A Dutch Book Theorem for Quantificational Credences

Ergo: An Open Access Journal of Philosophy 4 (2017)
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Abstract

In this paper, I present an argument for a rational norm involving a kind of credal attitude called a quantificational credence – the kind of attitude we can report by saying that Lucy thinks that each record in Schroeder’s collection is 5% likely to be scratched. I prove a result called a Dutch Book Theorem, which constitutes conditional support for the norm. Though Dutch Book Theorems exist for norms on ordinary and conditional credences, there is controversy about the epistemic significance of these results. So, my conclusion is that if Dutch Book Theorems do, in general, support norms on credal states, then we have support for the suggested norm on quantificational credences. Providing conditional support for this norm gives us a fuller picture of the normative landscape of credal states.

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Benjamin Lennertz
Colgate University

Citations of this work

Noncognitivism and the Frege‐Geach Problem in Formal Epistemology.Benjamin Lennertz - 2021 - Philosophy and Phenomenological Research 102 (1):184-208.

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References found in this work

Risk and Rationality.Lara Buchak - 2013 - Oxford University Press.
Truth and Probability.Frank Ramsey - 1926 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 52-94.
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Belief and the Will.Bas C. van Fraassen - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. Routledge. pp. 235-256.
Distorted Reflection.Rachael Briggs - 2009 - Philosophical Review 118 (1):59-85.

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