Abstract Objects: For And Against

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