Identity in Physics: A Historical, Philosophical, and Formal Analysis | |||

French (Steven) & Krause (Décio) | |||

This Page provides (where held) the Abstract of the above Book and those of all the Papers contained in it. | |||

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**BOOK ABSTRACT: **__Inside Cover Blurb__

- Can quantum particles be regarded as individuals, just like books, tables and people? According to the 'received' view - articulated by several physicists in the immediate aftermath of the quantum revolution - quantum physics itself tells us they cannot: quantum particles, unlike their classical counterparts, must be regarded as 'non-individuals' in some sense. However, recent work has indicated that this is not the whole story and that the theory is also consistent with the position that such particles can be taken to be individuals, albeit at a metaphysical price.
- Drawing on philosophical accounts of identity and individuality, as well as the histories of both classical and quantum physics, the authors explore these two alternative metaphysical packages. In particular, they argue that if quantum particles are regarded as individuals, then Leibniz's famous Principle of the Identity of Indiscernibles
^{1}is in fact violated. Recent discussions of this conclusion are analysed in detail and, again, the costs involved in saving the Principle are carefully considered. - Taking the alternative package, the authors deploy recent work in non-standard logic and set theory to indicate how we can make sense of the idea that objects can be non-individuals. The concluding chapter suggests how these results might then be extended to quantum field theory.
*Identity in Physics*brings together a range of work in this area and further develops the authors' own contributions to the debate. Uniquely, as the title indicates, it situates this work in the appropriate formal, historical, and philosophical contexts.

*Identity in Physics*is a very significant contribution to debate about, well, identity in physics, but it deserves attention from general philosophers of science and metaphysicians too.

→*Katherine Hawley, International Studies in Philosophy of Science*- Steven French and Décio Krause have written what bids fair to be, for years to come, the definitive philosophical treatment of the problem of the individuality of elementary particles in quantum mechanics
^{2}and quantum field theory.

→*Don Howard, Metascience*

- Preface – xi
- Introduction – 1

→ 1.1. Individuality, Distinguishability, and Identity – 4

→ 1.2. ‘Bundle' Individuality – 8

→ 1.3. Transcendental Individuality – 11

→ 1.4. Self-Identity – 14

→ 1.5. Distinguishability – 15

→ 1.6. Haecceitism – 17

→ 1.7. Trans-temporal Identity – 19

→ 1.8. Summary – 21 - Individuality in Classical Physics – 22

→ 2.1. A Brief History of Classical Statistical Mechanics – 24

→ 2.2. Classical Statistical Mechanics and Individuality Revisited – 40

→ 2.3. A Field-Theoretic Approach – 51

→ 2.4. Individuality and Space-Time – 65

→ 2.5. Conclusion: The Metaphysics of Classical Physics – 81 - Quantum Statistics and Non-Individuality – 84

→ 3.1. The Early History of Quantum Statistics – 85

→ 3.2. The Later History of Quantum Statistics – 94

→ 3.3. The Impact of Quantum Statistics: Quantum Non-Individuality – 104

→ 3.4. Bohr's View of Particle Individuality – 107

→ 3.5. Born and Structural Invariants – 115

→ 3.6. Schrodinger and the Loss of Identity – 119

→ 3.7. Weyl and the Analysis of Aggregates – 127

→ 3.8. Back to the History: Parastatistics – 131 - Individuality and Non-Individuality in Quantum Mechanics
^{3}– 139

→ 4.1. Indistinguishability and Individuality – 140

→ → 4.1.1. Challenge No. 1: Classical Particles as Non-Individuals – 144

→ → 4.1.2. Challenge No. 2: Quantum Particles as Individuals – 146

→ → 4.1.3. The Indistinguishability Postulate as an Initial Condition – 148

→ 4.2. The Individuality of Quantum Particles – 149

→ → 4.2.1. Quantum Mechanics^{4}and the Principle of Identity of Indiscernibles^{5}– 150

→ 4.3. Space-Time Individuality and Configuration Space – 173

→ 4.4. Individuality, Bell and Non-Supervenient Relations – 179

→ 4.5. The Underdetermination of Metaphysics by Physics – 189 - Names, Nomological Objects and Quasets – 198

→ 5.1. The Role of Names in Science – 199

→ 5.2. Names and the Practice of Physics – 210

→ 5.3. Names, Possible Worlds and Particle Statistics – 212

→ 5.4. Names and Nomological Objects – 221

→ 5.5. Quasets – 232

→ → 5.5.1. Quaset Theory – 233

→ 5.6. Conclusion – 237 - A Problem for Present-Day Mathematics – 238

→ 6.1. The Statement of the Problem – 239

→ 6.2. The Use of ‘Standard Languages' – 245

→ → 6.2.1. The Lack of Identity – 247

→ 6.3. Identity in Classical Logic and Mathematics – 250

→ → 6.3.1. Identity in First-Order Classical Logic – 251

→ → 6.3.2. Identity in Higher-Order Logic – 254

→ 6.4. Set Theory and Individuation^{6}– 258

→ 6.5. Characterizing Indistinguishability – 260

→ → 6.5.1. Weyl's Strategy – 261

→ → 6.5.2. Indiscernibility and Structures – 264

→ → 6.5.3. The Implications for the Philosophy of Quantum Theory^{7}– 267 - The Mathematics of Non-Individuality – 272

→ 7.1. The Name of the Game – 273

→ 7.2. The Quasi-Set Theory**Q**– 275

→ → 7.2.1. Relations and Quasi-Functions – 281

→ → 7.2.2. Quasi-Cardinals – 284

→ → 7.2.3. ‘Weak' Extensionality – 290

→ → 7.2.4. Replacement Axioms – 291

→ → 7.2.5. The Strong Singleton – 292

→ → 7.2.6. Permutations are not Observable – 295

→ → 7.2.7. The Axiom of Choice – 297

→ → 7.2.8. Remark on the Existence of Atoms: The Theory**Q**^{m}– 297

→ 7.3. Relative Consistency – 298

→ 7.4. Quaset Ideas within Quasi-Set Theory – 303

→ 7.5. Changes in Time: The Theory**Q**^{t}– 306

→ 7.6. Quantum Statistics within**Q**– 310

→ 7.7. On Justifying Quasi-Set Theory – 317

→ 7.7.1. Quasi-Sets and Quasets: A New Look – 318 - Non-Reflexive Quantum Logics – 321

→ 8.1. Motivation – 322

→ 8.2. First-Order Systems – 324

→ 8.3. Higher-Order Schrodinger Logics – 326

→ → 8.3.1. Identity and Absolute Indistinguishability – 328

→ 8.4. A ‘Classical' Semantics for S_{w}– 329

→ → 8.4.1. Identity and Indistinguishability Revisited – 334

→ 8.5. The Intensional System S_{w}I – 334

→ 8.6. Generalized Quasi-Set Semantics – 336

→ → 8.6.1. The Theory S_{w}I – 340

→ → 8.6.2. Soundness and Generalized Completeness – 340

→ → 8.6.3. Comprehension and Other Axioms – 342

→ → 8.6.4. General Discussion – 343

→ 8.7. Quantum Sortal^{8}Predication – 344

→ → 8.7.1. Sortal^{9}Predication – 344

→ → 8.7.2. Quantum-Sortal^{10}Predicates – 347

→ → 8.7.3. Sortal^{11}Logics – 351

→ 8.8. Semantical Analysis – 352 - The Logic of Quanta – 354

→ 9.1. The Nature of QFT – 355

→ 9.2. Metaphysical Options – 365

→ 9.3. Models and the Fock Space Formalism – 370

→ → 9.3.1. A Suppes Predicate for QFT – 374

→ 9.4. Quasi-Sets and the Objectivity of Quanta – 379

References – 385

Index – 415

OUP Oxford; Reprint edition (4 Nov 2010)

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