Distinctively mathematical explanation and the problem of directionality: A quasi-erotetic solution

The increasing preponderance of opinion that some natural phenomena can be explained mathematically has inspired a search for a viable account of distinctively mathematical explanation. Among the desiderata for an adequate account is that it should solve the problem of directionality —the reversals of distinctively mathematical explanations should not count as members among the explanatory fold but any solution must also avoid the exclusion of genuine explanations. In what follows, I introduce and defend what I refer to as a quasi-erotetic solution which provides a remedy to the problem in the form of an additional necessary condition on explanation.     

Realizability and the varieties of explanation

What realization is has been convincingly presented in relation to the way we determine what counts as the realizers of realized properties. The way we explain a fact of realization includes a reference to what realization should be; therefore it informs in turn our understanding of the nature of realization. Conceptions of explanation are thereby included in the views of realization as a metaphysical property.Recently, several major views of realization such as Polger and Shapiro's or Gillett and Aizawa's, however competing, have relied on the neo-mechanicist theory of explanations (e.g,. Darden and Caver 2013), currently popular among philosophers of science. However, it has also been increasingly argued that some explanations are not mechanistic (e.g., Batterman 2009).Using an account given in Huneman (2017), I argue that within those explanations the fact that some mathematical properties are instantiated is explanatory, and that this defines a specific explanatory type called “structural explanation”, whose subtypes could be: optimality explanations (usually found in economics), topological explanations, etc. This paper thereby argues that all subtypes of structural explanation define several kinds of realizability, which are not equivalent to the usual notion of realization tied to mechanistic explanations, onto which many of the philosophical investigations are focused. Then it draws some consequences concerning the notion of multiple realizability.     

Anachronism and retrospective explanation: in defence of a present-centred history of science

This paper defends the right of historians to make use of their knowledge of the remote consequences of past actions. In particular, it is argued that the disciplinary cohesion of the history of science relies crucially upon our ability to target, for further investigation, those past activities ancestral to modern science. The history of science is not limited to the study of those activities but it is structured around them. In this sense, the discipline is inherently ‘present-centred’: its boundaries are determined, in part, by judgements inaccessible to the historical actors. Present-centredness of this sort, it is urged, should not be regarded as a problem; its methodological consequences are minimal.     

Confirmational holism and its mathematical (w)holes

I critically examine confirmational holism as it pertains to the indispensability arguments for mathematical Platonism. I employ a distinction between pure and applied mathematics that grows out of the often overlooked symbiotic relationship between mathematics and science. I argue that this distinction undercuts the notion that (pure) mathematical theories fall under the holistic scope of the confirmation of our scientific theories.     

Perspectivism, inconsistent models, and contrastive explanation

It is widely recognized that scientific theories are often associated with strictly inconsistent models, but there is little agreement concerning the epistemic consequences. Some argue that model inconsistency supports a strong perspectivism, according to which claims serving as interpretations of models are inevitably and irreducibly perspectival. Others argue that in at least some cases, inconsistent models can be unified as approximations to a theory with which they are associated, thus undermining this kind of perspectivism. I examine the arguments for perspectivism, and contend that its strong form is defeasible in principle, not merely in special cases. The argument rests on the plausibility of scientific knowledge concerning non-perspectival, dispositional facts about modelled systems. This forms the basis of a novel suggestion regarding how to understand the knowledge these models afford, in terms of a contrastive theory of what-questions.     

Collaborative explanation and biological mechanisms

This paper motivates and outlines a new account of scientific explanation, which I term ‘collaborative explanation.’ My approach is pluralist: I do not claim that all scientific explanations are collaborative, but only that some important scientific explanations are—notably those of complex organic processes like development. Collaborative explanation is closely related to what philosophers of biology term ‘mechanistic explanation’ (e.g., Machamer et al., Craver, 2007). I begin with minimal conditions for mechanisms: complexity, causality, and multilevel structure. Different accounts of mechanistic explanation interpret and prioritize these conditions in different ways. This framework reveals two distinct varieties of mechanistic explanation: causal and constitutive. The two have heretofore been conflated, with philosophical discussion focusing on the former. This paper addresses the imbalance, using a case study of modeling practices in Systems Biology to reveals key features of constitutive mechanistic explanation. I then propose an analysis of this variety of mechanistic explanation, in terms of collaborative concepts, and sketch the outlines of a general theory of collaborative explanation. I conclude with some reflections on the connection between this variety of explanation and social aspects of scientific practice.     

Mechanistic explanation,cognitive systems demarcation,and extended cognition

Approaches to the Internalism–Externalism controversy in the philosophy of mind often involve both (broadly) metaphysical and explanatory considerations. Whereas originally most emphasis seems to have been placed on metaphysical concerns, recently the explanation angle is getting more attention. Explanatory considerations promise to offer more neutral grounds for cognitive systems demarcation than (broadly) metaphysical ones. However, it has been argued that explanation-based approaches are incapable of determining the plausibility of internalist-based conceptions of cognition vis-à-vis externalist ones. On this perspective, improved metaphysics is the route along which to solve the Internalist–Externalist stalemate. In this paper we challenge this claim. Although we agree that explanation-orientated approaches have indeed so far failed to deliver solid means for cognitive system demarcation, we elaborate a more promising explanation-oriented framework to address this issue. We argue that the mutual manipulability account of constitutive relevance in mechanisms, extended with the criterion of ‘fat-handedness’, is capable of plausibly addressing the cognitive systems demarcation problem, and thus able to decide on the explanatory traction of Internalist vs. Externalist conceptions, on a case-by-case basis. Our analysis also highlights why some other recent mechanistic takes on the problem of cognitive systems demarcation have been unsuccessful. We illustrate our claims with a case on gestures and learning.     

Historicity and explanation

Some scientific explanations are distinctively historical. The aim of this paper is to say what gives such explanations their historical character. A secondary aim is to describe what makes an explanation a stronger or weaker historical explanation. We begin with a critical discussion of John Beatty's and Eric Desjardins' work on historicity and historical narrative. We then offer an alternative account of historical explanation that draws on the work of earlier philosophers (Gallie, Danto, Mink, and Hull). In that alternative account, we highlight four features of narrative explanation that Beatty and Desjardins underemphasize: central subjects; historical trajectories; the idea that historical narratives are known retrospectively; and criteria for determining what is a stronger or weaker historical narrative.     

Narrative possibility and narrative explanation

Narratives are about not only what actually happened, but also what might have. And narrative explanations make productive use of these unrealized possibilities. I discuss narrative explanation as a form of counterfactual, difference-making explanation, with a demanding qualification: the counterfactual conditions are historically or narratively (not merely logically or physically) possible. I consider these issues in connection with literary, historical and scientific narratives.     

Mechanistic artefact explanation

One thing about technical artefacts that needs to be explained is how their physical make-up, or structure, enables them to fulfil the behaviour associated with their function, or, more colloquially, how they work. In this paper I develop an account of such explanations based on the familiar notion of mechanistic explanation. To accomplish this, I (1) outline two explanatory strategies that provide two different types of insight into an artefact’s functioning, and (2) show how human action inevitably plays a role in artefact explanation. I then use my own account to criticize other recent work on mechanistic explanation and conclude with some general implications for the philosophy of explanation.     

Narrative ordering and explanation

This paper investigates the important role of narrative in social science case-based research. The focus is on the use of narrative in creating a productive ordering of the materials within such cases, and on how such ordering functions in relation to ‘narrative explanation’. It argues that narrative ordering based on juxtaposition - using an analogy to certain genres of visual representation - is associated with creating and resolving puzzles in the research field. Analysis of several examples shows how the use of conceptual or theoretical resources within the narrative ordering of ingredients enables the narrative explanation of the case to be resituated at other sites, demonstrating how such explanations can attain scope without implying full generality.     

Transcendental philosophy and mathematical physics

This paper explores the relationship between Kant’s views on the metaphysical foundations of Newtonian mathematical physics and his more general transcendental philosophy articulated in the Critique of pure reason. I argue that the relationship between the two positions is very close indeed and, in particular, that taking this relationship seriously can shed new light on the structure of the transcendental deduction of the categories as expounded in the second edition of the Critique.     

Inference to the best explanation and Norton's material theory of induction

I argue that we should consider Norton's material theory of induction as consisting of two largely independent claims. First, there is the claim that material facts license inductions - a claim which I interpret as a type of contextualism about induction. Second, there is the claim that there are no universal rules of induction. While a good case can be made for the first claim, I believe that Norton's arguments for the second claim are lacking. In particular, I spell out Norton's argument against the claim that all induction may be reduced to inference to the best explanation, and argue that it is not persuasive. Rejecting this part of Norton's theory does not however require us to abandon the first claim that material facts license inductions. In this way, I distinguish the parts of the material theory of induction we should happily accept from the parts about which we should be more skeptical.     

BonJour on explanation and skepticism

Laurence BonJour, among others, has argued that inference to the best explanation allows us to reject skeptical hypotheses in favor of our common-sense view of the world. BonJour considers several skeptical hypotheses, specifically: (i) our experiences arise by mere chance, uncaused; (ii) the simple hypothesis which states merely that our experiences are caused unveridically; and (iii) an elaborated hypothesis which explains in detail how our unveridical experiences are brought about. A central issue is whether the coherence of one’s experience makes that experience more likely to be veridical. BonJour’s recent treatment of “analog” and “digital” skeptical hypotheses is also discussed. I argue that, although there are important lessons to be learned from BonJour’s writings, his use of inference to the best explanation against skepticism is unsuccessful.     

Ordinary language philosophy,explanation, and the historical turn in philosophy of science

Taking a cue from remarks Thomas Kuhn makes in 1990 about the historical turn in philosophy of science, I examine the history of history and philosophy of science within parts of the British philosophical context in the 1950s and early 1960s. During this time, ordinary language philosophy's influence was at its peak. I argue that the ordinary language philosophers' methodological recommendation to analyze actual linguistic practice influences several prominent criticisms of the deductive-nomological model of scientific explanation and that these criticisms relate to the historical turn in philosophy of science. To show these connections, I primarily examine the work of Stephen Toulmin, who taught at Oxford from 1949 to 1954, and Michael Scriven, who completed a dissertation on explanation under Gilbert Ryle and R.B. Braithwaite in 1956. I also consider Mary Hesse's appeal to an ordinary language-influenced account of meaning in her account of the role of models and analogies in scientific reasoning, and W.H. Watson's Wittgensteinian philosophy of science, an early influence on Toulmin. I think there are two upshots to my historical sketch. First, it fills out details of the move away from logical positivism to more historical- and practice-focused philosophies of science. Second, questions about linguistic meaning and the proper targets and aims of philosophical analysis are part and parcel of the historical turn, as well as its reception. Looking at the philosophical background during which so-called linguistic philosophers also had a hand in bringing these questions to prominence helps us understand why.     

Margaret Cavendish and Joseph Glanvill: science, religion, and witchcraft

Many scholars point to the close association between early modern science and the rise of rational arguments in favour of the existence of witches. For some commentators, it is a poor reflection on science that its methods so easily lent themselves to the unjust persecution of innocent men and women. In this paper, I examine a debate about witches between a woman philosopher, Margaret Cavendish (1623-1673), and a fellow of the Royal Society, Joseph Glanvill (1636-1680). I argue that Cavendish is the voice of reason in this exchange—not because she supports the modern-day view that witches do not exist, but because she shows that Glanvill’s arguments about witches betray his own scientific principles. Cavendish’s responses to Glanvill suggest that, when applied consistently, the principles of early modern science could in fact promote a healthy scepticism toward the existence of witches.     

Ernst Cassirer's transcendental account of mathematical reasoning

Cassirer's philosophical agenda revolved around what appears to be a paradoxical goal, that is, to reconcile the Kantian explanation of the possibility of knowledge with the conceptual changes of nineteenth and early twentieth-century science. This paper offers a new discussion of one way in which this paradox manifests itself in Cassirer's philosophy of mathematics. Cassirer articulated a unitary perspective on mathematics as an investigation of structures independently of the nature of individual objects making up those structures. However, this posed the problem of how to account for the applicability of abstract mathematical concepts to empirical reality. My suggestion is that Cassirer was able to address this problem by giving a transcendental account of mathematical reasoning, according to which the very formation of mathematical concepts provides an explanation of the extensibility of mathematical knowledge. In order to spell out what this argument entails, the first part of the paper considers how Cassirer positioned himself within the Marburg neo-Kantian debate over intellectual and sensible conditions of knowledge in 1902–1910. The second part compares what Cassirer says about mathematics in 1910 with some relevant examples of how structural procedures developed in nineteenth-century mathematics.     

Constitutive relevance in cognitive science: The case of eye movements and cognitive mechanisms

In this paper I assess whether the recently proposed “No De-Coupling” (NDC) theory of constitutive relevance in mechanisms is a useful tool to reconstruct constitutive relevance investigations in scientific practice. The NDC theory has been advanced as a framework theoretically superior to the mutual manipulability (MM) account of constitutive relevance in mechanisms but, in contrast to the MM account, has not yet been applied to detailed case studies. I argue that the NDC account is also applicable to empirical practice and that it fares better than the MM account on both theoretical and empirical grounds. I elaborate these claims in terms of applications of the NDC theory to two case studies of cognitive science research on the role of eye movements in mechanisms for cognitive capacities.