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The following article was originally published in PHILOSOPHICAL STUDIES in 1995 (Volume 79, pp. 283-310).

A certain controversy about explaining all contingent beings erupted in the 18th century and has continued up to the present day. The controversy began with the publication of Samuel Clarke’s Demonstration of the Being and Attributes of God and Hume’s reply to Clarke in Dialogues Concerning Natural Religion. The controversy is susceptible of a pithy formulation: if each being in an infinite series of contingent beings is caused by an earlier being in that series, does that fact constitute a causal explanation of why the infinite series of contingent beings exist? By “an infinite series of contingent beings” is meant a beginningless succession of modally contingent beings, such that the succession of beings occupies an infinite number of equal-lengthened temporal intervals (e.g. an aleph-zero number of past years).

One aim of this paper is to show that contemporary contributions to this controversy are vitiated by an inadequate understanding of the relation between a cause external to a whole and the whole itself (in the broad sense of “whole” that includes sets, mereological sums, aggregates and organic unities). A second aim is to show that there can be an external cause of the whole series of contingent beings only if this whole is defined as an organic unity and a certain version of quantum mechanics is true. Before I embark on these tasks, I shall formulate more precisely the nature of the controversy.

 This controversy should not be confused with four somewhat similar controversies. This is not the same controversy as to whether the cosmological argument for God’s existence is sound, since atheists as well as theists may accept a negative answer to the question in which we are interested, the question if each being in an infinite series of contingent beings is caused by an earlier being in that series, does that fact constitute a causal explanation why the infinite series of contingent beings exist? The theist may argue that there is an external cause of the infinite series of beings, namely, God, and the atheist may admit that even though each being in the series has a cause, the infinite series itself has no causal explanation.

 Nor is this controversy the same issue discussed by Aquinas in his arguments involving causes of change and motion. Aquinas did not assert that there is an infinite series of causes that requires an external cause in addition to the causes that are members of the series, but instead argued for a first cause that is a member of a causal series of a certain kind. More exactly, Aquinas believed that a series of per se or ssentially ordered causes requires a first member, even though a series of accidentally ordered causes may be beginningless.

 Nor is this issue whether the proposition there exists contingent beings entails there exists some necessary being, where “contingent” means exists in some but not all possible worlds and “necessary” means exists in all possible worlds. The issue about whether there is an external cause of the whole series of contingent beings is sometimes inadequately separated from the issue about contingent and necessary beings, since the cause of the whole series is often identified with a necessary being. For example, Leibniz writes that “the reasons of the world then lie in something extra-mundane, different from the chain of states, or series of things, whose aggregate constitute the world. And so we must pass from physical or hypothetical necessity, which determines the subsequent things of the world by the earlier, to something which is of absolute or metaphysical necessity, for which no reason can be given.” (Leibniz, 1934: 33) The issue of whether the infinite succession needs an external cause is different than the issue of whether the existence of modally contingent beings require the existence of a modally necessary being. For example, we can say

 (1) There contingently exists an infinite succession of states of the universe

 entails

 (2) There necessarily exists some abstract objects, namely, numbers.

 Given this, we can agree that there exists contingent beings entails there exists some necessary being, but the argument from (1) to (2) is not the argument that interests us. Philosophers such as Leibniz would like to argue that the existence of the causal chain of contingent beings entails not merely that some necessary being exists, but also that some necessary being is an external cause of the chain of contingent beings. In order to establish this, however, one must establish the prior thesis that the existence of the whole succession of contingent beings is not sufficiently causally explained by the fact that each being is caused by an earlier contingent being in the succession. This prior thesis is the subject of this paper. I should note in addition that some argue that there is an external cause of the whole series but that the external cause is itself a contingent being. For example, Swinburne believes God is a modally contingent being (Swinburne, 1979: 92-93, 120, 130) and is a cause of the infinite succession of contingent beings that constitute the universe.

 The fourth issue that must be distinguished from our issue is whether every state of the universe is caused by an earlier state entails there is a purpose for the existence of the universe. We are dealing only with efficient causes, not final causes.

 The main purpose of this article is not to provide a historical summary of the controversy but rather to develop some sound arguments that resolve the controversy in its contemporary forms. I shall begin by exposing some fallacious arguments that a universe with an infinite number of past years requires an external cause in order to be causally explained, under the assumption that the universe is a set, mereological sum or aggregate (Part Two). If the universe has a finite past but has no first instant and in this sense is “beginningless”, these same criticisms of the “external cause” theory apply (Part Three). I will then show (in Part Four) that if the universe is an organic unity (rather than a set, mereological sum or aggregate) and if the Copenhagen Interpretation of quantum mechanics applies to the universe as a whole, then the universe does have an external cause. I shall conclude by arguing that it is metaphysically possible (“possible” in the broadly logically sense) that the Copenhagen Interpretation of quantum mechanics applies to the universe as a whole, but that this is not nomologically possible.

 

I shall preface my criticisms of the relevant arguments by setting forth the historical origin of the controversy about whether there needs to be an external cause of the succession of contingent beings. This origin is found in some writings of Clarke and Hume’s response to Clarke. The related controversy that arose from Kant’s response to Leibniz, in Kant’s fourth antinomy in the Critique of Pure Reason, concerns the modal version of the causal argument, i.e. the argument from contingent beings to an external cause that necessarily exists, which I nave pointed out to be different from the controversy that is the subject of this article.

 Clarke stated a version of the argument for an external cause of the whole series in his Demonstration of the Being and Attributes of God. Clarke supposes that every being either has a sufficient reason for existing in the necessity of its own nature or has a sufficient reason for existing in the causal efficacy of some other being. He writes:

Whatever Exists, has a Cause, a Reason, a Ground of its Existence; (a Foundation, on which its Existence relies; a Ground or Reason why it doth exist, rather than not exist😉 either in the Necessity of its own Nature, and then it must have been of it self Eternal: Or in the Will of some Other Being; and then That Other Being must, at least in the order of Nature and Causality, have Existed before it (Clarke, 1738: 9).

Clarke means by “the Will of some Other Being” the causal efficacy of some other being. In another passage about the controversy we are examining, Clarke uses “dependent being” to mean a being that has the reason for its existence in the causal efficacy of some other being. Clarke’s dependent beings are modally contingent and I shall regard them as beginning and ceasing to exist, so they may be identified with successive states of the universe. Clarke continues:

But, if we consider such an infinite progression, as one entire endless series of dependent beings; ’tis plain this whole series can have no [natural] cause from without, of its existence; because in it are supposed to be included all [natural] things that are or ever were in the universe: And ’tis plain it can have no reason within itself, or its existence; because no one being in this infinite succession is supposed to be self-existent or necessary . . . . An infinite succession therefore of merely dependent beings, without any original independent cause; is a series of beings that has neither necessity, nor cause, nor any reason or ground at all of its existence, either within itself or from without. (Clarke, 1738: 12-15. My italics.)

The aspects of Clarke’s argument with which we are concerned is his suggestion that “an infinite succession . . . of merely dependent beings, without any [external] cause . . . is a series of beings that has [no] cause”. More precisely, put, Clarke may be interpreted as suggesting that

 (S) Each dependent being is an effect of an earlier dependent being

 does not entail

 (C) There is a causal explanation of why the infinite series of dependent beings exists.

 I name these sentences “S” and “C”, with “S” intended to suggest the succession of causally related beings and “C” the causal explanation of the succession.

 We now turn to Hume’s response, in his Dialogues Concerning Natural Religion, to the argument that (S) does not entail (C). Hume’s response is directed specifically to Clarke’s statement of the argument. Hume argues that if each dependent being has a cause, then, contra Clarke, the series of beings has a sufficient causal explanation. Hume writes:

In such a chain, too, or succession of objects, each part is caused by that which preceded it, and cause that which succeeds it. Where then is the difficulty? But the whole, you say, wants a cause . . . Did I show you the particular cause 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. (Hume, 1948: 59ff.)

Hume’s position, accordingly, is that (S) entails (C). Thus, by the end the 18th century, the two opposing positions had been laid out and the controversy commenced.

 

In this century, Paul Edwards aligned himself with Hume and suggested the sort of fallacy that Clarke allegedly committed. According to Edwards (1967: 113-114), to suppose the series requires a causal explantion is to suppose that “the series” denotes some individual above and beyond the individuals that constitute the series. “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 . . . Like the expression ‘this dog’ or ‘this man’ the phrase ‘this series’ is easily taken to designate an individual object. But reflection shows this to be an error” (Edwards, 1967: 113-114).

 Edwards does seem to have a point, at least with regards to some contemporary defenders of Clarke’s position. Richard Taylor’s formulation of the issue commits the sort of fallacy diagnosed by Edwards. Taylor defends the argument for a cause or reason for the world by stating: “But it is at the least very odd and arbitrary to deny of this existing world the need for any sufficient reason, whether independent of itself or not while presupposing that there is a reason for every other thing that ever exists” (1963: 87 (my italics)). Taylor’s assumption that the world is a thing in addition to the things in the world contradicts his own definition of the world, for he says he means “by ‘the world’ simply everything that ever does exist, except God, in case there is a god” ( 1963: 87). Now if every thing (apart from God) that ever does exist has a reason, then it is tautologically true that the world has a reason, given that the world is just every thing (apart from God) that ever does exist. Thus, Taylor appears to have committed the fallacy mentioned by Edwards.

 However, Edwards general point nonetheless seems to be mistaken since “this series” may plausibly be regarded as designating some particular distinct from the members of which it is composed. For example, it may be regarded as an abstract particular, a set, that is distinct from the proper parts of the set. The set is a distinct individual object, albeit an abstract individual object, by virtue of having different properties than any of its proper members. (The set is an improper subset of itself.) Each proper member has the property of being a concrete individual, but the set has the property of being an abstract individual.

 But if the infinite series of dependent beings is a set, does it require or admit of a causal explanation distinct from the several causal explanations of its proper members?

 

Richard Swinburne (1979) seems to think so. Swinburne says of the universe that “if the only causes of its past states are prior past states, the set of past states as a whole will have no cause and so no explanation” (1979: 124. My italics). Swinburne argues that there will be an explanation if God causes the set of past states. But Swinburne’s point seems to be poorly stated at best and fallacious at worst. If past states form a set, they compose an abstract object and it is a standard definition of an abstract object that it cannot enter into causal relations. It would be a fallacy to suppose that the set of past states is similar to the past states themselves in being an item that is capable of entering into causal relations with other concrete states or objects. If Ruth Marcus is caused by her parent’s act of conception, it is a logical fallacy to then ask for the cause of the unit set of Ruth Marcus.

 Swinburne’s complete argument for an external cause is of course more complex than this simple assertion about the set of past states, but it is doubtful that any way of formulating his argument can make it appear plausible. He says that the set of past states will have no cause “if each state has a complete scientific explanation in terms of a prior state, and so God is not involved. For although each state of the universe will have a complete explanation . . ., the whole infinite series will have no explanation, for there will be no causes of members of the series, lying outside of the series” (1979: 124). This remark about the external cause or causes being “causes of members of the series” (rather than of the set composed of the members) suggests that Swinburne is taking the set of past states in extension, so that there is no abstract object, the set, in distinction from the members. Given this interpretation of Swinburne, the possible relata of causal relations are only the past states themselves.

 But this argument appears implicitly self-contradictory. According to Swinburne, if a state S2 has a complete scientific explanation, then there is some prior state S1 and some set of natural laws L such that S1 and L together necessitate the occurrence of S2. A proposition reporting S1 and L will entail a proposition reporting S2 (1979: 73). (For purposes of simplifying the discussion, mention of probabilistic laws and causes are omitted.) However, if the set of past states is taken in extension, so that there are only the past states, and no abstract object, a set, distinct from them, then the only candidates for being effects are the past states themselves. However, by Swinburne’s hypothesis, these past states have sufficient causal explanations in terms of other states and laws. According to Swinburne’s account of scientific explanation, it is true that

 (1) For each past state S2, there is a set of natural laws L and an earlier state S1 that are causally sufficient for the occurrence of S2.

 It is also the case that

 (2) Either the set of past states is an abstract object and thus is not a possible candidate for being an effect of a cause, or the set of past states is taken in extension, so that it is not something distinct from the past states.

 It follows from (1) and (2) that

 (3) There is nothing internally causally unexplained that is a candidate for external causal explanation, since the only candidates for causal explanation are past states and every past state is internally causally explained by a prior state and set of natural laws L.

 Thus, Swinburne’s claim that without an external cause “the whole infinite series will have no causal explanation” is false for one of two reasons. First, if “the whole infinite series” means “each past state”, this claim is false since (1) is true. Second, if “the whole infinite series” refers to something distinct than the past states themselves, namely, to the set of past states (taken in intension), Swinburne’s claim is false since (2) is true.

 

William Rowe’s (1989; 1975) comprehensive challenge to the thesis that the universe is explanatorily self-complete is in one respect advantaged over Swinburne’s since he explicitly admits at the outset that the set of states of the universe is not a candidate for causal explanation. The infinite series of states is a set and qua abstract object is not a possible relatum of a causal relation. He emphasizes that the question “why does the infinite series exist?” should not be construed as asking for a causal reason for the set’s existence (since an abstract object cannot have a cause of its existence); rather, it should be construed as asking for a causal reason for the fact that the set has these members rather than some other members or no members at all. Suppose “A is the set of dependent beings. In asking why A exists we are not asking for an explanation of the existence of an abstract entity; we are asking why A has the members it has rather than some other members or none at all” (1989: 150). According to Rowe, this question may be coherently answered by saying that A has the members it actually possesses because some being apart from the members is causally responsible for A having these members.

 Rowe does not present himself as defending the original claim of Clarke, since he believes Clarke “never saw clearly that the infinite collection of dependent beings is not itself a dependent being. [Clarke] tended to confuse the question of why the set of dependent beings has members (rather than not having any) with the altogether different question of why a certain being exists” (1975: 146).

 Thus, Rowe believes he has shown that

 (S) Each dependent being is an effect of an earlier dependent being

 does not entail

 (C) There is a causal explanation of why the infinite series of dependent beings exists.

 However, it seems to me that Rowe’s discussion of (S) and (C) involves a fallacy about sets. A set essentially contains all and only the members it actually contains. Accordingly, the question “why does the set A contain the members it actually contains?”, if it makes sense at all, has the trivial answer “because every set essentially contains all and only the members it actually contains”. Rowe’s question therefore cannot admit of the answer “the set A of dependent beings contains all and only the beings it actually contains because God caused A to contain these beings rather than some other beings”. This answer is based on the false assumption that the set A contingently contains its members and therefore that it was a matter of contingent divine choice that A contain these members rather than some other members or no members at all. However, analytic truths, such as truths about the identity conditions of sets, are not matters left up to a divine decision.

 Of course, it may be felt that Rowe was getting at a genuine problem of external explanation and that his formulation of the problem is merely sloppy, rather than altogether wrong headed. But what, exactly, is this problem?

 

William F. Vallicella (private communication) offers a reformulation of Rowe’s argument that attempts to capture this problem and avoid Rowe’s set-theoretic fallacy. Vallicella suggests we take the phrase “the set of dependent beings” as a nonrigid designator. In the actual world, this phrase designates the set A, but in other worlds it designates sets of other dependent beings and in some worlds it designates an empty set. Accordingly, the question, “why does the set of dependent beings contain the members it actually contains rather than some other members, or not members at all”, may be reformulated as the question

 (Q) Why does the nonrigid definite description, “the set of dependent beings”, designate the set A rather than some other set?

 I think the answer to this question is analogous to the answer to other questions about the designation of nonrigid definite descriptions. Consider the nonrigid definite description “the inventor of bifocals”. About this description, we may pose the question: Why does “the inventor of bifocals” designate Ben Franklin, rather than some other person or nobody at all? The answer to this question is: Because one and only one person invented bifocals and that person is Ben Franklin. In other words, the answer is that Ben Franklin meets the conditions implied by the rules of use of “the invention of bifocals” for being the referent of this description. Of course, we may then ask why Ben Franklin invented bifocals, but that is a different question with a different answer. The answer would refer to Franklin’s inventive capacities, the external circumstances and internal motives that led him to invent bifocals and the like.

 Analogously, the answer to (Q) is that “the set of dependent beings” designates the set A, rather than some other set, since A meets the conditions implied by the rules of use of “the set of dependent beings” for being the referent of this expression. The answer is that the members of A exist and the members of other sets of dependent beings do not exist. As to the further question of why the members of A exists, we may answer as follows. Let the set A of dependent beings be the set that contains no earliest member, the set [. . . x, y, z]. The answer to the question of why . . . x, y, and z exist is that z exists because y exists, y exists because x exists, and so on ad infinitum.

 

It may nonetheless be felt that we not have really plumbed the depths of Rowe’s question, which pertain to a metaphysical issue that our answers have so far left untouched. But what is this metaphysical issue?

 Some may feel that the real issue that Rowe was getting at is the question about why this possible world is actual rather than some other possible world. However. I will show that this question logically requires the answer “for no reason” and in any case that this question is distinct from the question about an external cause of the universe.

 Let us call the actual world W1. The question, “Why is W1 actual rather than some other world?” requires the answer “for no reason”, even if it is true that God created the universe. This can be demonstrated by the following argument. A possible world is a maximal proposition W, such that for every proposition p, W entails p or the negation of p (Smith, 1988). Thus a world is a maximal proposition and the actuality of a world is the being true of a maximal proposition. Note that the universe is not the actual world; the universe is not a maximal proposition but the series of all dependent beings (or, if you prefer, the series of three dimensional spatial slices of a four dimensional spacetime). Now suppose that the proposition God created the universe is one of the conjuncts of the actual world W1. We may then formulate the questions: What explains why W1 is actual rather than some world in which it is true that God created a different universe? And what explains why WI is actual rather than some world in which it is true that God does not create any universe?

 If God’s decision to create the universe is free, and his freedom is understood (as it is standardly understood by classical theists) on the libertarian model of free will, then there can be no reason why it is true that God created the universe. God freely decided to create the universe and thus his decision has no cause and is not logically determined to occur. Thus, no proposition such as God’s benevolent character causally determined him to decide to create the universe can explain why it is true that God created the universe. (Of course, in a certain sense God’s created the universe “for the reason that it is good that the universe exists”, but if we introduce this moral and teleological explanation then our question may be reformulated as a question about why God chose to act in this morally purposive way. The answer to this latter question cannot refer to any reason, if God is free in the libertarian sense.)

 If there is no reason why it is true that God created the universe, then the truth of this proposition cannot explain why the world W1 is actual. The truth of the proposition, God created the universe, explains why many conjuncts of Wl are true (for example, it explains why it is true that the universe exists) but it cannot explain why the maximal proposition W1 is itself true. The reason for this is that if there is one conjunct of W1 whose truth is unexplained, then the truth of W is unexplained. The truth of a conjunction has an explanation only if the truth of each of its conjuncts has an explanation. There is an explanation of the truth of the conjunction, it is raining in Kalamazoo, Michigan and there is a supermassive black hole at the center of the Milky Way Galaxy only if there is an explanation of the truth of it is raining in Kalamazoo, Michigan and an explanation of the truth of there is a supermassive black hole at the center of the Milky Way Galaxy. We have seen, however, that the conjunct, God created the universe, has no explanation. It follows, therefore, that there is no explanation of why the world W1 is the actual world rather than some other possible world.

 There is also an argument for the more general thesis that it is logically impossible that there be an explanation of why any possible world is actual. Each possible world contains among its conjuncts both necessary propositions and contingent propositions. Take any contingent proposition T that belongs to any possible world W. Suppose W is actual and that T is true. T’s being true explains why W is true only if T explains why each conjunct in W is true. But no contingent truth T is such that T’s being true explains T’s being true. Since T’s being true cannot explain why T is true, T cannot explain why each conjunct in W is true. Therefore, T’s being true cannot explain why W is true. Nor can any necessary truth explain why W is true, since no necessary truth can explain why any contingent proposition is true and the maximal proposition W is contingently true. Consequently, it is logically impossible that there be an explanation of the truth of W. For any possible world W, if W is actual, it is logically impossible that there be an explanation of why W is actual.

 

We have seen the “possible worlds” formulation of the explanatory question does not provide us with a question that admits of any positive answer and in any case is different from the issue we are addressing, which is about the causal explanation of the universe rather than the actual world. Our issue is whether there is any need or room for an external cause of the universe if each state of the universe has its cause in an earlier state. Let us return again to the suggestion that the whole composed of all the states of the universe is something distinct from the states themselves and ask if there is some sense of “whole” that allows the whole series to be an effect of an external cause. even if each part of the whole is caused by an earlier part. Let us pursue the issue of concrete wholes.

 If sets (taken intentionally) cannot be candidates for causal explanations since they are abstract, may not concrete wholes, such as mereological sums and aggregates, be such candidates? Let us consider first mereological sums in the sense of mereological essentialism.

 We are interested in the concept of a mereological sum because a sum is concrete and therefore allegedly can be an effect of a cause and thus can provide the “additional being” that needs to be caused apart from the various dependent beings that belong to the sum. One problem with this suggestion is that if the sum is caused, then the sum of dependent beings is itself a dependent being. This entails it is false that all dependent beings are parts of this sum. But even if we ameliorate this problem, by defining the sum as “the sum of all dependent beings other than itself” or else by borrowing a principle from set theory and saying “the sum of all dependent beings is an improper part of itself”, a difficulty still remains. The difficulty is that the sum cannot be an effect of a cause, for the following reason.

 If each proper part of a sum is caused to exist by an earlier part, then the existence of the sum is logically guaranteed by this fact. There needs to be no extra causal act directed upon the sum itself; indeed, any such act is logically precluded. It is impossible to bring something into existence by an act of causation directly specifically upon it if that thing logically supervenes upon other things that have been brought into existence by distinct acts of causation. If the parts of the sum exist, that entails the sum exists, and thus the causation of the parts is a logically sufficient condition of the existence of the sum. The sum, therefore, is not a candidate for being an effect of an external cause.

 Clarke writes: “An infinite succession therefore of merely dependent beings, without any original independent cause; is a series of beings that has neither necessity, nor cause, nor any reason or ground at all of its existence, either within itself or from without (Clarke, 1738: 12-15)”. However, if “infinite succession” refers to a mereological sum, then this sentence is problematic. It is true that the infinite sum has no cause, but it does not follow that there is no explanation of its existence. Its existence is explained by the fact that (a) each of its parts has a causal explanation in an earlier part and (b) if each of its parts has a causal explanation, that is a logically sufficient condition of the sum existing.

 Another type of concrete whole besides mereological sums are aggregates. A mereological sum is similar to a set in that it essentially contains all and only the members it actually contains. An aggregate, however, does not contain all its members essentially. A human being is an aggregate, but if I lose one of my skin cells I remain the same aggregate. The Earth is also an aggregate and remains the same if one of its parts is lost (by being sent into outer space in a rocket). An aggregate’s identity is not determined by enumerating its parts but instead by a certain property of the aggregate itself. The Earth, for example, is that aggregate which uniquely possesses the property being the third planet from the sun.

 Suppose the universe is an aggregate. (For an argument that the universe is an aggregate, see (Smith, 1986: 200-210; 296-301)). Let us consider the hypothesis that the universe is the aggregate defined by the property, being composed of whatever causally connected physical states there are. If each state of the universe is caused by an earlier state, would the universe qua aggregate be available as a candidate for a causal explanation in terms of an external cause? The answer is negative, since a logically sufficient condition of the aggregate’s existence is the existence of the parts of the aggregate. In this respect, the aggregate is no different than a mereological sum. If there is a beginningless succession of physical states, each caused by an earlier state, that entails the universe exists, and any causal act directed upon universe itself is superfluous.

 

I shall now show that the need for an external cause of the series of dependent beings (or better, successive states of the universe) is absent even if it is true both that the universe begun to exist and that every state of the universe has a cause. This can best be demonstrated in terms of Michael Burke’s (1984) attack on the Humean thesis. Burke characterizes the Humean thesis about infinitude and explanation as follows:

 (H) For every member of the infinite succession of past physical events, there is an explanation of why that event occurred. Collectively, these explanations constitute an explanation of why there has been an infinite succession of physical events.

 Burke’s strategy is to present a version of (H) which he believes vulnerable to a counterexample. The version is

 (P) For any set S of times and any physical object x: If for every time belonging to S there is an explanation of why x exists at that time, these explanations, taken collectively, explain why it is that x exists at every time belonging to S.

 Burke asks us to suppose that a fully grown duck sprang into existence onto our table. The duck exists throughout a finite interval of time I that is half-open in the earlier direction; there is no first instant at which the duck exists. For every instant t at which the duck exists, there is a causal explanation of why the duck exists at t; the explanation is that the duck existed at some instant t’ earlier than t and it is a natural law that a healthy duck would endure throughout the brief period from t’ to t.

 Burke asservates that this does not explain why the duck exists at every time in the interval I rather than at no time during I. He maintains that in this case we would say the duck spontaneously came into existence, with no cause or explanation of its existence, and that we have here a clear violation of the principle of causality.

 Burke need not appeal to this fantastic scenario in order to make his point. This scenario is arguably metaphysically impossible if Kripke’s theory of the necessity of origins is true. (Ducks would necessarily have their origins in gametes of a certain natural kind.) Burke could have appealed to a realistic example that is directly pertinent to the matter at hand, namely, to the current theory that the universe began to exist about 15 billion years ago, that the first interval of time is half-open in the earlier direction, and that every instantaneous state of the universe has a sufficient cause in a prior instantaneous state of the universe. This would correspond to the “standard hot big bang cosmological model”, with the initial big bang singularity “cut out” to make the first interval half-open in the earlier direction (see (Smith and Craig, 1993)). In this case, the x in the principle P would be the universe and the instantaneous states of the universe would be the states that are causally explained.

 I shall shortly argue that Burke’s example and my example of the “standard hot big bang model” do not show that P is false. But first I should point out that Burke’s argument against Hume is in a sense an ignoratio elenchi since P is not relevantly analogous to the Humean thesis H. Hume is responding to Clarke’s implicit supposition that there is a series of beings (or states of the universe, if you prefer) that occupy an infinite number of intervals of equal length, not to the supposition that there is a series of beings that occupy an infinite number of zero-duration instants. For any finite interval, there is a nondenumerably infinite number of instants in that interval, but the case relevant to the Humean thesis H involves a denumerably infinite number of equal intervals, e.g. an aleph-zero number of past seconds. Of course, the interval/instant distinction, Cantor’s transfinite cardinals and the contemporary concept of the continuum was not before the minds of Clarke and Hume but it seems clear that the scenario they tacitly had in mind (and that formed the basis of the subsequent discussions by Edwards, Swinburne and others) corresponds to the contemporary theory of intervals rather than instants.

 These remarks indicate that the principle relevantly analogous to the Humean thesis H is not P but rather P’:

 P’: For any set S of intervals of equal length and any physical object x: If for every interval belonging to S there is an explanation of why x exists throughout that interval, these explanations, taken collectively, explain why it is that x exists throughout every interval in S.

 P’ will be satisfied in those cases where the set S has the order type z * ( . . . – 3 – 2 – 10) or the order type z * + z ( . . . – 3 – 2 – 1 0 1 2 3 . . .). In either case the set contains an infinite number of equal-lengthened intervals of past time. P’ is the principle relevant to the Humean thesis H, but Burke’s example and the example from standard hot big bang cosmology does nothing to impugn the falsity of P’. In short, the issue that divides Clarke and Hume concerns a universe that is temporally extended for an infinite number of past years and considerations about the instantaneous states of a universe that began a finite number of years ago are not relevant.

 But there is an even stronger response to Burke’s argument, namely, that his example of the duck and our example of the big bang universe do not even refute Burke’s priniciple P. Concentrating on our example from general relativity, we may say that if the universe exists only throughout a finite interval J that is bounded by a first and last instant, then there would be no explanation of the universe’s existence throughout J if there is no explanation of the universe’s existence at the first instant of the interval. If the first instant is the instant of the big bang singularity, and it is uncaused, then it follows that the universe began to exist without a cause. However, if the universe exists only throughout a finite interval K that is half-open in the earlier direction, then each instantaneous state of the universe has a cause in earlier instantaneous states of the universe. (It does not have its cause in the immediately prior instantaneous state, since there is no immediately prior state, given that time is continuous.) Let us suppose for specificity’s sake that an instant is an instantaneous state of the universe (relative to the cosmic reference frame; see (Smith, 1990)). An interval is a set of instantaneous states of the universe. If each instantaneous state in the interval K has a causal explanation, this fact suffices to explain why the universe exists throughout the interval K. If one denies this, one becomes entangled in two set-theoretic fallacies. First, if one argues that “if every instant in the interval K has a cause, that still leaves open the question of whether the interval K itself has a cause”, then one runs afoul of the fact that the interval is a set and thus not a proper candidate for a causal explanation. Second, one is refuted by the fact that the existence of the instants in the interval is a logically sufficient condition of the existence of the interval, and thus if the existence of each of the instants is explained, that suffices to explain why the interval exists. (Thus, if the interval is defined as a mereological sum or aggregate, Burke’s argument still fails.) Accordingly, we may conclude that an argument of Burke’s sort fails to demonstrate that the existence of an infinitely or finitely old universe must be causally unexplained if it has no external cause.

 

I shall now shift the direction of my arguments and show that if the universe is conceived in a certain way, then there will be an external cause of the universe, consistently with each state of the universe being caused by an earlier state.

 First, we begin with Richard Gale’s argument (1991: 252-284) against Hume’s and Edwards’ thesis that a causal explanation of each part of the whole suffices to explain causally the existence of the whole. Gale formulates the principle he takes to underlie the Hume-Edwards objection to Clarke and Company, the principle,

 HE. If the existence of every member of a collection (group, succession, and the like) is explained, the existence of the collection, and the like, is thereby explained.

 Gale points out that HE is false. For example, the existence of each part of an automobile has a causal explanation (e.g. the carburetor is made by Delco-Remy in Chicago, the starter motor by United Motors in Kansas City, and so on). But this does not explain the existence of the automobile. The explanation of its existence is that its various parts are assembled by certain workers in a Detroit assembly plant. The notion of assembling particulars into a whole is crucial to refuting the principle HE.

 Gale is correct that HE is refuted by the proposition that there are assembled wholes, but he does not go on to demonstrate that or how this leaves room for an external cause of the universe. The demonstration of this funkier thesis requires showing that the universe is in some sense an “assembly” and that its external cause is an “assembler” of the parts of the universe. The universe or “infinite series of successive physical states” must be relevantly analogous to an automobile. In order for an external cause to come into the picture, the external cause must be an “assembler” that assembles the states of the universe into a single infinite succession.

 In order to develop such a conception, we need to introduce a fourth kind of whole in addition to sets, mereological sums, and aggregates. The fourth kind of whole is an organic unity. An organic unity is such that its parts are terms of some relation R and the relation R is some specific type of ordering relation that finds together the teens of R. The order among the terms is that which makes the terms parts of a whole and the whole (qua something distinct from the parts) may be identified with the order of the parts, such that “there is an external cause of the whole” means “there is an external cause of the ordering together of the terms”.

 In the case of the universe, the order among the parts is causal. Two states S1 and S2 are ordered to each other by the casual relation; S1 causes S2. If there is an external cause of the universe, then this cause will bring it about that S1 and S2 stand in the asymmetrical relation of causation. This would be consistent with principle

 (C’) Each state of the universe is caused by an earlier state.

 Principle (C’) entails that each state is not caused by an external cause (since each state is caused instead by a cause internal to the series, an earlier state). However, (C’) is consistent with the causal interrelatedness of the various states being caused by an external cause.

 Since this is possible in the broadly logical sense (i.e., it is metaphysically possible), the next question to ask if it is nomologically possible, i.e. consistent with the boundary conditions (e.g. the quantity and arrangement of mass-energy) and laws of nature that obtain in the actual world. I will discuss this issue in the next sections and will eventually conclude that this theory is nomologically impossible.

 

If general relativity holds true of the universe, then it is nomologically impossible for there to be an external cause of the causal inter-relatedness of the states of the universe. But if the Copenhagen interpretation of quantum mechanics holds true of the universe, then this is nomologically possible (and indeed, actual).

 According to the standard hot big bang model of the universe, the causal laws that govern the evolution of the universe involve certain differential equations, namely, Friedman’s solutions to the equations of general relativity. These causal laws are deterministic. Any determinist causal law governing the universe has the form:

 (L) If the universe is in a state of kind K₁ at t₁, this will produce a state of kind K₂ at time t₂.

 According to the standard hot big bang model, our universe is presently evolving according to the following law, which in simplified form reads:

 (L1) If the universe is in a state S₁ with the radius R, density D, velocity V at time t₁, this will cause a state S2 with the larger radius R’ > R. a lower density D’ < D and slower expansion velocity V’ < V at time t₂.

 If we take (Ll) as our nomological premise and add the particular premise

 (1) The universe is in a state S₁ with the radius density D, and expansion velocity V at time t₀

 then the conclusion will follow

 (2) There is caused by S₁ a state S₂ with the larger radius R’ > R. a lower density D’ < D and slower expansion velocity V’ < V at time t₂.

 The thesis that an external cause brings it about that S₁ stands to S₂ in the relation of causation is inconsistent with the conclusion (2). Since (L1) is a causal law and (1) a statement of fact, the externalist thesis is inconsistent with the conjunction of a causal law and a factual statement. The reason for this is that (L1) implies that if S₁ occurs, that is sufficient for S₁ to cause a later state S₂. If the occurrence of S₁ is sufficient for S₁ to cause S₂, then there is no need for an external cause to make S₁ cause S₂. If there were such an external cause, then the occurrence of S₁ would be insufficient for S₁ to cause S₂, contradicting (L1). Accordingly, if the laws of general relativity, specifically Friedman’s laws, govern our universe, then there is no room for an external cause of the universe considered as an organic unity.

 But an external cause is required if the Copenhagen Interpretation of quantum mechanics is the theory that describes our universe.

 

Although physicists do not apply the traditional version of quantum mechanics, the Copenhagen Interpretation, to the universe as a whole, this can be done and is consistent with the wave function equations. According to the Copenhagen interpretation of quantum mechanics, the wave function equation represents the various possible outcomes of a measurement-like interaction. In order for one of these possibilities to become actualized, something or somebody outside of the system being measured needs to “collapse the wave function”. Now suppose we formulate a wave function of the entire universe, a wave function that represents the various possible future states of the universe. Who or what will then collapse the wave function? It cannot be any part of the universe or the universe as a whole, since the universe is the system being measured. It must be something external to the universe. This could be the role a deity plays and could give a coherent meaning to the traditional dictum “God continuously creates the universe”.

 This idea has not been taken up by theists (Craig (1990) mentions but does not endorse this thesis), and it has been mainly noted by the physicist John Barrow. Barrow writes that if we apply the Copenhagen Interpretation to the whole universe, “we are left asking the question, ‘who or what collapses the wave function of the universe?’ – some ‘Ultimate Observer’ at the world’s end, or outside the Universe of space and time altogether?” (Barrow, 1988: 156). “The theologians have not been very eager to ascribe to God the role of Ultimate Observer who brings the entire quantum Universe into being, but such a picture is logically consistent with the mathematics” (1988: 232).

 Now if we adopt as our cosmological theory the Copenhagen Interpretation of quantum mechanics, then we may suppose that an external cause brings it about that an existent state S₁ of the universe stands in a causal relation to a subsequent state S₂. If state S₁ exists at t₁, then at this time there is a wave function representing the various possible future states of the universe. However, S₁ as represented by the wave function does not possess the property of causing the future state S₂ of the universe. Indeed, S₁ does not even possess property of causing some future state of the universe. The reason for this is that S₁ is insufficient by itself to produce any subsequent state of the universe. In order for there to be a future state, the wave function representing the possible future states must be collapsed by something distinct from S₁ and external to the universe. By virtue of collapsing this wave function, the external agent brings it about that one of the possible future states, S₂, is the effect of S₁.

 A feature of the Copenhagen Interpretation is that causality is probabilistic. How should we understand this in relation to the theory of an external cause of the universe? The wave function equation provides each possible state of the universe with a certain probability value; thus, prior to the collapse of the wave function, the state S₂ has a probability less than 100% of occurring. This is the sense in which causality is probabilistic. However, the external cause’s act of collapsing the wave function makes the probability 100% that S₂ is the effect of S₁. In this sense, the external cause makes S₁ stand to S₂ in the relation of sufficient causation.

 If such external causation takes place, it remains true that the principle (S) entails the principle (C). Phrased in terms of states of the universe, the argument goes

 (S) Each state of the universe is an effect of an earlier state of the universe

 entails

 (C) There is a causal explanation of why the universe exists.

 There is an entailment, since in each possible world in which this theistic quantum cosmology and (S) are true, (C) is true. This is because each state of the universe is an effect of an earlier state only if there is an external cause that causes the earlier state to cause the later state. More precisely, if (a) the universe is a beginningless succession of states (b) the universe qua whole is an organic unity, and (c) the organic unity is the causal interrelatedness of the states, then each state is caused by an earlier state only if the causal interrelatedness of the states has a causal explanation in terms of an external cause.

 This suggests that Clarke, Taylor, Swinburne and company are barking up the wrong tree when they attack the claim that (S) entails (C). The fact that (S) entails (C) is so far from entailing atheism that it is itself an entailment of the only known version of theism that is consistent with the principle (S), namely, the Copenhagen quantum cosmological version of theism.

 Note that (S) entails (C) even if the thesis Gale criticized, HE, is false. HE is false since the causal explanations of each part of each organic whole do not necessarily provide a causal explanation of the organic whole itself, why the parts are assembled into a whole. But this is consistent with the fact that (S) entails (C). This has been demonstrated in previous sections for theories that interpret the universe as a set, mereological sum or aggregate. In this part, I have argued that (S) entails (C) for theories that interpret the universe as an organic unity based on causal interrelatedness. This entailment goes through regardless of whether or not there is an external cause of this organic unity. If each part of the organic whole (the universe) is caused by another part of that whole and the organic whole is just the causal order among these parts, then either the occurrence of each state is sufficient for that state to cause a later state (e.g. as is the case with the standard hot big bang model), or it is not sufficient and there is an external cause (as on the Copenhagen model) that causally explains why these parts are causally interrelated. In either case, the fact that each part is caused by an earlier part entails the fact that there is a causal explanation (internal or external) for the parts being causally interrelated.

 These considerations show that it is possibly true that the universe has an external cause, even if each state is caused by an earlier state. Contrary to the assumptions of classical and contemporary theism, this is possible only if the Copenhagen Interpretation of quantum mechanics applies to the universe as a whole. But the fact that this is possible does not imply, of course, that the actual world is one of the worlds where the wave function of the universe is collapsed by an external cause. In order for that implication to follow, further argument is needed. For example, it needs to be shown that the cosmological application of the Copenhagen Interpretation of quantum mechanics is a more reasonable cosmological hypothesis than other versions of quantum mechanics or general relativity. This has not been shown or even been argued by any physicist or philosopher. Thus, there exists no reason to think that this theory is true or even consistent with the physical theories that are currently argued to be true.

 In fact, there is positive reason to think that the application of the Copenhagen Interpretation of quantum mechanics to the universe as a whole is nomologically impossible. This reason is twofold. First, the theistic cosmological version of the Copenhagen Interpretation postulates something nonphysical, a disembodied mind, that exists external to our universe, and the postulation of a disembodied mental particular contravenes the basic methodological tenet of physics, which is to postulate only physical particulars. John Barrow is right that quantum theism is “logically consistent with the equations of quantum mechanics, but it is a further question as to whether quantum theism its consistent with the methodology of physics. Quantum theism is a metaphysical or theological theory, not a physical theory. Second, there are alternative versions of quantum mechanics that apply to the universe as a whole and that do not involve postulating a disembodied mind, such as Everett’s Many Worlds Interpretation, J. S. Bell’s “one world” interpretation and the “consistent histories” interpretation of Griffiths, Omnes, Hartle and others (which, like Bell’s interpretation, does not postulate many universes). The “consistent histories” interpretation (developed in the mid and late 1980s) is the one favored by quantum cosmologists today, even though philosophers of quantum mechanics have yet to evince a familiarity with this interpretation in their publications.

 It may be said that I am ruling out by fiat the theistic interpretation of quantum mechanics, by simply ruling out any physical theory that postulates a disembodied mind. This is correct: I am simply ruling it out. But this is nonetheless a sound argument for the claim that the theistic version of quantum mechanics is nomologically impossible. It is true that it contravenes the methodology of physics to postulate a disembodied mind as an explanatory agent, and thus it is true that the laws of physics cannot incorporate a reference to such a mind. The laws of physics are just that, laws of physical entities that postulate only physical entities. If the theist has the impression that my argument is question-begging, then she is confusing the claim that quantum theism is nomologically impossible with the claim that it is metaphysically impossible. I agree that quantum theism is metaphysically possible. However, it is not consistent with the methodology of physics to suppose that it is physically (nomologically) possible. If there is to be an argument for quantum theism, it must be on metaphysical grounds, not on the grounds of physics, and the resultant theory will be a metaphysical theory, not a physical theory.

 It might be objected that we cannot predict in advance where physics will lead us, and thus that we cannot legislate in advance that it cannot incorporate a reference to a disembodied mind in its laws. However, even if I concede this objection for the sake of argument, it still fails to carry the point. For if (a) there are several alternate ways to formulate the quantum mechanical laws of the universe, and (b) one formulation postulates a disembodied mind and the other only physical entities, and (c) the observational evidence does not decide among them, then it is a requirement upon physicists to accept one of the purely physical formulations. The objection to my a prioristic ruling out of disembodied minds should be taken as implying only that physics can postulate a disembodied mind as a last resort, to explain something that physically requires to be explained but that cannot be explained by postulating anything but a disembodied mind. However, there currently are alternative versions of quantum mechanics that apply to the universe as a whole, most notably the “consistent histories” interpretation, and that are able to explain what needs to be explained and yet do not postulate a disembodied mind. Accordingly, we are required on physical grounds to adopt such an explanation. Thus, even granting the objection, we still are constrained to conclude (on the basis of present day physics) that the theistic version of quantum mechanics is nomologically impossible. Quantum theism is inconsistent with the quantum mechanical laws as they are formulated in the “consistent histories” version of quantum mechanics (the most plausible version that applies to the universe as a whole) and for this reason is nomologically impossible.

 We should conclude, then, that the philosophical arguments in this essay and the status of present day physics entail that it is nomologically necessary that a beginningless universe has an internal causal explanation (be it deterministic or probabilistic) but no external causal explanation.

 

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 Department of Philosophy

Western Michigan University

Kalamazoo, Ml 49008

USA