Abstract
The role of measure theoretic atomicity in common cause closedness of general probability theories with non-distributive event structures is raised and investigated. It is shown that if a general probability space is non-atomic then it is common cause closed. Conditions are found that entail that a general probability space containing two atoms is not common cause closed but it is common cause closed if it contains only one atom. The results are discussed from the perspective of the Common Cause Principle.
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Acknowledgments
We thank the audience of the “Causes and Tenses—Formal Perspectives” Workshop, Department of Philosophy, Jagiellonian University, Cracow, Poland September 10–11, 2011, for discussion related to the topic of this paper. Work supported in part by the Hungarian Scientific Research Found (OTKA), contract number: 100715.
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Gyenis, Z., Rédei, M. Atomicity and Causal Completeness. Erkenn 79 (Suppl 3), 437–451 (2014). https://doi.org/10.1007/s10670-013-9456-1
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DOI: https://doi.org/10.1007/s10670-013-9456-1