, Volume 30, Issue 1, pp 3-15

First online:

Triviality Pursuit

  • Alan HájekAffiliated withResearch School of Social Sciences, Australian National University Email author 

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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.


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