1981, ’Two Recent Theories of Conditionals’, in W. L. Harper et al. (1981), pp. 211 s– 247.Google Scholar
  45. Goodman, N. 1947’The Problem of Counterfactual Conditionals’The Journal of Philosophy44113128Google Scholar
  46. Grandy, R. E. and R. Warner (eds.): 1986, Philosophical Grounds of Rationality, Clarendon Press, Oxford.Google Scholar
  47. Hájek, A.: 1994, ’Triviality on the Cheap?’, in E. Eells and B. Skyrms (1994), pp. 113 – 140.Google Scholar
  48. Hájek, A. and N. Hall: 1994, ’The Hypothesis of the Conditional Construal of Conditional Probability’, in E. Eells and B. Skyrms (1994), pp. 75 – 110.Google Scholar
  49. Hall, N.: 1994, ’Back in the CCCP’, in E. Eells and B. Skyrms (1994), pp. 141 – 160.Google Scholar
  50. Harper, W. L.: 1976, ’Rational Belief Change, Popper Functions, and Counterfactuals’, in W. L. Harper and C. A. Hooker (1976), pp. 73 – 115.Google Scholar
  51. Harper, W. L.: 1981, ’A Sketch of Some Recent Developments in the Theory of Conditionals’, in W. L. Harper et al. (1981), pp. 3 – 38.Google Scholar
  52. Harper, W. L. and C. A. Hooker (eds.): 1976, Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. 1 ofThe University of Western Ontario Series in Philosophy of Science, Reidel, Dordrecht.Google Scholar
  53. Harper, W. L., R. Stalnaker, and G. Pearce (eds.): 1981, Ifs: Conditionals, Belief, Decision, Chance, and Time, Reidel, Dordrecht.Google Scholar
  54. Hausman, D.M. 1998Causal AsymmetriesCambridge University PressCambridgeGoogle Scholar
  55. Hughes, G., Cresswell, M. 1996A New Introduction to Modal LogicRoutledgeOxfordGoogle Scholar
  56. Iatridou, S. 2000’The Grammatical Ingredients of Counterfactuality’Linguistic Inquiry31231270CrossRefGoogle Scholar
  57. Jackson, F. 1979’On Assertion and Indicative Conditionals’Philosophical Review88565589Google Scholar
  58. Jackson, F. 1987ConditionalsBasil BlackwellOxfordGoogle Scholar
  59. James, D. 1982’Past Tense and the Hypothetical: A Cross-Linguistic Study’Studies in Language6375403Google Scholar
  60. Jeffrey, R.C. 1964’If’Journal of Philosophy61702703Google Scholar
  61. Jeffrey, R. C. (ed.): 1980, Studies in Inductive Logic and Probability, Vol. 2, University of California Press.Google Scholar
  62. Jeffrey, R. C.: 1991, ’Matter-of-fact Conditionals’, in Aristotelian Society (1991), Supplementary Volume 65, pp. 161–183.Google Scholar
  63. Karttunen, L., Peters, S. 1979

    ’Conventional Implicature’

    Oh, C.-K.Dinneen, D. eds. Presupposition,Vol. 11 of Syntax and SemanticsAcademic PressNew York156
    Google Scholar
  64. Kaufmann, S. 2001a’Aspects of the Meaning and Use of Conditionals’, Ph.D. thesisStanford UniversityStanfordGoogle Scholar
  65. Kaufmann, S. 2001b

    ’Probabilities of Conditionals’

    Hastings, R.Jackson, B.Zvolenszky, Z. eds. , Proceedings of SALT XI, held at New York University.CLC PublicationsIthaca, NY248267
    Google Scholar
  66. Kaufmann, S.: 2001c, ’Tense Probabilism Properly Conceived’, in R. van Rooy and M. Stokhof (eds.), Proceedings of the Thirteenth Amsterdam Colloquium, pp. 132 – 137.Google Scholar
  67. Kaufmann, S.: 2004, ’Conditional Truth and Future Reference’, semanticsarchive.net.Google Scholar
  68. Kratzer, A. 1979

    ’Conditional Necessity and Possibility’

    Egli, U.Bäuerle, R.Stechow, A. eds. Semantics from Different Points of ViewSpringerBerlin117147
    Google Scholar
  69. Kratzer, A. 1991

    ’Conditionals’

    Stechow, A.Wunderlich, D. eds. Semantik: Ein internationals Handbuch der zeitgenössischen Forschung[=Semantics], de GruyterBerlin/New York651656
    Google Scholar
  70. Lance, M. 1991’Probabilistic Dependence among Conditionals’Philosophical Review100269276Google Scholar
  71. Lewis, D. 1973CounterfactualsHarvard University PressCambridge, MAGoogle Scholar
  72. Lewis, D. 1976’Probabilities of Conditionals and Conditional Probabilities’Philosophical Review85298315Google Scholar
  73. Lewis, D. 1979’Counterfactual Dependence and Time’s Arrow’Noûs13455476Google Scholar
  74. Lewis, D.: 1980, ’A Subjectivist’s Guide to Objective Chance’, in R. C. Jeffrey (1980), pp.263 – 293.Google Scholar
  75. Lewis, D. 1981’Ordering Semantics and Premise Semantics for Counterfactuals’Journal of Philosophical Logic10217234CrossRefGoogle Scholar
  76. Lewis, D. 1986’Probabilities of Conditionals and Conditional Probabilities II’Philosophical Review95581589Google Scholar
  77. Lewis, D. 1994’Humean Supervenience Debugged’Mind103473490Google Scholar
  78. Mackie, P. 1973Truth, Probability and ParadoxClarendon PressOxfordGoogle Scholar
  79. Mårtensson, J. 1999Subjunctive Conditionals and Time: A Defense of the Classical Approach, No. 10 in Acta Philosophica Gothoburgensia, Department of PhilosophyUniversity of GöteborgGöteborgGoogle Scholar
  80. McGee, V. 1989’Conditional Probabilities and Compounds of Conditionals’The Philosophical Review98485541Google Scholar
  81. Mellor, D. H. (ed.): 1978, Foundations: Essays in Philosophy, Logic, Mathematics and Economics, Routledge and Kegan Paul, London.Google Scholar
  82. Mellor, D. H. (ed.): 1990, Philosophical Papers: F. P. Ramsey, Cambridge University Press, Cambridge.Google Scholar
  83. Mellor, D.H. 1993’How to Believe a Conditional’The Journal of Philosophy90233248Google Scholar
  84. Milne, P. 1997’Bruno de Finetti and the Logic of Conditional Events’British Journal for the Philosophy of Science48195232CrossRefGoogle Scholar
  85. Nute, D. 1980Topics in Conditional LogicReidelDordrechtGoogle Scholar
  86. Nute, D.: 1984, ’Conditional Logic’, in D. Gabbay and F. Guenthner (1984), pp. 387 – 439.Google Scholar
  87. Palmer, F.R. 1983’Future Time Reference in the Conditional Protasis: A Comment on Comrie’Australian Journal of Linguistics3241243Google Scholar
  88. Pearl, J. 2000Causality: Models, Reasoning, and InferenceCambridge University PressCambridgeGoogle Scholar
  89. Pendlebury, M. 1989’The Projection Strategy and the Truth Conditions of Conditional Statements’Mind98179205Google Scholar
  90. Prior, A. 1967Past, Present and FutureOxford University PressOxfordGoogle Scholar
  91. Quirk, R., Greenbaum, S., Leech, G., Svartvik, J. 1985A Comprehensive Grammar of the English LanguageLongmanLondonGoogle Scholar
  92. Ramsey, F. P.: 1929, ’General Propositions and Causality’, printed in R. B. Braithwaite (1931), pp. 237 – 255, Meller (1978), pp. 133 – 151; Meller (1990), pp. 145 – 163.Google Scholar
  93. Read, S.: 1995, ’Conditionals and the Ramsey Test’, in Aristotelian Society (1995), Supplementary Volume 69.Google Scholar
  94. Reichenbach, H. 1956The Direction of TimeUniversity of Berkeley PressBerkeley/Los Angeles CAGoogle Scholar
  95. Roberts, C. 1989’Modal Subordination and Pronomial Anaphora in Discourse’Linguistics and Philosophy12683721CrossRefGoogle Scholar
  96. van Rooy, R.: 1997, ’Attitudes and Changing Contexts’, Ph.D. thesis, Institut für maschinelle Sprachverarbeitung (Stuttgart).Google Scholar
  97. Skyrms, B.: 1981, ’The Prior Propensity Account’, in W. L. Harper et al. (1981), pp. 259 – 265.Google Scholar
  98. Skyrms, B. 1984Pragmatics and EmpiricismYale University PressNew Haven/LondonGoogle Scholar
  99. Skyrms, B.: 1988, ’Conditional Chance’, in J. H. Fetzer (1988), pp. 161 – 178.Google Scholar
  100. Skyrms, B.: 1994, ’Adams Conditionals’, in E. Eells and B. Skyrms (1994), pp. 13 – 26.Google Scholar
  101. Slote, M.A. 1978’Time in Counterfactuals’The Philosophical Review87327Google Scholar
  102. Spirtes, P., Glymour, C., Scheines, R. 2000Causation, Prediction, and SearchMIT PressCambridge, MAGoogle Scholar
  103. Spohn, W.: 2001, ’Bayesian Nets are All there is to Causal Dependence’, in M. C. Galavotti et al. (2001), pp. 157 – 172.Google Scholar
  104. Stalnaker, R.: 1968, ’A Theory of Conditionals’, in Studies in Logical Theory, American Philosophical Quarterly, Monograph: 2, Blackwell, Oxford, pp. 98 – 112.Google Scholar
  105. Stalnaker, R. 1970’Probability and Conditionals’Philosophy of Science376480CrossRefGoogle Scholar
  106. Stalnaker, R. 1975’Indicative Conditionals’Philosophia5269286Google Scholar
  107. Stalnaker, R.: 1976, ’Letter to van Fraassen’, in W. L. Harper and C. A. Hooker (1976), pp.302 – 306.Google Scholar
  108. Stalnaker, R.: 1991, ’Letter to Richard Jeffrey’, included in Jeffrey (1991), pp. 178 – 183.Google Scholar
  109. Stalnaker, R. and R. Jeffrey: 1994, ’Conditionals as Random Variables’, in E. Eells and B.Skyrms (1994), pp. 31– 46.Google Scholar
  110. Strawson, P. F.: 1986, ’ ’If’ and ” ’, in R. E. Grandy and R. Warner (1986), pp. 229 – 242.Google Scholar
  111. Suppes, P. 1970A Probabilistic Theory of CausalityNorth HollandAmsterdamGoogle Scholar
  112. Tedeschi, P. 1981

    ’Some Evidence for a Branching-Futures Semantic Model’

    Tedeschi, P.Zaenen, A. eds. Tense and Aspect,Vol.14of Syntax and SemanticsAcademic PressNew York239270
    Google Scholar
  113. Thomason, R.H. 1970’Indeterminist Time and Truth Value Gaps’Theoria36264281Google Scholar
  114. Thomason, R. H.: 1984, ’Combinations of Tense and Modality’, in D. Gabbay and F.Guenthner (1984), pp. 135 – 165.Google Scholar
  115. Thomason, R. H. and A. Gupta: 1981, ’A Theory of Conditionals in the Context of Branching Time’, in W. L. Harper et al. (1981), pp. 299 – 322.Google Scholar
  116. Tichý, P. 1976’A Counterexample to the Lewis-Stalnaker Analysis of Counterfactuals’Philosophical Studies29271273CrossRefGoogle Scholar
  117. Traugott, E. C., A. ter Meulen, J. Snitzer Reilly, and C. A. Ferguson (eds.): 1986, On Conditionals, Cambridge University Press, Cambridge.Google Scholar
  118. Veltman, F.: 1976, ’Prejudices, Presuppositions and the Theory of Conditionals’, in J. Groenendijk and M. Stokhof (eds.), Proceedings of the First Amsterdam Colloquium [=Amsterdam Papers in Formal Grammar, Vol. 1], pp. 248 – 281.Google Scholar
  119. Veltman, F. 1985’Logics for Conditionals’, Ph.D. thesisUniversity of AmsterdamAmsterdamGoogle Scholar
  120. Woods, M. 1997ConditionalsClarendon PressOxfordGoogle Scholar
  121. Woodward, J.: 2001, ’Probabilistic Causality, Direct Causes and Counterfactual Dependence’, in M. C. Galavotti et al. (2001), pp. 39 – 63.Google Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Linguistics DepartmentNorthwestern UniversityEvanstonUSA

Personalised recommendations