This year I will be trying to come up with a draft of a book that I have been planning for some time, but that I have been quite unsure how to organize. The general issue is the prevalence of mathematics in science and whether there is a philosophical problem lurking here that can be productively discussed. My current angle of attack is to focus on the contribution of this or that part of mathematics to a particular scientific representation. ("Representation" is meant to include both theories and models.) So, we can ask for a given physical situation, context, and mathematical representation of the situation, (i) what does the mathematics contribute to the representation, (ii) how does it make this contribution and (iii) what must be in place for this contribution to occur?
To avoid devolving into a list of examples, I am also trying to come up with different sorts of representations and different ways that mathematics might contribute. At the moment these are: (i) the math is intrinsic/extrinsic to the content of the representation, (ii) the representation is causal concrete or abstract acausal, (iii) the representation is concrete fixed (i.e. a fixed interpretation) or abstract varying, (iv) the scale of the representation and (v) the global (as in a constitutive framework) or local character of the representation. In future posts I will try to clarify these dimensions and offer examples of different ways in which mathematics contributes to them.
The main point of the book, though, is to argue that the contribution that mathematics makes in all these different kinds of cases can generally be classified as epistemic. That is, mathematics helps us to formulate representations that we can confirm given the data we can actually collect. So, there will be many issues related to confirmation and epistemology that I will try to explore here as well.
Pointers to similar projects or projects pursuing this issue in a different way are welcome!