Functional robustness refers to a system’s ability to maintain a function in the face of perturbations to the causal structures that support performance of that function. Modularity, a crucial element of standard methods of causal inference and difference-making accounts of causation, refers to the independent manipulability of causal relationships within a system. Functional robustness appears to be at odds with modularity. If a function is maintained despite manipulation of some causal structure that supports that function, then the relationship between that (...) structure and function fails to be manipulable independent of other causal relationships within the system. Contrary to this line of reasoning, I argue that functional robustness often attends feedback control, rather than failures of modularity. Feedback control poses its own challenges to causal explanation and inference, but those challenges do not undermine modularity—and indeed, modularity is crucial to grappling with them. (shrink)

The manipulationist account of causation provides a conceptual analysis of cause-effect relationships in terms of hypothetical experiments. It also explains why and how experiments are used for the empirical testing of causal claims. This paper attempts to apply the manipulationist account of causation to a broader range of experiments—a range that extends beyond experiments explicitly designed for the testing of causal claims. I aim to show that the set of causal inferences afforded by an experiment is determined solely on the (...) basis of contrasting case structures that I call “experimental series”, and that the conditions that suffice for causal inference obtain quite commonly, even among “ordinary” experiments that are not explicitly designed for the testing of causal claims. (shrink)

In the causal inference framework of Spirtes, Glymour, and Scheines, inferences about causal relationships are made from samples from probability distributions and a number of assumptions relating causal relations to probability distributions. The most controversial of these assumptions is the Causal Faithfulness Assumption, which roughly states that if a conditional independence statement is true of a probability distribution generated by a causal structure, it is entailed by the causal structure and not just for particular parameter values. In this paper we (...) show that the addition of the Causal Faithfulness Assumption plays three quite different roles in the SGS framework: it reduces the degree of underdetermination of causal structure by probability distribution; computationally, it justifies reliable causal inference algorithms that would otherwise have to be slower in order to be reliable; and statistically, it implies that those algorithms reliably obtain the correct answer at smaller sample sizes than would otherwise be the case. We also consider a number of variations on the Causal Faithfulness Assumption, and show how they affect each of these three roles. (shrink)

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)

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)

I would like to congratulate James Woodward for another landmark accomplishment, after publishing his Making things happen: A theory of causal explanation. Making things happen gives an elegant interventionist theory for understanding explanation and causation. The new contribution relies on that theory and further makes a big step towards empirical inference of causal relations from non-experimental data. In this paper, I will focus on some of the emerging computational methods for finding causal relations from non-experimental data and attempt to complement (...) Woodward's contribution with discussions on 1) how these methods are connected to the interventionist theory of causality, 2) how informative the output of the methods is, including whether they output directed causal graphs and how they deal with confounders, and 3) the assumptions underlying the asymptotic correctness of the output of the methods about causal relations. Different causal discovery methods may rely on different aspects of the joint distribution of the data, and this discussion aims to provide a technical account of the assumptions. (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)

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)

Jim Joyce has argued that David Lewis’s formulation of causal decision theory is inadequate because it fails to apply to the “small world” decisions that people face in real life. Meanwhile, several authors have argued that causal decision theory should be developed such that it integrates the interventionist approach to causal modeling because of the expressive power afforded by the language of causal models, but, as of now, there has been little work towards this end. In this paper, I propose (...) a variant of Lewis’s causal decision theory that is intended to meet both of these demands. Specifically, I argue that Lewis’s causal decision theory can be rendered applicable to small world decisions if one analyzes his dependency hypotheses as causal hypotheses that depend on the interventionist causal modeling framework for their semantics. I then argue that this interventionist variant of Lewis’s causal decision theory is preferable to interventionist causal decision theories that purportedly generalize Lewis’s through the use of conditional probabilities. This is because Lewisian interventionist decision theory captures the causal decision theorist’s conviction that any correlation between what the agent does and cannot cause should be irrelevant to the agent’s choice, while purported generalizations do not. (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)

We clarify the status of the so-called causal minimality condition in the theory of causal Bayesian networks, which has received much attention in the recent literature on the epistemology of causation. In doing so, we argue that the condition is well motivated in the interventionist (or manipulability) account of causation, assuming the causal Markov condition which is essential to the semantics of causal Bayesian networks. Our argument has two parts. First, we show that the causal minimality condition, rather than an (...) add-on methodological assumption of simplicity, necessarily follows from the substantive interventionist theses, provided that the actual probability distribution is strictly positive. Second, we demonstrate that the causal minimality condition can fail when the actual probability distribution is not positive, as is the case in the presence of deterministic relationships. But we argue that the interventionist account still entails a pragmatic justification of the causal minimality condition. Our argument in the second part exemplifies a general perspective that we think commendable: when evaluating methods for inferring causal structures and their underlying assumptions, it is relevant to consider how the inferred causal structure will be subsequently used for counterfactual reasoning. (shrink)

We begin by considering two principles, each having the form causal completeness ergo screening-off. The first concerns a common cause of two or more effects; the second describes an intermediate link in a causal chain. They are logically independent of each other, each is independent of Reichenbach's principle of the common cause, and each is a consequence of the causal Markov condition. Simple examples show that causal incompleteness means that screening-off may fail to obtain. We derive a stronger result: in (...) a rather general setting, if the composite cause C1 & C2 & … & Cn screens-off one event from another, then each of the n component causes C1, C2, …, Cn must fail to screen-off. The idea that a cause may be ordinally invariant in its impact on different effects is defined; it plays an important role in establishing this no-go theorem. Along the way, we describe how composite and component causes can all screen-off when ordinal invariance fails. We argue that this theorem is relevant to assessing the plausibility of the two screening-off principles. The discovery of incomplete causes that screen-off is not evidence that causal completeness must engender screening-off. Formal and epistemic analogies between screening-off and determinism are discussed. (shrink)

This article suggests a revision of the theory of causal nets. In section 1 we introduce an axiomatization of TCN based on a realistic understanding. It is shown that the causal Markov condition entails three independent principles. In section 2 we analyze indeterministic decay as the major counterexample to one of these principles: screening off by common causes. We call SCC-violating common causes interactive causes. In section 3 we develop a revised version of TCN, called TCN*, which accounts for interactive (...) causes. It is shown that there are interactive causal models that admit of no faithful noninteractive reconstruction. (shrink)

Two key ideas of scientific explanation−explanation as causal information and explanation as unification-have frequently been set into mutual opposition. This paper proposes a “dialectical solution” to this conflict, by arguing that causal explanations are preferable to non-causal ones, because they lead to a higherdegree of unification at the level of explaining statistical regularities. The core axioms of the theory of causal nets (TC) are justified because they offer the best if not the only unifying explanation of two statistical phenomena: screening (...) off and linking up. Alternative explanations of the two phenomena are discussed and it isshown why they don’t work. It is demonstrated that although the core axioms of TC are empirically vacuous, extended versions of TC have empirical content by means of which they can generate independently testable predictions.Con frecuencia se han planteado como contrapuestas dos ideas clave en la explicacion cientifica (explicacion como informacion causal y explicacion como unificacion). El presente articulo propone una “solucion dialectica” argumentando que las explicaciones causales son preferibles a las no-causales porque aquellas comportan un mayor grado de unificacion en la explicacion de regularidades estadisticas. Los axiomas centrales de la teoria de redes causales (TC) estan justificados porque ofrecen la mejor, si no la unica, explicacion unificada de dos fenomenos estadisticos: neutralizacion (screening off) y vinculacion (linking up). Se discuten las explicaciones alternativas de estos dos fenomenos y se razona por que no funcionan. Se demuestra ademas que aunque los axiomas centrales de TC son empiricamente vacuos, las versiones extendidas de TC tienen un contenido empirico gracias al cual pueden generar predicciones independientemente contrastables. (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)

Many investigations into the world, including philosophical ones, aim to discover causal knowledge, and many experimental methods have been developed to assist in causal discovery. More recently, algorithms have emerged that can also learn causal structure from purely or mostly observational data, as well as experimental data. These methods have started to be applied in various philosophical contexts, such as debates about our concepts of free will and determinism. This paper provides a “user's guide” to these methods, though not in (...) the sense of specifying exact button presses in a software package. Instead, we explain the larger “pipeline” within which these methods are used and discuss key steps in moving from initial research idea to validated causal structure. (shrink)

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.

Some writers have urged that evolutionary theory produces generalizations that hold only ceteris paribus, that is, provided “everything else is equal.” Others have claimed that all laws in the special sciences, or even all laws in science generally, hold only ceteris paribus. However, if we lack a way to determine when everything else really is equal, hedging generalizations with the phrase ceteris paribus renders those generalizations vacuous. I propose a solution to this problem for the case of causal equations from (...) classical population genetics. When coupled with the right proviso, equations in classical population genetics function as strict laws. (shrink)

In this paper I argue that constitutive relevance relations in mechanisms behave like a special kind of causal relation in at least one important respect: Under suitable circumstances constitutive relevance relations produce the Markov factorization. Based on this observation one may wonder whether standard methods for causal discovery could be fruitfully applied to uncover constitutive relevance relations. This paper is intended as a first step into this new area of philosophical research. I investigate to what extent the PC algorithm, originally (...) developed for causal search, can be used for constitutive relevance discovery. I also discuss possible objections and certain limitations of a constitutive relevance discovery procedure based on PC. (shrink)

In this paper we develop an analysis of dispositions by means of causal Bayes nets. In particular, we analyze dispositions as cause-effect structures that increase the probability of the manifestation when the stimulus is brought about by intervention in certain circumstances. We then highlight several advantages of our analysis and how it can handle problems arising for classical analyses of dispositions such as masks, mimickers, and finks.

Recent approaches to causal modelling rely upon the causal Markov condition, which specifies which probability distributions are compatible with a directed acyclic graph. Further principles are required in order to choose among the large number of DAGs compatible with a given probability distribution. Here we present a principle that we call frugality. This principle tells one to choose the DAG with the fewest causal arrows. We argue that frugality has several desirable properties compared to the other principles that have been (...) suggested, including the well-known causal faithfulness condition. _1_ Introduction _2_ The Causal Markov Condition _3_ Faithfulness _4_ Frugality _4.1_ Basic independences and frugality _4.2_ General properties of directed acyclic graphs satisfying frugality _4.3_ Connection to minimality assumptions _5_ Frugality as a Parsimony Principle _6_ Conclusion Appendix. (shrink)

This survey presents some of the main principles involved in discovering causal relations. They belong to a large array of possible assumptions and conditions about causal relations, whose various combinations limit the possibilities of acquiring causal knowledge in different ways. How much and in what detail the causal structure can be discovered from what kinds of data depends on the particular set of assumptions one is able to make. The assumptions considered here provide a starting point to explore further the (...) foundations of causal discovery procedures, and how they can be improved. (shrink)

Causal reasoning is an aspect of learning, reasoning, and decision-making that involves the cognitive ability to discover relationships between causal relata, learn and understand these causal relationships, and make use of this causal knowledge in prediction, explanation, decision-making, and reasoning in terms of counterfactuals. Can we fully automate causal reasoning? One might feel inclined, on the basis of certain groundbreaking advances in causal epistemology, to reply in the affirmative. The aim of this paper is to demonstrate that one still has (...) good skeptical grounds for resisting any conclusions in favour of the automation of causal reasoning. If by causal reasoning is meant the entirety of the process through which we discover causal relationships and make use of this knowledge in prediction, explanation, decision-making, and reasoning in terms of counterfactuals, then one relies besides on tacit knowledge, as might be constituted by or derived from the epistemic faculty virtues and abilities of the causal reasoner, the value systems and character traits of the causal reasoner, the implicit knowledge base available to the causal reasoner, and the habits that sustain our causal reasoning practices. While certain aspects of causal reasoning may be axiomatized and formalized and algorithms may be implemented to approximate causal reasoning, one has to remain skeptical about whether causal reasoning may be fully automated. This demonstration will involve an engagement with Meno’s Paradox. (shrink)

Gebharter has proposed using one of the best known Bayesian network causal discovery algorithms, PC, to identify the constitutive dependencies underwriting mechanistic explanations. His proposal assumes that mechanistic constitution behaves like deterministic direct causation, such that PC is directly applicable to mixed variable sets featuring both causal and constitutive dependencies. Gebharter claims that such mixed sets, under certain restrictions, comply with PC’s background assumptions. The aim of this article is to show that Gebharter’s proposal incurs severe problems, ultimately rooted in (...) the widespread non-compliance of mechanistic systems with PC’s assumptions. This casts severe doubts on the attempt to implicitly define constitution as a form of deterministic direct causation complying with PC’s assumptions. (shrink)

The essential precondition of implementing interventionist techniques of causal reasoning is that particular variables are identified as so-called intervention variables. While the pertinent literature standardly brackets the question how this can be accomplished in concrete contexts of causal discovery, the first part of this paper shows that the interventionist nature of variables cannot, in principle, be established based only on an interventionist notion of causation. The second part then demonstrates that standard observational methods that draw on Bayesian networks identify intervention (...) variables only if they also answer the questions that can be answered by interventionist techniques—which are thus rendered dispensable. The paper concludes by suggesting a way of identifying intervention variables that allows for exploiting the whole inferential potential of interventionist techniques. (shrink)

I present three reasons why philosophers of science should be more concerned about violations of causal faithfulness (CF). In complex evolved systems, mechanisms for maintaining various equilibrium states are highly likely to violate CF. Even when such systems do not precisely violate CF, they may nevertheless generate precisely the same problems for inferring causal structure from probabilistic relationships in data as do genuine CF-violations. Thus, potential CF-violations are particularly germane to experimental science when we rely on probabilistic information to uncover (...) the DAG, rather than already knowing the DAG from which we could predict the right experiments to ‘catch out’ the hidden causal relationships. (shrink)

The reduction of grounding to causation, or each to a more general relation of which they are species, has sometimes been justified by the impressive inferential capacity of structural equation modelling, causal Bayes nets, and interventionist causal modelling. Many criticisms of this assimilation focus on how causation is inadequate for grounding. Here, I examine the other direction: how treating grounding in the image of causation makes the resulting view worse for causation. The distinctive features of causal modelling that make this (...) connection appealing are distorted beyond use by forcing them to fit onto grounding. The very inferential strength that makes causation attractive is only possible because of a narrow construal of what counts as a causal relation; as soon as that broadens, the inferential capacity markedly diminishes. Making causation suitable for application to grounding spoils what was appealing about causation for this task in the first place. However, grounding need not appeal to causation: causal modelling does not have exclusive claim to structural equation modeling or other formal techniques of modelling structure. I offer a case in favour of a different kind of metaphysical frugality, which tend towards narrow, more restrictive construals of relations like causation or grounding, because then each relation behaves more homogenously. This more homogenous behavior delivers stronger inferential power per relation even though there may be more relations to which one is committed. (shrink)

Casini, Illari, Russo, and Williamson (2011) suggest to model mechanisms by means of recursive Bayesian networks (RBNs) and Clarke, Leuridan, and Williamson (2014) extend their modelling approach to mechanisms featuring causal feedback. One of the main selling points of the RBN approach should be that it provides answers to questions concerning manipulation and control. In this paper I demonstrate that the method to compute the effects of interventions the authors mentioned endorse leads to absurd results under the additional assumption of (...) faithfulness, which can be expected to hold for many RBN models of mechanisms. (shrink)

Spirtes, Glymour and Scheines [Causation, Prediction, and Search Springer] described a pointwise consistent estimator of the Markov equivalence class of any causal structure that can be represented by a directed acyclic graph for any parametric family with a uniformly consistent test of conditional independence, under the Causal Markov and Causal Faithfulness assumptions. Robins et al. [Biometrika 90 491–515], however, proved that there are no uniformly consistent estimators of Markov equivalence classes of causal structures under those assumptions. Subsequently, Kalisch and B¨uhlmann (...) [J. Mach. Learn. Res. 8 613–636] described a uniformly consistent estimator of the Markov equivalence class of a linear Gaussian causal structure under the Causal Markov and Strong Causal Faithfulness assumptions. However, the Strong Faithfulness assumption may be false with high probability in many domains. We describe a uniformly consistent estimator of both the Markov equivalence class of a linear Gaussian causal structure and the identifiable structural coefficients in the Markov equivalence class under the Causal Markov assumption and the considerably weaker k-Triangle-Faithfulness assumption. (shrink)

The current consensus view of causation in physics, as commonly held by scientists and philosophers, has several serious problems. It fails to provide an epistemology for the causal knowledge that it claims physics to possess; it is inapplicable in a prominent area of physics (classical thermodynamics); and it is difficult to reconcile with our everyday use of causal concepts and claims. In this dissertation, I use historical examples and philosophical arguments to show that the interventionist account of causation constitutes a (...) promising alternative for a “physically respectable” account of causation. The interventionist account explicates important parts of the experimental practice of physics and important aspects of the ways in which physical theory is used and applied. Moreover, the interventionist account succeeds where the consensus view of causation in physics fails. I argue that the interventionist account provides an epistemology of causal knowledge in physics that is rooted in experiment. On the interventionist view, there is a close link between experiment and the testing of causal claims. I give several examples of experiments from the early history of thermodynamics that scientists used in interventionist-type arguments. I also argue that interventionist claims made in the context of a physical theory can be epistemically justified by reference to the experimental interventions and observations that serve as evidence for the theory. I then show that the interventionist account of causation is well-suited to the patterns of reasoning that are intrinsic to thermodynamic theory. I argue that interventionist reasoning constitutes the structural foundation of thermodynamic theory, and that thermodynamic theory can provide clear answers to meaningful questions about whether or not a certain variable is a cause of another in a given context. Finally, I argue that the interventionist account offers the prospect of a unification of “physically respectable” causation and our everyday notion of causation. I conclude the dissertation by sketching an anti-foundationalist unification of causation, according to which causal reasoning occurs in the same manner in physics as it does in other branches of life and scientific research. (shrink)

These preprints were automatically compiled into a PDF from the collection of papers deposited in PhilSci-Archive in conjunction with the PSA 2012.