Barker on Chance and Cause II

In my last post, I discussed Barker's CC1. I said I'd leave discussion of CC2 for later, and here it is. CC2, recall, is this principle

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 t_c 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?

Barker on Chance and Cause

In our dispositions reading group, we've been reading some of the papers from Toby Handfield's recent OUP collection Dispositions and Causes. Yesterday Luke Glynn, Barbara Vetter, Alastair Wilson and myself discussed Stephen Barker's paper 'Leaving things to take their chances: Cause and disposition grounded in chance'. We had a number of concerns about the argument. I'm going to skip our worries about what seems to be significant circularity in the account, and the fact that in abandoning the claim that chances are probabilities, Barker leaves a central plank of his thesis fatally unclear.

What I want to discuss are Barker's central claims connecting chance and cause, which he calls CC1 and CC2.

CC1: If c causes e, c contributes to the chance of e at t_c, the time at which c occurs.

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.

We found both of these principles objectionable. In this post I'll discuss some of our worries about CC1; I'll discuss CC2 in a later post I hope.

Discussing CC1, Barker says:

The general argument for CC1 might be summed up thus: causes explain their effects. If c causes e, then c explains e, and thus, at time t, c is a potential explanation of e. How then can c at t not contribute to fixing the chance of e at t?

The obvious problem we saw with this argument came from cases like Hesslow's birth control pill example, where it could be that taking the pill causes thrombosis despite the fact that it makes no difference to the chances of an individual getting a thrombosis (because it exactly balances the risk, by inhibiting pregnancy, a potent promotor of thrombosis), and hence doesn't make a contribution to fixing them at their actual values—or, at least, no more of a contribution than non-causes do. Perhaps Barker is using 'fixing the chance' in some non-standard way, but he gives no indication of doing so

There are other problems too. If backwards causation is possible, as seems plausible in light of the possibility of time travel (and perhaps of some interpretations of quantum mechanics, such as those Huw Price has defended), then CC1 entails that some past events have non-trivial chances. But how can this be? If H is the history up until t, then no matter how or whether history fixes chances, it should be that the present chance of an event in a world w should be the same as the chance conditional on the history:

1. Ch_wt(A|H) = x and H is true iff Ch_wt(A) = x.

(1) doesn't commit us to a Humean picture of chance; its simply the thought that conditioning the present chances on the actual history shouldn't give different chances. (1) entails that if H implies A, then the present chance of A is 1; so the past isn't chancy after all. Barker's response to this line of objection will presumably be to reject the thought that all past events are in the history; if c causes e, and e is in the past, then e won't be in the history. But I am at a loss to understand how this is supposed to work.

Barker mentions Lewis in this connection, as someone who accepts (1), and says

The spirit of CC1 is that there may be non-trivial backwards-directed chances. Lewis then must be wrong to have taken this line. Indeed, it is not clear why he takes it. Lewis accepts a chance-raising view about causation, and embraces the conceptual possibility of backwards causation.

But Lewis does not accept a chance-raising view about backwards causation—in that case he explicitly thinks that (the ancestral of) regular non-backtracking counterfactual dependence is what enables prior effects to be caused (this is the case where a non-backtracking counterfactual just happens to have an antecedent made true after the time the consequent is made true, and doesn't have the evidential reading of backtracking counterfactuals). So I'm left no happier with CC1 despite these remarks about Lewis.

There are other worries about CC1 (e.g., Barker's invocation of infinitesimals despite the fact that it is no longer clear whether they can help with the problems of zero chance events, as Williamson recently argued). But I'll leave them, and invite comments on these problems here. Any defenders of CC1? I'm aware that the considerations I gave in favour of (1) aren't completely compelling, so anyone want to argue against it?