Abstract

INDEX PREFACE......................................................................................................... i CHAPTER 1: INTRODUCTION........................................................................... 1 0.- Purposes and Importance of the Research:1 1.- Preliminaries: 1 a.- Overview of the Logical System to Be Used: 2 b.- Different Versions of the Principles of Excluded Middle and of Non Contradiction: 5 c.- Two Formulations of the Principle of Bivalence: 6 d.- Vagueness or Fuzziness?: 6 e.- Semantics, Pragmatics, Realism and Pragmatism. General Orientation of the Present Work: 7 i.- Pragmatist and Realist Views on Meaning and Truth: 8 ii.- Pragmatist and Realist Views on Vagueness and the Sorites: 10 2.- What Are the Problems?: 12 3.- The Problems of Fuzziness: 12 a.- The Bearer of Fuzziness: 12 b.- The Nature of Fuzziness: 14 i) Indeterminacy?: 14 ii) Borderline Cases: 17 iii) No Boundaries?: 18 iv) Sorites Susceptibility: 20 c.- The Alethic Status of Fuzzy Sentences: 21 4.- The Sorites Paradox: 21 a.- Origins: 22 b.- Informal Structure of the Argument: 22 c.- Formalization of the Argument: 23 d.- The Soritical Series: 24 e.- Sorites for an Unbounded Property:26 5.- Denials of the Major Premise: 27 6.- The Refusal of the Slippery Slope: 29 7.- The Tasks of a Theory of Fuzziness: 31 8.- Degrees and Opposites in Ancient Philosophy: 31 a.- Heraclitus and the Unity of Opposites: 31 b.- Parmenides and the Principle of Exclusion of Intermediary Situations: 32 c.- Anaxagoras and the Principle of Universal Mixture: 33 d.- Plato and Degrees of Being, Non-Being, and the Intermediate Things: 34 e.- Gradualist Aristotle?: 35 9.- Summary: 38 CHAPTER 2: AGNOSTICISM............................................................................. 39 1.- Quine: 39 a.- Evaluation: 40 2.- Dummett vs. Strong Bivalence: 40 3.- Williamson's Agnosticism: 42 a.- Basic Tenets: 42 b.- The Unknowability of the Sharp Boundary: 44 c.- The Supervenience of Vagueness: 46 i.- The Discussion on the Determination of Meaning: 47 d.- On the Alleged Incoherence of Non-Bivalence: 49 i.- Discussion: 50 e.- Continuing the Debate: 55 i.- With Crispin Wright: 55 ii.- With Machina and Deutsch: 56 iii.- With Stephen Schiffer: 57 iv.- With Peter Mott: 59 v.- With Peter Simons: 61 f.- Summary: 62 4.- Sorensen's Agnosticism: 62 a.- Assessment: 64 5.- Conclusion: 64 CHAPTER 3: INDETERMINISM AND SUPERVALUATIONISM.............................. 66 1.- Russell: 66 a.- Assessment: 67 2.- Supervaluationism: 68 a.- Fine: 68 i.- The Precisification of Vagueness: 68 ii.- Super-Truth and Validity: 70 iii.- Why the Falsity of the Major Premise Does Not Entail Sharp Boundaries?: 70 b.- Keefe's defence of Supervaluationism: 71 c.- Assessing Supervaluationism: 73 3.- Michael Tye's Indeterminism: 75 a.- There Is No Determinate Fact of the Matter about whether a is F: 76 b.- Indefinite Premises and Higher Order Vagueness: 77 c.- Criticism: 78 CHAPTER 4. THE MANY-VALUED, FUZZY VIEW................................................ 80 1.- Engel: 80 a.- There Are Gradual Properties: 80 b.- Against Dichotomies: 81 2.- Goguen: 82 a.- Semantics of the Predicate 'Short': 82 b.- Connectives: 83 c.- Gradual Validity: 84 d.- How Does the Sorites Function?: 84 e.- Conclusion: 87 3.- Lakoff: 87 a.- Hedges: 89 b.- Assessment: 89 4.- Machina: 89 a.- The Philosophical Understanding of Vagueness: 89 b.- The Logic of Vagueness: 92 c.- Explaining the Plausibility of the Sorites: 94 d.- Assessment: 96 5.- Smith: 97 a.- Vagueness as Closeness: 97 b.- Degree Functions and Blurry Sets: 99 c.- Gradual Validity: 100 d.- The Sorites: 100 e.- Assessment: 101 f.- Smith's Defence of Degrees of Truth: 103 6.- On the Measure of Degrees of Truth and of Membership: 106 7.- On Williamson's Objections Against Many-Valued Logics: 107 CHAPTER 5. OTHER APPROACHES.................................................................. 110 1.- Wright's Intuitionism: 110 a.- The Beginnings and Maturation of the Reflection: 110 b.- The Quandary and Permissibility Views of Borderline Cases: 112 c.- The Intuitionist Solution to the Sorites: 114 d.- Closing Commentary: 114 2.- Nihilism: 115 a.- Unger: 115 i.- Criticism: 117 b.- Horgan: 119 i.- Criticism: 120 3.- Paraconsistent Approaches: 122 a.- Subvaluationism: 122 b.- Relevantism:124 c.- Vagueness-Adaptive Logic: 125 4.- Raffman's Contextualism: 127 a.- Criticism: 129 CHAPTER 6: CONTRADICTORIAL GRADUALISM VS. DISCONTINUISM................ 131 1.- The Soritical Series Again: 131 2.- The Nature and the Cause of the Transition: 133 3.- Is the Transition Possible?: 133 4.- The Nihilist Answer: 134 5.- The Discontinuist Proposal: 135 a.- Abrupt Transition: 135 b.- Unaccounted Change: 136 6.- Contradictorial Gradualism: 138 a.- Fuzziness: 138 b.- Degrees of Properties: 140 c.- Degrees of Truth: 141 d.- Minimalism vs. Maximalism: 143 e.- From Degrees to Contradictions: 146 f.- Gradual Transition: 147 7.- Conclusion: 147 CHAPTER 7: CONCLUSION. FUZZINESS VINDICATED AS GRADUAL AND CONTRADICTORY.......................... 149 BIBLIOGRAPHY............................................................................................... 155.