Rel. Stud. 31, pp. 323-328. Copyright ? 1995 Cambridge University Press JAMES CAIN THE HUME-EDWARDS PRINCIPLE In such a chain too, or succession of objects, each part is caused by that which preceded it, and causes that which succeeds it. Where then is the difficulty? But the WHOLE, you say, wants a cause. I answer, that the uniting of these parts into a whole, like the uniting of several distinct counties into one kingdom, or several distinct members into one body, is performed merely by an arbitrary act of the mind, and has no influence on the nature of things. Did I show you the particular causes of each individual in a collection of twenty particles of matter, I should think it very unreasonable, should you afterwards ask me, what was the cause of the whole twenty. This is sufficiently explained in explaining the cause of the parts. (David Hume1) The demand to find the cause of the series as a whole rests on the erroneous assumption that the series is something over and above the members of which it is composed_ If we have explained the individual members there is nothing ad? ditional left to be explained. (Paul Edwards2) In discussions of the cosmological argument for the existence of God, in particular the Leibniz-Clarke versions of the argument, the following gen? eral methodological principle governing causal explanation is sometimes put forward : HEP: Given a collection of parts which jointly compose a whole, an explanation which assigns a cause to each of these parts provides a causal explanation of the whole. I call this the Hume-Edwards Principle and abbreviate it as 'HEP', though it is perhaps somewhat broader ranging than the principle expounded in the above quotations from Hume and Edwards. We might usefully consider two more specific forms of HEP. First we might restrict consideration to cases in which the parts that make up the wholes are individuals. Call this restricted principle HEP(i). Alteratively, we might restrict consideration to cases where the parts are events. Call this principle HEP(e). Hume and Edwards seem to have HEP(i) in mind in the above quotations. HEP is intended to apply to cases in which the number of parts under consideration is either finite or infinite. In particular, Hume and Edwards argue that if a changing universe has always existed and what exists at any given time is caused by what previously existed, then it is mistaken to ask for a cause of the existence of the whole enduring process which extends infinitely into the past at least this is a mistake if it is a request for a cause outside 1 Dialogues Concerning Natural Religion, part ix. 2 'A Critique of the Cosmological Argument', in Louis P. Pojman (ed.), Philosophy of Religion: an Anthology (Belmont, California: Wadsworth Publishing Co., 1987), p. 16; originally published in The Rationalist Annual for the Tear ig^g. 324 JAMES CAIN the process, for by giving causes of the parts a causal explanation of the whole has already been given. HEP, of course, has had its detractors.3 A good example is Swinburne's discussion of the above passage from Hume. (Swinburne uses the term 'full cause of E" to refer to 'a set of factors which together were sufficient for the occurrence of...event i?.'4) One principle which might be proposed in this connection is that a cause of the occurrence of a collection of states is any collection of the causes of each. More particularly, a full cause of the occurrence of a collection of states is any collection of full causes of each. This principle clearly holds for any finite set of effects, where none of the causes of any member of the collection of effects is itself a member of the collection of effects.... However, the principle must be modified if it is to take account of cases where the cause of some member of a collection of effects is itself a member of that collection. For when b is the cause of a, and c is the cause of b, we say that the cause of a + b is c, not b + c.5 Swinburne proceeds to modify the principle to say, ' a (full) cause of the occurrence of a collection of states, is any collection of (full) causes of each, whose states as they cause are not members of the former collection.'6 With this modified principle, Hume's contention that an explanation of the causes of the parts of a whole will provide an explanation of the cause of the whole will work (for full causes) in cases where there are a finite number of parts (at least if we grant that causation cannot go 'in a circle'7), for then the collection of causes for the parts must provide us with a subcollection outside the whole which will then explain the whole. But if there are an infinite number of parts, an explanation of each part may not provide a causal explanation of the whole ; in particular it will not if each part is explained by the causal activity of other parts functioning within the whole. Though I am rather sympathetic to Swinburne's line of thought here, I suspect that most people who initially support HEP (in either form) probably are not. I will attempt to show, by another line of reasoning, that there are grounds for holding that HEP (in both forms) fails to provide us with an intuitively obvious a priori methodological principle governing causal expla? nation. I will not try to show that it is in fact false, for, as was suggested above, if it turned out by luck, so to speak that there is not an infinity of effects, HEP might well come out true. We will begin by looking at HEP (e). Let's imagine that an explosion takes place. This event, E, consists of the rapid expansion of some material over an interval of time. Suppose that someone supplies the following explanation of E. (Note that in assessing the 3 See William L. Rowe, 'Two Criticisms of the Cosmological Argument', The Monist, vol. 54, no. 3 (1970), and Chapter 3 of The Cosmological Argument (Princeton University Press, 1973). See also Chapter 7 of Richard Swinburne, The Existence of God (Oxford: Clarendon Press, 1992). 4 Ibid. p. 24. 5 Ibid. p. 123. 6 Ibid. p. 124. 7 For a discussion of the cosmological argument in which the supposition that causation cannot ' go in a circle' is abandoned, see Robin Le Poidevin, 'Creation in a Closed Universe Or, Have Physicists Disproved the Existence of God?', Religious Studies 27 (March 1991 ), pp. 39-48. THE HUME-EDWARDS PRINCIPLE 325 explanation I will not be concerned with whether it provides an empirically adequate explanation in the sense that it would stand up to criticisms levelled by chemists or physicists. Rather I will be concerned with what we are to make of it in light of HEP (e).) The interval of time (whose end points we will arbitrarily label o and 1 ) over which E took place is the open-closed interval of time (o, i].8 Now this interval is the union of all open-closed intervals (a, b], such that o < a < b  1. For any such interval (a, b] in (o, 1], there is an earlier interval (c, d] in (o, 1], (where o<c<d^a<b^ 1). Let us consider a particular sequence of such intervals, sx, s2, s3,..., where s? = (1/2, i], s2 = (1/4,1/2], s3 = (1/8, 1/4], etc. (o, 1] is the union of these ^'s. Let ei be the part of the explosion which took place over the interval sv We can see that each part of the explosion ei+1 caused the next part of the explosion ei as follows_ Here follows an explanation of how ei+1 caused ei which we leave out. I see no a priori reason why each ei+1 should not have caused eiy and so find nothing incoherent in this part of the account. Let us see how HEP(e) applies here. Note that even if we accepted the above account we might still ask the question, ? What if anything brought about explosion ??' HEP (e), however, tells us that this question is confused to the extent that it asks for an explanation of the whole, E, that cannot be satisfactorily given merely by providing explanations of the parts, i.e. the ^'s. But surely this is an un? warranted restriction set down by HEP (e). Just as each of the ^'s is a process which is a part of a larger process, the explosion E, so it may well be the case that E itself is a part of an even larger continuous process (one in which, perhaps, the chemicals that exploded were first heated). And just as each of the ??'s was caused by something outside of itself, so E may have an outside cause (the heating of the chemicals). The above causal explanations of the ?i's fail to provide a cause for E's occurrence. It is perfectly reasonable to ask what, if anything, caused E to occur; in doing so we are asking for a cause of the whole (the sum of the ês) which is not given in giving the above explanation of the causes of the parts (the ês). In saying this I am not saying that E must have been caused by something outside itself, I am only claiming that (1) we can reasonably ask whether E had a cause, and (2) a cause for E will not be provided by the explanations of the ês in terms of previous ^'s. There may of course be problems in the account of the explosion sketched out above. Perhaps time is not infinitely divisible; perhaps events do not take place over open-closed intervals of time, and so on. Here I am not concerned to argue out the nature of time, rather my point is that if one is to defend HEP(e) as an a priori principle to be used in assessing calls for causal explanations, then one ought to be able to show on a priori grounds that these sorts of presuppositions of my example are really untenable. I do not think this is a trivial task, and so think that one would be hard pressed to defend HEP (e) as an intuitively obvious a priori principle. 8 By the open-closed interval of time (o, i], I mean all the moments of time after time o and up to and including time i, i.e. {t\o < t < i}. 326 JAMES CAIN We have been looking at HEP(e). Let us turn to HEP(i), which perhaps presents us with a more complicated case. We can set out examples par? alleling our explosion example where now instead of having a succession of parts of an event we have a succession of objects. Imagine that you leave your desk for a minute and are surprised to find a ball on it when you return. You are curious about this ball and its causal history. You make inquiries and someone provides the following causal explanation. Note that nothing will hinge upon the correctness or even the plausibility of the proposed explanation ; our concern will rather be with how we evaluate the explanation in terms of HEP (i). The explanation begins: Call your ball B0. We believe that there have previously existed an infinite succession of balls, B1,B2,B3,B4^? B0 was caused by B1; Bx was caused by B2, B2 by B3, etc. Here follows an account, which we will leave out, of the causal mechanisms by which each ball was caused by its predecessor. The following part of the explanation is worth our attention however: A surprising feature of the succession of balls Bx, B2, Bz,... is that it only existed during the span of one minute. Our hypothesis is that Bx existed for 1/2 minute before B0; B2 existed 1/4 minute before B1; B3 existed 1/8 minute before B2, etc. That is, letting t be the instant of time one minute before B0 began to exist, for each n > 0, ball Bn existed from t+ (1/2)11 minutes until /+ (i/2)n_1 minutes. Thus none of the balls existed until after t, and the entire sequence of balls Bl9B2,B3...only existed until the moment, t+ 1, that B0 began to exist. This hypothesis, startling as it might be, appears at first glance to be consistent. What reaction might one have who did not simply dismiss the hypothesis? Let B be the whole succession of balls, B0,B1,B2,BS,_I think that one of the first questions the hypothesis raises is 'What, if anything, made B come into existence?' Of course in asking this we are asking for a cause not given in the above causal explanations of the î's. Note that I am not claiming here that B could not come into existence uncaused. I am only claiming that a causal question would arise as to whether B had a cause, and this causal question could not be answered by explaining the causes of the parts of B (the B^s) as was done above. But if HEP (i) were correct, this would be a confusion: a causal explanation of the individual î's would give a causal explanation of the whole. I said earlier that I thought HEP (i) might present a more complicated case than HEP (e). Here is why. It seems easy to conceive how a continuous process (as in our explosion example) can be part of a larger continuous process and can be brought about by an earlier part of the larger process.9 But, in the case of a succession of objects with no first member, it may be 9 Take, for example, high school physics problems where we are asked to determine the path a projectile will take over an interval of time given its previous trajectory and the gravitational forces involved. Here a process taking place over one time interval is seen to be causally explicable in terms of an earlier process. Here too we are comfortable with treating a process taking place over an interval of time, like the falling of a body, as being decomposable into subprocesses of arbitrarily small size. THE HUME-EDWARDS PRINCIPLE 327 harder to fathom how there can be an outside cause of the whole. After all, we do not generally think in terms of there being an infinite succession of objects over a finite time span (as opposed to there being infinitely many subintervals in a finite interval). And if there could be an infinite succession of objects over a finite time, like the B?s, it is perhaps more difficult to see how it could have an outside cause. Call a succession of objects self-contained iff it is an infinite succession of objects containing no first (i.e. unpreceded) member and in it each member is caused by one or more preceding members. If we could rule out a priori either the existence of an infinite succession of objects over a finite span of time or an outside cause for a self-contained succession of individuals, then HEP (i) would be immune to my objection. I will present a prima facie case for holding that these cannot be ruled out a priori. I begin by noting that sometimes individuals are supervenient on pro? cesses. An example will indicate what I have in mind here. We can imagine someone investigating chemical processes taking place on the sea floor. One might investigate a very complex process in which molecules are constructed, broken down, spatially arranged, etc. This investigation could be carried out without recognizing the ' macroscopic ' features of the environment at the level of biological organisms. It might later be noticed that some complex continuous chemical process (involving the construction and interaction of proteins, lipids, nucleotides, etc.) in fact constituted the generation of, let us say, one sea anemone from another by budding. Here the existence of certain individuals, as well as the generation of one individual from the other, is supervenient on the chemical process.10 I have already suggested that there is no a priori reason to rule out there being a process, P, such that ( i ) P takes place over a finite interval of time, (2) P is infinitely subdividable into subprocesses P1,P2,P3,..., where Pi+1 precedes P?, (3) each Pi is caused by Pi+1, and (4) P itself has an outside cause, C. I suggest further that it is not to be ruled out a priori that a self-contained infinite succession, S, of individuals, ?l3 S2, S3,... (Si caused by Si+1), might be supervenient on just such a process, P, where each Si in S is supervenient on the subprocess Pv If that were to be the case then the self-contained succession of individuals, S, would have an outside cause, namely C, the outside cause of P. But then HEP (i) cannot be defended from my example on the basis of a supposed incoherence in either the notion of an externally caused self contained succession of objects or the notion of an infinite succession of objects spanning a finite length of time. Thus I think we should not accept HEP in either form as an intuitively obvious a priori principle that is, we should not accept it unless it is bolstered with a priori arguments which show that the sorts of cases I have sketched out are impossible. 10 I am assuming for the argument that sea anemones do not have an immaterial part. Also, I am not claiming that all individuals are supervenient on processes. 328 JAMES CAIN Before ending I will say something about how this relates to the cosmo? logical argument. There is a feature of the explosion, E, and the succession of objects, B, that makes it natural to raise the questions 'What made E happen?' and 'What caused B to exist?', namely E and B are things that came into existence. These questions lead us to a more general metaphysical question : If there were actually to be such infinite successions as E and B were hypothesized to be, would they have to be caused ? They would have to be if the following is correct : Nothing can come into existence unless it is caused. Whether this is a correct metaphysical principle is perhaps a tough question, but it is one that needs to be addressed freed from extraneous problems raised by HEP. Now let us turn to the Leibniz-Clarke version of the cosmological argu? ment. Basically it says that even if this universe has existed forever and even if what happens at one time can be explained in terms of what happened previously, the universe as a whole is nonetheless something contingent and nothing contingent can exist uncaused. Here we have two principles at work: Nothing contingent can exist unless it is caused. The universe as a whole is contingent. Whether or not these are true is again a tough problem, but they need to be investigated apart from confusions arising from HEP.11 Department of Philosophy, University of Louisville, Louisville, Kentucky 40292 11 And Hume does independently address these claims in the very section of the Dialogue in which we find HEP propounded.