Foundations of a Probabilistic Theory of Causal Strength*

This paper develops axiomatic foundations for a probabilistic theory of causal strength as difference-making. I proceed in three steps: First, I motivate the choice of causal Bayes nets as an adequate framework for defining and comparing measures of causal strength. Second, I prove several representation theorems for probabilistic measures of causal strength— that is, I demonstrate how these measures can be derived from a set of plausible adequacy conditions. Third, I use these results to argue for a specific measure of causal strength: the difference that interventions on the cause make for the probability of the effect. I conclude by discussing my results and outlining future research avenues. *Forthcoming in The Philosophical Review. The proofs of the theorems are contained in the supplemental material. †Contact information: Department of Philosophy and Educational Sciences, and Center for Logic, Language and Cognition (LLC), Università degli Studi di Torino, Via Sant’Ottavio 20, 10124 Torino, Italy. Email: [email protected]. Webpage: www.laeuferpaar.de