Contents: List of

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List of Figures xvii

List of Tables xix

PartI.

Background

1. Non-ClassicalandNihilisticApproaches 3

1.1 RespondingtotheSorites 5

1.2 Weakening Classical Logic 6

1.3 Nihilism 10

2. Classical Approaches: An Overview of the Current Debate 16

2.1 EpistemicismandSupervaluationism 17

2.2 DoesVaguenessInvolveIgnorance? 21

2.3 Does Vagueness Involve Truth Value Gaps? 22

2.4 Many Interpretations or One? 24

2.5 Is Validity Local or Global? 26

3. AnOutlineofatteoryofPropositionalVagueness 30

3.1 Is Vagueness Linguistic? 31

3.2 Booleanism 32

3.3 The Epistemology of Vagueness 36

3.4 Probabilism 38

3.5 LogicalFeatures 41

3.6 Vagueness-Related Uncertainty as a Special Sort of Psychological Attitude 43

Part II.

Epistemological Matters

4. Vagueness and Language 47

4.1 Grammar 50

4.2 Parameters 53

4.3 Can One Explain Propositional Borderlineness in Terms

of Sentential Borderlineness? 54

4.4 Quantifying In 57

style='font-size: 8.5pt'>4.5 Vague Objects 60

4.6 Montague’s Paradox 61

4.7 More Vague Propositions than Sentences 63

4.8 VaguenessandtheObjectsofThought 64

5. Vagueness and Ignorance 69

5.1 InFavourofVaguePropositions 69

5.2 Explaining Ignorance about the Vague 76

5.2.1 Explaining ignorance via metalinguistic safety principles 79

5.3 Denying Ignorance about the Vague 84

5.3.1 The fine-grained no-ignorance view 84

5.3.2 The coarse-grained no-ignorance view 86

5.3.3 Non-linguistic behaviour 88

5.3.4 The contextualist no-ignorance view 89

5.3.5 More on non-linguistic behaviour 92

6.size=1 face="Times New Roman"> Vagueness and Evidence 96

6.1 InexactEvidence 97

6.2 UpdatingonVagueEvidence 106

6.2.1 Conditioningonapreciseproposition 106

6.2.2 Jeffreyconditioning 109

6.2.3 Conditioning on a vague proposition 114

6.2.4 Evidence for the whereabouts of cutoff points 116

6.3 A Principle of Plenitude for Vague Propositions 117

6.4 Evidential Roles and Degrees of Truth 121

7. Probabilism, Assertion, and Higher-Order Vagueness 124

7.1 FieldsTheory 125

7.2 Uncertainty in the Face of Higher-Order Vagueness 127

7.2.1 Vagueness and assertion 131

7.2.2 The role of borderlineness 133

style='font-size: 8.5pt'>7.2.3 The forced march sorites 135

7.2.4 Paradoxes of higher-order vagueness 136

7.3 Should Our Credences in the Vague Obey the Probability Calculus? 138

7.3.1 Dutch book arguments 139

7.3.2 Comparative probability judgements 144

7.3.3 Is there anything special about vagueness-related uncertainty? 148

8. Vagueness and Uncertainty 150

8.1 Expressivism about Vagueness 152

8.2 Disagreements about Morals, Conditionals, and Epistemic Modals 157

8.3 Do All Rational Disagreements about the Vague Boil Down

to Disagreements about the Precise? 161

9. Vagueness and Decision 169

9.1 Vagueness and Decision Theory 171

9.2 Vagueness and Action 174

9.3 Vagueness and Preferences 182

class=a8 style='margin-left:0cm;text-indent:18.0pt'>9.4 ProbabilityintheAbsenceofUncertainty 185

10. Vagueness and Desire 191

10.1 TheViewthatVaguenessisMerelyaKindofIgnorance 191

10.2 The Indifference Principle 195

10.3 Caring about the Vague 196

10.4 Is it Always Possible to Articulate your Desires Using Precise Language? 200

Part III.

Logical Matters

11. Vague Propositions 205

11.1 FinenessofGrain 206

11.2 IndividuationConditions 210

11.3 ATheoryofPropositions 212

11.4 ModeratelyFine-GrainedTheoriesofContent 219

12. Vagueness and Precision 222

12.1 Borderlineness as Primitive 224

12.1.1 The modal characterization of precision 226

class=a8 style='margin-left:0cm;text-indent:18.0pt'>12.1.2 Supervaluationism 227

12.1.3 Degeneracy 229

12.1.4 DoXastic features of vague propositions 232

12.2 Are the Propositions of Physics Precise? 233

12.3 Vagueness as Primitive 235

12.3.1 Determinacy operators 237

13. SymmetrySemantics 238

13.1 WhereThingsStandsoFar 238

13.2 Symmetries 240

13.3 Vagueness and Precision 245

13.4 A Semantical Account of Precision in Terms of Symmetries 249

13.4.1 Higher-order vagueness 251

13.4.2 Determinacy and necessity 255

14. Vagueness and the World 258

14.1 Factual Propositions and Supervaluationism 260

14.2 The Problem of Higher-Order Vagueness 262

14.2.1 Factual propositions 264

14.2.2 Fundamental propositions 267

14.3 Vagueness All the Way Down 267

15. Vagueness and Modality 275

15.1 The Interaction of Vagueness and Modality 276

15.2 The Proper Logic of Vagueness and Modality 282

15.3 The Supervenience of the Vague on the Precise 284

15.4 A Representation Theorem? 289

16. Vague Objects 296

16.1 Vagueness Throughout the Type Hierarchy 297

16.2 Vague Identity 299

16.3 Vague Parthood 304

16.4size=1 face="Times New Roman"> Vague Objects 307

17. Beyond Vagueness 311

17.1 Semantic Indecision 312

17.2 Can We Get By without Semantic Indecision? 313

17.3 An Account of Semantic Indecision	318
17.4 Concluding Remarks	325
18. Appendices	327
18.1 AppendixA	327
18.2 Appendix B	328
Bibliography	331
Index	339

List of Figures

2.1. Theadmissibleculoffpoinlsforrichness 25

lang=EN-US style='font-size:9.0pt;line-height:122%;font-family:"Cambria",serif'>6.1. The proposition that Harry is bald (i) is entailed by the proposition

that Harry has at most 1 hair, (ii) entails the proposition that Harry has at most IO¹⁰ hairs, and (iii) neither entails nor is entailed by the proposition that Harry has at most N hairs 104

6.2. A smooth curve and a sharp curve of n against credence that Harry

has n hairs 106

6.3. The result of conditioning uniform priors on the proposition that the

tree is between 300cm and 500cm high 108

6.4. A graph of n against the proportion of epistemic states where the tree's

height is ncm where it's also about 400cm 114

7.1. The cutoff points for baldness, determinate baldness, and determinate*

baldness 132

8.1. Three different priors assigning different probabilities to four maximally strong consistent precise propositions—‘cells'—but agreeing on the proportion of each cell that the vague proposition P takes up.

In this diagram, a proposition is represented by a subregion of each square, and the probability is represented by the magnitude of

its area 162

8.2. Possible credence distributions, given permissivism about ur-priors 166

12.1. The space divided into four world propositions. The two diagrams

represent two divisions into precise propositions depending on the precisifications v₁ and v₂ 230

12.2. Logical space divided into cells of consistent propositions that are maximally strong among the propositions that are precise according to i 236

13.1. Asimplemodelofvaguenessatallorders 252

13.2. According to the indices i and j, logical space is partitioned into four maximally strong consistent precise propositions in two different ways 253

14.1. The space divided into four world propositions. The two diagrams

represent two divisions into precise propositions depending on the precisifications v₁ and v₂ 261

14.2. The left diagram represents the partition of logical space according to both i and k (the partition according to Orb(G(i)) and Orb(G(k))),

and the right diagram according to j and l (Orb(G(j)) and Orb(G(l))) 273

16.1. Amodelofborderlineidentity

16.2. A model of the determinate existence of borderline identities.

At i, it is determinate that there is a borderline identity, although it's indeterminate whether it is x = y or y = z that is borderline

16.3. A model of the determinate* existence of borderline identities. At i, it is determinate at all orders that there is a borderline identity: for some n it is borderline whether x_n = x_n+₁, although it is vague which n this holds for

301

302

303

List of Tables

3.1. AxiomsforBooleanalgebras

15.1. lang=EN-US>Interaction principles for vagueness and modality

284

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Source: Bacon Andrew. Vagueness and Thought. Oxford University Press,2018. — 361 p. — (Oxford Philosophical Monographs). 2018

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