Synthese

, Volume 194, Issue 6, pp 2101–2119 | Cite as

Probabilistic consistency norms and quantificational credences

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Abstract

In addition to beliefs, people have attitudes of confidence called credences. Combinations of credences, like combinations of beliefs, can be inconsistent. It is common to use tools from probability theory to understand the normative relationships between a person’s credences. More precisely, it is common to think that something is a consistency norm on a person’s credal state if and only if it is a simple transformation of a truth of probability (a transformation that merely changes the statement from one about probability to one about credences). Though it is common to challenge the right-to-left direction of this biconditional, I argue in this paper that the left-to-right direction is false for standard versions of probability theory. That is, I make the case that there are consistency constraints on credal states that are not simple transformations of truths of standard versions of probability theory. I do so by drawing on a newly discovered type of credal attitude, a quantificational credence, and by showing how the consistency norms on this attitude can’t be represented as simple transformations of truths of standard versions of probability theory. I conclude by showing that a probability theory that could avoid the result would have to be strikingly different from the standard versions—so different that I suspect many would hesitate to call it a theory of probability at all.

Keywords

Credences Consistency Probability Quantificational credences 

Notes

Acknowledgments

Thanks to Mark Schroeder, David Gray, Reid Blackman, Scott Soames, Shyam Nair, and two anonymous reviewers for comments on and/or discussion of earlier drafts of this paper.

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Philosophy DepartmentColgate UniversityHamiltonUSA

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