On the Explanatory Role of Mathematics in Empirical Science. Batterman, R. W. 61(1):1–25.
On the Explanatory Role of Mathematics in Empirical Science [link]Paper  doi  abstract   bibtex   
This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.
@article{battermanExplanatoryRoleMathematics2010,
  title = {On the Explanatory Role of Mathematics in Empirical Science},
  author = {Batterman, Robert W.},
  date = {2010-03},
  journaltitle = {The British Journal for the Philosophy of Science},
  volume = {61},
  pages = {1--25},
  issn = {1464-3537},
  doi = {10.1093/bjps/axp018},
  url = {https://doi.org/10.1093/bjps/axp018},
  abstract = {This paper examines contemporary attempts to explicate the explanatory role of mathematics in the physical sciences. Most such approaches involve developing so-called mapping accounts of the relationships between the physical world and mathematical structures. The paper argues that the use of idealizations in physical theorizing poses serious difficulties for such mapping accounts. A new approach to the applicability of mathematics is proposed.},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-4888351,epistemology,mathematics,theoretical-approach},
  number = {1}
}
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