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Conditionals, Comparative Probability, and Triviality: The Conditional of Conditional Probability Cannot Be Represented in the Object Language

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Abstract

In this paper we examine the thesis that the probability of the conditional is the conditional probability. Previous work by a number of authors has shown that in standard numerical probability theories, the addition of the thesis leads to triviality. We introduce very weak, comparative conditional probability structures and discuss some extremely simple constraints. We show that even in such a minimal context, if one adds the thesis that the probability of a conditional is the conditional probability, then one trivializes the theory. Another way of stating the result is that the conditional of conditional probability cannot be represented in the object language on pain of trivializing the theory.

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References

  • Adams, E.W.: 1975, The Logic of Conditionals, Dordrecht: Reidel.

    Google Scholar 

  • Appiah, A.: 1985, Conditionals and Assertion, Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Hajek, A.: 1989, 'Probabilities of Conditionals – Revisited', Journal of Philosophical Logic 18, 423–428.

    Article  Google Scholar 

  • Lewis, D.K.: 1976, 'Probabilities of Conditionals and Conditional Probability', Philosophical Review 85, 279–315.

    Google Scholar 

  • McCall, S.: 1994, A Model of the Universe, Oxford: Clarendon Press.

    Google Scholar 

  • Morgan, C.G.: 1984, 'Weak, Conditional Comparative Probability as a Formal Semantic Theory', Zeitschr.f.math.Logik und Grundlagen d.Math. 30, 199–212.

    Article  Google Scholar 

  • Morgan, C.G. and Mares, E.D.: 1995, 'Conditionals, Probability, and Non-triviality', Journal of Philosophical Logic 24, 455–467.

    Article  Google Scholar 

  • Popper, K.: 1959, The Logic of Scientific Discovery, New York, Basic Books.

    Google Scholar 

  • Stalnaker, R.C.: 1970, 'Probabilities of Conditionals', Philosophy of Science 37, 68–80.

    Article  Google Scholar 

  • van Fraassen, B.C.: 1976, 'Probabilities of Conditionals', in W.L. Harper and C.A. Hooker (Eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, vol. 1, Dordrecht: Reidel, pp. 261–300.

    Google Scholar 

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Authors
  1. Charles G. Morgan
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Morgan, C.G. Conditionals, Comparative Probability, and Triviality: The Conditional of Conditional Probability Cannot Be Represented in the Object Language. Topoi 18, 97–116 (1999). https://doi.org/10.1023/A:1006238120301

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  • DOI: https://doi.org/10.1023/A:1006238120301

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