When can statistical theories be causally closed?

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



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Author Profiles

Miklós Rédei
London School of Economics

References found in this work

The direction of time.Hans Reichenbach - 1956 - Mineola, N.Y.: Dover Publications. Edited by Maria Reichenbach.
The Direction of Time.Hans Reichenbach - 1956 - Philosophy 34 (128):65-66.
A Probabilistic Theory of Causality.P. Suppes - 1973 - British Journal for the Philosophy of Science 24 (4):409-410.

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