Alan Baker has written a helpful and somewhat critical review of my Cambridge Element on Mathematics and Explanation. One issue that Baker pursues at some length concerns how to formulate a model for inference to the best explanation (IBE) that helps both the scientific realist to support their claims to know about unobservable entities as well as the platonist to support their claims to know about platonic entities. In the Element I develop what I take to be an important challenge to this combination, but Baker raises some valuable objections. This is hopefully a debate that can be continued!
Category: Research updates
Paolo Mancosu, Francesca Poggiolesi and I have completed our substantial update to Paolo’s earlier SEP entry. See here for the updated entry.
A lot of exciting work has been done on this topic in the last five years, and it will be interesting to see how these debates develop in the next five years!
After a bit of a delay, my contribution to the Cambridge Elements in the Philosophy of Mathematics, co-edited by Stewart Shapiro and Penelope Rush, is now in press. The topic is Mathematics and Explanation. Here is a brief overview. I will post notes about the book’s four chapters in the coming weeks.
Summary: Some scientific explanations involve mathematics. Within mathematics, some proofs are said to explain. Do these practices tell us anything about the nature of explanation or mathematics? In this Element I divide this daunting topic into four parts. First, can any traditional theory of scientific explanation make sense of the place of mathematics in explanation? Each traditional theory that I will discuss is a monist theory because it supposes that what makes something a legitimate explanation is always the same (Ch. 1). Second, if traditional monist theories are inadequate, is there some way to develop a more flexible, but still monist, approach that will clarify how mathematics can help to explain (Ch. 2)? After considering the limitations of some recent flexible monist accounts, I examine the options for a pluralist approach. What sort of pluralism about explanation is best equipped to clarify how mathematics can help to explain in science and in mathematics itself? While a pluralist can allow that different sorts of explanations work differently, it still remains important to clarify the value of explanations (Ch. 3). Finally, how can the mathematical elements of an explanation be integrated into the physical world? Some of the evidence for a novel scientific posit may be traced to the explanatory power that this posit would afford, were it to exist. Can a similar kind of explanatory evidence be provided for the existence of mathematical objects, and if not, why not? (Ch. 4).
Update: This Element is now available here!
See here for a forthcoming paper “Understanding the Success of Science” along with a short “Reply to Potochnik.” This should appear in a volume edited by K. Khalifa, I. Lawler & E. Shech, Scientific Understanding and Representation: Modeling in the Physical Sciences, Routledge.
Potochnik’s contributions to the volume are available here: “Truth and Reality: How to Be a Scientific Realist Without Believing Scientific Theories Should Be True” and “Different Ways to Be a Realist: Reply to Pincock“.
Abstract: This chapter sketches a new defense of scientific realism based on understanding the success of science and then considers what features understanding must have for this defense to succeed. It argues that if scientific realism involves knowledge of unobservables, then the relevant state of understanding some phenomenon must involve grasping that the phenomenon occurs independently of the scientist’s actions or community. The chapter concludes by arguing that both Giere and Potochnik are unable to provide this type of defense of scientific realism.
See here for a preprint of this new article, which will appear as part of the Synthese topical collection Explanatory and Heuristic Power of Mathematics, edited by Sorin Bangu, Emiliano Ippoliti and Marianna Antonutti.
Abstract: This paper illustrates how an experimental discovery can prompt the search for a theoretical explanation and also how obtaining such an explanation can provide heuristic benefits for further experimental discoveries. The case considered begins with the discovery of Poiseuille’s law for steady fluid flow through pipes. The law was originally supported by careful experiments, and was only later explained through a derivation from the more basic Navier-Stokes equations. However, this derivation employed a controversial boundary condition and also relied on a contentious approach to viscosity. By comparing two editions of Lamb’s famous Hydrodynamics textbook, I argue that explanatory considerations were central to Lamb’s claims about this sort of fluid flow. In addition, I argue that this treatment of Poiseuille’s law played a heuristic role in Reynolds’ treatment of turbulent flows, where Poiseuille’s law fails to apply.
See here for a preprint of this article, which is scheduled to appear in a Synthese special issue “All Things Reichenbach”, edited by Flavia Padovani and Erik Curiel.
Abstract: This paper considers how to best relate the competing accounts of scientific knowledge that Russell and Reichenbach proposed in the 1930s and 1940s. At the heart of their disagreements are two different accounts of how to best combine a theory of knowledge with scientific realism. Reichenbach argued that a broadly empiricist epistemology should be based on decisions. These decisions or “posits” informed Reichenbach’s defense of induction and a corresponding conception of what knowledge required. Russell maintained that a scientific realist must abandon empiricism in favor of knowledge of some non-demonstrative principles with a non-empirical basis. After identifying the best versions of realism offered by Reichenbach and Russell, the paper concludes with a brief discussion of the limitations of these two approaches.
See here for a preprint of my forthcoming article “A Defense of Truth as a Necessary Condition on Scientific Explanation”, Erkenntnis.
Abstract: How can a reflective scientist put forward an explanation using a model when they are aware that many of the assumptions used to specify that model are false? This paper addresses this challenge by making two substantial assumptions about explanatory practice. First, many of the propositions deployed in the course of explaining have a non-representational function. In particular, a proposition that a scientist uses and also believes to be false, i.e. an “idealization”, typically has some non-representational function in the practice, such as the interpretation of some model or the specification of the target of the explanation. Second, when an agent puts forward an explanation using a model, they usually aim to remain agnostic about various features of the phenomenon being explained. In this sense, explanations are intended to be autonomous from many of the more fundamental features of such systems. I support these two assumptions by showing how they allow one to address a number of recent concerns raised by Bokulich, Potochnik and Rice. In addition, these assumptions lead to a defense of the view that explanations are wholly true that improves on the accounts developed by Craver, Mäki and Strevens.
See here for a working draft of my paper, “Russell and Logical Empiricism”. This paper has been written for the Oxford Handbook to Bertrand Russell, edited by Kevin Klement. I aim to discuss how Russell’s own epistemology and metaphysics were shaped through his philosophical interactions with Schlick, Neurath, Carnap and Reichenbach.
My paper “Concrete Scale Models, Essential Idealization, and Causal Explanation” is now available through Advance Access at the British Journal for the Philosophy of Science. Here is the abstract of the paper:
This paper defends three claims about concrete or physical models: (i) these models remain important in science and engineering, (ii) they are often essentially idealized, in a sense to be made precise, and (iii) despite these essential idealizations, some of these models may be reliably used for the purpose of causal explanation. This discussion of concrete models is pursued using a detailed case study of some recent models of landslide generated impulse waves. Practitioners show a clear awareness of the idealized character of these models, and yet address these concerns through a number of methods. This paper focuses on experimental arguments that show how certain failures to accurately represent feature X are consistent with accurately representing some causes of featureY, even when X is causally relevant to Y. To analyse these arguments, the claims generated by a model must be carefully examined and grouped into types. Only some of these types can be endorsed by practitioners, but I argue that these endorsed claims are sufficient for limited forms of causal explanation.