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Common-Causes are Not Common Common-Causes

Published online by Cambridge University Press:  01 January 2022

Gábor Hofer-Szabó ,
Miklós Rédei  and
László E. Szabó
Gábor Hofer-Szabó
Affiliation:
Department of Philosophy, Technical University of Budapest
Miklós Rédei
Affiliation:
Department of History and Philosophy of Science, Eötvös University, Budapest
László E. Szabó*
Affiliation:
Theoretical Physics Research Group of HAS, Department of History and Philosophy of Science, Eötvös University, Budapest
*
†Contact address: History and Philosophy of Science, Eötvös University, H-1518 Budapest Pf. 32, Hungary; [email protected]
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Abstract

A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common-cause and it is shown that there exists pairs of correlated events, probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common-cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach's definition of common-cause. The significance of the difference between common-causes and common common-causes is emphasized from the perspective of Reichenbach's Common Cause Principle.

Type
Research Article
Information
Philosophy of Science , Volume 69 , Issue 4 , December 2002 , pp. 623 - 636
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

Work supported by OTKA (contract numbers: T032771, T024841, T035234, T 025880 and TS 04089).

References

Cartwright, Nancy (1987), “How to tell a common cause: Generalization of the conjunctive fork criterion”, in Fetzer, J. H. (ed.), Probability and Causality, Boston: Reidel Pub. Co., 181−188.Google Scholar
Gillies, D. (2000), Philosophical Theories of Probability. London: Routledge.Google Scholar
Hofer-Szabó Gábor, Miklós Rédei, and Szabó, Lászlo E. (1999), “On Reichenbach’s Common Cause Principle and Reichenbach’s notion of common cause”, On Reichenbach’s Common Cause Principle and Reichenbach’s notion of common cause 50: 377–399.Google Scholar
Hofer-Szabó Gábor, Miklós Rédei, and Szabó, Lászlo E. (2000a), “Common cause completability of classical and quantum probability spaces”, Common cause completability of classical and quantum probability spaces 39: 913–919.Google Scholar
Hofer-Szabó Gábor, Miklós Rédei, and Szabó, Lászlo E. (2000b), “Reichenbach’s Common Cause Principle: Recent results and open questions”, Reichenbach’s Common Cause Principle: Recent results and open questions 20: 85–107.Google Scholar
Placek, T. (2000a), “Stochastic outcomes in branching space-time: Analysis of Bell’s theorem”, Stochastic outcomes in branching space-time: Analysis of Bell’s theorem 51: 445–475.Google Scholar
Placek, T. (2000b), Is Nature Deterministic?, Krakow: Jagellonian University Press.Google Scholar
Miklós, Rédei (1997), “Reichenbach’s Common Cause Principle and quantum field theory”, Reichenbach’s Common Cause Principle and quantum field theory 27: 1309–1321.Google Scholar
Miklós, Rédei (1998). Quantum Logic in Algebraic Approach, Dordrecht: Kluwer Academic Publishers.Google Scholar
Miklós, Rédei. (forthcoming), “Reichenbach’s Common Cause Principle and quantum correlations”, in Modality, Probability and Bell’s Theorems, Butterfield, J. and Placek, T. (eds.) Dordrecht: Kluwer Academic Publishers.Google Scholar
Rédei, M., and Summers, S.J. (2002), “Local Primitive Causality and the Common Cause Principle in quantum field theory”, Local Primitive Causality and the Common Cause Principle in quantum field theory 32: 335–355.Google Scholar
Reichenbach, Hans (1956), The Direction of Time. Los Angeles: University of California Press.10.1063/1.3059791CrossRefGoogle Scholar
Szabó, László. E. (2000), “Attempt to resolve the EPR-Bell paradox via Reichenbach’s concept of common cause”, Attempt to resolve the EPR-Bell paradox via Reichenbach’s concept of common cause 39: 901–911.Google Scholar
Van Frassen, Bas. C. (1982), “Rational belief and the common cause principle”, in McLaughlin, R. (ed.), What? Where? When? Why?. Boston: D. Reidel Pub. Co., 193−209.Google Scholar