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, Volume 30, Issue 1, pp 3–15 | Cite as

Triviality Pursuit

Article

Abstract

The thesis that probabilities of conditionals are conditional probabilities has putatively been refuted many times by so-called ‘triviality results’, although it has also enjoyed a number of resurrections. In this paper I assault it yet again with a new such result. I begin by motivating the thesis and discussing some of the philosophical ramifications of its fluctuating fortunes. I will canvas various reasons, old and new, why the thesis seems plausible, and why we should care about its fate. I will look at some objections to Lewis’s famous triviality results, and thus some reasons for the pursuit of further triviality results. I will generalize Lewis’s results in ways that meet the objections. I will conclude with some reflections on the demise of the thesis—or otherwise.

Keywords

Probabilities of conditionals Conditional probabilities Stalnaker’s thesis Triviality results Conditionalization Imaging Blurred imaging Maximum entropy Minimum cross entropy Boldness Moderation Revision rules 

Notes

Acknowledgments

I am indebted to Ned Hall, Richard Jeffrey, David Lewis, Bas van Fraassen, and Lyle Zynda for very helpful comments on a short, early precursor to this paper. I am grateful to participants in a reading group in Leuven for discussion of a resuscitated version of it—especially Jake Chandler, Igor Douven, and David Etlin. I have recently substantially revised and expanded it. For further valuable comments on this transmogrified version, I thank especially Rachael Briggs, John Cusbert, Daniel Greco, Aidan Lyon, Daniel Nolan, Wolfgang Schwarz, and Dan Singer. Thanks also to Brett Calcott and Ralph Miles for their help.

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Research School of Social SciencesAustralian National UniversityCanberraAustralia

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