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.
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References
Adams, E.W.: A Primer of Probability Logic. CSLI Publications (1998)
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)
Billingsley, P.: Probability and Measure. Wiley, New York (1995)
Hofer-Szabó, G., Rédei, M., Szabó, L.: Reichenbach’s common cause principle: recent results and open questions. Rep. Philos. 20, 85–107 (2000)
Hofer-Szabó, G., Rédei, M.: Reichenbachian common cause systems. Int. J. Theor. Phys. 43, 1819–1826 (2004)
Hofer-Szabó, G., Rédei, M.: Reichenbachian common cause systems of arbitrary finite size exist. Found. Phys. 36, 745–756 (2006)
Jech, T.: Set Theory. Springer, Berlin (2002)
Pearl, J.: Causality. Models, Reasoning and Inference. Cambridge University Press, Cambridge (2000)
Placek, T.: Is Nature Deterministic? A Branching Perspective on EPR Phenomena. Jagiellonian University Press, Krakow (2000)
Reichenbach, H.: The Direction of Time. University of Los Angeles Press, Berkeley (1956)
Spirtes, P., Glymour, C., Scheines, R.: Causation, Probability and Search. MIT Press, Cambridge (2000)
Szabó, L., Fine, A.: A local hidden variable theory for the GHZ experiment. Phys. Lett. A 295, 229–240 (2002)
van Fraassen, B.: The Charybdis of realism: epistemological implications of Bell’s inequality. Synthese 52, 25–38 (1982)
van Fraassen, B.: Rational belief and the common cause principle. In: McLaughlin, R. (ed.) What? Where? When? Why?, pp. 193–209. Reidel, Dordrecht (1982)
Williamson, J.: Bayesian Nets and Causality. Philosophical and Computational Foundations. Oxford University Press, London (2005)
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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
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DOI: https://doi.org/10.1007/s10701-010-9457-8