If you let X be incomplete like twanvl suggests, then you pretty much agree with my position of using probability as a useful tool, and disagree with Bayesian fundamentalism.

How is a distribution useful if it refuses to answer certain questions? I think I'm misunderstanding something you said, since I think that the essence of Bayesianism is the idea that probabilities must be used to make decisions, while you seem to be contrasting these two things.