Travis McKenna

It is an underappreciated fact within the philosophical literature on laws of nature that many scientific laws require the aid of a supporting cast of additional modelling ingredients (such as boundary conditions, material parameters, interfacial stipulations, rigidity constraints, and so on) in order to perform their traditional role in scientific inquiry. In this paper, I suggest that this underappreciated fact spells trouble for some recent reformulations of David Lewis's Best Systems Account (BSA) of laws of nature. Under the auspices of 'pragmatic Humeanism,' several philosophers have recently argued that the criteria of strength and simplicity that lay at the heart of Lewis's original formulation should be replaced with alternatives that are more sensitive to the role that laws play in scientific practice. Although the criteria that these philosophers put forward differ in a variety of ways, they are primarily concerned with the ability of laws to furnish us with predictions and encode information. This, I suggest, is a problem. If it is true that many scientific laws do not on their own perform some of the roles with which they are traditionally associated, then they are unlikely in isolation to make meaningful contributions to the predictive strength of a system or encode information about particular systems. Such laws are thus unlikely to end up in the best system, and so these accounts will have trouble conferring lawhood upon them.

‘Mapping accounts’ of applied mathematics hold that the application of mathematics in physical science is best understood in terms of ‘mappings’ between mathematical structures and physical structures. In this paper, I suggest that mapping accounts rely on the assumption that the mathematics relevant to any application of mathematics in empirical science can be captured in an appropriate mathematical structure. If we are interested in assessing the plausibility of mapping accounts, we must ask ourselves: how plausible is this assumption as a working hypothesis about applied mathematics? In order to do so, we examine the role played by mathematics in the multiscalar modelling of sea ice melting behaviour and examine whether we can indeed capture the mathematics involved in the kind of mathematical structure employed by the mapping account. Along the way, we note that the cases of applied mathematics that appear in discussions of mapping accounts almost exclusively involve the employment of a single clearly circumscribed mathematical field or domain. While the core assumption of mapping accounts may appear plausible in such situations, we ultimately suggest that the mapping account is not able to handle the important added complexities involved in our sea ice case study. In particular, the notion of mathematical structure around which such accounts are framed does not seem to be able to capture the way in which some applications of mathematics require that very different pieces of mathematics be related to one another on the basis of both mathematical and empirical information.

Marc Lange has recently raised three objections to the account of minimal model explanations offered by Robert Batterman and Collin Rice. In this article, I suggest that these objections are misguided. I suggest that the objections raised by Lange stem from a misunderstanding of the what it is that minimal model explanations seek to explain. This misunderstanding, I argue, consists in Lange’s seeing minimal model explanations as relating special types of models to particular target systems rather than seeing minimal model explanations as looking to explain robust patterns of behavior that are exhibited by a variety of physically diverse systems.