Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-13T01:13:09.038Z Has data issue: false hasContentIssue false
  • English
  • Français

Characterizing Common Cause Closed Probability Spaces

Published online by Cambridge University Press:  01 January 2022

Zalán Gyenis  and
Miklós Rédei
Get access Rights & Permissions [Opens in a new window]

Abstract

A probability space is common cause closed if it contains a Reichenbachian common cause of every correlation in it and common cause incomplete otherwise. It is shown that a probability space is common cause incomplete if and only if it contains more than one atom and that every space is common cause completable. The implications of these results for Reichenbach's Common Cause Principle are discussed, and it is argued that the principle is only falsifiable if conditions on the common cause are imposed that go beyond the requirements formulated by Reichenbach in the definition of common cause.

Type
Research Article
Information
Philosophy of Science , Volume 78 , Issue 3 , July 2011 , pp. 393 - 409
Copyright
Copyright © The Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

This work was supported in part by the Hungarian Scientific Research Foundation (OTKA), contract K68043.

References

Arntzenius, Frank. 1993. “The Common Cause Principle.” In PSA 1992: Proceedings of the 1992 Biennial Meeting of the Philosophy of Science Association, Vol. 2, ed. Hull, David L. and Forbes, Micky, 227–37. East Lansing, MI: Philosophy of Science Association.Google Scholar
Butterfield, Jeremy. 1989. “A Space-Time Approach to the Bell Inequality.” In Philosophical Consequences of Quantum Theory, ed. Cushing, J. and McMullin, E., 114–44. Notre Dame, IN: University of Notre Dame Press.Google Scholar
Butterfield, Jeremy. 2007. “Stochastic Einstein Locality Revisited.” British Journal for the Philosophy of Science 58:805–67.CrossRefGoogle Scholar
Cartwright, Nancy. 1987. “How to Tell a Common Cause: Generalization of the Conjunctive Fork Criterion.” In Probability and Causality, ed. Fetzer, J. H., 181–88. Boston: Reidel.Google Scholar
Chang, Hasok, and Cartwright, Nancy. 1993. “Causality and Realism in the EPR Experiment.” Erkenntnis 38:269–90.CrossRefGoogle Scholar
Grasshoff, G., Portmann, S., and Wüthrich, Adrian. 2005. “Minimal Assumption Derivation of a Bell-Type Inequality.” British Journal for the Philosophy of Science 56:663–80.CrossRefGoogle Scholar
Gyenis, Balázs, and Rédei, Miklós. 2004. “When Can Statistical Theories Be Causally Closed?” Foundations of Physics 34:1285–1303.CrossRefGoogle Scholar
Halmos, Paul. 1950. Measure Theory. New York: Nostrand.CrossRefGoogle Scholar
Henson, J. 2005. “Comparing Causality Principles.” Studies in History and Philosophy of Modern Physics 36:519–43.CrossRefGoogle Scholar
Hofer-Szabó, Gábor. 2008. “Separate—versus Common—Common-Cause-Type Derivations of the Bell Inequalities.” Synthese 163:199–215.CrossRefGoogle Scholar
Hofer-Szabó, Gábor. 2011. “Bell Inequalities Derived from Separate Common Causal Explanation of Almost Perfect EPR Anticorrelations.” Foundations of Physics, preprint, doi:10.1007/s10701-011-9555-2.CrossRefGoogle Scholar
Hofer-Szabó, Gábor, Rédei, Miklós, and Szabó, László. 1999. “On Reichenbach's Common Cause Principle and Reichenbach's Notion of Common Cause.” British Journal for the Philosophy of Science 50:377–98.CrossRefGoogle Scholar
Hofer-Szabó, Gábor, Rédei, Miklós, and Szabó, László. 2000. “Common Cause Completability of Classical and Quantum Probability Spaces.” International Journal of Theoretical Physics 39:913–19.CrossRefGoogle Scholar
Hofer-Szabó, Gábor, Rédei, Miklós, and Szabó, László. 2002. “Common-Causes Are Not Common Common-Causes.” Philosophy of Science 69 (20): 623–36.CrossRefGoogle Scholar
Hoover, K. D. 2003. “Non-stationary Time Series, Cointegration and the Principle of the Common Cause.” British Journal for the Philosophy of Science 54:527–51.CrossRefGoogle Scholar
Pearl, Judea. 2000. Causality: Models, Reasoning and Inference. New York: Cambridge University Press.Google Scholar
Placek, Tomasz. 2000a. Is Nature Deterministic? Cracow: Jagellonian University Press.Google Scholar
Placek, Tomasz. 2000b. “Outcomes in Branching Space-Time and GHZ-Bell Theorems.” British Journal for the Philosophy of Science 50:349–75.Google Scholar
Placek, Tomasz. 2000c. “Stochastic Outcomes in Branching Space-Time: An Analysis of Bell Theorems.” British Journal for the Philosophy of Science 51:445–75.CrossRefGoogle Scholar
Portmann, Samuel, and Wüthrich, Adrian. 2007. “Minimal Assumption Derivation of a Weak Clauser-Horne Inequality.” Studies in History and Philosophy of Modern Physics 38:844–62, http://arxiv.org/abs/quant-ph/0604216.CrossRefGoogle Scholar
Miklós, Rédei, and Summers, Stephen. 2002. “Local Primitive Causality and the Common Cause Principle in Quantum Field Theory.” Foundations of Physics 32:335–55.Google Scholar
Miklós, Rédei, and Summers, Stephen. 2007. “Remarks on Causality in Relativistic Quantum Field Theory.” International Journal of Theoretical Physics 46:2053–62.Google Scholar
Reichenbach, Hans. 1956. The Direction of Time. Los Angeles: University of California Press.CrossRefGoogle Scholar
Salmon, Wesley. 1978. “Why Ask “‘Why?’” In Proceedings and Addresses of the American Philosophical Association, vol. 51, 683–705. Newark, DE: American Philosophical Association.CrossRefGoogle Scholar
Salmon, Wesley. 1980. “Probabilistic Causality.” Pacific Philosophical Quarterly 61:50–74.CrossRefGoogle Scholar
Salmon, Wesley. 1984. Scientific Explanation and the Causal Structure of the World. Princeton, NJ: Princeton University Press.Google Scholar
Sober, Elliot. 1984. “Common Cause Explanation.” Philosophy of Science 51:212–41.CrossRefGoogle Scholar
Sober, Elliot. 1988. “The Principle of the Common Cause.” In Probability and Causality, ed. Fetzer, J. H., 211–28. Boston: Reidel.Google Scholar
Sober, Elliot. 2001. “Venetian Sea Levels, British Bread Prices, and the Principle of Common Cause.” British Journal for the Philosophy of Science 52:331–46.CrossRefGoogle Scholar
Sober, Elliot. 2008. Evidence and Evolution. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Spirtes, Peter, Glymour, Clarck, and Scheines, P.. 1993. Causation, Prediction and Search. Lecture Notes in Statistics. New York: Springer.CrossRefGoogle Scholar
Spohn, W. 1991. “On Reichenbach's Principle of the Common Cause.” In Logic, Language and the Structure of Scientific Theories, ed. Salmon, W. and Wolters, G.. Pittsburgh: University of Pittsburgh Press.Google Scholar
Suppes, Peter. 1970. A Probabilistic Theory of Causality. Amsterdam: North-Holland.Google Scholar
Szabó, László. 2000. “Attempt to Resolve the EPR-Bell Paradox via Reichenbach's Concept of Common Cause.” International Journal of Theoretical Physics 39:901–11.CrossRefGoogle Scholar
Uffink, Jos. 1999. “The Principle of the Common Cause Faces the Bernstein Paradox.” Philosophy of Science 66 (Proceedings): S512–S525.CrossRefGoogle Scholar
van Fraassen, Bas. 1982a. “The Charybdis of Realism: Epistemological Implications of Bell's Inequalities.” Synthese 52:97–113. Repr. in Philosophical Consequences of Quantum Theory, ed. Cushing, J. and McMullin, E., 97–113. Notre Dame, IN: University of Notre Dame Press.Google Scholar
van Fraassen, Bas. 1982b. “Rational Belief and the Common Cause Principle.” In What? Where? When? Why? ed. McLaughlin, R., 193–209. Boston: Reidel.CrossRefGoogle Scholar