Againt Armstrong on Causation

I’m working on a short paper arguing that Armstrong’s account of causation fails. The argument seems so simple that I’m worried I’ve missed something obvious. Any suggestions are much appreciated.

Armstrong identifies singular causal relations with instantiations of a law—with instances of the necessitation relation. Let N(P, Q) represent P’s necessitation of Q. In the case of determinism, N(P, Q) is something like P probabilifies Q to degree x.

I claim that Armstrong’s theory fails in indeterministic contexts. Whenever N(P, Q) holds, every instance of P is related by N to Q. After all, instances of universals are, according to Armstrong, nothing other than the universal itself. But then in cases where P occurs but does not cause Q, the instance of P is still related by N to Q. The law is instantiated, but causation does not occur. Hence, causation is not the instantiation of a law.

Here’s a slightly different way of putting the same problem: Assume indeterminism. Let it be an indeterministic law that N(P, Q). Assume there is an instance of P that is not followed by an instance of Q. (This is possible, given the assumption of indeterminism.) Either the instance of P is related by an instance of N to Q or it is not. Suppose it is. Then P caused Q, contrary to our assumption. On the other hand, suppose P is not related by N to Q. Then there is an instance of P not related by N to Q. But, then it can’t be a law that N(P, Q), contrary to our assumption.

It seems to me that Armstrong needs singular causal relations in addition to laws, so that in indeterministic contexts, the law can be instantiated without the singular causal relation holding.

Armstrong on Lewis on causation

Armstrong claims that truthmakers for causal claims, for Lewis, are entirely this-worldly:

"Lewis's talk of possible worlds here is to a degree miselading. It is important to realize, as I did not originally realize, and I think many others have not realized, that these counterfactuals are supposed to hold solely in virtue of features of the world in which the causal relation holds. As I would put it, the truthmaker for causal truths is to be found solely in the world in which the relation holds. (I think this follows straight from the contingency of the causal relation, a contingency that Lewis does not doubt.) In his theory of causation the possible worlds enter as mere calculational devices. He has given me as an example the way that we might say with truth that a person is a Montague rather than a Capulet, without being being committed to the view that these families are actual. The fictional families are used as no more than a calculational device." ("Going through the Open Door Again: Counterfactual versus Singularist Theories of Causation," p. 445)

I must confess that I don't understand, so perhaps you all can help me understand. If the possible worlds are merely a calculational device, then there should be some way to make the calculation with a different device. (I could explain what was meant by a person being a Montague rather than a Capulet with different concepts if you had never read Shakespeare.) Assume, then that there are no possible worlds. What is it, in this world, that makes causal counterfactuals—had c not occurred, e would not have occurred—true (when they are)? It must have something to do with laws, but I'm not sure how that would go.

(I assume that Armstrong does not mean merely that the possible worlds don't need to be Lewisian worlds, that they might be linguistic constructions or sets of abstract states of affairs. The claim is not that the truthmakers don't have to be other-worldly; it's that they are entirely this-worldy.)

I'm also puzzled by Armstrong's parenthetical remark, that the this-worldy nature of truthmakers for causal claims follows directly from the contingency of causation. How is that argument supposed to go?

Presentism, causation and truthmakers for the past

I’m working on both causation and the truthmaker objection to presentism, and it seems to me that it might be possible to kill two birds with one stone. What follows is the basic idea, and I’d love to hear your thoughts.

Suppose that presentism is true. What is the nature of causation? It’s the relation between what and what? Or, more relevantly, between when and when? Since, according to presentism, the past does not exist, either causation is a relation between nothing and something in the present, or causation is simultaneous, or causation is not a relation at all. The first option seems dubius. A two place relation (I’m ignoring contrastivism, for the moment) has two relata, after all, not one.

What, then, about the second option? C. B. Martin defends this view in The Mind in Nature—or, at any rate, that’s my understanding of what Martin defends. But it’s not clear how to make sense of causal processes on this view. (Persistence intuitively has causal constraints; how are we to make sense of these constraints if all causation is simultaneous?)

The third option seems to me the route to go. Here’s an initial proposal: Causation is a fact about presently existing (Armstrongian) states of affairs, or tropes if you have them. It is a fact about e, say, that c brought it about. Suppose, however, that existentialism is true, so that if x does not exist, there are no singular propositions about x. If c is a state of affairs and the particular that is a non-merelogical constitutent of c no longer exists, then the fact that c caused e is the fact about e that something c-like brought it about. If c is a trope no longer instantiated and the instantiation condition is true, so that uninstantiated properties do not exist, then too causation is the fact that something c-like brought about e.

How are we to understand “something c-like”? Here’s one proposal: Properties are or of necessity confer causal powers, so we can understand “something c-like” as “something with the following causal powers profile...” (Of course the Neo-Humeans can’t really accept this view, but how many Neo-Humeans are presentists?)

What should we say about the fact in question, that e was brought about by something c-like? It might be a property of the world, as in Bigelow’s “Presentism and Properties.” It might be a property of e. Or it might not be a property, but a fact grounded in something else. Or a primitive fact about e.

Whatever answer one gives here seems also to be an answer to the objection to presentism from truthmakers about the past. Hence the presentist, so long as they can offer a theory about the nature of the fact that e was brought about by something c-like, can kill two birds with one stone, a theory of causation and a response to the truthmaker objection.

Here’s an initial proposal. Take property instances to be tropes. Then, with certain other assumptions about tropes, events can be understood as tropes. So trope c caused trope e. That turns out to be a fact about e: that it was brought about by c. Since I’m inclined to accept both existentialism and the instantiation condition, this will turn out to be the fact, about e, that it was brought about by something c-like. The fact is a basic truth, and e alone is its truthmaker. This is analagous to e’s also being, in virtue of either being or of necessity conferring causal powers, (part of) the truthmaker for counterfactuals describing what objects with e would do in various circumstances. It is a truthmaker for future truths and for the past truth about c.

One further claim, and we have a theory of truthmakers for the past. These basic causal facts about tropes are cumulative. So the fact that e was brought about by c is the fact that e was brought about by something c-like which was brought about by something...., which was brought about by something..., and so on. As long as there is a causal chain from some present state of affairs to every past state of affairs, there is a present truthmaker for every past state of affairs.

Tropes carry with them their entire causal history and their entire power profile, and so are truthmakers for past and future truths. Present property instances do a lot of work on this view, but that’s about what we should have expected given presentism.

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?