Circularity,indispensability, and mathematical explanation in science

In this paper I consider the objection that the Enhanced Indispensability Argument (EIA) is circular and hence fails to support mathematical platonism. The objection is that the explanandum in any mathematical explanation of a physical phenomenon is itself identified using mathematical concepts. Hence the explanandum is only genuine if the truth of some mathematical theory is already presupposed. I argue that this objection deserves to be taken seriously, that it does sometimes undermine support for EIA, but that there is no reason to think that circularity is an unavoidable feature of mathematical explanation in science.     

The autonomy of models and explanation: anomalous molecular rearrangements in early twentieth-century physical organic chemistry

During the 1930s and 1940s, American physical organic chemists employed electronic theories of reaction mechanisms to construct models offering explanations of organic reactions. But two molecular rearrangements presented enormous challenges to model construction. The Claisen and Cope rearrangements were predominantly inaccessible to experimental investigation and they confounded explanation in theoretical terms. Drawing on the idea that models can be autonomous agents in the production of scientific knowledge, I argue that one group of models in particular were functionally autonomous from the Hughes–Ingold theory. Cope and Hardy’s models of the Claisen and Cope rearrangements were resources for the exploration of the Hughes–Ingold theory that otherwise lacked explanatory power. By generating ‘how-possibly’ explanations, these models explained how these rearrangements could happen rather than why they did happen. Furthermore, although these models were apparently closely connected to theory in terms of their construction, I argue that partial autonomy issued in extra-logical factors concerning the attitudes of American chemists to the Hughes–Ingold theory. And in the absence of a complete theoretical hegemony, a degree of consensus was reached concerning modelling the Claisen rearrangement mechanism.     

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.     

Science, truth and history, part II. Metaphysical bolt-holes for the Sociology of Scientific Knowledge?

Historians of science have frequently sought to exclude modern scientific knowledge from their narratives. Part I of this paper, published in the previous issue, cautioned against seeing more than a literary preference at work here. In particular, it was argued—contra advocates of the Sociology of Scientific Knowledge (SSK)—that a commitment to epistemological relativism should not be seen as having straightforward historiographical consequences. Part II considers further SSK-inspired attempts to entangle the currently fashionable historiography with particular positions in the philosophy of science. None, I argue, is promising. David Bloor’s proposed alliance with scientific realism relies upon a mistaken view of contrastive explanation; Andrew Pickering’s appeal to instrumentalism is persuasive for particle physics but much less so for science as a whole; and Bruno Latour’s home-grown metaphysics is so bizarre that its compatibility with SSK is, if anything, a further blow to the latter’s plausibility.     

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.     

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.     

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.     

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.     

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.     

One phenomenon, many models: Inconsistency and complementarity

The paper examines philosophical issues that arise in contexts where one has many different models for treating the same system. I show why in some cases this appears relatively unproblematic (models of turbulence) while others represent genuine difficulties when attempting to interpret the information that models provide (nuclear models). What the examples show is that while complementary models needn’t be a hindrance to knowledge acquisition, the kind of inconsistency present in nuclear cases is, since it is indicative of a lack of genuine theoretical understanding. It is important to note that the differences in modeling do not result directly from the status of our knowledge of turbulent flows as opposed to nuclear dynamics—both face fundamental theoretical problems in the construction and application of models. However, as we shall, the ‘problem context(s)’ in which the modeling takes plays a decisive role in evaluating the epistemic merit of the models themselves. Moreover, the theoretical difficulties that give rise to inconsistent as opposed to complementary models (in the cases I discuss) impose epistemic and methodological burdens that cannot be overcome by invoking philosophical strategies like perspectivism, paraconsistency or partial structures.     

Microbes,mathematics, and models

Microbial model systems have a long history of fruitful use in fields that include evolution and ecology. In order to develop further insight into modelling practice, we examine how the competitive exclusion and coexistence of competing species have been modelled mathematically and materially over the course of a long research history. In particular, we investigate how microbial models of these dynamics interact with mathematical or computational models of the same phenomena. Our cases illuminate the ways in which microbial systems and equations work as models, and what happens when they generate inconsistent findings about shared targets. We reveal an iterative strategy of comparative modelling in different media, and suggest reasons why microbial models have a special degree of epistemic tractability in multimodel inquiry.     

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.     

Science, truth and history, Part I. Historiography, relativism and the Sociology of Scientific Knowledge

Recently, many historians of science have chosen to present their historical narratives from the ‘actors’-eye view’. Scientific knowledge not available within the actors’ culture is not permitted to do explanatory work. Proponents of the Sociology of Scientific Knowledge (SSK) purport to ground this historiography on epistemological relativism. I argue that they are making an unnecessary mistake: unnecessary because the historiographical genre in question can be defended on aesthetic and didactic grounds; and a mistake because the argument from relativism is in any case incoherent.The argument of the present article is self-contained, but steers clear of metaphysical debates in the philosophy of science. To allay fears of hidden assumptions, the sequel, to be published in the following issue, will consider SSK’s prospects of succour from scientific realism, instrumentalism, and a metaphysical system of Bruno Latour’s own devising.     

Understanding,explanation, and unification

In this article I argue that there are two different types of understanding: the understanding we get from explanations, and the understanding we get from unification. This claim is defended by first showing that explanation and unification are not as closely related as has sometimes been thought. A critical appraisal of recent proposals for understanding without explanation leads us to discuss the example of a purely classificatory biology: it turns out that such a science can give us understanding of the world through unification of the phenomena, even though it does not give us any explanations. The two types of understanding identified in this paper, while strictly separate, do have in common that both consist in seeing how the individual phenomena of the universe hang together. Explanations give us connections between the phenomena through the asymmetric, ‘vertical’ relation of determination; unifications give us connections through the symmetric, ‘horizontal’ relation of kinship. We then arrive at a general definition of understanding as knowledge of connections between the phenomena, and indicate that there might be more than two types of understanding.     

Using computational models to discover and understand mechanisms

Areas of biology such as cell and molecular biology have been dominated by research directed at constructing mechanistic explanations that identify parts and operations that when organized appropriately are responsible for the various phenomena they investigate. Increasingly the mechanisms hypothesized involve non-sequential organization of non-linear operations and so exceed the ability of researchers to mentally rehearse their behavior. Accordingly, scientists rely on tools of computational modeling and dynamical systems theory in advancing dynamic mechanistic explanations. Using circadian rhythm research as an exemplar, this paper explores the variety of roles computational modeling is playing. They serve not just to determine whether the mechanism will produce the desired behavior, but in the discovery process of hypothesizing mechanisms and in understanding why proposed mechanisms behave as they do.     

Models, scientific realism, the intelligibility of nature, and their cultural significance

In this article, I will view realist and non-realist accounts of scientific models within the larger context of the cultural significance of scientific knowledge. I begin by looking at the historical context and origins of the problem of scientific realism, and claim that it is originally of cultural and not only philosophical, significance. The cultural significance of debates on the epistemological status of scientific models is then related to the question of ‘intelligibility’ and how science, through models, can give us knowledge of the world by presenting us with an ‘intelligible account/picture of the world’, thus fulfilling its cultural-epistemic role. Realists typically assert that science can perform this role, while non-realists deny this. The various strategies adopted by realists and non-realists in making good their respective claims, is then traced to their cultural motivations. Finally I discuss the cultural implications of adopting realist or non-realist views of models through a discussion of the views of Rorty, Gellner, Van Fraassen and Clifford Hooker on the cultural significance of scientific knowledge.