## I. REMARKS ON CHAPTER 3 OF CARTWRIGHT'SNATURE'S CAPACITIES AND THEIR MEASUREMENT

A. Summary of Highlights of Chapters 1 and 2

In general this book is a defense of the claim that the fundamental generic causal claims of science "are not reports of regularities but rather ascriptions of capacities, capacities to make things happen, case by case" (p. 3). The book is in many ways a difficult one, sometimes needlessly so. Nonetheless, I believe that it is fundamentally rightheaded, which is to say Aristotelian, in its main contentions.

Since Cartwright is coming out of the philosophy of science literature on causation, she is especially interested in the relation between probabilities and causes, and between our knowledge of probability relations and our knowledge of causes. Chapters 1 and 2 are devoted to showing how one might reasonably extract information about causes from information about probabilities, given that one has the right sort of causal background knowledge. (This includes enough knowledge to rule out certain putative causes right away--e.g., the Manchester hooters in Mackie's example--as well as enough knowledge to ensure that the putative cause and the putative effect are not both the effects of common causes with no direct causal connection between them.) Thus it is not the case that causality is reducible to probabilities; to the contrary, one needs a goodly amount of generic causal knowledge to be able to extract causal information from probabilities. This indicates that the right sort of probability relations are metaphysically posterior to causal processes rather than prior to them.

How exactly are causes correlated with probabilities? Suppose, first of all, that two factors A and B occur together with a probability exceeding the product of their individual probabilities of occurrence; that is, suppose that

P(A.B) > P(A) × P(B).
As we know, this does not by itself show that there is a direct causal connection between A and B. In order to show that there is no direct connection we look for a common cause C which satisfies the following four conditions for what Salmon calls a conjunctive fork:
P(A.B/C) = P(A/C) × P(B/C) [Independence of A and B given C]

P(A.B/not-C) = P(A/not-C) × P(B/not-C) [Independence of A and B given not-C

P(A/C) > P(A/not-C) [Relevance of C to A

P(B/C) > P(B/not-C) [Relevance of C to B]

So the idea is that one factor is a cause of another only if they are statistically relevant to one another and there is no other factor that is a common cause of both:
(CC) C causes E iff
P(E/C ± F1 ± . . . ± Fn) > P(E/not-C ± F1 ± . . . ± Fn), where {F1 . . . Fn, C} is a complete causal set for E.
That is, C must make E more probable within each of the populations defined by a possible arrangement of other factors (the F's) that are causally relevant to E. Ellery Eells puts the point this way:
"According to a standard theory of probabilistic causality, causes C raise the probability of their effects E within causally homogeneous background contexts. More precisely, let Ki's be maximal conjunctions of factors--not including C, not-C, or effects thereof--that are causally relevant to E. Then C causes E if and only if, for each i, P(E/Ki & C) > P(E/Ki & not-C). Alternatively, we may call this relation that of C's being causally positive for E, and characterizations of the relations of C's being causally negative and causally neutral for E can be obtained by substituting "<" and "=", respectively, for ">" ... According to the Pareto-dominance theory suggested by Skyrms, C need only raise the probability of E within some background context Ki" ("Probabilistic Causal Levels," p. 109).
In keeping with what was said above, Cartwright argues that such a formula presupposes lots of causal knowledge about E's possible causes:
"[Chapter 2 has developed] a connection between probabilities and causes outside of any formal framework. It begins with the hypothesis that the introduction of a cause should increase the level of the effect; and then considers what further conditions must obtain to ensure that this increase will reveal itself in the probabilities. The result is formula CC, a formula that demands a lot in terms of background knowledge; what matters, according to this formula, is whether the cause increases the probability of the effect in populations where all other causally relevant features are held fixed... This does not necessarily mean that one has to know all the other causes in order to find out about any one of them. There are methods that circumvent the need for full information. Nevertheless, the justification for those methods rests on a formula that involves conditionalizing on a complete set of other causal factors" (pp. 85-86).

B. Chapter Three: Singular Causes First

Cartwright summarizes her purpose here as follows:

"Chapter 2 argued ... [that] a regularity account of any particular generic causal truth ... must refer to other generic causal claims if the right regularities are to be picked out. Hence no reduction of generic causation to regularities is possible. This chapter will argue ... [that] to pick out the right regularities at the generic level requires not only other generic causal facts but singular causes as well. So singular causal facts are not reducible to generic ones. There is at best an inevitable mixing of the two levels" (p. 91).
1. Probabilities and Singular Causes

She begins by criticizing CC:

"Formula CC says that, for a generic causal claim to hold, the putative cause C must increase the probability of the effect E in every population that is homogeneous with respect to E's other causes. But this condition is too strong, for it holds fixed too much. The other factors relevant to E should be held fixed only in individuals for whom they are not caused by C itself" (p. 95).
Take the following example:

C ------------> F -----------------> E
^
F -----------------|

Our assumption is that C (your dialing my number) is a genuine cause in this case and acts through F (my phone's ringing) to cause E (my picking up the phone). As Cartwright points out, if you hold F fixed, you won't get the right result, since

P(E/C + F) = P(E/not-C + F) and

P(E/C - F) = P(E/not-C - F).

That is, F screens off C even for cases where C causes E through F. Likewise, if we fail to hold F fixed, i.e., if we do not look within the +F and -F populations, then it will turn out that we must count C as a cause of E even if your dialing is always preempted by the dialing of another friend who lives closer, since it will still be true in that case that P(E/C) > P(E/not-C). So Cartwright suggests the following as a replacement for CC:
CC*: Each test population of individuals for the law 'C causes E' must be homogeneous with respect to some complete set of E's causes (other than C). However, some individuals may have been causally influenced and altered by C itself; just these individuals should be reassigned to populations according to the value they would have had in the absence of C's influence.
As she then points out, "this means that what counts as the right populations in which to test causal laws by probabilities will depend not only on what other causal laws are true, but on what singular causal processes obtain as well. One must know, in each individual where F occurs, whether its occurrence was produced by C, or whether it came about in some other way."

Take the case at hand. The two modified relevant populations are (a) +F*, which excludes cases in which F is present but is caused by C, and (b) -F*, which includes cases in which F is present but only because it is caused by C. Then,

In +F*, P(E/C) = P(E/not-C), and

In -F*, P(E/C) > P(E/not-C).

This indicates two things. First, as Cartwright says, your background knowledge here must include not only generic causal laws but also knowledge of singular causes ("Is this one of the cases of F that should be put into +F* or not?"), and, second, the laws you come up with should be thought of as relativized to particular populations (Eell's suggestion). That is, the laws are not going to be perfectly general ones that range over every possible arrangement of E's other causes.

Now given that the application of CC presupposes that we are in a position to recognize instances of singular causality, there is another way to characterize the situation so that we can get a "general law" not relativized to populations. Since we know that C's sometimes cause E's, we can say that C's have a capacity to cause E's, a capacity (or tendency) that they carry into every causal situation but that is sometimes overridden (as in the population defined by +F*). So Cartwright's argument for the postulation of capacities depends essentially on the idea that what we are seeking are general causal claims true of every situation and applicable to every population (as CC says); and her contention is that the only viable candidates are capacity-ascriptions in which we presuppose that causes have stable capacities which are exercised under some conditions and overridden or modified in others.

The bulk of Chapter 3 is devoted to refuting objections against the first step in this argument, i.e., objections that try to establish that we need not presuppose knowledge of singular causation in applying CC. Cartwright discusses four possible strategies that avoid (or try to avoid) resorting to singular causation. It is in trying to show the inadequacy of these strategies that she discusses the birth control pill example ad nauseam.

2. Opposed strategies

I will discuss only the first strategy: Hold fixed just those causally relevant factors that are prior to or simultaneous with the putative cause.

This strategy works for the phone-calling example, since the relevant factor is my other friend's calling me (D).

C ------------> F ---------> E
^
D ------------> F ------------ |
And holding D fixed we get just the right results, viz.,
In +D, P(E/C) = P(E/not-C), and

In -D, P(E/C) > P(E/not-C).

However, Cartwright then shows how a cause with opposing tendencies, each of which is of course manifested only after the occurrence of the cause itself, cannot be handled on this account. This is especially clear in the birth control pill example if we assume that all the background causes (B) of P (pregnancy) and C" (production of the relevant chemical) act simultaneously with the putative cause, the use of birth control pills (C), to either produce or prevent thrombosis (T).
t1 ...................t2...................... t3

>--------------> not-P ------------> not-T

C

|

>---------------> C" ----------------> T

Here if you hold fixed only what occurs at t1, then you will not be able to get a fine-grained enough picture of the causal structure, since when you average over the four populations defined by C" and P, you will get either
In B, P(T/C) > P(T/not-C), in which case you find only the positive capacity, or

In B, P(T/C) < P(T/not-C), in which case you find only the negative capacity, or

In B, P(T/C) = P(T/not-C), in which case you find neither capacity.

As Cartwright later puts it on p. 119, "If only B is held fixed, anything can happen; the probability of the effect may go either up or down in the presence of the dual cause; it may even stay the same." By contrast, her own proposal is fine-grained enough to do the job (take my word for it!), but only because it defines the relevant populations by reference to which women would have P and C" in the absence of C's action. In one of these populations [+C" +P] P(T/C) < P(T/not-C), in another [-C" -P] P(T/C) > P(T/not-C), in a third [+C" -P] P(T/C) = P(T/not-C), and in the fourth [-C" +P] the results depend on the relative strengths of the two capacities.

Cartwright summarizes as follows:

"What does this imply about the possibility of testing causal claims? On the one hand the news is good. Although the analysis here is brief, and highly idealized, it should serve to show one way in which causal claims can be inferred from information about probabilities. A cause may have a number of different powers, which operate in different ways. In the simple example of the contraceptives, the cause has two routes to the effect--one positive and one negative. But this case can be generalized for cases of multiple capacities. The point is that, for each capacity the cause may have, there is a population in which this capacity will be revealed through the probabilities. But to pick out that population requires information not only about which of the other relevant factors were present and which were absent. It is also necessary to determine whether they acted or not. This is the discouraging part. It is discouraging for any investigator to realize that more fine-grained information is required. But the conclusion is a catastrophe for the Humean, who cannot even recognize the requisite distinction between the occurrence of a cause and its exercise" (p. 121).
The other three strategies, which I will not go into, fail for related reasons. The net upshot is that there is no plausible way to do away with the need to identify singular causal operations and processes in order to define the relevant populations correctly. Interestingly, the third strategy, which makes use of path-analysis, works well for the birth control pill example as set up above, but does not work when the contrary effects of a given cause are not produced independently of one another, as happens in many cases in physics and other sciences. More interesting yet, the path-analysis strategy works only when there are intermediate causes that intervene between the putative cause and its effects (recall the difficulty that Lewis had in cases of late preemption, where there are no intermediate effects) and only when the paths are fixed and specifiable:
"It should be apparent that, even failing confounding correlations [i.e., dependence relations among the exercises of contrary capacities], the strategy will work only in domains where trajectories between the cause and effect are assured. More than that, it must be supposed that for each capacity there is some fixed and specifiable set of routes by which it exercises itself; and that is what I want to call into question. It seems to me that the plausibility of that suggestion depends on a thoroughgoing and antecedent commitment to the associationist view, that it must the be paths that are laid down by nature with capacities to serve as summarizing devices. But there is the converse picture in which the capacities are primary, and in which whatever paths occur, from occasion to occasion, are a consequence of the manner in which the capacities exercise themselves, in the quite different circumstances that arise from one occasion to another. Within this picture the paths are likely to be quite unstable and heterogeneous, taking on the regularity and system required by path analysis only in the highly ordered and felicitously arranged conditions of a laboratory experiment" (p. 127).
3. Conclusions

Cartwright concludes:

"The immediate lesson I want to draw from the fact that each of the strategies in turn fail, and in particular from the analysis of the way in which they fail, is apparent: there is no way to avoid putting in singular causal facts if there is to be any hope of establishing causal laws from probabilities. But in fact I think the discussion indicates a far stronger conclusion ..." (p. 129)

"The view I shall urge in the next two chapters fashions a very close fit between the single case and the generic claim. I will argue that the metaphysics that underpins both our experimental and our probabilistic methods for establishing causes is a metaphysics of capacities. One factor does not produce the other haphazardly, or by chance; it will do so only if it has the capacity to do so. Generic causal laws record these capacities. To assert the causal law that aspirins relieve headaches is to claim that aspirins, by virtue of being aspirins, have the capacity to make headaches disappear. A single successful case is significant, since that guarantees that the causal factor does indeed have the capacity it needs to bring about the effect. That is why the generic claim and the singular claim are so close. Once the capacity exhibits itself, its existence can no longer be doubted...
"It is apparent from the discussion in this chapter that, where mixed capacities are involved, if causes are to be determined from population probabilities, a different population must be involved for each different capacity ... This naturally suggests a simple device for associating generic claims directly with probabilistic relations: relativize the generic claims to the populations ... [But] consider the population of women who have not become pregnant by time t2. On the proposal that lines up correlations and causes, only one generic relation between pills and thrombosis is possible, depending on whether the pills increase the probability of thrombosis or decrease it. For this case that is the law that says: 'In this population, pills cause thrombosis.' That much I agree with. But it is equally a consequence of the proposal that the law 'In this population, pills prevent thrombosis' is false; and that is surely a mistake. For as the case has been constructed, in this population most of the women will have been saved from thrombosis by the pills' action in preventing their pregnancy. What is true in this population, as in the population at large, is that pills both cause and prevent thrombosis" (pp. 136-138).

"The regularities are in no way ontologically fundamental. They are the consequences of the operation of capacities, and can be turned, when the circumstances are fortuitous, into a powerful epistemological tool. But a careful look at exactly how the tool works shows that it is fashioned to find out about the single case; and our account of what the law consists in must be tailored to make sense of that" (p. 140).

## REMARKS ON CHAPTER 4 OF CARTWRIGHT'SNATURE'S CAPACITIES AND THEIR MEASUREMENT

A. Causal Laws and Contextual Unanimity

In the standard probabilistic accounts of causality, a genuine cause must increase (or at least not decrease) the probability of the effect in every causally homogeneous background. This is the requirement of contextual unanimity. Cartwright's contention is that this requirement can be satisfied only if we think of the most fundamental causal generalizations are ascriptions of capacities that causes carry with them into every setup.

She approves of Ellery Eells's suggestion that 'causal laws', which have less generality than capacity ascriptions, really have three places in them, the last being filled by a specification of the distinctive test population within which the cause raises the probability of the effect:

"What is supposed to follow from an increase in probability of E on C in one of the specially selected populations [or 'test situations']? According to Chapter 3 what follows is that, in those special test populations, it can be regularly relied on that some Cs will produce Es. The argument has two parts. One is already presupposed by the reference to probabilities rather than to actual frequencies. The use of the probability concept guarantees that there will be reliably (on average or in the long run) more Es present when C is present than when C is absent. The further conclusion that at least some of the Es must be produced by Cs depends on the specific features these test populations are supposed to have. Roughly, enough is supposed to be true about them to guarantee that if there is an increase in the number of Es, there is no account possible except that C produced the excess. The point I want to make about this argument is that it justifies a very local kind of causal claim: if in a given test population we see the increase in probability that we are looking for, that guarantees that Cs cause Es there in that population. But it does not tell us any more. Since it is probabilities and not mere frequencies that are involved, it is assured that the causing of Es by C's will happen regularly--but regularly in that kind of population. Who knows what happens elsewhere?" (p. 144).
So on the view in question these causal laws invoke a limited sort of contextual unanimity, viz., contextual unanimity within a certain test population. Cartwright thinks that the sort of laws involved are indeed relative to a certain population, but believes that the relevant probabilities are only a sign of, and not as it were the essence of, the causal relation between Cs and Es:
"What I objected to in the last chapter was the claim that increase in probability in one of these special test populations constitutes the truth of the causal law there. What makes the causal law true that C causes E in T is not the increase in probability of E with C in T, but rather the fact that in T some Cs do regularly cause Es. The increase in probability is only a sign of that; and ... there will generally be other causal laws as well in the same population--laws which are not revealed in the probabilities" (pp. 144-45).
If we want a formula that covers all test situations, our only recourse is to say that once we have discovered what Cs actually do in a given special situation reflects a capacity that Cs, as Cs, carry with them into all such situations, even situations in which Es do not, because of circumstances, actually occur. It is only in this way that we can preserve unqualified contextual unanimity:
"If Cs ever succeed in causing Es (by virtue of being C), it must be because they have the capacity to do so. That capacity is something they can be expected to carry with them from situation to situation. So if the probability goes up in one test situation, thus witnessing to the capacity, it will do the same in all the others ... So my thesis in short is this: to believe in contextual unanimity is to believe in capacities, or at least it is a good way along the road to that belief" (p. 145).
B. Reductionistic Arguments

After showing that econometric method presupposes that the values of parameters remain constant over entirely different contexts, thus allowing that a theory itself can be inferred from data about probabilities, Cartwright goes on to consider the radical empiricist attempt to construe higher-level 'modalities' as mere summaries of lower-level 'modalities', with the lowest level being the non-modal level of occurrent regularities. Consider figure 4.1 on p. 160:

 Levels of Modality 4. Ascriptions of capacity: C has the capacity to cause E 3. Causal laws: C causes E in T  2. Functional relations and probabilities: In T, P(E/C) > P(E/not-C) Non-Modal Level 1. Occurrent regularities: In T, the ratio of E+C to E-C is r

On a radical empiricist view, each of the levels of modality is merely a metalinguistic (and thus mind-dependent) summary of facts about the next lowest level. That is, capacity ascriptions are summaries of facts about causal laws, causal laws are summaries about functional relations and probabilities, and functional relations and probabilities are summaries of regularities and frequencies at the non-modal level. Hence, the whole edifice of modalities is a mind-imposed device for summarizing regularities and helping us to systematize them in such a way that we will be able to draw inferences about what will occur in various situations:

"The claims at the higher level constrain what structure the total set of facts at the lower level can have, and thereby license inferences from one kind of fact at the lower level directly to another, without the need for any support from below ... [For the positivist] any set of so-called 'causal laws' [level 3] that produces the right constraints on the laws of association [level 2] is as good as any other. Correlatively, one should be able to tell whether a set of causal laws is acceptable or not just by looking at what relationships the probabilistic laws bear to one another ... [But] Chapter 3 shows that one has to look further. One needs to know some fundamentally causal information as well--one needs to know facts about singular causes. It is indeed possible to see causal laws as inference tickets from one probabilistic law to another--but only if the individual causal histories are right. There is thus a concealed ceteris paribus condition for the inference ticket to obtain; and that concealed condition brings in a notion of causality which is at the same modal level--or higher--than the one we are trying to eliminate." (pp. 160-61).
Cartwright poses two arguments against this reductionistic program.

Argument 1: The first is a complicated argument from the ceteris paribus clauses involving interactions. While the view of capacities proposed by Cartwright presupposes that capacities typically remain intact, it also allows for situations in which capacities fail to obtain for specifiable reasons. The most common cause of this failure is causal interaction, conceived of in such a way that their effects are not the combined issue of independently acting capacities, but a change in those very capacities. (Example: an acid and a base neutralizing one another.) Just as the exercise of a given stable capacity is subject to a ceteris paribus clause concerning other independently acting capacities ("so long as no other relevant capacity is being exercised"), so too we must prefix a ceteris paribus clause concerning interactions that alter the capacity in question. But, Cartwright continues

"How is this to be done without admiting interactions into the descriptive content of the world? I think it cannot be done. I have argued already that, one modal layer down, the ceteris paribus conditions on the inference patterns licensed by causal laws cannot be specified without already invoking strong notions of causality. This same kind of problem arises here. Causal interactions are interactions of causal capacities, and they cannot be picked out unless capacities themselves can be recognized. The attempt to 'modalize away' the capacities requires some independent characterization of interactions; and there is no general non-circular account available to do the job" (pp. 163-64).
So the argument is that just as information about singular causes is needed to get the right causal laws [level 2], so too information about specific capacities is needed to get the right account of causal interactions:
"What is needed for the positivist program to modalize away capacities is some separate, independent characterization of interaction, a characterization that employs no further problematic concepts like the concept of capacity itself. That is what we seem not to have, and for good reason, I have been arguing. For the concepts of capacity and interaction are genuine descriptive concepts, and are not in any way to be reduced to more primitive ideas. There are methods for determining when they obtain, but the methods cannot double as empirical reductions, for the two concepts are woven together in these methods and cannot be pried apart.
"I describe only the interplay between these two concepts; but that is too simple. A large number of other equally non-reducible concepts are involved as well, concepts like those of enabling conditions, precipitating factors, triggers, inhibitors, preventatives, and the like. These are the kinds of concept that will have to go into a proper account of what capacities are and how they operate" (p. 166).
Argument 2: The second argument is from mixed or dual capacities, as in the birth control pill example:
"Principle CC gives a preliminary version of the connection between causes and probabilities: a cause should increase the probability of its effect, and a preventative should lessen it, when all the other causes are held fixed. But Chapter 3 teaches a more complicated lesson. It is not sufficient to hold fixed just the other causal factors; one must hold fixed the operation of all the other capacities that may be at work as well, whether those capacities are attached to separate causal factors or to the very one under investigation. Otherwise facts about capacities and facts about probabilities will have no systematic connection with each other. Again, the program to modalize away capacities founders. An ascription of a capacity cannot be taken merely as an inference ticket to get from one fact about probabilities to another, that is, as an efficient summary of complicated facts about the pattern of pure probabilities; for the pattern it summarizes is not a pattern involving just the probabilities themselves but a more variegated pattern, involving both probabilities and capacities in an essential way" (pp. 166-67).
And, finally, in answer to the radical suggestion that the whole fabric of causal concepts and all the layers of modality should be rejected because of underdetermination by the "basic facts," Cartwright asks, "What is so special about the elementary facts with which you are willing to begin?" A good question, it seems to me.

The section of this chapter on Mill is pretty straightforward and requires no explanation. Note the closing diatribe against an appeal to regularities as something suited to constitute the level of special basic facts:

"This chapter begins with a picture of layered modalities: first laws of association, then causal laws, then capacities. But ... the capacities are more than modalities; they are something in the world. Where, then, does that leave the lower modal levels, and in particular the laws of association [level 2]? The popular view, which I want to attack, takes these as nature's givens ... But I want to urge a very different picture that is open to us once we admit capacities into our world. It is not the laws that are fundamental, but rather the capacities. Nature selects the capacities that different factors shall have and sets bounds on how they can interplay. Whatever associations occur in nature arise as a consequence of the actions of these more fundamental capacities. In a sense, there are no laws of association at all. They are epiphenomena.
"One of the chief strengths of an ontology which takes capacities as fundamental and associations as secondary is the quite important one that it can hope to give a far more realistic picture than can the alternative. We all know that the regularity of nature so central to the more conventional picture is a pretence ... Nature, as it usually occurs, is a changing mix of different causes, coming and going; a stable pattern of association can emerge only when the mix is pinned down over some period or in some place. Indeed, where is it that we really do see associations that have the kind of permanence that could entitle them to be called lawlike? The ancient examples are in the heavens, where the perturbing causes are rare or small in their influence; and the modern examples are in the physics laboratory, where our control is so precise that we ourselves can regulate the mix of causes at work. Otherwise, it seems to me, these vaunted laws of association are still very-long-outstanding promissory notes: laws of association are in fact quite uncommon in nature, and should not be seen as fundamental to how it operates" (pp. 181-82).