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Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist

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Abstract

A partition \(\{C_i\}_{i\in I}\) of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite natural number n > 2, the probability space (Ω,p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation.

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Authors and Affiliations

  1. Department of Philosophy and History of Science, Budapest University of Technology Economics, Budapest, Hungary

    Gábor Hofer-Szabó

  2. Department of History and Philosophy of Science, Eötvös University, Budapest, Hungary

    Miklós Rédei

Authors
  1. Gábor Hofer-Szabó
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  2. Miklós Rédei
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Correspondence to Gábor Hofer-Szabó.

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Hofer-Szabó, G., Rédei, M. Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist. Found Phys 36, 745–756 (2006). https://doi.org/10.1007/s10701-005-9040-x

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  • DOI: https://doi.org/10.1007/s10701-005-9040-x

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