Table Of ContentOUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
Epistemic Risk and the Demands
of Rationality
OUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
OUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
Epistemic Risk and
the Demands of
Rationality
RICHARD PETTIGREW
OUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
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OUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
Contents
Abstract ix
Acknowledgements xi
1. Introduction 1
I. A PERMISSIVE THEORY OF EPISTEMIC
RATIONALITY
2. VarietiesofPermissivism 11
2.1 WhatSortofDoxasticState? 11
2.2 InterpersonalorIntrapersonal? 14
2.3 RadicalorNot? 15
2.4 CommonorRare? 16
2.5 MyBrandofPermissivism 17
3. EpistemicRiskandEpistemicUtilityforBeliefs 19
4. EpistemicRiskandEpistemicUtilityforCredences 30
4.1 MeasuringtheEpistemicUtilityofanIndividualCredence 30
4.2 MeasuringtheEpistemicUtilityofanEntireCredalState 33
4.3 WhyShouldOurMeasuresBeStrictlyProper? 36
5. FoundationalResultsinEpistemicUtilityTheory 46
5.1 Probabilism 46
5.2 ThePrincipalPrinciple 47
5.3 PlanConditionalization 49
6. EpistemicRiskandPickingPriorsI:TheDecisionRule 53
6.1 Risk-SensitiveDecision-MakingUnderRisk 54
6.1.1 ExpectedUtilityTheoryandtheDiminishingMarginal
UtilityofMoney 55
6.1.2 Risk-WeightedExpectedUtilityandtheAllaisPreferences 56
6.2 Risk-SensitiveDecision-MakingUnderUncertainty 61
6.2.1 SubjectiveBayesianism 64
6.2.2 ObjectiveBayesianism 64
6.2.3 Risk-WeightedSubjectiveBayesianism 65
6.2.4 Risk-WeightedObjectiveBayesianism 66
OUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
vi contents
6.2.5 Wald’sMaximinRule 66
6.2.6 Hurwicz’sCriterionofRealism 67
6.2.7 TheGeneralizedHurwiczCriterion 69
6.3 CharacterizingOurRules 71
6.3.1 TheAxioms 72
6.3.2 TheRepresentationTheorems 78
6.4 Appendix:Proofs 81
6.4.1 AUsefulLemma 81
6.4.2 ProofofTheorem7(i):CharacterizingSubjective
Bayesianism 82
6.4.3 ProofofTheorem7(ii):CharacterizingObjective
Bayesianism 83
6.4.4 ProofofTheorem7(iii):CharacterizingSubjective
Risk-WeightedBayesianism 83
6.4.5 ProofofTheorem7(iv):CharacterizingObjective
Risk-WeightedBayesianism 84
6.4.6 Proof of Theorem 7(vi): Characterizing the Hurwicz
Criterion 85
6.4.7 ProofofTheorem7(v):CharacterizingMinimax 86
6.4.8 ProofsofTheorems7(vii):Characterizingthe
GeneralizedHurwiczCriterion 86
7. EpistemicRiskandPickingPriorsII:TheConsequences
oftheRule 89
7.1 DecomposingOptionsintoTheirComponentParts 90
7.2 TheCredalConsequencesoftheRules 95
7.2.1 TheCredalConsequencesoftheOtherRules 95
7.2.2 TheCredalConsequencesofGHC 97
7.3 Appendix:Proofs 105
7.3.1 ProofofTheorem9 105
8. EpistemicRiskandPickingPosteriors 116
8.1 GHCForever 116
8.2 PriorsandPlansTogether 120
8.3 UsingPriorstoPickPosteriors 122
8.4 TyingUpLooseEnds 126
8.4.1 MaximizingExpectedEpistemicUtilityfromWhose
PointofView? 126
8.4.2 InFavourofMaximizingExpectedUtility 127
8.5 Appendix:Proofs 134
OUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
contents vii
II. PUTTING THE THEORY TO WORK
9. WhatIstheValueofRationality? 141
9.1 TheValueofRationality 141
9.2 DeferringtoRationality 148
9.2.1 Levinstein’sDeferenceArgumentAgainstPermissivism 150
9.2.2 GrecoandHeddenontheConceptofRationality 159
9.3 LifeontheEdgeofRationality 161
10. IsBruteShufflingIrrational? 168
11. PriorsthatAllowYoutoLearnInductively 175
12. Clifford’sShipowner,ConspiracyTheories,andChoosing
withandforOthers 183
12.1 ChoosingforOthers 183
12.2 ChoosingwithOthers 191
13. SummingUp 201
References 203
Index 209
OUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
OUPCORRECTEDPROOF – FINAL,16/6/2022,SPi
Abstract
Theshortabstract:Epistemicutilitytheory+permissivismaboutattitudes
toepistemicrisk⇒permissivismaboutrationalcredences.
The longer abstract: I argue that epistemic rationality is permissive. More
specifically,Iarguefortwoclaims.First,aradicalversionofinterpersonal
permissivismaboutrationalcredence:formanybodiesofevidence,thereis
awiderangeofcredalstatesforwhichthereissomeindividualwhomight
rationally adopt that state in response to that evidence. Second, a slightly
lessradicalversionofintrapersonalpermissivismaboutrationalcredence:
formanybodiesofevidenceandformanyindividuals,thereisanarrower
butstillwiderangeofcredalstatesthattheindividualmightrationallyadopt
inresponsetothatevidence.Myargumentproceedsfromtwopremises:(1)
epistemicutilitytheory;and(2)permissivismaboutattitudestoepistemic
risk.Epistemicutilitytheorysaysthis:Whatitisepistemicallyrationalfor
you to believe is what it would be rational for you to choose if you got to
pick your beliefs and, when picking them, you cared only for their purely
epistemic value. So, to say which credences it is epistemically rational for
youtohave,wemustsayhowyoushouldmeasurepurelyepistemicvalue,
and which decision rule it is appropriate for you to use when you face
the hypothetical choice between the possible credences you might adopt.
Permissivismaboutattitudestoepistemicrisksaysthatrationalitypermits
many different attitudes to epistemic risk. These attitudes can show up in
epistemicutilitytheoryintwoways:inthewaythatyoumeasureepistemic
value;andinthedecisionrulethatyouusetopickyourcredences.Iexplore
whathappensifweencodeourattitudestoepistemicriskinourepistemic
decisionrule.Theresultistheinterpersonalandintrapersonalpermissivism
describedabove:differentattitudestoepistemicriskleadtodifferentchoices
ofpriors;givenmostbodiesofevidenceyoumightacquire,differentpriors
leadtodifferentposteriors;andevenoncewefixyourattitudestoepistemic
risk, if they are at all risk-inclined, there is a range of different priors and
thereforedifferentposteriorstheypermit.Theessayendsbyconsideringa
rangeofobjectionstothesortofpermissivismforwhichI’veargued.
