Reichenbachian Common Cause Systems

Hofer-Szabó, Gábor and Redei, Miklos (2003) Reichenbachian Common Cause Systems. UNSPECIFIED. (In Press)

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Abstract

A partition $\{C_i\}_{i\in I}$ of a Boolean algebra $\cS$ in a probability measure space $(\cS,p)$ is called a Reichenbachian common cause system for the correlated pair $A,B$ of events in $\cS$ if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set $I$ is called the size of the common cause system. It is shown that given any correlation in $(\cS,p)$, and given any finite size $n>2$, the probability space $(\cS,p)$ can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size $n$ for the correlation. It also is shown that every totally ordered subset in the partially ordered set of all partitions of \cS\$ contains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated.

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Item Type: Other Paper presented at IQSA 2001 conference (Cesenatico, Italy). Forthcoming in International Journal of Theoretical Physics. common cause, probabilistic causation General Issues > Causation Miklos Redei 01 Jul 2003 27 Jun 2014 17:48 1246 No http://philsci-archive.pitt.edu/id/eprint/1246