THE COSMOLOGICAL ARGUMENT

Introduction

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 which is formally and informally valid and consists of true premisses which 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 which seeks to prove God's existence apart from the resources of authoritative divine revelation. In this brief essay I shall focus on the so-called cosmological argument for the existence of God.

The cosmological argument is a family of arguments which 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.

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, which 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 about 15 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 which 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 a set of properties which serve to define what that thing is. Now if an essence is to be instantiated or exemplified, 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 be exemplified. For the same reason no substance can actualize itself; for in order to bestow being upon 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 which 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" (Exod. 3.15).

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. "The first question which should rightly be asked," he wrote, "is this: why is there something rather than nothing?"[1] Leibniz meant this question to be truly universal, not merely to apply to finite things. On the basis of his Principle of Sufficient Reason, that "no fact can be real or existent, no statement true, unless there be a sufficient reason why it is so and not otherwise,"[2] Leibniz held that this question must have an answer. It will not do to say that the universe (or even God) just exists as a brute fact. 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 which comprise the universe, nor in earlier states of the universe, even if these regress infinitely. Therefore, there must exist an ultra-mundane being which is metaphysically necessary in its existence, that is to say, its non-existence is impossible. It is the Sufficient Reason for its own existence as well as for the existence of every contingent thing.

The Leibnizian Cosmological Argument

In evaluating these arguments, let us consider them in reverse order. A simple statement of a Leibnizian cosmological argument might run as follows[3]:

1. Every existing thing has an explanation of its existence, either in the necessity of its own nature or in an external cause.

2. If the universe has an explanation of its existence, that explanation is God.

3. The universe is an existing thing.

4. Therefore the explanation of the existence of the universe is God.

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 which 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. For premiss (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 premiss is compatible with there being brute facts or states of affairs about the world. What it precludes is that there could exist things-- substances exemplifying properties--which 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 being: 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. Numbers might be prime candidates for the first sort of being, while familiar physical objects fall under the second kind of being.

            Premiss (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. [4] In so saying, the atheist implicitly recognizes that if the universe has an explanation, then God exists as its explanatory ground. This seems quite plausible, for if the universe, by definition, includes all of physical reality, then it is hard to see how it could have an explanation, or at least a better one, other than its being caused by God.

Finally, premiss (3) states the obvious, that there is a universe.[5] Since the universe is obviously an existing thing (especially evident in its very early stages when its density was so extreme), possessing many unique properties such as a certain density, pressure, temperature, spacetime curvature, and so on, 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?"[6]

This is an extremely bold suggestion on the part of the atheist. It runs precisely counter to the conviction driving the Swinburnian formulation of the argument, namely that there must be some ultimately inexplicable contingent being. Even if we reject that assumption, we have, I 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 with which we are familiar[7]; if we are to do otherwise with respect to the universe's contingency, then the atheist needs to provide some reason for such scepticism other than his desire to avoid theism.

The Thomist Cosmological Argument

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 upon 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 upon 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.[8]

The Kalam Cosmological Argument

But what about the kalam cosmological argument? An essential property of a metaphysically necessary being is eternality, that is to say, being without beginning or end. It has been countered that a being with a temporal beginning or end could, nonetheless, be metaphysically necessary in that it is caused to exist in all possible worlds. But this understanding of metaphysical necessity fails to take tense seriously and is therefore inadequate. Metaphysicians have in recent years begun to appreciate the metaphysical importance of whether time is tensed or tenseless, that is to say, whether items in the temporal series are ordered objectively as past, present, or future, or whether, alternatively, they are ordered merely by tenseless relations of earlier than, simultaneous with, and later than.[9] Possible worlds semantics is a tenseless semantics and so is incapable of expressing the significance of one's view of time. In particular, it is evident that a truly necessary being, one whose non-existence is impossible, must exist at every moment in every world. It is not enough for it to exist at only some moment or moments in every possible world, for the fact that there exist moments in various worlds at which it fails to exist shows that its non-existence not impossible. By the same token, a truly metaphysically necessary being must exist either timelessly or sempiternally in any tensed world in which it exists, for otherwise its coming into being or ceasing to be would again make it evident that its existence is not necessary. [10]  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 which 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:

1. Whatever begins to exist has a cause.

2. The universe began to exist.

3. Therefore, the universe has a cause.

Conceptual analysis of what it means to be a cause of the universe then helps to establish some of the theologically significant properties of this being.

1. Whatever Begins to Exist Has a Cause

Premiss (1) seems obviously true--at the least, more so than its negation. It is rooted in the metaphysical intuition that something cannot come into being from nothing. Moreover, this premiss is constantly confirmed in our experience. The conviction that an origin of the universe requires a causal explanation seems quite reasonable, for 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.

Nevertheless, a number of atheists, in order to avoid the argument’s conclusion, have denied the first premiss. Sometimes it is said that sub-atomic physics furnishes an exception to premise (1), since on the sub-atomic level events are said to be uncaused. In the same way, certain theories of cosmic origins are interpreted as showing that the whole universe could have sprung into being out of the sub-atomic vacuum.  Thus the universe is said to be the proverbial “free lunch.”

            This objection, however, is based on misunderstandings. In the first place, not all scientists agree that sub-atomic events are uncaused. A great many physicists today are quite dissatisfied with this view (the so-called Copenhagen Interpretation) of sub-atomic physics and are exploring deterministic theories like that of David Bohm. Thus, sub-atomic physics is not a proven exception to premise (1). Second, even on the traditional, indeterministic interpretation, particles do not come into being out of nothing. They arise as spontaneous fluctuations of the energy contained in the sub-atomic vacuum, which constitutes an indeterministic cause of their origination. Third, the same point can be made about theories of the origin of the universe out of a primordial vacuum. Popular magazine articles touting such theories as getting “something from nothing” simply do not understand that the vacuum is not nothing but is a sea of fluctuating energy endowed with a rich structure and subject to physical laws. Thus, there is no basis for the claim that quantum physics proves that things can begin to exist without a cause, much less that universe could have sprung into being uncaused from literally nothing.

            Other critics have said that premise (1) is true only for things in the universe, but it is not true of the universe itself. But, first, this objection misconstrues the nature of the premise. Premise (1) does not state merely a physical law like the law of gravity or the laws of thermodynamics, which are valid for things within the universe. Premise (1) is not a physical principle. Rather premise (1) is a metaphysical principle: being cannot come from non-being; something cannot come into existence uncaused from nothing. The principle therefore applies to all of reality, and it is thus metaphysically absurd that the universe should pop into being uncaused out of nothing.

Second, until the premise's detractors are able to explain the relevant difference between embedded moments of time and a first moment of time, there seems to be no reason to think it more plausible that things can come into being uncaused at a first moment than at a later moment of time. What is the relevant difference between something's coming into existence within time and something's coming into existence at the beginning of time? Indeed, given a dynamic or tensed view of time, every moment of time is a fresh beginning, qualitatively indistinguishable from a first moment of time, for when any moment is present, earlier moments have passed away and do not exist. Thus, if the universe could exist uncaused at a first moment of time, it could exist uncaused at any moment of time. It follows that if the latter is metaphysically impossible, so is the former.

Third, the objection stifles scientific exploration of cosmological questions. The absolute beginning of time predicted by the Standard Friedman-Lemaître Big Bang model was the crucial factor in provoking not only the formulation of the Steady State model of continuous creation, but a whole series of subsequent models all aimed at avoiding the origin ex nihilo of our universe predicted by the Standard Model. Both philosophers and physicists have been deeply disturbed at the prospect of a beginning of time and an absolute origination of the universe and so have felt constrained to posit the existence of causally prior entities like quantum vacuum states, inflationary domains, imaginary time regimes, and even timelike causal loops. The history of twentieth century astrophysical cosmology would be considerably different if there were thought to be no need of a causal explanation of the origin of time and the universe. The theist cannot be similarly accused of stifling science because the theist's identification of the cause of the universe as a being of religious significance comes only with the conceptual analysis of the argument's conclusion, and he will in any case welcome attempts to falsify his theistic hypothesis in hopes of corroboration of his preferred hypothesis by the failure of such naturalistic explanations.

            Recently some critics of the 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 cosmological argument. On a static or tenseless of time 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 which is finitely extended in the earlier than direction. If time is tenseless, then 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 in virtue of its having a first event, anymore than a meter stick begins to exist in virtue of having a first centimeter. In affirming that things which 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 non-zero finite duration:

            A. x begins to exist at t iff x comes into being at t.

B. x comes into being at t iff (i) x exists at t, and the actual world includes no state of affairs in which x exists timelessly, (ii) t is either the first time at which x exists or is separated from any t’< t at which x existed by an interval during which x does not exist, and (iii) x’s existing at t is a tensed fact.

The key clause in (B) is (iii). By presupposing a dynamic or tensed 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 premiss is the objectivity of tense and temporal becoming.

2. The Universe Began to Exist

Premiss (2) may be supported by both deductive, philosophical arguments and inductive, scientific arguments.

2. 1. First Argument

The first argument I shall consider is the argument based on the impossibility of the existence of an actual infinite. It may be formulated as follows:

2. 1. 1. An actual infinite cannot exist.

2. 1. 2. An infinite temporal regress of events is an actual infinite.

2. 1. 3. Therefore an infinite temporal regress of events cannot exist.

In order to assess this argument, it will be helpful to define some terms. By an actual infinite, I mean any collection having at a time t a number of definite and discrete members which 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 which is equal to some natural number but which over time increases endlessly toward infinity as a limit. By "exist" I mean "have extra‑mental existence," or "be instantiated in the real world." By an "event," I 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, non-zero duration. In order that all the events comprising the temporal regress of past events be of equal duration, we arbitrarily stipulate 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 is comprised of an actually infinite number of events or not. If not, then since the universe is not distinct from the series of past 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 non-zero, finite temporal interval which was absolutely first, that is, not preceded by any equal interval.

Premiss (2. 1. 1) asserts, then, that an actual infinite cannot exist in the real, spatio-temporal 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 may be taken to be 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 spatio-temporal world, for this would involve counter‑intuitive absurdities. One can try to show this is by way of concrete examples, like the famous Hilbert’s Hotel[11], that illustrate the various absurdities that would result if an actual infinite were to be instantiated in the real world. I am quite happy to grant the coherence and consistency of infinite set theory and transfinite arithmetic, while denying that the actual infinite can exist in reality. In any case, should the intuitionists turn out to be right in allowing only potential infinites to exist even in the realm of mathematics, I shall not weep for infinite set theory. But my argument does not require so strong a thesis as that mathematical theories of the infinite are incoherent. It is the real existence of the actual infinite which I reject.

It is sometimes thought that the existence of abstract objects provides a decisive counter-example to the claim that an actual infinite cannot exist. But I see no reason to accept this counter-example, for it begs the question by assuming Platonism or realism to be true. But why make this assumption? In order to defeat this putative defeater, all the defender of the kalam argument has to do is deny that Platonism has been shown to be true. In other words, the burden of proof rests on the objector to prove that realism is true before his counter-example can even be launched. A conceptualist understanding of abstract objects combined with the simplicity of God’s cognition is at least a tenable alternative to Platonism. Indeed, historically, this has been the mainstream theistic tradition, from Boethius through Ockham. In fact, theists had better hope that there is such an alternative to Platonism, since the latter entails a metaphysical pluralism which leaves God as but one infinitesimal being among an unimaginable plenitude of beings existing independently of Him, in contradiction to divine aseity and the doctrine of creatio ex nihilo.

Sometimes it is said that we can find counter-examples to the claim that an actually infinite number of things cannot exist, so that premiss (2. 1. 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. While one can continue to divide any distance for as long as one wants, such a series is merely potentially infinite, in that infinity serves as a limit which one endlessly approaches but never reaches. If one assumes that any distance is already composed out of an actually infinite number of parts, then one is begging the question. The objector is assuming what he is supposed to prove, namely that there is a clear counter-example to the claim that an actually infinite number of things cannot exist.

Finally, it is sometimes objected that God’s existence entails the existence of an actual infinite. But this seems far from inevitable. In general, God’s infinity is a qualitative, not a quantitative, notion. It has nothing to do with an infinite number of definite and discrete finite particulars. Attributes like omnipotence, moral perfection, timelessness, aseity, omnipresence, and so on just are not quantitative notions.[12] Even omniscience need not entail that God has an actually infinite number of true beliefs if, with William Alston and in line with Christian tradition, we take God’s knowledge to be non-propositional in nature, though represented by us finite cognizers as knowledge of individual propositions.[13] In short, the objections typically loged against the first premise are lees than decisive.

The second premise (2. 1. 2) states that an infinite temporal regress of events is an actual infinite. The second premise 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, spatio-temporal 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 events had a beginning.  And this implies the second premise of the original syllogism of the kalam cosmological argument.

2. 2. Second Argument

The second argument which we shall consider is the argument based on the impossibility of forming an actual infinite bysuccessive addition. It may be formulated as follows:

2. 2. 1. The temporal series of events is a collection formed by successive addition.

2. 2..2. A collection formed by successive addition cannot be an actual infinite.

2. 2. 3. Therefore, the temporal series of events cannot be an actual infinite.

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.

Premiss (2. 2. 1) presupposes once again a tensed teory 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 co-exist. 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 manifold, all of whose members are equally real. Rather the members of the series come to be and pass away one after another.

Premiss (2. 2. 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 will 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 Betrand 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 a tensed 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 which is finitely distant from the last recorded day.[14]  

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? 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 slight-of-hand trick like Zeno's paradoxes of motion. Even though Achilles must pass through an infinite number of halfway points in order to cross the stadium, somehow he manages to do so! But such a response 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 which 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, it remains mysterious how we could have traversed 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 which I am 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 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 events is not beginningless.

2. 3. Third Argument

The third argument for the universe's beginning 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 which 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 pre-existing, 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”[15] 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 which is not eternal in the past, but which 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 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.”[16]  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.”[17] He finally felt forced to conclude, “The beginning seems to present insuperable difficulties unless we agree to look on it as frankly supernatural.”[18]

Sometimes objectors appeal to non-Standard models of the expanding universe in an attempt to avert the absolute beginning predicted by the Standard Model. But while such theories are possible, it has been the overwhelming verdict of the scientific community than none of them is more probable than the Big Bang theory. The devil is in the details, and once we get down to specifics we find that there is no mathematically consistent model which has been so successful in its predictions or as corroborated by the evidence as the traditional Big Bang theory.[19] For example, some theories, like the Oscillating Universe (which expands and re-contracts forever) or the Chaotic Inflationary Universe (which continually spawns new universes), do have a potentially infinite future but turn out to have only a finite past. Vacuum Fluctuation Universe theories (which postulate an eternal vacuum out of which our universe is born) cannot explain why, if the vacuum was eternal, we do not observe an infinitely old universe. The Quantum Gravity Universe theory propounded by the famous physicist Stephen Hawking, if interpreted realistically, still involves an absolute origin of the universe even if the universe does not begin in a singularity, as it does in the Standard Big Bang theory. In sum, according to Hawking, "Almost everyone now believes that the universe, and time itself, had a beginning at the Big Bang."[20]

2. 4. Fourth Argument

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.  Now our interest in the law is 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. What this seems to imply then is 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.

There are two possible types of heat death for the universe. If the universe will eventually re‑contract, it will die a “hot” death.  As it contracts, the stars gain energy, causing them to burn more rapidly so that they finally explode or evaporate. As everything in the universe grows closer together, the black holes begin to gobble up everything around them, and eventually begin themselves to coalesce. In time, all the black holes finally coalesce into one large black hole that is coextensive with the universe, from which the universe will never re‑emerge.

On the other hand if, as is more likely, the universe will expand forever, then its death will be cold, as the galaxies turn their gas into stars, and the stars burn out. At 10³⁰ years the universe will consist of 90% dead stars, 9% supermassive black holes formed by the collapse of galaxies, and 1% atomic matter, mainly hydrogen. Elementary particle physics suggests that thereafter protons will decay into electrons and positrons so that space will be filled with a rarefied gas so thin that the distance between an electron and a positron will be about the size of the present galaxy. Eventually all black holes will completely evaporate and all the matter in the ever‑expanding universe will be reduced to a thin gas of elementary particles and radiation. Equilibrium will prevail throughout, and the entire universe will be in its final state, from which no change will occur.

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.”[21]

Some people have tried to escape this conclusion by adopting an oscillating model of the universe which never reaches a final state of equilibrium.  But even apart from the physical and observational problems plaguing such a model, the thermodynamic properties of this model imply the very beginning of the universe that its proponents sought to avoid. For entropy increases from cycle to cycle in such a model, which has the effect of generating larger and longer oscillations with each successive cycle. Thus, as one traces the oscillations back in time, they become progressively smaller until one reaches a first and smallest oscillation. Hence, the oscillating model has an infinite future, but only a finite past. In fact, it is estimated on the basis of current entropy levels that the universe cannot have gone through more than 100 previous oscillations.

Even if this difficulty were avoided, a universe oscillating from eternity past would require an infinitely precise tuning of initial conditions in order to last through an infinite number of successive bounces. A universe rebounding from a single, infinitely long contraction is, if entropy increases during the contracting phase, thermodynamically untenable and incompatible with the initial low entropy condition of our expanding phase. Postulating an entropy decrease during the contracting phase in order to escape this problem would require us to postulate inexplicably special low entropy conditions at the time of the bounce in the life of an infinitely evolving universe. Such a low entropy condition at the beginning of the expansion is more plausibly accounted for by the presence of a singularity or some sort of quantum creation event.

So whether one adopts a re‑contracting model, an ever‑expanding model, or an oscillating model, thermodynamics suggests that the universe had a beginning. According to P. C. W. Davies, the universe must have been created a finite time ago and is in the process of winding down. Prior to the creation, says Davies, the universe simply did not exist.  Even though we may not like it, he concludes, we must say that the universe’s energy was somehow simply “put in” at the creation as an initial condition.[22]

3. The Universe Has a Cause

From the first premiss—that whatever begins to exist has a cause—and the second premiss—that the universe began to exist—it follows logically that the universe has a cause. This conclusion ought to stagger us, to fill us with awe, for it means that the universe was brought into existence by something which is greater than and beyond it.

But what is the nature of this first cause of the universe? A conceptual analysis of what properties must be possessed by such an ultra-mundane cause enables us to recover a striking number of the traditional divine attributes. An analysis of what it is to be cause of the universe reveals that

4. If the universe has a cause, then an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.

From (3) and (4), it follows that

5. Therefore, an uncaused, personal Creator of the universe exists, who sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful.

As the cause of space and time, this entity must transcend space and time and therefore exist atemporally and non-spatially, at least sans 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 out of nothing.

Finally, and most strikingly, such a transcendent cause is plausibly to be regarded as personal. Three reasons can be given for this conclusion. First, as Swinburne points out, there are two types of causal explanation: 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 which 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.