Statistical Theories of Causation

Kim’s causal exclusion argument purports to demonstrate that the non-reductive physicalist must treat mental properties (and macro-level properties in general) as causally inert. A number of authors have attempted to resist Kim’s conclusion by utilizing the conceptual resources of Woodward’s interventionist conception of causation. The viability of these responses has been challenged by Gebharter, who argues that the causal exclusion argument is vindicated by the theory of causal Bayesian networks (CBNs). Since the interventionist conception of causation relies crucially on CBNs (...) for its foundations, Gebharter’s argument appears to cast significant doubt on interventionism’s anti-reductionist credentials. In the present article, we both (1) demonstrate that Gebharter’s CBN-theoretic formulation of the exclusion argument relies on some unmotivated and philosophically significant assumptions (especially regarding the relationship between CBNs and the metaphysics of causal relevance), and (2) use Bayesian networks to develop a general theory of causal inference for multi-level systems that can serve as the foundation for an anti-reductionist interventionist account of causation.1. (shrink)

Cartwright (Synthese 121(1/2):3–27, 1999a; The dappled world, Cambridge University Press, Cambridge, 1999b) attacked the view that causal relations conform to the Markov condition by providing a counterexample in which a common cause does not screen off its effects: the prominent chemical factory. In this paper we suggest a new way to handle counterexamples to Markov causation such as the chemical factory. We argue that Cartwright’s as well as similar scenarios feature a certain kind of non-causal dependence that kicks in once (...) the common cause occurs. We then develop a representation of this specific kind of non-causal dependence that allows for modeling the problematic scenarios in such a way that the Markov condition is not violated anymore. (shrink)

This monograph looks at causal nets from a philosophical point of view. The author shows that one can build a general philosophical theory of causation on the basis of the causal nets framework that can be fruitfully used to shed new light on philosophical issues. Coverage includes both a theoretical as well as application-oriented approach to the subject. The author first counters David Hume’s challenge about whether causation is something ontologically real. The idea behind this is that good metaphysical concepts (...) should behave analogously to good theoretical concepts in scientific theories. In the process, the author offers support for the theory of causal nets as indeed being a correct theory of causation. Next, the book offers an application-oriented approach to the subject. The author shows that causal nets can investigate philosophical issues related to causation. He does this by means of two exemplary applications. The first consists of an evaluation of Jim Woodward’s interventionist theory of causation. The second offers a contribution to the new mechanist debate. Introductory chapters outline all the formal basics required. This helps make the book useful for those who are not familiar with causal nets, but interested in causation or in tools for the investigation of philosophical issues related to causation. (shrink)

The principle of common cause asserts that positive correlations between causally unrelated events ought to be explained through the action of some shared causal factors. Reichenbachian common cause systems are probabilistic structures aimed at accounting for cases where correlations of the aforesaid sort cannot be explained through the action of a single common cause. The existence of Reichenbachian common cause systems of arbitrary finite size for each pair of non-causally correlated events was allegedly demonstrated by Hofer-Szabó and Rédei in 2006. (...) This paper shows that their proof is logically deficient, and we propose an improved proof. (shrink)

Recently, it has been argued that the use of Big Data transforms the sciences, making data-driven research possible and studying causality redundant. In this paper, I focus on the claim on causal knowledge by examining the Big Data project EXPOsOMICS, whose research is funded by the European Commission and considered capable of improving our understanding of the relation between exposure and disease. While EXPOsOMICS may seem the perfect exemplification of the data-driven view, I show how causal knowledge is necessary for (...) the project, both as a source for handling complexity and as an output for meeting the project’s goals. Consequently, I argue that data-driven claims about causality are fundamentally flawed and causal knowledge should be considered a necessary aspect of Big Data science. In addition, I present the consequences of this result on other data-driven claims, concerning the role of theoretical considerations. I argue that the importance of causal knowledge and other kinds of theoretical engagement in EXPOsOMICS undermine theory-free accounts and suggest alternative ways of framing science based on Big Data. (shrink)

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)

Can drinking coffee help people live longer? What makes a stock's price go up? Why did you get the flu? Causal questions like these arise on a regular basis, but most people likely have not thought deeply about how to answer them. This book helps you think about causality in a structured way: What is a cause, what are causes good for, and what is compelling evidence of causality? Author Samantha Kleinberg shows you how to develop a set of tools (...) for thinking more critically about causes. You'll learn how to question claims, identify causes, make decisions based on causal information, and verify causes through further tests. Whether it's figuring out what data you need, or understanding that the way you collect and prepare data affects the conclusions you can draw from it, Why will help you sharpen your causal inference skills. (shrink)

The paper argues that a causal explanation of the correlated outcomes of EPR-type experiments is desirable and possible. It shows how Bohmian mechanics and the GRW mass density theory offer such an explanation in terms of a non-local common cause.

In this paper we show that the application of Occam’s razor to the theory of causal Bayes nets gives us a neat definition of direct causation. In particular we show that Occam’s razor implies Woodward’s (2003) definition of direct causation, provided suitable intervention variables exist and the causal Markov condition (CMC) is satisfied. We also show how Occam’s razor can account for direct causal relationships Woodward style when only stochastic intervention variables are available.

In most academic and non-academic circles throughout history, the world and its operation have been viewed in terms of cause and effect. The principles of causation have been applied, fruitfully, across the sciences, law, medicine, and in everyday life, despite the lack of any agreed-upon framework for understanding what causation ultimately amounts to. In this engaging and accessible introduction to the topic, Douglas Kutach explains and analyses the most prominent theories and examples in the philosophy of causation. The book is (...) organized so as to respect the various cross-cutting and interdisciplinary concerns about causation, such as the reducibility of causation, its application to scientific modeling, its connection to influence and laws of nature, and its role in causal explanation. Kutach begins by presenting the four recurring distinctions in the literature on causation, proceeding through an exploration of various accounts of causation including determination, difference making and probability-raising. He concludes by carefully considering their application to the mind-body problem. _Causation_ provides a straightforward and compact survey of contemporary approaches to causation and serves as a friendly and clear guide for anyone interested in exploring the complex jungle of ideas that surround this fundamental philosophical topic. (shrink)

In recent years part of the literature on probabilistic causality concerned notions stemming from Reichenbach’s idea of explaining correlations between not directly causally related events by referring to their common causes. A few related notions have been introduced, e.g. that of a “common cause system” (Hofer-Szabó and Rédei in Int J Theor Phys 43(7/8):1819–1826, 2004) and “causal (N-)closedness” of probability spaces (Gyenis and Rédei in Found Phys 34(9):1284–1303, 2004; Hofer-Szabó and Rédei in Found Phys 36(5):745–756, 2006). In this paper we (...) introduce a new and natural notion similar to causal closedness and prove a number of theorems which can be seen as extensions of earlier results from the literature. Most notably we prove that a finite probability space is causally closed in our sense iff its measure is uniform. We also present a generalisation of this result to a class of non-classical probability spaces. (shrink)

Using a variety of different results from the literature, I show how causal discovery with experiments is limited unless substantive assumptions about the underlying causal structure are made. These results undermine the view that experiments, such as randomized controlled trials, can independently provide a gold standard for causal discovery. Moreover, I present a concrete example in which causal underdetermination persists despite exhaustive experimentation and argue that such cases undermine the appeal of an interventionist account of causation as its dependence on (...) other assumptions is not spelled out. (shrink)

The Principle of the Common Cause is usually understood to provide causal explanations for probabilistic correlations obtaining between causally unrelated events. In this study, an extended interpretation of the principle is proposed, according to which common causes should be invoked to explain positive correlations whose values depart from the ones that one would expect to obtain in accordance to her probabilistic expectations. In addition, a probabilistic model for common causes is tailored which satisfies the generalized version of the principle, at (...) the same time including the standard conjunctive-fork model as a special case. (shrink)

Concrete Causation centers about theories of causation, their interpretation, and their embedding in metaphysical-ontological questions, as well as the application of such theories in the context of science and decision theory. The dissertation is divided into four chapters, that firstly undertake the historical-systematic localization of central problems (chapter 1) to then give a rendition of the concepts and the formalisms underlying David Lewis' and Judea Pearl's theories (chapter 2). After philosophically motivated conceptual deliberations Pearl's mathematical-technical framework is drawn on for (...) an epistemic interpretation and for emphasizing the knowledge-organizing aspect of causality in an extension of the interventionist Bayes net account of causation (chapter 3). Integrating causal and non-causal knowledge in unified structures ultimately leads to an approach towards solving problems of (causal) decision theory and at the same time facilitates the representation of logical-mathematical, synonymical, as well as reductive relationships in efficiently structured, operational nets of belief propagation (chapter 4). (shrink)

The starting point in the development of probabilistic analyses of token causation has usually been the naïve intuition that, in some relevant sense, a cause raises the probability of its effect. But there are well-known examples both of non-probability-raising causation and of probability-raising non-causation. Sophisticated extant probabilistic analyses treat many such cases correctly, but only at the cost of excluding the possibilities of direct non-probability-raising causation, failures of causal transitivity, action-at-a-distance, prevention, and causation by absence and omission. I show that (...) an examination of the structure of these problem cases suggests a different treatment, one which avoids the costs of extant probabilistic analyses. (shrink)

We present a probabilistic extension to active path analyses of token causation (Halpern & Pearl 2001, forthcoming; Hitchcock 2001). The extension uses the generalized notion of intervention presented in (Korb et al. 2004): we allow an intervention to set any probability distribution over the intervention variables, not just a single value. The resulting account can handle a wide range of examples. We do not claim the account is complete --- only that it fills an obvious gap in previous active-path approaches. (...) It still succumbs to recent counterexamples by Hiddleston (2005), because it does not explicitly consider causal processes. We claim three benefits: a detailed comparison of three active-path approaches, a probabilistic extension for each, and an algorithmic formulation. (shrink)

Suppose that two geysers, about one mile apart, erupt at irregular intervals, but usually erupt almost exactly at the same time. One would suspect that they come from a common source, or at least that there is a common cause of their eruptions. And this common cause surely acts before both eruptions take place. This idea, that simultaneous correlated events must have prior common causes, was first made precise by Hans Reichenbach (Reichenbach 1956). It can be used to infer the (...) existence of unobserved and unobservable events, and to infer causal relations from statistical relations. Unfortunately it does not appear to be universally valid, nor is there agreement as to the circumstances in which it is valid. (shrink)

A definition of causation as probability-raising is threatened by two kinds of counterexample: first, when a cause lowers the probability of its effect; and second, when the probability of an effect is raised by a non-cause. In this paper, I present an account that deals successfully with problem cases of both these kinds. In doing so, I also explore some novel implications of incorporating into the metaphysical investigation considerations of causal psychology.

The aim of this talk unpublished until now, and that constitutes the last contribution of the author to this topic, is to show how Hans Reichenbach’s work “Die Kausalstruktur der Welt und der Unterschied zwischen Vergangenheit und Zukunft” , published in 1925, and significantly expanded and revised in the posthumously published book in 1956, The Direction of Time, inspires substantially part of the work that is carried out in the domain of causality at the beginning of the twenty first century.

In this paper we give a positive answer to a problem posed by Hofer-Szabó and Rédei (Int. J. Theor. Phys. 43:1819–1826, 2004) regarding the existence of infinite Reichenbachian common cause systems (RCCSs). An example of a countably infinite RCCS is presented. It is also determined that no RCCSs of greater cardinality exist.

Experimental studies suggest that people’s ordinary causal judgments are affected not only by statistical considerations but also by moral considerations. One way to explain these results would be to construct a model according to which people are trying to make a purely statistical judgment but moral considerations somehow distort their intuitions. The present paper offers an alternative perspective. Specifically, the author proposes a model according to which the very same underlying mechanism accounts for the influence of both statistical and moral (...) considerations. On this model, it appears that ordinary causal judgments are quite different from the sorts of judgments one might find in the systematic sciences.Keywords: Causation; Causal cognition; Experimental philosophy; Cognitive science. (shrink)

This paper deals with causal analysis in the social sciences. We first present a conceptual framework according to which causal analysis is based on a rationale of variation and invariance, and not only on regularity. We then develop a formal framework for causal analysis by means of structural modelling. Within this framework we approach causality in terms of exogeneity in a structural conditional model based which is based on (i) congruence with background knowledge, (ii) invariance under a large variety of (...) environmental changes, and (iii) model fit. We also tackle the issue of confounding and show how latent confounders can play havoc with exogeneity. This framework avoids making untestable metaphysical claims about causal relations and yet remains useful for cognitive and action-oriented goals. (shrink)

We offer a review of some of the most influential views on the status of Reichenbach’s Principle of the Common Cause (RPCC) for genuinely indeterministic systems. We first argue that the RPCC is properly a conjunction of two distinct claims, one metaphysical and another methodological. Both claims can and have been contested in the literature, but here we simply assume that the metaphysical claim is correct, in order to focus our analysis on the status of the methodological claim. We briefly (...) review the most entrenched or classical positions, including Salmon’s ‘interactive forks’, van Fraassen’s scepticism, and Cartwright’s generalisation of the fork criterion. We then go on to review the results of the ‘Budapest school’ on the existence of formally defined screening­ off events for any correlation —by means of the ideas of probability space extensibility and (Reichenbachian common cause) completability. We distinguish the Budapest doctrine clearly from any of the classical conceptions, and thus present an overall framework for discussions of causal inference in quantum mechanics. We argue that this review is preliminary essential work for a thorough assessment of the conditions under which RCCP may be a reliable tool for causal inference in a genuinely probabilistic (indeterministic) context. (shrink)

This chapter provides an overview of a range of probabilistic theories of causality, including those of Reichenbach, Good and Suppes, and the contemporary causal net approach. It discusses two key problems for probabilistic accounts: counterexamples to these theories and their failure to account for the relationship between causality and mechanisms. It is argued that to overcome the problems, an epistemic theory of causality is required.

It is often argued that no local common cause models of EPR correlation exist. However, Szabó and Rédei pointed out that such arguments have the tacit assumption that plural correlations have the same common causes. Furthermore, Szabó showed that for EPR correlation a local common cause model in his sense exists. One of his requirements is that common cause events are statistically independent of apparatus settings on each side. However, as Szabó knows, to meet this requirement does not entail that (...) different combinations of common cause events (e.g. meet and join in lattice-theoretic terminology) are statistically independent of measurement settings. This further condition is formulated in two ways. First, the apparatus settings are completely independent of such combinations. Second, the apparatus settings on each side are independent of such combinations. Does a common cause model which meets the former and the latter respectively exist? This problem is considered. In particular, the latter version is Szabó’s and Rédei’s open problem. Negative answers are given to both versions. (shrink)

Standard derivations of the Bell inequalities assume a common common cause system that is a common screener-off for all correlations and some additional assumptions concerning locality and no-conspiracy. In a recent paper (Grasshoff et al., 2005) Bell inequalities have been derived via separate common causes assuming perfect correlations between the events. In the paper it will be shown that the assumptions of this separate-common-cause-type derivation of the Bell inequalities in the case of perfect correlations can be reduced to the assumptions (...) of common-common-cause-system-type derivation. However, in the case of non-perfect correlations a non-reducible separate-common-cause-type derivation of some Bell-like inequalities can be given. The violation of these Bell-like inequalities proves Szabó's (2000) conjecture concerning the non-existence of a local, non-conspiratorial, separate-common-cause-model for a delta δ-neighborhood of perfect EPR correlations. (shrink)

Nancy Cartwright believes that we live in a Dappled World– a world in which theories, principles, and methods applicable in one domain may be inapplicable in others; in which there are no universal principles. One of the targets of Cartwright’s arguments for this conclusion is the Causal Markov condition, a condition which has been proposed as a universal condition on causal structures.1 The Causal Markov condition, Cartwright argues, is applicable only in a limited domain of special cases, and thus cannot (...) be used as a universal principle in causal discovery. I have no dispute with any of these claims here. Rather, I wish to argue for a very limited thesis: that the Causal Markov condition is applicable in the specific domain of microscopic quantum mechanical systems; further, that the condition can fruitfully be applied to the much discussed EPR setup. This is perhaps a surprising conclusion, for it is precisely in this domain that Cartwright’s arguments against the Causal Markov condition have been considered to be the most successful. (shrink)

Despite recent efforts to improve on counterfactual theories of causation, failures to explain how effects depend on their causes are still manifest in a variety of cases. In particular, theories that do a decent job explaining cases of causal preemption have problems accounting for cases of causal intransitivity. Moreover, the increasing complexity of the counterfactual accounts makes it difficult to see why the concept of causation would be such a central part of our cognition. In this paper, I propose an (...) account of our causal thinking that not only explains the hitherto puzzling variety of causal judgments, but also makes it intelligible why we would employ such an elusive concept. (shrink)

Understanding causal structure is a central task of human cognition. Causal learning underpins the development of our concepts and categories, our intuitive theories, and our capacities for planning, imagination and inference. During the last few years, there has been an interdisciplinary revolution in our understanding of learning and reasoning: Researchers in philosophy, psychology, and computation have discovered new mechanisms for learning the causal structure of the world. This new work provides a rigorous, formal basis for theory theories of concepts and (...) cognitive development, and moreover, the causal learning mechanisms it has uncovered go dramatically beyond the traditional mechanisms of both nativist theories, such as modularity theories, and empiricist ones, such as association or connectionism. (shrink)

In 1935, Einstein, Podolsky, and Rosen (EPR) published an important paper in which they claimed that the whole formalism of quantum mechanics together with what they called a “Reality Criterion” imply that quantum mechanics cannot be complete. That is, there must exist some elements of reality that are not described by quantum mechanics. They concluded that there must be a more complete description of physical reality involving some hidden variables that can characterize the state of affairs in the world in (...) more detail than the quantum mechanical state. This conclusion leads to paradoxical results. -/- As Bell proved in 1964, under some further but quite plausible assumptions, this conclusion that there are hidden variables implies that, in some spin-correlation experiments, the measured quantum mechanical probabilities should satisfy particular inequalities (Bell-type inequalities). The paradox consists in the fact that quantum probabilities do not satisfy these inequalities. And this paradoxical fact has been confirmed by several laboratory experiments since the 1970s. -/- Some researchers have interpreted this result as showing that quantum mechanics is telling us nature is non-local, that is, that particles can affect each other across great distances in a time too brief for the effect to have been due to ordinary causal interaction. Others object to this interpretation, and the problem is still open and hotly debated among both physicists and philosophers. It has motivated a wide range of research from the most fundamental quantum mechanical experiments through foundations of probability theory to the theory of stochastic causality as well as the metaphysics of free will. (shrink)

A partition $\{C_i\}_{i\in I}$ of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite (...) natural number n > 2, the probability space (Ω,p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation. (shrink)

Standard statistical measures of strength of association, although pioneered by Pearson deliberately to be acausal, nowadays are routinely used to measure causal efficacy. But their acausal origins have left them ill suited to this latter purpose. I distinguish between two different conceptions of causal efficacy, and argue that: 1) Both conceptions can be useful 2) The statistical measures only attempt to capture the first of them 3) They are not fully successful even at this 4) An alternative definition more squarely (...) based on causal thinking not only captures the second conception, it can also capture the first one better too. (shrink)

Is the common cause principle merely one of a set of useful heuristics for discovering causal relations, or is it rather a piece of heavy duty metaphysics, capable of grounding the direction of causation itself? Since the principle was introduced in Reichenbach’s groundbreaking work The Direction of Time (1956), there have been a series of attempts to pursue the latter program—to take the probabilistic relationships constitutive of the principle of the common cause and use them to ground the direction of (...) causation. These attempts have not all explicitly appealed to the principle as originally formulated; it has also appeared in the guise of independence conditions, counterfactual overdetermination, and, in the causal modelling literature, as the causal markov condition. In this paper, I identify a set of difficulties for grounding the asymmetry of causation on the principle and its descendents. The first difficulty, concerning what I call the vertical placement of causation, consists of a tension between considerations that drive towards the macroscopic scale, and considerations that drive towards the microscopic scale—the worry is that these considerations cannot both be comfortably accommodated. The second difficulty consists of a novel potential counterexample to the principle based on the familiar Einstein Podolsky Rosen (EPR) correlations in quantum mechanics. (shrink)

Opening Remarks of the Chairman at “Wesley C. Salmon, 1925–2001”: A Symposium Honoring his Contributions to the Philosophy of Science.

I argue that the orthodox account of probabilistic causation, on which probabilistic causes determine the probability of their effects, is inconsistent with certain ontological assumptions implicit in scientific practice. In particular, scientists recognize the possibility that properties of populations can cause the behavior of members of the populations. Such emergent population‐level causation is metaphysically impossible on the orthodoxy.

Elliot Sober ([2001]) forcefully restates his well-known counterexample to Reichenbach's principle of the common cause: bread prices in Britain and sea levels in Venice both rise over time and are, therefore, correlated; yet they are ex hypothesi not causally connected, which violates the principle of the common cause. The counterexample employs nonstationary data—i.e., data with time-dependent population moments. Common measures of statistical association do not generally reflect probabilistic dependence among nonstationary data. I demonstrate the inadequacy of the counterexample and of (...) some previous responses to it, as well as illustrating more appropriate measures of probabilistic dependence in the nonstationary case. A challenge to the principle of the common causeSober's argument and the attempts to rescue the principleProbabilistic dependenceNonstationary time seriesProbabilistic dependence in nonstationary time seriesDo Venetian sea levels and British bread prices violate the principle of the common cause? (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.

My dissertation defends the theory of probabilistic causation called "the unanimity theory" against three challenges, which I call "the metaphysical challenge", "the conceptual challenge" and "the methodological challenge". I argue that the unanimity theory meets these three challenges, and coheres with each of the three theories of probabilistic causation that have been naturally inspired by the three challenges. I conclude that the unanimity theory constitutes a foundation of the three theories, which in fact reveals the versatility of the unanimity theory. (...) ;In Chapter 1, I introduce the conceptual foundations of the theory of type-level probabilistic causation called "the unanimity theory". I critically examine John Dupre's theory and his objections to the unanimity theory. ;In Chapter 2, I discuss the "metaphysical challenge" to the unanimity theory. According to Nancy Cartwright, the unanimity theory does not fully reveal the "capacities" that causal laws assume. I argue that the unanimity theory in fact reveals these capacities. ;In Chapter 3, I discuss the "conceptual challenge" to the unanimity theory. According to Christopher Hitchcock, the comparison of the probability of a factor Y in the presence of a factor X with the probability of Y in the absence of X does not provide us with appropriate information about causal relevance. Hitchcock proposes a different theory of probabilistic causation called "the ternary theory." I argue that the unanimity theory meets the problems Hitchcock poses for it. I argue that the unanimity theory explicates the same causal relevance relations that the ternary theory is intended to explicate. ;In Chapter 4, I discuss the "methodological challenge" to the unanimity theory. According to Daniel Hausman, the unanimity theory cannot guide an agent's decision in two kinds of epistemic circumstances. The challenge requires us to consider a new theory called "the theory of irregular causation". I elucidate the pragmatic significance of the theory of irregular causation and the relation between the two theories, and conclude that the unanimity theory constitutes a foundation of the theory of irregular causation. (shrink)