Do Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist?
This work corrects a foundational error in the philosophical and probabilistic literature on causality, which is important for researchers in philosophy of science and causal inference.
The paper identifies a logical flaw in a 2006 proof by Hofer-Szabó and Rédei that claimed to demonstrate the existence of Reichenbachian common cause systems of arbitrary finite size for non-causally correlated events, and provides an improved proof to address this deficiency.
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.