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 tWe 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._{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.

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:

- Ch
_{wt}(A|H) = x and H is true iff Ch_{wt}(A) = x.

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?

CC1 can probably be saved from the Hesslow example by saying that the pill does contribute positively towards the chance of getting a thrombosis, *as well as* contributing negatively. If we can make sense of c making multiple distinct contributions to the chance of e, then CC1 says that as long as at least one of these contributions is a positive one then c is a potential cause of e.

ReplyDeleteThe worry, of course, is how we distinguish (without appealing to causation) cases where a chance is unaffected by c because two contributions cancel, from cases where a chance is unaffected by c because c is completely irrelevant to the chance. But we seem to be able to do this in practice, by appeal to known contributions made by c to chances of distinct types of events which themselves are chance-raisers or lowerers (eg pregnancy).

Three problems are raised by Eagle for CC1.

ReplyDelete1. Hesslow's birth control pill example. Eagle writes ‘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 promoter 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.’

My reply: Yes ‘fixing the chance’ is being used in a non-standard way. However, this use is explained in the paper and it’s not unintuitive. In the pill-case, the taking of the pill contributes to the chance in the sense that it along with other facts can be used to explain why there is a non-zero chance of thrombosis. This idea of explaining of explaining a non-zero chance of an outcome is examined in the paper, and I briefly look at it below. Note: Eagle says that taking the pill contributes, in some sense of ‘contributes’, to the chance no more than non-causes do. Maybe that is true, but it’s irrelevant to CC1. CC1 says that if A causes B then A contributes to the chance of B. That’s not falsified by non-causing contributing to the chance of B. Furthermore, the non-causes, will not explain how there is a positive chance of the cause.

2. The backwards causation case. What about where A causes B in the past, and so, there must be a backwards chance of B to which A contributes. This is also explicitly considered in the paper. The problem raised by Eagle is that we may want to accept the thesis that conditioning the present chances on the actual history don’t give different chances. That is:

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

But this may be a problem since if we incorporate B into history, you might think, the chance of B at the time of A has to be one. In other words, all backwards chances are zero or one. There aren’t any non-trivial backwards chances reflecting backwards cause.

My response: It strikes me that the history conditioning principle is obviously false. It just builds in a temporal asymmetry prejudice about chance—it’s dismissing by fiat the idea of backwards chance. Take Dummett’s dancing chief whose dancing functions retroactively. The chief dances in the hope that the braves will win yesterday’s battle. But let’s say he is a probabilistic dancing chief. He is 90% effective. The chief’s dancing results in a backward chance of 90% of victory, leaving aside other interfering factors, such as counter-dancing from the enemy chief. But let’s say that in fact the braves have lost the battle. Still, the backwards chance of their winning wasn’t zero, it was 90%. Compare a future directed case. The chief’s brother on the same day dances for the victory of another set of braves in the battle tomorrow. He is 90% effective too. But let’s say in fact that the braves for whom he is dancing lose the battle tomorrow. That’s no reason to say that the chance of victory the next day at the time of second cheif’s dancing was 0%. So why do we suppose that the fact that the braves lost the battle the day before means that the chance of their winning at the time of the first chief’s dancing is 0%? Apparently, accepting the history conditioning principle above requires that. So we ought to reject it—it just affirms an temporal asymmetry where there is none.

Eagle writes: ‘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.’

My response: Well, I am not rejecting that e is part of history. It’s just irrelevant to the chance, at the time of c of e. That leaves us with a question about what chances are, but we are not totally in the dark. We can tentatively say that what’s relevant to a chance at t of some outcome e earlier is some selection of facts at t. (Those facts cannot be tensed facts, like the fact that e happened earlier, and so on.)

3: Zero chances and infinitesimals. Say the spinning of the roulette wheel caused it to land on some point. There are an finite number of points. What’s the chance of the wheel landing on the point, zero or infinitesimal? If zero, CC1 looks in trouble. I suppose I am betting on the thesis that we want to distinguish the probability of logically impossible events and logically possible events. If we can do that, there’s hope yet for CC1.

Thanks for commenting Stephen!

ReplyDeleteQuickly: on the history conditioning principle. One of the things it is supposed to get at is the idea that what's chancy is just what is not open. In that sense, it's like the Future Principle Schaffer discusses in 'Deterministic Chance' (BJPS 2007), and the Basic Chance Principle of Bigelow, Collins and Pargetter (BJPS 1993). And I followed those authors in assuming that if

eis part of the history, then it is no longer open as to whethere, so that conditioning on the history won't fix any of the open facts and hence won't alter the chances.Stephen's position in the comment seems to be that the chances are entirely fixed by some subset of the facts, so that including more facts will change the chances. This is obviously true about future facts and present chances for an eternalist; so one way I thought Stephen could go here is to reject Lewis' notion of

admissibilityas always permitting facts about the past to be admissible. (This is not quite what Stephen says, but I can't see how what he says will work: he says that the fact that e is not 'relevant' to the chance of e, in which case we should be able to condition on it and leave the chances unchanged, which we cannot do. So I think it more charitable to argue that the fact that e is inadmissible; this preserves the symmetry between past and future chances that the indian chief cases seem to involve.)In this framework, chances are only accidentally to do with what's open; its just that what is open is generally inadmissible, but maybe some things no longer open are also inadmissible. Then the task is to spell out inadmissibility; none of the attempts I know of will rule out past facts from being admissible, but maybe it can be done.