When scientist investigate why things happen, they aim at giving an explanation. But what does a scientific explanation look like? In the first chapter (Theories of Scientific Explanation) of this book, the milestones in the debate on how to characterize scientific explanations are exposed. The second chapter (How to Study Scientific Explanation?) scrutinizes the working-method of three important philosophers of explanation, Carl Hempel, Philip Kitcher and Wesley Salmon and shows what went wrong. Next, it is (...) the responsibility of current philosophers of explanation to go on where Hempel, Kitcher and Salmon failed. However, we should go on in a clever way. We call this clever way the pragmatic approach to scientific explanation and clarify briefly what this approach consists in. The third chapter (A Toolbox for Describing and Evaluating Explanatory Practices) elaborates the pragmatic approach by presenting a toolbox for analysing scientific explanation. In the last chapter (Examples of Descriptions and Evaluations of Explanatory Practices) the approach is illustrated with real-life examples of scientists aiming at explaining. (shrink)

Issues concerning scientific explanation have been a focus of philosophical attention from Pre- Socratic times through the modern period. However, recent discussion really begins with the development of the Deductive-Nomological (DN) model. This model has had many advocates (including Popper 1935, 1959, Braithwaite 1953, Gardiner, 1959, Nagel 1961) but unquestionably the most detailed and influential statement is due to Carl Hempel (Hempel 1942, 1965, and Hempel & Oppenheim 1948). These papers and the reaction to them have structured subsequent discussion (...) concerning scientific explanation to an extraordinary degree. After some general remarks by way of background and orientation (Section 1), this entry describes the DN model and its extensions, and then turns to some well-known objections (Section 2). It next describes a variety of subsequent attempts to develop alternative models of explanation, including Wesley Salmon's Statistical Relevance (Section 3) and Causal Mechanical (Section 4) models and the Unificationist models due to Michael Friedman and Philip Kitcher (Section 5). Section 6 provides a summary and discusses directions for future work. (shrink)

Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic (...) theory faces. The final view appeals to relevance logic and uses resources in information theory to understand the explanatory relationship between mathematical and physical facts. 1Introduction2Anchoring3The Basic Deductive-Mathematical Account4The Genuineness Problem5Irrelevance6Relevance and Information7Objections and Replies 7.1Against relevance logic7.2Too epistemic7.3Informational containment8Conclusion. (shrink)

Among philosophers of science, there is now a widespread agreement that the DN model of explanation is poorly equipped to account for explanations in biology. Rather than identifying laws, so the consensus goes, researchers explain biological capacities by constructing a model of the underlying mechanism.We think that the dichotomy between DN explanations and mechanistic explanations is misleading. In this article, we argue that there are cases in which biological capacities are explained without constructing a model of the underlying mechanism. (...) Although these explanations do not conform to Hempel’s DN model, they do invoke more or less stable generalisations. Because they invoke generalisations and have the form of an argument, we call them inferential explanations. We support this claim by considering two examples of explanations of biological capacities: pigeon navigation and photoperiodism. Next, we will argue that these non-mechanistic explanations are crucial to biology in three ways: sometimes, they are the only thing we have, they are heuristically useful, and they provide genuine understanding and so are interesting in their own right.In the last sections we discuss the relation between types of explanations and types of experiments and situate our views within some relevant debates on explanatory power and explanatory virtues. (shrink)

In this paper we argue that quantum mechanics provides a genuine kind of structural explanations of quantum phenomena. Since structural explanations only rely on the formal properties of the theory, they have the advantage of being independent of interpretative questions. As such, they can be used to claim that, even in the current absence of one agreed-upon interpretation, quantum mechanics is capable of providing satisfactory explanations of physical phenomena. While our proposal clearly cannot be taken to solve all interpretive issues (...) raised by quantum theory, we will argue that it can be successfully applied to some of its most puzzling phenomena, such Heisenberg's uncertainty relations and quantum non-locality. The discussion of these two case studies will also serve to illustrate the main properties of structural explanations and compare them to the DN and the unificationist models. Finally, we briefly discuss how structural explanations might relate to structural realism. (shrink)

This chapter contains sections titled: The DN Model The SR Model The Causal Mechanical Model Unificationist Models Conclusion and Directions for Future Work.

The essays in this volume grew out of a seminar examining the possibility of the emergence of a new consensus in the philosophy of science. While that issue is not resolved, we are presented with the most thorough examination of problems associated with the deductive-nomological model of explanation and its variants since the publication of Hempel's Aspects of Scientific Explanation and other Essays in the Philosophy of Science. The discussion begins with Wesley Salmon's monograph-length review of the past (...) forty years of work in the tradition initiated by Hempel and Oppenheim in their groundbreaking article "Studies in the Logic of Explanation". As one of the major players in the debates, Salmon's personal account is informative; it provides a useful introduction to the topic and covers the recent history of work on explanation in a manner that allows the uninitiated to follow the arguments and intricacies of the essays that follow. A main theme in Salmon's essay, as in much of his work, is the relation between the theory of explanation and the concept of causation. Given that the notion of causal laws plays a dominant role in DN explanations, this discussion is most welcome. Causation is also a clear concern of many of the other papers. The resolution of some of the tensions between Salmon's approach to causation, and the various roles of explanation in the philosophy of science, is, in fact, one of the main objectives of the extended concluding piece by Philip Kitcher. For Kitcher, explanations serve as unifying mechanisms for theories within different disciplines. Unification in turn also serves as a criterion for choosing between competing theories. The interplay between, on the one hand, Salmon's attention to the problems deriving from Hempel's initial formulation of DN and, on the other hand, Kitcher's concerns with Salmon's conceptualization of causation, produces one of the more fascinating dialectics of the volume. By attending to their dialogue, we see just how far the theory of explanation has come in the last forty years and yet how slow progress can be when fundamental problems are deeply entrenched. Causation continues to bedevil us. With one exception, the remaining contributors to this volume seem to confirm that judgment. Matti Sintonen, Paul Humphreys, David Papineau, Nancy Cartwright, James Woodward, and Merilee Salmon explore the many facets of causation as it applies to clarifying our explanatory objectives. Peter Railton is an exception. In his paper Railton reminds us that behind the epistemological and pragmatic concerns of most of the other contributors, Wesley Salmon included, there lies a set of metaphysical concerns. A thorough analysis of causation and, hence, a resolution to many of the DN model's problems requires a logically prior assessment of the relation between the epistemology of causation and the metaphysics of necessity. How one decides that issue or cluster of issues, Railton reminds us, will play heavily in the controversies between realists and nonrealists over the proper use of the principle of inference to the best explanation. (shrink)

The paper explores a deductive-nomological account of metaphysical explanation: some truths metaphysically explain, or ground, another truth just in case the laws of metaphysics determine the latter truth on the basis of the former. I develop and motivate a specific conception of metaphysical laws, on which they are general rules that regulate the existence and features of derivative entities. I propose an analysis of the notion of ‘determination via the laws’, based on a restricted form of logical entailment. I (...) argue that the DN-account of ground can be defended against the well-known objections to the DN-approach to scientific explanation. The goal of the paper is to show that the DN-account of metaphysical explanation is a well-motivated and defensible theory. (shrink)

Berkeley, Newton, Explanation, and Causation -/- I argue in this paper that Berkeley’s conception of natural law explanations, which echoes Newton’s, fails to solve a fundamental problem, which I label “explanatory asymmetry"; that the model of explanation Berkeley uses fails to distinguish between explanations and justifications, particularly since Berkeley denies real (efficient causes) in non-minded nature. At the end I suggest Berkeley might endorse a notion of understanding, say in astronomy or mechanics, which could be distinguished from (...) class='Hi'>explanation. (shrink)

In the beginning, there was the DN (Deductive Nomological) model of explanation, articulated by Hempel and Oppenheim (1948). According to DN, scientific explanation is subsumption under natural law. Individual events are explained by deducing them from laws together with initial conditions (or boundary conditions), and laws are explained by deriving them from other more fundamental laws, as, for example, the simple pendulum law is derived from Newton's laws of motion.

Husserl’s early picture of explanation in the sciences has never been completely provided. This lack represents an oversight, which we here redress. In contrast to currently accepted interpretations, we demonstrate that Husserl does not adhere to the much maligned deductive-nomological (DN) model of scientific explanation. Instead, via a close reading of early Husserlian texts, we reveal that he presents a unificationist account of scientific explanation. By doing so, we disclose that Husserl’s philosophy of scientific explanation is (...) no mere anachronism. It is, instead, tenable and relevant. We discuss how Husserl and other contemporary thinkers draw theoretical inspiration from the same source—namely, Bernard Bolzano. Husserl’s theory of scientific explanation shares a common language and discusses the same themes as, for example, Phillip Kitcher and Kit Fine. To advance our novel reading, we discuss Husserl’s investigations of grounding, inter-lawful explanation, intra-mathematical explanation, and scientific unification. (shrink)

Theories of explanation seek to tell us what distinctively explanatory information is. The most ambitious ones, such as the DN-account, seek to tell us what an explanation is, tout court. Less ambitious ones, such as causal theories, restrict themselves to a particular domain of inquiry. The least ambitious theories constitute outright skepticism, holding that there is no reasonably unified phenomenon to give an account of. On these views, it is impossible to give any theories of explanation at (...) all. I argue that both the less ambitious and outright skeptical varieties are committed to a certain context-sensitivity of our explanatory discourse. And though this discourse is almost certainly context-sensitive in some respects, it does not exhibit the context-sensitivity less than fully ambitious theories are committed to. Therefore, all accounts that seek to restrict themselves in scope, including causal accounts of explanation, fail. (shrink)

David Landy starts his book by delineating the received view of David Hume’s position on scientific explanation. He thinks that many still hold the view, thanks to the program of logical positivism and empiricism, that Hume subscribes to the Deductive-Nomological (DN) account of scientific explanation. Then he assimilates the DN account with Graciela De Pierris’ Newton-inspired inductivist reading. Landy has some sympathies toward the New Humean reading about explanation. The unobservable reality of causal powers and forces is (...) productive to the manifest phenomena. Landy clarifies that he disagrees with the New Humeans, because he accepts knowledge about the “descriptive content of such substances.” Accordingly, a central claim of his book is “that Hume’s view occupies a middle ground on the spectrum between De Pierris’s “inductivist” interpretation of him and that of the New Humeans. (shrink)

This paper examines a recent attempt by Evan Jobe to account for the asymmetric character of many scientific explanations. It is argued that a purported counterexample to Jobe's account, from Clark Glymour, is inconclusive, but that the account faces independent objections. It is also suggested, contrary to Jobe, that the explanatory relation is not always asymmetric. Sometimes a singular sentence C can figure in a DN derivation of another singular sentence E and E can also figure in a DN derivation (...) of C. Yet while we are inclined to regard the first derivation as an explanation of E, we are not inclined to regard the second derivation as an explanation of C. As Sylvain Bromberger pointed out in a now classic article (1966), one can explain the period of a pendulum by reference to its length and yet, although one can give a DN derivation of the length of a pendulum by reference to its period, this derivation does not seem to represent an explanation. Evan Jobe has recently offered an interesting account of such explanatory asymmetries and Clark Glymour has in turn proposed a counterexample which seems to show that Jobe's account is defective. The aim of this paper is two-fold. I shall attempt to show that (a) Glymour's proposed counterexample can be rejected on the grounds that it violates an independently plausible restriction on the role that equalities may play in DN explanation, and that (b) although Glymour's counterexample can be avoided in this way, Jobe's account is defective in several other respects. (shrink)

The current antireductionist consensus rests in part on the indefensibility of the deductive-nomological model of explanation, on which classical reductionism depends. I argue that the DN model is inessential to the reductionist program and that mechanism provides a better framework for thinking about reductionism. This runs counter to the contemporary mechanists’ claim that mechanism is an alternative to reductionism. I demonstrate that mechanists are committed to reductionism, as evidenced by the historical roots of the contemporary mechanist program. This view (...) shares certain core commitments with reductionism. It is these shared commitments that constitute the essential elements of the reductionist program. (shrink)

In this study the notion of mechanistic entities is analyzed as it has been conceptualized by Hermann Lotze in his article Life. Vital Force (1842), the metaphysical foundation of which has recourse to his Metaphysik (1841) and Logik (1843). According to Lotze, explanations in the sciences are arguments which have a syntactic and a semantic structure—similar to that which became later known as the DN-model of explanation. The syntactic structure is delineated by ontological forms, the semantic by cosmological ones; (...) the latter comprise the preconditions for the construction of appearances in accord with the ontological forms. Mechanisms are embedded into this logical framework by representing the more complex spatio-temporal arrangements of cosmological entities. The coordinated model of a mechanism is a reductive type of explanation. This study also demonstrates how Lotze made use of his concept of mechanisms in order to explain law-like and probabilistic events in organic and inorganic nature, thereby establishing an original ‘oligomeric’ (i. e., a fraction of the parts of a system determines its development) variant of a preformative theory of ontogenesis which anticipates modern concepts of genetic determination. In this context, Lotze alludes to paradigms of dissipative structures. The relevance of these reflections for subsequent theories is shown by contrasting them with Schrödinger’s theory of organisms. Finally, a comparison of some aspects of Lotze’s concept of mechanisms with equivalent aspects of current normative approaches confirms that essential elements of the latter versions can be retrieved in the former one. Above that, Lotze employs the teleological aspect of ontological forms in order to determine the extent of the mechanistic system under consideration. He further differentiates three modal states of mechanisms and includes a concept to explain exceptions or irregularities. The concept of ‘activity’ is strictly excluded from his account and shown to be a metaphysical illusion. (shrink)

Resumen En este artículo se examina el Darwinismo Neural en su explicación de la evolución de la conciencia humana, contrastando su metodología con la utilizada por Richard Lewontin, Richard Levins y Steven Rose, quienes han hecho importantes aportaciones en el estudio de los sistemas vivos desde un punto de vista dialéctico. Concluimos que la explicación interaccionista de la evolución de la conciencia planteada en el DN, supera muchas de las deficiencias del determinismo biológico; sin embargo, al compartir algunos lineamientos con (...) el cartesianismo, mantiene un carácter a-histórico insuficiente para la explicación de la conciencia humana. Finalmente, proponemos la adopción de una teoría explicativa de la conciencia humana que considere las relaciones existentes en ella, no sólo como interacciones sino también como interpenetraciones ontogénicas y filogenéticas.This article examines Neural Darwinism proposed as an explanation of evolution of human consciousness. His methodology is contrasted with that used by Richard Lewontin, Richard Levins, and Steven Rose, who made important contributions to the study of living systems from a dialectical point of view. We conclude that the interactionist explanation of the evolution of conscience put forward in ND overcomes many of the deficiencies proper to biological determinism. However, as ND also shares many of the foundations of the Cartesian approach, it maintains a non-historical character, insufficient for the account of human consciousness. We suggest the adoption of an alternative theory, able to fully explain human conscience which must consider the whole of existing relations in it, and, instead of merely considering them as interactions, they have to be observed as dialectical interpenetrations. (shrink)

Resumen En este artículo se examina el Darwinismo Neural en su explicación de la evolución de la conciencia humana, contrastando su metodología con la utilizada por Richard Lewontin, Richard Levins y Steven Rose, quienes han hecho importantes aportaciones en el estudio de los sistemas vivos desde un punto de vista dialéctico. Concluimos que la explicación interaccionista de la evolución de la conciencia planteada en el DN, supera muchas de las deficiencias del determinismo biológico; sin embargo, al compartir algunos lineamientos con (...) el cartesianismo, mantiene un carácter a-histórico insuficiente para la explicación de la conciencia humana. Finalmente, proponemos la adopción de una teoría explicativa de la conciencia humana que considere las relaciones existentes en ella, no sólo como interacciones sino también como interpenetraciones ontogénicas y filogenéticas.This article examines Neural Darwinism proposed as an explanation of evolution of human consciousness. His methodology is contrasted with that used by Richard Lewontin, Richard Levins, and Steven Rose, who made important contributions to the study of living systems from a dialectical point of view. We conclude that the interactionist explanation of the evolution of conscience put forward in ND overcomes many of the deficiencies proper to biological determinism. However, as ND also shares many of the foundations of the Cartesian approach, it maintains a non-historical character, insufficient for the account of human consciousness. We suggest the adoption of an alternative theory, able to fully explain human conscience which must consider the whole of existing relations in it, and, instead of merely considering them as interactions, they have to be observed as dialectical interpenetrations. (shrink)

The reductive strategies, such as the deductive-nomological (DN) model of explanation, or the Nagel–Schaffner reduction, have been perceived negatively ever since their first applications in historical inquiry. However, the role of the analysis of inter-theory relations, such as the preservation of success and retrospective rationality, has hardly ever received much attention from historians of science. In this paper, I am exploring the applicability of the analysis of inter-theory relations for the rational reconstruction of the development of science. I demonstrate (...) that the historiography of Anneliese Maier is a good example of a few reductive strategies at play in historical inquiry that do not submit to the same criticism that the synchronic reductive analysis of theories is submitted to. (shrink)

Zusammenfassung Oft genügen geschichtswissenschaftliche Erklärungen nicht den strengen Maßstäben einer Kausalerklärung, wie sie etwa in der Physik vorkommen mag. Das heißt aber nicht, daß es in der Geschichtswissenschaft keine Erklärungen gibt. Wir haben an Beispielen gesehen, daß Historiker und Historikerinnen (i) sehr wohl auch 'Warum?'-Fragen zu beantworten versuchen, und daß sich (ii) diese Antworten zum Teil sogar in direkte DN-bzw. IS-Erklärungen umformen lassen. Es besteht also keine Ursache, die Geschichtswissenschaft von den sogenannten "theoretischen Wissenschaften" methodologisch scharf zu trennen. Außerdem liefern (...) nicht wenige Erklärungen in geschichtswissenschaftlichen Kontexten Beispiele für normalerweise epistemisch befriedigende Erklärungsepisoden, die nicht in das Schema der strikten Kausalerklärung passen. Dazu zählen aufgrund der differenzierten Fragestellungen an Historiker auch bloße detaillierte Geschehensbeschreibungen oder teleologische Erklärungen von Handlungen. (shrink)

Resumen En este artículo se examina el Darwinismo Neural en su explicación de la evolución de la conciencia humana, contrastando su metodología con la utilizada por Richard Lewontin, Richard Levins y Steven Rose, quienes han hecho importantes aportaciones en el estudio de los sistemas vivos desde un punto de vista dialéctico. Concluimos que la explicación interaccionista de la evolución de la conciencia planteada en el DN, supera muchas de las deficiencias del determinismo biológico; sin embargo, al compartir algunos lineamientos con (...) el cartesianismo, mantiene un carácter a-histórico insuficiente para la explicación de la conciencia humana. Finalmente, proponemos la adopción de una teoría explicativa de la conciencia humana que considere las relaciones existentes en ella, no sólo como interacciones sino también como interpenetraciones ontogénicas y filogenéticas.This article examines Neural Darwinism proposed as an explanation of evolution of human consciousness. His methodology is contrasted with that used by Richard Lewontin, Richard Levins, and Steven Rose, who made important contributions to the study of living systems from a dialectical point of view. We conclude that the interactionist explanation of the evolution of conscience put forward in ND overcomes many of the deficiencies proper to biological determinism. However, as ND also shares many of the foundations of the Cartesian approach, it maintains a non-historical character, insufficient for the account of human consciousness. We suggest the adoption of an alternative theory, able to fully explain human conscience which must consider the whole of existing relations in it, and, instead of merely considering them as interactions, they have to be observed as dialectical interpenetrations. (shrink)

The aim of this paper is to defend some of C. G. Hempel's basic theses concerning the logic of explanation and prediction against criticisms recently made by W. Stegmüller. It is argued (very concisely) thatthese is no need for essentially pragmatic conditions in DN-arguments;only the structural identity sub-thesis “Every adequate prediction is ... an adequate explanation” can be held instead of the one Hempel has in mind;the notion of the ambiguity of probabilistic explanations should be reformulated;there is no (...) need for more than one knowledge situation;systematizations with low inductive probability do not give rational predictions or explanations of singular events. (shrink)

Resumen En este artículo se examina el Darwinismo Neural en su explicación de la evolución de la conciencia humana, contrastando su metodología con la utilizada por Richard Lewontin, Richard Levins y Steven Rose, quienes han hecho importantes aportaciones en el estudio de los sistemas vivos desde un punto de vista dialéctico. Concluimos que la explicación interaccionista de la evolución de la conciencia planteada en el DN, supera muchas de las deficiencias del determinismo biológico; sin embargo, al compartir algunos lineamientos con (...) el cartesianismo, mantiene un carácter a-histórico insuficiente para la explicación de la conciencia humana. Finalmente, proponemos la adopción de una teoría explicativa de la conciencia humana que considere las relaciones existentes en ella, no sólo como interacciones sino también como interpenetraciones ontogénicas y filogenéticas.This article examines Neural Darwinism proposed as an explanation of evolution of human consciousness. His methodology is contrasted with that used by Richard Lewontin, Richard Levins, and Steven Rose, who made important contributions to the study of living systems from a dialectical point of view. We conclude that the interactionist explanation of the evolution of conscience put forward in ND overcomes many of the deficiencies proper to biological determinism. However, as ND also shares many of the foundations of the Cartesian approach, it maintains a non-historical character, insufficient for the account of human consciousness. We suggest the adoption of an alternative theory, able to fully explain human conscience which must consider the whole of existing relations in it, and, instead of merely considering them as interactions, they have to be observed as dialectical interpenetrations. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore (...) overlapping causal patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

This collection addresses a post-WWII shift in the hierarchy of scientific explanations, where the highest goal moves from reductionism towards some ...

Tibetan translation of Darwin's On the origin of species.

The philosophical theory of scientific explanation proposed here involves a radically new treatment of causality that accords with the pervasively statistical character of contemporary science. Wesley C. Salmon describes three fundamental conceptions of scientific explanation--the epistemic, modal, and ontic. He argues that the prevailing view is untenable and that the modal conception is scientifically out-dated. Significantly revising aspects of his earlier work, he defends a causal/mechanical theory that is a version of the ontic conception. Professor Salmon's theory furnishes (...) a robust argument for scientific realism akin to the argument that convinced twentieth-century physical scientists of the existence of atoms and molecules. To do justice to such notions as irreducibly statistical laws and statistical explanation, he offers a novel account of physical randomness. The transition from the "reviewed view" of scientific explanation to the causal/mechanical model requires fundamental rethinking of basic explanatory concepts. (shrink)

This paper investigates conceptions of explanation, teleology, and analogy in the works of Immanuel Kant (1724-1804) and Georges Cuvier (1769-1832). Richards (2000, 2002) and Zammito (2006, 2012, 2018) have argued that Kant’s philosophy provided an obstacle for the project of establishing biology as a proper science around 1800. By contrast, Russell (1916), Outram (1986), and Huneman (2006, 2008) have argued, similar to suggestions from Lenoir (1989), that Kant’s philosophy influenced the influential naturalist Georges Cuvier. In this article, I wish (...) to expand on and further the work of Russell, Outram, and Huneman by adopting a novel perspective on Cuvier and considering (a) the similar conceptions of proper science and explanation of Kant and Cuvier, and (b) the similar conceptions of the role of teleology and analogy in the works of Kant and Cuvier. The similarities between Kant and Cuvier show, contrary to the interpretation of Richards and Zammito, that some of Kant’s philosophical ideas, whether they derived from him or not, were fruitfully applied by some life scientists who wished to transform life sciences into proper sciences around 1800. However, I also show that Cuvier, in contrast to Kant, had a workable strategy for transforming the life sciences into proper sciences, and that he departed from Kant’s philosophy of science in crucial respects. (shrink)

Some properties are causally relevant for a certain effect, others are not. In this paper we describe a problem for our understanding of this notion and then offer a solution in terms of the notion of a program explanation.

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore (...) overlapping causal patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Explanation has been an important topic of study in philosophy of science, in epistemology, and in other areas of philosophy. In parallel, psychologists have been studying children's and adults’ explanations, including their role in inference and in learning. This entry reviews recent work that begins to bridge the philosophy and psychology of explanation, with sections introducing recent empirical work on explanation by philosophers, formal and functional accounts of explanation, inference to the best explanation, the role (...) of explanation in discovery, and the implications of empirical work on explanation for the “negative program” in experimental philosophy. (shrink)

Explanations are very important to us in many contexts: in science, mathematics, philosophy, and also in everyday and juridical contexts. But what is an explanation? In the philosophical study of explanation, there is long-standing, influential tradition that links explanation intimately to causation: we often explain by providing accurate information about the causes of the phenomenon to be explained. Such causal accounts have been the received view of the nature of explanation, particularly in philosophy of science, since (...) the 1980s. However, philosophers have recently begun to break with this causal tradition by shifting their focus to kinds of explanation that do not turn on causal information. The increasing recognition of the importance of such non-causal explanations in the sciences and elsewhere raises pressing questions for philosophers of explanation. What is the nature of non-causal explanations – and which theory best captures it? How do non-causal explanations relate to causal ones? How are non-causal explanations in the sciences related to those in mathematics and metaphysics? This volume of new essays explores answers to these and other questions at the heart of contemporary philosophy of explanation. The essays address these questions from a variety of perspectives, including general accounts of non-causal and causal explanations, as well as a wide range of detailed case studies of non-causal explanations from the sciences, mathematics and metaphysics. (shrink)

A compelling idea holds that reality has a layered structure. We often disagree about what inhabits the bottom layer, but we agree that higher up we find chemical, biological, geological, psychological, sociological, economic, /etc./, entities: molecules, human beings, diamonds, mental states, cities, interest rates, and so on. How is this intuitive talk of a layered structure of entities to be understood? Traditionally, philosophers have proposed to understand layered structure in terms of either reduction or supervenience. But these traditional views face (...) well-known problems. A plausible alternative is that layered structure is to be explicated by appeal to explanations of a certain sort, termed / grounding explanations/. Grounding explanations tell us what obtains in virtue of what. Unfortunately, the use of grounding explanations to articulate the layered conception faces a problem, which I call /the collapse/. The collapse turns on the question of how to ground the facts stated by the explanations themselves. In this paper I make a suggestion about how to ground explanations that avoids the collapse. Briefly, the suggestion is that the fact stated by a grounding explanation is grounded in its /explanans/. (shrink)

Pure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical entities. Neither example supports this inference or the mathematical realism it is intended to establish. Both incorrectly assume that facts about mathematical optimality drove selection for the respective traits and explain why they exist. We show (...) how this problem can be avoided, identify limitations of explanatory indispensability arguments, and attempt to clarify the nature of mathematical explanation. (shrink)