Causal reasoning, causal probabilities, and conceptions of causation.

The present paper deals with the tools that can be used to represent causation and to reason about it and, specifically, with their diversity. It focuses on so-called "causal probabilities"--that is, probabilities of effects given one of their causes--and critically surveys a recent paper in which Joyce (2010) argues that the values of these probabilities do not depend on one's conception of causation. I first establish a stronger independence claim: I show that the very definition of causal probabilities is independent of one's conception of causation. Second, I investigate whether causal probabilities indeed take the same values under their different possible definitions.