A robustly inferential conception of the role of mathematics in science

In the thesis, I develop and defend a novel account of mathematical scientific representations, the Robustly Inferential Conception (RIC). According to RIC, mathematics places constraints on what a representation’s target system must be like by specifying inferences that must preserve truth if the representation is accurate in all respects. A mathematical scientific representation is treated as having three ingredients:

(RIC1) A partial physical interpretation of the language in which the relevant mathematics is expressed,
(RIC2) An initial description of the target system in this physically interpreted mathematical language, and
(RIC3) A set of mathematical inference patterns licensed by the relevant mathematics.

The informational content of the representation, according to RIC, is given by the closure of the statements in RIC2 under the inference patterns in RIC3, under the interpretation RIC1.

I argue that RIC has three significant advantages over its most prominent alternative, the mapping account. First, it can be applied in a wider range of cases. Second, it is more successful as a meta-level representational device to be used by philosophers of science to represent philosophically salient features of scientific practices in which mathematics is applied. Third, it makes fewer assumptions about the nature of mathematics.

I spend most of the thesis substantiating the second of these points, which I take to be the strongest case for RIC. In particular, I show how RIC can be used to shed light on philosophical issues concerning applications of inconsistent and otherwise unrigorous mathematics and the role of mathematics in scientific explanations and scientific understanding.