Applying Mathematics

Immersion, Inference, Interpretation

Otavio Bueno and Steven French

An original explanation of how and why mathematics is so readily applicable to the physical world
Illuminates the philosophical issues through case-studies in the history of 20th-century physics
Non-technical: expertise in mathematics or physics not required
Co-authored by two well-known philosophers of science

Applying Mathematics

Immersion, Inference, Interpretation

Otavio Bueno and Steven French

Description

How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? What has been called 'the unreasonable effectiveness of mathematics' sets a challenge for philosophers. Some have responded to that challenge by arguing that mathematics is essentially anthropocentric in character, whereas others have pointed to the range of structures that mathematics offers. Otavio 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.

Applying Mathematics

Immersion, Inference, Interpretation

Otavio Bueno and Steven French

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?
10. Conclusion: Between Optimism and Opportunism

Applying Mathematics

Immersion, Inference, Interpretation

Otavio Bueno and Steven French

Author Information

Otavio Bueno taught in California and South Carolina before moving to the University of Miami, where is now Professor of Philosophy and Chair of the Philosophy Department. He works in the philosophies of science, of mathematics and of logic, epistemology, and philosophy of art, and is the author of many books and articles. He is Editor-in-Chief of Synthese.

Steven French taught at universities in Brazil and the USA before moving to Leeds in 1993, where he is Professor of Philosophy of Science. He is the author of numerous books and papers in the philosophy of science and is Co-Editor-in-Chief of The British Journal for the Philosophy of Science.

Applying Mathematics

Immersion, Inference, Interpretation

Otavio Bueno and Steven French

Reviews and Awards

"a valuable addition to the ongoing debates about the partial-structures approach in philosophy of physics, presenting a coherent account of the position of the authors, argued through a series of detailed and interesting case studies of advances in quantum physics that are so complex that no superficial account would serve the philosophical analyses sought after. . . . an elaborate exposition and defence of a promising, practice-sensitive approach to philosophy of physics. To the broader community of historians and philosophers of science, the book is also a valuable addition, perhaps mainly for its philosophically focused analyses of important historical events which build upon, but also contribute to, the existing specialized scholarship and the account for how mathematical surplus structure can function in theory development." -- Henrik Kragh Sørensen, Metascience

"a readable, informative, and compelling account of mathematics as it is deployed in physical theory ... you will want to have this book around to refer to if you do any work in the philosophy of mathematics/physics/science. And if you work on mathematical application and explanation, you should read and carefully consider the book in its entirety." -- Anthony F. Peressini, Philosophia Mathematica

"[an] important and richly detailed contribution to our better understanding of mathematical models" -- Atoosa Kasirzadeh & James Robert Brown , Philosophy of Science

"Otávio Bueno and Steven French have produced a readable, informative, and compelling account of mathematics as it is deployed in physical theory. . . .Âyou will want to have this book around to refer to if you do any work in the philosophy of mathematics/physics/science. And if you work on mathematical application and explanation, you should read and carefully consider the book in its entirety." -- Anthony Peressini , Philosophia Mathematica