TY - JOUR
T1 - Screening off generalized
T2 - Reichenbach’s legacy
AU - Atkinson, David
AU - Peijnenburg, Jeanne
N1 - Funding Information:
We thank two anonymous referees for very useful suggestions, and Bill Roche and Tomoji Shogenji for helpful and entertaining discussions on an earlier version of this paper. Thanks also to the participants of the agreeable conference ‘All Things Reichenbach’, organized by Erik Curiel and Flavia Padovani in July 2019 in Munich, for their searching questions and remarks.
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/12
Y1 - 2021/12
N2 - Eells and Sober proved in 1983 that screening off is a sufficient condi- tion 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 condi- tion, one that can be made as weak as one wishes.
AB - Eells and Sober proved in 1983 that screening off is a sufficient condi- tion 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 condi- tion, one that can be made as weak as one wishes.
KW - Probabilistic support
KW - Reichenbach
KW - Screening off
KW - Sufficient conditions
KW - Transitivity
UR - http://www.scopus.com/inward/record.url?scp=85107650678&partnerID=8YFLogxK
U2 - 10.1007/s11229-021-03165-w
DO - 10.1007/s11229-021-03165-w
M3 - Article
AN - SCOPUS:85107650678
SN - 1573-0964
VL - 199
SP - 8335
EP - 8354
JO - Synthese
JF - Synthese
IS - 3-4
ER -