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Conditionals, Indeterminacy, Probability and Truth

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Conditionals

Part of the book series: Palgrave Studies in Pragmatics, Language and Cognition ((PSPLC))

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Abstract

A conditional probability is not the probability of the truth of a proposition. This chapter explores an idea of Richard Bradley’s, who shows that there is nevertheless a semantic entity more complex than an ordinary proposition, such that the probability of its truth is the conditional probability of its consequent on the supposition of its antecedent. I argue that while truth conditions for conditionals are restored on this proposal, often the truth value of a conditional will be not merely uncertain but indeterminate; yet probabilistic assessment is unproblematic. I relate this to work on vagueness. I show how compounds of conditionals are unproblematic on this view.

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Notes

  1. 1.

    Suppose two premises, A and B, entail C. Then ¬C entails (¬A or ¬B). So p(¬C) ≤ p(¬A or ¬B) ≤ p(¬A) + p(¬B). This two-premise case easily extends to any number of premises.

  2. 2.

    See, for example, Bruno de Finetti (1936), Nuel Belnap (1970).

  3. 3.

    An exception would be a case in which your hand hovers over two balls, such that if you don’t pick one you will pick the other.

  4. 4.

    That is why Lewis (1979a) required ‘small miracles’, relative to the laws of the actual world, in assessing counterfactuals, under the assumption of determinism.

  5. 5.

    This example is from Sorensen (2001), p. 58.

  6. 6.

    Bradley continues to speak, in Stalnaker-Lewis terms, of the ‘nearest’ A-world; but as there is no ordering relation of worlds, this name is not apt.

  7. 7.

    This hyper-realism has a history in Jesuit theology, and is sometimes called ‘Molinism’ after the sixteenth-century Jesuit theologian Luis de Molina.

  8. 8.

    I discuss these alternative approaches in more detail in Edgington (2020).

  9. 9.

    See e.g. Vann McGee (1989), Richard Jeffrey (1991), and Stalnaker and Jeffrey (1994).

  10. 10.

    In the case of incompatible antecedents, the expected value of the conjunction turns out to be p(A&B)p(C|¬A) + p(¬A&C)p(B|A) which simplifies to p(B|A)p(C|¬A).

  11. 11.

    Mark Lance (1991) has a similar example: there is a werewolf. It’s 50% likely to be in our area tonight. If it is, it kills everyone outside. ‘If John went out, he was killed’ gets 0.5. ‘If John went out the front door, he was killed, and if John went out the back door, he was killed’ still deserves 0.5; but it gets only 0.25 on the present proposal.

  12. 12.

    I could have listed the eight ordered triples alongside the following eight lines (e.g. line 1 is <w1, w1, w1> and line 2 is <w1, w1, w2>). But I thought this would be less useful than my explanation above.

  13. 13.

    Bradley makes brief remarks about nested conditionals, which will involve ordered pairs as members of ordered pairs, but the details have still to be worked out. Quantification should be unproblematic.

  14. 14.

    My thanks to Scott Sturgeon and to two anonymous reviewers for helpful comments.

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Authors and Affiliations

  1. Birkbeck, University of London, London, UK

    Dorothy Edgington

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  1. Dorothy Edgington
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Correspondence to Dorothy Edgington .

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Editors and Affiliations

  1. Department of Linguistics, University of Connecticut, Storrs Mansfield, CT, USA

    Stefan Kaufmann

  2. Department of Psychology, Durham University, Durham, UK

    David E. Over

  3. Department of South Asian Studies, National Institute of Oriental Languages and Civilisations (INALCO), Paris, France

    Ghanshyam Sharma

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Edgington, D. (2023). Conditionals, Indeterminacy, Probability and Truth. In: Kaufmann, S., Over, D.E., Sharma, G. (eds) Conditionals. Palgrave Studies in Pragmatics, Language and Cognition. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-031-05682-6_2

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  • DOI: https://doi.org/10.1007/978-3-031-05682-6_2

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