Abstract Objects: For And Against

Description

This volume examines the question “Do abstract objects exist?”, presenting new work from contributing authors across different branches of philosophy. The introduction overviews philosophical debate which considers: what objects qualify as abstract, what do we mean by the word "exist” and indeed, what evidence should count in favor or against the thesis that abstract objects exist. Through subsequent chapters readers will discover the ubiquity of abstract objects as each philosophical field is considered. Given the ubiquitous use of expressions that purportedly refer to abstract objects, we think that it is relevant to attend to the controversy between those who want to advocate the existence of abstract objects and those who stand against them. Contributions to this volume depict positions and debates that directly or indirectly involve taking one position or other about abstract objects of different kinds and categories. The volume provides a variety of samples of how positions for or against abstract objects can be used in different areas of philosophy in relation to different matters. Preface......Page 6 References......Page 18 Contents......Page 20 Contributors......Page 22 1.1 What Is an Abstract Object?......Page 24 1.2 Why Debating over the Existence of Abstract Objects?......Page 26 1.3 How Should We Conduct the Debate?......Page 32 References......Page 35 Part I Enhanced Indispensability and Type Theories......Page 38 2.1 Introduction......Page 39 2.2 The Cicadas......Page 40 2.3 Bistability......Page 45 2.4 Carrying the Explanatory Load......Page 49 2.5 Conclusion......Page 55 References......Page 56 3 Description, Explanation and Ontological Committment......Page 57 3.1 Introduction......Page 58 3.2 Understanding substantial Mathematical Involvement in Scientific Explanation......Page 60 3.2.1 Baker's Account of Substantive Mathematical Involvement in Explanation......Page 61 3.2.2 Knowles and Saatsi on Substantive Mathematical Involvement in Scientific Explanation......Page 63 3.2.3 Baron on Genuine Mathematical Explanation......Page 66 3.3 From Their Criteria for Ontological Commitment to the Underlying Metaphysical Pictures......Page 70 3.3.1 Baker's Criterion for Ontological Commitment......Page 71 3.3.2 Knowles and Saatsi and Ontological Commitment......Page 72 3.3.3 Baron and Ontological Commitment......Page 73 3.4 Conclusion......Page 76 References......Page 77 4 Typed Object Theory......Page 80 4.1 Relational vs. Functional Type Theory......Page 82 4.1.1 Why Relations in RTT Were Interpreted as Functions......Page 84 4.1.2 Identity in Typed Object Theory......Page 90 4.2 Intensional Type Theory: I......Page 93 4.3 Nominalized Propositions......Page 99 4.4.1 Response to an Argument Against Henkin Models......Page 103 4.4.2 Comparison of the Ontologies......Page 105 4.5 Conclusion......Page 106 Bibliography......Page 107 Part II Fictionalism or Realism in Philosophy of Mathematics......Page 110 5.1 Introduction......Page 111 5.2.1 Platonism's Central Features......Page 112 5.2.2 Existence......Page 113 5.2.3 Necessity......Page 115 5.2.4 Mathematical Universes......Page 117 5.3 An Alternative Approach: Agnosticism......Page 119 5.4 Mathematical Pluralism and Contingent Mathematics......Page 121 5.4.1 Mathematical Pluralism......Page 122 5.4.2 Contingent Mathematics......Page 125 5.5 Conclusion......Page 127 References......Page 128 6.1 Introduction......Page 130 6.2 Abstract Objects: The Quinean Way......Page 132 6.3 Naturalistic Scruples About Quine's Criterion of Ontological Commitment......Page 135 6.4.1 Yablo's Critique – Difficulties with the Metaphorical/Literal Distinction......Page 137 6.4.2 Azzouni's Critique – The Impossibility of Arguing for a CRD......Page 140 6.5 A More Thoroughgoing Naturalism......Page 141 6.6 A More Thoroughgoing Skepticism?......Page 144 6.7 Summary......Page 147 References......Page 149 Part III Fictionalism or Realism in Philosophy of Empirical Sciences......Page 150 7.1 Introduction......Page 151 7.2 The EPS Account......Page 157 7.3 A Tractarian Dispensation of (Unnecessary) Abstract Objects......Page 162 7.4 Concluding Remarks......Page 165 References......Page 166 8.1 Introduction......Page 168 8.2 Cartwright's dictum and Fictional Entities......Page 169 8.3 For SMs as Abstract Objects, but Without Dual Nature......Page 176 8.4 Scientific Models as Intensional Entities......Page 178 8.5 External, Internal and Transfictional Sentences......Page 182 References......Page 187 9.1 Introduction......Page 189 9.2 Models as Abstract Entities: An Example......Page 191 9.3.1 Aristotelian Abstraction......Page 196 9.3.2 Newtonian Abstraction......Page 198 9.3.3 Duhemian Abstraction......Page 199 9.4.1 Traditional Fictionalism......Page 202 9.4.2 Pretence Theory: Models as Make-Believe......Page 203 9.4.3 Neo-fictionalism......Page 205 9.5 Conclusions......Page 209 References......Page 210 10.1 Introduction......Page 212 10.2 Antirealism About Models......Page 215 10.3 Object-Directed Thoughts and Mental Files......Page 217 10.4 Revisiting Models......Page 221 10.5 Reverberations......Page 225 10.6 DEKI......Page 227 10.7 Conclusions......Page 230 References......Page 232 Part IV Fictionalism or Realism in Philosophy of Language......Page 235 11.1 Introduction......Page 236 11.2 Intentional Identity......Page 237 11.3 Fictional Discourses: Realism and Irrealism......Page 239 11.4 The Cart and the Horse......Page 244 References......Page 248 12.1 Frameworks......Page 251 12.2 A Challenge......Page 255 12.3 A View of Metaphysics as a Theory of Objects. What Is Going on with `Concrete' and `Abstract'......Page 257 12.4 Conclusion: Sketch of Argumentation for a Philosopher with a Different Temperament......Page 261 References......Page 264 13.1 Introduction......Page 266 13.2 Abstract Objects, Natural Language, and the Core-Periphery Distinction......Page 268 13.3 Natural Language Ontology......Page 270 13.4.1 The Core-Periphery Distinction in Natural Language Ontology......Page 273 13.4.2 The Core-Periphery Distinction in Semantics and Philosophical Conceptual Theory......Page 275 13.4.3 The Core-Periphery Distinction in Syntax and Phonology......Page 278 13.5 Abstract Objects and the Core-Periphery Distinction: A Potential Universal of Natural Language Ontology......Page 279 13.6 The Ontology Reflected in Abstract Terms in the Periphery......Page 282 Appendix: Some Potential Issues for the Abstract Object Hypothesis......Page 284 References......Page 285 14.1 Introduction......Page 288 14.2 Fictional Creationism and Its Varieties......Page 289 14.3 The Ontological Criticisms......Page 291 14.4 The Metaphysical Criticisms......Page 298 References......Page 303 Part V Fictionalism or Realism in Moral Philosophy and Philosophy of Arts......Page 306 15 Moral Folkism and the Deflation of (Lots of) Normative and Metaethics......Page 307 15.1 Introduction......Page 308 15.2 The Vast Plurality of Wrong-Like Properties......Page 309 15.3 Conceptual Analysis......Page 311 15.3.1 Metaphysical Privilege I—Platonistic Privilege......Page 312 15.3.3 Metaphysical Privilege II—Rigidity and Semantic Externalism......Page 316 15.3.4 Metaphysical Privilege III—Lewis-Sider-Style Naturalness......Page 317 15.3.5 Metaphysical Privilege IV—Exemplars......Page 318 15.3.7 Theoretical Role......Page 319 15.4 Pushing the Argument Further......Page 320 15.5 Deflationary Consequences for Normative and Metaethics......Page 321 15.6 Why Moral Folkism Doesn't Entail That Applied-Ethical Disputes Are Settled by Facts About Folk Meaning......Page 322 15.7 Why Moral Folkism Doesn't Undermine Moral Realism (or Error Theory)......Page 323 15.8 Is This Real Realism?......Page 327 References......Page 328 16 Methodology in the Ontology of Artworks: Exploring Hermeneutic Fictionalism......Page 329 16.1 Semantic Descriptivism and Hermeneutic Fictionalism......Page 330 16.2.1 Amie Thomasson's Global Descriptivism......Page 337 16.2.2 Andrew Kania's Local Descriptivism......Page 341 16.2.3 Julian Dodd's Folk-Theoretic Modesty......Page 343 16.2.4 David Davies' Rational Accountability View......Page 344 16.3 Conclusion: The Advantages of Hermeneutic Fictionalism......Page 345 References......Page 346 17.1 Introduction......Page 348 17.2 Subjective Warrant and Action......Page 352 17.3 Scepticism and Other Threats to Subjective Warrant......Page 356 17.4 The Problem with Belief, and the Fictionalist Fix......Page 357 17.5 Conclusion......Page 363 References......Page 364