Carl Hempel (1965) argued that probabilistic hypotheses are limited in what they can explain. He contended that a hypothesis cannot explain why E is true if the hypothesis says that E has a probability less than 0.5. Wesley Salmon (1971, 1984, 1990, 1998) and Richard Jeffrey (1969) argued to the contrary, contending that P can explain why E is true even when P says that E’s probability is very low. This debate concerned noncontrastive explananda. Here, a view of contrastive causal (...) explanation is described and defended. It provides a new limit on what probabilistic hypotheses can explain; the limitation is that P cannot explain why E is true rather than A if P assign E a probability that is less than or equal to the probability that P assigns to A. The view entails that a true deterministic theory and a true probabilistic theory that apply to the same explanandum partition are such that the deterministic theory explains all the true contrastive propositions constructable from that partition, whereas the probabilistic theory often fails to do so. (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)

Seungbae Park argues that Bas van Fraassen’s rejection of inference to the best explanation (IBE) is problematic for his contextual theory of explanation because van Fraassen uses IBE to support the contextual theory. This paper provides a defense of van Fraassen’s views from Park’s objections. I point out three weaknesses of Park’s objection against van Fraassen. First, van Fraassen may be perfectly content to accept the implications that Park claims to follow from his views. Second, even if van Fraassen rejects (...) IBE he may still endorse particular arguments that instantiate IBE. Third, van Fraassen does not, in fact, use IBE to support his contextual theory. (shrink)

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

In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron’s distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron’s non-causal (...) notion of mathematical difference-making is not effective in justifying any symmetry-breaking between mathematics and idealization. The function of making a difference that Baron attributes to mathematics cannot be referred to physical facts, but to the features of quantities, such as step lengths or time intervals taken into account in the models. It appears, indeed, that it does not follow from Baron’s argument that idealizations do not help to carry the explanatory load at least for two reasons: mathematics is not independent of idealizations in modelling and idealizations help mathematics to carry the explanatory load of a model in different degrees. (shrink)

The paper addresses the question of whether heritability can be useful in establishing genetics as an explanation for an individual’s display of some trait or behavior. After reviewing the fundamental philosophical challenge to heritability—that heritability is a population level measure—an argument is presented for rethinking the role heritability occupies in both causal and explanatory claims. It is argued that heritability can be useful for genetically based explanations of individual traits, if the conditions for proper genetic explanation are modestly reconceived, and (...) the measure is seen as an evidential tool which conforms to standard methods for determining causal factors. (shrink)

Explanation is a central concept in human psychology. Drawing upon philosophical theories of explanation, psychologists have recently begun to examine the relationship between explanation, probability and causality. Our study advances this growing literature in the intersection of psychology and philosophy of science by systematically investigating how judgments of explanatory power are affected by the prior credibility of a potential explanation, the causal framing used to describe the explanation, the generalizability of the explanation, and its statistical relevance for the evidence. Collectively, (...) the results of our five experiments support the hypothesis that the prior credibility of a causal explanation plays a central role in explanatory reasoning: first, because of the presence of strong main effects on judgments of explanatory power, and second, because of the gate-keeping role it has for other factors. Highly credible explanations were not susceptible to causal framing effects. Instead, highly credible hypotheses were sensitive to the effects of factors which are usually considered relevant from a normative point of view: the generalizability of an explanation, and its statistical relevance for the evidence. These results advance current literature in the philosophy and psychology of explanation in three ways. First, they yield a more nuanced understanding of the determinants of judgments of explanatory power, and the interaction between these factors. Second, they illuminate the close relationship between prior beliefs and explanatory power. Third, they clarify the relationship between abductive and probabilistic reasoning. (shrink)

In this paper, I consider the relationship between Inference to the Best Explanation and Bayesianism, both of which are well-known accounts of the nature of scientific inference. In Sect. 2, I give a brief overview of Bayesianism and IBE. In Sect. 3, I argue that IBE in its most prominently defended forms is difficult to reconcile with Bayesianism because not all of the items that feature on popular lists of “explanatory virtues”—by means of which IBE ranks competing explanations—have confirmational import. (...) Rather, some of the items that feature on these lists are “informational virtues”—properties that do not make a hypothesis \ more probable than some competitor \ given evidence E, but that, roughly-speaking, give that hypothesis greater informative content. In Sect. 4, I consider as a response to my argument a recent version of compatibilism which argues that IBE can provide further normative constraints on the objectively correct probability function. I argue that this response does not succeed, owing to the difficulty of defending with any generality such further normative constraints. Lastly, in Sect. 5, I propose that IBE should be regarded, not as a theory of scientific inference, but rather as a theory of when we ought to “accept” H, where the acceptability of H is fixed by the goals of science and concerns whether H is worthy of commitment as research program. In this way, IBE and Bayesianism, as I will show, can be made compatible, and thus the Bayesian and the proponent of IBE can be friends. (shrink)

Contributing to the recent debate on whether or not explanations ought to be differentiated from arguments, this article argues that the distinction matters to science education. I articulate the distinction in terms of explanations and arguments having to meet different standards of adequacy. Standards of explanatory adequacy are important because they correspond to what counts as a good explanation in a science classroom, whereas a focus on evidence-based argumentation can obscure such standards of what makes an explanation explanatory. I provide (...) further reasons for the relevance of not conflating explanations with arguments (and having standards of explanatory adequacy in view). First, what guides the adoption of the particular standards of explanatory adequacy that are relevant in a scientific case is the explanatory aim pursued in this context. Apart from explanatory aims being an important aspect of the nature of science, including explanatory aims in classroom instruction also promotes students seeing explanations as more than facts, and engages them in developing explanations as responses to interesting explanatory problems. Second, it is of relevance to science curricula that science aims at intervening in natural processes, not only for technological applications, but also as part of experimental discovery. Not any argument enables intervention in nature, as successful intervention specifically presupposes causal explanations. Students can fruitfully explore in the classroom how an explanatory account suggests different options for intervention. (shrink)

I begin by retracing an argument from Aristotle for final causes in science. Then, I advance this ancient thought, and defend an argument for a stronger conclusion: that no scientific explanation can succeed, if Naturalism is true. The argument goes like this: (1) Any scientific explanation can be successful only if it crucially involves a natural regularity. Next, I argue that (2) any explanation can be successful only if it crucially involves no element that calls out for explanation but lacks (...) one. From (1) and (2) it follows that (3) a scientific explanation can be successful only if it crucially involves a natural regularity, and this regularity does not call out for explanation while lacking one. I then argue that (4) if Naturalism is true, then all natural regularities call out for explanation but lack them. From (3) and (4) it follows that (5) if Naturalism is true, then no scientific explanation can be successful. If you believe that scientific explanation can be (indeed, often has been) successful, as I do, then this is a reason to reject Naturalism. (shrink)

In The Explanatory Dispensability of Idealizations, Sam Baron suggests a possible strategy enabling the indispensability argument to break the symmetry between mathematical claims and idealization assumptions in scientific models. Baron’s distinction between mathematical and non-mathematical idealization, I claim, is in need of a more compelling criterion, because in scientific models idealization assumptions are expressed through mathematical claims. In this paper I argue that this mutual dependence of idealization and mathematics cannot be read in terms of symmetry and that Baron’s non-causal (...) notion of mathematical difference-making is not effective in justifying any symmetry-breaking between mathematics and idealization. The function of making a difference that Baron attributes to mathematics cannot be referred to physical facts, but to the features of quantities, such as step lengths or time intervals taken into account in the models. It appears, indeed, that it does not follow from Baron’s argument that idealizations do not help to carry the explanatory load at least for two reasons: mathematics is not independent of idealizations in modelling and idealizations help mathematics to carry the explanatory load of a model in different degrees. (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)

This is a critique of Lloyd's theory which appeared in his book, Simple Minds.

The official model of explanation proposed by the logical empiricists, the covering law model, is subject to familiar objections. The goal of the present paper is to explore an unofficial view of explanation which logical empiricists have sometimes suggested, the view of explanation as unification. I try to show that this view can be developed so as to provide insight into major episodes in the history of science, and that it can overcome some of the most serious difficulties besetting the (...) covering law model. (shrink)

Adolf Grünbaum is one of the giants of 20th century philosophy of science. This volume is the first of three collecting his most essential and highly influential work. The essays collected in this first volume focus on three related areas. They discuss scientific rationality-the problem of what it takes for a theory to be called scientific, and ask whether it is plausible to draw a clear distinction between science and non-science as was famously proposed by Karl Popper. They delve into (...) the debate between determinism and indeterminism, in both science and in the humanities. Grünbaum defends the position of the Humane Determinist, which then leads to a thorough criticism of the current theological approaches to ethics and morality-where Grünbaum defends an explicit Secular Humanism-as well as of prominent theistic interpretations of twentieth century physical cosmologies. The second volume is devoted to Grünbaum's writings on the Philosophy of Physics and Space-Time, and the third to his lectures on the Philosophy of Psychology and Psychoanalysis, including his 1985 Gifford Lectures, which are to be published for the first time. (shrink)

Abductive reasoning assigns special status to the explanatory power of a hypothesis. But how do people make explanatory judgments? Our study clarifies this issue by asking: How does the explanatory power of a hypothesis cohere with other cognitive factors? How does probabilistic information affect explanatory judgments? In order to answer these questions, we conducted an experiment with 671 participants. Their task was to make judgments about a potentially explanatory hypothesis and its cognitive virtues. In the responses, we isolated three constructs: (...) Explanatory Value, Rational Acceptability, and Entailment. Explanatory judgments strongly cohered with judgments of causal relevance and with a sense of understanding. Furthermore, we found that Explanatory Value was sensitive to manipulations of statistical relevance relations between hypothesis and evidence, but not to explicit information about the prior probability of the hypothesis. These results indicate that probabilistic information about statistical relevance is a strong determinant of Explanatory Value. More generally, our study suggests that abductive and probabilistic reasoning are two distinct modes of inference. (shrink)

Surprisingly, many ethical realists and anti-realists, naturalists and not, all accept some version of the following normative appeal to the natural (NAN): evaluative and normative facts hold solely in virtue of natural facts, where their naturalness is part of what fits them for the job. This paper argues not that NAN is false but that NAN has no adequate non-parochial justification (a justification that relies only on premises which can be accepted by more or less everyone who accepts NAN) to (...) back up this consensus. I show that we cannot establish versions of NAN which are interesting in their own right (and not merely as instances of a general naturalistic ontology) by appealing to the nature of natural properties or the kind of in-virtue-of relation to which NAN refers, plus other plausible nonparochial assumptions. On the way, I distinguish different types of 'in virtue of claims. I conclude by arguing that the way in which assessment of meta-ethical hypotheses is theory-dependent predicts the failure of non-parochial justifications of NAN. (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)

Use of argumentation methods applied to legal reasoning is a relatively new field of study. The book provides a survey of the leading problems, and outlines how future research using argumentation-based methods show great promise of leading to useful solutions. The problems studied include not only these of argument evaluation and argument invention, but also analysis of specific kinds of evidence commonly used in law, like witness testimony, circumstantial evidence, forensic evidence and character evidence. New tools for analyzing these kinds (...) of evidence are introduced. (shrink)

This paper describes an alternative to the common view that explanation in the special sciences involves subsumption under laws. According to this alternative, whether or not a generalization can be used to explain has to do with whether it is invariant rather than with whether it is lawful. A generalization is invariant if it is stable or robust in the sense that it would continue to hold under a relevant if it is stable or robust in the sense that it (...) would continue to hold under a relevant class of changes. Unlike lawfulness, invariance comes in degrees and has other features that are well suited to capture the characteristics of explanatory generalizations in the special sciences. For example, a generalization can be invariant even if it has exceptions or holds only over a limited spatio-temporal interval. The notion of invariance can be used to resolve a number of dilemmas that arise in standard treatments of explanatory generalizations in the special sciences. (shrink)

This article defends the use of interventionist counterfactuals to elucidate causal and explanatory claims against criticisms advanced by James Bogen and Peter Machamer. Against Bogen, I argue that counterfactual claims concerning what would happen under interventions are meaningful and have determinate truth values, even in a deterministic world. I also argue, against both Machamer and Bogen, that we need to appeal to counterfactuals to capture the notions like causal relevance and causal mechanism. Contrary to what both authors suppose, counterfactuals are (...) not "unscientific" - a substantial tradition within statistics and the causal modelling literature makes heavy use of them. (shrink)

The phenomenon of regression toward the mean is notoriously liable to be overlooked or misunderstood; regression fallacies are easy to commit. But even when regression phenomena are duly recognized, it remains perplexing how they can feature in explanations. This article develops a philosophical account of regression explanations as “statistically autonomous” explanations that cannot be deepened by adducing details about causal histories, even if the explananda as such are embedded in the causal structure of the world. That regression explanations have statistical (...) autonomy was first suggested by Ian Hacking and has recently been defended and elaborated by André Ariew, Yasha Rohwer, and Collin Rice. However, I will argue that these analyses fail to capture what regression’s statistical autonomy consists in and how it sets regression explanations apart from other kinds of explanation. The alternative account I develop also shows what is amiss with a recent denial of regression’s statistical autonomy. Marc Lange has argued that facts that can be explained as regression phenomena can in principle also be explained by citing a conjunction of causal histories. The account of regression explanation developed here shows that his argument is based on a misunderstanding of the nature of statistical autonomy. (shrink)

Realists about laws of nature and their Humean opponents disagree on whether laws ‘govern’. An independent commitment to the ‘governing conception’ of laws pushes many towards the realist camp. Despite its significance, however, no satisfactory account of governance has been offered. The goal of this article is to develop such an account. I base my account on two claims. First, we should distinguish two notions of governance, ‘guidance’ and ‘production’, and secondly, explanatory phenomena other than laws are also candidates for (...) governance. My goal is to develop a unified account which captures both guidance and production as well as the governance of phenomena, such as essence and logical consequence. The account of governance I develop belongs to the family of modal accounts, which was popularized by David Armstrong, but it also employs essentialist resources. If successful, this modal-essentialist account not only reveals the costs that proponents of governance incur, but it also puts that important notion on a solid theoretical foundation. (shrink)

According to Michael Friedman’s theory of explanation, a law X explains laws Y1, Y2, …, Yn precisely when X unifies the Y’s, where unification is understood in terms of reducing the number of independently acceptable laws. Philip Kitcher criticized Friedman’s theory but did not analyze the concept of independent acceptability. Here we show that Kitcher’s objection can be met by modifying an element in Friedman’s account. In addition, we argue that there are serious objections to the use that Friedman makes (...) of the concept of independent acceptability. (shrink)

RésuméSi on la définit comme une action contraire au bon jugement de l'agent, l'action acrasique se trouve exclue par le principe selon lequel une personne a forcément l'intention de faire ce qu'elle juge devoir faire. Une fois ce principe rejeté, comme je le propose ici, le problème traditionnel de l'acrasie, qui est celui de sa possibilité même, s'évanouit. Je soutiens, cependant, qu'un problème plus limité semble se poser si nous admettons que les actions acrasiques doivent s'expliquer par des raisons, et (...) je requiers que les explications en de tels cas soient de type naturaliste. Je montre que la difficulté se trouve résolue par une compréhension adéquate de la nature des explications naturalistes. (shrink)

As machine learning has gradually entered into ever more sectors of public and private life, there has been a growing demand for algorithmic explainability. How can we make the predictions of complex statistical models more intelligible to end users? A subdiscipline of computer science known as interpretable machine learning (IML) has emerged to address this urgent question. Numerous influential methods have been proposed, from local linear approximations to rule lists and counterfactuals. In this article, I highlight three conceptual challenges that (...) are largely overlooked by authors in this area. I argue that the vast majority of IML algorithms are plagued by (1) ambiguity with respect to their true target; (2) a disregard for error rates and severe testing; and (3) an emphasis on product over process. Each point is developed at length, drawing on relevant debates in epistemology and philosophy of science. Examples and counterexamples from IML are considered, demonstrating how failure to acknowledge these problems can result in counterintuitive and potentially misleading explanations. Without greater care for the conceptual foundations of IML, future work in this area is doomed to repeat the same mistakes. (shrink)

Direct inferences identify certain probabilistic credences or confirmation-function-likelihoods with values of objective chances or relative frequencies. The best known version of a direct inference principle is David Lewis’s Principal Principle. Certain kinds of statements undermine direct inferences. Lewis calls such statements inadmissible. We show that on any Bayesian account of direct inference several kinds of intuitively innocent statements turn out to be inadmissible. This may pose a significant challenge to Bayesian accounts of direct inference. We suggest some ways in which (...) these challenges may be addressed. (shrink)

This paper offers a dialogue theory of explanation. A successful explanation is defined as a transfer of understanding in a dialogue system in which a questioner and a respondent take part. The questioner asks a special sort of why-question that asks for understanding of something and the respondent provides a reply that transfers understanding to the questioner. The theory is drawn from recent work on explanation in artificial intelligence (AI), especially in expert systems, but applies to scientific, legal and everyday (...) conversational explanations. (shrink)

Normative explanations of why things are wrong, good, or unfair are ubiquitous in ordinary practice and normative theory. This paper argues that normative explanation is subject to a justification condition: a correct complete explanation of why a normative fact holds must identify features that would go at least some way towards justifying certain actions or attitudes. I first explain and motivate the condition I propose. I then support it by arguing that it fits well with various theories of normative reasons, (...) makes good sense of certain legitimate moves in ordinary normative explanatory discourse, and helps to make sense of our judgments about explanatory priority in certain cases of normative explanation. This last argument also helps to highlight respects in which normative explanation won’t be worryingly discontinuous with explanations in other domains even though these other explanations aren’t subject to the justification condition. Thus the paper aims not only to do some constructive theorizing about the relatively neglected topic of normative explanation but also to cast light on the broader question of how normative explanation may be similar to and different from explanations in other domains. (shrink)

The investigation of probabilistic causality has been plagued by a variety of misconceptions and misunderstandings. One has been the thought that the aim of the probabilistic account of causality is the reduction of causal claims to probabilistic claims. Nancy Cartwright (1979) has clearly rebutted that idea. Another ill-conceived idea continues to haunt the debate, namely the idea that contextual unanimity can do the work of objective homogeneity. It cannot. We argue that only objective homogeneity in combination with a causal interpretation (...) of Bayesian networks can provide the desired criterion of probabilistic causality. (shrink)

The article begins by describing two longstanding problems associated with direct inference. One problem concerns the role of uninformative frequency statements in inferring probabilities by direct inference. A second problem concerns the role of frequency statements with gerrymandered reference classes. I show that past approaches to the problem associated with uninformative frequency statements yield the wrong conclusions in some cases. I propose a modification of Kyburg’s approach to the problem that yields the right conclusions. Past theories of direct inference have (...) postponed treatment of the problem associated with gerrymandered reference classes by appealing to an unexplicated notion of projectability . I address the lacuna in past theories by introducing criteria for being a relevant statistic . The prescription that only relevant statistics play a role in direct inference corresponds to the sort of projectability constraints envisioned by past theories. (shrink)