Do you know Jon Williamson's work? It seems to give an answer to your question (but I've not read it yet). Here's the first paragraph of Section 9.1 “Mental yet Objective” of his book “Bayesian Nets and Causality”:
Epistemic causality embodies the following position. The causal relation is mental rather than physical: a causal structure is part of an agent’s representation of the world, just as a belief function is, and causal claims do not directly supervene on mind-independent features of the world. But causality is objective rather than subjective: some causal structures are more warranted than others on the basis of the agent’s background knowledge, so if two people disagree about what causes what, one may be right and the other wrong. Thus epistemic causality sits between a wholly subjective mental account and a physical account of causality, just as objective Bayesianism sits between strict subjectivism and physical probability.
Here's a link to his papers on causality. At least the fifth, “Causality”, contains an introduction to epistemic causality.
Nope, I wasn't familiar. Very interesting, thanks!
Most people here seem to endorse the following two claims:
1. Probability is "in the mind," i.e., probability claims are true only in relation to some prior distribution and set of information to be conditionalized on;
2. Causality is to be cashed out in terms of probability distributions á la Judea Pearl or something.
However, these two claims feel in tension to me, since they appear to have the consequence that causality is also "in the mind" - whether something caused something else depends on various probability distributions, which in turn depends on how much we know about the situation. Worse, it has the consequence that ideal Bayesian reasoners can never be wrong about causal relations, since they always have perfect knowledge of their own probabilities.
Since I don't understand Pearl's model of causality very well, I may be missing something fundamental, so this is more of a question than an argument.