1. Introduction.

Among the current philosophical attempts to understand causation two seem to be the most prominent. The first is James Woodward's counterfactual approach; the second is the mechanistic approach advocated by Peter Machamer, Lindley Darden, Carl Craver, Jim Bogen and Stuart Glennan. The counterfactual approach takes it that causes make a difference to their effects. This difference-making is cashed out in counterfactual terms: the relationship among some variables (or magnitudes) X and Y is causal if, if an intervention changed the value of X appropriately, the relationship between X and Y would remain invariant and the value of Y would change. The mechanistic approach takes it that two events are causally related if and only if there is a mechanism that connects them.

Mechanisms are taken to be complex systems, which are composed of parts, have internal structure or organisation and certain spatio-temporal locations. The mechanism has a characteristic behaviour in virtue of the properties, dispositions or capacities of its parts as well as in virtue of how these parts are organised and interact with each other. What the mechanism is doing (its characteristic activity, its behaviour or its output) is caused and explained by the details of how it is doing it. These details include the internal workings of the mechanism. Both approaches are, in a sense, anti-metaphysical.

Both concentrate on how causal relations can be understood and established, if we take on board the ways scientists themselves try to discover and establish causal connections and causal facts. Though there may be dissenting voices from within each approach, they both take it that they do not offer an analysis of causation, and in particular an analysis of causation in non-causal terms. On the face of it, the two approaches need not be in conflict. The mechanisms might satisfy (or depend on) certain interventionist counterfactuals and, conversely, the interventionist counterfactuals might be made true by the presence of certain mechanisms. But, overall, both approaches tend to be imperialistic. Advocates of each argue that their own approach fairs much better than their opponents'. Characteristically, Jim Bogen (2003) (and, I suspect, other mechanists too) claims that the notion of a counterfactual intervention is too obscure to serve as the basis of an account of causation.

He thinks that the mechanistic approach has distinctive advantages over the counterfactual approach, most salient of which is that it avoids an appeal to counterfactuals. Woodward (2003a), in reply to Bogen, argues for the primacy of interventionist counterfactuals. And in his (2002), he argues that the concept of a mechanism can be fully accommodated within his own counterfactual framework. The question then is this: are we forced to choose between the mechanistic approach and the counterfactual one? In this paper, I will argue that, as they stand, both approaches face some important problems that need to be fixed. I shall also argue that there is a sense in which the counterfactual approach is more basic than the mechanistic, though the former will benefit from a better understanding of the mechanisms that are at work in causal connections. So both approaches can work together to offer a better understanding of causation. If they work in tandem, they can offer us a glimpse of what Hume famously called "the secret connexion". But in so far as the 'secret connexion' is an intrinsic relation between the causal relata, neither of the above approaches tells us what this relation is.

2. Early Views.

J L Mackie's work on causation is the recent common source of both approaches under discussion. Mackie explicitly appealed to counterfactuals in his definition of the meaning of singular causal statements. He (1974, 31) argued that a causal statement of the form 'c caused e' should be understood as follows:

c was necessary in the circumstances for e,

where c and e are distinct event-tokens. Necessity-in-the-circumstances, he added, should be understood as follows:

if c hadn't happened, then e wouldn't have happened.

Mackie's main thought was that counterfactual statements are not, strictly speaking, true or false: they do not describe, or fail to describe, "a fully objective reality" (1974, xi). Instead, they are reasonable or unreasonable assertions, whose cogency depends on the inductive evidence that supports them (cf. 1974,
229-30). Take the statement 'If this match had been struck, it would have lit'. In assessing this counterfactual, the evidence plays a double role. It first establishes inductively a generalisation. But then, "it continues to operate separately in making it reasonable to assert the counterfactual conditionals which look like an extension of the law into merely possible worlds" (1974,

203). So for Mackie, it is general propositions (via the evidence we have for them) that carry the weight of counterfactual assertions. If, in the actual world, there is strong evidence for the general proposition 'All Fs are Gs', then "we feel justified in extending [it]" beyond its observed instances "not only to other actual instances but to merely possible ones" (1974, 55). We base our confidence that 'if x had been an F it would have been a G' on the evidence that supports the general proposition. Mackie was no realist about possible worlds. He did not think that they were as real as the actual. Hence, his talk of possible worlds was a mere facon de parler (cf. 1974, 199). Still, he thought it convenient to think in terms of possible worlds when counterfactuals are assessed. These evidence- based counterfactuals cannot ground a fully objective distinction between causal sequences of events and non-causal ones.

This created a tension in Mackie's overall project. For although he explicitly aimed to identify an intrinsic feature of a causal sequence of events that makes the sequence causal, his dependence on evidence-based counterfactuals jeopardised this attempt: whether a sequence of events will be deemed causal will depend, on his view, on an extrinsic feature, viz., on whether there is evidence to support the relevant counterfactual conditional. It is for this reason that Mackie went on to try to uncover an intrinsic feature of causation, in terms of a mechanism that connects the cause and the effect. As Hume famously noted, the alleged necessary tie between cause and effect is not observable. Mackie thought, not unreasonably, that we might still hypothesise that there is such a tie, and then try to form an intelligible theory about what it might consist in. His hypothesis is that the tie consists in a "causal mechanism", that is, "some continuous process connecting the antecedent in an observed (...) regularity with the consequent" (1974, 82). Where Humeans, generally, refrain from accepting anything other than spatiotemporal contiguity between cause and effect, Mackie thinks that mechanisms might well constitute "the long-searched-for link between individual cause and effect which a pure regularity theory fails, or refuses, to find" (1974, 228-9). Mackie's own view was that this mechanism consists in the qualitative or structural continuity, or persistence, exhibited by certain processes, which can be deemed causal (1974, 218ff).

There needn't be some general feature (or structure) that persists in every causal process. What these features are will depend on the details of the actual "laws of working" that exist in nature. For instance, what persists can be "the total energy" of a system, or the "number of particles", or "the mass and energy" of a system (cf. 1974, 217-8). But insofar as something persists in a certain process, this feature can be what connects together the several stages of this process and renders it causal. So, early versions of both current views about causation can be found in Mackie's work. In fact, it turns out that the mechanistic view was more central in Mackie's overall approach, since it promised to offer a more objective account of causation and to avoid the notorious context- sensitivity of counterfactual assertions. Yet, Mackie's attempt to spell out mechanisms in terms of persistence was deeply problematic.

After Mackie, the counterfactual and the mechanistic approaches parted their ways. They were separately pursued and developed by other able philosophers. The locus of the standard counterfactual theories of causation is the work of the Late David Lewis (1986). Unlike Mackie, Lewis (1973) put forward a quasi- objectivist theory of counterfactuals, based on possible-words semantics. For lack of space, I will not review this approach here. I will only make the following point, which is relevant to what follows. Lewis's theory makes causation an extrinsic relation between events, since it analyses causation in terms of counterfactual dependence among events and it analyses counterfactuals in terms of relations of similarity among possible worlds. In fact, it should be noted that there is a rather important reason why counterfactual theories cannot offer an intrinsic characterisation of causation. If causation amounts to counterfactual dependence among events, then the truth of the claim that c causes e will depend on the absence of causal overdeterminers, since if the effect e is causally overdetermined, it won't be counterfactually dependent on any of its causes.

But the presence or absence of overdeterminers is certainly not an intrinsic feature of a causal sequence. The locus of the standard mechanistic theories of causation is the work of the Late Wesley Salmon. Unlike Mackie, Salmon (1984) thought we should try to characterise directly when a process is causal, thereby finding the mechanism that links cause and effect. So he took processes rather than events to be the basic entities in a theory of physical causation. Here again, I will not review Salmon's views here, due to lack of space. A general note, however, is important for what follows. Roughly put, Salmon characterised causal those (and only those) processes that transmit marks. Now, Salmon's original promise was for a theory of causation that does not involve counterfactuals. The promise, however, was not to be fulfilled. What was central to Salmon's theory is the ability of a process to transmit a mark. But the ability is a capacity or a disposition, and it is essential for Salmon that it is so. For he wants to insist that a process is causal, even if it is not actually marked (cf. 1984,
147).

So, a process is causal if it could be marked. Counterfactuals loom large! All this is explained in some detail in my (2002, 112-8). But the message is clear: Salmon's original mechanistic approach cannot do away with counterfactuals. In fact, Salmon's appeal to counterfactuals has led some philosophers (e. g., Kitcher 1989) to argue that, in the end, Salmon has offered a variant of the counterfactual approach to causation. Salmon has always been very sceptical about the objective character of counterfactual assertions. So as he (1997, 18) said, it was "with regret philosophical regret", that he took counterfactuals on board in his account of causation. So far, we have been engaged in some stage-setting. Our focus is the current versions of the counterfactual and the mechanistic approaches. Though more can be said, it seems enough to state that Woodward's development of the counterfactual approach is an attempt to provide an account that avoids the metaphysical extremes and epistemological nightmares of the Lewis view, and that the mechanistic approaches of Glennan and Machamer, Darden and Craver try to provide an account of causal mechanisms that is more in tune with the epistemic and explanatory practices of scientists who study mechanisms.

3. Counterfactual Manipulation.

In a series of papers and a book, Woodward (2000; 2003a; 2003b) offers an account of causation based on the idea of counterfactual manipulation. As noted in the introduction, his theory is counterfactual in the following sense: what matters is what would happen to a relationship, were interventions to be carried out. A relationship among some variables (or magnitudes) X and Y is causal if, were one to intervene to change the value of X appropriately, the relationship between X and Y wouldn't change and the value of Y would change. To use a stock example, the force exerted on a spring causes a change of its length, because it is true that if an intervention changed the force exerted on the spring, the length of the spring would change too (but the relationship between the two magnitudes-expressed by Hooke's law-would remain invariant, within a certain range of interventions). Woodward (1997; 2000; 2003b) has analysed further the central notions of invariance and intervention. The gist of his characterisation of an intervention is this. A change of the value of X counts as an intervention I if it has the following characteristics: a) the change of the value of X is entirely due to the intervention I; b) the intervention changes the value of Y, if at all, only through changing the value of X. The first characteristic makes sure that the change of X does not have causes other than the intervention I, while the second makes sure that the change of Y does not have causes other than the change of X (and its possible effects). These characteristics are meant to ensure that Y-changes are exclusively due to X-changes, which, in turn, are exclusively due to the intervention I. As Woodward notes, there is a close link between intervention and manipulation. Yet, his account makes no special reference to human beings and their (manipulative) activities. Insofar as a process has the right characteristics, it counts as an intervention. So, interventions can occur 'naturally', even if they can be highlighted by reference to "an idealised experimental manipulation" (2000, 199).

Woodward proceeds to link the notion of intervention with the notion of invariance. A certain relation (or a generalisation) is invariant, Woodward says, "if it would continue to hold-would remain stable or unchanged-as various other conditions change" (2000, 205). What really matters for the characterisation of invariance is that the generalisation remains stable under a set of actual and counterfactual interventions. For instance, Newton's law of gravity remains invariant under actual and counterfactual interventions, which would change the values of the masses of the gravitating bodies or the distance between them. So Woodward notes:

the notion of invariance is obviously a modal or counterfactual notion [since it has to do] with whether a relationship would remain stable if, perhaps contrary to actual fact, certain changes or interventions were to occur (2000, 235).

Counterfactuals have been reprimanded on the ground that they are context-dependent: whether they are true or false will depend on what factors are held fixed. Take, for instance, the following counterfactual: 'If he had not smoked so heavily, he would have lived a few years more'. How are we to assess this? Obviously, any attempt at an assessment, were it to be possible at all, would require holding fixed some things. For instance, we could hold fixed other aspects of his health, assuming that other factors
(e. g., a weak heart) wouldn't cause a premature death, anyway. If we didn't do this, the foregoing counterfactual would not be meaningful at all. But what things to hold fix is not, necessarily, an objective matter. Or, consider the following two counterfactuals: 'If Verdi had been a compatriot of Bizet, then Verdi would have been French'; and 'If Bizet had been a compatriot of Verdi, then Bizet would have been Italian'. Both of them are true, I suppose, if we hold fixed the nationality of Bizet in the first, and of Verdi in the second. Both of them have equivalent antecedents. However, if we hold both of them, we end up in a contradiction: Bizet and Verdi would be compatriots and yet Bizet would be Italian and Verdi French.

3.1 Experimental Counterfactuals.

Woodward is very careful in his use of counterfactuals. Not all of them are of the right sort for the evaluation of a whether a relation is causal. Only counterfactuals that are related to interventions can be of help. An intervention gives rise to an "active counterfactual", that is, to a counterfactual whose antecedent is made true "by interventions"
(1997, S31; 2000, 199). In his (2003b, 171) he stresses that the appropriate counterfactuals for elucidating causal claims are not just any counterfactuals but rather counterfactuals of a very special sort: those that have to do with the outcomes of hypothetical interventions. (.) it does seem plausible that counterfactuals that we do not know how to interpret as (or associate with) claims about the outcomes of well-defined interventions will often lack a clear meaning or truth value.

In his (2003a, 3), he very explicitly characterises the appropriate counterfactuals in terms of experiments: they are understood as claims about what would happen if a certain sort of experiment were to be performed.

Consider a case he (2003a, 4-5) discusses. Take Ohm's law (that the voltage E of a current is equal to the product of its intensity I times the resistance R of the wire) and consider the following two counterfactuals:

(1) If the resistance were set to R=r at time t, and the voltage were set to E=e at t, then the current I would be i=e/r at t.

(2) If the resistance were set to R=r at time t, and the voltage were set to E=e at time t, then the current I would be i* ? e/r at t.

There is nothing mysterious here, says Woodward, "as long as we can describe how to test them" (2003a, 6). We can perform the experiments at a future time t* in order to see whether (1) or (2) is true. If, on the other hand, we are interested in what would have happened had we performed the experiment in a past time t, Woodward invites us to rely on the "very good evidence" we have "that the behaviour of the circuit is stable over time" (2002, 5). Given this evidence, we can assume, in effect, that the actual performance of the experiment at a future time t* is as good for the assessment of (1) and (2) as a hypothetical performance of the experiment at the past time t. For Woodward, the truth-conditions of counterfactual statements (and their truth-values) are not specified by means of an abstract metaphysical theory, e. g., by means of abstract relations of similarity among possible worlds. He calls his own approach "pragmatic". That's how he puts it:

For it to be legitimate to use counterfactuals for these goals [understanding causal claims and problems of causal inference], I think that it is enough that (a) they be useful in solving problems, clarifying concepts, and facilitating inference, that (b) we be able to explain how the kinds of counterfactual claims we are using can be tested or how empirical evidence can be brought to bear on them, and (c) we have some system for representing counterfactual claims that allows us to reason with them and draw inferences in a way that is precise, truth-preserving and so on (2003a, 4).

Recall that Mackie had an evidence-based view of counterfactuals. He thought that counterfactual statements were not, strictly speaking, true or false. Rather, they are warranted only when there is evidence for a relevant generalisation. Unlike Mackie's, Woodward's view is meant to be realist and objectivist. He is quite clear that counterfactual conditionals have non-trivial truth-values independently of the actual and hypothetical experiments by virtue of which it can be assessed whether they are true or false. He says:

On the face of things, doing the experiment corresponding to the antecedent of [1] and [2] doesn't make [1] and [2] have the truth values they do. Instead the experiments look like ways of finding out what the truth values of [1] and [2] were all along. On this view of the matter, [1] and [2] have non-trivial truth values-one is true and the other false-even if we don't do the experiments of realizing their antecedents. Of course, we may not know which of [1] and [2] is true and which false if we don't do these experiments and don't have evidence from some other source, but this does not mean that [1] and [2] both have the same truth-value
(2003a, 5).

This point is repeated in his (2003b, 171-2), where he stresses that

We think instead of [a counterfactual such as (1) above] as having a determinate meaning and truth value whether or not the experiment is actually carried out- it is precisely because the experimenters want to discover whether [this counterfactual] is true or false that they conduct the experiment.

There are a few delicate issues here to be reckoned with. I will restrict myself to the following: what are the truth-conditions of counterfactual assertions? Woodward doesn't take all counterfactuals to be meaningful and truth-valuable. As we have seen, he takes only a subclass of them, the active counterfactuals, that is those whose antecedents can be realised by an actual or hypothetical experiment, to be such. However, he does not want to say that the truth- conditions of active counterfactuals are fully specified by (are reduced to, or supervene upon) actual and hypothetical experiments.

If he said this, he could no longer say that active counterfactuals have determinate truth-conditions independently of the (actual and hypothetical) experiments that can test them. In other words, Woodward wants to distinguish between the truth-conditions of counterfactuals and their evidence-(or test-)conditions, which are captured by certain actual and hypothetical experiments. The problem that arises is this. Though we are given a relatively detailed account of the evidence-conditions of counterfactuals, we are not given anything remotely like this for their truth-conditions. What, in other words, is it that makes a certain counterfactual conditional true? It would not help to offer a Tarski-style meta-linguistic account of their truth-conditions of the form

(T) 'If x had been the case, then y would have been the case' is true iff if x had been the case, then y would have been the case.

This move is not terribly informative. We don't know when to assert the right hand-side. And the question is precisely this: when is it right to assert the right-hand side? Suppose we were to tell a story in terms of actual and hypothetical experiments that realise the antecedent of the right-hand side of (T). The obvious problem with this move is that the truth-conditions of the counterfactual conditional would be specified in terms of its evidence-conditions, which is exactly what Woodward wants to block. Besides, if we just stayed with (T) above, without any further explication of its right-hand side, any counterfactual assertion (and not just the active counterfactuals) would end up meaningful and truth-valuable. Here again, Woodward's project would be undermined. Woodward is adamant: "Just as non counterfactual claims (e. g., about the past, the future, or unobservables) about which we have no evidence can nonetheless possess non-trivial truth-values, so also for counterfactuals" (2003a, 5). This is fine. But in the case of claims about the past or about unobservables there are well-known stories to be told as to what the difference is between truth- and evidence-conditions. When it comes to Woodward's counterfactuals, we are not told such a story. In light of the above, there are two options available. The first is to collapse the truth-conditions of counterfactuals to their evidence-conditions.

One can see the prima facie attraction of this move. Since evidence-conditions are specified in terms of actual and hypothetical experiments, the right sort of counterfactuals
(the active counterfactuals) and only those end up being meaningful and truth-valuable. But there is an important drawback. Recall counterfactual assertion (1) above. On the option presently considered, what makes (1) true is that its evidence-conditions obtain. Under this option, counterfactual conditionals lose, so to speak, their counterfactuality. (1) becomes a shorthand for a future prediction and/or the evidence that supports the relevant law. If t is a future time, (1) gives way to an actual conditional (a prediction).

If t is a past time, then, given that there is good evidence for Ohm's law, all that (1) asserts under the present option is that there has been good evidence for the law. We might not have tested the law for some particular values of R and I at the particular past time t, but given the other actual evidence that supports the law, this is unnecessary: the law itself implies that it holds for values of R and I for which it has not been actually tested. In any case, Woodward seems keen to keep evidence- and truth-conditions apart. Then, some informative story should be told as to what the truth-conditions of counterfactual conditionals are and how they are connected with their evidence-conditions (that is, with actual and hypothetical experiments). There may be a number of stories to be told here. But the one I favour ties the truth-conditions of counterfactual assertions to laws of nature. It is then easy to see how the evidence-conditions (that is, actual and hypothetical experiments) are connected with the truth-conditions of a counterfactual: actual and hypothetical experiments are evidence for the presence of a law. There is a hurdle to be jumped, however. It is notorious that many attempts to distinguish between genuine laws of nature and accidentally true generalisations rely on the claim that laws do, while accidents do not, support counterfactuals. So counterfactuals are called for to distinguish laws from accidents. If at the same time laws are called for to tell when a counterfactual is true, we go around in circles. Fortunately, there is the Mill-Ramsey-Lewis view of laws (see my 2002, chapter 5). Laws are those regularities which are members of a coherent system of regularities, in particular, a system which can be represented as an ideal deductive axiomatic system striking a good balance between simplicity and strength. On this view, laws are identified independently of their ability to support counterfactuals. Hence, they can be used to specify the conditions under which a counterfactual is true. I want to consider here one relevant thought that is central to Woodward's approach. He takes laws to be relations that remain invariant under (a range of) actual and counterfactual interventions. If this is so, when checking whether a generalisation or any relationship among magnitudes or variables is invariant we need to subject it to some variations/changes/interventions. What changes will it be subjected to? The obvious answer is: those that are permitted, or are permissible, by the prevailing laws of nature. Suppose that we test Ohm's law.

Suppose also that one of the interventions envisaged was to see whether it would remain invariant, if the measurement of the intensity of the current was made on a spaceship, which moved faster than light. This, of course, cannot be done, because it is a law that nothing travels faster than light. So, some laws must be in place before, based on considerations of invariance, it is established that some generalisation is invariant under some interventions. Hence, Woodward's notion of "invariance under interventions" (2000, 206) cannot offer an adequate analysis of lawhood, since laws are required to determine what interventions are possible.

Couldn't Woodward say that even basic laws-those that determine what interventions and changes are possible-express just relations of invariance? Take, once more, the law that nothing travels faster than light. Can the fact that it is a law be the result of subjecting it to interventions and changes? It's not clear it can. For it itself establishes the limits of possible interventions and control. I do not doubt that it may well be the case that genuine laws express relations of invariance. But this is not the issue. For, the manifestation of invariance might well be the symptom of a law, without being constitutive of it. Naturally, it is right to say that had I not brushed my teeth this morning, Newton's laws would still hold. But this is neither here not there. Are we equally willing to say that had the curvature of space-time been different, Newton's laws would still hold? It is obvious that if we allow some laws to be violated, then other laws won't remain invariant. One final point. The counterfactual approach provides an extrinsic way to identify a sequence of events as causal, viz., that the sequence remains invariant under certain interventions. Woodward (2000, 204) stresses:

what matters for whether X causes (.) Y is the 'intrinsic' character of the X-Y relationship but the attractiveness of an intervention is precisely that it provides an extrinsic way of picking out or specifying this intrinsic feature.

This, I think, should be taken to imply that there is a conceptual distinction between causation and invariance-under-interventions: there is an intrinsic feature of a relationship in virtue of which it is causal, an extrinsic symptom of which is its invariance under interventions. In his (2003b, 175) Woodward seems to endorse this reading when he says "there is a certain kind of relationship with intrinsic features that we exploit or make use of when we bring about B by bringing about A". If I have got Woodward right, causation has excess content over invariance-under-interventions, even though the former are 'exploited' when certain interventions occur. So there is more to causation-qua an intrinsic relation-than invariance-under-actual-and-counterfactual-interventions. To sum up. We need to be told more about the truth-conditions of counterfactual conditionals. If Woodward ties to close a not between counterfactuals and actual and hypothetical experiments, then it seems that counterfactual claims may reduce to claims about actual and hypothetical experiments (without any excess content). If, on the other hand, Woodward wants to insist that counterfactuals have their truth-conditions independently of their evidence-conditions, then it is an entirely open option that the truth-conditions of counterfactual assertions involve laws of nature.

3.2 Causal Inference and Counterfactuals.

In the last twenty years, there has been an increasing interest in causal inference among statisticians and social scientists and counterfactuals have loomed large in some key attempts to model it. Prominent among them is Rubin's model, which has been advanced by Donald Rubin (1978) and Paul Holland (1986). This model focuses on the discovery of the effects of causes. Suppose, to use a simple example, we want to find out whether taking an aspirin makes a difference to a specific subject's relief from headache. We would like to give a certain subject u an aspirin in order to see what happens to the headache episode-let's call the result Y. But we would also like, at the same time, to withhold giving aspirin to the very same subject u, in order to see what happens to the headache episode-let's call this result Y'. The difference, if any, between Y and Y' would naturally be considered the actual causal effect of aspirin-taking on the headache episode of subject u. But this kind of experiment is impossible: the experimenter cannot give and not give an aspirin to the same subject u at the same time.

Rubin's and Holland's main idea is that an appeal to counterfactuals allows us to make an inference about the causal effect. Let's consider a population U of individuals, or units, u Î U. In a typical experiment, the experimenter applies one treatment, say i, out of a set of possible treatments T, to each unit u and observes the resulting responses Y. The experimental units are chosen and separated into two groups (the experimental group and the control group) by randomisation. To simplify matters, let the treatment set T consist of two actions (treatment-t, and control-c). For instance, t may be taking the aspirin and c may be taking a placebo. Let, also, Y consist of two responses, e. g., headache relief-Yt, and headache persistence-Yc). Though it is crucial that each unit is potentially exposable to any one of the treatments, to each unit u just one treatment is actually given, i. e., either t or c. Similarly, for each unit u, there is just one response that is actually observed, i. e., either Yt=Y(t, u) or Yc=Y(c, u). Rubin's model defines the two responses in counterfactual terms. That is, Y(t, u) is the value of the response that would be observed if the unit u were exposed to treatment t and Y(c, u) is the value that would be observed on the same unit u if it were exposed to c.

A key assumption of Rubin's model is that both values Y(t, u) are Y(c, u) are well-defined and determined. In particular, it is assumed that even if subject u is actually given treatment t and has response Y(t, u), there is still a fact of the matter about what the subject's u response would have been, had she been given treatment c. The task is to figure out the so-called individual causal effect, that is the difference

(3) t(u)=Y(t, u) - Y(c, u)

which measures the effect of treatment t on u, relative to treatment c. In each particular experiment, either Y(t, u) or Y(c, u) (but not both) ceases to be counterfactual. Yet, given that one of Y(t, u) and Y(c, u) becomes observable, the other has to be unobservable. Holland has called a situation such as this "the fundamental problem of causal inference". As he (1986, 947) put it:

It is impossible to observe the value of Y(t, u) and Y(c, u) on the same unit and, therefore, it is impossible to observe the effect of t on u.

Does it follow that figuring out (3) above is impossible? Suppose that we give treatment t to u and we observe Y(t, u). The question then is how could we possibly figure out the value of Y(c, u)? Recall that Y(c, u) is a counterfactual: the response that would be observed if the unit u were exposed to treatment c
(given that it was in fact exposed to treatment t and the observed value was Y(t, u)). The important insight of Rubin's model is that when certain assumptions are in place, there are ways to assess counterfactuals such as the above. Here is how we may proceed. Given that unit u got treatment t, we may try treatment c to a different unit u', which is very much like u, except that it was given treatment c instead. That is, instead of assessing the counterfactual conditional Y(c, u), which is impossible, we assess the factual conditional Y(c, u')-the response of unit u' if she is given treatment c-and claim that this tells indirectly what the value of Y(c, u) is. If this move is to be plausible at all, we need an assumption of unit homogeneity. We need to assume that u and u' are so similar that the actual response of u' to treatment c is the same as the response that unit u would have to treatment c. Under this assumption, we take it that Y(t, u)=Y(t, u') and Y(c, u) = Y(c, u'). Then, the individual causal effect can be calculated, since (3) becomes thus:

(4) t(u) = Y(t, u) - Y(c, u) = Y(t, u) - Y(c, u').

This is all fine and I am prepared to say that, modulo the uniformity assumption, it does tell us something about the individual causal effect. But something strange has happened. (3) involves essentially a counterfactual conditional (Y(c, u)). (4) does not. (4) is indeed measurable, but the counterfactuals are gone. Instead, (4) has two factual conditionals, one for unit t who received treatment t and another for unit u' who received treatment c. In a sense, we are still asking: what would have happened to u, had we given it treatment c? But it also seems that we have now reduced this question to two different ones: a) what does happen to u', if we give it treatment c?, and b) assuming unit homogeneity and Y(t, u), what is the causal effect of t on u? These questions involve no counterfactuals. The content of the counterfactual conditional Y(c, u) seems exhausted by the joined content of the factual conditional Y(c, u') and the unit homogeneity assumption. In other words, the unit homogeneity assumption renders the counterfactual conditional Y(c, u) not so much a claim about the specific unit u but rather a claim about any of the homogeneous units. It is because of this fact that the counterfactual becomes testable. Unit homogeneity is a powerful assumption. But, in fact, an even stronger assumption is needed for the evaluation of t(u).

A population may be homogeneous and yet there may be different "unit-treatment" interactions, as Philip Dawid (2000, 411) has called them. That is, different units might differ in their responses to the same treatment, or even the very same unit might differ in its responses to the same treatment, over time. If this unit- treatment interaction is significant, t(u) above cannot be calculated. If, however, we make a stronger assumption, viz., uniformity of the units (as opposed to mere homogeneity), then we can assume that all units have the same unit-treatment interaction, and hence we can calculate t(u). There is another way we might proceed in our attempt to calculate t(u). This time, instead of giving treatment t to unit u and treatment c to (uniform) unit u', we give treatment c to unit u at time t1 and treatment t to the very same unit u at a later time t2. As Holland
(1986, 948) notes, this move requires another assumption, viz., temporal stability. This, he says, "asserts the constancy of response over time". It also requires an assumption of "causal transience", since it implies that "the effect of the cause c and the measurement process that results in Y(c, u) is transient and does not change u enough to affect Y(t, u) measured later" (1986, 948). So, if my taking a placebo at time t1 changes some properties of mine enough to affect my response to taking an aspirin at a later time t2, the causal effect of taking aspirin on my headache episode ceases to be calculable. Under these assumptions, we take it that Y(tt1, u)=Y(tt2, u) and Y(ct1, u) = Y(ct2, u). If this is so, then the individual causal effect can be calculated, since (3) becomes thus:

(5) t(u)= Y(t, u) - Y(c, u) = Y(tt2, u) - Y(ct1, u).

The points made about (4) can be repeated about (5) too. (5) has no counterfactuals and it seems that the content of (3)-which does involve the counterfactual Y(c, u)-reduces to the joined content of two factual conditionals (Y(tt2, u) and Y(ct1, u)) together with the two further assumptions of causal transience and temporal stability. I am willing to allow that I may be wrong here. That is, it might be the case that counterfactuals such as the ones we have been discussing do have excess content over the joint content of the relevant factual conditionals and the relevant assumptions. Still, what matters is that counterfactual conditional can be assessed in terms of truth and falsity only when certain assumptions are in place. Those assumptions might fail. If, however, there are reasons to believe they do not, then causal inference seems quite safe. This is really an important achievement of Rubin's model. But we shouldn't lose sight of the fact that these assumptions are characteristics of stable causal or nomological structures. Consider unit homogeneity. For it to hold, it must be the case that two units u and u' are alike in all causally relevant respects other than treatment status.

If this is so, we can substitute u for u' and vice versa. This simply means that there is a causal law connecting the treatment and its characteristic effect which holds for all homogeneous units and hence is independent of the actual unit chosen (or could have been chosen) to test it. In effect, this holds for temporal stability too, since the latter is the temporal version of unit homogeneity. It does indeed make sense to wonder what would the value of the voltage in a resistor would have been, if the intensity of the current was I instead of the actual I0 precisely because Ohm's law provides a stable nomological structure to address this counterfactual. As it does make sense to assert that had I caught the 7.05 train from Athens to Thessaloniki I would have been in Thessaloniki by lunchtime, because there is a (relatively) stable causal structure
(perhaps quite rudimentary) at work. But suppose we wanted to check the counterfactual that had the election taken place at an earlier time, the government would have been re-elected. Here it is obvious that temporal stability cannot be assumed because there is no stable nomological structure to back it up. Law- backed counterfactuals can indeed be assessed precisely because the laws make sure that the required assumptions are in place. In light of the above, it might not be surprising that according to Pearl (2000, 428), who is one of the champions of the counterfactual approach, "the word 'counterfactual' is a misnomer". In the case of individual causal effects, Pearl notes, we are interested in finding out things such as this:

QII: The probability that my headache would have stayed had I not taken aspirin, given that I did in fact take aspirin and the headache has gone.

It does not matter for present purposes that Pearl formulates the issue in terms of probabilities. What matters is that QII is a counterfactual claim of which Pearl stresses:

(.) [c]ounterfactual claims are merely conversational shorthand for scientific predictions. Hence QII stands for the probability that a person will benefit from taking aspirin in the next headache episode, given that aspirin proved effective for that person in the past (.) Therefore, QII is testable in sequential experiments where subjects' reactions to aspirin are monitored repeatedly over time (2000, 429).

Nothing said so far is meant to belittle causal inference. Whether or not we view it as involving an ineliminably counterfactual element, we can certainly draw safe causal conclusions when the relevant assumptions are fulfilled. Actually, both the advocates of the counterfactual approach (e. g., Holland 1986; Cox & Wermuth 2001) and their opponents (e. g., Dawid 2000) agree that we can get valuable information about the so-called average causal effect. This is the average causal effect on the whole population, i. e., the difference between the expected value of responses to treatment t and the expected value of responses to treatment c. Indeed, randomised controlled experiments are important precisely because they let us know about average causal effects. However, to get from the average causal effect in a population to the individual causal effect on a specific unit u, we need the further assumption of "constant effect"
(Holland 1986, 948) or "unit-treatment additivity" (Cox 1986, 963).

According to this, the effect of treatment t on each and every unit u is the same. Whether this holds or not is a largely empirical matter. To sum up. The counterfactual approach to causation we have been discussing is a big step forward, especially when it comes to the characterisation and the workings of causal inference. Yet, the very possibility of the latter rests on (and gets its purchase from) certain powerful assumptions (unit homogeneity, temporal stability, causal transience, constant effect). In a sense, these assumptions remove the counterfactual element from Rubin's model. But even if this is not quite right, these assumptions characterise the stable causal or nomological structure that needs to be in place in order for the counterfactuals to be meaningful and truth-valuable.

4. Mechanisms.

Recent philosophical interest in mechanisms stems from two sources. One is the recognition of the fact that scientists themselves try to identify and understand the mechanisms that explain certain phenomena or underlie certain functions, e. g., the mechanism of reproduction, of gene-transmission, of chemical bonding, of face-recognition etc. The other is a general dissatisfaction with standard philosophical views of causation, which fail to explain, or take account of, the mechanisms by which certain causes bring about certain effects.

4.1 Mechanisms and Counterfactuals.

Mechanisms are complex systems (or objects) which bring about a certain activity or are responsible for a certain behaviour. A thermostat might be a stock example of a mechanism. A conventional thermostat works like an on-off switch. A bimetallic coil tips a small mercury-filled glass bottle. The bimetallic coil is made from two different metal strips that have been sandwiched together and then rolled into a coil. As the temperature changes, the two metals expand differently and the coil winds or unwinds. As it does, it tips the glass bottle and the mercury rolls from one end of the bottle to the other. When the mercury falls to one end, it allows an electric current to flow between two wires and the furnace turns on. When the mercury falls to the other end of the bottle, the current stops flowing and the furnace turns off. According to Glennan
(2002, S344):

(M) A mechanism for a behavior is a complex system that produces that behavior by the interaction of a number of parts, where the interactions between parts can be characterized by direct, invariant, change-relating generalizations.

Mechanisms, he adds, "are not mechanisms simpliciter, but mechanisms for behaviors". For the very same complex system may issue in two different behaviours (e. g., the heart is a mechanism that pumps blood and makes noise.) What the mechanism does determines its boundaries, its division into parts and the relevant modes of interaction among these parts. Broadly understood, a mechanism consists of some parts (its building blocks) and a certain organisation of these parts, which determines how the parts interact with each other to produce a certain output. The parts of the mechanism should be stable and robust, that is their properties must remain stable, in the absence of interventions. The organisation should also be stable, that is the system as a whole should have stable dispositions, which produce the behaviour of the mechanism. Thanks to the organisation of the parts, a mechanism is more than the sum of its parts: each of the parts contributes to the overall behaviour of the mechanism more than it would have achieved if it acted on its own. Mechanisms can be contained within larger mechanisms. In his (1996), Glennan took his mechanistic approach to offer a rather robust solution to the problem of counterfactuals. He took laws that are mechanically explicable (in the sense that there is a mechanism that underpins them) to show in "an unproblematic way" how "to understand the counterfactuals which they sustain" (1996, 63). The key idea is that the presence of the mechanism (e. g., the thermostat) explains why a certain counterfactual holds, e. g., if the temperature had risen, the furnace would have turned off.

Similarly, the breakdown of a mechanism would explain why certain counterfactuals fail to hold. This is an attractive feature of mechanisms. In his more recent work (see (M) above), Glennan characterises the interaction of the parts of the mechanism in terms of Woodward's invariant, change-relating generalizations, that is generalisations that remain invariant under actual and counterfactual interventions. But then, it seems that Glennan is moving in a circle. According to the earlier view, mechanisms explain via mechanical laws when certain counterfactuals hold. According to the later view, it is certain interventionist counterfactuals that explain (or ground) the laws that govern the interaction of the parts of the mechanism. Consider the thermostat: it is a mechanical law
(ultimately, the law that metals expand when heated) which explains why it is the case that had the temperature been higher, the switch would have closed. But why is this a law? Because, had we intervened to change one magnitude (e. g., the temperature), the law (that metals expand when heated) wouldn't change and the other magnitude (e. g., the length of the metal strips in the bimetallic coil) would have changed. The circle is obvious, though I am not entirely sure it is really vicious. But I am not sure either where it can be broken so that the described relation between mechanism and interventionist counterfactuals can get going. A central and stable feature of Glennan's views is a distinction between the fundamental laws of physics and what he calls mechanically explicable laws. He notes, quite plausibly, that the fundamental laws of physics are not mechanically explicable and claims that "all laws are either mechanically explicable or fundamental, tertium non datur" (1996, 61). A mechanically explicable law is a law which is underpinned by a mechanism, or as Glennan says, which "is explained by the behaviour of some mechanism" (1996, 62). He takes it that mechanically explicable laws characterise all the special sciences and "much of physics itself" (1996, 50). Glennan agonises a lot about how exactly to formulate his view of the mechanical explication of laws, but let's leave all this to one side. I want to focus on a possible problem that this distinction creates. If fundamental laws are not mechanically explicable, and if they too support counterfactuals
(as they do, I suppose), it is not necessary for the truth of a counterfactual that there is a mechanical explanation of it. So, the presence of a mechanically explicable law (and hence of a mechanism) is not a necessary condition for the truth of a counterfactual conditional. Glennan agrees on this; still, he thinks it is a sufficient condition. Even is he is right, his theory is incomplete: if some counterfactuals are true even though a mechanism is absent, then there is more to the link between laws and counterfactuals than Glennan's theory admits. Suppose Glennan is right in taking mechanisms to underpin non-fundamental laws. He also subscribes to some kind of supervenience thesis: the non-fundamental laws supervene on the fundamental laws (cf. 1996, 62 & 66; 2002, 346 & 352).

Indeed, it seems that he must accept something like this at least when it comes to the non-fundamental laws of physics (most of which Glennan takes to be mechanically explicable), since, clearly, they supervene on the fundamental laws. So on Glennan's view, non-fundamental laws are underpinned by mechanisms and supervene on fundamental laws, which are not underpinned by mechanisms. Here is the problem, then. What is the relation between the mechanisms that realise the non-fundamental laws and the more fundamental laws on which the non-fundamental laws supervene? Glennan does not explain. To be sure, he asserts:

Although the mechanism responsible for connecting two events may supervene upon other lower-level mechanisms, and ultimately on mechanically inexplicable laws of physics, it is not these laws which make the causal claim true; rather it is the structure of the higher level mechanism and the properties of its parts
(1996, 66).

But this is hardly an explanation of what is going on. One plausible thought is that the fundamental laws govern the interactions of the parts of the mechanism, which realises the non-fundamental law. If this is so (as I think it is), then it would be odd to say that the mechanism that explains, say, Ohm's law is ultimately determined
(supervenience is a kind of determination) by the fundamental laws that govern the interaction of fundamental particles but that these fundamental laws are not
(part of) the truth-makers of Ohm's law. Once identified, the mechanism might well have explanatory and epistemic autonomy. But, if supervenience holds, the mechanism does not have metaphysical autonomy. If this line of thought is right, then the following seems reasonable. The presence of a mechanism is part of a sufficient condition for the truth of certain counterfactuals; the fully sufficient condition includes some facts about the fundamental laws that, ultimately, govern the behaviour of the mechanism. This, of course, is entirely consistent with the thought that in most practical situations when it comes to asserting the truth of a certain counterfactual, it is enough to cite the mechanism. The rest of the sufficient condition is not thereby rendered metaphysically redundant, but only explanatorily so.

There are two major attractions of Glennan's mechanistic theory. The first is that it is descriptively more adequate than the mechanistic approach of Salmon and Dowe. Both of them characterise interactions in terms of the exchange of conserved quantities. To be sure, they do aim at a mechanistic theory of physical causation. Still, this account is too narrow to describe cases of causation among higher-level entities. Consider, Glennan says, "a social mechanism whereby information is disseminated through a phone-calling chain" (2002, S346). It is surely otiose and unimformative to try to describe this mechanism in terms of exchange of conserved quantities. As we have just seen, Glennan does not deny that the interactions involved in telephone calls supervene on basic physical interactions. But he is surely right in saying that we would miss something out if we tried to explain them in those terms. We would lose out the fact that higher- level interactions form higher-level kinds. So, Glennan's mechanistic view is broad enough to account for mechanisms at levels higher than physics. It does not impose a priori restriction on the types of interactions that should satisfy (M). The explanatory autonomy of higher-level mechanisms is, I think, a lesson that we should take to heart. The other attraction of Glennan's mechanistic theory relates to his demand that understanding causal claims requires knowing what their underlying mechanisms are (cf. 1996, 66). In fact, Glennan wants to make a stronger point, viz., that

a relation between two events (other than fundamental physical events) is causal when and only when these events are connected in the appropriate way by a mechanism

(1996, 56).

I don't think the stronger claim is warranted. But the weaker claim is very plausible. Given its centrality on the positive argument of my paper, which will be advanced in section 5, I will postpone its discussion until then.

4.2 Mechanisms and Activities.

Machamer, Darden and Craver (henceforth MDC) claim:

Mechanisms are entities and activities organised such that they are productive of regular changes from start or set-up to finish or termination conditions (2000,
3).

At a surface level, the MDC characterisation of a mechanism is fairly similar to Glennan's. On closer inspection, there is a central difference. MDC introduce the concept of activity as a means to account for the interaction between the parts of the mechanism and its overall causal efficacy. The MDC approach is exciting, especially when it comes to the detailed description and classification of how mechanisms are taken to operate in neurobiology. But for the purposes of this paper, I will examine only the notion of activity. As I see it, their view is that an adequate understanding of the concept of mechanism requires an ontological shift: we need to accept the existence of activities on top of the usual commitments to entities, properties and processes. This unparsimonious move is recommended on the basis of their claim that mechanisms are "active": "they do things" (2000, 5). They think that unless activities are accepted as ontological bed-fellows of entities, properties and processes, mechanisms will be passive: things might be done via them, but not because of them. They also claim that appeals to causal laws, or to invariant generalisations, fail to capture the productivity of a mechanism, which "requires the productive nature of activities" (2000,
4). MDC's "dualism", as they put it, requires that there is a fine distinction between entities (with their properties) and activities. But is there? As is usual in philosophy, we are first given some examples. So, cases such as bonding, diffusion, depolarisation, attraction and repulsion etc. are cases of activity. But what do all these share in common in virtue of which they are activities? What we are told is that "activities are the producers of change" (2000, 3). But production is itself an activity. So, we are not given an illuminating account of that which some things share in common, in virtue of which they are activities. One way to circumscribe what-it-is-for-x-to-be-an-activity is to look at its relations to other things accepted, e. g., entities. MDC say the following of the relation between entities and activities:

Entities and a specific subset of their properties determine the activities in which they are able to engage. Conversely, activities determine what types of entities
(and what properties of those entities) are capable for being the basis of such acts. (.) Entities and activities are correlatives. They are interdependent (2000, 6).

It follows that entities and activities are ontically on a par: they determine each other. They say this more explicitly when they claim that

(t)here are no activities without entities, and entities do not do anything without activities (2000, 8).

I think the supposed ontic parity between entities and activities is wrong-headed. First, it's conceivable that there are entities without activities. Indeed, there may be entities capable of engaging in certain activities, but the prevailing circumstances, or the laws of nature, may be such that they fail to engage in these activities. (Apropos, if what matters is the ability of an entity to engage in an activity and not the actual occurrence of this activity, then it is clear that MDC have to rely on counterfactuals to illuminate the link between entities and activities.) Second, I cannot see how activities can determine what types of entities can engage in them. There may well be an open-ended list of types of objects that can engage in some activity, and they may share very little, if anything, in common. Take the activity of playing. It's hard to say that it determines what kinds of entities (and what properties) are involved in this activity. Admittedly, this is a case of a highly generic activity and it might be problematic precisely because of this. There are cases of more specific activities, where the activity is performed by certain types of objects. It then might seem that the activity does determine what types of object can engage in it. An example of such a specific activity might be the activity of pushing. It seems that this activity determines that the objects involved in it must have certain properties, e. g., rigidity, bulk etc. But I think appearances are deceptive. Epistemically, we might first classify a certain type of activity and then identify what kinds of objects engage in it. But from this it does not follow that this is the order of ontic dependence too. On the contrary, objects can engage in certain activities because they have certain properties and not the other way around. Consider the activity of chemical bonding. Does this activity determine that entities that engage in it must have a certain electronic structure? Not really. Chemical bonding could not exist without some entities having the right electronic structure. So not only is the latter presupposed ontically for the activity, but also it fully determines this activity: the activity of bonding consists in the fact that certain entities with certain electronic structure behave in a certain way when they are in proximity.

The dependence of the activity on the properties of entities becomes clear when the activity fails to take place. Consider the case were chemical bonding does not take place, e. g., the case of noble gases. There, you have the entities without the activity of chemical bonding precisely because the entities and their properties determine that a certain activity cannot take place. The situation is exactly symmetrical when the activity does take place. The conclusion I draw is that activities cannot be ontically on a par with entities. But one may wonder: why should MDC want to hypostatise activities? Why isn't enough to talk in terms of entities and their properties? MDC are right in protesting against process-theorists that entities are indispensable in understanding mechanisms. They rightly claim that the programme of reducing entities to processes is "problematic at best". But they also want to argue against "substantivalists", that is those who "confine their attention to entities and properties, believing that it is possible to reduce talk of activities to talk of properties and their transitions" (2000, 4). Against them, MDC claim that entities and their properties are not enough for the characterisation of mechanisms: activities are also required. Now, the substantivalists that MDC have in mind take the properties of the entities to be dispositional; they equate them with capacities or active powers. This is a quite powerful ontology. The friends of active powers would surely protest that given that active powers are granted to entities, talk of activities as distinct from these powers is redundant. MDC offer two arguments for activities on top of capacities. I think they are both problematic. The first argument is this:

in order to identify a capacity of an entity, on must first identify the activities in which that entity engages (2000, 4).

Even if right, this is irrelevant. It only raises an epistemic point: we cannot know what capacities an entity has, unless we first know what it does. From this, it does not follow that activities are ontically on a par with capacities. Nor does it follow that it is not the capacities of an entity which determine what activities it engages in. Quite the contrary. To use their own example, it is because aspirin has the capacity to relieve headaches (a capacity which we take it to be grounded in its chemical composition) that aspirin engages in this activity, i. e., headache- relieving. If capacities are granted, then activities supervene on them. And this remains so, even if, from an epistemic point of view, we need to attend to the (observed) activities in order to conjecture about the capacities. The second argument that MDC offer is this:

state transitions have to be more completely described in terms of the activities of the entities and how those activities produce changes that constitute the next change

(2000, 5).

Here the emphasis is on the production. As they explain, activities add the "productivity" by which changes in properties (state-transitions) are effected. But isn't this question-begging? Many would just deny that there is anything like a productive continuity in state transitions. All there is, they would argue, is just regular succession. In any case, the friends of capacities would argue that there is productive continuity in state transitions, but that this is grounded in the natures of the entities engaged in state transitions. If water has the capacity to dissolve salt, and if this capacity is grounded in the natures of water and salt, then all that is needed for the dissolution of salt in water

(that is, the activity) is that the circumstances are right and the two substances are brought into contact. I suspect that MDC hypostatise activities by being
(partly) misled by ordinary language. Consider what Craver says:

Verbs provide the productive continuity in the mechanism, intelligibly linking earlier states to later stages. (.) Substantivalists nominalise or neglect active features of scientific ontology, the diverse kinds of changing that underlie regularities; they leave out the verbs (2002, 72).

Leaving aside that this passage confuses a mechanism (which does not include verbs) with its description (which does include verbs), it should be obvious that nothing much follows from the fact that some relations between entities are described by verbs (e. g., x dissolves y) while others are not (e. g., x is taller than y). It's not as if all relations described by verbs are causal relations-compare 'x loves y'. Conversely, it's not the case that causal relations are described exclusively by transitive verbs. We make a causal ascription when we say that the volcano erupted no less than when we say that Demetra tore the book. I think MDC get things the wrong way around here. We don't get causal relations from verbs. Rather we get verbs from a prior understanding of causal relations. The nature of causation, whatever that is, is not captured by the language we use to describe causal facts. I have a final worry about MDC: they cannot avoid counterfactuals. Counterfactuals may enter at two places. The first is the activities themselves.

Activities, such as bonding, repelling, breaking, dissolving etc., are supposed to embody causal connections. But, one may argue that causal connections are distinguished, at least in part, from non-causal ones by means of counterfactuals. If 'x broke y' is meant to capture the claim that 'x caused y to brake', then 'x broke y' must issue in a counterfactual of the form 'if x hadn't struck y, then y wouldn't have broken'. So, talk about activities is, in a sense, disguised talk about counterfactuals. The second entry-point for counterfactuals is the characterisation of interactions within the mechanism. We have already seen Glennan insisting that this interaction should be captured in terms of the invariance of the relationships among the parts of the mechanism under actual and counterfactual interventions. MDC are not quite clear on what the interaction within the mechanism consists in. Note that it wouldn't help to try to explain the interaction between two parts of a mechanism (say parts A and B) by positing an intermediate part C. For then we would have to explain the interaction between parts A and C by positing another intermediate part D and so on (ad infinitum?). I take this to be a crucial problem of the mechanistic approach. In a sense, this approach fills in the 'chain' that connects the cause and the effect with intermediate loops. But there is still no explanation of how the loops interact. Here, it might well be the case that the most general and informative thing that can be said about these interactions is that there are relations of counterfactual dependence among the parts of the mechanism. Even if we posited activities, as MDC do, we would still need counterfactuals to make sense of them, as we have just seen. In any case, if I am right, there is more to causation than mechanisms.

5. Both Mechanisms and Counterfactuals are Helpful.

We can describe things thus far as follows. Mechanisms need counterfactuals; but counterfactuals do not need mechanisms. Recall, however, what was noted at the end of section 4.1, viz., that the understanding of causal relations requires understanding of the underlying mechanisms. Is this really so? Imagine a perfectly randomised experiment in which t (for treatment) produces higher response than c (for control). Has a causal connection been established? If we treat the randomised experiment as a black box, then in so far as it is a good experiment, we have established a causal connection. But what is inside the black box? Some might think that without a specification of the mechanism by which the higher response t was effected, the causal connection has not been established. This is a delicate issue. As I noted in the end of the last section, establishing the causal status of each part of a mechanism would require finding out (or estimating) its causal effect. And the best way to do this is by non-mechanistic means, and in particular by means of the counterfactual approach outlined in section 3.2. So, there seems to be a genuine asymmetry here. The causal effect can be found out, at least in favourable circumstances, without understanding the causal mechanisms, if any, involved; but the causal mechanisms, even if they are present, cannot be understood without the notion of the causal effect.

But there are at least three things that show how mechanistic considerations can help the counterfactual approach. First, mechanistic considerations can help testing the stability assumptions (unit homogeneity, temporal stability) that are necessary for the counterfactual inference. I take this to be fairly obvious, so I won't elaborate on it further. Second, mechanistic considerations can help deal with the endogeneity problem. Briefly put, the problem of endogeneity is this. It might happen that the values taken by the so-called explanatory (or causal) variable, are consequences, rather than causes, of the values of the dependent variable. In a perfectly controlled experiment this cannot happen because the variables that are manipulated are the explanatory variables. But in cases where the research is qualitative, or where an experiment is not possible at all, the counterfactual approach might well fail to solve the endogeneity problem. Consider one of the classic problems of the early twentieth century social science: Max Weber's claim a certain type of economic behaviour-the capitalist spirit-was induced by the Protestant ethic. Many social scientists have argued that this claim falls foul of the endogeneity problem. Opponents of Weber's Thesis claimed that the order of dependence goes the other direction: Europeans who already have had an interest in breaking free of the pre-capitalist mode of productions might have broken free of the Catholic Church precisely for that purpose. That is, it was the economic interests of certain groups that caused the Protestant ethic and not conversely. In cases such as this, a controlled experiment is out of the question. Besides, the assessment of intuitively relevant counterfactuals will be, to say the least, precarious. But an understanding of the mechanisms at play can well help resolve the endogeneity problem. These mechanisms, I presume, include a more detailed description of the explosion of the capitalist economic activity in the sixteenth century and of the economic behaviour of certain groups, e. g, in Venice and Florence or in England and Holland, which predate the emergence of Protestantism.

The third way in which mechanistic consideration can help the counterfactual approach concerns the possible confounders. In a perfectly randomised trial, the problem of confounding variables does not arise. The experimental method itself makes it very unlikely that the explanatory variable is correlated with possible confounders. But in qualitative research, or even when matching techniques are used, it is possible that the explanatory variable is correlated with a confounding variable. Take, for instance, the dependent variable to be participation in demonstrations and the explanatory variable to be the age of the participants. It might well be that a confounding variable (e. g., radicalness of beliefs) is correlated the explanatory variable and has an influence on the dependent variable. In cases such as this, knowledge of mechanisms can help identify possible confounders and control for them. Conversely, knowledge of mechanisms can explain why the experimenter need not control for some variables (e. g., the colour of the eyes of those who participate in demonstrations). Mechanisms cannot be the surrogate of a careful experiment. But we needn't see them as a surrogate. Both counterfactuals and mechanisms can work together to secure some causal knowledge. If we think of an experiment as a black box, then counterfactuals have a key role to play. After all, when certain assumptions hold, they can establish a causal relation. But without some knowledge of the mechanism inside the black box, we won't have full understanding of the causal relation. Nor can we solve, at least as effectively, some methodological problems of causal inference. Using the black box carefully does establish a causal link. Looking into the box does offer extra understanding, even if it does not, in and of itself, establish the causal relation. In so far as this link (Hume's secret connexion) is an intrinsic relation between cause and effect, we will get a glimpse of it, but not much more.

References

Bogen, Jim (2003) "Analyzing Causality: The Opposite of Counterfactual is Factual", forthcoming. Cox, D. R. (1986) "Comment", Journal of the American Statistical Association 81:963-4.

Cox, D. R. (1992) "Causality: Some Statistical Aspects", Journal of the Royal Statistical Society, A, 155: 291-301.

Cox, D. R & Wermuth, Nanny (2001) "Some Statistical Aspects of Causality" European Sociological Review 17: 65-74. Craver, Carl (2002) "Structure of Scientific Theories" in Machamer, P. & Silberstein, M. (eds.) The Blackwell Guide to the Philosophy of Science, Oxford: Blackwell.

Dawid, Philip (2000)"Causal Inference Without Counterfactuals", Journal of the American Statistical Association 95: 407-24.

Dowe, Phil (2000) Physical Causation, Cambridge: Cambridge University Press.

Glennan, Stuart (1996) "Mechanisms and the Nature of Causation", Erkenntnis 44:49-71.

Glennan, Stuart (2002) "Rethinking Mechanical Explanation", Philosophy of Science 69: S342-S353.

Harre, Rom (2001) "Active Powers and Powerful Actors" in A. O'Hear (ed.) Philosophy at the New Millennium, Cambridge: Cambridge University Press.

Holland, Paul (1986) "Statistics and Causal Inference", Journal of the American Statistical Association 81: 945-60.

Holland, Paul (1988) "Comment: Causal Mechanism or Causal Effect: Which is Best for Statistical Science?", Statistical Science 3: 186-8

Kitcher, Philip (1989) "Explanatory Unification and Causal Structure", Minnesota Studies in the Philosophy of Science, 13, Minneapolis: University of Minnesota Press, pp. 410-505.

Lange, Marc (2000) Natural Laws in Scientific Practice, Oxford: Oxford University Press. Lewis, David (1973) Counterfactuals, Cambridge MA: Harvard University Press.

Lewis, David (1986) "Causation" in his Philosophical Papers, Vol. II, Oxford: Oxford University Press, pp. 159-213.

Machamer, Peter, Darden, Lindley and Craver, Carl (2000) "Thinking About Mechanisms" Philosophy of Science 67: 1-25.

Machamer, Peter (2003) "Activities and Causation", forthcoming.

Mackie, J. L. (1974) The Cement of the Universe: A Study of Causation, Oxford: Clarendon Press.

Maldonado, George & Greenland, Sander (2002) "Estimating Causal Effects", International Journal of Epidemiology 31: 422-429.

Pearl, Judea (2000) "Comment", Journal of the American Statistical Association 95:428-31.

Psillos, Stathis (2002) Causation and Explanation, Acumen and McGill-Queens University Press.

Rubin, Donald B. (1978) "Bayesian Inference for Causal Effects: The Role of Randomization", The Annals of Statistics 6: 34-58.

Salmon, Wesley (1984) Scientific Explanation and the Causal Structure of the World, Princeton: Princeton University Press.

Salmon, Wesley (1997) Causality and Explanation, Oxford: Oxford University Press. Simon, Herbert A. & Rescher, Nicholas (1966) "Cause and Counterfactual", Philosophy of Science 33: 323-40.

Stone, Richard (1993) "The Assumptions on which Causal Inferences Rest", Journal of the Royal Statistical Society B, 55: 455-66.

Woodward, James (1997) "Explanation, Invariance and Intervention", Philosophy of Science 64 (Proceedings): S26-S41.

Woodward, James (2000) "Explanation and Invariance in the Special Sciences", The British Journal for the Philosophy of Science 51: 197-254.

Woodward, James (2002) "What is a Mechanism? A Counterfactual Account", Philosophy of Science 69:S366-S377.

Woodward, James (2003a) "Counterfactuals and Causal Explanation", forthcoming. Woodward, James (2003b) Making Things Happen: A Theory of Causal Explanation, New York: Oxford University Press.