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Rethinking the Acceptability and Probability of Indicative Conditionals

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Conditionals

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

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Abstract

The chapter is devoted to the probability and acceptability of indicative conditionals. Focusing on three influential theses, the Equation, Adams’ thesis, and the qualitative version of Adams’ thesis, Sikorski argues that none of them is well supported by the available empirical evidence. In the most controversial case of the Equation, the results of many studies which support it are, at least to some degree, undermined by some recent experimental findings. Sikorski discusses the Ramsey Test, and Lewis’ triviality proof, with special attention dedicated to the popular ways of blocking it. Sikorski concludes that the role of the three theses in future studies of conditionals should be rethought, and he presents alternative proposals.

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Notes

  1. 1.

    For the details and motivation of the view see, e.g., Bennett (2003) or Edgington (1995). For the critical discussion see: Douven (2015).

  2. 2.

    The source of this formulation is Douven and Verbrugge (2012).

  3. 3.

    For a detailed discussion of the difference between the two notions and an experiment indicating that \(\Delta P\) predicts intuitive relevance better than the difference measure, see Skovgaard-Olsen et al. (2016a).

  4. 4.

    For example McGee, 1989: “Ernest Adams (1965, 1975) has advanced a probabilistic account of conditionals, according to which the probability of a simple English indicative conditional is the conditional probability of the consequent given the antecedent. The theory describes what English speakers assert and accept with unfailing accuracy, yet the theory has won only limited acceptance.”

  5. 5.

    See, e.g., Over and Cruz (2018) or Evans and Over (2004).

  6. 6.

    E.g., “If Adidas get more superstars to wear their new football boots then the sales of these boots will increase” or “If the cost of petrol increases then traffic congestion will improve.”

  7. 7.

    For the discussion see: Douven et al. 2017.

  8. 8.

    E.g., “Most theorists of conditionals accept the Ramsey test thesis for indicatives” Bennett (2003).

  9. 9.

    See, e.g., Evans and Over (2004, pp. 21–22).

  10. 10.

    See, e.g., Bennett (2003) or Evans and Over (2004).

  11. 11.

    see e.g., Kölbel (1997).

  12. 12.

    In fact Adams (1975) claims that this natural interpretation of probability is not applicable to conditionals. He seems to be aware of how problematic the consequences of NTV are, for example:

    “The author’s very tentative opinion on the ‘right way out’ of the triviality argument is that we should regard the inapplicability of probability to compounds of conditionals as a fundamental limitation of probability, on a par with the inapplicability of truth to simple conditionals.”

    Adams (1975, p. 35).

  13. 13.

    Example from Kölbel (2000).

  14. 14.

    The Equation is sometimes called Stalnaker Hypothesis(SH), therefore its generalized version is called Generalized Stalnaker Hypothesis (GSH).

  15. 15.

    It is also discussed in Jackson (1987): “When A is consistent, there is something quite generally wrong with asserting both \(( A \rightarrow B )\) and \(( A \rightarrow\) not-B). We cannot assert in the one breath ‘If it rains, the match will be cancelled’ and ‘If it rains, the match will not be cancelled’. This conforms nicely with [AT]; for, by it, we have \(As (A\rightarrow B) = 1 - As (A\rightarrow\) not-B), from the fact that \(P ( B / A ) = 1 - P (\)not-B/A). Thus, the fact that \(( A \rightarrow B )\) and \(( A \rightarrow\)not-B) cannot be highly assertible together when A is consistent is nicely explained by [AT] as a reflection of the fact that P(B/A) and P(not-B/A) cannot both be high when A is consistent. Indeed, [AT] explains the further fact that \(( A \rightarrow B )\) and \(( A \rightarrow\)not-B) have a kind of ‘see-saw’ relationship. As the assertibility of one goes up, the assertibility of the other goes down.”

  16. 16.

    For discussion see: Hájek and Hall (1994).

  17. 17.

    Adams (1975) reject SP for conditionals but as far as I understand, he does not provide an alternative. At the same time, his theory is usually interpreted as describing the acceptability of conditionals rather than their probability.

  18. 18.

    See de Finetti (n.d.) and Baratgin et al. (2018) for discussion.

  19. 19.

    See e.g., Egré et al. (2019). For discussion of defective truth tables see: Baratgin et al. (2018) or Over and Baratgin (2017).

  20. 20.

    See e.g., van Wijnbergen-Huitink et al. 2015.

  21. 21.

    LT seems to be quite popular, see, e.g., Foley (2009).

  22. 22.

    Alternative theories are usually more complex see, e.g., Proust (2012).

  23. 23.

    As we have seen the material implication theory is an exception. It provides us with truth conditions that can be easily translated into the definition of probability. Sadly, both the definition of probability and truth conditions proposed by the material implication theory are unintuitive.

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Acknowledgments

I would like to thank Jan Sprenger, Rafał Urbaniak, Vincenzo Crupi, Andrea Iacona, Matteo Colombo, Karolina Krzyżanowska, Igor Douven, and the anonymous referees for their useful comments. I would also thank the editors of this volume, David E. Over and Stefan Kaufmann for the many suggestions which helped me to improve the paper.

Funding

The research was supported by Starting Investigator Grant No. 640638 (“OBJECTIVITY—Making Scientific Inferences More Objective”) of the European Research Council (ERC).

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  1. Warsaw University of Technology, Warsaw, Poland

    Michał Sikorski

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Correspondence to Michał Sikorski .

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  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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Sikorski, M. (2023). Rethinking the Acceptability and Probability of Indicative Conditionals. 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_5

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