Defenders of Inference to the Best Explanation claim that explanatory factors should play an important role in empirical inference. They disagree, however, about how exactly to formulate this role. In particular, they disagree about whether to formulate IBE as an inference rule for full beliefs or for degrees of belief, as well as how a rule for degrees of belief should relate to Bayesianism. In this essay I advance a new argument against non-Bayesian versions of IBE. My argument focuses on (...) cases in which we are concerned with multiple levels of explanation of some phenomenon. I show that in many such cases, following IBE as an inference rule for full beliefs leads to deductively inconsistent beliefs, and following IBE as a non-Bayesian updating rule for degrees of belief leads to probabilistically incoherent degrees of belief. (shrink)

Inference to the Best Explanation (IBE) and Bayesianism are our two most prominent theories of scientific inference. Are they compatible? Van Fraassen famously argued that they are not, concluding that IBE must be wrong since Bayesianism is right. Writers since then, from both the Bayesian and explanationist camps, have usually considered van Fraassen’s argument to be misguided, and have plumped for the view that Bayesianism and IBE are actually compatible. I argue that van Fraassen’s argument is actually not so misguided, (...) and that it causes more trouble for compatibilists than is typically thought. Bayesianism in its dominant, subjectivist form, can only be made compatible with IBE if IBE is made subservient to conditionalization in a way that robs IBE of much of its substance and interest. If Bayesianism and IBE are to be fit together, I argue, a strongly objective Bayesianism is the preferred option. I go on to sketch this objectivist, IBE-based Bayesianism, and offer some preliminary suggestions for its development. (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)

Causation is a central topic in many areas of philosophy. In metaphysics, philosophers want to know what causation is, and how it is related to laws of nature, probability, action, and freedom of the will. In epistemology, philosophers investigate how causal claims can be inferred from statistical data, and how causation is related to perception, knowledge and explanation. In the philosophy of mind, philosophers want to know whether and how the mind can be said to have causal efficacy, and in (...) ethics, whether there is a moral distinction between acts and omissions and whether the moral value of an act can be judged according to its consequences. And causation is a contested concept in other fields of enquiry, such as biology, physics, and the law. This book provides an in-depth and comprehensive overview of these and other topics, as well as the history of the causation debate from the ancient Greeks to the logical empiricists. The chapters provide surveys of contemporary debates, while often also advancing novel and controversial claims; and each includes a comprehensive bibliography and suggestions for further reading. The book is thus the most comprehensive source of information about causation currently available, and will be invaluable for upper-level undergraduates through to professional philosophers. (shrink)

Probability theory is a key tool of the physical, mathematical, and social sciences. It has also been playing an increasingly significant role in philosophy: in epistemology, philosophy of science, ethics, social philosophy, philosophy of religion, and elsewhere. This Handbook encapsulates and furthers the influence of philosophy on probability, and of probability on philosophy. Nearly forty articles summarise the state of play and present new insights in various areas of research at the intersection of these two fields. The articles will be (...) of special interest to practitioners of probability who seek a greater understanding of its mathematical and conceptual foundations, and to philosophers who want to get up to speed on the cutting edge of research in this area. The volume begins with a primer on those parts of probability theory that we believe are most important for philosophers to know, and the rest is divided into seven main sections: History; Formalism; Alternatives to Standard Probability Theory; Interpretations and Interpretive Issues; Probabilistic Judgment and Its Applications; Applications of Probability: Science; and Applications of Probability: Philosophy. (shrink)

This article compares inference to the best explanation with Bayes’s rule in a social setting, specifically, in the context of a variant of the Hegselmann–Krause model in which agents not only update their belief states on the basis of evidence they receive directly from the world, but also take into account the belief states of their fellow agents. So far, the update rules mentioned have been studied only in an individualistic setting, and it is known that in such a setting (...) both have their strengths as well as their weaknesses. It is shown here that in a social setting, inference to the best explanation outperforms Bayes’s rule according to every desirable criterion. 1 What Is Inference to the Best Explanation?2 Judging the Rules—By Which Lights?3 From an Individualistic to a Social Perspective 3.1 The Hegselmann–Krause model 3.2 A probabilistic extension of the Hegselmann–Krause model 3.3 Simulations4 Results and Discussion5 Interpretation6 Conclusion. (shrink)

Bayesians have traditionally taken a dim view of the Inference to the Best Explanation, arguing that, if IBE is at variance with Bayes ' rule, then it runs afoul of the dynamic Dutch book argument. More recently, Bayes ' rule has been claimed to be superior on grounds of conduciveness to our epistemic goal. The present paper aims to show that neither of these arguments succeeds in undermining IBE.

This article introduces and defends a probabilistic measure of the explanatory power that a particular explanans has over its explanandum. To this end, we propose several intuitive, formal conditions of adequacy for an account of explanatory power. Then, we show that these conditions are uniquely satisfied by one particular probabilistic function. We proceed to strengthen the case for this measure of explanatory power by proving several theorems, all of which show that this measure neatly corresponds to our explanatory intuitions. Finally, (...) we briefly describe some promising future projects inspired by our account. (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)

What is required for something to be evidence for a hypothesis? In this fascinating, elegantly written work, distinguished philosopher of science Peter Achinstein explores this question, rejecting typical philosophical and statistical theories of evidence. He claims these theories are much too weak to give scientists what they want--a good reason to believe--and, in some cases, they furnish concepts that mistakenly make all evidential claims a priori. Achinstein introduces four concepts of evidence, defines three of them by reference to "potential" evidence, (...) and characterizes the latter using a novel epistemic interpretation of probability. The resulting theory is then applied to philosophical and historical issues. Solutions are provided to the "grue," "ravens," "lottery," and "old-evidence" paradoxes, and to a series of questions. These include whether explanations or predictions furnish more evidential weight, whether individual hypotheses or entire theoretical systems can receive evidential support, what counts as a scientific discovery, and what sort of evidence is required for it. The historical questions include whether Jean Perrin had non-circular evidence for the existence of molecules, what type of evidence J. J. Thomson offered for the existence of the electron, and whether, as is usually supposed, he really discovered the electron. Achinstein proposes answers in terms of the concepts of evidence introduced. As the premier book in the fabulous new series Oxford Studies in Philosophy of Science, this volume is essential for philosophers of science and historians of science, as well as for statisticians, scientists with philosophical interests, and anyone curious about scientific reasoning. (shrink)

The final work of a distinguished physicist, this remarkable volume examines the emotive significance of time, the time order of mechanics, the time direction of thermodynamics and microstatistics, the time direction of macrostatistics, and the time of quantum physics. Coherent discussions include accounts of analytic methods of scientific philosophy in the investigation of probability, quantum mechanics, the theory of relativity, and causality. "[Reichenbach’s] best by a good deal."—Physics Today. 1971 ed.

Recent work on inference to the best explanation has come to an impasse regarding the proper way to coordinate the theoretical virtues in explanatory inference with probabilistic confirmation theory, and in particular with aspects of Bayes's Theorem. I argue that the theoretical virtues are best conceived heuristically and that such a conception gives us the resources to explicate the virtues in terms of ceteris paribus theorems. Contrary to some Bayesians, this is not equivalent to identifying the virtues with likelihoods or (...) priors per se; the virtues may be more accessible epistemically than likelihoods or priors. I then prove a ceteris paribus theorem regarding theoretical consilience, use it to correct a recent application of Reichenbach's common cause principle, and apply it to a test case of scientific reasoning. Explanation and confirmation The heuristic conception of theoretical virtues Abduction and the accessibility of explanatory power Evidential and theoretical consilience A test case: gravitational lensing Conclusion Thus natural science appears completely to lose from sight the large and general questions; but all the more splendid is the success when, groping in the thicket of special questions, we suddenly find a small opening that allows a hitherto undreamt of outlook on the whole. (L. Boltzmann, Theoretical Physics and Philosophical Problems). (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)

In this new explanationist account of epistemic justification, Poston argues that the explanatory virtues provide all the materials necessary for a plausible account of justified belief. There are no purely autonomous reasons. Rather reasons occur only within an explanatory coherent set of beliefs.

Science depends on judgments of the bearing of evidence on theory. Scientists must judge whether an observation or the result of an experiment supports, disconfirms, or is simply irrelevant to a given hypothesis. Similarly, scientists may judge that, given all the available evidence, a hypothesis ought to be accepted as correct or nearly so, rejected as false, or neither. Occasionally, these evidential judgments can be make on deductive grounds. If an experimental result strictly contradicts a hypothesis, then the truth of (...) the evidence deductively entails the falsity of the hypothesis. In the great majority of cases, however, the connection between evidence and hypothesis is nondemonstrative or inductive. In particular, this is so whenever a general hypothesis is inferred to be correct on the basis of the available data, since the truth of the data will not deductively entail the truth of the hypothesis. It always remains possible that the hypothesis is false even though the data are correct. (shrink)

In this article, I consider an important challenge to the popular theory of scientific inference commonly known as ‘inference to the best explanation’, one that has received scant attention.1 1 The problem is that there exists a wide array of rival models of explanation, thus leaving IBE objectionably indeterminate. First, I briefly introduce IBE. Then, I motivate the problem and offer three potential solutions, the most plausible of which is to adopt a kind of pluralism about the rival models of (...) explanation. However, I argue that how ranking explanations on this pluralistic account of IBE remains obscure and pluralism leads to contradictory results. In light of these objections, I attempt to dissolve the problem by showing why IBE does not require a ‘model’ of explanation and by giving an account of what explanation consists in within the context of IBE. (shrink)

Despite decades of focused philosophical investigation, Inference to the Best Explanation still lacks a precise articulation and compelling defense. The primary reason for this is that it is not at all clear what it means for a hypothesis to be the best available explanation of the evidence. This paper first seeks to rectify this problem by developing a formal explication of the explanatory virtue of power. A resulting account of IBE is then evaluated as a form of uncertain inference. Overall, (...) this paper offers a precise account and novel defense of one important version of IBE. (shrink)

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned.Each argument concludes that rationality requires your credences to be probabilities.I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and a corresponding (...) argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. I discuss the extent to which the original arguments can be buttressed.1. Introduction2. The Dutch Book Argument2.1. Saving the Dutch Book argument2.2. ‘The Dutch Book argument merely dramatizes an inconsistency in the attitudes of an agent whose credences violate probability theory’3. Representation Theorem-based Arguments4. The Calibration Argument5. The Gradational Accuracy Argument6. Conclusion. (shrink)

The thesis of underdetermination presents a major obstacle to the epistemological claims of scientific realism. That thesis is regularly assumed in the philosophy of science, but is puzzlingly at odds with the actual history of science, in which empirically adequate theories are thin on the ground. We propose to advance a case for scientific realism which concentrates on the process of scientific reasoning rather than its theoretical products. Developing an account of causal–explanatory inference will make it easier to resist the (...) thesis of underdetermination. For, if we are not restricted to inference to the best explanation only at the level of major theories, we will be able to acknowledge that there is a structure in data sets which imposes serious constraints on possible theoretical alternatives. We describe how Differential Inference, a form of inference based on contrastive explanation, can be used in order to generate causal hypotheses. We then go on to consider how experimental manipulation of differences can be used to achieve Difference Closure, thereby confirming claims of causal efficacy and also eliminating possible confounds. The model of Differential Inference outlined here shows at least one way in which it is possible to ‘reason from the phenomena’. (shrink)

William Roche and Elliott Sober argue that explanatoriness is evidentially irrelevant. This conclusion is surprising since it conflicts with a plausible assumption—the fact that a hypothesis best explains a given set of data is evidence that the hypothesis is true. We argue that Roche and Sober's screening-off argument fails to account for a key aspect of evidential strength: the weight of a body of evidence. The weight of a body of evidence affects the resiliency of probabilities in the light of (...) new evidence. Thus, Roche and Sober are mistaken. Explanatoriness is evidentially relevant. (shrink)

Four important arguments for probabilism—the Dutch Book, representation theorem, calibration, and gradational accuracy arguments—have a strikingly similar structure. Each begins with a mathematical theorem, a conditional with an existentially quantified consequent, of the general form: if your credences are not probabilities, then there is a way in which your rationality is impugned. Each argument concludes that rationality requires your credences to be probabilities. I contend that each argument is invalid as formulated. In each case there is a mirror-image theorem and (...) a corresponding argument of exactly equal strength that concludes that rationality requires your credences not to be probabilities. Some further consideration is needed to break this symmetry in favour of probabilism. (shrink)

Two of the most influential theories about scientific inference are inference to the best explanation and Bayesianism. How are they related? Bas van Fraassen has claimed that IBE and Bayesianism are incompatible rival theories, as any probabilistic version of IBE would violate Bayesian conditionalization. In response, several authors have defended the view that IBE is compatible with Bayesian updating. They claim that the explanatory considerations in IBE are taken into account by the Bayesian because the Bayesian either does or should (...) make use of them in assigning probabilities to hypotheses. I argue that van Fraassen has not succeeded in establishing that IBE and Bayesianism are incompatible, but that the existing compatibilist response is also not satisfactory. I suggest that a more promising approach to the problem is to investigate whether explanatory considerations are taken into account by a Bayesian who assigns priors and likelihoods on his or her own terms. In this case, IBE would emerge from the Bayesian account, rather than being used to constrain priors and likelihoods. I provide a detailed discussion of the case of how the Copernican and Ptolemaic theories explain retrograde motion, and suggest that one of the key explanatory considerations is the extent to which the explanation a theory provides depends on its core elements rather than on auxiliary hypotheses. I then suggest that this type of consideration is reflected in the Bayesian likelihood, given priors that a Bayesian might be inclined to adopt even without explicit guidance by IBE. The aim is to show that IBE and Bayesianism may be compatible, not because they can be amalgamated, but rather because they capture substantially similar epistemic considerations. 1 Introduction2 Preliminaries3 Inference to the Best Explanation4 Bayesianism5 The Incompatibilist View : Inference to the Best Explanation Contradicts Bayesianism5. 1 Criticism of the incompatibilist view6 Constraint - Based Compatibilism6. 1 Criticism of constraint - based compatibilism7 Emergent Compatibilism7. 1 Analysis of inference to the best explanation7. 1. 1 Inference to the best explanation on specific hypotheses7. 1. 2 Inference to the best explanation on general theories7. 1. 3 Copernicus versus Ptolemy7. 1. 4 Explanatory virtues7. 1. 5 Summary7. 2 Bayesian account8 Conclusion. (shrink)

We are addicted to explanation, constantly asking and answering why-questions. But what does an explanation give us? I will consider some of the possible goods, intrinsic and instrumental, that explanations provide. The name for the intrinsic good of explanation is `understanding', but what is this? In the first part of this paper I will canvass various conceptions of understanding, according to which explanations provide reasons for belief, make familiar, unify, show to be necessary, or give causes. Three general features of (...) explanation will serve as tests of these varied conceptions. These features are: a) the distinction between knowing that a phenomena occurs and understanding why it does; b) the possibility of giving explanations that are not themselves explained; c) the possibility of explaining a phenomenon in cases where the phenomenon itself provides an essential part of the reason for believing that the explanation is correct. There are many other aspects of our explanatory practices that a good account of explanation and understanding should capture, but these simple tests provide surprisingly effective diagnostic tools for the evaluation of broad conceptions of the nature of understanding. It will turn out that the causal conception of understanding does particularly well on the tests, though of course it too faces various difficulties. The balance of this essay focuses on the causal conception. After addressing some of the difficulties it faces, I will ask.. (shrink)

The underconsideration argument against inference to the best explanation and scientific realism holds that scientists are not warranted in inferring that the best theory is true, because scientists only ever conceive of a small handful of theories at one time, and as a result, they may not have considered a true theory. However, antirealists have not developed a detailed alternative account of why explanatory inference nevertheless appears so central to scientific practice. In this paper, I provide new defences against some (...) recent objections to the underconsideration argument, while also developing an account of explanatory inference that both survives these criticisms and does not entail realism. (shrink)

In this paper I reconsider a standard counterexample to the chance-raising theory of singular causation. Extant versions of this theory are so different that it is difficult to formulate the core thesis that they all share, despite the guiding idea that causes raise the chance of their effects. At one extreme, ‘Humean’ theories – which can be traced to Reichenbach – say that a particular event of type C is the cause of a particular event of type E only if (...) P(E|C & K) > P(E|~C & K) where K is a set of background conditions and where the probabilities are interpreted as relative frequencies. At the other extreme, explicitly non-Humean theories take chance to be a physical, particular, local feature of the world. (shrink)

Metaphysicians speak of laws of nature in terms of necessity and universality; scientists, in terms of symmetry and invariance. In this book van Fraassen argues that no metaphysical account of laws can succeed. He analyzes and rejects the arguments that there are laws of nature, or that we must believe there are, and argues that we should disregard the idea of law as an adequate clue to science. After exploring what this means for general epistemology, the author develops the empiricist (...) view of science as a construction of models to represent the phenomena. (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)

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