Nancy Cartwright introduced an interesting distinction in the context of her study of the history of the evolution of our understanding of superconductivity. She emphasized the distinction between mathematical theories (such as the microscopic BCS theory developed in 1957) and basic mathematical models (such as the London-London model of 1935). According to Cartwright, the emergence of a full-fledged mathematical theory often depends on first developing a basic mathematical model, in a step Cartwright refers to as phenomenological model-building (I think she uses "phenomenological" in the sense of "empirical" but I may be wrong). Of course the full-fledged mathematical theory is applied not to the original phenomenon but rather to the basic mathematical model. I am wondering about the following.
Has this distinction been explored further in recent work?
The relevant papers are the following:
Cartwright, Nancy; Shomar, Towfic; Su'arez, Mauricio. The tool box of science. Tools for the building of models with a superconductivity example. Poznan Studies in the Philosophy of the Sciences and the Humanities 44 (1995), 137--149.
Su'arez, Mauricio; Cartwright, Nancy. Theories: Tools versus models. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, Vol. 39, Issue 1 (2008), 62--81. https://doi.org/10.1016/j.shpsb.2007.05.004.
The following useful input has been provided at the MO.SE site:
Cartwright's case study, model building for the theory of superconductivity, has been explored further in the Ph.D. thesis The Role of Concrete Models in the Revolution in Superconductivity (A. Chattoraj, 2015).
More generally, one of Cartwright's former students, Roman Frigg, has developed this approach in a monograph, Models and theories: A philosophical inquiry (2022).
Any further input would be appreciated.
