International Journal of Theoretical Physics

, Volume 43, Issue 7, pp 1819–1826

Reichenbachian Common Cause Systems

  • G. Hofer-Szabó
  • Miklós Rédei
Article

DOI: 10.1023/B:IJTP.0000048822.29070.0c

Cite this article as:
Hofer-Szabó, G. & Rédei, M. International Journal of Theoretical Physics (2004) 43: 1819. doi:10.1023/B:IJTP.0000048822.29070.0c

Abstract

A partition Cii∈ I of a Boolean algebra \(\mathcal{S}\) in a probability measure space \((\mathcal{S},p)\) is called a Reichenbachian common cause system for the correlated pair A,B of events in \(\mathcal{S}\) 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 correlation in \((\mathcal{S},p)\), and given any finite size n>2, the probability space \((\mathcal{S},p)\) 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. It also is shown that every totally ordered subset in the partially ordered set of all partitions of \(\mathcal{S}\) contains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated.

common cause correlation causation Reichenbach 

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • G. Hofer-Szabó
    • 1
  • Miklós Rédei
    • 2
  1. 1.Department of PhilosophyTechnical University of BudapestBudapest
  2. 2.Department of History and Philosophy of ScienceEötvös UniversityBudapest

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