Conditionals, comparative probability, and triviality: The conditional of conditional probability cannot be represented in the object language

Topoi 18 (2):97-116 (1999)
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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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Citations of this work

Lewis’ Triviality for Quasi Probabilities.Eric Raidl - 2019 - Journal of Logic, Language and Information 28 (4):515-549.

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References found in this work

The Logic of Scientific Discovery.K. Popper - 1959 - British Journal for the Philosophy of Science 10 (37):55-57.
The Logic of Conditionals.Ernest Adams, Ernest W. Adams, Jaakko Hintikka & Patrick Suppes - 1965 - Journal of Symbolic Logic 39 (3):609-611.
A Model of the Universe.Storrs McCall - 1994 - Philosophical Quarterly 47 (186):113-115.

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