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Do Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist?

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Abstract

The principle of common cause asserts that positive correlations between causally unrelated events ought to be explained through the action of some shared causal factors. Reichenbachian common cause systems are probabilistic structures aimed at accounting for cases where correlations of the aforesaid sort cannot be explained through the action of a single common cause. The existence of Reichenbachian common cause systems of arbitrary finite size for each pair of non-causally correlated events was allegedly demonstrated by Hofer-Szabó and Rédei in 2006. This paper shows that their proof is logically deficient, and we propose an improved proof.

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Notes

  1. For alternative formalisations of the principle see [2,3,4,5]. For some criticism, see for instance [6] and [7]. For a comprehensive review of the current status of the principle in probabilistic causal modelling, see [8].

  2. Whether \(\textit{RCCS}\)s are an accurate generalisation of conjunctive forks is controversial. See [11] and [12] for two opposing views on this matter.

  3. Notice that the logical direction of the proof is opposite to the direction in which it is presented.

  4. The restriction to \(i \ne j\) in the sum of (2.20) is trivially obtained since the sum in the first term of (2.21) is zero when \(i = j\).

References

  1. Reichenbach, H.: The Direction of Time. University of California Press, Berkeley (1956)

    Google Scholar 

  2. Salmon, W.C.: Scientific Explanation and the Causal Structure of the World. Princeton University Press, Princeton (1984)

    Google Scholar 

  3. Cartwright, N.: How to Tell a Common Cause: Generalizations of the Common Cause Criterion. In: Fetzer, J.H. (ed.) Probability and Causality: Essays in Honor of Wesley C. Salmon, pp. 181–188. D. Reidel Publishing Company, Dordrecht (1988). https://doi.org/10.1007/978-94-009-3997-4_8

    Chapter  Google Scholar 

  4. Cartwright, N.: Nature’s Capacities and Their Measurement. Clarendon Press, Oxford (1989)

    Google Scholar 

  5. Mazzola, C.: Correlations, deviations and expectations: the extended principle of the common cause. Synthese 190, 2853 (2013). https://doi.org/10.1007/s11229-012-0089-8

    Article  MathSciNet  MATH  Google Scholar 

  6. Arntzenius, F.: The common cause principle. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, vol. 2, p. 227 (1992). https://doi.org/10.1086/psaprocbienmeetp.1992.2.192838

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

    MATH  Google Scholar 

  8. Hofer-Szabó, G., Rédei, M., Szabó, L.E.: The Principle of the Common Cause. Cambridge University Press, Cambridge (2013)

    Book  MATH  Google Scholar 

  9. Hofer-Szabó, G., Rédei, M., Szabó, L.E.: On Reichenbach’s common cause principle and Reichenbach’s notion of common cause. Br. J. Philos. Sci. 50, 377 (1999). https://doi.org/10.1093/bjps/50.3.377

    Article  MathSciNet  MATH  Google Scholar 

  10. Hofer-Szabó, G., Rédei, M.: Reichenbachian common cause systems. Int. J. Theor. Phys. 43, 1819 (2004). https://doi.org/10.1023/B:IJTP.0000048822.29070.0c

    Article  MathSciNet  MATH  Google Scholar 

  11. Mazzola, C.: Reichenbachian common cause systems revisited. Found. Phys. 42, 512 (2012). https://doi.org/10.1007/s10701-011-9622-8

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Stergiou, C.: Explaining correlations by partitions. Found. Phys. 45, 1599 (2015). https://doi.org/10.1007/s10701-015-9945-y

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Hofer-Szabó, G., Rédei, M.: Reichenbachian common cause systems of arbitrary finite size exist. Found. Phys. 36, 745 (2006). https://doi.org/10.1007/s10701-005-9040-x

  14. Wroński, L., Marczyk, M.: Only countable Reichenbachian common cause systems exist. Found. Phys. 40, 1155 (2010). https://doi.org/10.1007/s10701-010-9457-8

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Marczyk, M., Wroński, L.: Completion of the causal completability problem. Br. J. Philos. Sci. 66, 307 (2015). https://doi.org/10.1093/bjps/axt030

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

We are appreciative of useful discussion with Michał Marczyk and Leszek Wroński, and comments from Gábor Hofer-Szabó and an anonymous referee. Both authors acknowledge the support of the University of Queensland. PWE would like to acknowledge funding support from the Templeton World Charity Foundation (TWCF 0064/AB38) and the Australian Government through the Australian Research Council (DE170100808).

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Authors and Affiliations

  1. UQ Critical Thinking Project, School of Historical and Philosophical Inquiry, University of Queensland, Saint Lucia, QLD, 4072, Australia

    Claudio Mazzola

  2. School of Historical and Philosophical Inquiry, University of Queensland, Saint Lucia, QLD, 4072, Australia

    Peter W. Evans

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  1. Claudio Mazzola
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  2. Peter W. Evans
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Correspondence to Peter W. Evans.

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Mazzola, C., Evans, P.W. Do Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist?. Found Phys 47, 1543–1558 (2017). https://doi.org/10.1007/s10701-017-0124-1

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