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Characterizing common cause closed probability spaces

Gyenis, Zalán and Rédei, Miklós (2010) Characterizing common cause closed probability spaces. [Preprint]

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    A classical probability measure space was defined in earlier papers \cite{Hofer-Redei-Szabo1999}, \cite{Gyenis-Redei2004} to be 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 classical probability measure space is common cause incomplete if and only if it contains more than one atom. Furthermore, it is shown that every probability space can be embedded into a common cause closed one; which entails that every classical probability space is common cause completable with respect to any set of correlated events. 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.

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    Item Type: Preprint
    Keywords: Reichenbachian common cause, Common Cause Principle, causally closed theories
    Subjects: Specific Sciences > Probability/Statistics
    General Issues > Causation
    Specific Sciences > Physics
    Depositing User: Zalan Gyenis
    Date Deposited: 05 Jun 2010
    Last Modified: 07 Oct 2010 11:19
    Item ID: 5390

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