Abstract

Eells and Sober proved in 1983 that screening off is a sufficient condition for the transitivity of probabilistic causality, and in 2003 Shogenji noted that the same goes for probabilistic support. We start this paper by conjecturing that Hans Reichenbach may have been aware of this fact. Then we consider the work of Suppes and Roche, who demonstrated in 1986 and 2012 respectively that screening off can be generalized, while still being sufficient for transitivity. We point out an interesting difference between Reichenbach’s screening off and the generalized version, which we illustrate with an example about haemophilia among the descendants of Queen Victoria. Finally, we embark on a further generalization: we develop a still weaker condition, one that can be made as weak as one wishes.

Highlights

  • In their instructive entry on Hans Reichenbach in the Stanford Encyclopedia of Philosophy, Clark Glymour and Frederick Eberhardt note that “the fruits of some of [Reichenbach’s] insights are only belatedly having their full impact”; in addition they observe that some of these insights have re-emerged in recent philosophy “without notice of the connection” to Reichenbach’s work.1 As an example of the former they mention contemporary ideas about causality that can be traced back to Reichenbach’sThis article belong to the topical collection on All things Reichenbach, edited by Erik Curiel and Flavia Padovani

  • We bring to mind the proof of Eells and Sober (1983) that screening off is a sufficient condition for the transitivity of probabilistic causality, and we recall Tomoji Shogenji’s argument that the same applies to probabilistic support (Shogenji 2003)

  • In this paper we have argued that Reichenbach’s thoughts on screening off illustrate both of their claims

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Summary

Introduction

In their instructive entry on Hans Reichenbach in the Stanford Encyclopedia of Philosophy, Clark Glymour and Frederick Eberhardt note that “the fruits of some of [Reichenbach’s] insights are only belatedly having their full impact”; in addition they observe that some of these insights have re-emerged in recent philosophy “without notice of the connection” to Reichenbach’s work. As an example of the former they mention contemporary ideas about causality that can be traced back to Reichenbach’s. They find an example of the latter in the work by Michael Strevens and Harman and Kulkarni: Michael Strevens’ Bigger Than Chaos (Strevens 2003) reprises the views and arguments of Reichenbach’s doctoral thesis without the Kantian gloss. The idea that screening off guarantees transitivity of probabilistic support reappeared in recent philosophy without mention of the connection to Reichenbach’s work. We bring to mind the proof of Eells and Sober (1983) that screening off is a sufficient condition for the transitivity of probabilistic causality, and we recall Tomoji Shogenji’s argument that the same applies to probabilistic support (Shogenji 2003). We introduce what we call ‘generalized screening off’, by which we mean the weaker sufficient condition for transitivity described by William Roche in (2012), preceded by Patrick Suppes in (1986).

Reichenbach’s screening off
Generalized screening off
The royal disease
A further generalization
Digging deeper
Conclusion
A Shogenji’s Identity Modified Lemma The following identities hold:
B Haemophilia
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