Type of Publication:  Journal article 
Author:  Räz, Tim; Sauer, Tilman 
Year of publication:  2015 
Published in:  Studies in History and Philosophy of Science / Part B: Studies in History and Philosophy of Modern Physics ; 49 (2015).  pp. 5772.  ISSN 13552198.  eISSN 18792502 
DOI (citable link):  https://dx.doi.org/10.1016/j.shpsb.2015.01.004 
Summary: 
We outline a framework for analyzing episodes from the history of science in which the application of mathematics plays a constitutive role in the conceptual development of empirical sciences. Our starting point is the inferential conception of the application of mathematics, recently advanced by Bueno and Colyvan (2011). We identify and discuss some systematic problems of this approach. We propose refinements of the inferential conception based on theoretical considerations and on the basis of a historical case study. We demonstrate the usefulness of the refined, dynamical inferential conception using the wellresearched example of the genesis of general relativity. Specifically, we look at the collaboration of the physicist Einstein and the mathematician Grossmann in the years 1912–1913, which resulted in the jointly published “Outline of a Generalized Theory of Relativity and a Theory of Gravitation,” a precursor theory of the final theory of general relativity. In this episode, independently developed mathematical theories, the theory of differential invariants and the absolute differential calculus, were applied in the process of finding a relativistic theory of gravitation. The dynamical inferential conception not only provides a natural framework to describe and analyze this episode, but it also generates new questions and insights. We comment on the mathematical tradition on which Grossmann drew, and on his own contributions to mathematical theorizing. The dynamical inferential conception allows us to identify both the role of heuristics and of mathematical resources as well as the systematic role of problems and mistakes in the reconstruction of episodes of conceptual innovation and theory change.

Subject (DDC):  100 Philosophy 
Keywords:  Applicability of Mathematics, Genesis of general relativity, Absolute differential calculus, Inferential conception, Einstein, Grossmann 
Bibliography of Konstanz:  Yes 
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RÄZ, Tim, Tilman SAUER, 2015. Outline of a dynamical inferential conception of the application of mathematics. In: Studies in History and Philosophy of Science / Part B: Studies in History and Philosophy of Modern Physics. 49, pp. 5772. ISSN 13552198. eISSN 18792502. Available under: doi: 10.1016/j.shpsb.2015.01.004
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