David Lewis’s latest theory of causation defines the causal link in terms of the relation of influence between events. It turns out, however, that one event’s influencing another is neither a necessary nor sufficient condition for its being a cause of that event. In the article one particular case of causality without influence is presented and developed. This case not only serves as a counterexample to Lewis’s influence theory, but also threatens earlier counterfactual analyses of causation by admitting a particularly (...) troublesome type of preemption. The conclusion of the article is that Lewis’s influence method of solving the preemption problem fails, and that we need a new and fresh approach to the cases of redundant causation if we want to hold on to the counterfactual analysis of causation. (shrink)

In this paper, we propose a regularity theory of causation. The theory aims to be reductive and to align with our pre‐theoretic understanding of the causal relation. We show that our theory can account for a wide range of causal scenarios, including isomorphic scenarios, omissions, and scenarios which suggest that causation is not transitive.

When evaluating theories of causation, intuitions should not play a decisive role, not even intuitions in flawlessly-designed thought experiments. Indeed, no coherent theory of causation can respect the typical person’s intuitions in redundancy (pre-emption) thought experiments, without disrespecting their intuitions in threat-and-saviour (switching/short-circuit) thought experiments. I provide a deductively sound argument for these claims. Amazingly, this argument assumes absolutely nothing about the nature of causation. I also provide a second argument, whose conclusion is even stronger: the typical person’s causal intuitions (...) are thoroughly unreliable. This argument proceeds by raising the neglected question: in what respects is information about intermediate and enabling variables relevant to reliable causal judgment? (shrink)

The non-reductive physicalist would like to believe that mental properties are not identical to physical properties; that there are complete causal explanations of all events in terms of physical properties; and that there are sometimes explanations of events in terms of mental properties. However, some have argued that these claims cannot all be true, since they are collectively inconsistent with a principle of causal exclusion. In this paper I argue that the best formulation of the interventionist theory of causation entails (...) the falsity of the exclusion principle. However, I argue that it does so at the cost of revealing a weakness in the interventionist theory itself. (shrink)

Philosophy and Literature is an internationally renowned refereed journal founded by Denis Dutton at the University of Canterbury, Christchurch. It is now published by the Johns Hopkins University Press. Since its inception in 1976, Philosophy and Literature has been concerned with the relation between literary and philosophical studies, publishing articles on the philosophical interpretation of literature as well as the literary treatment of philosophy. Philosophy and Literature has sometimes been regarded as iconoclastic, in the sense that it repudiates academic pretensions, (...) insidious jargon and institutional vogue. Dutton, who remains the editor, still writes a regular column. A distinctive feature of Philosophy and Literature was the annual Bad Writing Contest, held from 1995–98, which sought to identify (and publish) the ‘most stylistically lamentable passages’ of academic prose, often to great amusement. (shrink)

Philosophers have already recognized the importance of causal preemption involving “positive” events. First, preemption with positive events raises problems for counterfactual theories of causation. Second, theories of moral and legal responsibility rely heavily on the concept of causation, so accurately assessing responsibility in preemption cases requires correctly assessing their causal structure. However, philosophers have not discussed preemption involving “negative” events or omissions. This paper argues that cases of preemptive omissions exist and have important implications for theories of causation and for (...) moral and legal responsibility. Of theoretical importance, the alterations made to counterfactual theories of causation to address preemption with positive events do not seem to work for accommodating preemptive omissions. Of practical importance, there have been actual legal cases involving preemptive omissions, and at least one such case was, this paper contends, decided incorrectly on erroneous causal grounds. This paper identifies what must happen for preemptive omissions to obtain. It then argues for the existence of preemptive omissions by constructing a series of cases and drawing structural parallels between preemption cases with positive events and cases with omissions. It ultimately presents a formula for generating preemptive omissions and examines both why “traditional” methods of generating preemption fail for omissions and why the proposed method avoids such concerns. (shrink)

Causal theories of action, perception and knowledge are each beset by problems of so-called ‘deviant’ causal chains. For each such theory, counterexamples are formed using odd or co-incidental causal chains to establish that the theory is committed to unpalatable claims about some intentional action, about a case of veridical perception or about the acquisition of genuine knowledge. In this paper I will argue that three well-known examples of a deviant causal chain have something in common: they each violate Yablos proportionality (...) constraint on causation. I will argue that this constraint provides the key to saving causal theories from deviant chains. (shrink)

Explanation is usually taken to be a relation between certain entities. The aim of this paper is to discuss what entities are suitable as explanatory relata of singular causal explanations, i.e., explanations concerning singular causality relating particular events or other appropriate entities. I outline three different positions. The purely causal approach stipulates that the same entities that are related in the singular causal relation are also linked by the explanatory relation. This position, however, has a problem to distinguish between causation (...) and explanation, two distinct relations allegedly obtaining between the same entities. The linguistic approach states that explanatory relata are linguistic entities of some sort, e.g., statements, propositions, etc. There are various versions of this position. I deal with two of them and try to show that they are unsatisfactory because they transform explanation into some other type of relation. On the first version, explanation is very close to interpretation or clarification of intension and on the second version it seems to be indistinguishable from an evidential relation or justification. I consider these transformations in understanding explanation unnecessary, and consequently reject linguistic views of explanatory relata. The most promising proposal concerning explanatory relata seems to be the mixed view, according to which propositions explain events or other fitting extra-linguistic entities. (shrink)

Um dos grandes desafios da era da informação consiste em filtrar informações claras, rigorosas e atualizadas sobre tópicos importantes. O mesmo vale para a filosofia. Como encontrar conteúdo filosófico confiável em meio a milhares de artigos publicados diariamente na internet? Para ir ainda mais longe, como encontrar uma introdução a algum tópico com uma lista de referências bibliográficas atualizadas e que seja organizada por um especialista da área? Já que você começou a ler este livro, é provável que tenha ouvido (...) falar em algum momento da Enciclopédia Stanford de Filosofia, disponível gratuitamente na internet desde 1995. A página da Stanford faz exatamente isso. Ela cobre inúmeros verbetes sobre quase tudo em filosofia, oferecendo informação confiável sobre temas como feminismo, filosofia na América Latina, zumbis, metafísica e milhares de outros tópicos. A sugestão típica aos profissionais da filosofia que têm interesse em começar a estudar algum tópico, mas não sabem sequer por onde começar, é procurar pelo verbete relevante da Stanford. Infelizmente, o grande empecilho da página para o nosso contexto é que todos os verbetes estão disponíveis apenas em inglês, algo que cria um obstáculo a inúmeros estudantes e interessados que não dominam a língua. Neste sentido, acreditamos que esta publicação preencha um hiato importante na filosofia brasileira. Embora a filosofia no Brasil tenha se profissionalizado e expandido ao longo dos anos, há ainda lacunas em diversas áreas, e os verbetes foram aqui selecionados cuidadosamente no intuito de preencher ao menos algumas dessas lacunas. Este livro apresenta quatro verbetes cruciais para a filosofia, aqui divididos em quatro capítulos: (1) condições necessárias e suficientes, (2) referência (3) causação e (4) consciência. (shrink)

A main message from the causal modelling literature in the last several decades is that under some plausible assumptions, there can be statistically consistent procedures for inferring (features of) the causal structure of a set of random variables from observational data. But whether we can control the error probabilities with a finite sample size depends on the kind of consistency the procedures can achieve. It has been shown that in general, under the standard causal Markov and Faithfulness assumptions, the procedures (...) can only be pointwise but not uniformly consistent without substantial background knowledge. This implies the impossibility of choosing a finite sample size to control the worst case error probabilities. In this paper, I consider the simpler task of inferring causal directions when the skeleton of the causal structure is known, and establish a similarly negative result concerning the possibility of controlling error probabilities. Although the result is negative in form, it has an interesting positive implication for causal discovery methods. (shrink)

Much of the recent work on the epistemology of causation has centered on two assumptions, known as the Causal Markov Condition and the Causal Faithfulness Condition. Philosophical discussions of the latter condition have exhibited situations in which it is likely to fail. This paper studies the Causal Faithfulness Condition as a conjunction of weaker conditions. We show that some of the weaker conjuncts can be empirically tested, and hence do not have to be assumed a priori. Our results lead to (...) two methodologically significant observations: (1) some common types of counterexamples to the Faithfulness condition constitute objections only to the empirically testable part of the condition; and (2) some common defenses of the Faithfulness condition do not provide justification or evidence for the testable parts of the condition. It is thus worthwhile to study the possibility of reliable causal inference under weaker Faithfulness conditions. As it turns out, the modification needed to make standard procedures work under a weaker version of the Faithfulness condition also has the practical effect of making them more robust when the standard Faithfulness condition actually holds. This, we argue, is related to the possibility of controlling error probabilities with finite sample size (“uniform consistency”) in causal inference. (shrink)

The framework of causal Bayes nets, currently influential in several scientific disciplines, provides a rich formalism to study the connection between causality and probability from an epistemological perspective. This article compares three assumptions in the literature that seem to constrain the connection between causality and probability in the style of Occam's razor. The trio includes two minimality assumptions—one formulated by Spirtes, Glymour, and Scheines (SGS) and the other due to Pearl—and the more well-known faithfulness or stability assumption. In terms of (...) logical strength, it is fairly obvious that the three form a sequence of increasingly stronger assumptions. The focus of this article, however, is to investigate the nature of their relative strength. The comparative analysis reveals an important sense in which Pearl's minimality assumption is as strong as the faithfulness assumption and identifies a useful condition under which it is as safe as SGS's relatively secure minimality assumption. Both findings have notable implications for the theory and practice of causal inference. 1 Introduction2 Background: Inference of Causal Structure in Markovian Causal Models3 Three Assumptions of Simplicity4 A Comparison of P-minimality and Faithfulness5 A Comparison of P-minimality and SGS-minimality6 Methodological Formulations and Prior Knowledge of Causal Order7 Conclusion. (shrink)

This paper presents a counterfactual account of what a mechanism is. Mechanisms consist of parts, the behavior of which conforms to generalizations that are invariant under interventions, and which are modular in the sense that it is possible in principle to change the behavior of one part independently of the others. Each of these features can be captured by the truth of certain counterfactuals.

This paper presents a counterfactual account of what a mechanism is. Mechanisms consist of parts, the behavior of which conforms to generalizations that are invariant under interventions, and which are modular in the sense that it is possible in principle to change the behavior of one part independently of the others. Each of these features can be captured by the truth of certain counterfactuals.

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)

This paper examines the relationship between causality and intrinsicality. Construed in one way, that relationship can be defended against some proposed counterexamples. However, I argue that trumping cases pose a more serious, if not fatal, problem. I then examine an alternative way of thinking about the relationship, but suggest that this too meets the same fate.

Some have argued that our intuitive reactions to a number of cases of moral responsibility can only be preserved at the expense of a unified account of moral responsibility for acts and omissions. I argue against this conclusion, proposing that a plausible condition on responsibility, the Causal Condition can, when properly elaborated, justify the relevant intuitive data.

Within the causal modeling literature, debates about the Causal Faithfulness Condition have concerned whether it is probable that the parameters in causal models will have values such that distinct causal paths will cancel. As the parameters in a model are fixed by the probability distribution over its variables, it is initially puzzling what it means to assign probabilities to these parameters. I propose that to assign a probability to a parameter in a model is to treat that parameter as a (...) function of a variable in an augmented model. By combining this proposal with widely adopted principles regarding which variables must be included in a model, I argue that the various proposed counterexamples to CFC involving coordinated parameters are not genuine counterexamples. I then consider the cases in which CFC fails due not to coordination, but by coincidence, and propose explanatory and predictive bases for ruling out such coincidences without presuming that they are improbable. The aim of the proposed defenses is not to show that CFC never fails, but rather to argue that its use in a particular context may be defended using general modeling assumptions rather than by relying on claims about how often it fails. (shrink)

Nancy Cartwright begins her recent book, Hunting Causes and Using Them, by noting that while a few years ago real causal claims were in dispute, nowadays “causality is back, and with a vengeance.” In the case of the social sciences, Keith Morrison writes that “Social science asks ‘why?’. Detecting causality or its corollary—prediction—is the jewel in the crown of social science research.” With respect to the health sciences, Judea Pearl writes that the “research questions that motivate most studies in the (...) health sciences are causal in nature.” However, not all data used by people interested in making causal claims come from experiments that use random assignment to control and treatment groups. Indeed, much research in the social and health science depends on non-experimental, observational data. Thus, one of the most important problems in the social and health sciences concerns making warranted causal claims using non-experimental, observational data; viz., “Can observational data be used to make etiological inferences leading to warranted causal claims?” This paper examines one method of warranting causal claims that is especially widespread in epidemiology and the health sciences generally—the use of causal criteria. It is argued that cases of complex causation generally, and redundant causation—both causal overdetermination and causal preemption—specifically, undermine the use of such criteria to warrant causal claims. (shrink)

Though common sense says that causes must temporally precede their effects, the hugely influential interventionist account of causation makes no reference to temporal precedence. Does common sense lead us astray? In this paper, I evaluate the power of the commonsense assumption from within the interventionist approach to causal modeling. I first argue that if causes temporally precede their effects, then one need not consider the outcomes of interventions in order to infer causal relevance, and that one can instead use temporal (...) and probabilistic information to infer exactly when X is causally relevant to Y in each of the senses captured by Woodward’s interventionist treatment. Then, I consider the upshot of these findings for causal decision theory, and argue that the commonsense assumption is especially powerful when an agent seeks to determine whether so-called “dominance reasoning” is applicable. (shrink)

When two rocks shatter the window at once, what causes the window to shatter? Is the throwing of each individual rock a cause of the window shattering, or are the throwings only causes collectively? This question bears on the analysis of causation, and the metaphysics of macro-causation. I argue that the throwing of each individual rock is a cause of the window shattering, and generally that individual overdeterminers are causes.

Grounding is often glossed as metaphysical causation, yet no current theory of grounding looks remotely like a plausible treatment of causation. I propose to take the analogy between grounding and causation seriously, by providing an account of grounding in the image of causation, on the template of structural equation models for causation.

Causation is widely assumed to be a binary relation: c causes e. I will argue that causation is a quaternary, contrastive relation: c rather than C* causes e rather than E*, where C* and E* are nonempty sets of contrast events. Or at least, I will argue that treating causation as contrastive helps resolve some paradoxes.

We start this paper by arguing that causality should, in analogy with force in Newtonian physics, be understood as a theoretical concept that is not explicated by a single definition, but by the axioms of a theory. Such an understanding of causality implicitly underlies the well-known theory of causal nets and has been explicitly promoted by Glymour. In this paper we investigate the explanatory warrant and empirical content of TCN. We sketch how the assumption of directed cause–effect relations can be (...) philosophically justified by an inference to the best explanation. We then ask whether the explanations provided by TCN are merely post-facto or have independently testable empirical content. To answer this question we develop a fine-grained axiomatization of TCN, including a distinction of different kinds of faithfulness. A number of theorems show that although the core axioms of TCN are empirically empty, extended versions of TCN have successively increasing empirical content. (shrink)

What is the relationship between moral responsibility and causation? Plainly, we are not morally responsible for everything that we cause. For we cause a multitude of things, including things that we couldn't possibly foresee we would cause and with respect to which we cannot be assessed morally. Thus, it is clear that causing something does not entail being morally responsible for it. But, does the converse entailment hold? Does moral responsibility require causation? Intuitively, it does: intuitively, we can only be (...) morally responsible for things that we cause. (shrink)

In ‘Proportionality in Causation, Part I: Theories’, I presented various ways of understanding the idea that causes which are ‘proportional’ to their effects are in some sense preferable. In this companion article, I discuss the principal applications of the resulting theories of proportionality, and the challenges they face.

How do we determine whether some candidate causal factor is an actual cause of some particular outcome? Many philosophers have wanted a view of actual causation which fits with folk intuitions of actual causation and those who wish to depart from folk intuitions of actual causation are often charged with the task of providing a plausible account of just how and where the folk have gone wrong. In this paper, I provide a range of empirical evidence aimed at showing just (...) how and where the folk go wrong in determining whether an actual causal relation obtains. The evidence suggests that folk intuitions of actual causation are generated by two epistemically defective processes. I situate the empirical evidence within a background discussion of debunking, arguing for a two-pronged debunking explanation of folk intuitions of actual causation. I conclude that those who wish to depart from folk intuitions of actual causation should not be compelled to square their account of actual causation with the verdicts of the folk. In the dispute over actual causation, folk intuitions deserve to be rejected. (shrink)

Frankfurt‐style cases suggest that an agent's moral responsibility for an action supervenes on the causal history of that action—at least when epistemic considerations are held constant. However, PAP‐style cases suggest that moral responsibility does not supervene on causal history, for judgments concerning an agent's responsibility for an action are also sensitive to the presence of alternative—and causally idle—possibilities. I appeal to the causal modeling tradition and the definitions of actual causation that derive therefrom in an attempt to resolve this contradiction. (...) I show that even the weakest definitions of actual causation proposed in the literature establish that some PAP‐style cases constitute genuine counterexamples to the supervenience thesis. I consider several responses to these counterexamples on behalf of the defenders of supervenience and show that they fail. Our best current thinking on causation thus appears to be inconsistent with an intuitive and widely held claim concerning the nature of moral responsibility. (shrink)

This is the first instalment of a two-part paper on the counterfactual theory of causation. It is well known that this theory is ridden with counterexamples. Specifically, the following four features of the theory suffer from problems: it understands causation as a relation between events; counterfactual dependence is understood using a metric of similarity among possible worlds; it defines a non-discriminatory concept of causation; and it understands causation as transitive. A number of philosophers have recently proposed that causation is contrastive (...) because making contrasts explicit defuses counterexamples. A contrastive causal claim has the following form: C rather than C* causes E rather than E*, where C* and E* are alternative or contrast events. In this paper, I show that making contrasts explicit does indeed defuse some counterexamples. However, I also argue that the examples discussed in the literature all share a common feature, viz. that the original causal judgement is ambiguous in one way or another. Contrasting does not help with counterexamples that do not have this feature. Part II of this paper then takes up the hard cases. (shrink)

A probabilistic and counterfactual theory of causality is developed within the framework of branching time. The theory combines ideas developed by James Fetzer, Donald Nute, Patrick Suppes, Ming Xu, John Pollock, David Lewis and Mellor among others.

Pre-emption cases have been taken by almost everyone to imply the unviability of the simple counterfactual theory of causation. Yet there is ample motivation from scientific practice to endorse a simple version of the theory if we can. There is a way in which a simple counterfactual theory, at least if understood contrastively, can be supported even while acknowledging that intuition goes firmly against it in pre-emption cases—or rather, only in some of those cases. For I present several new pre-emption (...) cases in which causal intuition does not go against the counterfactual theory, a fact that has been verified experimentally. I suggest an account of framing effects that can square the circle. Crucially, this account offers hope of theoretical salvation—but only to the counterfactual theory of causation, not to others. Again, there is (admittedly only preliminary) experimental support for this account. (shrink)

Causal contextualism holds that sentences of the form ‘c causes e’ have context-sensitive truth-conditions. We consider four arguments invoked by Jonathan Schaffer in favor of this view. First, he argues that his brand of contextualism helps solve puzzles about transitivity. Second, he contends that how one describes the relata of the causal relation sometimes affects the truth of one’s claim. Third, Schaffer invokes the phenomenon of contrastive focus to conclude that causal statements implicitly designate salient alternatives to the cause and (...) effect. Fourth, he claims that the appropriateness of a causal statement depends on what is contextually taken for granted or made salient. We show that causal invariantism can explain these linguistic data at least as well as contextualism. We then argue that pace Schaffer, some causal sentences are always correct and can never be plausibly denied, regardless of the context. (shrink)

This essay takes up two questions. First, what does it mean to say that someone creates her own luck? At least colloquially speaking, luck is conceived as something out of an agent's control. So how could an agent increase or decrease the likelihood that she'll be lucky? Building on some recent work on the metaphysics of luck, the essay argues that there is a sense in which agents can create their own luck because people with more skill tend to have (...) more opportunities to benefit from luck. Second, what implications does this conception of luck have for related topics such as how we evaluate performances (like shooting an arrow), including coming to know something? The ubiquitous presence of luck in our actions is often underappreciated. The essay argues that when we combine an expected outcomes view of luck with a counterfactual view of causation, the distinction between environmental and intervening veritic luck seems to disappear. We need a more nuanced view of how luck sometimes undermines credit for success in agents' actions. The upshot of this view is that while luck may undermine the creditworthiness of an agent's success, it only partially undermines creditworthiness. (shrink)

It is commonly assumed that causation is transitive and in this paper I aim to reconcile this widely-held assumption with apparent evidence to the contrary. I will discuss a familiar approach to certain well-known counterexamples, before introducing a more resistant sort of case of my own. I will then offer a novel solution, based on Yablo’s proportionality principle, that succeeds in even these more resistant cases. There is a catch, however. Either proportionality is a constraint on which causal claims are (...) true, and the solution works, or it is not and causation is not transitive after all. I will argue that the first horn has unacceptable consequences and should be rejected, but that the second horn is less costly than it might initially appear. (shrink)

What is it for an event not to occur? This is an urgent, yet under explored, question for counterfactual analyses of causation quite generally. In this paper I take a lead from Lewis in identifying two different possible standards of non-occurrence that we might adopt and I argue that we need to apply them asymmetrically: one standard for the cause, another for the effect. This is a surprising result. I then offer a contextualist refinement of the Lewis approach in light (...) of initial problems, and discuss how the asymmetry remained hidden until now. I then relate the non-occurrence problem to issues of transitivity and proportionality in causation, before showing that a parallel problem exists for contrastivist and interventionist approaches to causation too. (shrink)

This paper argues that a counterpart-theoretic treatment of events, combined with a counterfactual theory of causation, can help resolve three puzzles from the causation literature. First, CCT traces the apparent contextual shifts in our causal attributions to shifts in the counterpart relation which obtains in those contexts. Second, being sensitive to shifts in the counterpart relation can help diagnose what goes wrong in certain prominent examples where the transitivity of causation appears to fail. Third, CCT can help us resurrect the (...) much-maligned fragility response to the problems of late pre-emption by understanding fragility in counterpart-theoretic terms. Some reasons to prefer this CCT approach to rivals are discussed. (shrink)

Causal exclusion arguments are taken to threaten the autonomy of the special sciences, and the causal efficacy of mental properties. A recent line of response to these arguments has appealed to “independently plausible” and “well grounded” theories of causation to rebut key premises. In this paper I consider two papers which proceed in this vein and show that they share a common feature: they both require causes to be proportional to their effects. I argue that this feature is a bug, (...) and one that generalises: any attempt to rescue the autonomy of the special sciences, or the efficacy of the mental, from exclusion worries had better not look to proportionality for help. (shrink)

Common sense suggests that counterfactuals are capable of truth and falsity, and that their truth values depend on more than just the actual course of events. Projectivists, like Mackie, deny the first; reductivists, like Lewis, deny the second. I criticize Mackie's and Lewis's theories, thereby defending realism. There are parallel issues and positions concerning the other concepts of the natural necessity family. A realist theory may also have a positive part, consisting of an account of some of the conceptual relations (...) within this family. I try to cast light on the counterfactual by postulating a relation of accessibility between possible worlds - accessibility at the 'point' at which an event occurs. (shrink)

It is natural to think of causes as difference-makers. What exact difference causes make, however, is an open question. In this paper, I argue that the right way of understanding difference-making is in terms of causal processes: causes make a difference to a causal process that leads to the effect. I will show that this way of understanding difference-making nicely captures the distinction between causing an outcome and helping determine how the outcome happens and, thus, explains why causation is not (...) transitive. Moreover, the theory handles tricky cases that are problematic for competing accounts of difference-making. (shrink)

Many theories of actual causation implicitly endorse the claim that if c is an actual cause of e, then either c causes e directly or every intermediary by which c indirectly causes e is itself both an actual cause of e and also an actual effect of c. We think this compositionality constraint is plausible. However, as we show, it is not always satisfied by the causal attributions ordinary people make. We conclude by considering what philosophers working on causation should (...) do when the deliverances of their theories diverge from what ordinary people say. (shrink)

According to the traditional view of the causal structure of a coincidence, the several parts of a coincidence are produced by independent causes. I argue that the traditional view is mistaken; even the several parts of a coincidence may have a common cause. This has important implications for how we think about the relationship between causation and causal explanation—and in particular, for why coincidences cannot be explained.

David Lewis’s counterfactual analysis of cause consisted of the counterfactual conditional closed under transitivity.2 Namely, a sufficient condition for A’s being a cause of C is that ∼A > ∼C be true; and a necessary as well as sufficient condition is that there be a series of true counterfactuals ∼A > ∼E1, ∼E1 > ∼E2, . . . , ∼En >∼C (n > 0).