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)

It has been the dominant view that probabilistic explanations of particular facts must be inductive in character. I argue here that this view is mistaken, and that the aim of probabilistic explanation is not to demonstrate that the explanandum fact was nomically expectable, but to give an account of the chance mechanism(s) responsible for it. To this end, a deductive-nomological model of probabilistic explanation is developed and defended. Such a model has application only when the probabilities occurring (...) in covering laws can be interpreted as measures of objective chance, expressing the strength of physical propensities. Unlike inductive models of probabilistic explanation, this deductive model stands in no need of troublesome requirements of maximal specificity or epistemic relativization. (shrink)

An account of distinctively mathematical explanation (DME) should satisfy three desiderata: it should account for the modal import of some DMEs; it should distinguish uses of mathematics in explanation that are distinctively mathematical from those that are not (Baron [2016]); and it should also account for the directionality of DMEs (Craver and Povich [2017]). Baron’s (forthcoming) deductive-mathematical account, because it is modelled on the deductive-nomological account, is unlikely to satisfy these desiderata. I (...) provide a counterfactual account of DME, the Narrow Ontic Counterfactual Account (NOCA), that can satisfy all three desiderata. NOCA appeals to ontic considerations to account for explanatory asymmetry and ground the relevant counterfactuals. NOCA provides a unification of the causal and the non-causal, the ontic and the modal, by identifying a common core that all explanations share and in virtue of which they are explanatory. (shrink)

According to the backing law account of causation a singular causal claim is to be analyzed (or “justified”) by reference to a suitable nomic theory which, together with the given singular statement describing a cause, deductively supports or explains the statement describing the effect. This backing law (or deductive-nomological) account of singular causation has recently become the target of several kinds of criticism. First, the possibility of giving a detailed and elaborate account of the required (...) nomic or explanatory backing has been doubted. Secondly, it has been claimed that the deductive-nomological account is bound to lead to unacceptable ontological difficulties (see Kim [1969] and [1973a]). Thirdly, it has been argued that the backing law account fails to give a satisfactory analysis of certain conditional or counterfactual aspects of causation (see Lewis [1973b]). Fourthly, it has been claimed that this approach does not work at least within the social and historical sciences as there are no laws and theories of the required sort to be found there. (shrink)

The purpose of this essay is to defend the deductive-nomological model of explanation against a number of criticisms that have been made of it. It has traditionally been thought that scientific explanations were causal and that scientific explanations involved deduction from laws. In recent years, however, this three-fold identity has been challenged: there are, it is argued, causal explanations that are not scientific, scientific explanations that are not deductive, deductions from laws that are neither causal explanations nor (...) scientific explanations, and causal explanations that involve no deductions from laws. The aim of the present essay is to defend the traditional identities, and to show that the more recent attempts at invalidating them fail in their object. More specifically, this essay argues that a Humean version of the deductive-nomological model of explanation can be defended as the correct account of scientific explanation of individual facts and processes, and as the correct account of causal explanations of individual facts and processes. The deductive-nomological model holds that to explain an event E, say that a is G, one must find some initial conditions C, say that a is F, and a law or theory T such that T and C jointly entail E, and both are essential to the deduction. (shrink)

I propose a deductive-nomological model for mathematical scientific explanation. In this regard, I modify Hempel’s deductive-nomological model and test it against some of the following recent paradigmatic examples of the mathematical explanation of empirical facts: the seven bridges of Königsberg, the North American synchronized cicadas, and Hénon-Heiles Hamiltonian systems. I argue that mathematical scientific explanations that invoke laws of nature are qualitative explanations, and ordinary scientific explanations that employ mathematics are quantitative explanations. I analyse the repercussions (...) of this deductivenomological model on causal explanations. (shrink)

The discussion on mathematical explanation has inherited the same sense of dissatisfaction that philosophers of science expressed, in the context of scientific explanation, towards the deductive-nomological model. This model is regarded as unable to cover cases of bona fide mathematical explanations and, furthermore, it is largely ignored in the relevant literature. Surprisingly, the reasons for this ostracism are not sufficiently manifest. In this paper I explore a possible extension of the model to the case of mathematical explanations and (...) I claim that there are at least two reasons to judge the deductive-nomological picture of explanation as inadequate in that context. (shrink)

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)

The article introduces and defends the Nomological Account of ground, a reductive account of the notion of metaphysical explanation in terms of the laws of metaphysics. The paper presents three desiderata that a theory of ground should meet: it should explain the modal force of ground, the generality of ground, and the interplay between ground and certain mereological notions. The bulk of the paper develops the Nomological Account and argues that it meets the three desiderata. (...) The Nomological Account relies on two central notions: the notion of a ‘law of metaphysics’ and the notion of ‘determination via the laws’. The paper offers the constructional conception of the laws of metaphysics, on which the metaphysical laws are general principles that characterize construction–operations such as composition, constitution, or set-formation. The role of determination in the account is explained and some reductive approaches to the notion are sketched. The case for the Nomological Account presented in this article is also a case for the laws of metaphysics. Since the Nomological Account offers a promising approach to metaphysical explanation we should take the laws of metaphysics seriously. (shrink)

In recent years philosophy of science has seen a resurgence of interest in metaphysical issues, especially those concerning laws, causation,and explanation. Although this book takes only the latter two words for its title, it is also about laws of nature. It is divided into three sections: the first is on causation, the second is on laws, and the third is on explanation: this is entirely appropriate because the debates about them are closely related. Ever since Hume argued that causation is (...) nothing more than regularities, laws have been more respectable than causes in philosophy. Perhaps this is also because science is replete with specially named laws which seem to play a central role in theories and explanations. Yet, as many philosophers have recently pointed out, contrary to Russell’s famous pronouncement that causation is a relic of a bygone age (quoted p. 3 by Psillos), the contemporary special sciences are very much concerned with the identification and investigation of all manner of causal structures. This raises the question of whether the apparent causal powers attributed to kinds in the special sciences are anything over and above a way of talking about the result of the operations of physical laws governing their microconstituents. Hence the logical empiricist’s project of showing how the laws of the special sciences reduce to those of physics. On their view, explanation, and in particular causal explanation, is nothing more than argument using the laws of nature as premises. However, this coveringlaw model of explanation has been subjected to intense criticism, and there have been attempts to construct alternatives that rely on the idea that to explain an event is to cite its real cause, where this cause need not be subsumed under any law. Since the demise of logical empiricism, or at least the waning of its influence, there has been a proliferation of theories about laws, causation and explanation, many of which differ radically from one another. (shrink)

We revive the idea that a deductive-nomological explanation of a scientific theory by its successor may be defensible, even in those common and troublesome cases where the theories concerned are mutually incompatible; and limiting, approximating and counterfactual assumptions may be required in order to define a logical relation between them. Our solution is based on a general characterization of limiting relations between physical theories using the method of nonstandard analysis.

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)

According to the deductive-nomological account of ground, a fact A grounds another fact B in case the laws of metaphysics determine the existence of B on the basis of the existence of A. Accounts of grounding of this particular variety have already been developed in the literature. My aim in this paper is to sketch a new version of this account. My preferred account offers two main improvements over existing accounts. First, the present account (...) is able to deal with necessitarian as well as non-necessitarian cases of grounding by acknowledging the existence of two types of metaphysical laws. I will argue that we should assume that metaphysical laws come in the necessitarian as well as in the non-necessitarian varietyclosely paralleling the distinction between strict and non-strict laws in the philosophy of science. The second main improvement of the present account is that this account is able to provide an explanation of why the laws of metaphysics have a direction built into them. I will argue that we should characterize metaphysical laws with the help of Theodore Sider’s (2011) notion of structure, which is a descendent of David Lewis’s (1983) notion of naturalness. According to the account of metaphysical laws developed in this paper, metaphysical laws express in their antecedents either perfectly structural truths or more structural truths than in their consequents. Since on Sider’s account structural features of reality are fundamental features of reality, the account is able to explain as to why the laws of metaphysics take us from the fundamental to the derivative. (shrink)

This paper discusses the important paper by Paul Thagard on the pathway version of mechanistic explanation that is currently used in chemical explanation. The author claims that this method of explanation has a respectable pedigree and can be traced back to the Chemical Revolution in the arguments used by the Lavoisier School in their theoretical duels with Richard Kirwan, the proponent of a revised phlogistonian theory. Kirwan believed that complex chemical reactions could be explained by recourse to affinity tables that (...) catalogued the attraction that various simple bodies possessed towards each other. To explain was in effect to make a delayed prediction, it is not enough just to show how a phenomenon fits into the discernible patterns of the world. Lavoisier, Fourcroy and their colleagues used pathway reasoning, although disguising this fact by suggesting that affinities varied when subjected to n-body situations. (shrink)

In this paper I reconstruct and critically examine the reasoning leading to the famous prediction of the ‘omega minus’ particle by M. Gell-Mann and Y. Ne’eman (in 1962) on the basis of a symmetry classification scheme. While the peculiarity of this prediction has occasionally been noticed in the literature, a detailed treatment of the methodological problems it poses has not been offered yet. By spelling out the characteristics of this type of prediction, I aim to underscore the challenges raised by (...) this episode to standard scientific methodology, especially to the traditional deductive-nomological account of prediction. (shrink)

In "Studies In The Logic Of Explanation" (Philosophy of Science, XV, 1948) Hempel and Oppenheim analyze the basic pattern of scientific explanation. One of the difficult problems which they acknowledge is "whether and how the analysis of explanation can be extended from the case where all general ex- planatory principles invoked are of a strictly universal or 'deterministic' form to the case where explanatory reference is made to statistical hypotheses." It is hoped that the remarks which follow may contribute a (...) little toward clarifying the issue. (shrink)

This paper addresses a fundamental line of research in neuroscience: the identification of a putative neural processing core of the cerebral cortex, often claimed to be “canonical”. This “canonical” core would be shared by the entire cortex, and would explain why it is so powerful and diversified in tasks and functions, yet so uniform in architecture. The purpose of this paper is to analyze the search for canonical explanations over the past 40 years, discussing the theoretical frameworks informing this research. (...) It will highlight a bias that, in my opinion, has limited the success of this research project, that of overlooking the dimension of cortical development. The earliest explanation of the cerebral cortex as canonical was attempted by David Marr, deriving putative cortical circuits from general mathematical laws, loosely following a deductive-nomological account. Although Marr’s theory turned out to be incorrect, one of its merits was to have put the issue of cortical circuit development at the top of his agenda. This aspect has been largely neglected in much of the research on canonical models that has followed. Models proposed in the 1980s were conceived as mechanistic. They identified a small number of components that interacted as a basic circuit, with each component defined as a function. More recent models have been presented as idealized canonical computations, distinct from mechanistic explanations, due to the lack of identifiable cortical components. Currently, the entire enterprise of coming up with a single canonical explanation has been criticized as being misguided, and the premise of the uniformity of the cortex has been strongly challenged. This debate is analyzed here. The legacy of the canonical circuit concept is reflected in both positive and negative ways in recent large-scale brain projects, such as the Human Brain Project. One positive aspect is that these projects might achieve the aim of producing detailed simulations of cortical electrical activity, a negative one regards whether they will be able to find ways of simulating how circuits actually develop. (shrink)

Reconstructing Popper's research programme for the Human Sciences, Noretta Koertge (Inquiry, Vol. 18 [1975]) has given a deductive?nomological account of explanations of actions by means of a Rationality Principle. It is argued here that such a Rationality Principle is fundamentally redundant. Neither is it logically necessary in order to deduce a cognitive action?explanandum, nor can it be given a semantic non?empty interpretation, at least not within Koertge's own syllogism. Any attempt to save the Rationality Principle as unfalsifiablc (...) but nevertheless indispensable for action explanations is rejected in the light of possible alternative action explanations by empirical and therefore in principle falsifiable psychological laws. (shrink)

SummaryHempel's Deductive‐Nomological model of explanation is compared to Sellars' brand of essentialism. The source of their differences is shown to lie in their views on the explanatory role of inductively based generalizations. An adequate explanation requires a reasoned account of why an empirical generalization fails. On Sellars' view this entails concentrating on the nature of the things whose behavior is in question. We thereby remove ourselves from the misleading positivist methodology in which one counterinstance renders a generalization (...) uninteresting. It is suggested instead that “disconfirmed” generalizations are of crucial positive methodological importance for purposes of theory development.RésuméLe modèle déductif‐nomologique de Hempel est comparéà l'essentialisme dans la version qu'en propose Sellars. L'auteur montre que leurs différences proviennent de ce qu'ils jugent différemment le rôle explicatif des généralisations inductives et les raisons de l'échec d'une généralisation empirique. D'après Sellars, il faut par conséquent se concentrer sur la nature des choses dont on observe le comportement; on évite ainsi les problèmes méthodologiques soulevés par les théories positivistes standard de la confirmation. L'auteur conclut en montrant que des généralisations infirmées ont une importance positive capitale pour le développement des théories. (shrink)

As Aristotle stated, scientific explanation is based on deductive argument--yet, Wesley C. Salmon points out, not all deductive arguments are qualified explanations. The validity of the explanation must itself be examined. _Four Decades of Scientific Explanation_ provides a comprehensive account of the developments in scientific explanation that transpired in the last four decades of the twentieth century. It continues to stand as the most comprehensive treatment of the writings on the subject during these years. Building on the (...) historic 1948 essay by Carl G. Hempel and Paul Oppenheim, "Studies in the Logic of Explanation,” which introduced the deductive-nomological model on which most work on scientific explanation was based for the following four decades, Salmon goes beyond this model's inherent basis of describing empirical knowledge to tells us “not only _what,_ but also _why_.” Salmon examines the predominant models in chronological order and describes their development, refinement, and criticism or rejection. _Four Decades of Scientific Explanation_ underscores the need for a consensus of approach and ongoing evaluations of methodology in scientific explanation, with the goal of providing a better understanding of natural phenomena. (shrink)

This essay analyzes and develops recent views about explanation in biology. Philosophers of biology have parted with the received deductive-nomological model of scientific explanation primarily by attempting to capture actual biological theorizing and practice. This includes an endorsement of different kinds of explanation (e.g., mathematical and causal-mechanistic), a joint study of discovery and explanation, and an abandonment of models of theory reduction in favor of accounts of explanatory reduction. Of particular current interest are philosophical accounts of complex explanations (...) that appeal to different levels of organismal organization and use contributions from different biological disciplines. The essay lays out one model that views explanatory integration across different disciplines as being structured by scientific problems. I emphasize the philosophical need to take the explanatory aims pursued by different groups of scientists into account, as explanatory aims determine whether different explanations are competing or complementary and govern the dynamics of scientific practice, including interdisciplinary research. I distinguish different kinds of pluralism that philosophers have endorsed in the context of explanation in biology, and draw several implications for science education, especially the need to teach science as an interdisciplinary and dynamic practice guided by scientific problems and explanatory aims. (shrink)

In this article, I explore the compatibility of inference to the best explanation (IBE) with several influential models and accounts of scientific explanation. First, I explore the different conceptions of IBE and limit my discussion to two: the heuristic conception and the objective Bayesian conception. Next, I discuss five models of scientific explanation with regard to each model’s compatibility with IBE. I argue that Kitcher’s unificationist account supports IBE; Railton’s deductive–nomological–probabilistic model, Salmon’s statistical-relevance model, and van Fraassen’s (...) erotetic account are incompatible with IBE; and Salmon’s causal–mechanical model is merely consistent with IBE. In short, many influential models of scientific explanation do not support IBE. I end by outlining three possible conclusions to draw: (1) either philosophers of science or defenders of IBE have seriously misconstrued the concept of explanation, (2) philosophers of science and defenders of IBE do not use the term ‘explanation’ univocally, and (3) the ampliative conception of IBE, which is compatible with any model of scientific explanation, deserves a closer look. (shrink)

Explaining socio-economic phenomena is one important aim of economics. There is very little agreement, however, on what precisely constitutes an adequate economic explanation. Starting from the very influential but defective ‘deductive-nomological model’ of explanation, this article describes and criticizes the major contemporary competitors for such an account (the probabilistic–causal, the mechanistic–causal and the unificationist models) and argues that none of them can by itself capture all aspects of a good explanation. When seeking to explain a socio-economic phenomenon (...) it should therefore be borne in mind that different types of explanation serve different purposes. (shrink)

According to a causal model of explanation, we explain phenomena by giving their causes or, where the phenomena are themselves causal regularities, we explain them by giving a mechanism linking cause and effect. If we explain why smoking causes cancer, we do not give the cause of this causal connection, but we do give the causal mechanism that makes it. The claim that to explain is to give a cause is not only natural and plausible, but it also avoids many (...) of the objections to other accounts of explanation, such as the views that to explain is to give a reason to believe the phenomenon occurred, to somehow make the phenomenon familiar, or to give a Deductive-Nomological argument. Unlike the reason for belief account, a causal model makes a clear distinction between understanding why a phenomenon occurs and merely knowing that it does, and the model does so in a way that makes understanding unmysterious and objective. Understanding is not some sort of super-knowledge, but simply more knowledge: knowledge of the phenomenon and knowledge of its causal history. A causal model makes it clear how something can explain without itself being explained, and so avoids the regress of whys, since we can know a phenomenon's cause without knowing the cause of the cause. It also accounts for legitimate self-evidencing explanations, explanations where the phenomenon is an essential part of the evidence that the explanation is correct, so the explanation can not supply a non-circular reason for believing the phenomenon occurred. There is no barrier to knowing a cause through its effects and also knowing that it is their cause. The speed of recession of a star explains its observed red-shift, even though the shift is an essential part of the evidence for its speed of recession. The model also avoids the most serious objection to the familiarity view, which is that some phenomena are familiar yet not understood, since a phenomenon can be perfectly familiar, such as the blueness of the sky or the fact that the same side of the moon always faces the earth, even if we do not know its cause. Finally, a causal model avoids many of the objections to the Deductive-Nomological model. Ordinary explanations do not have to meet the requirements of the Deductive-Nomological model, because one does not need to give a law to give a cause, and one does not need to know a law to have good reason to believe that a cause is a cause. As for the notorious over-permissiveness of the Deductive-Nomological model, the reason recession explains red-shift but not conversely, is simply that causes explain effects but not conversely, and the reason a conjunction of laws does not explain its conjuncts is that conjunctions do not cause their conjuncts. (shrink)

Today, mechanisms and mechanistic explanation are very popular in philosophy of science and are deemed a welcome alternative to laws of nature and deductive‐nomological explanation. Starting from Mitchell's pragmatic notion of laws, I cast doubt on their status as a genuine alternative. I argue that (1) all complex‐systems mechanisms ontologically must rely on stable regularities, while (2) the reverse need not hold. Analogously, (3) models of mechanisms must incorporate pragmatic laws, while (4) such laws themselves need not always (...) refer to underlying mechanisms. Finally, I show that Mitchell's account is more encompassing than the mechanistic account *Received August 2008; revised January 2010. †To contact the author, please write to: Centre for Logic and Philosophy of Science, Ghent University, Blandijnberg 2, B‐9000 Belgium; e‐mail: [email protected]. (shrink)

This paper attempts a critical reappraisal of Nagel's (1961, 1970) model of reduction taking into account both traditional criticisms and recent defenses. This model treats reduction as a type of explanation in which a reduced theory is explained by a reducing theory after their relevant representational items have been suitably connected. In accordance with the deductive-nomological model, the explanation is supposed to consist of a logical deduction. Nagel was a pluralist about both the logical form of the (...) connections between the reduced and reducing theories (which could be conditionals or biconditionals) and their epistemological status (as analytic connections, conventions, or synthetic claims). This paper defends Nagel's pluralism on both counts and, in the process, argues that the multiple realizability objection to reductionism is misplaced. It also argues that the Nagel model correctly characterizes reduction as a type of explanation. However, it notes that logical deduction must be replaced by a broader class of inferential techniques that allow for different types of approximation. Whereas Nagel (1970), in contrast to his earlier position (1961), recognized the relevance of approximation, he did not realize its full import for the model. Throughout the paper two case studies are used to illustrate the arguments: the putative reduction of classical thermodynamics to the kinetic theory of matter and that of classical genetics to molecular biology. (shrink)

In a recent paper, Erasmus et al. (2021) defend the idea that the ambiguity of the term “explanation” in explainable AI (XAI) can be solved by adopting any of four different extant accounts of explanation in the philosophy of science: the Deductive Nomological, Inductive Statistical, Causal Mechanical, and New Mechanist models. In this chapter, I show that the authors’ claim that these accounts can be applied to deep neural networks as they would to any natural phenomenon is mistaken. (...) I also provide a more general argument as to why the notion of explainability as it is currently used in the XAI literature bears little resemblance to the traditional concept of scientific explanation. It would be more fruitful to use the label “understandable AI” to avoid the confusion that surrounds the goal and purposes of XAI. In the second half of the chapter, I argue for a pragmatic conception of understanding that is better suited to play the central role attributed to explanation in XAI. Following De Regt (2017) and Kuorikoski and Ylikoski (2015), the conditions of satisfaction for understanding an ML system are fleshed out in terms of an agent’s success in using the system. (shrink)

The purpose of this paper is to provide a systematic defense of the single-case propensity account of probabilistic explanation from the criticisms advanced by Hanna and by Humphreys and to offer a critical appraisal of the aleatory conception advanced by Humphreys and of the deductive-nomological-probabilistic approach Railton has proposed. The principal conclusion supported by this analysis is that the Requirements of Maximal Specificity and of Strict Maximal Specificity afford the foundation for completely objective explanations of probabilistic explananda, (...) so long as they are employed on the basis of propensity criteria of explanatory relevance. (shrink)

This paper makes a phenomenological contribution to the distinction between personal and subpersonal types of explanation. I expound the little-known fact that Husserl gives an account of personal level explanation via his exposition of our capacity to express the understanding of another’s motivational nexus when we are in the personalistic attitude. I show that Husserl’s unique exposition of the motivational nexus conveys its concrete, internally coherent, and intentional nature, involving relationships amongst the sense contents of acts of consciousness. Moreover, (...) the motivational nexus is a generative space of possibility and choice. I show that, for these reasons, motivational explanation is not causal, nor deductive nomological, nor does it reduce to subpersonal explanation. I finish with the comment that the uniqueness of personal level explanation points towards the possibility that the human sciences ought also employ types of explanations not found in natural sciences. (shrink)

The question of the dimensionality of space has informed the development of physics since the beginning of the twentieth century in the quest for a unified picture of quantum processes and gravitation. Scientists have worked within various approaches to explain why the universe appears to have a certain number of spatial dimensions. The question of why space has three dimensions has a genuinely philosophical nature that can be shaped as a problem of justifying a contingent necessity of the world. In (...) contrast to explanations of three-dimensionality based on anthropic arguments, we support the search for a theory that provides a justification for the dimensionality of space based on a combination of deductive and inductive reasoning applied to science. In doing so, we argue that Kant correctly approached the question in “Thoughts on the true estimation of living forces” by connecting space dimensionality and the inverse square law. In expounding the strategy of Kant’s argument, we describe the main features of a general Kantian explanation of the dimensionality of space and discuss them with respect to current accounts of explanation in the philosophy of science, such as inference to the best explanation and the deductive-nomological model. (shrink)

In a recent article, Erasmus, Brunet, and Fisher (2021) argue that Artificial Neural Networks (ANNs) are explainable. They survey four influential accounts of explanation: the Deductive-Nomological model, the Inductive-Statistical model, the Causal-Mechanical model, and the New-Mechanist model. They argue that, on each of these accounts, the features that make something an explanation is invariant with regard to the complexity of the explanans and the explanandum. Therefore, they conclude, the complexity of ANNs (and other Machine Learning models) does not (...) make them less explainable. In this reply, it is argued that Erasmus et al. left out one influential account of explanation from their discussion: the Unificationist model. It is argued that, on the Unificationist model, the features that makes something an explanation is sensitive to complexity. Therefore, on the Unificationist model, ANNs (and other Machine Learning models) are not explainable. It is emphasized that Erasmus et al.’s general strategy is correct. The literature on explainable Artificial Intelligence can benefit by drawing from philosophical accounts of explanation. However, philosophical accounts of explanation do not settle the problem of whether ANNs are explainable because they do not unanimously declare that explanation is invariant with regard to complexity. (shrink)

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. (shrink)

The point of departure for all discussions of nonstatistical explanation in the philosophy of science has been the deductive‐nomological or covering law model of explanation that was given its most influential exposition by Carl Hempel, who was also the pioneering figure in the discussion of statistical explanation (see statistical explanation). On this account, to explain a particular event, we cite other particular events together with a general law or laws which "cover" what we want to explain. For (...) example, we might explain why a balloon expanded when placed on a radiator, by citing the fact that the radiator was hot together with the relevant laws relating heat to expansion. (shrink)

I examine two claims that arise in Brown’s account of inertial motion. Brown claims there is something objectionable about the way in which the motions of free particles in Newtonian theory and special relativity are coordinated. Brown also claims that since a geodesic principle can be derived in Einsteinian gravitation, the objectionable feature is explained away. I argue that there is nothing objectionable about inertia and that while the theorems that motivate Brown’s second claim can be said to figure (...) in a deductive-nomological explanation, their main contribution lies in their explication rather than their explanation of inertial motion. (shrink)

The notion of how-possibly explanations emerged with William Dray in response to Carl Hempel’s influential deductive-nomological model of scientific explanation. Dray’s aim was to distinguish explanations of states of affairs that might occur, in contrast to the aim of D-N explanations working to establish that states of affairs must actually occur. More recently, interest in how-possibly explanations has been particularly keen among philosophers of biology. One of the concerns philosophers of biology have focused on is whether how-possibly explanations (...) are “complete” explanations. Dray considered how-possibly explanations to be complete explanations, but the view that they are incomplete explanations became prominent with Robert Brandon’s articulation of successful adaptation explanation in evolutionary biology. According to Brandon, how-possibly adaptation explanations are incomplete, since they lack the requisite empirical evidence. Moreover, Brandon’s characterization of how-possibly explanation can be seen as having set the stage for thinking broadly about how-possibly explanations in biology. Echoing Brandon’s account for adaptation explanations, for example, David Resnik contends that how-possibly explanations are inherently incomplete, and yet they serve an important heuristic role throughout biology by setting out an agenda for future research. (shrink)

Philosophical discussions of mechanisms and mechanistic explanation have often been framed by contrast to laws and deductive-nomological explanation. A more adequate conception of lawfulness and nomological necessity, emphasizing the role of modal considerations in scientific reasoning, circumvents such contrasts and enhances understanding of mechanisms and their scientific significance. The first part of the paper sketches this conception of lawfulness, drawing upon Haugeland, Lange, and Rouse. This conception emphasizes the role of lawful stability under relevant counterfactual suppositions in (...) scientific reasoning across the sciences, in place of traditional conceptions of law that are primarily confined to the physical sciences. It also extends lawful stability beyond verbally or mathematically expressed law-statements, to encompass other ways of conjoining patterns in the world with scientific pattern recognition. The remainder of this paper shows how and why mechanisms constructively exemplify this conception of lawfulness in scientific practice: • Mechanisms are robust, counterfactually stable and inductively projectible patterns, even though they are not exceptionless “laws of nature”. • Mechanistic explanations often take non-verbal forms, which consequently resist philosophical inclinations to semantic ascent, but understanding lawfulness in terms of counterfactually stable pattern recognition accounts for these ways in which scientific understanding outruns the expressive capacities of natural languages; • Mechanisms are sometimes characterized as real patterns in the world, and sometimes as epistemic representations; understanding mechanisms as modal patterns shows why both conceptions are needed, as mutually supportive. • Mechanisms are typically open-ended, and only partially specified, in ways open to and directive toward further articulation and revision. Understanding mechanisms as modal patterns incorporates this aspect of mechanistic understanding within a broader conception of scientific understanding as embedded in research practice, rather than in bodies of knowledge extracted from it. • Mechanistic explanation has often been placed on the causal side of an opposition between causal and nomological explanation, but understanding mechanisms as modal patterns helps overcome that opposition, and contributes to a pluralist conception of causal relations and their characteristic forms of counterfactual invariance. • The recognition of mechanisms as modal patterns allows for a new way to think about the relations among distinct levels of a mechanistic hierarchy, and the broader scientific significance of mechanistic understanding. (shrink)

Using Coffa's paper as a point of departure, this brief note is designed to show that Hempel's inductive-statistical model of explanation implicitly construes explanations of that type as defective deductive-nomological explanations, with the consequence that there is no such thing as genuine inductive-statistical explanation according to Hempel's account. This result suggests a possible implicit commitment to determinism behind Hempel's theory of scientific explanation.

Scientific explanation is an important goal of scientific practise. Philosophers have proposed a striking diversity of seemingly incompatible accounts of explanation, from deductive-nomological to statistical relevance, unification, pragmatic, causal-mechanical, mechanistic, causal intervention, asymptotic, and model-based accounts. In this dissertation I apply two novel methods to reexamine our evidence about scientific explanation in practise and thereby address the fragmentation of philosophical accounts. I start by collecting a data set of 781 articles from one year of the journal Science. Using (...) automated text mining techniques I measure the frequency and distribution of several groups of philosophically interesting words, such as "explain", "cause", "evidence", "theory", "law", "mechanism", and "model". I show that "explain" words are much more common in scientific writing than in other genres, occurring in roughly half of all articles, and that their use is very often qualified or negated. These results about the use of words complement traditional conceptual analysis. Next I use random samples from the data set to develop a large number of small case studies across a wide range of scientific disciplines. I use a sample of "explain" sentences to develop and defend a new general philosophical account of scientific explanation, and then test my account against a larger set of randomly sampled sentences and abstracts. Five coarse categories can classify the explanans and explananda of my cases: data, entities, kinds, models, and theories. The pair of the categories of the explanans and explanandum indicates the "form" of an explanation. The explain-relation supports counterfactual reasoning about the dependence of qualities of the explanandum on qualities of the explanans. But for each form there is a different "core relation" between explanans and explanandum that supports the explain-relation. Causation, modelling, and argument are the core relations for different forms of scientific explanation between different categories of explanans and explananda. This flexibility allows me to resolve some of the fragmentation in the philosophical literature. I provide empirical evidence to show that my general philosophical account successfully describes a wide range of scientific practise across a large number of scientific disciplines. (shrink)

(1) In the first part of this paper, I review Chomsky's meandering journey from the formalism/mentalism of Syntactic Structures, through several methodological positions, to the minimalist theory of his latest work. Infected with mentalism from first to last, each and every position vitiates Chomsky's repeated claims that his theories will provide useful guidance to later theories in such fields as cognitive psychology and cognitive neuroscience. With the guidance of his insights, he claims, psychologists and neuroscientists will be able to avoid (...) costly dead-end lines of research. -/- (2) This never happened. As I have shown, this never could have happened. (See Johnston, 2018). What has happened, instead, is that current neurolinguistic research (with the arguable exception of the now-dated Lemma Model of Willem Levelt) proceeds without reference to Chomsky. It also wholeheartedly rejects the mentalism of the associated Language of Thought theory of Jerry Fodor. (See Johnston, 2018). -/- (3) I make this argument in the first part of this paper. I would also like to point out that most of my argument was developed in 1972, when I was a graduate student. I know of no other sustained criticisms of Chomsky at that time, and certainly none along the lines I had developed back then. -/- (4) In the second part of this paper, I present my own account of the methodology of science. When I was a graduate student, philosophy of science was dominated by an attempt to describe a methodology common to all the specific sciences, i.e. Hempel’s deductive-nomological model. These days, Hempel’s emphasis on the methodological unity of science has been rejected by such “dis-unity” philosophers of science as Ian Hacking, Patrick Suppes and Nancy Cartwright (see Cat, 2021). -/- (5) I view this change as the swing of a pendulum or, to change the metaphor, a journey from one end point of a continuum to another. As the level of abstraction at which one tries to describe scientific method is raised, the descriptions become increasingly general. Whether or not unity-of-science theories become so general as to be vacuous, is ultimately a subjective judgment. And so I expect that philosophers will eventually become tired of increasingly specific “close to the workbench” descriptions of how scientists work, and begin to turn back to methodological “big pictures”, finding in them powerful abstractions rather than empty irrelevancies. -/- (6) In the second part of this paper, I present my own account of the methodology of science, which I would situate somewhere between the “unity” and “dis-unity” accounts. However, I am not a scientist. My own views about scientific method have three origins: -/- (6a) my work as a graduate student from 1966 until I passed my comprehensive exams in 1973 (at a different university); -/- (6b) reading every issue of Scientific American from 1972 until nearly 2000, (at which point I continued to read it only sporadically, since I concluded that, around that time, it had evolved from a serious science magazine to a popular science magazine); and -/- (6c) my three-year immersion in the cognitive neuroscience of language after I retired, based on repeated study of and note-taking for (Banesh & Compton, 2018), (Kemmerer, 2015), several other books and, finally, numerous articles not hidden behind a paywall. -/- So, as always with my writings: caveat emptor. (shrink)

Primitive, unanalysable grounding relations are considered by many to be indispensable constituents of the metaphysician’s toolkit. Yet, as a primitive ontological posit, grounding must earn its keep by explaining features of the world not explained by other tools already at our disposal. Those who defend grounding contend that grounding is required to play two interconnected roles: accounting for widespread intuitions regarding what is ontologically prior to what, and forming the backbone of a theory of metaphysical explanation, in much the same (...) way that causal relations have been thought to underpin theories of scientific explanation. This thesis undermines the need to posit grounding relations to perform either of these jobs. With regard to the first, it is argued that a pair of human psychological mechanisms—for which there is substantial empirical support—can provide a more theoretically virtuous explanation of why we have the intuitions that we do. With regard to the second, I begin by considering what we want from a theory of explanation, and go on to develop three attractive (yet grounding-free) theories of metaphysical explanation. I offer: i) a psychologistic theory that calls upon the aforementioned psychological mechanisms, as well as the modal relations of necessitation and supervenience, ii) a metaphysical variant of the deductive-nomological theory of scientific explanation, and iii) a metaphysical variant of the unificationist theory of scientific explanation. Furthermore, these theories draw upon mechanisms and relations (both logical and ontological) to which we are already committed. Thus, to posit grounding relations in order to explain our priority intuitions, or in order to develop a theory of metaphysical explanation, is ontologically profligate. I conclude that we should not posit relations of ground. (shrink)

1. Introduction: a look back at the reasons vs. causes debate. 2. The interventionist account of causation. 3. Four objections to interventionism. 4. The counterfactual analysis of event causation. 5. The role of free agency. 6. Causality in the human sciences. -- The reasons vs. causes debate reached its peak about 40 years ago. Hempel and Dray had debated the nature of historical explanation and the broader issue of whether explanations that cite an agent’s reasons are causal or not. (...) Melden, Peters, Winch, Kenny and Anscombe had contributed their anticausal conceptions. The neo-Wittgensteinians seemed to be winning the day when in 1963 Donald Davidson published his seminal paper “Actions, Reasons, and Causes”. Davidson’s paper devastated the Wittgensteinian camp. It contained, among other things, a powerful attack on the logical connection argument. Davidson argued that the existence of a logical or conceptual connection between descriptions can never eliminate a causal relation, which holds between events simpliciter, not between events under certain descriptions. Davidson maintained that in a way, reasons can be causes. When somebody acts for a certain reason, his intentional attitudes, or rather changes in his attitudes, cause his bodily movements. Davidson also argued that rationalization is a species of causal explanation. For the definition of action, he argued that intentional actions are bodily movements caused in the right way by beliefs and desires that rationalize them. Davidson’s paper paved the way for causal theories of action, which superseded neo-Wittgensteinian analyses in the following decades. The causal theory was rapidly adopted by Alvin Goldman, David Armstrong, Paul Churchland, Myles Brand and many others, entering the mainstream and dominating the philosophy of action to this very day. In 1971 Georg Henrik von Wright published his book "Explanation and Understanding". The second chapter did not deal with agency, but with causation. It developed a new account of causation, the interventionist or experimentalist account. Focusing on causation, von Wright remedied a major shortcoming of the reasons vs. causes debate. The concept of causality, and the nature of the causal relation, received little attention in this debate, a fact that holds true for both camps. Mostly it was simply taken for granted that, as Hempel had declared, “causal explanation is a special type of deductive-nomological explanation”. One camp then aligned intentional explanations with D-N explanations, while the other camp insisted on their disparity. So strictly speaking, the label “reasons/causes debate” was a misnomer. The controversy dealt primarily with the question as to whether intentional explanations can take the form of D-N explanations, while the notion of causation, and the metaphysics of the causal relation, were left obscured. With von Wright’s new approach, the situation changed. Von Wright was primarily concerned with causation, but his approach contained an implicit attack on the causal theory of action as well. His core idea was that the notion of causality is intimately linked with, or even derived from, the notion of intentionally making something happen. Other philosophers, even Hume, had considered such a connection before, but often just to reject this view, regarding it as a kind of myth belonging to the infancy of the human mind. Von Wright took the idea seriously. He submitted the analysis that p is the cause of q if and only if by doing p we could bring about q. The causal theory of action was also concerned with the relation between causation and agency, to which its name bears witness. The causal theory of action holds that actions are bodily movements with a certain causal history. This is why von Wright’s account constituted a momentous challenge to the causal theory: it reversed the direction of conceptual dependency between both notions. Davidson and his followers tried to define what an intentional action is by using the notion of causation. The causal condition which the causal theory sets is part of the definition of “doing something intentionally”. Von Wright claimed that the conceptual dependency is the other way round. He used the notions of doing, and bringing about, to explain what causal relations are. So, instead of a causal theory of action, he advocated an agency theory of causation, as it may be dubbed. It is remarkable how seldom this clash of opinions about conceptual primacy is reflected in the literature. There are few exceptions: Fred Stoutland noticed the conflict, and he published a number of papers in which he compared Davidson’s and von Wright’s views. Von Wright’s book "Explanation and Understanding" was widely read and discussed in the seventies, especially in Europe. But it strikes me that especially in North America, where the causal theory of action became the orthodoxy of the day, von Wright’s challenge went largely unnoticed. Even Davidson did not seem to take it seriously. He nowhere takes notice of the interventionist theory of causation, while he does discuss von Wright’s earlier book "Norm and Action". As is well-known, Davidson favoured an alternative account of causation, based on “the principle of the nomological character of causality”, as he somewhat clumsily called it, or, later and less clumsily, “the cause-law thesis”. Davidson’s firm adherence to a nomological theory of causality may explain why he did not take much interest in alternative accounts. [...] -/- . (shrink)

An examination is made of the dispute between the proponents of rational explanation of actions and of the deductive nomological pattern of explanation. A rapprochement between these two positions is suggested, with the aim of accounting for the normative character of reasons for acting. It is argued that the disputed area is an area of intersection between facts and values, and that far from it being the case that the normative and descriptive components can be separated or isolated, (...) the underlying precepts are to be viewed as both explanatory (descriptive) and normative. The discussion is divided into two general areas: (1) the normative force of reasons for acting; and (2) the normative character of rationality. (shrink)

Peter Railton (1978) has introduced the influential deductive-nomological-probabilistic (DNP) model of explanation which is the culmination of a tradition of formal, non-pragmatic accounts of scientific explanation. The other models in this tradition have been shown to be susceptible to a class of counterexamples involving intervening causes which speak against their sufficiency. This treatment has never been extended to the DNP model; we contend that the usual form of these counterexamples is ineffective in this case. However, we develop below (...) a new version which overcomes these difficulties. Thus we claim that all of the models in this tradition, DNP included, have an equal status with respect to sufficiency. (shrink)