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Applying mathematics : immersion, inference, interpretation /
How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? Bueno and French offer a new approach to the puzzle of the applicability of mathematics, through a detailed examination of a series of case studies from the history of twentieth-centu...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford, United Kingdom :
Oxford University Press,
2018.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Applying Mathematics: Immersion, Inference, Interpretation; Copyright; Dedication; Preface; Contents; Acknowledgements; List of Illustrations; 1: Just How Unreasonable is the Effectiveness of Mathematics?; 1.1 Introduction; 1.2 Mystery Mongering; 1.3 Mathematical Optimism; 1.4 Mathematical Opportunism; 2: Approaching Models: Formal and Informal; 2.1 Introduction; 2.2 One Extreme: The Structuralists; 2.3 The Other Extreme: Giere's Account of Models; 2.4 Surplus Structure; 2.5 Partial Structures; 2.6 Problems with Isomorphism; 2.7 The Inferential Conception; 2.8 Conclusion.
- 3: Scientific Representation and the Application of Mathematics3.1 Introduction; 3.2 General Challenge: Reducing all Representations to the Mental; 3.3 Specific Challenges to the Formal Account; 3.3.1 Necessity; 3.3.2 Sufficiency; 3.3.3 Logic; 3.3.4 Mechanism; 3.3.5 Style; 3.3.6 Misrepresentation; 3.3.7 Ontology; 3.4 The Formal Account Defended; 3.4.1 Preamble: Informational vs Functional Accounts; 3.4.2 Necessity; 3.4.3 Logic and Sufficiency; 3.4.4 Mechanism; 3.4.5 Style; 3.4.6 Misrepresentation; 3.4.7 Ontology; 4: Applying New Mathematics: Group Theory and Quantum Mechanics.
- 4.1 Introduction4.2 The Historical Context; 4.3 Applying Group Theory to Atoms; 4.3.1 A (Very) Brief History of Quantum Statistics; 4.3.2 The 'Wigner Programme'; 4.3.3 The 'Weyl Programme'; 4.4 Applying Group Theory to Nuclei; 4.5 Conclusion; 5: Representing Physical Phenomena: Top-Down and Bottom-Up; 5.1 Introduction; 5.2 From the Top: The Applicability of Mathematics; 5.3 Bose-Einstein Statistics and Superfluidity; 5.3.1 The Liquid Degeneracy of Helium; 5.3.2 The Application of Bose-Einstein Statistics; 5.4 The Autonomy of London's Model; 5.5 Conclusion.
- 6: Unifying with Mathematics: Logic, Probability, and Quantum States6.1 Introduction; 6.2 Group Theory, Hilbert Spaces, and Quantum Mechanics; 6.3 Logic and Empiricism; 6.4 The 1937 Manuscript: Logics and Experience; 6.5 The Status of Mathematics; 7: Applying Problematic Mathematics, Interpreting Successful Structures: From the Delta Function to the Positron; 7.1 Introduction; 7.2 Dirac and the Delta Function; 7.2.1 Introducing the Delta Function; 7.2.2 Dispensing with the Delta Function; 7.2.3 The Status of the Delta Function; 7.3 The Pragmatic and Heuristic Role of Mathematics in Physics.
- 7.4 The Discovery of Antimatter7.5 Conclusion; 8: Explaining with Mathematics? From Cicadas to Symmetry; 8.1 Introduction; 8.2 The Strong Claim and Indispensability; 8.3 The Enhanced Indispensability Argumentand Explanation; 8.3.1 Indexing and Representing; 8.3.2 Explaining; 8.4 The Weak Claim and the Hybridity of Spin; 8.5 Conclusion; 9: Explaining with Mathematics?: Idealization, Universality, and the Criteria for Explanation; 9.1 Introduction; 9.2 Immersion, Inference, and Partial Structures; 9.3 Idealization and Surplus Structure; 9.4 The Rainbow.
- 9.5 Accommodating Process and Limit Operations.