Mathematics as quasi-matter to build models as instruments

I have argued elsewhere that models should be distinguished from theories.1 They are not theories about the world but instruments through which we can see the world and so gain some understanding of it. As mathematical representations, models should also be distinguished from pure formal objects. They should be seen as devices that help us to see the phenomena more clearly. Models are instruments of investigation, epistemological equivalent to the microscope and the telescope. In a textbook on optical instruments, we find the following description:

The primary function of a lens or lens system will usually be that of making a pictorial representation or record of some object or other, and this record will usually be much more suitable for the purpose for which it is required than the original object.2

If one replaces "lens or lens system" by "model", one has an adequate description of the way that models are understood and treated in this paper.