[Nancy Cartwright](https://en.wikipedia.org/wiki/Nancy_Cartwright_(philosopher)) introduced an interesting distinction with regard to modeling of physical phenomena. According to Cartwright, a mathematical theory is not applied directly to such phenomena. Rather, one first builds a basic mathematical model of the phenomenon in question, 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). Only then does one exploit a full-fledged mathematical theory, applied not to the original phenomenon but rather to the basic mathematical model. Since I am not familiar with the relevant literature, I am wondering if this distinction has 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>.



Nancy Cartwright's dichotomy
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](https://uwspace.uwaterloo.ca/bitstream/handle/10012/9818/Chattoraj__Ananya.pdf;sequence=1) (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](https://library.oapen.org/bitstream/handle/20.500.12657/57620/9781000609530.pdf?sequence=1) (2022).


