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Characterizing Common Cause Closed Probability Spaces

Published online by Cambridge University Press:  01 January 2022

Zalán Gyenis  and
Miklós Rédei
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Abstract

A probability space is common cause closed if it contains a Reichenbachian common cause of every correlation in it and common cause incomplete otherwise. It is shown that a probability space is common cause incomplete if and only if it contains more than one atom and that every space is common cause completable. The implications of these results for Reichenbach's Common Cause Principle are discussed, and it is argued that the principle is only falsifiable if conditions on the common cause are imposed that go beyond the requirements formulated by Reichenbach in the definition of common cause.

Type
Research Article
Information
Philosophy of Science , Volume 78 , Issue 3 , July 2011 , pp. 393 - 409
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

This work was supported in part by the Hungarian Scientific Research Foundation (OTKA), contract K68043.

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