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- N. Hall (2007). Structural Equations and Causation. Philosophical Studies 132 (1):109 - 136.Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.
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I argue (1) that it is not philosophically significant whether causation is linguistically represented by a predicate or by a sentence connective; (2) that there is no philosophically significant distinction between event- and states-of-affairs-causation; (3) that there is indeed a philosophically significant distinction between agent- and event-causation, and that event-causation must be regarded as an analog of agent-causation. Developing this point, I argue that event-causation's being in the image of agent-causation requires, mainly, (a) that the cause is temporally prior to the effect, (b) that the cause necessitates (is sufficient with necessity) for the effect. Causal necessity is explained as a derivative of nomological necessity, and finally, via a definition of the causal sentence connective, the logic of event-causation is shown to be a part of temporal modal logic.
It has recently been objected that structural realism, in its various guises, is unable to adequately account for causal phenomena (see, for example, Psillos 2006). In this talk, I consider whether structural realism has the resources to address this objection.
Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error” or “disturbance” terms), and an associated path diagram corresponding to the functional composition of variables specified by the structural equations and the correlations among the error terms. It is often thought that the path diagram is nothing more than a heuristic device for illustrating the assumptions of the model. However, in this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling.
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This paper argues that econometricians' explicit adoption of identification conditions in structural equation modelling commits them to read the functional form of their equations in a strong, nonmathematical way. This content, which is implicitly attributed to the functional form of structural equations, is part of what makes equation structural. Unfortunately, econometricians are not explicit about the role functional form plays in signifying structural content. In order to remedy this, the second part of this paper presents an interpretation of the functional form based on Herbert Simon's definition of causal order. This begins to set out just what the functional form of structural equations represents. ‡I would like to thank Nancy Cartwright and attendants at UCSD Graduate Seminar 2006 for helpful comments. I also want to thank the AHRC for supporting the research for this paper. †To contact the author, please write to: Centre for Philosophy of Natural and Social Science, London School of Economics, London WC2A 2AE, United Kingdom; e-mail: d.j.fennell@lse.ac.uk.
Linear structural equation models (SEMs) are widely used in sociology, econometrics, biology, and other sciences. A SEM (without free parameters) has two parts: a probability distribution (in the Normal case specified by a set of linear structural equations and a covariance matrix among the “error” or “disturbance” terms), and an associated path diagram corresponding to the causal relations among variables specified by the structural equations and the correlations among the error terms. It is often thought that the path diagram is nothing more than a heuristic device for illustrating the assumptions of the model. However, in this paper, we will show how path diagrams can be used to solve a number of important problems in structural equation modelling.
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Judea Pearl (2000) has recently advanced a theory of token causation using his structural equations approach. This paper examines some counterexamples to Pearl's theory, and argues that the theory can be modified in a natural way to overcome them.
This paper examines some counterexamples to Judea Pearl's theory of token-causation within his structural equations framework. It argues that it is possible to modify the theory in natural ways to overcome these counterexamples.
One part of the true theory of actual causation is a set of conditions responsible for eliminating all of the non-causes of an effect that can be discerned at the level of counterfactual structure. I defend a proposal for this part of the theory.
Hall [(2007), Philosophical Studies, 132, 109–136] offers a critique of structural equations accounts of actual causation, and then offers a new theory of his own. In this paper, I respond to Hall’s critique, and present some counterexamples to his new theory. These counterexamples are then diagnosed.
This paper criticizes a recent account of token causation that states that negative causation involving absences of events is of a fundamentally different kind from positive causation involving events. The paper employs the structural equations framework to advance a theory of token causation that applies uniformly to positive and negative causation alike.
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