Screening-Off and Causal Incompleteness: A No-Go Theorem

Abstract

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 incompleteness 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 causes C1, 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 invariance 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 epistemic analogies between screening-off and determinism are discussed. 1 Introduction 2 Influence and Non-degeneracy Conditions 3 A No-Go Theorem for Two Dichotomous Causes and its Limitations 4 A More General No-Go Theorem: Allowing Several Causes, Possibly Non-dichotomous 5 Examples Illustrating Corollary 3 and Theorem 5a 6 Determinism and Screening-Off: Disanalogy and Analogy Appendix