Screening-off and causal incompleteness: A no-go theorem

We begin by considering two principles, each having the form causal completeness ergo screening-off. The first concerns a common cause of two or more effects; the second describes an intermediate link in a causal chain. They are logically independent of each other, each is independent of Reichenbach’s principle of the common cause, and each is a consequence of the causal Markov condition. Simple examples show that causal incom-pleteness means that screening-off may fail to obtain. We derive a stronger result: in a rather general setting, if the composite cause C1 & C2 &... & Cn screens-off one event from another, then each of the n component causesC1,C2,...,Cn must fail to screen-off. The idea that a cause may be ordinally invariant in its impact on different effects is defined; it plays an important role in establishing this no-go theorem. Along the way, we describe how composite and component causes can all screen-off when ordinal in-variance fails. We argue that this theorem is relevant to assessing the plausibility of the two screening-off principles. The discovery of incomplete causes that screen-off is not evidence that causal completeness must engender screening-off. Formal and epistemi