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)

By combining experimental interventions with search procedures for graphical causal models we show that under familiar assumptions, with perfect data, N - 1 experiments suffice to determine the causal relations among N > 2 variables when each experiment randomizes at most one variable. We show the same bound holds for adaptive learners, but does not hold for N > 4 when each experiment can simultaneously randomize more than one variable. This bound provides a type of ideal for the measure of (...) success of heuristic approached in active learning methods of casual discovery, which currently use less informative measures. (shrink)

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)

Randomized controlled trials (RCTs) are widely taken as the gold standard for establishing causal conclusions. Ideally conducted they ensure that the treatment ‘causes’ the outcome—in the experiment. But where else? This is the venerable question of external validity. I point out that the question comes in two importantly different forms: Is the specific causal conclusion warranted by the experiment true in a target situation? What will be the result of implementing the treatment there? This paper explains how the probabilistic theory (...) of causality implies that RCTs can establish causal conclusions and thereby provides an account of what exactly that causal conclusion is. Clarifying the exact form of the conclusion shows just what is necessary for it to hold in a new setting and also how much more is needed to see what the actual outcome would be there were the treatment implemented. (shrink)

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

Non-reductive interventionist theories of causation and methodologies of causal reasoning embedded in that theoretical framework have become increasingly popular in recent years. This paper argues that one variant of an interventionist account of causation, viz. the one presented, for example, in Woodward (2003 ), is unsuited as a theoretical fundament of interventionist methodologies of causal reasoning, because it renders corresponding methodologies incapable of uncovering a causal structure in a finite number of steps. This finding runs counter to Woodward's own assessment (...) and to other recent studies which presume that Woodward's version of interventionism is effectively applicable to uncover causal structures, e.g. Campbell (2007 ) or Shapiro and Sober (2007 ). (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.

The literature on causal discovery has focused on interventions that involve randomly assigning values to a single variable. But such a randomized intervention is not the only possibility, nor is it always optimal. In some cases it is impossible or it would be unethical to perform such an intervention. We provide an account of ‘hard' and ‘soft' interventions and discuss what they can contribute to causal discovery. We also describe how the choice of the optimal intervention(s) depends heavily on the (...) particular experimental setup and the assumptions that can be made. ‡The first author is funded by the Causal Learning Collaborative Initiative supported by the James S. McDonnell Foundation. Many aspects of this paper were inspired by discussions with members of the collaborative. †To contact the authors, please write to: Department of Philosophy, Carnegie Mellon University, Pittsburgh, PA 15213; e-mail: [email protected] and [email protected]. (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)

In this important book, Ellery Eells explores and refines philosophical conceptions of probabilistic causality. In a probabilistic theory of causation, causes increase the probability of their effects rather than necessitate their effects in the ways traditional deterministic theories have specified. Philosophical interest in this subject arises from attempts to understand population sciences as well as indeterminism in physics. Taking into account issues involving spurious correlation, probabilistic causal interaction, disjunctive causal factors, and temporal ideas, Professor Eells advances the analysis of what (...) it is for one factor to be a positive causal factor for another. A salient feature of the book is a theory of token level probabilistic causation in which the evolution of the probability of a later event from an earlier event is central. This will be a book of crucial significance to philosophers of science and metaphysicians; it will also prove stimulating to many economists, psychologists, and physicists. (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, defences, objections, and replies into a convincing defence of the core of his theory, which is that we can analyse causation by appeal to the notion of manipulation.

Causal discovery becomes especially challenging when the possibility of latent confounding and/or selection bias is not assumed away. For this task, ancestral graph models are particularly useful in that they can represent the presence of latent confounding and selection effect, without explicitly invoking unobserved variables. Based on the machinery of ancestral graphs, there is a provably sound causal discovery algorithm, known as the FCI algorithm, that allows the possibility of latent confounders and selection bias. However, the orientation rules used in (...) the algorithm are not complete. In this paper, we provide additional orientation rules, augmented by which the FCI algorithm is shown to be complete, in the sense that it can, under standard assumptions, discover all aspects of the causal structure that are uniquely determined by facts of probabilistic dependence and independence. The result is useful for developing any causal discovery and reasoning system based on ancestral graph models. (shrink)

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

Nancy Cartwright's recent criticisms of efforts and methods to obtain causal information from sample data using automated search are considered. In addition to reviewing that effort, I argue that almost all of her criticisms are false and rest on misreading, overgeneralization, or neglect of the relevant literature.

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)

Methodological reductionists practice ‘wannabe reductionism’. They claim that one should pursue reductionism, but never propose how. I integrate two strains in prior work to do so. Three kinds of activities are pursued as “reductionist”. “Successional reduction” and inter-level mechanistic explanation are legitimate and powerful strategies. Eliminativism is generally ill-conceived. Specific problem-solving heuristics for constructing inter-level mechanistic explanations show why and when they can provide powerful and fruitful tools and insights, but sometimes lead to erroneous results. I show how traditional metaphysical (...) approaches fail to engage how science is done. The methods used do so, and support a pragmatic and non-eliminativist realism. (shrink)

The Dappled World: A Study of the Boundaries of Science. nancy cartwright. Plato's Reception of Parmenides. john a. palmer.

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)

For nearly as long as the word “correlation” has been part of statistical parlance, students have been warned that correlation does not prove causation, and that only experimental studies, e.g., randomized clinical trials, can establish the existence of a causal relationship. Over the last few decades, somewhat of a consensus has emerged between statisticians, computer scientists, and philosophers on how to represent causal claims and connect them to probabilistic relations. One strand of this work studies the conditions under which evidence (...) accumulated from non-experimental (observational) studies can be used to infer a causal relationship. In this paper, I compare the typical conditions required to infer that one variable is a direct cause of another in observational and experimental studies. I argue that they are essentially the same. (shrink)

Whenever the use of non-experimental data for discovering causal relations or predicting the outcomes of experiments or interventions is contemplated, two difficulties are routinely faced. One is the problem of latent variables, or confounders: factors influencing two or more measured variables may not themselves have been measured or recorded. The other is the problem of sample selection bias: values of the variables or features under study may themselves influence whether a unit is included in the data sample.

We further develop the mathematical theory of causal interventions, extending earlier results of Korb, Twardy, Handfield, & Oppy, (2005) and Spirtes, Glymour, Scheines (2000). Some of the skepticism surrounding causal discovery has concerned the fact that using only observational data can radically underdetermine the best explanatory causal model, with the true causal model appearing inferior to a simpler, faithful model (cf. Cartwright, (2001). Our results show that experimental data, together with some plausible assumptions, can reduce the space of viable explanatory (...) causal models to one. (shrink)

How should we reason with causal relationships? Much recent work on this question has been devoted to the theses (i) that Bayesian nets provide a calculus for causal reasoning and (ii) that we can learn causal relationships by the automated learning of Bayesian nets from observational data. The aim of this book is to..

The problem facing us in this paper is that of how to analyze the notion of causal relevance. This is the inverse relation of causal dependence: A is causally irrelevant to C iff C is causally independent of A. As an example of causal relevance, consider: Example 1: A - The American astronaut on Mir scratched his left ear exactly an hour ago B - I am writing this paper right now. Intuitively, A was not causally relevant to B. It (...) is this kind of intuition that I’ll mostly be relying on when analyzing the notion of causal relevance. (shrink)

There have been many efforts to infer causation from association byusing statistical models. Algorithms for automating this processare a more recent innovation. In Humphreys and Freedman[(1996) British Journal for the Philosophy of Science 47, 113–123] we showed that one such approach, by Spirtes et al., was fatally flawed. Here we put our arguments in a broader context and reply to Korb and Wallace [(1997) British Journal for thePhilosophy of Science 48, 543–553] and to Spirtes et al.[(1997) British Journal for the (...) Philosophy of Science 48, 555–568]. Their arguments leave our position unchanged: claims to have developed a rigorous engine for inferring causation from association are premature at best, the theorems have no implications for samples of any realistic size, and the examples used to illustrate the algorithms are indicative of failure rather than success. The gap between association and causation has yet to be bridged. (shrink)