Bernoulli Semantics and Ordinal Semantics for Conditionals

Journal of Philosophical Logic 52 (1):199-220 (2023)
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Abstract

Conditionals with conditional constituents pose challenges for _the Thesis_, the idea that the probability of a conditional is the corresponding conditional probability. This note is concerned with two proposals for overcoming those challenges, both inspired by early work of van Fraassen: the _Bernoulli Semantics_ associated with Stalnaker and Jeffrey, and augmented with a mechanism for obtaining “local probabilities” by Kaufmann; and a proposal by Bacon which I dub _Ordinal Semantics_. Despite differences in mathematical details and emphasis of presentation, both proposals lend themselves for use as a basis for a modal-theoretic interpretation of embedded conditionals. The goal of this note is to compare the two frameworks by implementing a model for the interpretation of conditionals in each, based on the same underlying probability model for non-conditional sentences. I show that in the Ordinal model, certain sentences are assigned probabilities that do not accord with intuitions. This problem is familiar from the literature on Bernoulli models and can be addressed by introducing Kaufmann-style local probabilities into Ordinal models. I then show that Bernoulli Semantics has other limitations, in that it assigns probabilities in violation of the Thesis to certain very complex formulas. The upshot is that a fusion of the theories may be our best shot at getting the predictions right.

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Stefan Kaufmann
University of Connecticut

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References found in this work

Studies in the Way of Words.Herbert Paul Grice - 1989 - Cambridge: Harvard University Press.
On conditionals.Dorothy Edgington - 1995 - Mind 104 (414):235-329.
Philosophical Guide to Conditionals.Jonathan Bennett - 2003 - Oxford University Press UK.

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