It is often supposed that the spectacular successes of our modern mathematical sciences support a lofty vision of a world completely ordered by one single elegant theory. In this book Nancy Cartwright argues to the contrary. When we draw our image of the world from the way modern science works - as empiricism teaches us we should - we end up with a world where some features are precisely ordered, others are given to rough regularity and still others behave in (...) their own diverse ways. This patchwork makes sense when we realise that laws are very special productions of nature, requiring very special arrangements for their generation. Combining classic and newly written essays on physics and economics, The Dappled World carries important philosophical consequences and offers serious lessons for both the natural and the social sciences. (shrink)

The Description for this book, Theory and Evidence, will be forthcoming.

Probability is a guide to life partly because it is a guide to causality. Work over the last two decades using Bayes nets supposes that probability is a very sure guide to causality. I think not, and I shall argue that here. Almost all the objections I list are well-known. But I have come to see them in a different light by reflecting again on the original work in this area by Wolfgang Spohn and his recent defense of it in (...) a paper titled “Bayesian Nets Are All There Is to Causality”. (shrink)

Woodward's long awaited book is an attempt to construct a comprehensive account of causation explanation that applies to a wide variety of causal and explanatory claims in different areas of science and everyday life. The book engages some of the relevant literature from other disciplines, as Woodward weaves together examples, counterexamples, criticisms, defenses, objections, and replies into a convincing defense of the core of his theory, which is that we can analyze causation by appeal to the notion of manipulation.

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.

Ever since David Hume, empiricists have barred powers and capacities from nature. In this book Cartwright argues that capacities are essential in our scientific world, and, contrary to empiricist orthodoxy, that they can meet sufficiently strict demands for testability. Econometrics is one discipline where probabilities are used to measure causal capacities, and the technology of modern physics provides several examples of testing capacities (such as lasers). Cartwright concludes by applying the lessons of the book about capacities and probabilities to the (...) explanation of the role of causality in quantum mechanics. (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)

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I propose an amendment of Lewis's counterfactual analysis of causation, designed to overcome some difficulties concerning redundant causation.

In recent years, there has been a philosophical cottage industry producing arguments that our concept of causation is not univocal: that there are in fact two concepts of causation, corresponding to distinct species of causal relation. Papers written in this tradition have borne titles like “Two Concepts of Cause” and “Two Concepts of Causation”. With due apologies to Charles Dickens, I hereby make my own contribution to this genre.

Previous asymptotically correct algorithms for recovering causal structure from sample probabilities have been limited even in sparse graphs to a few variables. We describe an asymptotically correct algorithm whose complexity for fixed graph connectivity increases polynomially in the number of vertices, and may in practice recover sparse graphs with several hundred variables. From..

This essay explains what the Causal Markov Condition says and defends the condition from the many criticisms that have been launched against it. Although we are skeptical about some of the applications of the Causal Markov Condition, we argue that it is implicit in the view that causes can be used to manipulate their effects and that it cannot be surrendered without surrendering this view of causation.

This paper explores the relationship between a manipulability conception of causation and the causal Markov condition (CM). We argue that violations of CM also violate widely shared expectations—implicit in the manipulability conception—having to do with the absence of spontaneous correlations. They also violate expectations concerning the connection between independence or dependence relationships in the presence and absence of interventions.

The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.

The common cause principle states that correlations have prior common causes which screen off those correlations. I argue that the common cause principle is false in many circumstances, some of which are very general. I then suggest that more restricted versions of the common cause principle might hold, and I prove such a restricted version.

Most causal discovery algorithms in the literature exploit an assumption usually referred to as the Causal Faithfulness or Stability Condition. In this paper, we highlight two components of the condition used in constraint-based algorithms, which we call “Adjacency-Faithfulness” and “Orientation- Faithfulness.” We point out that assuming Adjacency-Faithfulness is true, it is possible to test the validity of Orientation- Faithfulness. Motivated by this observation, we explore the consequence of making only the Adjacency-Faithfulness assumption. We show that the familiar PC algorithm has (...) to be modified to be correct under the weaker, Adjacency-Faithfulness assumption. The modified algorithm, called Conservative PC (CPC), checks whether Orientation- Faithfulness holds in the orientation phase, and if not, avoids drawing certain causal conclusions the PC algorithm would draw. Howtion: ever, if the stronger, standard causal Faith-. (shrink)

The paper displays the similarity between the theory of probabilistic causation developed by Glymour et al. since 1983 and mine developed since 1976: the core of both is that causal graphs are Bayesian nets. The similarity extends to the treatment of actions or interventions in the two theories. But there is also a crucial difference. Glymour et al. take causal dependencies as primitive and argue them to behave like Bayesian nets under wide circumstances. By contrast, I argue the behavior of (...) Bayesian nets to be ultimately the defining characteristic of causal dependence. (shrink)

Causality in Macroeconomics examines causality while taking macroeconomics seriously. A pragmatic and realistic philosophy is joined to a macroeconomic foundation that refines Herbert Simon's well-known work on causal order to make a case for a structural approach to causality. The structural approach is used to understand modern rational expectations models, regime switching models, Granger causality, vector autoregressions, the Lucas critique, and concept exogeneity. Techniques of causal inference based on patterns of stability and instability in the face of identified regime changes (...) are developed and illustrated in two empirical case studies. (shrink)

Chris Meek. Strong-Completeness and Faithfulness in Belief Networks.

The faithfulness condition (FC) is a useful principle for inferring causal structure from statistical data. The usual motivation for the FC appeals to theorems showing that exceptions to it have probability zero, provided that some apparently reasonable assumptions obtain. However, some have objected that, the theorems notwithstanding, exceptions to the FC are probable in commonly occurring circumstances. I argue that exceptions to the FC are probable in the circumstances specified by this objection only given the presence of a condition that (...) I label homogeneity, and furthermore that this condition typically does not obtain in the FC’s intended domain of application. (shrink)

A fundamental question in causal inference is whether it is possible to reliably infer the manipulation effects from observational data. There are a variety of senses of asymptotic reliability in the statistical literature, among which the most commonly discussed frequentist notions are pointwise consistency and uniform consistency (see, e.g. Bickel, Doksum [2001]). Uniform consistency is in general preferred to pointwise consistency because the former allows us to control the worst case error bounds with a finite sample size. In the sense (...) of pointwise consistency, several reliable causal inference algorithms have been established under the Markov and Faithfulness assumptions [Pearl 2000, Spirtes et al. 2001]. In the sense of uniform consistency, however, reliable causal inference is impossible under the two assumptions when time order is unknown and/or latent confounders are present [Robins et al. 2000]. In this paper we present two natural generalizations of the Faithfulness assumption in the context of structural equation models, under which we show that the typical algorithms in the literature are uniformly consistent with or without modifications even when the time order is unknown. We also discuss the situation where latent confounders may be present and the sense in which the Faithfulness assumption is a limiting case of the stronger assumptions. (shrink)

S There is a long tradition of representing causal relationships by directed acyclic graphs (Wright, 1934 ). Spirtes ( 1994), Spirtes et al. ( 1993) and Pearl & Verma ( 1991) describe procedures for inferring the presence or absence of causal arrows in the graph even if there might be unobserved confounding variables, and/or an unknown time order, and that under weak conditions, for certain combinations of directed acyclic graphs and probability distributions, are asymptotically, in sample size, consistent. These results (...) are surprising since they seem to contradict the standard statistical wisdom that consistent estimators of causal effects do not exist for nonrandomised studies if there are potentially unobserved confounding variables. We resolve the apparent incompatibility of these views by closely examining the asymptotic properties of these causal inference procedures. We show that the asymptotically consistent procedures are ‘pointwise consistent’, but ‘uniformly consistent’ tests do not exist. Thus, no finite sample size can ever be guaranteed to approximate the asymptotic results. We also show the nonexistence of valid, consistent confidence intervals for causal effects and the nonexistence of uniformly consistent point estimators. Our results make no assumption about the form of the tests or estimators. In particular, the tests could be classical independence tests, they could be Bayes tests or they could be tests based on scoring methods such as  or . The implications of our results for observational studies are controversial and are discussed briefly in the last section of the paper. The results hinge on the following fact: it is possible to find, for each sample size n, distributions P and Q such that P and Q are empirically indistinguishable and yet P and Q correspond to different causal effects. (shrink)

The growing availability of computer power and statistical software has greatly increased the ease with which practitioners apply statistical methods, but this has not been accompanied by attention to checking the assumptions on which these methods are based. At the same time, disagreements about inferences based on statistical research frequently revolve around whether the assumptions are actually met in the studies available, e.g., in psychology, ecology, biology, risk assessment. Philosophical scrutiny can help disentangle 'practical' problems of model validation, and conversely, (...) a methodology of statistical model validation can shed light on a number of issues of interest to philosophers of science. (shrink)