On Reichenbach's Principle of the Common Cause

it has become one of the focal points of the continuing discussion of causation. The paper addresses five questions. Section 1 asks: What does the principle say? And section 2 asks: What is its philosophical significance? The most important question, of course, is this: Is the principle true? To answer that question, however, one must first consider how one might one argue about it at all. One can do so by way of examples, the subject of section 3, or more theoretically, which is the goal of section 4. Based on an ex-plication of probabilistic causation proposed by me in (1980), (1983), and (1990), section 4 shows that a variant of the principle is provable within a classical framework. The question naturally arises whether the proved variant is adequate, or too weak. This is pursued in section 5. My main conclusion will be that some version of Reichenbach's principle is prov-ably true, and others may be. This may seem overly ambitious, but it is not. The paper does not make any progress on essential worries about the common cause principle arising in the quantum domain; it only establishes more rigorously what has been thought to be plausible at least within a classical framework. 2 1. What does the principle say? The principle of the common cause specifies an important relation between probability and causality. Though requiring some explanation, its statement is straightforward: Let A and B be two positively correlated events, i.e. events which satisfy the condition Then one of the events causes the other or there is a further event C which is a common cause of A and of B such that and B are independent conditional on C and on C.equalities reversed, would also imply (1), whereas (2), with only one inequality reversed, would imply the reversal of (1). This formulation slightly generalizes Reichenbach's original statement in a way suggested by Salmon (1980, 61). The original principle is obtained by assuming additionally that A and B occur simultaneously in which case the principle leaves no alternative to a common cause of A and B because there cannot be a causal influence running from A to B or the other way around. But what does all of this really mean? Since the common cause principle seems to be about events (though I shall argue in section 5 that it should rather be viewed as being about (random) variables), …