Perspectival realists often appeal to the methodology of science to secure a realist account of the retention and continued success of scientific claims through the progress of science (e.g. Massimi, 2016). However, in the context of modern physics, the retention and continued success of scientific claims is typically only definable within a mathematical framework. In this paper, I argue that this concern leaves the perspectivist open to Cassirer’s (1910) neo-Kantian critique of the applicability of mathematics in the natural sciences. To support this criticism, I present a case study on the conservation of energy in modern physics.
Gauge symmetries provide one of the most puzzling examples of the applicability of mathematics in physics. The presented work focuses on the role of analogical reasoning in the gauge argument, motivated by Mark Steiner's claim that the application of the gauge principle relies on a Pythagorean analogy whose success undermines naturalist philosophy. In this paper, we present two different views concerning the analogy between gravity, electromagnetism, and nuclear interactions, each providing a different philosophical response to the problem of the applicability of mathematics in the natural sciences. The first is based on an account of Weyl's original work, which first gave rise to the gauge principle. Drawing on his later philosophical writings, we develop an idelaist reading of the mathematical analogies in the gauge argument. On this view, mathematical analogies serve to ensure a conceptual harmony in our scientific account of nature. We further discuss the construction of Yang and Mills's gauge theory in light of this idealist reading. The second account presents a naturalist alternative, formulated in terms of John Norton's account of a material analogy, according to which the analogy succeeds in virtue of a physical similarity between the different interactions. This account is based on the methodological equivalence principle, a simple conceptual extension of the gauge principle that allows us to understand the relation between coordinate transformations and gravity as a manifestation of the same method. The physical similarity between the different cases is based on attributing the success of this method to the dependence of the coupling on relational physical quantities. We conclude by reflecting on the advantages and limits of the idealist, naturalist, and anthropocentric
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.