Abstract
Answering a problem posed by Z. Gyenis and M. Rédei, we show that there exist strongly causally closed classical probability spaces and that all classical probability spaces are strongly causally completable with respect to the relation of logical independence.
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Notes
- 1.
For a collection of references on both philosophical and formal issues related to the Common Cause Principle, see Wroński (2010).
- 2.
I.e. “Any event C which is not identical as a set to event A or event B”.
- 3.
Notice that our n-closedness a different notion from that of “causal N-completeness” employed by Gyenis and Rédei (2010). There the framework is that of general probability spaces and the correlations under investigation hold between random variables. Also, the choice of a specific notion of correlation is left open; whereas here, since we are talking about events, no such choice arises.
- 4.
M. Rédei gave the definitions of strong causal closedness and completability as well as stated the problems during the “New Directions in the Philosophy of Science” conference in Bertinoro, October 17th–20th 2012; a similar problem is the first one in Sect. 4 of Gyenis and Rédei (2013).
References
Beebee, H. 1998. Do causes raise the chances of effects? Analysis 58(3): 182–190.
Fremlin, D. 2001. Measure theory, vol. 2. Colchester: Torres Fremlin.
Gyenis, B., and M. Rédei. 2004. When can statistical theories be causally closed? Foundations of Physics 34(9): 1284–1303.
Gyenis, B., and M. Rédei. 2010. Causal completeness in general probability theories. In Probabilities, causes, and propensities in physics. Vol. 347, of Synthese library, ed. M. Suárez, 157–171. Dordrecht: Springer
Gyenis, Z., and M. Rédei. 2011. Characterizing common cause closed probability spaces. Philosophy of Science 78: 393–409.
Gyenis, Z., and M. Rédei. 2013. Atomicity and causal completeness. Erkenntnis. doi:10.1007/s10670-013-9456-1.
Hofer-Szabó, G., and M. Rédei. 2004. Reichenbachian common cause systems. International Journal of Theoretical Physics 43(7/8): 1819–1826.
Hofer-Szabó, G., M. Rédei, and L.E. Szabó. 1999. On Reichenbach’s common cause principle and Reichenbach’s notion of common cause. The British Journal for the Philosophy of Science 50(3): 377–399.
Hofer-Szabó, G., M. Rédei, and L.E. Szabó. 2013. The common cause principle. Cambridge: Cambridge University Press.
Marczyk, M., and L. Wroński. 2013, in forthcoming. A completion of the causal completability problem. The British Journal for the Philosophy of Science.
Reichenbach, H. 1971. The direction of time, Repr. of the 1956 edn. Berkeley: University of California Press.
Wroński, L. 2010. The common cause principle. Explanation via screening off. PhD thesis, Jagiellonian University, Kraków, archived at jagiellonian.academia.edu/LeszekWrońnski. Forthcoming as a book from Versita Publishing.
Wroński, L., and M. Marczyk. 2010. Only countable Reichenbachian common cause systems exist. Foundations of Physics 40: 1155–1160.
Wroński, L., and M. Marczyk. 2013. A new notion of causal closedness. Erkenntnis. doi:10.1007/s10670-013-9457-0.
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Marczyk, M., Wroński, L. (2014). A Note on Strong Causal Closedness and Completability of Classical Probability Spaces. In: Galavotti, M., Dieks, D., Gonzalez, W., Hartmann, S., Uebel, T., Weber, M. (eds) New Directions in the Philosophy of Science. The Philosophy of Science in a European Perspective, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-04382-1_30
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