Skip to main content
Log in

Only Countable Reichenbachian Common Cause Systems Exist

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

In this paper we give a positive answer to a problem posed by Hofer-Szabó and Rédei (Int. J. Theor. Phys. 43:1819–1826, 2004) regarding the existence of infinite Reichenbachian common cause systems (RCCSs). An example of a countably infinite RCCS is presented. It is also determined that no RCCSs of greater cardinality exist.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Adams, E.W.: A Primer of Probability Logic. CSLI Publications (1998)

  2. Arntzenius, F.: The Common Cause Principle. In: PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, Vol. 1992, Volume Two: Symposia and Invited Papers, pp. 227–237 (1992)

  3. Billingsley, P.: Probability and Measure. Wiley, New York (1995)

    MATH  Google Scholar 

  4. Hofer-Szabó, G., Rédei, M., Szabó, L.: Reichenbach’s common cause principle: recent results and open questions. Rep. Philos. 20, 85–107 (2000)

    Google Scholar 

  5. Hofer-Szabó, G., Rédei, M.: Reichenbachian common cause systems. Int. J. Theor. Phys. 43, 1819–1826 (2004)

    Article  MATH  Google Scholar 

  6. Hofer-Szabó, G., Rédei, M.: Reichenbachian common cause systems of arbitrary finite size exist. Found. Phys. 36, 745–756 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Jech, T.: Set Theory. Springer, Berlin (2002)

    Google Scholar 

  8. Pearl, J.: Causality. Models, Reasoning and Inference. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  9. Placek, T.: Is Nature Deterministic? A Branching Perspective on EPR Phenomena. Jagiellonian University Press, Krakow (2000)

    Google Scholar 

  10. Reichenbach, H.: The Direction of Time. University of Los Angeles Press, Berkeley (1956)

    Google Scholar 

  11. Spirtes, P., Glymour, C., Scheines, R.: Causation, Probability and Search. MIT Press, Cambridge (2000)

    Google Scholar 

  12. Szabó, L., Fine, A.: A local hidden variable theory for the GHZ experiment. Phys. Lett. A 295, 229–240 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. van Fraassen, B.: The Charybdis of realism: epistemological implications of Bell’s inequality. Synthese 52, 25–38 (1982)

    Article  MathSciNet  Google Scholar 

  14. van Fraassen, B.: Rational belief and the common cause principle. In: McLaughlin, R. (ed.) What? Where? When? Why?, pp. 193–209. Reidel, Dordrecht (1982)

    Google Scholar 

  15. Williamson, J.: Bayesian Nets and Causality. Philosophical and Computational Foundations. Oxford University Press, London (2005)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Leszek Wroński.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wroński, L., Marczyk, M. Only Countable Reichenbachian Common Cause Systems Exist. Found Phys 40, 1155–1160 (2010). https://doi.org/10.1007/s10701-010-9457-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-010-9457-8

Keywords

Navigation