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STRUCTURAL EQUATIONS AND BEYOND

Published online by Cambridge University Press:  08 July 2013

FRANZ HUBER*
Affiliation:
Department of Philosophy, University of Toronto
*
*DEPARTMENT OF PHILOSOPHY UNIVERSITY OF TORONTO JACKMAN HUMANITIES BUILDING 170 ST. GEORGE ST.TORONTO CANADA, ON M5R 2M8 E-mail: franz.huber@utoronto.ca

Abstract

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the “(causal) laws” or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended causal models with their two modalities can be subsumed under so called “counterfactual models” which contain just one modality. These two constraints will be formally precise versions of Lewis’ (1979) familiar “system of weights or priorities” governing overall similarity between possible worlds.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2013 

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References

BIBLIOGRAPHY

Briggs, R. (2012). Interventionist counterfactuals. Philosophical Studies, 160, 139166.Google Scholar
Collins, J., Hall, N., & Paul, L. A. (2004). Counterfactuals and causation: History, problems, and prospects. In Collins, J., Hall, N., and Paul, L. A., editors. Causation and Counterfactuals. Cambridge, MA: MIT Press, pp. 157.Google Scholar
Field, H. (1978). A note on Jeffrey conditionalization. Philosophy of Science, 45, 361367.Google Scholar
Glymour, C., Danks, D., Glymour, B., Eberhardt, F., Ramsey, J., Scheines, R., Spirtes, P., Teng, C. M., & Zhang, J. (2010). Actual causation: A stone soup essay. Synthese, 175, 169192.Google Scholar
Hájek, A. (ms). Most Counterfactuals Are False.Google Scholar
Hall, N. (2007). Structural equations and causation. Philosophical Studies, 132, 109136.Google Scholar
Halpern, J. Y. (2008). Defaults and normality in causal structures. Proceedings of the Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pp. 198208.Google Scholar
Halpern, J. Y. (2013). From causal models to counterfactual structures. The Review of Symbolic Logic, 6, 305322.Google Scholar
Halpern, J. Y., & Hitchcock, C. R. (2010). Actual causation and the art of modelling. In Dechter, R., Geffner, H., and Halpern, J., editors. Heuristics, Probability, and Causality. London, UK: College Publications, pp. 383406.Google Scholar
Halpern, J. Y., & Hitchcock, C. R. (forthcoming). Compact representations of extended causal models. Cognitive Science.Google Scholar
Halpern, J. Y., & Pearl, J. (2005a). Causes and explanations: A structural-model approach. Part I: Causes. British Journal for the Philosophy of Science, 56, 843887.Google Scholar
Halpern, J. Y., & Pearl, J. (2005b). Causes and explanations: A structural-model approach. Part II: Explanations. British Journal for the Philosophy of Science, 56, 889911.CrossRefGoogle Scholar
Hiddleston, E. (2005). Causal powers. British Journal for the Philosophy of Science, 56, 2759.Google Scholar
Hitchcock, C. R. (2001). The intransitivity of causation revealed in equations and graphs. Journal of Philosophy, XCVIII, 273299.Google Scholar
Hitchcock, C. R. (2007). Prevention, preemption, and the principle of sufficient reason. Philosophical Review, 116, 495532.CrossRefGoogle Scholar
Huber, F. (ms 1). What Should I Believe About What Would Have Been the Case? Unpublished manuscript.Google Scholar
Huber, F. (ms 2). New Foundations for Counterfactuals. Unpublished manuscript.Google Scholar
Kistler, M. (forthcoming). The interventionist account of causation and non-causal association laws. Erkenntnis.Google Scholar
Kroedel, T., & Huber, F. (forthcoming). Counterfactual dependence and arrow. Noûs.Google Scholar
Leitgeb, H. (2012a). A probabilistic semantics for counterfactuals. Part A. Review of Symbolic Logic, 5, 2684.Google Scholar
Leitgeb, H. (2012b). A probabilistic semantics for counterfactuals. Part B. Review of Symbolic Logic, 5, 85121.CrossRefGoogle Scholar
Lewis, D. K. (1973a). Causation. Journal of Philosophy, 70, 556567.Google Scholar
Lewis, D. K. (1973b). Counterfactuals. Cambridge, MA: Harvard University Press.Google Scholar
Lewis, D. K. (1979). Counterfactual dependence and time’s arrow. Noûs 13, 455476.CrossRefGoogle Scholar
Lewis, D. K. (1986). Postscripts to “Causation”. In Lewis, D., editor. Philosophical Papers II. Oxford, UK: Oxford University Press, pp. 172213.Google Scholar
Lewis, D. K. (2000). Causation as influence. Journal of Philosophy, 97, 182197.CrossRefGoogle Scholar
Menzies, P. (2004). Difference-making in context. In Collins, J., Hall, N., and Paul, L. A., editors. Causation and counterfactuals. Cambridge, MA: MIT Press, pp. 139180.Google Scholar
Paul, L. A. (2000). Aspect causation. Journal of Philosophy, XCVII, 235256.Google Scholar
Pearl, J. (2009). Causality: Models, Reasoning, and Inference (second edition).Cambridge: Cambridge University Press.Google Scholar
Shenoy, P. P. (1991). On Spohn’s rule for revision of beliefs. International Journal of Approximate Reasoning, 5, 149181.CrossRefGoogle Scholar
Spirtes, P., Glymour, C., & Scheines, R. (2000). Causation, Prediction, and Search (second edition). Cambridge, MA: MIT Press.Google Scholar
Spohn, W. (1988). Ordinal conditional functions: A dynamic theory of epistemic states. In Harper, W. L., and Skyrms, B., editors. Causation in Decision, Belief Change, and Statistics II. Dordrecht, The Netherlands: Kluwer, pp. 105134.Google Scholar
Spohn, W. (2006). Causation: An alternative. British Journal for the Philosophy of Science, 57, 93119.Google Scholar
Spohn, W. (2010). The structural model and the ranking theoretic approach to causation: A comparison. In Dechter, R., Geffner, H., and Halpern, J., editors. Heuristics, Probability, and Causality. London, UK: College Publications, pp. 507522.Google Scholar
Stalnaker, R. C. (1968). A theory of conditionals. In Rescher, N., editor. Studies in Logical Theory. American Philosophical Quaterly. Monograph Series, Vol. 2. Oxford, UK: Blackwell, pp. 98112.Google Scholar
Woodward, J. (2003). Making Things Happen: A Theory of Causal Explanation. Oxford, UK: Oxford University Press.Google Scholar