The applicability of mathematics in science : indispensability and ontology
Sorin Bangu
Bok · Engelsk · 2012
| Utgitt | Houndmills : Palgrave Macmillan , 2012
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| Omfang | XIII, 252 s. : fig.
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| Opplysninger | 1. Introduction: The Question --pt. I Naturalism, Indispensability and Posit Realism --2. Naturalism: Science as the Measure of All Things --2.1. Introduction --2.2. Naturalism, realism and causation --2.3. Ontology and science -- 2.4. Regimentation and ontological commitment -- 2.5. Conclusion --3. Holism --3.1. Introduction --3.2. Confirmational holism -- 3.3. Unapplied mathematics and mathematical practice -- 3.4. Conclusion --4. Posit Realism -- 4.1. Introduction -- 4.2. Fictionalism --4.3. Posit realism: 'swelling ontology to simplify theory' -- 4.3.1. Ontology historicized? -- 4.3.2. Posits v. abbreviations --4.3.3. The realism of the Indispensability Argument --4.4. Indispensabilist posit realism and scientific realism -- 4.5. Conclusion -- pt. II The Vantage Point: Mathematics in Science --5. Standard and Non-standard Applications --5.1. Introduction --5.2. Standard applications --5.2.1. Fruits, roots, semantics and metaphysics --5.2.2. Weighing --5.2.3. Thinking outside the box -- 5.2.4. A tale of two rocks --5.3. Non-standard applications: discovering new elementary particles --5.3.1. The omega-minus prediction --5.3.2. The positron prediction --5.3.3. DN e-predictions --5.3.4. The Identification Principle -- 5.3.4.1. Anomaly --5.3.4.2. Interaction -- 5.3.4.3. Summary -- 5.3.5. A new kind of prediction? --5.3.6. Discovery strategies -- 5.4. Conclusion -- 6. Mathematics and Scientific Discovery --6.1. Introduction -- 6.2. Wigner's and Steiner's puzzles --6.3. Steiner's argument --6.4. Anthropocentrism -- 6.5. Two criticisms -- 6.6. Definabilism and anthropocentrism -- 6.7. Conclusion --7. Wigner's Puzzle Revisited --7.1. Introduction --7.2. Solutions --7.2.1. The 'many failures' solution --7.2.2. The 'fudging' solution --7.2.3. The 'statistical' solution --7.2.4. The 'empirical origins' solution -- 7.2.5. Improving the 'empirical origins' solution: indirect applicability --7.3. Conclusion: the puzzle in crossfire -- pt. III Explanation and Mathematical Realism --8. Inference to the Best Mathematical Explanation -- 8.1. Introduction -- 8.2. The explanationist strategy -- 8.2.1. Mathematical explanations -- 8.2.2. Four desiderata --8.2.2.1. 'Simplicity' -- 8.2.2.2. 'Nominalization', 'Indispensability' and 'Explanation' -- 8.2.2.3. Why the cicada (example) doesn't fly -- 8.3. The banana game -- 8.3.1. Some clarifications -- 8.3.2. Hopes and troubles for the nominalist -- 8.3.3. New hopes --8.3.4. New troubles -- 8.4. Conclusion -- 9. Explanation, Holism, and Ontological Commitment: The Objection from Scientific Practice -- 9.1. Introduction -- 9.2. Holism and scientific practice -- 9.3. Too small to believe in: the case of atoms -- 9.4. Idealizations -- 9.4.1. Ineliminable idealizations -- 9.4.2. Singularities and fluctuations --9.5. The 'open question' issue -- 9.6. Conclusion: confirmation, still holistic after all these years -- 10. Concluding Remarks.. - This examination of a series of philosophical issues arising from the applicability of mathematics to science consists of scientifically-informed philosophical analysis and argument. One distinctive feature of this project is that it proposes to look at issues in philosophy of mathematics within the larger context of philosophy of science.
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| Emner | |
| Dewey | |
| ISBN | 0230285201. - 9780230285200
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