1. Introduction

In his 1913 paper “On the Notion of Cause,” Bertrand Russell famously complained that “the word ‘cause’ is so inextricably bound up with misleading associations as to make its complete extrusion from the philosophical vocabulary desirable” (Reference Russell1913, 1). Russell went on to give a number of arguments to the effect that the concept of cause can play no role in the advanced sciences. An argument very similar to one of Russell's has been put forward more recently by Noah Latham (Reference Latham1987) and is endorsed by Hartry Field (Reference Field, Loux and Zimmerman2003). Yet the notion of causation seems to have survived these attacks and thrives both in philosophy and in science. Indeed Nancy Cartwright (Reference Cartwright1979) has argued that causal laws are not just useful, they are essential to our scientific understanding of the world. This conflict between Russell and Cartwright poses a challenge to our understanding of causation. Field goes so far as to suggest that the problem of reconciling Russell's arguments against causation with Cartwright's arguments for causation is “probably the central problem in the metaphysics of causation” (443). The aim of this paper is to develop an account of causation that will allow just such a reconciliation.

My strategy is as follows: in Sections 2 and 3, I give a brief account of the arguments for and against causal laws. In Section 4, I show that the Russell-Latham argument against causal laws is of the same form as an argument that Cartwright has put forward against the idea that the laws of nature describe exceptionless regularities. In Section 5, I consider a popular response to Cartwright's argument, and in Section 6, I show that this response can be adapted to provide an answer to the Russell-Latham argument. My response in this section involves a new analysis of causation, and the analysis is sketched here. The last two sections draw out some of the consequences of my proposal.

2. The Case for Causation

A brief survey of the literature is enough to see that the word ‘cause’ has not been completely eliminated from the philosophical and scientific vocabularies—far from it. A search for the words ‘cause’, ‘causation’, or ‘causality’ in the Philosopher's Index, for example, produces over 7,500 hits, more than 2,300 of these from the last decade. A search for these words in the titles of papers cataloged in the Science Citation Index since 1995 produces over 18,700 hits. It seems safe to conclude that causation remains an interesting and useful concept.

Nancy Cartwright argues that causation is not just a useful concept; it is indispensable. Her argument centers on the difference between effective and ineffective strategies. It is clear that there is a real distinction between effective and ineffective strategies: if you want to be rich, going out and buying an expensive car is not the most effective way to fulfill this desire. It is far more effective to save your money and invest it wisely. Cartwright's claim is that the distinction between such strategies cannot be grounded in laws of mere association; the distinction must be grounded in causal laws. Strategies that introduce a cause of the desired outcome are likely to be effective. Strategies that introduce something that is merely correlated with the desired outcome may or may not be effective.

Chemotherapy, for example, is a fairly effective strategy for curing childhood leukemia. But chemotherapy has the unfortunate side effect of making the patient's hair fall out. For this reason, among children, the curing of leukemia is highly correlated with baldness. It would be a very poor strategy, however, to shave your child's head as a cure for leukemia. But why is this a poor strategy? There is a perfectly good law of association that states that the curing of leukemia in children is associated with baldness—is that not enough? Clearly, the answer is that a mere correlation is not enough, the right causal relation is required. It is the structure of causal relations, not of statistical correlations, that accounts for the difference between effective and ineffective strategies. Furthermore, Cartwright (Reference Cartwright1979) provides a strong argument for the claim that all attempts to reduce such causal relations to relations of mere correlation will fail. Thus causation is ineliminable from our understanding of the world.

Cartwright is in good company. For example, Wesley Salmon once thought that scientific explanation could be subsumed under statistical generalizations, and in Statistical Explanation and Statistical Relevance (Salmon, Jeffrey, and Greeno Reference Salmon, Jeffrey and Greeno1971), he tried to give a detailed account of how to subsume causal facts under such general statistical laws. After much work, and many years of effort, however, Salmon concluded that it was not possible to eliminate the notion of causation from the analysis of scientific explanation (see, e.g., Salmon Reference Salmon1984). Having seen why we might want to defend the concept of causation, let us now turn our attention to Russell's challenge.

3. The Case against Causal Laws

Russell's (Reference Russell1913) paper contains many complaints against the traditional notion of causation, but his actual arguments are not as clear as one might like. Field, however, has distilled and developed two main lines of argument from Russell's paper. One line of argument concerns the asymmetry of the causal relation, and I will call it the asymmetry argument. The second argument concerns the possibility of interventions that can interfere with causal laws, so I will call it the intervention argument.

The asymmetry argument is well known and is still popular today; it runs as follows. Causal laws describe relations of determination between cause and effect (or alternatively they describe probability-raising relations). Furthermore, the cause-effect relation is essentially asymmetric—being a cause is quite different from being an effect. The fundamental equations of physics, on the other hand, are (almost) completely time-symmetric: if the state of a system at time t determines the future states of the system according to these equations, then it will equally determine the past states of the system. Thus, we must conclude that the causal relation is not one of the determination relations described by the equations of physics.

Note that the asymmetry argument does not by itself lead to the conclusion that the notion of causation is useless or irrelevant to physics. One can reach this strong conclusion only if one assumes a particularly strong version of physicalism, according to which nothing is of relevance to science except that which is explicitly described by, or reducible to, the equations of physics. There seems to be no independent reason to accept this strong physicalist assumption, and without it the asymmetry argument poses no challenge to those of us who, like Cartwright, believe that causal laws play an essential role in science. Indeed, Cartwright accepts the conclusions of the asymmetry argument and takes this as a reason to reject strong physicalism.

The intervention argument, on the other hand, poses a direct challenge to Cartwright's position, so let us turn our attention to it. Causal laws state that when one type of event occurs, some other particular type of event will occur. Now, if such a law is to be informative or useful, Russell argues, then the events mentioned by the law must be the kind of things that can be repeated. For if the events were not the kind of thing that can occur more than once, then the ‘law’ could have only one instance and would be trivial.

Now the world in which we live is complex and ever changing. If we restrict our attention to small parts of the world, we find events that are repeated—the beating of our hearts, the changing of the seasons, the demand to pay taxes. If we look at a larger or more comprehensive state of the world, however, we find that such states are not repeated. The state of the earth at the moment, with each animal and plant where it is right now, is a state that has not existed previously in human history, and we have good reason to believe that it has never before existed and never will again. We can be even more sure that the state of our entire universe at any time has not and will not be repeated. It follows that if causal laws are to play any nontrivial role in this world, then the descriptions of the events mentioned in a causal law must be considerably less specific than a description of the state of the whole universe at a given time.

But, Russell argues, if we do not include a very large amount of information about the state of the universe in our statement of a causal law, then it is always possible that the cause described by a causal law could occur, but something else could intervene to prevent the effect from happening. So, for example, we might be inclined to say that striking a match causes it to ignite. But in a situation in which there is no oxygen present or in which there is a very strong wind, striking a match will not result in its lighting. In order to be sure of the expected effect, says Russell, we must know that nothing in the environment will prevent the effect from occurring. Any given causal law will apply only in a very specific environment. But if we include a complete description of the environment in our description of the causal law, the probability of repetition becomes almost nil. Thus, the purported law will be either trivial or almost certainly false.

A third possibility, which has been the focus of much discussion in the recent literature but is overlooked by Russell, is that the laws in question are ceteris paribus laws—laws that hold only in the right kind of circumstances. Unfortunately, it is notoriously difficult to specify the content of the claim that a law holds ceteris paribus (see Earman, Roberts, and Smith Reference Earman, Roberts and Smith2002; Woodward Reference Woodward2002). The claim cannot simply be that the law holds when it holds, but any attempt to specify the conditions under which the law holds will run directly into Russell's problem: the conditions under which the law holds are conditions that involve a very large part of the environment. In order to avoid Russell's problem, the conditions must remain painfully unspecified and unspecifiable. At the very least, I suggest, if ceteris paribus laws can be avoided, they should be.

Field points out that Russell's argument is very similar to an argument put forward more recently by Noah Latham (Reference Latham1987). Latham's argument is directed against Davidson's Principle of the Nomological Character of Causality (PNCC; see Davidson Reference Davidson1980, 208). The PNCC is the claim that events related as cause and effect fall under strict deterministic laws. The PNCC is supposed to capture an essential feature of our notion of causation. It is certainly implicit in Russell's discussion of causation, and it is implied by what Hartry Field calls the “traditional view” of causation, which assumes the existence of laws that have the following form: “when a finite number of quite localized things hold at one time, some other particular thing must happen a short time later” (Field Reference Field, Loux and Zimmerman2003, 438). So, for example, if Thor throws a rock at a window causing the window to break, the traditional view (and the PNCC) would hold that these events are an instance of a law that states “throwing a large stone at a window must cause the window to break.” This law relates the localized event of Thor's throwing the stone to the event of the window breaking.

The problem, says Latham (and Field endorses his claim), is that, if modern physics is correct, any laws of the form assumed by the traditional view will simply be false. For according to physics, it is always possible that an event in the past light cone of the expected effect could intervene to prevent the effect from happening (say, by sending an extremely powerful pulse of energy). So, for example, Thor might throw a large stone at a window and Winifred, who is sick of Thor constantly breaking windows to make philosophical points, might intervene by catching the stone before it hits the window. In such a case the law that states that the window will break would be shown to be false.

To rule out possible interferences to a law relating cause and effect, we will need to fix the state of an entire space-like cross section of the past light cone of the effect in question. As Field puts it “information about what happens at an earlier time can't suffice to determine the event unless it includes information about each point at that time that is within the past light cone” (Field Reference Field, Loux and Zimmerman2003, 439; italics in original). Thus a localized, finite description of an event will not suffice to determine that any particular event will follow.

Latham considers only strict deterministic laws, but Field argues that the point is little changed if we allow the possibility of indeterministic laws. The general point, he says, is that “no reasonable law of physics, whether deterministic or indeterministic, will make the probability of what happens at a time depend on only finitely many localised antecedent states, one will need an entire cross-section of the light cone to make the determination” (439).

If Russell and Latham are correct, then we cannot claim that some finite, localized set of events is the cause of some other event. Rather, the cause must include every event in the past light cone of the effect. But if we include all these events as part of the cause, says Field, the notion of causation will lose its point. For then Sam's praying that the fire would go out will be just as much a cause of its going out as Sara's aiming the water hose at it. Indeed, the fact that Winifred was watching television in the house down the street would be just as much a part of the cause.

The only way to avoid such a conclusion, says Field, is to include the nonoccurrence of certain interventions as part of the cause, rather than including every concrete event from the past light cone. Then we can say that it was not Sam's praying that helped cause the fire to go out but, rather, the fact that he did not do anything to actively prevent Sara from putting it out. The “clear truth” behind the Russell-Latham argument, says Field, is that the nonoccurrence of interventions must be included among the causes of any event.

However, including nonoccurrences as causes has costs. As Field points out, if we allow nonoccurrences to be causes, then we must rule out the view, advocated by Davidson (Reference Davidson1967), that only fairly concrete events can count as causes. Another cost, which Field does not mention, lies in the fact that there are an infinite number of possible interventions that must fail to occur if a given effect is to come about. Not only must Sam not prevent Sara from putting out the fire, but also Winifred must not do anything to prevent it, Sara must not get struck by a meteorite, Darth Vader must not suddenly appear out of thin air and cut Sara's hose with his light saber, and so on. Once we allow negative facts to be part of the cause, causal laws will have much more to do with what is not going on than with what is.

Perhaps the costs of negative causes are not intolerable, but I, for one, would rather not pay them. In Section 6 I will suggest a way to avoid the intervention argument, a way that does not involve ceteris paribus laws, does not rule out a Davidsonian position on causes, and does not posit an infinite number of nonoccurrences as part of the cause of any event.

4. Cartwright and the Laws of Nature

Notice that if the intervention argument is successful, then it poses a problem not only for causal laws, but also for all laws that posit a regular association between states A and B, where A is something less than a complete cross-section of B's backward light cone. The intervention argument, then, may be even more worrying for our view of science than it is for our view of causation, since the traditional view of scientific laws is precisely that they describe such regularities (see, e.g., Hempel and Oppenheim Reference Hempel and Oppenheim1948).

Consider Newton's law of gravitation, which states that between any two masses $m_{1}$ and $m_{2}$ separated by a distance d there will be an attractive force f given by $f=Gm_{1}m_{2}/ d^{2}$ , where G is the gravitational constant. According to this law there will be an attractive force of about $6.7\times 10^{-11}N$ between two 1-kilogram masses separated by a distance of 1 meter. If we combine this law with Newton's second law of motion, $f=ma$ , we can conclude that any two 1-kilogram masses separated by 1 meter will accelerate toward each other with an acceleration of $6.7\times 10^{-11}ms^{-2}$ . Thus, Newton's laws together seem to imply that the acceleration of the masses is determined by a rather local state of affairs: the mass and relative positions of the two objects.

But, of course, this acceleration will occur only if some other influence does not prevent it. For example, if there is a rigid rod keeping the two masses apart, no such acceleration will take place. In fact, in the actual world, where there are no perfectly isolated systems, there will always be outside influences interfering with the predicted motions of the two masses. The mere existence of other matter or energy in the backward light cone of one of the masses will affect the motion of that mass. It would seem, then, that one or both of Newton's laws must be strictly false; because of outside influences, masses never behave in the way predicted by these laws.

One might respond to this argument by stating that Newton's second law applies only to the total force on an object. But to calculate the total force on an object we need to know the state of an entire cross-section of the backward light cone of that object, and if we need this much information in order to apply Newton's laws, then the laws are useless. So Newton's laws seem to be in exactly the same position as causal laws: either they are false or else they are useless. Furthermore, it should be clear that this argument is not specific to Newton's laws; it would apply just as well to general relativity or quantum physics. If the intervention argument is correct, it seems, then almost any general law will be either false or useless. Of course, Newton's laws are not useless: we have used them very effectively to build bridges, calculate eclipses, and land spacecraft on Mars. In light of the intervention argument, the question is, How is it that are we able to use these laws?

In fact there are two different kinds of worry that one might be led to via the intervention argument: one epistemological, the other metaphysical. Suppose that we are applying Newton's law of gravitation to predict the accelerations of a pair of objects, when we suddenly realize that their behavior will be gravitationally influenced by other objects. The intervention argument suggests that due to these outside gravitational influences we would (strictly speaking) have to know the state of a very large part of the universe in order to apply the law. But as long as we are focusing on outside influences of a gravitational nature, the problem has to do only with our epistemic limitations—we cannot know enough to apply the law. Since the outside influences are all correctly described by Newton's law, there is no problem for the truth of the law itself. However, if we consider that there may be nongravitational influences at play as well, then one might be even more worried. For in addition to the epistemological worry about applying the law, one might be worried that Newton's law of gravitation must actually be false; the accelerations predicted by the law will not be those that actually occur. Because other factors are always at play, the argument goes, there simply is no regularity linking the acceleration of objects to their mass and relative position. Thus, if Newton's law of gravitation is to correctly describe a regularity in the world, then the nongravitational forces must somehow be incorporated into the law (which makes little sense) or else they must be included in a ceteris paribus clause, which, as mentioned above, is notoriously difficult.

Readers familiar with the work of Cartwright (Reference Cartwright1983, Reference Cartwright1999) will recognize that the argument above (in its metaphysical form) is very similar to the argument she has put forward to conclude that there are almost no true universal laws of nature. Ironically, then, it turns out that the argument Cartwright puts forward in defense of her criticism of universal laws is the very argument that Field identifies as the greatest challenge to her position on causation. But this is good news for us, as there are already a number of suggestions as to how to avoid Cartwright's argument. We may be able to transform one of these responses to Cartwright's argument against universal laws into a response to Russell's intervention argument against causal laws.

Perhaps the most obvious response to the question of how it is possible to apply Newton's laws is that we can apply the total-force law (which the intervention argument does not show is false) in situations in which we know some of the component forces and have good reason to believe that the forces we do not know are small (and thus we do not need to know the complete state). Unfortunately this response is not as straightforward as it seems. The claim that certain component forces are negligible is most naturally justified by employing the component force law, but, according to the intervention argument, the component force law is false. Now, it is not clear to me whether this problem is fatal to the total-force response; there is, perhaps, a way to avoid the problem by appealing to the mathematical form of the total-force equations. What does seem clear, however, is that this total-force response will not translate directly into a response to Russell's intervention argument against causation. For not only do we not have a total-cause equation to play the role of the total-force equation, but also our goal is precisely to save a concept of causation according to which causes can be less than total.

In the next section we will consider a response to Cartwright that I believe saves some of the intuitions behind the total-force response and that will translate into a response to Russell. But first, I think it will be instructive to look at Cartwright's own response to her argument against universal laws.

Cartwright is not in as bad a position with regard to the intervention argument against causation as Field would have us believe. Cartwright will simply accept the conclusion that there are no universal causal regularities. She can nonetheless hold on to the view that causation is an essential concept in science because she proposes an account of causation and causal laws that does not involve such regularities. According to Cartwright (Reference Cartwright1999), causal claims are, at bottom, claims about the capacities of objects to produce certain effects in the right circumstances. Although these capacities may remain constant over time, the behavior they produce will depend on their environment. Causal laws, then, are ceteris paribus laws, not strict regularities; they have the form ‘Whenever C happens, it causes E to happen, unless there is an interference with the capacities involved in C’.

So Cartwright does have an answer to the intervention argument, but this answer comes at a price. For Cartwright has to deny the traditional notion that causal laws entail true regularities in the course of events (and thus deny Davidson's PNCC). Thus, Cartwright makes a major concession to Russell and so is faced with the task of showing that her notion of cause is of some use and should not be completely eliminated from the philosophical vocabulary.

I believe that there is a way to get around the intervention argument without paying this price. What we need to do is adapt the component-forces response to Cartwright. In the next section I will sketch out this response, and in the section after that we will see how to adapt it to respond to Russell's intervention argument.

5. Component Forces

A number of authors have pointed out that Cartwright's argument against universal regularities can be avoided if we are willing to be realists about component forces (see, e.g., Creary Reference Creary1981; Forster Reference Forster, Fine and Leplin1988a, Reference Forster1988b; Earman et al. Reference Earman, Roberts and Smith2002).

Consider the following situation. Suppose that the universe consists of nothing but a mass of 1 kilogram resting on a spring at the surface of the earth. Physics tells us that the system consisting of the mass, the spring, and the earth will settle into a state of equilibrium in which none of the three objects are moving with respect to the others. But are there any forces on the mass when it is in such a state of equilibrium? If we do not accept the reality of component forces, we must answer no—the mass does not accelerate and hence the total force is zero. But a realist about component forces could answer yes, there are two forces of equal size pulling in different directions: a gravitational force pulling the mass toward the earth and a tension in the spring (consisting of many electromagnetic forces between the molecules of the spring) pushing the mass away from the earth. Even though the effect by which we identify forces (i.e., acceleration) fails to occur, the realist will say that the component forces are still there, acting in opposite directions.

The nice thing about the realist interpretation of component forces is that it allows us to hold that the laws of Newtonian physics hold in all situations. Newton's law of gravitation, for example, tells us that a gravitational force will exist between any two massive objects. The nonrealist, however, tells us that there are no forces at all acting on the mass in our thought experiment, despite the fact that it is suspended above the earth. So, the nonrealist must hold that Newton's law of gravitation is defeasible, that there are exceptions to the rule. In fact, since there are no two particles that are isolated from the rest of the universe, it seems that the nonrealist will have to claim that Newton's law of gravitation is never really instantiated at all. The realist about component forces, on the other hand, can claim that Newton's law of gravitation always holds. There really is a gravitational force between the mass and the earth in our thought experiment, but it is counteracted by an electromagnetic force in the opposite direction.

Cartwright rejects realism about component forces as a response to her argument, saying that component forces are “no concept for an empiricist” since it is only ever possible to measure the total force on an object, not the component forces (Cartwright Reference Cartwright1999, 82). In response, however, see Earman et al. (Reference Earman, Roberts and Smith2002), who suggest that some component forces can be measured (bathroom scales, for example, measure the gravitational component force on an object, not the total force—which is approximately zero), and Forster (Reference Forster, Fine and Leplin1988a, Reference Forster1988b), who argues that component forces are essential to the possibility of explanatory unification in Newtonian mechanics. What is more, component forces seem no less empirical than Cartwright's ‘capacities’, which—as she herself states (Reference Cartwright1999, 84)—can be truly measured only in unobtainable ideal situations.

6. Causal Realism and Causal Influence

We have just seen that laws describing the existence and operation of forces in physics can avoid Russell's intervention argument if we adopt a realist attitude toward component forces. What I would like to suggest is that the intervention argument against causal laws can be defused if we adopt a similarly realist attitude toward causation. If causal relations are real entities, then following the example of component forces in Newtonian physics, we may be able to argue that the laws describing causes hold in all situations—even in cases in which the cause is frustrated by the existence of other causal influences. In this picture, just as an acceleration is the result of all the forces acting on a mass, an effect is the result of all the causal relations in play at the time. Thus it is possible for component causes to exist as posited by some causal law, even though their characteristic effects do not occur.

There are, however, two major hurdles to the causal realist strategy suggested above. The first problem is highlighted by the way that I have been describing causation as a relation that exists between a cause and an effect. If causation is a two-place relation of this sort, then causal relations cannot exist in cases in which the effect does not occur, for in such cases one of the relata of the relation does not exist. Thus we are faced with a dilemma: either the description of causation as a relation between cause and effect is incorrect, or we cannot use the causal realist strategy to avoid Russell's argument in the way that the realist about component forces does.

The second problem is that, in contrast to the case of forces, we have no way of adding causal relations together to determine the total cause in a given case. Suppose that A caused B and that if X had occurred instead of A then it too would have caused B. What would we say if both A and X had occurred? That B would be caused twice as much? Surely not. Causal relations just don't seem to be the sort of thing that one can add together, so the analogy between forces and causes breaks down.

The solution to the first problem, I believe, is to accept the first horn of the dilemma; we should accept that the causal relation is not straightforwardly a relation between cause and effect. To see this, notice that causal relations typically produce changes in something or other. Hitting a ball with a bat causes the motion of the ball to change. When smoking causes lung cancer, it causes lungs to change from a noncancerous to a cancerous state. But if causal relations produce changes from one state to another, then perhaps the general form of the causal relation is something like a three-place relation rather than a two-place one: A causes B to change to C. (If we thought that all causes were also changes of some kind, then we might want a four-place relation. But this possibility will make no difference to the argument here.) For simplicity, I have stated this relation in terms of objects changing their properties, but it could be stated just as easily in terms of states of affairs—state of affairs A acting on state of affairs B brings about state of affairs C.

Does changing to a three-place relation help with our problem? Suppose that A and B are the case but C does not come about. With our new three-place relation in hand, we might hope to claim that there was a causal relation between A and B even though C never came about. Then we could say that the causal relation exists even though its characteristic effect does not. Unfortunately, things are not so easy, for C is one of the relata of our three-place relation and if C does not exist, then the relation cannot exist either.

There is, however, a formal way out of the problem. We can stop thinking of causation as a single relation and instead posit a different relation for each possible change C. Labeling the different causal relations with a subscript we can replace the three-place relation ‘A acts on B to produce C’, with the two-place relation ‘A causes_C B’. This two-place relation can exist as long as A and B do; it is not necessary for C to exist also.

But what on earth does ‘A causes_C B’ mean? Written like this, it looks extremely odd. The problem is that the word ‘cause’ is a success verb; we apply it only in cases in which the causal relation has been successful. I think that we will do better if we replace talk about causing with talk about influencing. It is quite common for us to talk about someone exerting their influence but to no avail, so ‘influence’ does not seem to imply success. Further, we must realize that influence (and causation in general) is directed. When I vote in an election, I do not merely influence the outcome of the election, I influence it in a certain direction—in favor of my chosen candidate. Similarly, when A acts on B to produce C, A exerts an influence on B that is directed toward the production of C. My suggestion, then, is that the basic causal relation has the following form: A has a C-directed causal influence on B. The causal relation is then a two-place relation, and it could conceivably hold between A and B even if the change to C did not come about.

Note that the comparison between causal influences and the efforts of human agents is meant only to be illustrative. Human beings can, of course, be causes, but I am not suggesting that all causes involve intentional agents striving to bring about some effect. Perhaps the notion of influence I have in mind is better illustrated by another comparison to forces. When two charged particles are brought together, each will exert a force on the other that tends to produce a particular acceleration. Each particle influences the other in a certain way, but this influence can be thwarted by outside influences.

So much for the first problem. The second problem for the causal realist strategy was that we have no way to add causal relations as we add forces and hence no way to make sense of the claim that changes are the result of the ‘total cause’. But now that we have analyzed causal relations in terms of influences, this objection does not seem to have the same bite it used to. We often think of influences as having magnitudes. We say things such as “I don't have as much influence over her as you do,” and it makes perfect sense to speak of influences combining in various ways. So if A and X individually influence B in the C-direction, then it is quite coherent to say that the combination of A and X provides an even stronger influence in this direction. It may well be true that we do not know how to add causal influences in the right way, and the composition of causes may be more complex than simple vector addition. But the change to talk of causal influences means that it is no longer plausible to argue that composition of causes simply makes no sense.

Putting these ideas to work, we see that causal realism does not save causal laws of the form ‘When a finite number of quite localized things hold at one time, some other particular thing must happen a short time later’. Rather, causal realism allows us to formulate laws of the form ‘When a finite number of quite localized things hold at one time, there will be a causal influence directed toward some particular effect’. Since such causal influences can exist even if the effect they tend to bring about does not, the possibility of external influences messing things up does not threaten the law. Thus, such causal laws do not fall prey to the intervention argument. Furthermore, the causal laws that are recognized by causal realism can do everything that Cartwright demands of causal laws. Causal influences can explain why some strategies are effective and others are not. If one wants to cure cancer, then it makes sense to bring into existence causal influences that are directed toward the curing of cancer. Chemotherapy introduces such influences; head shaving does not. Causal realism, therefore, allows us to reconcile Cartwright's defense of causation with Russell's arguments against causal laws.

Notice that I have not given an analysis of what it means to say that A caused C. In the most basic case, I imagine that such an analysis would go something like the following. Suppose that A has a C-directed causal influence on B. Suppose that no other causal factors get in the way and that C really comes about. Then we can express the relation between A, B, and C in a number of ways. We can say that A acting on B produced C, or that A caused the change from B to C, or even that A caused C (the different ways of stating this fact are partly responsible, I think, for the confusion over what the real relata of the causal relation are). In more complex cases in which there is more than one influence in play, we may need a more complex analysis. Given such an analysis, it would be interesting to see how it deals with difficult cases such as preemption and overdetermination. Unfortunately, I will not be providing such a complete analysis here. The aim of this paper is to suggest a new conceptual basis for causal reasoning and to show how this new basis can be used to avoid Russell's intervention argument. A full analysis of causal talk that employs this new conceptual basis is a job for another paper.

As an aside, I note that one might be worried that the analysis I have given of causal influences is overly deterministic. It seems to follow from my analysis that although A may have a C-directed causal influence on B without actually producing C, A always does produce C in the absence of other interfering influences. Thus my analysis seems to rule out, a priori, the possibility of probabilistic causal laws. In light of some interpretations of quantum physics, however, such a priori dismissal of probabilistic laws may be regarded as undesirably restrictive. But determinism plays no essential role in my analysis, and the story can be modified quite easily to accommodate probabilistic causation. All we need to do to introduce probabilistic causal laws into the picture is to claim that even in ideal circumstances, without any interference, a causal influence may have only a certain probability of bringing out the effect to which it is directed. Indeed it seems to me that propensity interpretations of probability are strongly suggestive of the existence of something like a probabilistic causal influence.

7. Causes and Forces

In order to avoid the intervention argument against causation, I have posited that there are a plethora of causal relations differentiated by magnitude and direction, and that there is a sense in which (at least some of) these causal relations can be added. But Russell also complained that causation is too imprecise a notion to be used in science. Before finishing, then, I would like briefly to consider what might be done to make the notion more precise.

Ideally what we would do is find a mathematical structure in which all possible causal influences are represented in terms of their magnitude and direction, while the addition of such influences is represented by an operator on this space. Of course Nature may not be so kind. It may be that the complexity and diversity of causal influences cannot be represented in such a structure. Perhaps, for example, some kinds of influence act independently of each other (and so the addition operator on these influences should be linear) while other kinds of influence do not (so addition of them should be nonlinear). But a situation like this would not be the end of the world, for maybe we could identify subspaces within which we can define a unique addition operator.

Indeed there is one class of causal influence for which we already have a very precise mathematical model. Causal influences that produce changes in velocity can be differentiated with regard to the magnitude and direction of this change. Changes in velocity, furthermore, inherit a precise vector space structure from the geometric vector space of displacements. It turns out, then, that we can use the vector space of displacements to impose a vector space structure on the space of causal influences that produce changes in velocity. Such causal influences are called forces. If my analysis of causation is correct, then there is not merely a close analogy between forces and causal relations; forces just are causal relations. (On this point I am in agreement with Bigelow, Ellis, and Pargetter Reference Bigelow, Ellis and Pargetter1988).

At this point, you may be worried about how we reconcile the symmetric equations that physics uses to describe forces with the asymmetric nature of causes. But note that I am not claiming that causes can be reduced to or explained by the equations of physics. Rather, the claim is that the equations of physics describe causal relations, and there is no logical problem with describing an asymmetric relation with a temporally symmetric equation. Look again at component forces in Newtonian physics. These forces are clearly asymmetric; each and every force has a particular direction. Yet the dynamical equations of Newtonian physics are temporally symmetric. It is, of course, very interesting that most of physics is temporally symmetric, and perhaps this gives us reason to doubt the utility of an asymmetric concept of causation, but there is no obvious contradiction between the equations of physics and causal asymmetry.

As a final note on this point, recall that Cartwright agrees with Russell that the laws of physics are mere laws of association that make no mention of causation. Again I think that Cartwright has conceded too much. For if I am right that forces just are a species of causal relation, then not only are causal relations essential to science, but they are also dealt with explicitly, right there in the equations of physics.

8. Conclusion

Russell argued that the concept of causation is irrelevant to science; Cartwright argued that it is indispensable. On this point I take Cartwright's side. But in order to avoid Russell's intervention argument, I have suggested that we should revise our understanding of causation. My proposed revision involves two related claims:

1. 1. The primary causal concept is something like what is expressed by the verb ‘to influence’ rather than the success verb that ‘to cause’ is usually thought to be.

2. 2. Causation is actually a family of relations rather than a single relation.

Although my suggested revision may appear radical, its appeal actually lies in how conservative it is. For—unlike Cartwright's view of causation, say—my revision preserves the traditional view of causal laws as strict regularities. Furthermore, this way of thinking about causes can be used to maintain that the laws of physics are strict universal laws that describe the causal structure of the world in the face of Cartwright's arguments that there are no such universal laws and that the laws of physics are mere laws of association that leave out all the causal information.

There is much work that still needs to be done. It would be nice, for instance, to develop a more detailed account of the structure of causal influences or to explore how my suggestions relate to counterfactual analyses of causation (especially David Lewis's notion of causal influence; see Lewis Reference Lewis2000) or to Pearl's (Reference Pearl2000) causal models. But these tasks will have to wait for another day. The aim of this paper is merely to point in the direction of an analysis of causation and to show the advantages that this approach promises to offer.