Applying Mathematics: Immersion, Inference, Interpretation 1st Edition – Ebook Instant Download/Delivery ISBN(s): 9780192558978, 0192558978, 9780198815044, 0198815042

Product details:

• ISBN-10: 0192558978
• ISBN-13: 9780192558978
• Author: Otávio Bueno; Steven French

Otávio Bueno and Steven French offer a middle way, which focuses on the moves that have to be made in both the mathematics and the relevant physics in order to bring the two into appropriate relation. This relation can be captured via the inferential conception of the applicability of mathematics, which is formulated in terms of immersion, inference, and interpretation. In particular, the roles of idealisations and of surplus structure in science and mathematics respectively are brought to the fore and captured via an approach to models and theories that emphasize the partiality of the available information: the partial structures approach. The discussion as a whole is grounded in a number of case studies drawn from the history of quantum physics, and extended to contest recent claims that the explanatory role of certain mathematical structures in scientific practice supports a realist attitude towards them. The overall conclusion is that the effectiveness of mathematics does not seem unreasonable at all once close attention is paid to how it is actually applied in practice.

Table contents:

1. Just How Unreasonable is the Effectiveness of Mathematics?

2. Approaching Models: Formal and Informal

3. Scientific Representation and the Application of Mathematics

4. Applying New Mathematics: Group Theory and Quantum Mechanics

5. Representing Physical Phenomena: Top-Down and Bottom-Up

6. Unifying with Mathematics: Logic, Probability, and Quantum States

7. Applying Problematic Mathematics, Interpreting Successful Structures: From the Delta Function to the Positron

8. Explaining with Mathematics? From Cicadas to Symmetry

9. Explaining with Mathematics? Idealization, Universality, and the Criteria for Explanation

10. Conclusion: Between Lazy Optimism and Unbridled Opportunism

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