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.
I agree with vallinder's point, and would also like to add that arguments for moral realism which aren't theistic or contractarian in nature typically appeal to moral intuitions. Thus, instead of providing positive arguments for realism, they at best merely show that arguments for the unreliability of realists' intuitions are unsound. (For example, IIRC, Russ Shafer-Landau in this book tries to use a parity argument between moral and logical intuitions, so that arguments against the former would have to also apply to the latter.) But clearly this is an essentially defensive maneuver which poses no threat to the orthogonality thesis (even if motivational judgment internalism is true), because the latter works just as well when you substitute "moral intuition" for "goal."