Can Mathematics Explain Physical Phenomena?

Batterman ([2010]) raises a number of concerns for the inferential conception of the applicability of mathematics advocated by Bueno and Colyvan ([2011]). Here, we distinguish the various concerns, and indicate how they can be assuaged by paying attention to the nature of the mappings involved and emphasizing the significance of interpretation in this context. We also indicate how this conception can accommodate the examples that Batterman draws upon in his critique. Our conclusion is that ‘asymptotic reasoning’ can be straightforwardly accommodated within the inferential conception. 1 Introduction2 Immersion, Inference and Partial Structures3 Idealization and Surplus Structure4 Renormalization and the Stability of Mathematical Representations5 Explanation and Eliminability6 Requirements for Explanation7 Interpretation and Idealization8 Explanation, Empirical Regularities and the Inferential Conception9 Conclusion.
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DOI 10.1093/bjps/axr017
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References found in this work BETA
Robert Batterman (2010). On the Explanatory Role of Mathematics in Empirical Science. British Journal for the Philosophy of Science 61 (1):1-25.
Alisa Bokulich (2008). Can Classical Structures Explain Quantum Phenomena? British Journal for the Philosophy of Science 59 (2):217-235.

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Citations of this work BETA
Otávio Bueno (2012). Styles of Reasoning: A Pluralist View. Studies in History and Philosophy of Science Part A 43 (4):657-665.

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Robert Batterman (2010). On the Explanatory Role of Mathematics in Empirical Science. British Journal for the Philosophy of Science 61 (1):1-25.

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