1. A New Condition for Transitivity of Probabilistic Support
- Author
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David Atkinson, Jeanne Peijnenburg, High-Energy Frontier, and Other personnel
- Subjects
Transitive relation ,Property (philosophy) ,Logic ,As is ,05 social sciences ,Probabilistic logic ,06 humanities and the arts ,050905 science studies ,0603 philosophy, ethics and religion ,Simpson's paradox ,Constraint (information theory) ,Philosophy ,060302 philosophy ,Ontology ,0509 other social sciences ,Mathematical economics ,Mathematics - Abstract
As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity.
- Published
- 2023