Consider the following claims: 1. Rational credences are real-valued.2. A rational agent is more confident in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5115_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation> than in <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5115_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(B\)</EquationSource> </InlineEquation> just in case appropriate set-theoretic relations between the relevant events and/or appropriate inequalities between her numerical credences, whether conditional or not, hold.3. If a rational agent’s conditional credence in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5115_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation>, given <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5115_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\cup B\)</EquationSource> </InlineEquation>, is greater than her conditional credence in <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5115_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(B\)</EquationSource> </InlineEquation>, given <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5115_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="49" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\cup B\)</EquationSource> </InlineEquation>, then she is more confident in <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5115_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(A\)</EquationSource> </InlineEquation> than in <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5115_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(B\)</EquationSource> </InlineEquation>.4. There are two distinct and particular ways of ordering the events in a lottery over the naturals, for each of which there exists a rational agent whose comparative confidence ordering corresponds to that ordering.Versions of the first three claims have been defended by various authors, though not necessarily in conjunction, and I claim that the fourth is at least plausible. In this paper, I show that the conjunction of these four claims is inconsistent. Thus, at least one claim must be rejected.

Not staying regular?

期刊论文
发表日期：

2025年7月14日

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Joshua Thong

摘要

Consider the following claims:

1. Rational credences are real-valued.

2. A rational agent is more confident in \(A\) than in \(B\) just in case appropriate set-theoretic relations between the relevant events and/or appropriate inequalities between her numerical credences, whether conditional or not, hold.

3. If a rational agent’s conditional credence in \(A\) , given \(A\cup B\) , is greater than her conditional credence in \(B\) , given \(A\cup B\) , then she is more confident in \(A\) than in \(B\) .

4. There are two distinct and particular ways of ordering the events in a lottery over the naturals, for each of which there exists a rational agent whose comparative confidence ordering corresponds to that ordering.

Versions of the first three claims have been defended by various authors, though not necessarily in conjunction, and I claim that the fourth is at least plausible. In this paper, I show that the conjunction of these four claims is inconsistent. Thus, at least one claim must be rejected.