On the Explanatory Role of Mathematics in Empirical Science

By Robert W. Batterman. British Journal for the Philosophy of Science, 2010

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Less is Different: Emergence and Reduction Reconciled (2011, background): “It is best to think instead in terms of some kind of genuine qualitative change in the system at a given scale’ ([ 10 ], p. 22); ‘fluids are composed of a finite number of molecules’ ([8], p. 903); ‘water in real tea kettles consists of a finite number of molecules’ ([10], p. 7; this quotation also ”
Moving Beyond Causes: Optimality Models and Scientific Explanation (2015, background): “…role in scientific explanations precisely because they remove—or abstract away from—the various causal details of a system in order to capture the dominant (and sometimes noncausal) features that are responsible for a phenomenon (Batterman 2002b, 2009, 2010; Huneman 2010; Rice 2012; Weslake 2010).”
Minimal Model Explanations (2014, background): “However, there are several reasons why the explanation provided by a model might be improved by removing various details concerning causal mechanisms ðCartwright 1983; Batterman 2002b, 2009, 2010; Rice 2012, 2013Þ.”