Statistical Explanation

In this note, I discuss the simplicity of rival statistical explanations of a correlation, couched in terms of Reichenbachian Common Cause Systems. Simplicity is analyzed in two components, the so-called intrinsic and contextual simplicity. I show that if one disentangles simplicity from explanatory power then the size of the system provides an adequate for simplicity in both of its dimensions.

Evolutionary biology distinguishes differences in survival and reproduction rates due to selection from those due to drift. The distinction is usually thought to be founded in probabilistic facts: a difference in (say) two variants' average lifespans over some period of time that is due to selection is explained by differences in the probabilities relevant to survival; in the purest cases of drift, by contrast, the survival probabilities are equal and the difference in lifespans is a matter of chance. When there (...) is a difference in actual average lifespans there is always a difference in causal histories, but in drift, the causal differences make no contribution to the relevant probabilities. Some writers have claimed that the framework that determines which causes contribute to the probabilities, and so the framework that determines when the relevant probabilities differ and when they are equal, is imposed by modelers rather than being an objective fact of nature, and so that the distinction between selection and drift, however practically useful, is unreal. This paper uses my work on biological probabilities (Bigger than Chaos) and probabilistic explanation (Depth) to argue for the objectivity of, and the importance of the objectivity of, the distinction between selection and drift. (shrink)

What explains the outcomes of chance processes? We claim that their setups do. Chances, we think, mediate these explanations of outcome by setup but do not feature in them. Facts about chances do feature in explanations of a different kind: higher-order explanations, which explain how and why setups explain their outcomes. In this paper, we elucidate this 'mediator view' of chancy explanation and defend it from a series of objections. We then show how it changes the playing field in four (...) metaphysical disputes concerning chance. First, it makes it more plausible that even low chances can have explanatory power. Second, it undercuts a circularity objection against reductionist theories of chance. Third, it redirects the debate about a prominent argument against epistemic theories of chance. Finally, it sheds light on potential chancy explanations of the Universe's origin. (shrink)

Gignac and Zajenkowski (2020) find that “the degree to which people mispredicted their objectively measured intelligence was equal across the whole spectrum of objectively measured intelligence”. This Comment shows that Gignac and Zajenkowski’s (2020) finding of homoscedasticity is likely the result of a recoding choice by the experimenters and does not in fact indicate that the Dunning-Kruger Effect is a mere statistical artifact. Specifically, Gignac and Zajenkowski (2020) recoded test subjects’ responses to a question regarding self-assessed comparative IQ onto a (...) linear IQ scale when a normal IQ scale would likely have been more appropriate. More generally, researchers studying self-assessed intelligence should be aware of potential measurement problems that may arise when transforming an ordinal scale onto an interval scale. (shrink)

Explanatory realism is the view that explanations work by providing information about relations of productive determination such as causation or grounding. The view has gained considerable popularity in the last decades, especially in the context of metaphysical debates about non-causal explanation. What makes the view particularly attractive is that it fits nicely with the idea that not all explanations are causal whilst avoiding an implausible pluralism about explanation. Another attractive feature of the view is that it allows explanation to be (...) a partially epistemic, context-dependent phenomenon. In spite of its attractiveness, explanatory realism has recently been subject to criticism. In particular, Taylor :197–219, 2018). has presented four types of explanation that the view allegedly cannot account for. This paper defends explanatory realism against Taylor’s challenges. We will show that Taylor’s counterexamples are either explanations that turn out to provide information about entities standing in productive determination relations or that they are not genuine explanations in the first place. (shrink)

A common way of characterizing Boltzmann’s explanation of thermodynamics in term of statistical mechanics is with reference to three ingredients: the dynamics, the past hypothesis, and the statistical postulate. In this paper I focus on the statistical postulate, and I have three aims. First, I wish to argue that regarding the statistical postulate as a probability postulate may be too strong: a postulate about typicality would be enough. Second, I wish to show that there is no need to postulate anything, (...) for the typicality postulate can be suitably derived from the dynamics. Finally, I discuss how the attempts to give preference to certain stochastic quantum theories (such as the spontaneous collapse theory) over deterministic alternatives on the basis that they do not need the statistical postulate fail. (shrink)

Statistical reasoning is an integral part of modern scientific practice. In The Seven Pillars of Statistical Wisdom Stephen Stigler presents seven core ideas, or pillars, of statistical thinking and the historical developments of each of these pillars, many of which were concurrent with developments in biology. Here we focus on Stigler’s fifth pillar, regression, and his discussion of how regression to the mean came to be thought of as a solution to a challenge for the theory of natural selection. Stigler (...) argues that the purely mathematical phenomenon of regression to the mean provides a resolution to a problem for Darwin’s evolutionary theory. Thus, he argues that the resolution to the problem for Darwin’s theory is purely mathematical, rather than causal. We show why this argument is problematic. (shrink)

In this paper, I aim to provide access to the current debate on non-causal explanations in philosophy of science. I will first present examples of non-causal explanations in the sciences. Then, I will outline three alternative approaches to non-causal explanations – that is, causal reductionism, pluralism, and monism – and, corresponding to these three approaches, different strategies for distinguishing between causal and non-causal explanation. Finally, I will raise questions for future research on non-causal explanations.

Shapiro and Sober claim that Walsh, Ariew, Lewens, and Matthen give a mistaken, a priori defense of natural selection and drift as epiphenomenal. Contrary to Shapiro and Sober’s claims, we first argue that WALM’s explanatory doctrine does not require a defense of epiphenomenalism. We then defend WALM’s explanatory doctrine by arguing that the explanations provided by the modern genetical theory of natural selection are ‘autonomous-statistical explanations’ analogous to Galton’s explanation of reversion to mediocrity and an explanation of the diffusion ofgases. (...) We then argue that whereas Sober’s theory of forces is an adequate description of Darwin’s theory, WALM’s explanatory doctrine is required to understand how themodern genetical theory of natural selection explains large-scale statistical regularities. 1 Introduction2 Shapiro and Sober’s ‘Epiphenomenalism Do’s and Don’ts’3 WALM’s Explanatory Doctrine4 Galton’s Autonomous-Statistical Explanation5 A Second Example: The Statistical Explanation of the Diffusion of Gases6 Distinguishing Two Theories of Evolution by Natural Selection7 A Possible Objection: Are Statistical Laws Sufficient for Explanation?8 Conclusion. (shrink)

This thesis examines philosophical controversies surrounding the evaluation of medical treatments, with a focus on the evidential roles of randomised trials and mechanisms in Evidence-Based Medicine. Current 'best practice' usually involves excluding non-randomised trial evidence from systematic reviews in cases where randomised trials are available for inclusion in the reviews. The first paper challenges this practice and evaluates whether adding of evidence from non-randomised trials might improve the quality and precision of some systematic reviews. The second paper compares the alleged (...) methodological benefits of randomised trials over observational studies for investigating treatment benefits. It suggests that claims about the superiority of well-conducted randomised controlled trials over well-conducted observational studies are justified, especially when results from the two methods are contradictory. The third paper argues that postulating the unpredictability paradox in systematic reviews when no detectable empirical differences can be found requires further justification. The fourth paper examines the problem of absence causation in the context of explaining causal mechanisms and argues that a recent solution is incomplete and requires further justification. Solving the problem by describing absences as causes of 'mechanism failure' fails to take into account the effects of absences that lead to vacillating levels of mechanism functionality. The fifth paper criticises literature that has emphasised functioning versus 'broken' or 'non-functioning' mechanisms emphasising that many diseases result from increased or decreased mechanism function, rather than complete loss of function. Mechanistic explanations must account for differences in the effectiveness of performed functions, yet current philosophical mechanistic explanations do not achieve this. The last paper argues that the standard of evidence embodied in the ICE theory of technological function is too permissive for evaluating whether the proposed functions of medical technologies have been adequately assessed and correctly ascribed. It argues that high-quality evidence from clinical studies is necessary to justify functional ascriptions to health care technologies. (shrink)

Two key ideas of scientific explanation−explanation as causal information and explanation as unification-have frequently been set into mutual opposition. This paper proposes a “dialectical solution” to this conflict, by arguing that causal explanations are preferable to non-causal ones, because they lead to a higherdegree of unification at the level of explaining statistical regularities. The core axioms of the theory of causal nets (TC) are justified because they offer the best if not the only unifying explanation of two statistical phenomena: screening (...) off and linking up. Alternative explanations of the two phenomena are discussed and it isshown why they don’t work. It is demonstrated that although the core axioms of TC are empirically vacuous, extended versions of TC have empirical content by means of which they can generate independently testable predictions.Con frecuencia se han planteado como contrapuestas dos ideas clave en la explicacion cientifica (explicacion como informacion causal y explicacion como unificacion). El presente articulo propone una “solucion dialectica” argumentando que las explicaciones causales son preferibles a las no-causales porque aquellas comportan un mayor grado de unificacion en la explicacion de regularidades estadisticas. Los axiomas centrales de la teoria de redes causales (TC) estan justificados porque ofrecen la mejor, si no la unica, explicacion unificada de dos fenomenos estadisticos: neutralizacion (screening off) y vinculacion (linking up). Se discuten las explicaciones alternativas de estos dos fenomenos y se razona por que no funcionan. Se demuestra ademas que aunque los axiomas centrales de TC son empiricamente vacuos, las versiones extendidas de TC tienen un contenido empirico gracias al cual pueden generar predicciones independientemente contrastables. (shrink)

Perhaps the topic of acceptable risk never had a sexier and more succinct introduction than the one Edward Norton, playing an automobile company executive, gave it in Fight Club: “Take the number of vehicles in the field (A), multiply it by the probable rate of failure (B), and multiply the result by the average out of court settlement (C). A*B*C=X. If X is less than the cost of the recall, we don’t do one.” Of course, this dystopic scene also gets (...) to the heart of the issue in another way: acceptable risk deals with mathematical calculations about the value of life, injury, and emotional wreckage, making calculation a difficult matter ethically, politically, and economically. This entry will explore the history of this idea, focusing on its development alongside statistics into its wide importance today. (shrink)

In an incendiary 2010 Nature article, M. A. Nowak, C. E. Tarnita, and E. O. Wilson present a savage critique of the best-known and most widely used framework for the study of social evolution, W. D. Hamilton’s theory of kin selection. More than a hundred biologists have since rallied to the theory’s defence, but Nowak et al. maintain that their arguments ‘stand unrefuted’. Here I consider the most contentious claim Nowak et al. defend: that Hamilton’s rule, the core explanatory principle (...) of kin selection theory, ‘almost never holds’. I first distinguish two versions of Hamilton’s rule in contemporary theory: a special version (HRS) that requires restrictive assumptions, and a general version (HRG) that does not. I then show that Nowak et al. are most charitably construed as arguing that HRS almost never holds, while HRG buys its generality at the expense of explanatory power. While their arguments against HRS are fairly uncontroversial, their arguments against HRG are more contentious, yet these have been largely overlooked in the ensuing furore. I consider the arguments for and against the explanatory value of HRG, with a view to assessing what exactly is at stake in the debate. I suggest that the debate hinges on issues concerning the causal interpretability of regression coefficients, and concerning the explanatory function Hamilton’s rule is intended to serve. (shrink)

It is shown that three common conditions for scientific explanations are violated by a widely used class of domain-independent explanations. These explanations can accommodate both complex and noncomplex systems and do not require the use of detailed models of system-specific processes for their effectiveness, although they are compatible with such model-based explanations. The approach also shows how a clean separation can be maintained between mathematical representations and empirical content.

?Those ice cubes melted because by melting total entropy increased and entropy increase has a very high objective chance.? What role does the chance in this explanation play? I argue that it contributes to the explanation by entailing that the melting was almost necessary, and defend the claim that the fact that some event was almost necessary can, in the right circumstances, constitute a causal explanation of that event.

Probabilistic phenomena are often perceived as being problematic targets for contrastive explanation. It is usually thought that the possibility of contrastive explanation hinges on whether or not the probabilistic behaviour is irreducibly indeterministic, and that the possible remaining contrastive explananda are token event probabilities or complete probability distributions over such token outcomes. This paper uses the invariance-under-interventions account of contrastive explanation to argue against both ideas. First, the problem of contrastive explanation also arises in cases in which the probabilistic behaviour (...) of the explanandum is due to unobserved causal heterogeneity. Second, it turns out that, in contrast to the case of pure indeterminism, the plausible contrastive explananda under causal heterogeneity are not token event probabilities, but population-level statistical facts. (shrink)

Why-questions and how-possibly-questions are two common forms of explanation request. Answers to the former ones require factual assertions, but the latter ones can be answered by displaying a representation of the targeted phenomenon. However, in an extreme case, a representation could come accompanied by the assertion that it displays the only possible way a phenomenon could develop. Using several historical controversies concerning statistical modeling, it is argued that such cases must inevitably involve tacit or explicit empirical assumptions.

The roles of linguistic, cognitive, and social-pragmatic processes in word learning are well established. If statistical mechanisms also contribute to word learning, they must interact with these processes; however, there exists little evidence for such mechanistic synergy. Adults use co-occurrence statistics to encode speech–object pairings with detailed sensitivity in stochastic learning environments (Vouloumanos, 2008). Here, we replicate this statistical work with nonspeech sounds and compare the results with the previous speech studies to examine whether exclusion constraints contribute equally to the (...) statistical learning of speech–object and nonspeech–object associations. In environments in which performance could benefit from exclusion, we find a learning advantage for speech over nonspeech, revealing an interaction between statistical and exclusion processes in associative word learning. (shrink)

Some philosophers, most notably Hempel and Salmon, have tried to reduce explanation to probability by proposing analyses of explanation in probabilistic terms. Hempel claims, roughly, that a hypothesis H explains a datum D if and only if the conditional probability P is close to 1. It is well known that such an account fails in cases where H is irrelevant for D. Even though it is highly likely that Tom will not become pregnant, given that he regularly takes his wife’s (...) birth control pills, the latter does not explain the former. Neither does an idea work which is in the proximity of Salmon’s, namely, that H explains D if and only if P > P. Suppose Susan swallows a pound of arsenic in order to commit suicide. Shortly after, however, she dies because she is run over by a bus. The probability of dying, given that one ingests a pound of arsenic, is usually higher than the prior probability of dying. Nonetheless, it is not the arsenic but the collision with the bus which explains Susan’s death. The aforementioned objections are directed against …. (shrink)

The statistical interpretation of the Theory of Natural Selection claims that natural selection and drift are statistical features of mathematical aggregates of individual-level events. Natural selection and drift are not themselves causes. The statistical interpretation is motivated by a metaphysical conception of individual priority. Recently, Millstein, Skipper, and Dietrich (2009) have argued (a) that natural selection and drift are physical processes, and (b) that the statistical interpretation rests on a misconception of the role of mathematics in biology. Both theses are (...) contested. (shrink)

A hitherto neglected form of explanation is explored, especially its role in population genetics. “Statistically abstractive explanation” (SA explanation) mandates the suppression of factors probabilistically relevant to an explanandum when these factors are extraneous to the theoretical project being pursued. When these factors are suppressed, the explanandum is rendered uncertain. But this uncertainty traces to the theoretically constrained character of SA explanation, not to any real indeterminacy. Random genetic drift is an artifact of such uncertainty, and it is therefore wrong (...) to reify it as a cause of evolution or as a process in its own right. *Received July 2009. †To contact the author, please write to: Department of Philosophy, University of Toronto, 170 St. George St., Toronto, ON M5R 2M8, Canada; e‐mail: [email protected] (shrink)

Approaches to explanation -- Causal and explanatory relevance -- The kairetic account of /D making -- The kairetic account of explanation -- Extending the kairetic account -- Event explanation and causal claims -- Regularity explanation -- Abstraction in regularity explanation -- Approaches to probabilistic explanation -- Kairetic explanation of frequencies -- Kairetic explanation of single outcomes -- Looking outward -- Looking inward.

It's been 41 years since the publication of Ernst Mayr's Cause and Effect in Biology wherein Mayr most clearly develops his version of the influential distinction between ultimate and proximate causes in biology. In critically assessing Mayr's essay I uncover false statements and red-herrings about biological explanation. Nevertheless, I argue to uphold an analogue of the ultimate/proximate distinction as it refers to two different kinds of explanations, one dynamical the other statistical.

It is widely accepted within philosophy of science that indeterministic explanation is possible. In this dissertation I attempt to show that the arguments supporting indeterministic explanation do not warrant the predominance of this view. The arguments play out across two areas of contention. The first concerns meta-theoretical principles that at one time commanded broad acceptance as conditions of adequacy for any proposed model of scientific explanation. These conditions include Principle P, which states that if A explains B, then A cannot (...) also explain -B, and the contrast class condition, which requires that for A to explain B, A must explain why B occurred rather than -B. Under Explanatory Deductivist interpretations, these adequacy conditions block indeterministic explanation, as do Deductive Nomological models of explanation which satisfy these conditions. We find, however, that under non-deductivist interpretations these same adequacy conditions are compatible with indeterministic explanation. This fact shifts the debate to the contention between competing models of explanation, viz. Inductive-Statistical and probabilistic causal models on the one hand accommodating indeterministic explanation, and D-N models that block indeterministic explanation. ;I introduce the debate through a widely cited treatment by Wolfgang Stegmuller. I then confront five distinct arguments against explanatory deductivism and conclude that D-N models remain viable and provide a secure basis for opposing indeterministic explanation. Finally, I engage with arguments defending indeterministic explanation advanced by Carl Hempel, Peter Railton, Paul Humphreys and Wesley Salmon. While I concede that probabilistic causal models provide a coherent and persuasive accommodation of indeterministic explanation, I conclude that the arguments against indeterministic explanation that rely on D-N models maintain significant substance and force. I provide an account of idealization in scientific explanation as a part of my defense of ED, and argue that D-N models properly capture the scientific knowledge represented in examples cited as exemplars of indeterministic explanation. (shrink)

Recent work on self organization promises an explanation of complex order which is independent of adaptation. Self-organizing systems are complex systems of simple units, projecting order as a consequence of localized and generally nonlinear interactions between these units. Stuart Kauffman offers one variation on the theme of self-organization, offering what he calls a ``statistical mechanics'' for complex systems. This paper explores the explanatory strategies deployed in this ``statistical mechanics,'' initially focusing on the autonomy of statistical explanation as it applies in (...) evolutionary settings and then turning to Kauffman's analysis. Two primary morals emerge as a consequence of this examination: first, the view that adaptation and self-organization should be seen as competing theories or models is misleading and simplistic; and second, while we need a synthesis treating self-organization and adaptation as geared toward different problems, at different levels of organization, and deploying different methods, we do not yet have such a synthesis. (shrink)

It is widely held that the size of a probability makes no difference to the quality of a probabilistic explanation. I argue that explanatory practice in statistical physics belies this claim. The claim has gained currency only because of an impoverished conception of probabilistic processes and an unwarranted assumption that all probabilistic explanations have a single form.

Any theory of explanation must account for the explanatory successes of statistical scientific theories. This should not be done by endorsing determinism. These considerations have been taken as sufficient ground for rejecting the demand on explanations to be deductive. The arguments for doing so, in Coffa (1974) and Salmon (1977, 1984, 1988), are, however, not persuasive. Deductivism is a viable position. Considering that doubts can be raised against the explanatory validity of probabilistic causal relations and the intuitive plausibility of deductivism, (...) it is also a recommendable position, though elaboration is needed in accounting for some of the uses of statistical theories in explanations. (shrink)

Several philosophers of science have advanced an instrumentalist thesis about the use of probabilities in evolutionary biology. I investigate the consequences of instrumentalism on evolutionary explanations. I take issue with Barbara Horan's (1994) argument that probabilities are unnecessary to explain evolutionary change given the underlying deterministic character of evolutionary processes. First, I question Horan's deterministic assumption. Then, I attempt to undermine her Laplacian argument by demonstrating that whether probabilities are necessary depends upon the sort of questions one is asking.

Standard models of statistical explanation face two intractable difficulties. In his 1984 Salmon argues that because statistical explanations are essentially probabilistic we can make sense of statistical explanation only by rejecting the intuition that scientific explanations are contrastive. Further, frequently the point of a statistical explanation is to identify the etiology of its explanandum, but on standard models probabilistic explanations often fail to do so. This paper offers an alternative conception of statistical explanations on which explanations of the frequency of (...) a property consist in the derivation of that frequency from a statistical specification of the mechanism by which instances of the relevant property are produced. Such explanations are contrastive precisely because they identify the determinate causal etiologies of their explananda. (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)

My purpose here is to elaborate the reasons I maintain that Salmon has not been completely successful in reporting the history of work on explanation. The most important limitation of his account is that it does not emphasize the critical necessity to embrace a suitable conception of probability in the development of the theory of probabilistic explanation.

The corpus of physical theory is a paradigm of knowledge. The evolution of modern physical theory constitutes the clearest exemplar of the growth of knowledge. If the development of physical theory does not constitute an example of progress and growth in what we know about the Universe nothing does. So anyone interested in the theory of knowledge must be interested consequently in the evolution and content of physical theory. Crucial to the conception of physics as a paradigm of knowledge is (...) the way in which physical theory provides explanations of a vast diversity of natural phenomena on the basis of a very few fundamental principles. A central problem for the epistemologist is therefore what is theoretical explanation in physics? Here we can get good insight from what Redhead has said. Indeed one could agree with almost everything Redhead says and simply endorse much of his careful and extensive defence of the covering law account of explanation in the physical sciences at least as an ideal. However I shall, I fear, try the reader's patience by extending some of the considerations he introduced and raising those issues where we disagree, especially in the important area of statistical explanation. (shrink)

In what sense do the sciences explain? Or do they merely describe what is going on without answering why-questions at all. But cannot description at an appropriate ‘level’ provide all that we can reasonably ask of an explanation? Well, what do we mean by explanation anyway? What, if anything, gets left out when we provide a so-called scientific explanation? Are there limits of explanation in general, and scientific explanation, in particular? What are the criteria for a good explanation? Is it (...) possible to satisfy all the desiderata simultaneously? If not, which should we regard as paramount? What is the connection between explanation and prediction? What exactly is it that statistical explanations explain? These are some of the questions that have generated a very extensive literature in the philosophy of science. In attempting to answer them, definite views will have to be taken on related matters, such as physical laws, causality, reduction, and questions of evidence and confirmation, of theory and observation, realism versus antirealism, and the objectivity and rationality of science. I will state my own views on these matters, in the course of this essay. To argue for everything in detail and to do justice to all the alternative views, would fill a book, perhaps several books. I want to lead up fairly quickly to modern physics, and review the explanatory situation there in rather more detail. (shrink)

Good scientific explanations sometimes appear to make use of averages. Using concrete examples from current economic theory, I argue that some confusions about how averages might work in explanations lead to both philosophical and economic problems about the interpretation of the theory. I formulate general conditions on potentially proper uses of averages to refine a notion of average explanation. I then try to show how this notion provides a means for resolving longstanding philosophical problems in economics and other quantitative social (...) sciences. (shrink)

In an explanation, what does the explaining and what gets explained? What are the relata of the explanation relation? Candidates include: people, events, facts, sentences, statements, and propositions.

An argument has been recently proposed by Watkins, whose objective is to show the impossibility of a statistical explanation of single events. This present paper is an attempt to show that Watkins's argument is unsuccessful, and goes on to argue for an account of statistical explanation which has much in common with Hempel's classic treatment.

In this paper an attempt is made at developing the notion of a real and complete empirical explanation as excluding all forms of potential or incomplete explanations. This explanation is, however, no longer conceived as the proper aim of empirical science, for it can certainly be gleaned from recent epistemological publications that no comprehensive notion of a real and complete scientific explanation is likely to be constructed from within empirical science. Contrary to common understanding the empirical explanation, deductive-nomological as well (...) as statistical explanation, is considered here only as motive of scientific activities, i.e., as common aim of a transcending cooperation of scientific and non-scientific social practice. Following from this the proper aim of empirical science now consists in the development of practically relevant explanatory theories.This redetermination of the aim of scientific activities of empirical science also means criticism of the unification of deductive-nomological and statistical explanations, as it has been proposed by Wolfgang Stegmüller in his pragmatisch-epistemische Wende. For both forms of empirical explanation must be referred to fundamentally different kinds of practical relevance, the former playing a more important role in the advancement of social practice. Stegmüller's development of a comprehensive probabilistic notion of empirical explanation, as tied up to pragmatic knowledge-situations, in a way already transcends a scientifically immanent determination of it, but he seems to have stopped halfway on the road to practically relevant empirical explanations. Several insufficiencies with his probabilistic notion of empirical explanation are shown up in this paper as a consequence of his abiding by pragmatic, and not penetrating to practical, knowledge-situations. The final result of it, however, consists in a clarification and a modification of the concept of deductive-nomological explanation, originally developed by Hempel and Oppenheim. (shrink)

Since the publication of Carl Hempel and Paul Oppenheim's ground-breaking work "Studies in the Logic of Explanation," the theory of explanation has remained a major topic in the philosophy of science. This valuable collection provides readers with the opportunity to study some of the classic essays on the theory of explanation along with the best examples of the most recent work being done on the topic. In addition to the original Hempel and Oppenheim paper, the volume includes Scriven's critical reaction (...) to it, Wilfrid Sellars's discussion of the problem of theoretical explanation, and pieces by Salmon, Railton, van Fraassen, Friedman, Kitcher, and Achinstein in which they demonstrate the vitality of the subject by extending the scope of the inquiry. (shrink)

(1988). Explanation, subjunctives and statistical theories. International Studies in the Philosophy of Science: Vol. 3, No. 1, pp. 80-96. doi: 10.1080/02698598808573326.

Causal modeling methods such as path analysis, used in the social and natural sciences, are also highly relevant to philosophical problems of probabilistic causation and statistical explanation. We show how these methods can be effectively used (1) to improve and extend Salmon's S-R basis for statistical explanation, and (2) to repair Cartwright's resolution of Simpson's paradox, clarifying the relationship between statistical and causal claims.

This paper is an assessment of an attempt, by James Greeno, to measure the explanatory power of statistical theories by means of the notion of transmitted information (It). It is argued that It has certain features that are inappropriate in a measure of explanatory power. In particular, given a statistical theory T with explanans variables St and explanandum variables Mj, it is argued that no plausible measure of explanatory power should depend on the probability P(Si) of occurrence of initial conditions (...) in the systems to which T applies or the magnitudes of the conditional probabilities P(Mj/Si), in the manner in which Ir does. (shrink)