A new role of mathematics in science: Measurement normativity

Abstract

The applicability of mathematics in science has received renewed attention in recent years. The most influential recent approaches focus on how mathematical structures relate to empirical structures. I argue that these accounts leave an important normative aspect of mathematics, which is key for scientific measurement, unaddressed. Building on the later Wittgenstein’s philosophy of mathematics, I characterize how mathematical models have both an empirical and a normative aspect: sometimes they are falsified or refined, but on other occasions they are used as rules of measurement. Thus, the normative aspect of mathematics contributes to its applicability in science in practice without precluding (but at the expense of) its empirical aspect. I illustrate this dual character with two simple examples first and then with a more substantial case study in neuroscience. While the normative aspect of mathematics is often desirable, the epistemic circularity that it entails may be epistemically harmful in some scenarios.

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