CC2: If at a time t, there is a non-zero chance of e and e obtains, then at least some of the conditions at t that determine the chance of e at t, caused e.Of this principle, Barker says 'Unlike CC1, CC2 is bound to be controversial'; given our discussion of CC1, I guess this makes CC2 really controversial!
And indeed we found it objectionable. The easiest way to see it is to rehearse Humphreys' problem for propensity theories: if chances are probabilities, Bayes' theorem entails that in general if Ch(e|c) is non-trivial (i.e., not zero or one), then Ch(c|e) will be non-trivial. And this looks weird if this is conceived of as a conditional chance in line with CC2; if e occurs, then it looks like at the time of e, c will generally have some non-trivial chance, and e will be a condition which determines the chance of c but doesn't cause it. In general, as Barker notes, effects are evidence for causes, and so give their causes a probability, which cannot be a chance consistently with CC2 unless there is far more backwards causation than usually thought.
Barker doesn't opt for the idea that backwards causation is widespread. His primary response is that past-directed probabilities, like those that effects give to causes and that appear in inverse conditional probabilities, 'are not real chances'. And if they aren't real chances, then CC2 won't give us 'bogus backward causation'.
Now of course any counterexample can be defined away, which is in effect what Barker does here. But this isn't completely ad hoc, since he does offer an argument. Barker appeals to this principle:
RC: Where c and e occur, if the chance at tc of e would have been lower, had c not obtained, then if there is no redundant causation in operation, c caused e.RC basically expresses the counterfactual chance-raising account of causation, without the usual restriction to non-backtracking counterfactuals. As such, even when e is prior to c, RC still holds; so if there were widespread backwards chances, there would be widespread backwards causation. This is absurd; so Barker rejects the assumption that these backwards probabilities are chances.
Now, when some assumptions collectively lead to an absurdity, we are only required to reject some one of them, not any particular one. But it seemed to us that Barker had clearly chosen the wrong one: it is RC that has to go, not the assumption that chances are probabilities. I can't imagine even those who defend the counterfactual chance-raising view of causation as liking RC as a way of expressing what's right about it.
But let's say we do accept Barker's way out. If chances aren't probabilities, then what are they? About this I really am in the dark. They can't be the things that govern credences, since Lewis' arguments in 'A Subjectivist's Guide to Objective Chance' suggest that whatever function it is that regulates credence will be a probability function. They won't have much to do with frequencies, since past conditional frequencies will approximate the past probabilities which aren't the past chances, according to Barker. They won't obey the Basic Chance Principle of Bigelow, Collins, and Pargetter—or indeed many of the platitudes that circumscribe the conceptual role of chance that Jonathan Schaffer has recently outlined. (It won't meet these platitudes both through failing to be a probability, and because CC1 and the existence of backwards causation entail the existence of backwards chances, inconsistent with many of these platitudes, notably Schaffer's Realization Principle, Future Principle, and Lawful Magnitude Principle) Maybe Barker-chance meets other platitudes; but will it be genuinely chance if it doesn't meet these platitudes or something like them? It looks like only a probability can play the chance role.
One last thing: in his discussion of apparently spontaneous uncaused events, Barker makes the point that even in those cases the structure of the entities involved can be the cause. He discusses a case of radioactive decay; the decay is, he says, caused by the structure of the element that decays. Fine; but he then says that if the decay does not occur, it is not caused by the structure of the element. This I didn't see: it seems to me that the chance of decay is fixed by the structure, so why not say it causes the lack of decay just as much as the decay? Barker says 'one could not say that there was no decay because [the element] was present'—but why not?