The Existence of God I
25
The Existence of God I
For it is owing to their wonder that men both now begin and at first began to philosophize; they wondered originally at the obvious difficulties, then advanced little by little and stated difficulties about the greater matters, e.g., about the phenomena of the moon and those of the sun and the stars, and about the origin of the universe.
Aristotle, Metaphysics A.2.982B10-15
No question is more sublime than why there is a Universe: why there is anything rather than nothing.
Derek Parfit, “Why Anything? Why This?” London Review of Books, January 22, 1998
1—Introduction
One of the second-order disciplines of philosophy that is of special interest to the Christian is philosophy of religion. As it appears on the contemporary scene, there are actually two rather different disciplines under the name of philosophy of religion. What we shall be concerned with here is the second-order discipline pursued by professional philosophers, who typically participate in a professional society like the American Philosophical Association. Philosophy of religion is also a second-order discipline of religious studies, where it is typically carried out by professors of religion or theology who are active professionally in societies like the American Academy of Religion. These two approaches to philosophy of religion have a very different texture. Loosely speaking, we may say that the former is concerned with philosophizing about problems raised by religious truth claims, whereas the latter tends to philosophize about the phenomenon of religion itself. The latter therefore resembles more closely than the former the discipline of comparative religion, and when its practitioners do reflect on a problem of philosophical significance, they often lack the conceptual tools furnished by training in analytic philosophy, which is the dominant tradition in philosophy of religion as it is pursued by professional philosophers today. Although philosophy of religion has been recognized as a delineated second-order discipline of philosophy as far back as the German philosopher G. W. F. Hegel, who lectured on the subject, analytic philosophy of religion is a recent movement of the last half century or so, which is one of the most exciting and burgeoning areas of contemporary Anglo-American philosophy.
Within the discipline of philosophy of religion certain standard topics have emerged, such as the nature of religious language (Do sentences having religious content make factual assertions that are either true or false?), religious epistemology (How can one can be justified or warranted in believing religious truth claims?), the existence of God (Is there such a being as God?), the coherence of theism (Does the concept of God make sense?), the problem of evil (Does the suffering in the world preclude God’s existence?), comparative religions (How are the religious truth claims of other religious faiths to be evaluated?), the problem of miracles (How should divine action in the natural world be understood?), the soul and immortality (What is the nature of man and life after death?), religious experience (Can we experience God and how?), and revealed religious doctrines (How are we to understand doctrines such as the Trinity, the incarnation, the atonement, heaven and hell, providence, predestination, biblical inspiration, and a host of other doctrines?).
It is evident that philosophy of religion overlaps not only with several other disciplines of philosophy but also with the concerns of systematic theology. Indeed, it is difficult to see how the task of the Christian philosopher of religion differs greatly from that of the systematic theologian. Although some Christian thinkers would say that systematic theology differs from philosophy of religion in that the systematic theologian alone presupposes the truth of Scripture, it is difficult to see why the Christian philosopher should be peculiarly hamstrung, restricted to natural reason alone rather than permitted to avail himself of all sources of truth, of which he believes Scripture to be one. Insofar as he philosophizes as a Christian rather than affects an epistemological stance that misrepresents his actual beliefs, he is, in effect, indistinguishable from the systematic theologian, at least insofar as the latter is engaged in the formulation and defense of Christian doctrine. Indeed, the most interesting and important work in exploring issues in systematic theology today is increasingly being done, not by theologians, but by analytic philosophers of religion.
In this section we shall, due to constraints of space, restrict ourselves to the discussion of some of the most central topics in philosophy of religion insofar as these topics have not already been addressed elsewhere in this book. Specifically, in this and the succeeding chapter we shall explore the question of the existence of God.
2—The Existence of God
It has become conventional wisdom that in light of the critiques of Hume and Kant there are no good arguments for the existence of God. But insofar as we mean by a “good argument” an argument that is formally and informally valid and consists of true premises that are more plausible than their negations, there do appear to be good arguments for God’s existence, and there are on the contemporary scene many philosophers who think so. Indeed, it would be fair to say that the rise of analytic philosophy of religion has been accompanied by a resurgence of interest in natural theology, that branch of theology that seeks to prove God’s existence apart from the resources of authoritative divine revelation. Alvin Plantinga, perhaps the most important philosopher of religion now writing, has defended what he calls two dozen (or so) arguments for God’s existence. In the space of these chapters we shall examine four of the most important.
2.1 The Cosmological Argument
The cosmological argument is a family of arguments that seek to demonstrate the existence of a Sufficient Reason or First Cause of the existence of the cosmos. The roll of the defenders of this argument reads like a Who’s Who of Western philosophy: Plato, Aristotle, ibn Sina, al-Ghazali, Maimonides, Anselm, Aquinas, Scotus, Descartes, Spinoza, Leibniz, and Locke, to name but some. The arguments can be grouped into three basic types: the kalam cosmological argument for a First Cause of the beginning of the universe, the Thomist cosmological argument for a sustaining Ground of Being of the world, and the Leibnizian cosmological argument for a Sufficient Reason why something exists rather than nothing.
2.1.1 Exposition of the Arguments
The kalam cosmological argument derives its name from the Arabic word designating medieval Islamic scholasticism, the intellectual movement largely responsible for developing the argument. It aims to show that the universe had a beginning at some moment in the finite past and, since something cannot come out of nothing, must therefore have a transcendent cause that brought the universe into being. Classical proponents of the argument sought to demonstrate that the universe began to exist on the basis of philosophical arguments against the existence of an infinite, temporal regress of past events. Contemporary interest in the argument arises largely out of the startling empirical evidence of astrophysical cosmology for a beginning of space and time. Today the controlling paradigm of cosmology is the standard big bang model, according to which the space-time universe originated ex nihilo fewer than fifteen billion years ago. Such an origin ex nihilo seems to many to cry out for a transcendent cause.
By contrast the Thomist cosmological argument, named for the medieval philosophical theologian Thomas Aquinas, seeks a cause that is first, not in the temporal sense, but in the sense of rank. Aquinas agreed that “if the world and motion have a first beginning, some cause must clearly be posited for this origin of the world and of motion” (Summa contra gentiles 1.13.30). But since he did not regard the kalam arguments for the past’s finitude as demonstrative, he argued for God’s existence on the more difficult assumption of the eternity of the world. On Aquinas’s Aristotelian-inspired metaphysic, every existing finite thing is composed of essence and existence and is therefore radically contingent. A thing’s essence is an individual nature that serves to define what that thing is. Now if an essence is to exist, there must be conjoined with that essence an act of being. This act of being involves a continual bestowal of being, or the thing would be annihilated. Essence is in potentiality to the act of being, and therefore, without the bestowal of being, the essence would not exist. For the same reason no substance can actualize itself; for in order to bestow being on itself it would have to be already actual. A pure potentiality cannot actualize itself but requires some external cause. Now although Aquinas argued that there cannot be an infinite regress of causes of being (because in such a series all the causes would be merely instrumental and so no being would be produced, just as no motion would be produced in a watch without a spring even if it had an infinite number of gears) and that therefore there must exist a First Uncaused Cause of being, his actual view was that there can be no intermediate causes of being at all, that any finite substance is sustained in existence immediately by the Ground of Being. This must be a being that is not composed of essence and existence and, hence, requires no sustaining cause. We cannot say that this being’s essence includes existence as one of its properties, for existence is not a property, but an act, the instantiating of an essence. Therefore, we must conclude that this being’s essence just is existence. In a sense, this being has no essence; rather, it is the pure act of being, unconstrained by any essence. It is, as Thomas says, ipsum esse subsistens, the act of being itself subsisting. Thomas identifies this being with the God whose name was revealed to Moses as “I am” (Ex 3:14).
The German polymath Gottfried Wilhelm Leibniz, for whom the third form of the argument is named, sought to develop a version of the cosmological argument from contingency without the Aristotelian metaphysical underpinnings of the Thomist argument. In his essay “The Principles of Nature and of Grace, Based on Reason,” Leibniz wrote, “The first question which should rightly be asked is this: why is there something rather than nothing?” Leibniz meant this question to be truly universal, not merely to apply to finite things. On the basis of his principle of sufficient reason, as stated in his treatise The Monadology, that “no fact can be real or existent, no statement true, unless there be a sufficient reason why it is so and not otherwise,” Leibniz held that his question must have an answer. It will not do to say that the universe (or even God) just exists as a brute fact, a simple fact that cannot be explained. There must be an explanation why it exists. He went on to argue that the sufficient reason cannot be found in any individual thing in the universe, nor in the collection of such things that constitute the universe, nor in earlier states of the universe, even if these regress infinitely. Therefore, there must exist an ultramundane being that is metaphysically necessary in its existence, that is to say, its nonexistence is impossible. It is the sufficient reason for its own existence as well as for the existence of every contingent thing.
2.1.2 Evaluation of the Arguments
In evaluating these arguments, let us consider them in reverse order. A simple statement of a Leibnizian cosmological argument runs as follows:
Is this a good argument? One of the principal objections to Leibniz’s own formulation of the argument is that the principle of sufficient reason as stated in The Monadology seems evidently false. There cannot be an explanation of why there are any contingent states of affairs at all, for if such an explanation is contingent, then it too must have a further explanation, whereas if it is necessary, then the states of affairs explained by it must also be necessary. Some theists have responded to this objection by agreeing that one must ultimately come to some explanatory stopping point that is simply a brute fact, a being whose existence is unexplained. For example, Richard Swinburne claims that in answering the question, why is there something rather than nothing? we must finally come to the brute existence of some contingent being. This being will not serve to explain its own existence (and, hence, Leibniz’s question goes unanswered), but it will explain the existence of everything else. Swinburne argues that God is the best explanation of why everything other than the brute Ultimate exists because as a unique and infinite being God is simpler than the variegated and finite universe.
But the above formulation of the Leibnizian argument avoids the objection without retreating to the dubious position that God is a contingent being. Premise (1) merely requires any existing thing to have an explanation of its existence, either in the necessity of its own nature or in some external cause. This premise is compatible with there being brute facts about the world. What it precludes is that there could exist things—substances exemplifying properties—that just exist inexplicably. This principle seems quite plausible, at least more so than its contradictory, which is all that is required for a successful argument. On this analysis, there are two kinds of beings: necessary beings, which exist of their own nature and so have no external cause of their existence, and contingent beings, whose existence is accounted for by causal factors outside themselves.
Premise (2) is, in effect, the contrapositive of the typical atheist response to Leibniz that on the atheistic worldview the universe simply exists as a brute contingent thing. Atheists typically assert that, there being no God, it is false that everything has an explanation of its existence, for the universe, in this case, just exists inexplicably. In so saying, the atheist implicitly recognizes that if the universe has an explanation, then God exists as its explanatory ground. Since, as premise (3) states, the universe is obviously an existing thing (especially evident in its very early stages when its density was so extreme), it follows that God exists.
It is open to the atheist to retort that while the universe has an explanation of its existence, that explanation lies not in an external ground but in the necessity of its own nature. In other words, (2) is false; the universe is a metaphysically necessary being. This was the suggestion of David Hume, who demanded, “Why may not the material universe be the necessarily existent being?” Indeed, “How can anything, that exists from eternity, have a cause, since that relation implies a priority in time and a beginning of existence?” (Dialogues Concerning Natural Religion, part 9).
This is an extremely bold suggestion on the part of the atheist. We have, we think we can safely say, a strong intuition of the universe’s contingency. A possible world in which no concrete objects exist certainly seems conceivable. We generally trust our modal intuitions on other matters; if we are to do otherwise with respect to the universe’s contingency, then atheists need to provide some reason for such skepticism other than their desire to avoid theism. But they have yet to do so.
Still, it would be desirable to have some stronger argument for the universe’s contingency than our modal intuitions alone. Could the Thomist cosmological argument help us here? If successful, it would show that the universe is a contingent being causally dependent on a necessary being for its continued existence. The difficulty with appeal to the Thomist argument, however, is that it is very difficult to show that things are, in fact, contingent in the special sense required by the argument. Certainly things are naturally contingent in that their continued existence is dependent on a myriad of factors including particle masses and fundamental forces, temperature, pressure, entropy level, and so forth, but this natural contingency does not suffice to establish things’ metaphysical contingency in the sense that being must continually be added to their essences lest they be spontaneously annihilated. Indeed, if Thomas’s argument does ultimately lead to an absolutely simple being whose essence is existence, then one might well be led to deny that beings are metaphysically composed of essence and existence if the idea of such an absolutely simple being proves to be unintelligible (see discussion of divine simplicity in chap. 28).
But what about the kalam cosmological argument? An essential property of a metaphysically necessary and ultimate being is that it be eternal, that is to say, without beginning or end. If the universe is not eternal, then it could not be, as Hume suggested, a metaphysically necessary being. But it is precisely the aim of the kalam cosmological argument to show that the universe is not eternal but had a beginning. It would follow that the universe must therefore be contingent in its existence. Not only so, the kalam argument shows the universe to be contingent in a very special way: it came into existence out of nothing. The atheist who would answer Leibniz by holding that the existence of the universe is a brute fact, an exception to the principle of sufficient reason, is thus thrust into the very awkward position of maintaining not merely that the universe exists eternally without explanation, but rather that for no reason at all it magically popped into being out of nothing, a position that might make theism look like a welcome alternative. Thus the kalam argument not only constitutes an independent argument for a transcendent Creator but also serves as a valuable supplement to the Leibnizian argument.
The kalam cosmological argument may be formulated as follows:
Or, more modestly:
Conceptual analysis of what it means to be a cause of the universe then aims to establish some of the theologically significant properties of this being.
Premise (1) seems obviously true—at the least, more so than its negation. It is rooted in the metaphysical intuition that something cannot come into existence from nothing. The causal principle therefore applies to all of reality, since it is metaphysically absurd that the universe should pop into being from nothing. It needs to be clearly kept in mind that the word nothing, despite its being grammatically a pronoun, is logically merely a negative universal quantifier (see chap. 2), meaning “not anything.” When cosmologists say that there was nothing prior to the big bang, they do not mean that there was something prior to it and that was a state of nothingness; rather they mean that there was not anything prior to the big bang. Scientific popularizers who say things like “There are a variety of forms of nothing,” “The laws of quantum mechanics tell us that nothing is unstable,” “70 percent of the dominant stuff in the universe is nothing,” “Nothing is almost everything,” are being misled by grammar to treat nothing as though it were a term referring to something, when in fact it is just a term of universal negation. On the atheistic view, there was not even the potentiality of the universe’s existence prior to the big bang, since nothing is prior to the big bang. But then how could the universe become actual if there was not even the potentiality of its existence? It makes much more sense to say that the potentiality of the universe lay in the power of God to create it.
Recently some critics of the kalam cosmological argument have denied that in beginning to exist the universe became actual or came into being. They thereby focus attention on the theory of time underlying the kalam argument (see chap. 20). On a static or so-called B-theory of time (according to which all moments of time are equally existent) the universe does not in fact come into being or become actual at the big bang; it just exists tenselessly as a four-dimensional space-time block that is finitely extended in the earlier than direction. If time is tenseless, then the critics are right that the universe never really comes into being, and therefore the quest for a cause of its coming into being is misconceived. Although Leibniz’s question, “Why is there [tenselessly] something rather than nothing?” should still rightly be asked, there would be no reason to look for a cause of the universe’s beginning to exist, since on tenseless theories of time the universe did not truly begin to exist by virtue of its having a first event, anymore than a meter stick begins to exist by virtue of its having a first centimeter. In affirming that things that begin to exist need a cause, the proponent of the kalam cosmological argument assumes the following understanding of that notion, where x ranges over any entity and t ranges over times, whether instants or moments of nonzero finite duration:
The key clause in (B) is (iii). By presupposing a dynamic or so-called A-theory of time, according to which temporal becoming is real, the proponent of the kalam cosmological argument justifiably assumes that the universe’s existing at a first moment of time represents the moment at which the universe came into being. Thus the real issue separating the proponent of the kalam cosmological argument and critics of the first premise is the objectivity of tense and temporal becoming.
Premise (2), The universe began to exist, has been supported by both deductive philosophical arguments and inductive scientific arguments. The first of four arguments for this premise that we will consider is the argument based on the impossibility of the existence of an actual infinite. It may be formulated as follows:
In order to assess this argument, it will be helpful to define some terms. By an actual infinite, the argument’s defender means any collection having at a time t a number of definite and discrete members that is greater than any natural number {0, 1, 2, 3, . . . }. This notion is to be contrasted with a potential infinite, which is any collection having at any time t a number of definite and discrete members that is equal to some natural number but that over time increases endlessly toward infinity as a limit. By exist proponents of the argument mean “have extramental existence,” or “be instantiated in the real world.” By a “physical event,” they mean any change occurring within the space-time universe. Since any change takes time, there are no instantaneous events. Neither could there be an infinitely slow event, since such an “event” would in reality be a changeless state. Therefore, any event will have a finite, nonzero duration. In order that all the events constituting the temporal regress of past events be of equal duration, one arbitrarily stipulates some event as our standard and, taking as our point of departure the present standard event, we consider any series of such standard events ordered according to the relation earlier than. The question is whether this series of events comprises an actually infinite number of events or not. If not, then since the universe is not distinct from the series of past physical events, the universe must have had a beginning, in the sense of a first standard event. It is therefore not relevant whether the temporal series had a beginning point (a first temporal instant). The question is whether there was in the past an event occupying a nonzero, finite temporal interval that was absolutely first, that is, not preceded by any equal interval.
Premise (1) asserts, then, that an actual infinite cannot exist in the real, spatiotemporal world. It is usually alleged that this sort of argument has been invalidated by Georg Cantor’s work on the actual infinite and by subsequent developments in set theory. But this allegation misconstrues the nature of both Cantor’s system and modern set theory, for the argument does not in fact contradict a single tenet of either. The reason is this: Cantor’s system and set theory are simply a universe of discourse, a mathematical system based on certain adopted axioms and conventions. The argument’s defender may hold that while the actual infinite may be a fruitful and consistent concept within the postulated universe of discourse, it cannot be transposed into the spatiotemporal world, for this would involve counterintuitive absurdities. This can be shown by concrete examples that illustrate the various absurdities that would result if an actual infinite were to be instantiated in the real world.
Take, for example, Hilbert’s Hotel, a product of the mind of the great German mathematician David Hilbert. As a warm-up, let us first imagine a hotel with a finite number of rooms. Suppose, furthermore, that all the rooms are full. When a new guest arrives asking for a room, the proprietor apologizes, “Sorry, all the rooms are full,” and that is the end of the story. But now let us imagine a hotel with an infinite number of rooms and suppose once more that all the rooms are full. There is not a single vacant room throughout the entire infinite hotel. Now suppose a new guest shows up, asking for a room. “But of course!” says the proprietor, and he immediately shifts the person in room 1 into room 2, the person in room 2 into room 3, the person in room 3 into room 4, and so on out to infinity. As a result of these room changes, room one now becomes vacant, and the new guest gratefully checks in. But remember, before he arrived, all the rooms were full! Equally curious, according to the mathematicians, there are now no more persons in the hotel than there were before: the number is just infinite. But how can this be? The proprietor just added the new guest’s name to the register and gave him his keys—how can there not be one more person in the hotel than before?
But the situation becomes even stranger. For suppose an infinity of new guests show up at the desk, asking for a room. “Of course, of course!” says the proprietor, and he proceeds to shift the person in room 1 into room 2, the person in room 2 into room 4, the person in room 3 into room 6, and so on out to infinity, always putting each former occupant into the room number twice his own. Because any natural number multiplied by two always equals an even number, all the guests wind up in even-numbered rooms. As a result, all the odd-numbered rooms become vacant, and the infinity of new guests is easily accommodated. And yet, before they came, all the rooms were full! And again, strangely enough, the number of guests in the hotel is the same after the infinity of new guests check in as before, even though there were as many new guests as old guests. In fact, the proprietor could repeat this process infinitely many times, and yet there would never be one single person more in the hotel than before.
But Hilbert’s Hotel is even stranger than the German mathematician made it out to be. For suppose some of the guests start to check out. Suppose the guest in room 1 departs. Is there not now one fewer person in the hotel? Not according to the mathematicians! Suppose the guests in rooms 1, 3, 5, . . . check out. In this case an infinite number of people have left the hotel, but according to the mathematicians, there are no fewer people in the hotel! In fact, we could have every other guest check out of the hotel and repeat this process infinitely many times, and yet there would never be any fewer people in the hotel. Now suppose the proprietor doesn’t like having a half-empty hotel (it looks bad for business). No matter! By shifting occupants as before, but in reverse order, he transforms his half-vacant hotel into one that is jammed to the gills. You might think that by these maneuvers the proprietor could always keep this strange hotel fully occupied. But you would be wrong. For suppose that the persons in rooms 4, 5, 6, . . . checked out. At a single stroke the hotel would be virtually emptied, the guest register would be reduced to three names, and the infinite would be converted to finitude. And yet it would remain true that the same number of guests checked out this time as when the guests in rooms 1, 3, 5, . . . checked out! Can anyone believe that such a hotel could exist in reality?
Hilbert’s Hotel certainly seems absurd. Since nothing hangs on the illustration’s involving a hotel, the argument, if successful, would show in general that it is impossible for an actually infinite number of things to exist in spatiotemporal reality. Students sometimes react to such illustrations as Hilbert’s Hotel by saying that we really do not understand the nature of infinity and, hence, these absurdities result. But this attitude is simply mistaken. Infinite set theory is a highly developed and well-understood branch of mathematics, and these absurdities can be seen to result precisely because we do understand the notion of a collection with an actually infinite number of members.
Sometimes it is said that we can find counterexamples to the claim that an actually infinite number of things cannot exist, so that premise (1) must be false. For instance, is not every finite distance capable of being divided into 1/2, 1/4, 1/8, . . . , on to infinity? Does that not prove that there are in any finite distance an actually infinite number of parts? The defender of the argument may reply that this objection confuses a potential infinite with an actual infinite. He will point out that while you can continue to divide any distance for as long as you want, such a series is merely potentially infinite, in that infinity serves as a limit that you endlessly approach but never reach. If you assume that any distance is already composed out of an actually infinite number of parts, then you are begging the question. You are assuming what the objector is supposed to prove, namely, that there is a clear counterexample to the claim that an actually infinite number of things cannot exist.
Again, it is worth reiterating that nothing in the argument need be construed as an attempt to undermine the theoretical system bequeathed by Cantor to modern mathematics. Indeed, some of the most eager enthusiasts of the system of transfinite mathematics are only too ready to agree that these theories have no relation to the real world. Thus Hilbert, who exuberantly extolled Cantor’s greatness, nevertheless held that the Cantorian paradise exists only in the ideal world invented by the mathematician and is nowhere to be found in reality. The case against the existence of the actual infinite need say nothing about the use of the idea of the infinite in conceptual mathematical systems.
The second premise states that an infinite temporal regress of events is an actual infinite. This asserts that if the series or sequence of changes in time is infinite, then these events considered collectively constitute an actual infinite. The point seems obvious enough, for if there has been a sequence composed of an infinite number of events stretching back into the past, then an actually infinite number of events have occurred. If the series of past events were an actual infinite, then all the absurdities attending the real existence of an actual infinite would apply to it.
In summary: if an actual infinite cannot exist in the real, spatiotemporal world and an infinite temporal regress of events is such an actual infinite, we can conclude that an infinite temporal regress of events cannot exist; that is to say, the temporal series of past physical events had a beginning. And this implies the second premise of the original syllogism of the kalam cosmological argument.
The second argument against the possibility of an infinite past that we will consider is the argument based on the impossibility of forming an actual infinite by successive addition. It may be formulated as follows:
Here one does not assume that an actual infinite cannot exist. Even if an actual infinite can exist, it is argued that the temporal series of events cannot be such, since an actual infinite cannot be formed by successive addition, as the temporal series of events is.
Premise (1) presupposes once again an A-theory of time. On such a theory the collection of all past events prior to any given event is not a collection whose members all tenselessly coexist. Rather, it is a collection that is instantiated sequentially or successively in time, one event coming to pass on the heels of another. Since temporal becoming is an objective feature of the physical world, the series of past events is not a tenselessly existing continuum, all of whose members are equally real. Rather, the members of the series come to be and pass away one after another.
Premise (2) asserts that a collection formed by successive addition cannot be an actual infinite. Sometimes this is described as the impossibility of traversing the infinite. In order for us to have “arrived” at today, temporal existence has, so to speak, traversed an infinite number of prior events. But before the present event could arrive, the event immediately prior to it would have to arrive, and before that event could arrive, the event immediately prior to it would have to arrive, and so on ad infinitum. No event could ever arrive, since before it could elapse there will always be one more event that had to have happened first. Thus, if the series of past events were beginningless, the present event could not have arrived, which is absurd.
This argument brings to mind Bertrand Russell’s account of Tristram Shandy, who, in the novel by Sterne, writes his autobiography so slowly that it takes him a whole year to record the events of a single day. Were he mortal, he would never finish, asserts Russell, but if he were immortal, then the entire book could be completed, since to each day there would correspond a year, and both are infinite. Russell’s assertion is untenable on an A-theory of time, however, since the future is in reality a potential infinite only. Though he write forever, Tristram Shandy would only get farther and farther behind, so that instead of finishing his autobiography, he will progressively approach a state in which he would be infinitely far behind. But he would never reach such a state because the years and hence the days of his life would always be finite in number though indefinitely increasing.
But let us turn the story about: suppose Tristram Shandy has been writing from eternity past at the rate of one day per year. Should not Tristram Shandy now be infinitely far behind? For if he has lived for an infinite number of years, Tristram Shandy has recorded an equally infinite number of past days. Given the thoroughness of his autobiography, these days are all consecutive days. At any point in the past or present, therefore, Tristram Shandy has recorded a beginningless, infinite series of consecutive days. But now the question inevitably arises: Which days are these? Where in the temporal series of events are the days recorded by Tristram Shandy at any given point? The answer can only be that they are days infinitely distant from the present. For there is no day on which Tristram Shandy is writing that is finitely distant from the last recorded day.
If Tristram Shandy has been writing for one year’s time, then the most recent day he could have recorded is one year ago. But if he has been writing two years, then that same day could not have been recorded by him. For since his intention is to record consecutive days of his life, the most recent day he could have recorded is the day immediately after a day at least two years ago. This is because it takes a year to record a day, so that to record two days he must have two years. Similarly, if he has been writing three years, then the most recent day recorded could be no more recent than three years ago plus two days. In fact, the recession into the past of the most recent recordable day can be plotted according to the formula: (present date – n years of writing) + (n – 1) days. In other words, the longer he has written the further behind he has fallen. But what happens if Tristram Shandy has, ex hypothesi, been writing for an infinite number of years? The first day of his autobiography recedes to infinity, that is to say, to a day infinitely distant from the present. Nowhere in the past at a finite distance from the present can we find a recorded day, for by now Tristram Shandy is infinitely far behind. The beginningless, infinite series of days he has recorded are days that lie at an infinite temporal distance from the present. What therefore follows from the Tristram Shandy story is that an infinite series of past events is absurd, for there is no way to traverse the distance from an infinitely distant event to the present or, more technically, for an event that was once present to recede to an infinite temporal distance.
But now a deeper absurdity bursts into view. For if the series of past events is an actual infinite, then we may ask, why did Tristram Shandy not finish his autobiography yesterday or the day before, since by then an infinite series of moments had already elapsed? Given that in infinite time he would finish the book, then at any point in the infinite past he should already have finished. No matter how far along the series of past events one regresses, Tristram Shandy would have already completed his autobiography. Therefore, at no point in the infinite series of past events could he be finishing the book. We could never look over Tristram Shandy’s shoulder to see if he were now writing the last page. For at any point an actually infinite sequence of events would have transpired and the book would have already been completed. Thus at no time in eternity will we find Tristram Shandy writing, which is absurd, since we supposed him to be writing from eternity. And at no point will he finish the book, which is equally absurd, because for the book to be completed, he must at some point have finished. What the Tristram Shandy story really tells us is that an actually infinite temporal regress is absurd.
Sometimes critics indict this argument as a sleight-of-hand trick like Zeno’s paradoxes of motion. Zeno argued that before Achilles could cross the stadium, he would have to cross halfway; but before he could cross halfway, he would have to cross a quarter of the way; but before he could cross a quarter of the way, he would have to cross an eighth of the way; and so on to infinity. It is evident that Achilles could not even move! Therefore, Zeno concluded, motion is impossible. Now even though Zeno’s argument is very difficult to refute, nobody really believes that motion is impossible. Even if Achilles must pass through an infinite number of halfway points in order to cross the stadium, somehow he manages to do so! The argument against the impossibility of traversing an infinite past, some critics allege, must commit the same fallacy as Zeno’s paradox.
But such an objection fails to reckon with two crucial disanalogies of an infinite past to Zeno’s paradoxes: whereas in Zeno’s thought experiments the intervals traversed are potential and unequal, in the case of an infinite past the intervals are actual and equal. The claim that Achilles must pass through an infinite number of halfway points in order to cross the stadium is question-begging, for it already assumes that the whole interval is a composition of an infinite number of points, whereas Zeno’s opponents, like Aristotle, take the line as a whole to be conceptually prior to any divisions that we might make in it. Moreover, Zeno’s intervals, being unequal, sum to a merely finite distance, whereas the intervals in an infinite past sum to an infinite distance. Thus his thought experiments are crucially disanalogous to the task of traversing an infinite number of equal, actual intervals to arrive at our present location.
It is frequently objected that this sort of argument illicitly presupposes an infinitely distant starting point in the past and then pronounces it impossible to travel from that point to today. But if the past is infinite, then there would be no starting point whatever, not even an infinitely distant one. Nevertheless, from any given point in the past, there is only a finite distance to the present, which is easily “traversed.” But in fact no proponent of the kalam argument of whom we are aware has assumed that there was an infinitely distant starting point in the past. (Even the Tristram Shandy paradox does not assert that there was an infinitely distant first day, but merely that there were days infinitely distant in the past.) The fact that there is no beginning at all, not even an infinitely distant one, seems only to make the problem worse, not better. To say that the infinite past could have been formed by successive addition is like saying that someone has just succeeded in writing down all the negative numbers, ending at -1. And, we may ask, how is the claim that from any given moment in the past there is only a finite distance to the present even relevant to the issue? The defender of the kalam argument could agree to this happily. For the issue is how the whole series can be formed, not a finite portion of it. Does the objector think that because every finite segment of the series can be formed by successive addition that the whole infinite series can be so formed? That is as logically fallacious as saying because every part of an elephant is light in weight, the whole elephant is light in weight. The claim is therefore irrelevant.
In summary: If a collection formed by successive addition cannot be an actual infinite, then since the temporal series of events is a collection formed by successive addition, it follows that the temporal series of events cannot be an actual infinite. This implies, of course, that the temporal series of past physical events is not beginningless.
The third argument for the universe’s beginning advanced by contemporary proponents of the kalam cosmological argument is an inductive argument based on the expansion of the universe. In 1917, Albert Einstein made a cosmological application of his newly discovered gravitational theory, the general theory of relativity (GTR). In so doing he assumed that the universe exists in a steady state, with a constant mean mass density and a constant curvature of space. To his chagrin, however, he found that GTR would not permit such a model of the universe unless he introduced into his gravitational field equations a certain “fudge factor” in order to counterbalance the gravitational effect of matter and so ensure a static universe. Unfortunately, Einstein’s static universe was balanced on a razor’s edge, and the least perturbation would cause the universe either to implode or to expand. By taking this feature of Einstein’s model seriously, the Russian mathematician Alexander Friedman and the Belgian astronomer Georges Lemaître were able to formulate independently in the 1920s solutions to the field equations that predicted an expanding universe.
In 1929 the astronomer Edwin Hubble showed that the red-shift in the optical spectra of light from distant galaxies was a common feature of all measured galaxies and was proportional to their distance from us. This red-shift was taken to be a Doppler effect indicative of the recessional motion of the light source in the line of sight. Incredibly, what Hubble had discovered was the isotropic expansion of the universe predicted by Friedman and Lemaître on the basis of Einstein’s GTR.
According to the Friedman-Lemaître model, as time proceeds, the distances separating galactic masses become greater. It is important to understand that as a GTR-based theory, the model does not describe the expansion of the material content of the universe into a preexisting, empty space, but rather the expansion of space itself. The ideal particles of the cosmological fluid constituted by the galactic masses are conceived to be at rest with respect to space but to recede progressively from one another as space itself expands or stretches, just as buttons glued to the surface of a balloon would recede from one another as the balloon inflates. As the universe expands, it becomes less and less dense. This has the astonishing implication that as one reverses the expansion and extrapolates back in time, the universe becomes progressively denser until one arrives at a state of “infinite density” at some point in the finite past. This state represents a singularity at which space-time curvature, along with temperature, pressure, and density, becomes infinite. It therefore constitutes an edge or boundary to space-time itself. The term “big bang” is thus potentially misleading, since the expansion cannot be visualized from the outside (there being no “outside,” just as there is no “before” with respect to the big bang).
The standard big bang model, as the Friedman-Lemaître model came to be called, thus describes a universe that is not eternal in the past but that came into being a finite time ago. Moreover—and this deserves underscoring—the origin it posits is an absolute origin ex nihilo. For not only all matter and energy but also space and time themselves come into being at the initial cosmological singularity. There can be no natural, physical cause of the big bang event, since, in Quentin Smith’s words, “it belongs analytically to the concept of the cosmological singularity that it is not the effect of prior physical events. The definition of a singularity . . . entails that it is impossible to extend the spacetime manifold beyond the singularity. . . . This rules out the idea that the singularity is an effect of some prior natural process.” Sir Arthur Eddington, contemplating the beginning of the universe, opined that the expansion of the universe was so preposterous and incredible that “I feel almost an indignation that anyone should believe in it—except myself.” He finally felt forced to conclude, “The beginning seems to present insuperable difficulties unless we agree to look on it as frankly supernatural.”
Sometimes objectors appeal to nonstandard models of the expanding universe in an attempt to avert the absolute beginning predicted by the standard model. But while such past-eternal scenarios are possible, it has been the overwhelming verdict of the scientific community that none of them is more probable than a universe with a beginning. The devil is in the details, and once you get down to specifics you find that there is no mathematically consistent model that has been so successful in its predictions or as corroborated by the evidence as big bang models with a beginning.
Meanwhile, a series of remarkable singularity theorems has increasingly tightened the loop around empirically tenable models by showing that under more and more generalized conditions, a beginning is inevitable. In 2003 Arvind Borde, Alan Guth, and Alexander Vilenkin were able to show that any universe that is, on average, in a state of cosmic expansion throughout its history cannot be infinite in the past but must have a beginning. That goes for multiverse scenarios too. In 2012 Vilenkin showed that models which do not meet this one condition still fail for other reasons to avert the beginning of the universe. Vilenkin concluded, “None of these scenarios can actually be past eternal.” “All the evidence we have says that the universe had a beginning.”
The Borde-Guth-Vilenkin theorem proves that classical space-time, under a single, very general condition, cannot be extended to past infinity but must reach a boundary at some time in the finite past. Now either there was something on the other side of that boundary or not. If not, then that boundary just is the beginning of the universe. If there was something on the other side, then it will be a region described by the yet-to-be-discovered theory of quantum gravity. In that case, Vilenkin says, it will be the beginning of the universe.
Both Vilenkin and, more famously, James Hartle and Stephen Hawking have proposed models of the universe according to which classical space-time emerges from a quantum gravity regime that eliminates the initial singularity by transforming the conical geometry of classical space-time into a smooth, curved geometry having no edge. If there is such a nonclassical region, then it is not past eternal in the classical sense. Hawking describes it as “completely self-contained and not affected by anything outside itself. It would be neither created nor destroyed. It would just BE.” But this regime cannot exist literally timelessly, akin to the way in which philosophers consider abstract objects like numbers to be timeless, or theologians take God to be timeless. For this region is in a state of constant flux, which is sufficient for before/after relations. Moreover, it is supposed to have somehow existed before the classical era, and the classical era is supposed to have emerged from it, which seems to posit a temporal relation between the quantum gravity era and the classical era.
Therefore, it seems that even if time as defined in classical physics does not exist at such a quantum gravity era, some sort of time would. But if the quantum gravity era is in some sense temporal, it cannot be extended infinitely in time, for such a quantum state is not stable and so would either produce the universe from eternity past or not at all. As Anthony Aguirre and John Kehayias argue, “It is very difficult to devise a system—especially a quantum one—that does nothing ‘forever,’ then evolves. A truly stationary or periodic quantum state, which would last forever, would never evolve, whereas one with any instability will not endure for an indefinite time.” Hence, the quantum gravity era would itself have to have had a beginning in order to explain why it transitioned just some fourteen billion years ago into classical time and space. Hence, whether at the boundary or at the quantum gravity regime, the universe began to exist.
The fourth argument for the finitude of the past is also an inductive argument, this time on the basis of the thermodynamic properties of the universe. According to the second law of thermodynamics, processes taking place in a closed system always tend toward a state of equilibrium. Our interest in the law concerns what happens when it is applied to the universe as a whole. The universe is, on a naturalistic view, a gigantic closed system, since it is everything there is and there is nothing outside it. This seems to imply that, given enough time, the universe and all its processes will run down, and the entire universe will come to equilibrium. This is known as the heat death of the universe. Once the universe reaches this state, no further change is possible. The universe is dead.
Now the question that needs to be asked is this: If given enough time the universe will reach heat death, then why is it not in a state of heat death now, if it has existed forever, from eternity? If the universe did not begin to exist, then it should now be in a state of equilibrium. Like a ticking clock, it should by now have run down. Since it has not yet run down, this implies, in the words of one baffled scientist, “In some way the universe must have been wound up.”
Recent discoveries indicate that the cosmic expansion is actually speeding up. Because the volume of space is increasing so rapidly, the universe actually becomes farther and farther from an equilibrium state in which matter and energy are evenly distributed. But the acceleration of the universe’s expansion only hastens its demise. For now the different regions of the universe become increasingly isolated from one another in space, and each marooned region becomes dark, cold, dilute, and dead. So again, why is our region not now in such a state if the universe has already existed for infinite time?
The obvious implication of all this is that the question is based on a false assumption, namely, that the universe has existed for infinite time. Today most physicists would say that the matter and energy were simply put into the universe as an initial condition, and the universe has been following the path plotted by the second law ever since its beginning a finite time ago.
Of course, attempts have been made to avoid the beginning of the universe predicted on the basis of the second law of thermodynamics. But none of them has been successful. Skeptics might hold out hope that quantum gravity will serve to avert the implications of the second law of thermodynamics. But in 2013, the cosmologist Aron Wall of the University of California was able to formulate a new singularity theorem that seems to close the door on that possibility. Wall shows that, given the validity of the generalized second law of thermodynamics in quantum gravity, the universe must have begun to exist, unless one postulates a reversal of the arrow of time (time runs backward!) at some point in the past, which, he rightly observes, involves a thermodynamic beginning in time that “would seem to raise the same sorts of philosophical questions that any other sort of beginning in time would.” Wall reports that his results require the validity of only certain basic concepts, so that “it is reasonable to believe that the results will hold in a complete theory of quantum gravity.”
Thus thermodynamics suggests that the universe had a beginning. The universe appears to have been created a finite time ago, and its energy was somehow simply put in at the creation as an initial condition.
On the basis of these four arguments for the finitude of the past, the proponent of the kalam cosmological argument seems to have good grounds for affirming the second premise of the argument: that the universe began to exist. It therefore follows that the universe has a cause. Conceptual analysis enables us to recover a number of striking properties that must be possessed by such an ultramundane being. For as the cause of space and time, this entity must transcend space and time and therefore exist atemporally and nonspatially, at least without the universe. This transcendent cause must therefore be changeless and immaterial, since timelessness entails changelessness, and changelessness implies immateriality. Such a cause must be beginningless and uncaused, at least in the sense of lacking any antecedent causal conditions. Ockham’s razor will shave away further causes, since we should not multiply causes beyond necessity. This entity must be unimaginably powerful, since it created the universe without any material cause.
Finally, and most remarkably, such a transcendent cause is plausibly taken to be personal. Three reasons can be given for this conclusion. First, there are two types of causal explanations: scientific explanations in terms of laws and initial conditions and personal explanations in terms of agents and their volitions. A first state of the universe cannot have a scientific explanation, since there is nothing before it, and therefore it can be accounted for only in terms of a personal explanation. Second, the personhood of the cause of the universe is implied by its timelessness and immateriality, since the only entities we know of that can possess such properties are either minds or abstract objects, and abstract objects do not stand in causal relations. Therefore, the transcendent cause of the origin of the universe must be of the order of mind. Third, this same conclusion is also implied by the fact that we have in this case the origin of a temporal effect from a timeless cause. If the cause of the origin of the universe were an impersonal set of necessary and sufficient conditions, it would be impossible for the cause to exist without its effect. For if the necessary and sufficient conditions of the effect are timelessly given, then their effect must be given as well. The only way for the cause to be timeless and changeless but for its effect to originate anew a finite time ago is for the cause to be a personal agent who freely chooses to bring about an effect without antecedent determining conditions. Thus we are brought, not merely to a transcendent cause of the universe, but to its personal Creator. He is, as Leibniz maintained, the Sufficient Reason why anything exists rather than nothing.
Chapter Summary
The cosmological argument is a family of arguments that seek to demonstrate the existence of a Sufficient Reason or First Cause of the existence of the cosmos. The arguments can be grouped into three basic types: the kalam cosmological argument for a First Cause of the beginning of the universe, the Thomist cosmological argument for a sustaining Ground of Being of the world, and the Leibnizian cosmological argument for a Sufficient Reason why something exists rather than nothing. A plausible version of the Leibnizian argument can be formulated on the basis of the following premises:
Premise (2) might be challenged by contending that the universe is a necessary being. Implausible as this might seem, an argument for the universe’s contingency would be desirable. Although the Thomist argument proffers such a proof, it is difficult to justify the real distinction between essence and existence at the heart of the argument. The kalam argument is more promising: through the demonstration that the universe began to exist its contingency is revealed. This central premise in the argument may be supported by philosophical arguments against the possibility of an infinite past based on either the impossibility of the existence of an actual infinite or on the impossibility of forming an actual infinite by successive addition and by scientific evidence for a beginning of the universe from astrophysical cosmology and thermodynamics. Taken together with the plausible premise that whatever begins to exist has a cause, the beginning of the universe implies the existence of an ultramundane being that is the cause of the universe. A conceptual analysis of what it is to be a cause of the universe enables us to deduce a number of the traditional divine attributes, including the personhood of the First Uncaused Cause.
Checklist of Basic Terms and Concepts
A-theory of time
act of being
actual infinite
B-theory of time
brute fact
contingency
contingent beings
cosmological argument
essence
expansion of the universe
heat death of the universe
Hilbert’s Hotel
kalam cosmological argument
Leibnizian cosmological argument
metaphysically necessary
natural theology
necessary being
objective moral duties
objective moral values
philosophy of religion
potential infinite
principle of sufficient reason
second law of thermodynamics
set theory
singularity
standard big bang model
systematic theology
Thomist cosmological argument
traversing the infinite
Tristram Shandy paradox
Zeno’s paradoxes of motion