The directionality of distinctively mathematical explanations

In “What Makes a Scientific Explanation Distinctively Mathematical?” (2013b), Lange uses several compelling examples to argue that certain explanations for natural phenomena appeal primarily to mathematical, rather than natural, facts. In such explanations, the core explanatory facts are modally stronger than facts about causation, regularity, and other natural relations. We show that Lange's account of distinctively mathematical explanation is flawed in that it fails to account for the implicit directionality in each of his examples. This inadequacy is remediable in each case by appeal to ontic facts that account for why the explanation is acceptable in one direction and unacceptable in the other direction. The mathematics involved in these examples cannot play this crucial normative role. While Lange's examples fail to demonstrate the existence of distinctively mathematical explanations, they help to emphasize that many superficially natural scientific explanations rely for their explanatory force on relations of stronger-than-natural necessity. These are not opposing kinds of scientific explanations; they are different aspects of scientific explanation.     

Introduction: Structuralists of the world unite

Key arguments and claims in Steven French's The Structure of the World are articulated and assessed. Differences between different forms of ontic structural realism are articulated, and some problems raised for some aspects of French's version.     

Structural realism,mathematics, and ontology

Over the last two decades structural realism has been given progressively more elaborated formulations. Steven French has been at the forefront of the development of the most conceptually sophisticated and historically sensitive version of the view. In his book, The Structure of the World (French (2014)), French shows how structural realism, the view according to which structure is all there is (ontic structural realism), is able to illuminate central issues in the philosophy of science: underdetermination, scientific representation, dispositions, natural modality, and laws of nature. The discussion consistently sheds novel light on the problems under consideration while developing insightful and provocative views. In this paper, I focus on the status of mathematics within French's ontic structural realism, and I raise some concerns about its proper understanding vis-à-vis the realist components of the view.     

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.     

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.     

A pragmatic account of mechanistic artifact explanation

A mechanistic artifact explanation is an explanation that accounts for an artifact behavior by describing the underlying mechanism. The article shows that there are different kinds of mechanistic artifact explanation: top-down and bottom-up explanation, and I also distinguish between less and more inclusive top-down explanations. To illustrate these different kinds of explanation, the behavior of a simple, fictional artifact is explained in different ways. I defend that which explanation is ideal, depends on pragmatic factors (e.g., the background knowledge of the explainee and the specific goal for which the explanation will be used). For each kind of explanation, the situations, goals and interests for which it is most appropriate are specified, resulting in a pragmatic theory of mechanistic artifact explanation. This theory is compared to Jeroen de Ridder’s account of the pragmatics of mechanistic artifact explanation.     

Science,self improvement and the first industrial revolution

This study considers Newton's views on space and time with respect to some important ontologies of substance in his period. Specifically, it deals in a philosophico-historical manner with his conception of substance, attribute, existence, to actuality and necessity. I show how Newton links these “features” of things to his conception of God's existence with respect of infinite space and time. Moreover, I argue that his ontology of space and time cannot be understood without fully appreciating how it relates to the nature of Divine existence. In order to establish this, the ontology embodied in Newton's theory of predication is analysed, and shown to be different from the presuppositions of the ontological argument. From the historical point of view Gassendi's influence is stressed, via the mediation of Walter Charleton. Furthermore, Newton's thought on these matters is contrasted with Descartes's and Spinoza's. In point of fact, in his earliest notebook Newton recorded observations on Descartes's version of the ontological argument. Soon, however, he was to oppose the Cartesian conception of the actuality of Divine existence by means of arguments similar to those of Gassendi. Lastly, I suggest that the nature and extent of Henry More's influence on Newton's conception of how God relates to absolute space and time bears further examination.     

Comments on papers by Sharlin and Wall

Wall is convincing on the Fuller court, but less so on Holmes, who may have understood Spencer's Social statics as a laissez faire rather than as a Darwinist document. Sharlin helps us to follow Spencer's attempt to universalize the concept of energy, even if Sharlin's explanation for Spencer's failure reduces to an application of the classical insight that physical phenomena are more predictable than social phenomena. Sharlin's conception of ‘scientism’ is helpful in some contexts, but less so in others; we need to remind ourselves that the role of values in scientism is active as well as passive.     

The silence of the norms: The missing historiography of The Structure of Scientific Revolutions

History has been disparaged since the late 19th century for not conforming to norms of scientific explanation. Nonetheless, as a matter of fact a work of history upends the regnant philosophical conception of science in the second part of the 20th century. Yet despite its impact, Kuhn’s Structure has failed to motivate philosophers to ponder why works of history should be capable of exerting rational influence on an understanding of philosophy of science. But all this constitutes a great irony and a mystery. The mystery consists of the persistence of a complete lack of interest in efforts to theorize historical explanation. Fundamental questions regarding why an historical account could have any rational influence remain not merely unanswered, but unasked. The irony arises from the fact that analytic philosophy of history went into an eclipse where it remains until this day just around the time that the influence of Kuhn’s great work began to make itself felt. This paper highlights puzzles long ignored regarding the challenges a work of history managed to pose to the epistemic authority of science, and what this might imply generally for the place of philosophy of history vis-à-vis the problems of philosophy.     

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.     

Quantum jumps,superpositions, and the continuous evolution of quantum states

The apparent dichotomy between quantum jumps on the one hand, and continuous time evolution according to wave equations on the other hand, provided a challenge to Bohr's proposal of quantum jumps in atoms. Furthermore, Schrödinger's time-dependent equation also seemed to require a modification of the explanation for the origin of line spectra due to the apparent possibility of superpositions of energy eigenstates for different energy levels. Indeed, Schrödinger himself proposed a quantum beat mechanism for the generation of discrete line spectra from superpositions of eigenstates with different energies.However, these issues between old quantum theory and Schrödinger's wave mechanics were correctly resolved only after the development and full implementation of photon quantization. The second quantized scattering matrix formalism reconciles quantum jumps with continuous time evolution through the identification of quantum jumps with transitions between different sectors of Fock space. The continuous evolution of quantum states is then recognized as a sum over continually evolving jump amplitudes between different sectors in Fock space.In today's terminology, this suggests that linear combinations of scattering matrix elements are epistemic sums over ontic states. Insights from the resolution of the dichotomy between quantum jumps and continuous time evolution therefore hold important lessons for modern research both on interpretations of quantum mechanics and on the foundations of quantum computing. They demonstrate that discussions of interpretations of quantum theory necessarily need to take into account field quantization. They also demonstrate the limitations of the role of wave equations in quantum theory, and caution us that superpositions of quantum states for the formation of qubits may be more limited than usually expected.     

Looking forward,not back: Supporting structuralism in the present

The view that the fundamental kind properties are intrinsic properties enjoys reflexive endorsement by most metaphysicians of science. But ontic structural realists deny that there are any fundamental intrinsic properties at all. Given that structuralists distrust intuition as a guide to truth, and given that we currently lack a fundamental physical theory that we could consult instead to order settle the issue, it might seem as if there is simply nowhere for this debate to go at present. However, I will argue that there exists an as-yet untapped resource for arguing for ontic structuralism – namely, the way that fundamentality is conceptualized in our most fundamental physical frameworks. By arguing that physical objects must be subject to the ‘Goldilock's principle’ if they are to count as fundamental at all, I argue that we can no longer view the majority of properties defining them as intrinsic. As such, ontic structural realism can be regarded as the most promising metaphysics for fundamental physics, and that this is so even though we do not yet claim to know precisely what that fundamental physics is.     

Why eliminativism?

A central thesis of Steven French's brand of ontic structural realism has always been his eliminativism about objects. Unsurprisingly, this bold and controversial thesis has seen a lot of critical discussion. In his book The Structure of the World—Metaphysics & Representation, French accordingly defends this thesis against a range of challenges. A novel feature of this defense is the use of dependence relations to articulate his eliminativism. In this paper I take a critical look at French's defense of eliminativism and argue that the dependence relations invoked do not eliminate objects.     

A new twist to the No Miracles Argument for the success of science

J. D. Trout has recently developed a new defense of scientific realism, a new version of the No Miracles Argument. I critically evaluate Trout's novel defense of realism. I argue that Trout's argument for scientific realism and the related explanation for the success of science are self-defeating. In the process of arguing against the traditional realist strategies for explaining the success of science, he inadvertently undermines his own argument.     

No understanding without explanation

Scientific understanding, this paper argues, can be analyzed entirely in terms of a mental act of “grasping” and a notion of explanation. To understand why a phenomenon occurs is to grasp a correct explanation of the phenomenon. To understand a scientific theory is to be able to construct, or at least to grasp, a range of potential explanations in which that theory accounts for other phenomena. There is no route to scientific understanding, then, that does not go by way of scientific explanation.     

Kant's universal conception of natural history

Scholars often draw attention to the remarkably individual and progressive character of Kant's Universal Natural History and Theory of the Heavens (1755). What is less often noted, however, is that Kant's project builds on several transformations that occurred in natural science during the seventeenth and eighteenth centuries. Without contextualising Kant's argument within these transformations, the full sense of Kant's achievement remains unseen. This paper situates Kant's essay within the analogical form of Newtonianism developed by a diverse range of naturalists including Georges Buffon, Albrecht von Haller and Thomas Wright. It argues that Kant's universal conception of natural history can be viewed within the free-thinking and anti-clerical movement associated with Buffon. This does not mean, however, that it breaks from the methodological rules of Newtonianism. The claim of this paper is that Kant's essay contributes to the transformation of natural history from a logical system of classification to an explanation for the physical diversity of natural products according to laws.     

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.     

Newton’s “satis est”: A new explanatory role for laws

In this paper I argue that Newton’s stance on explanation in physics was enabled by his overall methodology and that it neither committed him to embrace action at a distance nor to set aside philosophical and metaphysical questions. Rather his methodology allowed him to embrace a non-causal, yet non-inferior, kind of explanation. I suggest that Newton holds that the theory developed in the Principia provides a genuine explanation, namely a law-based one, but that we also lack something explanatory, namely a causal account of the explanandum. Finally, I argue that examining what it takes to have law-based explanation in the face of agnosticism about the causal process makes it possible to recast the debate over action at a distance between Leibniz and Newton as empirically and methodologically motivated on both sides.     

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.     

The problem of grounding natural modality in Kant's account of empirical laws of nature

One of the central problems of Kant's account of the empirical laws of nature is: What grounds their necessity? In this article I discuss the three most important lines of interpretation and suggest a novel version of one of them. While the first interpretation takes the transcendental principles as the only sources of the empirical laws' necessity, the second interpretation takes the systematicity of the laws to guarantee their necessity. It is shown that both views involve serious problems. The third interpretation, the “causal powers interpretation”, locates the source of the laws' necessity in the properties of natural objects. Although the second and third interpretations seem incompatible, I analyse why Kant held both views and I argue that they can be reconciled, because the metaphysical grounding project of the laws' necessity is accounted for by Kant's causal powers account, while his best system account explains our epistemic access to the empirical laws. If, however, causal powers are supposed to fulfil the grounding function for the laws' natural modality, then I suggest that a novel reading of the causal powers interpretation should be formulated along the lines of a genuine dispositionalist conception of the laws of nature.