Physical laws and the application of mathematics
This investigation addresses the problem of the effectiveness of mathematics in the articulation of physical laws. Since Eugene Wigner’s (1960) landmark statement of the problem, scientists, philosophers, and historians of science have reflected on whether mathematics’ effectiveness had to be deemed unreasonable after all.
One aspect of our research is this. We bring together two fields of research, namely: the history and philosophy of laws of nature, and the recent philosophy of applied mathematics, the latter including issues concerning modelling, representation, abstraction, and idealisation. From this perspective, the project has three main goals: first, to develop a philosophical framework for understanding the various contributions of mathematics to physical laws; second, to provide an analysis of nomic modality that accounts for the contribution of both physics and mathematics to the modal space of possibilities and necessities informed by physical laws; and third, to examine the distinction between mathematical and physical structures in physical laws.
Another aspect of our research advances a pluralist interpretation of scientific practices, one of whose core tenets within the framework of our project is this: physical laws need not be a central element in ontology, nor do they need to be equally present across epistemic practices. This will prove beneficial in various ways, especially since the talk of laws is not inane: it imposes a certain understanding of scientific practices (for example, some epistemic practices are successful at finding out about laws, whereas others are not), and a way to value their results (in particular, epistemic practices informing us about laws are somehow more important, and we should grant them priority because they provide what the Newtonian tradition considers genuine scientific knowledge). We cast doubt on this interpretation. We examine, indeed, whether we are currently writing the last chapter of the biography of laws, as Lorraine Daston’s framework for the biographical approach to scientific objects may suggest. Furthermore, laws may well be dispensed with in both ontology and scientific parlance, hence giving way to rather more egalitarian concepts and less demanding ontological presuppositions. For the latter points, we shall benefit from insights coming from both the history of science and the social studies of science.