A. Mackie gives the following synopsis of the theme and purpose of Hume's discussions of causality in the Treatise and first Inquiry:

"Causation as we observe it in 'objects' of any kind--physical processes, mental processes, the transition from willing to bodily movement, or anywhere else--is something that we might roughly describe as regular succession. Exactly what it is or may be, within the bounds of this rough description, does not matter for the present purpose. All that matters is (i) that it should be something that could, in those cases in which we form our idea of causation, give rise to a suitable association of ideas and hence, in accordance with my psychological theory of belief, to belief in the effect when the cause is observed or in the cause when the effect is, and (ii) that it should not be anything in which there is an observable necessity (or efficacy or agency or power or force or energy or productive quality) or anything at all that could supply a rival explanation of our idea of necessity, competing with the explanation given in terms of association, belief, and projection" (p. 6). 

• Necessity₁ = Whatever is the distinguishing feature of causal as opposed to non-causal sequences. 

• Necessity₂ = The supposed warrant for a priori inferences from cause to effect or from effect to cause. (Mackie makes the further distinction here between warrants for deductive inferences (necessity_2.1) and warrants for probabilistic inferences (necessity_2.2), a distinction that Hume is not sensitive to.)

• Necessity₃ = The supposed warrant for causal inference in both directions, but not for a priori inference. (Regular succession is a candidate here, but Hume rules it out as providing rational warrant because of the problem of induction.)

Mackie's considered view is that Hume has good reasons only for the assertion that necessity_2.1 is not revealed by any observable sequence, but that he does not have any argument for the assertion that necessity₁ is not revealed by any observable sequence. 

1.  The idea of causation: Our idea of causation combines three elements, viz., succession, contiguity, and necessary connection.

Mackie has this to say about necessary connection: " ... Hume is very far from holding a regularity theory of the meaning of causal statements. His answer to the question 'What do we ordinarily mean by "C causes E"?' is that we mean that C and E are such that E's following C is knowable a priori, in view of the intrinsic character of C and E, so that the sequence is not merely observable but intelligible. When at the conclusion of the discussion in the Enquiry he says 'we mean only that they have acquired a connexion in our thought', etc., he is telling us what we can properly mean rather than what we ordinarily mean. He thinks that the ordinary meaning is itself mistaken, and calls for reform.

"On this crucial issue, I think that Hume is right to assume that we have what in his terminology, with my subscripting, would be an idea of necessity₁; we do recognize some distinction between causal and non-causal sequences, and what is more we are inclined to think that, whatever this difference is, it is an intrinsic feature of each individual causal sequence. But I have argued that Hume is quite wrong to assume that our idea of necessity₁ is also an idea of necessity₂, that we ordinarily identify the differentia of causal sequences with something that would support a priori inference" (p. 20).

2. Causation in the objects: Causation in the objects is regular succession and nothing more. 
 

Mackie takes Hume's references to the "secret powers" of material objects to be tongue-in-cheek, but this seems dubious to me, since it is Hume's only decent argument against occasionalism.

3. Causation as we know it in the objects:

Here Hume makes three negative points and one positive point:

a. There are no logically necessary connections between causes and effects as we know them. 

b. Necessity₂ is not known as holding between causes and effects. 

c. We find nothing at all in causal sequences except regular succession and (perhaps) contiguity. 

d. Causation as we know it involves regular succession in all the cases observed thus far.

Mackie himself accepts (a) and also (b) as applied to necessity_2.1, but has problems with (c) and (d). He explains his own project as follows:

"Hume's discussion of causation, then, includes both strong points and weak ones. Accepting his exclusion of logically necessary connection and of necessity_2.1, and postponing consideration of necessity_2.2, we have still to consider what sort or sorts of regularity, if any, characterize causal sequences, what within our ordinary concept of causation differentiates causal sequences from non-causal ones, and what features--whether included in this ordinary concept or not--over and above 'regularity' are to found in causal relationships. We may start with the job that Hume only pretended to be doing, of identifying what we naturally take as the differentia of causal sequences; that is, we may ask again what our idea of necessary connection (necessity₁) is in an open-minded way, without assuming that it must be the idea of something that would license a priori inferences" (p. 28). 

 

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NOTES ON CHAPTER 2 OF MACKIE'S THE CEMENT OF THE UNIVERSE

A. Summary
 

It is crucial to keep in mind that in Chapter 2 Mackie's goal is to give an account of our idea of causation as opposed to an account of causation as it is in the objects. The latter is the topic of Chapter 3.

 

The general results of Chapter 2 consist in the following four theses:

 

(1) Our idea of a cause is the idea of that which is (i) necessary in the circumstances for the effect and (ii) causally prior to the effect.

 

(2) The idea of that which is necessary in the circumstances (an idea that corresponds to necessity₁ from Chapter 1) is to be spelled out in terms of counterfactual dependence. 

 

(3) This counterfactual dependence is not itself observable, but instead is mind-dependent in a way redolent of (though different from) Hume's own psychological account of the origin of the idea of necessary connection. Mackie spells this out by means of what Kim elsewhere dubs a 'nomic-inferential model' of counterfactual conditionals. 

 

(4) We must look to causation as it is in the objects to discover whether (i) there is any feature of it which can be taken (pace Hume) to confer rational warrant on our assertion of the relevant counterfactuals and whether (ii) there is anything corresponding to causal priority in the objects themselves. (These tasks are taken up in Chapters 3 and 7, respectively. In particular, regularity will be the feature of the world that undergirds our assertion of the counterfactuals.)

 

Given this outline, I will now briefly lay out the main features of Chapter 2. 

B. The Basic Idea of Causation (pp. 29-43)

According to Mackie, the heart of our idea of causation is the belief that a cause is necessary in the circumstances for the effect, where the notion of being necessary in the circumstances is spelled out as follows:

x is necessary in the circumstances for y just in case 

(i) x and y are distinct events, and

(ii) x occurs and y occurs, and
(iii) in the circumstances, if x had not occurred, y would not have occurred.

This, Mackie claims, is the "obvious" answer to the question of what, according to our ordinary idea of causation, distinguishes causal from non-causal sequences--though he is immediately forced to point out that this account runs into problems with common cause cases, overdetermination, and the distinction between conditions and causes. The last problem he tries to solve right away by (i) concocting the notion of a causal field to absorb some 'conditions' and (ii) appealing to pragmatic considerations to explain why other 'conditions', though they are "really" causes, are not counted as such for certain explanatory purposes. The first two problems he defers for later discussion (see below under 'C').

 

Comment: The claim that necessity in the circumstances is basic seems to me just wrong; our basic idea of causation is that of production/conservation, i.e., something like the communication of esse by the mediation of an action. (Sound familiar?) Even though, as we saw with Lewis, this notion corresponds with counterfactual dependence over a wide range of cases, there is no exact correspondence. That was why Lewis had to resort to 'quasi-causal dependence' in cases where our idea of causation diverged from straight counterfactual dependence, even via a causal chain.

 

Mackie then asks whether sufficiency in the circumstances is also part of our concept of causation. Here he distinguishes two senses of sufficiency. The first is this:

x is weakly sufficient in the circumstances for y just in case in the circumstances, if x occurs, y occurs, where the conditional is non-material but trivially true if x and y both occur. So this is already included in the above account of necessity in the circumstances.

The second sense is this:

x is strongly sufficient in the circumstances for y just in case in the circumstances, if y had not been going to occur, then x would not have occurred.

Mackie shows, via the candy-machine argument, that though this is often true in cases of deterministic causation, this sort of sufficiency is not endemic to our notion of causation. (This seems exactly right to me.) 

C. Worries (pp. 43-53)

At this point the following problems arise: (i) overdetermination, (ii) (early) preemption, (iii) collateral effects of a common cause, (iv) symmetry of counterfactual dependence in cases where the cause is strongly sufficient in the circumstances for the effect. (Mackie gives five examples on p. 44, and you can add them to your set of stock examples!) Here, in general, is how he handles them:

 

1. Overdetermination: Here he bites the bullet and declares that neither of the overdeterminers is a cause of the relevant effect, though their 'combination' is a cause. I will leave it as a homework assignment to figure out whether and how the 'combination' of two events is itself an event. 

 

2. (Early) Preemption: Here he goes Biel-ish (and a little Lewis-ish) by saying that the notion of necessity in the circumstances is the notion of necessity in the circumstances for the effect's coming about as it came about. (In most cases this will involve identifying a causal chain; Lewis is far superior and much more elegant on this score. Mackie also makes some weird remarks about the distinction between facts and events on pp. 46-47, but they are not crucial as long as we think of causes and effects as concrete events; so I will pass over them in silence.) 

 

3. Collateral Effects of Common Cause: Both y and z, which are unconnected collateral effects of x, are such that in the circumstances if the one had not occurred, the other would not have occurred. This is a toughie, which calls for strong medicine (see below). 

 

4. Symmetry of Cause and Effect: This is what Lewis called the problem of the effect. When a cause x is strongly sufficient in the circumstances for an effect y, it is unfortunately true that if y had not been to occur, x would not have occurred. Yet given our ordinary notion of causation, we have no problem saying that x is a cause of y, but not vice versa.

How to handle 3 and 4? Here Mackie resorts to the idea of causal priority. That is, in case 4 we count x, but not y, as a cause because in such a cases x is causally prior to y, but not vice versa; and in case 3 x is causally prior to both y and z, but y is not causally prior to z and z is not causally prior to y. Since Mackie believes that causal priority is found in the objects, I will defer discussion of it until chapter 3. What we have, then, is the following:

 

x is a cause of y, according to our ordinary concept of causation, iff

(i) x and y are distinct events, and

(ii) x occurs and y occurs, and
(iii) in the circumstances, if x had not occurred, y would not have occurred, and
(iv) x is causally prior to y.

(You should also note in passing Mackie's reply on pp. 49-50 to the claim that causation itself is a probabilistic concept to be analyzed in terms of the raising of probabilities. Rather, in his view probability enters in only insofar as some event-types are such that it is likely to degree n that tokens of them will be necessary in the circumstances and causally prior to tokens of the effect's event-type. This view of how probability figures into causality stands in marked contrast to what is said by Tooley, among others. In addition, it contrasts with what Lewis says, though Lewis is more sophisticated. See the Lewis handout on chancy causation. In any case, the Aristotelian will, I believe, side with Mackie here, but for an Aristotelian reason, viz., that in the cases in question the crucial question is: Which agents have acted to produce the effect in question? This means that the raising and lowering of probabilities for the effect is not basic but is instead to be explained in terms of the probability of an agent's acting in a given set of circumstances. This may not always be discoverable by us, and so I suppose that I am appealing to what Lewis disparagingly calls a 'hidden factor'. But so be it.)

D. The Mind-Dependence of Necessity in the Circumstances (pp. 53-58)

I will not spend much time on this, though it is worthwhile raising the question of how Mackie's claims here are related to Lewis's view. Neither of them allows us ultimately to raise the question of why the relevant counterfactuals hold. Lewis does not go beyond the counterfactuals at all, but seems to take them as simply ultimate facts about the world (is this a correct interpretation?), whereas Mackie takes them as mind-dependent but assertable on the basis of regularities, which themselves are the ultimate facts about the world. Mackie's position is more in the spirit of strict Humean empiricism; but Lewis seems to be in the same ballpark, despite the fact that he does not draw a sharp distinction between our idea of causation and causation as it is in the objects. In neither case, however, is there any ultimate appeal to the causal structures of substances or to their powers as the de re basis for mind-independent counterfactual truths. 

 

Mackie's view is this. A non-material conditional P-->Q is such that if (i) it is a counterfactual, i.e., if its antecedent is, as its user believes, unfulfilled, and if (ii) P does not entail Q, then to assert it is not to assert a proposition capable of being true or false. Instead, in such a case asserting P-->Q is equivalent to asserting "the existence of an argument whose premises include universal laws, the indicative form of P, and other singular statements of 'relevant conditions' and whose conclusion is the indicative form of Q" (Kim, "Causes and Events: Mackie and Causation," in the Sosa anthology, p. 50).

It follows that singular causal statements cannot be literally true, either, since their analysis essentially involves counterfactuals. Further, necessity₁ cannot be observed in the world (since it is counterfactual in nature). So just as Hume looked for the psychological origin of the idea of necessity₂, we must look for the psychological origin of the idea of necessity₁. Mackie makes an appeal to evolutionary adaptivity for our capacity and tendency to make suppositions and then appeals to primitive (imaginative) and sophisticated (Mill's methods) ways in which we feel justified in making judgments about how the world would go under counterfactual suppositions. But the next step is to see whether what goes on in the objects might give us further backing for reasoning according to counterfactual suppositions. 

 

 

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NOTES ON CHAPTER 3 OF MACKIE'S THE CEMENT OF THE UNIVERSE

A. Summary

In this chapter Mackie gives an account of causation as it occurs in the objects. His basic strategy is to replace necessity₁ in the account of our concept of causation with an appeal to regularity as necessity₃, i.e., as that which (i) is observable and (ii) gives rational warrant for our assertion of the counterfactuals alluded to in the account of what a cause is according to our concept of causation. So the basic task of this chapter is to lay out and defend a regularity account of causation.

I will also add to this the main outline of what Mackie says in chapter 7 about the other element required for a complete account of causation, viz., causal priority. (See section F.) 

B. Opening Remarks (pp. 59-60)

Here Mackie explains his purposes as noted above. In addition, he makes the passing claim that a regularity account of causation in the objects need not "introduce the mystery of a special sort of regularity, a 'nomic universal', to account for the ability of causal laws to sustain counterfactual conditionals" (p. 60). That is, we need not think, as Armstrong and Tooley do, that an empiricist account of causation must, to be successful, attribute some intrinsic modal property to lawlike statements in order to distinguish them from non-lawlike statements of regularities and to explain why lawlike statements, unlike their non-lawlike counterparts, support counterfactual assertions. (One problem, however, is that non-lawlike regularities may indeed support counterfactual assertions, e.g., in certain common cause cases.)

 

Comment: This requires closer scrutiny. To a certain extent, Mackie is able to solve some of the problems here by his appeal to causal priority as an additional factor in causation. However, the appeal to a special modal status for lawlike statements is meant at least in part to overcome the claim that empirical generalizations themselves cannot warrant claims that go beyond the already observed. Whether Mackie succeeds in quelling doubts on this matter later in this chapter remains to be seen. 

C. The Basic Regularity Account of Causation

In what follows I will presuppose with Mackie the applicability of the notion of a causal field, which is meant to capture the environment or circumstances in which a causal sequence occurs. Given this, there are three basic concepts:

ABnot-C is a minimum sufficient condition for P in causal field F iff

(i) ABnot-C is sufficient for P in F, and

(ii) no proper part of ABnot-C is sufficient for P in F.

A is an inus condition for P in F iff 

(i) A by itself is not a sufficient condition for P in F, 

(ii) and for some minimum sufficient condition M for P in F,

(a) A is a proper part of M, and

(b) M is not itself a necessary condition for P in F. 

A is at least an inus condition for P in F iff either

(i) A is an inus condition for P in F, or

(ii) A is a minimum sufficient condition for P in F, or
(iii) for some X, AX is a necessary and sufficient condition for P in F, or
(iv) A by itself is a necessary and sufficient condition for P in F. 

Then, 

 

(ABnot-C or DEnot-F or ... or XYnot-Z) is a full cause of P in F iff

(i) each of the disjuncts is itself a minimum sufficient condition for P in F, and

(ii) nothing else is a minimum sufficient condition for P in F. 

A is a (singular) cause, as it occurs in the objects, of P in F only if

(i) A and P are distinct events, and

(ii) A occurs in F and P occurs in F, and
(iii) A is at least an inus condition for P in F.

Question: How crucial is it to Mackie's project that a full cause should consist of just finitely many disjuncts? It does seem crucial if his argument against the postulation of powers is to even get off the ground. (After all, can scientists be said to aim at formulating infinitely long laws?) Notice, too, that the members of these disjunctions will include conditions and absences, and one might wonder about the appropriateness of saying that such things have a "tendency" to cause the effect in question (see p. 76). Also, it is not even clear that each of the disjuncts in a full cause will be finite or that F will be finite.

 

The sorts of question raised here cast doubt not only on the analysis of a cause but also on the usefulness of formulas of the sort in question for scientific inquiry. Mackie is not insensitive to these problems; later in the chapter he argues at some length that even extremely gappy knowledge of full causes is sufficient for explanation, prediction, and control.

Note: Here is a Sosa-inspired counterexample to an account of singular causation that takes the above conditions as both necessary and sufficient. (It may also pose a problem for Mackie's full account below). Suppose that AB is a minimum sufficient condition for P in F; then for any arbitrarily selected X such that neither BX nor (not-X or A)B is a minimum sufficient condition for P in F, X(not-X or A)B is a minimum sufficient condition for P in F, and hence X is an inus condition for P in F. 

 

The only escape is not to allow disjunctive states or events, etc., but then we need a lot more from Mackie by way of an ontology of events, states, etc. 

Mackie next argues that a full cause, if known, can in the appropriate circumstances warrant a counterfactual assertion to the effect that if A had not occurred, P would not have occurred. The idea is that if the formula in question does indeed give us a full cause and we know it, then the knowledge that all the other disjuncts failed to obtain in a given case warrants the claim that if any of the elements in ABnot-C had not obtained, then P would have failed to obtain. In cases of deterministic causation we will even be able to assert with warrant the contrapositive claim that if P had not been going to occur, then ABnot-C would not have occurred, either; and given our knowledge that B and not-C obtained in the circumstances, we can assert with warrant that if P had not been going to occur, then A would not have occurred. 

 

The obvious objection is that we don't and perhaps can't know full causes. In reply Mackie launches into an extended discussion of how gappy knowledge of full causes can still serve as a warrant for the relevant counterfactual assertions, though such assertions will be more tentative than those made on the basis of a complete knowledge of full causes. Much of what he says here seems to me unexceptionable, though this may simply reflect my own naivete regarding these epistemological issues. 

 

One thing that Mackie is after here is to undermine the idea that attributions of powers and tendencies (ala Geach, Harré and Madden, Cartwright) must be taken to be basic and irreducible. This is an important issue that divides empiricists from Aristotelians. Mackie's point is that such attributions are at best placeholders for gappy generalizations and are ultimately or ideally reducible to very complicated full causes. That is, we are forced to posit natures or powers or capacities only by our ignorance of full causes, i.e., only by our ignorance of filled-out accounts of necessary and sufficient conditions. This is a line of argument that we will have to ponder as we go on. Here is what Mackie says:

 

"It will be clear from what has been said above that though interference could not be brought into a doctrine of simple uniformities, it is easily accommodated in a doctrine of complex uniformities. Interference is the presence of a counteracting cause, a factor whose negation is a conjunct in a minimal sufficient condition (some of) whose other conjuncts are present. The fact that scientists rightly hesitate to assert that something always happens is explained by the point that the complex uniformities they try to discover are nearly always incompletely known. It would be quite consistent with an essentially Humean position--though an advance on what Hume himself says--to distinguish between a full complex physical law, which would state what always does happen, and the law as so far known, which tells us only what would, failing interference, happen; such a subjunctive conditional will be sustained by an incompletely known law. Moreover the rival doctrine can be understood only with the help of this one. What it would be for certain behaviour to be 'proper to this set of bodies in these circumstances', what Aquinas's tendencies or appetitus are, remains utterly obscure in Geach's account; but using the notion of complex regularity we can explain that A has a tendency to produce P if there is some minimally sufficient condition of P in which A is a non-redundant element. (This is, indeed, not the only sense of the terms 'tend' and 'tendency'. We could say that A tends to produce P not only where A conjoined with some set of other factors is always followed by P, but also where there is an indeterministic, statistical law to the effect that most, or some, instances of A, or some definite percentage of such instances, are followed by P, or perhaps where an A has a certain objective chance of being followed by a P. These statistical tendencies are not reducible even to complex regularities: if they occur, as contemporary science asserts, then they constitute something different from, though related to, strict deterministic causation. But they have little to do with Geach's problem of interference)." (p. 76).

Notice, however, that there may be a problem here akin to one that seems to do in behaviorism as an account of mental tendencies and dispositions. It seems logically possible for there to be tendencies or powers that are never actualized or (more interestingly) never exercised in "pure" circumstances where no counteracting causes are present. But then tendency-statements might be true in the absence of observed regularities, no matter how complex those regularities are. (Suppose that a given sample of salt as a matter of fact never dissolves when added to water because the water to which it is added is already salt-saturated.) Hence, tendency statements are not reducible to statements about regularities in behavior. Can a formidable objection to what Mackie says be formulated along these lines? 

E. The Full Regularity Account

Mackie explicitly denies that singular causal statements are implicitly general or that they imply either (i) complex but complete regularity statements or (ii) gappy regularity statements of the form F(AX or Y) is necessary and sufficient for F(P) or (iii) even "vague generalizations". Still, all three of the latter support singular causal statements. 

 

As for general causal statements, Mackie has this to say: 

 

"The statements that heating a gas causes it to expand, that hammering brass makes it brittle ... can indeed be interpreted as assertions that the cause mentioned or indicated is an inus condition of the effect. But even here it would be more appropriate to take the general statements as quantified variants of the corresponding singular ones, for example, as saying that heating a gas always or often or sometimes causes it to expand, where this 'causes' has the meaning 'caused' would have in a singular causal statement. However, the essential point is that singular causal statements are prior to general ones, whereas a regularity theory of the meaning of causal statements would reverse this priority" (p. 80). 

As Mackie admits, however, regularity by itself will not provide a complete account of causation in the objects themselves. The main problem here is that as a matter of fact there are both de facto unconditional regularities and counterfactually unconditional regularities, and it is only the latter that can be causal. But it is not even the case that all counterfactually unconditional regularities point to a direct causal connection. Collateral effects of a common cause (e.g., the Manchester hooters and the Londoners' leaving work) provide the best sort of counterexample here:

 

Suppose that A and B are not related as cause and effect, but that both have C as an inus condition, so that (i) CX or Y is necessary and sufficient in F for A, and (ii) CZ or W is necessary and sufficient in F for B. 

Then Anot-YZ is necessary and sufficient in F for B, and so A is at least an inus condition for B.

 

At this point Mackie invokes causal priority, and from what he says in Chapter 7 we can extract the following account:

X is causally prior to Y iff either
(a) there is some time when X is fixed and Y is unfixed, or
(b) (i) X is not fixed until it occurs, and (ii) there is no time when X is unfixed and Y is fixed, or
(c) (i) X is fixed before it occurs, and (ii) there is no time when X is unfixed and Y is fixed, and (iii) for some Z, (A) there is a causal chain from Z through X to Y, and (B) Z was not fixed until it occurred.
 

If A is the sounding of the Manchester Hooters and B is the London workers' going home, then A is not causally prior (even though it is temporally prior) to B. The reason, presumably, is that A and B are fixed together and there is no causal chain running from C through A to B. As Mackie admits, however, this account of causal priority will not do in a completely deterministic world, in which every event is fixed before it occurs. This seems like a serious defect, but Mackie is not worried:

 

"The further analysis, in terms of fixity and unfixity, could have objective application provided only that there is a real contrast between the fixity of the past and the present and the unfixity of some future events, free choices or indeterministic physical occurrences, which become fixed only when they occur. No we certainly do not know that there are no such events; we do not know that strict determinism holds; but neither do we know that it does not hold, though the balance of contemporary scientific opinion is against it. So we had better be content with hypothetical judgments here: if determinism does not hold, the concept of causal priority which I have tried to analyze will apply to the objects, but if determinism holds, it will not. If you have too much causation, it destroys one of its own most characteristic features (!!!!). Every event is equally fixed from eternity with every other, and there is no room left for any preferred direction of causing" (p. 192). [My exclamation points.]

So the full account of singular causation is as follows:
 

A is a (singular) cause, as it occurs in the objects, of P in F iff

(i) A and P are distinct events, and

(ii) A occurs in F and P occurs in F, and
(iii) A is at least an inus condition for P in F, and
(iv) A is causally prior to P in F. 

 
NOTE ON CHAPTER 3 OF MACKIE'S THE CEMENT OF THE UNIVERSE:

ON TENDENCIES AND INTERFERENCE

Recall Mackie's claim:

"It will be clear from what has been said above that though interference could not be brought into a doctrine of simple uniformities, it is easily accommodated in a doctrine of complex uniformities. Interference is the presence of a counteracting cause, a factor whose negation is a conjunct in a minimal sufficient condition (some of) whose other conjuncts are present. The fact that scientists rightly hesitate to assert that something always happens is explained by the point that the complex uniformities they try to discover are nearly always incompletely known. It would be quite consistent with an essentially Humean position--though an advance on what Hume himself says--to distinguish between a full complex physical law, which would state what always does happen, and the law as so far known, which tells us only what would, failing interference, happen; such a subjunctive conditional will be sustained by an incompletely known law. Moreover the rival doctrine can be understood only with the help of this one. What it would be for certain behaviour to be 'proper to this set of bodies in these circumstances', what Aquinas's tendencies or appetitus are, remains utterly obscure in Geach's account; but using the notion of complex regularity we can explain that A has a tendency to produce P if there is some minimally sufficient condition of P in which A is a non-redundant element." (p. 76). 

A. Tendencies

It is clear upon reflection that Mackie's account of what a tendency is simply won't wash: "using the notion of complex regularity we can explain that A has a tendency to produce P if there is some minimally sufficient condition of P in which A is a non-redundant element." 

Recall Geach's example:

Let A be the operation of a heating unit that by itself would raise the temperature of room R 25° in one hour; and let B be the operation of a cooling unit that by itself would lower the temperature of R 10° in one hour; and let ABX be a minimal sufficient condition for the temperature of R going up 15° in one hour in field F.

If Mackie is right, then A has a tendency to produce a 15° rise in temperature in R in one hour in field F--which seems wrong. But, more spectacularly, even B has a tendency to produce a 15° rise in temperature in R in one hour in field F--which just is wrong, not to mention wrong-headed. In general, on Mackie's view a thing or state has a tendency to produce whatever it is an inus condition for, and this is obviously crazy. The best that can be said is that Mackie confuses tendencies with the sort of evidence we can gather from complex situations for the attribution of tendencies.
 

B. Interference

What Mackie says gives us material for the following two accounts:

 

(I) A, failing interference, is a cause of P in F iff 

(a) for some MSC_i of P in F, MS_i = AXnot-Y, where X is a placeholder for all the positive conditions other than A and not-Y is a placeholder for each negation of a condition the presence of which would result, barring overdetermination, in P's not obtainining in F.

(b) A and X are present in F. 

(II) C interferes with A's being a cause of P in F iff

(a) A is present in F, and 

(b) for some MSC_i of P in F, (i) MSC_i = ABnot-CX, and (ii) B is present in F, and (iii) C is present in F, and
(c) there is no MSC_j such that (i) MSC_j = AX, and (ii) X is present in F. 

But there are some problems here, though these problems stem from Mackie's general account of causality and are simply highlighted by reflection on the notion of interference. 

 

First of all, if the account of a tendency is inadequate, this should immediately raise worries about whether the account of interference can be adequate. For instance, (I) tells us that when a pot of water is placed over a gas flame, the mere presence of the water is, failing interference, a cause of the water's boiling in F. This seems counterintuitive, since it is presumably agents alone that are, failing interference, causes of a given effect. But this is just a result of the fact that Mackie's account of an inus condition gives us no way to distinguish among agents, patients, and necessary conditions. 

 

Second, this account of interference shows how implausible Mackie's identification of a cause with an inus condition is. Take the example involving the electric current, the frayed wire, and the presence of inflammable material at the point of fraying. Presumably, one of the inus conditions of a fire's being produced in this situation (i.e., a candidate for not-C in (II)) is that no one should disconnect the wire from a source that generates electricity; and this, presumably, entails that for any adult human being H, H's not disconnecting the relevant wire is a cause of the fire's being produced. Perhaps I am overlooking something here. If so, what? In general, it seems that any MSC is going to include lots of negations of this sort, negations which it would be wildly implausible to consider causes. 

Does the notion of a field block this consequence? Perhaps it helps to some extent, but this would force us to distinguish 'plausible' from 'implausible' possible interferers, where plausible interferers are those who are 'in a position' to interfere during the time period in question. But even here we would probably have to let in a lot of intuitively unacceptable 'causes'. Indeed, what this suggests is than every MSC will be so complicated as to be not entertainable by any human mind.