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Causality in the Sciences$
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Phyllis McKay Illari, Federica Russo, and Jon Williamson

Print publication date: 2011

Print ISBN-13: 9780199574131

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199574131.001.0001

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Causal completeness of probability theories — Results and open problems

Causal completeness of probability theories — Results and open problems

Chapter:
(p.526) 25 Causal completeness of probability theories — Results and open problems
Source:
Causality in the Sciences
Author(s):

Miklós Rédei

Balázs Gyenis

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199574131.003.0025

A classical (Kolmogorovian) probability measure space is defined to be causally closed with respect to a causal independence relation between pairs of random events if the probability space contains a Reichenbachian common cause of every correlation between causally independent random events. A number of propositions are presented that characterize causal closedness. Generalizing the notion of Reichenbachian common cause in terms of non‐classical probability spaces, where the Boolean algebra of random events is replaced by a non‐distributive orthocomplemented lattice, the notion of causal closedness is defined for non‐classical probability spaces and propositions are presented that state causal closedness of certain non‐classical probability spaces as well. Based on the generalization of the notion of common cause to a common cause system containing N random events, causal N‐closedness is defined with respect to a common cause system both in classical and non‐classical probability spaces, and the problem of causal N‐closedness is formulated. Characterizing causal N‐closedness remains a largely open problem.

Keywords:   common cause, probabilistic causality, Reichenbach

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