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Probabilistic Semantics and Pragmatics for the Language of Uncertainty

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Book cover Soft Methods for Data Science (SMPS 2016)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 456))

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Abstract

The idea that the probability of a conditional is the corresponding conditional probability has led something of an embattled existence in philosophy and linguistics. Part of the reason for the reluctance to embrace it has to do with certain technical difficulties (especially triviality). Even though solutions to the triviality problem are known to exist, their widespread adoption is hindered by their narrow range of data coverage and unclear relationship to established frameworks for modeling the dynamics of belief and conversation. This paper considers the case of Bernoulli models and proposes steps towards broadening the coverage of their application.

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Notes

  1. 1.

    Van Fraassen dubbed them “Stalnaker Bernoulli models.” I avoid this label in deference to Robert Stalnaker’s contention that it suggests more credit for him than he deserves (p.c.).

  2. 2.

    Except, that is, for models with no more than two distinct propositions in the domain of the probability distribution. [24] called such models “trivial.”

  3. 3.

    Note that \(V^*(\varphi >\psi )\) is defined with probability 1 if \(P^*(\varphi ) > 0\), and undefined with probability 1 if \(P^*(\varphi ) = 0\). In the latter case, the expectation of the conditional’s truth value is undefined, as is the probability \(P^*(\psi |\varphi )\), at least when defined as the ratio \(P^*(\varphi \wedge \psi )/P^*(\varphi )\). But see [18] for a definition of conditional probability in Bernoulli models which is defined for certain zero-probability propositions on which one might want to conditionalize. ([8, 9] also define the “prevision” for \(\varphi >\psi \) in such a way that it includes the case that the prevision of \(\varphi \) is zero.).

  4. 4.

    I am grateful to two anonymous reviewers for helpful feedback.

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Authors and Affiliations

  1. Department of Linguistics, University of Connecticut, 365 Fairfield Way, Storrs, CT, 06269-1145, USA

    Stefan Kaufmann

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  1. Stefan Kaufmann
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Correspondence to Stefan Kaufmann .

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Editors and Affiliations

  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Maria Brigida Ferraro

  2. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Paolo Giordani

  3. Dept of Basic & Applied Sciences Engg, Sapienza University of Rome, Rome, Italy

    Barbara Vantaggi

  4. Dept of Stoc Metds,Polish Academy of Sci, Systems Research Institute, Warsaw, Poland

    Marek Gagolewski

  5. Dept of Statis&OR and MD, Univ de Oviedo, Oviedo, Spain

    María Ángeles Gil

  6. Dept of Stoc Metds,Polish Aca of Science, Systems Res Inst, Warsaw, Poland

    Przemysław Grzegorzewski

  7. Sys Res Inti, Dept of Stoch Methods, Polish Acadmy Sci in Warsaw, Warsaw, Poland

    Olgierd Hryniewicz

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Kaufmann, S. (2017). Probabilistic Semantics and Pragmatics for the Language of Uncertainty. In: Ferraro, M., et al. Soft Methods for Data Science. SMPS 2016. Advances in Intelligent Systems and Computing, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-42972-4_36

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  • DOI: https://doi.org/10.1007/978-3-319-42972-4_36

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