ISBN : 9780198815044
How is that when scientists need some piece of mathematics through which to frame their theory, it is there to hand? Otavio Bueno and Steven French address that question through a detailed examination of a series of case studies from the history of twentieth-century physics. Charting the various moves that were made in order to bring the mathematics and the science together, they then frame those moves within an account of the applicability of mathematics according to which some empirical phenomena are first 'immersed' into the mathematics, which allows certain inferences to be drawn, and which are then interpreted in terms of the original phenomena. This account is then applied to recent scientific examples that have been highlighted to support the claim that we should be realist about mathematics because of the explanatory role it plays, and it is argued that such claims should be resisted. The overall conclusion is that if we pay attention to the relevant scientific practices and hav
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