Foundations of Physics 34 (9):1285-1303 (2002)

Miklós Rédei
London School of Economics
The notion of common cause closedness of a classical, Kolmogorovian probability space with respect to a causal independence relation between the random events is defined, and propositions are presented that characterize common cause closedness for specific probability spaces. It is proved in particular that no probability space with a finite number of random events can contain common causes of all the correlations it predicts; however, it is demonstrated that probability spaces even with a finite number of random events can be common cause closed with respect to a causal independence relation that is stronger than logical independence. Furthermore it is shown that infinite, atomless probability spaces are always common cause closed in the strongest possible sense. Open problems concerning common cause closedness are formulated and the results are interpreted from the perspective of Reichenbach's Common Cause Principle.
Keywords Reichenbach's Common Cause Principle  causality  stochastic causality  causal closedness
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Reprint years 2004
DOI 10.1023/B:FOOP.0000044094.09861.12
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References found in this work BETA

A Probabilistic Theory of Causality.P. Suppes - 1973 - British Journal for the Philosophy of Science 24 (4):409-410.
The Pragmatics of Explanation.Bas C. Van Fraassen - 1977 - American Philosophical Quarterly 14 (2):143-150.
Probabilistic Causality.Wesley C. Salmon - 1980 - Pacific Philosophical Quarterly 61 (1/2):50.

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Completion of the Causal Completability Problem.Michał Marczyk & Leszek Wroński - 2015 - British Journal for the Philosophy of Science 66 (2):307-326.

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