Causality offers the first comprehensive coverage of causal analysis in many sciences, including recent advances using graphical methods. Pearl presents a unified account of the probabilistic, manipulative, counterfactual and structural approaches to causation, and devises simple mathematical tools for analyzing the relationships between causal connections, statistical associations, actions and observations. The book will open the way for including causal analysis in the standard curriculum of statistics, artificial intelligence, business, epidemiology, social science and economics.

We propose a new definition of actual causes, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions and resolves major difficulties in the traditional account.

A number of recent authors (Galles and Pearl, Found Sci 3 (1):151–182, 1998; Hiddleston, Noûs 39 (4):232–257, 2005; Halpern, J Artif Intell Res 12:317–337, 2000) advocate a causal modeling semantics for counterfactuals. But the precise logical significance of the causal modeling semantics remains murky. Particularly important, yet particularly under-explored, is its relationship to the similarity-based semantics for counterfactuals developed by Lewis (Counterfactuals. Harvard University Press, 1973b). The causal modeling semantics is both an account of the truth conditions of counterfactuals, and (...) an account of which inferences involving counterfactuals are valid. As an account of truth conditions, it is incomplete. While Lewis's similarity semantics lets us evaluate counterfactuals with arbitrarily complex antecedents and consequents, the causal modeling semantics makes it hard to ascertain the truth conditions of all but a highly restricted class of counterfactuals. I explain how to extend the causal modeling language to encompass a wider range of sentences, and provide a sound and complete axiomatization for the extended language. Extending the truth conditions for counterfactuals has serious consequences concerning valid inference. The extended language is unlike any logic of Lewis's: modus ponens is invalid, and classical logical equivalents cannot be freely substituted in the antecedents of conditionals. (shrink)

It is natural and important to have a formal representation of plain belief, according to which propositions are held true, or held false, or neither. (In the paper this is called a deterministic representation of epistemic states). And it is of great philosophical importance to have a dynamic account of plain belief. AGM belief revision theory seems to provide such an account, but it founders at the problem of iterated belief revision, since it can generally account only for one step (...) of revision. The paper discusses and rejects two solutions within the confines of AGM theory. It then introduces ranking functions (as I prefer to call them now; in the paper they are still called ordinal conditional functions) as the proper (and, I find, still the best) solution of the problem, proves that conditional independence w.r.t. ranking functions satisfies the so-called graphoid axioms, and proposes general rules of belief change (in close analogy to Jeffrey's generalized probabilistic conditionalization) that encompass revision and contraction as conceived in AGM theory. Indeed, the parallel to probability theory is amazing. Probability theory can profit from ranking theory as well since it is also plagued by the problem of iterated belief revision even if probability measures are conceived as Popper measures (see No. 11). Finally, the theory is compared with predecessors which are numerous and impressive, but somehow failed to explain the all-important conditional ranks in the appropriate way. (shrink)

Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

Several different approaches to the conceptual analysis of causation are guided by the idea that a cause is something that makes a difference to its effects. These approaches seek to elucidate the concept of causation by explicating the concept of a difference-maker in terms of better-understood concepts. There is no better example of such an approach than David Lewis’ analysis of causation, in which he seeks to explain the concept of a difference-maker in counterfactual terms. Lewis introduced his counterfactual theory (...) of causation with these words: 'We think of a cause as something that makes a difference, and the difference it makes must be a difference from what would have happened without it. Had it been absent, its effects—some of them, at least, and usually all—would have been absent as well.' (Lewis 1973b: pp. 160-1) According to Lewis, a cause c makes a difference to an effect e in the sense that if the cause c had not occurred, the effect e would not have occurred either. All we shall see in section 2, Lewis’ theory says there is more to the concept of causation than this counterfactual condition. Lewis is on the right track, I think, in saying that we think of a cause as something that makes a difference and that this thought is best explicated in terms of counterfactual concepts. However, I shall argue that the particular way in which Lewis spells out the concept of a cause as difference-maker is unsatisfactory. For Lewis’ articulation of this concept is distorted by a specific metaphysical assumption: specifically, that causation is an absolute relation, specifiable independently of any contextual factors. The distortion induced by this assumption is reflected in the undiscriminating manner in which his theory generates countless causes for any given effect. However, commonsense judgement is much more discriminating about causes than Lewis’ theory. Accordingly, I claim that Lewis' analysis faces the problem of profligate causes and I outline some specific problem cases in section 3.. (shrink)

A theory of the causal relate as aspects or property instances is developed. A supposed problem for transitivity is assessed and then resolved with aspects as the causal relata.

We propose a new definition of actual causes, using structural equations to model counterfactuals. We show that the definition yields a plausible and elegant account of causation that handles well examples which have caused problems for other definitions and resolves major difficultiesn in the traditional account.

Bayesian decision theory can be viewed as the core of psychological theory for idealized agents. To get a complete psychological theory for such agents, you have to supplement it with input and output laws. On a Bayesian theory that employs strict conditionalization, the input laws are easy to give. On a Bayesian theory that employs Jeffrey conditionalization, there appears to be a considerable problem with giving the input laws. However, Jeffrey conditionalization can be reformulated so that the problem disappears, and (...) in fact the reformulated version is more natural and easier to work with on independent grounds. (shrink)

Among the many philosophers who hold that causal facts1 are to be explained in terms of—or more ambitiously, shown to reduce to—facts about what happens, together with facts about the fundamental laws that govern what happens, the clear favorite is an approach that sees counterfactual dependence as the key to such explanation or reduction. The paradigm examples of causation, so advocates of this approach tell us, are examples in which events c and e— the cause and its effect— both occur, (...) but: had c not occurred, e would not have occurred either. From this starting point ideas proliferate in a vast profusion. But the remarkable disparity among these ideas should not obscure their common foundation. Neither should the diversity of opinion about the prospects for a philosophical analysis of causation obscure their importance. For even those philosophers who see these prospects as dim—perhaps because they suffer post-Quinean queasiness at the thought of any analysis of any concept of interest—can often be heard to say such things as that causal relations among events are somehow “a matter of” the patterns of counterfactual dependence to be found in them. (shrink)

This is part A of a paper in which we defend a semantics for counterfactuals which is probabilistic in the sense that the truth condition for counterfactuals refers to a probability measure. Because of its probabilistic nature, it allows a counterfactual ‘ifAthenB’ to be true even in the presence of relevant ‘Aand notB’-worlds, as long such exceptions are not too widely spread. The semantics is made precise and studied in different versions which are related to each other by representation theorems. (...) Despite its probabilistic nature, we show that the semantics and the resulting system of logic may be regarded as a naturalistically vindicated variant of David Lewis’ truth-conditional semantics and logic of counterfactuals. At the same time, the semantics overlaps in various ways with the non-truth-conditional suppositional theory for conditionals that derives from Ernest Adams’ work. We argue that counterfactuals have two kinds of pragmatic meanings and come attached with two types of degrees of acceptability or belief, one being suppositional, the other one being truth based as determined by our probabilistic semantics; these degrees could not always coincide due to a new triviality result for counterfactuals, and they should not be identified in the light of their different interpretation and pragmatic purpose. However, for plain assertability the difference between them does not matter. Hence, if the suppositional theory of counterfactuals is formulated with sufficient care, our truth-conditional theory of counterfactuals is consistent with it. The results of our investigation are used to assess a claim considered by Hawthorne and Hájek, that is, the thesis that most ordinary counterfactuals are false. (shrink)

We argue that current discussions of criteria for actual causation are ill-posed in several respects. (1) The methodology of current discussions is by induction from intuitions about an infinitesimal fraction of the possible examples and counterexamples; (2) cases with larger numbers of causes generate novel puzzles; (3) "neuron" and causal Bayes net diagrams are, as deployed in discussions of actual causation, almost always ambiguous; (4) actual causation is (intuitively) relative to an initial system state since state changes are relevant, but (...) most current accounts ignore state changes through time; (5) more generally, there is no reason to think that philosophical judgements about these sorts of cases are normative; but (6) there is a dearth of relevant psychological research that bears on whether various philosophical accounts are descriptive. Our skepticism is not directed towards the possibility of a correct account of actual causation; rather, we argue that standard methods will not lead to such an account. A different approach is required. (shrink)

The paper builds on the basically Humean idea that A is a cause of B iff A and B both occur, A precedes B, and A raises the metaphysical or epistemic status of B given the obtaining circumstances. It argues that in pursuit of a theory of deterministic causation this ‘status raising’ is best explicated not in regularity or counterfactual terms, but in terms of ranking functions. On this basis, it constructs a rigorous theory of deterministic causation that successfully deals (...) with cases of overdetermination and pre-emption. It finally indicates how the account's profound epistemic relativization induced by ranking theory can be undone. Introduction Variables, propositions, time Induction first Causation Redundant causation Objectivization. (shrink)

We propose new definitions of (causal) explanation, using structural equations to model counterfactuals. The definition is based on the notion of actual cause, as defined and motivated in a companion article. Essentially, an explanation is a fact that is not known for certain but, if found to be true, would constitute an actual cause of the fact to be explained, regardless of the agent's initial uncertainty. We show that the definition handles well a number of problematic examples from the literature.

We argue that a semantics for counterfactual conditionals in terms of comparative overall similarity faces a formal limitation due to Arrow’s impossibility theorem from social choice theory. According to Lewis’s account, the truth-conditions for counterfactual conditionals are given in terms of the comparative overall similarity between possible worlds, which is in turn determined by various aspects of similarity between possible worlds. We argue that a function from aspects of similarity to overall similarity should satisfy certain plausible constraints while Arrow’s impossibility (...) theorem rules out that such a function satisfies all the constraints simultaneously. We argue that a way out of this impasse is to represent aspectual similarity in terms of ranking functions instead of representing it in a purely ordinal fashion. Further, we argue against the claim that the determination of overall similarity by aspects of similarity faces a difficulty in addition to the Arrovian limitation, namely the incommensurability of different aspects of similarity. The phenomena that have been cited as evidence for such incommensurability are best explained by ordinary vagueness. (shrink)

Nancy Cartwright offers an account of causal powers, and argues that it explains some important general features of scientific method. Patricia Cheng argues that this theory is superior as a psychological theory of learning to standard models of conditioning. I extend and develop the theory, and argue that it provides the best explanation of a number of problem cases for philosophical theories of causation, including preemption, overdetermination and puzzles about transitivity. Hitchcock and Halpern & Pearl on ‘actual causes’ Problems and (...) morals 2.1 Puzzles about prevention 2.2 Counterfactuals Causal powers 3.1 Generative causal power 3.2 Preventative causal power Net and component powers ‘Actual’ or ‘successful’ causes Solutions to puzzle cases Conclusion. (shrink)

The key idea of the interventionist account of causation is that a variable A causes a variable B if and only if B would change if A were manipulated in the appropriate way. This paper raises two problems for Woodward's (2003) version of interventionism. The first is that the conditions it imposes are not sufficient for causation, because these conditions are also satisfied by non-causal relations of nomological dependence expressed in association laws. Such laws ground a relation of mutual manipulability (...) that is incompatible with the asymmetry of causation. Several ways of defending the interventionist account are examined and found unsatisfying. The second problem is that it often seems to be impossible, in a model that contains variables linked by an association law, to satisfy the conditions imposed on interventions on such variables. Various ways to solve this second problem, most importantly the analysis of manipulability in terms of difference making, are examined. Given that none solves the problem, I conclude that the interventionist conditions are neither sufficient nor necessary for causation. It is suggested that they provide an analysis of nomological dependence, which may be supplemented with the notion of a causal process to yield an analysis of causation. (shrink)

Galles & Pearl (l998) claimed that s [possible-worlds] framework.s framework. Recursive models are shown to correspond precisely to a subclass of (possible-world) counterfactual structures. On the other hand, a slight generalization of recursive models, models where all equations have unique solutions, is shown to be incomparable in expressive power to counterfactual structures, despite the fact that the Galles and Pearl arguments should apply to them as well. The problem with the Galles and Pearl argument is identified: an axiom that they (...) viewed as irrelevant, because it involved disjunction (which was not in their language), is not irrelevant at all. (shrink)

Judea Pearl (2000) was the first to propose a definition of actual causation using causal models. A number of authors have suggested that an adequate account of actual causation must appeal not only to causal structure but also to considerations of normality. In Halpern and Hitchcock (2011), we offer a definition of actual causation using extended causal models, which include information about both causal structure and normality. Extended causal models are potentially very complex. In this study, we show how it (...) is possible to achieve a compact representation of extended causal models. (shrink)

The concept of causation plays a central role in many philosophical theories, and yet no account of causation has gained widespread acceptance among those who have investigated its foundations. Theories based on laws, counterfactuals, physical processes, and probabilistic dependence and independence relations (the list is by no means exhaustive) have all received detailed treatment in recent years---{}and, while no account has been entirely successful, it is generally agreed that the concept has been greatly clari{}ed by the attempts. In this magni{}cent (...) book, Woodward aims to give a uni{}ed account of causation and causal explanation in terms of the notion of a manipulation (or intervention, terms which can be read interchangeably). Not only does he produce in my view the most illuminating and comprehensive account of causation on o{}er, his theory also opens a great many avenues for future work in the area, and has rami{}cations for many other areas of philosophy. Making Things Happen ought to be of interest not only to philosophers of causation and philosophers of science, but to any philosopher whose concerns involve assumptions about the nature of causation, laws, or explanation. (shrink)

The main ingredients of Spohn's theory of epistemic beliefs are (1) a functional representation of an epistemic state called a disbelief function and (2) a rule for revising this function in light of new information. The main contribution of this paper is as follows. First, we provide a new axiomatic definition of an epistemic state and study some of its properties. Second, we study some properties of an alternative functional representation of an epistemic state called a Spohnian belief function. Third, (...) we state a rule for combining disbelief functions that is mathematically equivalent to Spohn's belief revision rule. Whereas Spohn's rule is defined in terms of the initial epistemic state and some features of the final epistemic state, the rule of combination is defined in terms of the initial epistemic state and the incremental epistemic state representing the information gained. Fourth, we state a rule of subtraction that allows one to recover the addendum epistemic state from the initial and final epistemic states. Fifth, we study some properties of our rule of combination. One distinct advantage of our rule of combination is that besides belief revision, it can be used to describe an initial epistemic state for many variables when this information is given as several independent epistemic states each involving few variables. Another advantage of our reformulation is that we can show that Spohn's theory of epistemic beliefs shares the essential abstract features of probability theory and the Dempster-Shafer theory of belief functions. One implication of this is that we have a ready-made algorithm for propagating disbelief functions using only local computation. (shrink)