Thanks for clarifying the point about anticipations, that was very helpful and I'll have to give it more thought. I read Eliezer's article again, and while I don't think his intention was to give an account of the identity of facts, he does mention that if we're arguing over facts with identical anticipations, we may be arguing over a merely semantic point. That's very possibly what's going on here, but let me try to defend the idea that these are distinct facts one last time. If I cannot persuade you at all, I'll reconsider the worth of my argument.
In my comment to Alejandro1, I mentioned three sets of facts. I'll pare down that point here to its simplest form: the relationship between 'X is taller than Y' and 'Y is shorter than X' is different than the relationship between 'X carries Y' and 'Y is carried by X'. This difference is in the priority of the former and the latter fact in each set. In the case of taller and shorter, there is no priority of one fact over the other. They really are just different ways of saying the same thing.
In the case of carrying and being carried, there is a priority. Y's being carried is explained by X's carrying. Y is being carried, but because X is carrying it. It is not true that X is carrying because Y is being carried. In other words, X is related to Y as agent to patient (I don't mean agency in an intentional sense, this would apply to fire and what it burns). If we try to treat 'X carries Y' and 'Y is carried by X' as involving no explanatory priority (if we try to treat them as the same fact), the loose the explanatory priority, in this case, of agent over patient.
An example of this kind of explanatory priority (in the other direction) might be this set: 'A falling tree kills a deer' and 'a deer is killed by a falling tree'. Here, I think the explanatory priority is with the patient. It is only because a deer is such as to be killed that a tree could be a killer. We have to explain the tree's killing by reference to the deer's being killed. If the tree fell on a deer statue, there would be no explanatory priority.
But maybe my confusion is deeper, and maybe I'm just getting something wrong about the idea of a cause. Thanks for taking the time.
Apparently you're working in something that's akin to a mathematical system... you start with a few facts (the ones with high 'explanatory priority') and then you derive other facts (the ones with lower 'explanatory priority'). Which is nice and all, but this system doesn't really seem to reflect anything in reality. In reality, a deer getting killed by a tree is a tree killing a deer is a deer getting killed by a tree.
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