Vagueness: A Guide (eBook)

Giuseppina Ronzitti is specialized in philosophy of mathematics and defended her PhD thesis on mathematical intuitionism in 2002 in Genova (Italy). She has worked as a researcher in France (Archives Poincaré, Nancy) and in Finland (University of Helsinki) and has had longer and shorter stays in the Netherlands (Nijmegen), the US (University of Notre Dame, Indiana) and Norway (The Wittgenstein Archives, Bergen).

Introduction Vagueness and... 6
Contents 12
Contributors 13
Notes on the Contributors 14
1 The Sorites Paradox 16
1.1 The Sorites Puzzle 16
1.2 The Sorites Paradox 17
1.2.1 The Conditional Sorites 19
1.2.2 Responding to the Conditional Sorites 20
1.2.3 The Phenomenal Sorites 26
1.2.4 The Identity Sorites 27
1.2.5 The Mathematical Induction Sorites 28
1.2.6 The Line-Drawing Sorites 29
1.2.7 The Forced March Sorites 29
1.3 Soriticality and Vagueness 30
References 31
2 Vagueness and Metaphysics 33
2.1 Vague Objects and Vague Identity: Evans’s Argument 34
2.2 Is Evans’s Argument Question-Begging? 39
2.3 Lessons from the Parallel Between Evans’s Argument and the Barcan-Kripke Proof of the Necessity of Identity 40
2.4 A Stripped-Down Version of Evans’s Argument 43
2.5 A Plausible Example of Ontically Indeterminate Identity 46
2.6 The Paradox of the 1,001 Cats, the Problem of the Many, and Vagueness of Constitution 48
2.7 Vagueness and Persistence: Perdurance Versus Endurance 50
2.8 Vague Identity, Vague Existence, and Sorites-Style Reasoning 56
2.9 Does the Notion of Vague Existence Make Any Sense? 60
2.10 Concluding Remarks 65
References 66
3 Vagueness and Logic 68
3.1 Setting Up 68
3.2 The Ordinary Model Theory Will Do 70
3.3 Partial Interpretations, and Sharpenings Thereof 71
3.3.1 Supervaluation 75
3.3.2 Open-Texture 79
3.3.3 Inconsistency Again 82
3.3.4 Addendum: Running Up the Orders 84
3.4 Many-Values 85
3.4.1 Truth-Functionality 86
3.4.2 Non-truth-Functionality 89
3.4.3 Having Our Cake and Eating It, Too 90
3.4.4 Addendum: Running Up the Orders Again 92
References 93
4 Vagueness and Meaning 95
4.1 Introduction 95
4.2 The Governing View 100
4.2.1 The Governing View and Epistemicist Theories 102
4.2.2 The Governing View and Contextualist Theories 103
4.2.3 The Governing View and Indeterminist Theories 104
4.3 The Relation of Meaning to Use 104
4.3.1 Meaning, Use, and Epistemicist Theories 105
4.3.2 Meaning, Use, and Contextualist Theories 106
4.3.3 Meaning, Use, and Indeterminist Theories 106
4.4 Open Texture 109
4.4.1 Open Texture and Epistemicist Theories 110
4.4.2 Open Texture and Contextualist Theories 110
4.4.3 Open Texture and Indeterminist Theories 111
4.5 The Problem of Inappropriate Precision 112
4.5.1 The Problem of Inappropriate Precision and Epistemicist Theories 114
4.5.2 The Problem of Inappropriate Precision and Contextualist Theories 114
4.5.3 The Problem of Inappropriate Precision and Indeterminacy Theories 115
4.6 Conclusion 117
References 117
5 Vagueness and Observationality 119
5.1 The Two Difficulties 120
5.2 Indiscriminability and the Sorites 121
5.3 Non-transitivity and Phenomenal Continua 126
5.4 Unattended Phenomenal Differences: An Experiment 128
5.5 Conclusion 133
References 133
6 Vagueness and Linguistics 134
6.1 Introduction 134
6.2 What Is Vagueness? 135
6.3 Why Vagueness? 139
6.4 Gradable Adjectives 142
6.4.1 The Degree Based Account 142
6.4.2 The Delineation Approach 144
6.4.3 Absolute Terms and Comparison Classes 149
6.4.4 Comparison Classes and Relative Adjectives 153
6.4.5 Degrees and Measures 156
6.5 Tolerance and the Sorites Paradox 158
6.5.1 Semi-orders 158
6.5.2 Contextual Solutions to the Sorites Paradox 160
6.5.3 Boundaryless Concepts and Higher Order Vagueness 167
6.6 Vagueness and Granularity 169
6.6.1 Absolute Terms Revisited 169
6.6.2 Standards of Precision 171
6.6.3 Granularity and Relevance 175
6.7 Conclusion 178
References 179
7 Vagueness and Law 182
7.1 Law Is Reflexive 184
7.2 Vagueness in Law Is Extravagant 185
7.3 Extravagant Vagueness and the Regulation of the Life of a Community 188
7.3.1 The Need for Vague Legislation 188
7.3.2 Vagueness in Interpretation 190
7.3.3 Non-linguistic Vagueness in Customary Rules (and in the Framework Rules of the System in Particular) 191
7.3.4 Private Ordering 192
7.4 Discretion and the Rule of Law Problem 193
7.4.1 Bivalence in Law 194
7.4.2 Arbitrariness and the Rule of Law 198
7.5 Conclusion 199
References 201
Index 203