Citations of:
Explanatory Abstractions
British Journal for the Philosophy of Science 70 (3):817–844 (2019)
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This paper discusses Baker’s Enhanced Indispensability Argument for mathematical realism on the basis of the indispensable role mathematics plays in scientific explanations of physical facts, along with various responses to it. I argue that there is an analogue of causal explanation for mathematics which, of several basic types of explanation, holds the most promise for use in the EIA. I consider a plausible case where mathematics plays an explanatory role in this sense, but argue that such use still does not (...) 

A popular view presents explanations in the cognitive sciences as causal or mechanistic and argues that an important feature of such explanations is that they allow us to manipulate and control the explanandum phenomena. Nonetheless, whether there can be explanations in the cognitive sciences that are neither causal nor mechanistic is still under debate. Another prominent view suggests that both causal and noncausal relations of counterfactual dependence can be explanatory, but this view is open to the criticism that it is (...) 

Proponents of ontic conceptions of explanation require all explanations to be backed by causal, constitutive, or similar relations. Among their justifications is that only ontic conceptions can do justice to the ‘directionality’ of explanation, i.e., the requirement that if X explains Y , then notY does not explain notX . Using topological explanations as an illustration, we argue that nonontic conceptions of explanation have ample resources for securing the directionality of explanations. The different ways in which neuroscientists rely on multiplexes (...) 

Recent years have seen growing interest in modifying interventionist accounts of causal explanation in order to characterise noncausal explanation. However, one surprising element of such accounts is that they have typically jettisoned the core feature of interventionism: interventions. Indeed, the prevailing opinion within the philosophy of science literature suggests that interventions exclusively demarcate causal relationships. This position is so prevalent that, until now, no one has even thought to name it. We call it “intervention puritanism” (Ipuritanism, for short). In this (...) 

Mathematics clearly plays an important role in scientific explanation. Debate continues, however, over the kind of role that mathematics plays. I argue that if pure mathematical explananda and physical explananda are unified under a common explanation within science, then we have good reason to believe that mathematics is explanatory in its own right. The argument motivates the search for a new kind of scientific case study, a case in which pure mathematical facts and physical facts are explanatorily unified. I argue (...) 

Mathematics appears to play an explanatory role in science. This, in turn, is thought to pave a way toward mathematical Platonism. A central challenge for mathematical Platonists, however, is to provide an account of how mathematical explanations work. I propose a propertybased account: physical systems possess mathematical properties, which either guarantee the presence of other mathematical properties and, by extension, the physical states that possess them; or rule out other mathematical properties, and their associated physical states. I explain why Platonists (...) 

We demonstrate how real progress can be made in the debate surrounding the enhanced indispensability argument. Drawing on a counterfactual theory of explanation, wellmotivated independently of the debate, we provide a novel analysis of ‘explanatory generality’ and how mathematics is involved in its procurement. On our analysis, mathematics’ sole explanatory contribution to the procurement of explanatory generality is to make counterfactual information about physical dependencies easier to grasp and reason with for creatures like us. This gives precise content to key (...) 

This thesis starts with three challenges to the structuralist accounts of applied mathematics. Structuralism views applied mathematics as a matter of building mapping functions between mathematical and targetended structures. The first challenge concerns how it is possible for a nonmathematical target to be represented mathematically when the mapping functions per se are mathematical objects. The second challenge arises out of inconsistent early calculus, which suggests that mathematical representation does not require rigorous mathematical structures. The third challenge comes from renormalisation group (...) 

This paper examines some recent attempts that use counterfactuals to understand the asymmetry of noncausal scientific explanations. These attempts recognize that even when there is explanatory asymmetry, there may be symmetry in counterfactual dependence. Therefore, something more than mere counterfactual dependence is needed to account for explanatory asymmetry. Whether that further ingredient, even if applicable to causal explanation, can fit noncausal explanation is the challenge that explanatory asymmetry poses for counterfactual accounts of noncausal explanation. This paper argues that several recent (...) 

Recently, many have argued that there are certain kinds of abstract mathematical explanations that are noncausal. In particular, the irrelevancy approach suggests that abstracting away irrelevant causal details can leave us with a noncausal explanation. In this paper, I argue that the common example of Renormalization Group explanations of universality used to motivate the irrelevancy approach deserves more critical attention. I argue that the reasons given by those who hold up RG as noncausal do not stand up to critical scrutiny. (...) 

Recent philosophical work has explored the distinction between causal and noncausal forms of explanation. In this literature, topological explanation is viewed as a clear example of the noncausal variety–it is claimed that topology lacks temporal information, which is necessary for causal structure. This paper explores the distinction between topological and causal forms of explanation and argues that this distinction is not as clear cut as the literature suggests. One reason for this is that some explanations involve both topological and causal (...) 

We explore the prospects of a monist account of explanation for both noncausal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation (CTE) for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both noncausal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us (...) 

Contribution to a review symposium on Marc Lange's Because without cause: Noncausal explanation in science and mathematics. Oxford: Oxford University Press, 2017. 

In the last couple of years a few seemingly independent debates on scientific explanation have emerged, with several key questions that take different forms in different areas. For example, the questions what makes an explanation distinctly mathematical and are there any noncausal explanations in sciences sometimes take a form of the question what makes mathematical models explanatory, especially whether highly idealized models in science can be explanatory and in virtue of what they are explanatory. These questions raise further issues about (...) 

Recent literature on noncausal explanation raises the question as to whether explanatory monism, the thesis that all explanations submit to the same analysis, is true. The leading monist proposal holds that all explanations support changerelating counterfactuals. We provide several objections to this monist position. 1Introduction2ChangeRelating Monism's Three Problems3Dependency and Monism: Unhappy Together4Another Challenge: Counterfactual Incidentalism4.1Highgrade necessity4.2Unity in diversity5Conclusion. 

This chapter examines issues surrounding inference to the best explanation, its justification, and its role in different arguments for scientific realism, as well as more general issues concerning explanations’ ontological commitments. Defending the reliability of inference to the best explanation has been a central plank in various realist arguments, and realists have drawn various ontological conclusions from the premise that a given scientific explanation best explains some phenomenon. This chapter stresses the importance of thinking carefully about the nature of explanation (...) 

This chapter defends a (minimal) realist conception of progress in scientific understanding in the face of the ubiquitous plurality of perspectives in science. The argument turns on the counterfactualdependence framework of explanation and understanding, which is illustrated and evidenced with reference to different explanations of the rainbow. 

Recent discussions of emergence in physics have focussed on the use of limiting relations, and often particularly on singular or asymptotic limits. We discuss a putative example of emergence that does not fit into this narrative: the case of phonons. These quasiparticles have some claim to be emergent, not least because the way in which they relate to the underlying crystal is almost precisely analogous to the way in which quantum particles relate to the underlying quantum field theory. But there (...) 

In the spirit of explanatory pluralism, this chapter argues that causal and noncausal explanations of a phenomenon are compatible, each being useful for bringing out different sorts of insights. After reviewing a modelbased account of scientific explanation, which can accommodate causal and noncausal explanations alike, an important core conception of noncausal explanation is identified. This noncausal form of modelbased explanation is illustrated using the example of how Earth scientists in a subfield known as aeolian geomorphology are explaining the formation of (...) 

It is commonly claimed that the universality of critical phenomena is explained through particular applications of the renormalization group. This article has three aims: to clarify the structure of the explanation of universality, to discuss the physics of such RG explanations, and to examine the extent to which universality is thus explained. The derivation of critical exponents proceeds via a realspace or a fieldtheoretic approach to the RG. Building on work by Mainwood, this article argues that these approaches ought to (...) 