2. Timelessness without Creation

OUR STUDY OF GOD and time is nearly complete. We have examined rival conceptions of time, the dynamic versus the static, and have concluded that time is dynamic: Tensed facts and temporal becoming are real. But then it follows from God’s creative activity and omniscience that, given the existence of a temporal world, God is also temporal. God quite literally exists now.

Since God never begins to exist nor ever ceases to exist, it follows that God is omnitemporal. He exists at every time that ever exists; that is to say, He endures throughout all eternity. This might seem to imply that God has existed for infinite time in the past and will exist for infinite time in the future. But what if the temporal world has not always existed? According to the Christian doctrine of creation, the world is not infinite in the past but was brought into being out of nothing a finite time ago. Did time itself also have a beginning? Did God exist literally before creation or is He timeless without the world?

According to current cosmological theory, time and space came into existence with the Big Bang. The standard model of the expanding universe predicts that in the past the universe was denser than it is today. This has implications for the finitude of past time. As the British physicist P. C. W. Davies explains,

If we extrapolate this prediction to its extreme, we reach a point when all distances in the universe have shrunk to zero. An initial cosmological singularity therefore forms a past temporal extremity to the universe. We cannot continue physical reasoning or even the concept of spacetime, through such an extremity. For this reason most cosmologists think of the initial singularity as the beginning of the universe. On this view the big bang represents the creation event, the creation not only of all the matter and energy in the universe, but also of spacetime itself.¹

On such an understanding, the universe did not spring into being at a point in a previously existing empty space. Rather space and time themselves came into being along with the universe, which implies creation out of absolutely nothing. Thus, Barrow and Tipler assert, “At this singularity, space and time came into existence; literally nothing existed before the singularity, so, if the Universe originated at such a singularity, we would truly have a creation ex nihilo.”²

This feature of the standard Big Bang model has appeared especially baffling to philosophically minded cosmologists, particularly those with an atheistic bent. For example, the Russian astrophysicist Andrei Linde acknowledges quite frankly the problem the standard model poses for him: “The most difficult aspect of this problem is not the existence of the singularity itself, but the question of what was before the singularity. . . . This problem lies somewhere at the boundary between physics and metaphysics.”³ In order to avoid this question, Linde therefore proposed an eternal inflationary model of the universe, according to which our observable universe was birthed by a prior universe, which was born of a yet prior universe, and so on ad infinitum. But in 1994 two other cosmologists, Arvind Borde and Alexander Vilenkin, showed that inflationary scenarios such as Linde’s cannot avoid an initial singularity. They conclude, “A physically reasonable spacetime that is eternally inflating to the future must possess an initial singularity. . . . The fact that inflationary spacetimes are past incomplete forces one to address the question of what, if anything, came before?”⁴

Other cosmologists have tried to eliminate the initial space-time singularity by introducing speculations about quantum gravity, as in Stephen Hawking’s famous theory. On such models, imaginary numbers are assigned to the time variable in the equations, which has the effect of suppressing the singular point. But as Hawking himself acknowledges, such models in “imaginary time” are not realistic descriptions of the universe but have mere instrumental value.⁵ “When one goes back to the real time in which we live,” Hawking admits, “there will still appear to be singularities.”⁶ In any case, as Barrow emphasizes, such models still involve a merely finite past and so imply the beginning of space and time: “This type of quantum universe has not always existed; it comes into being just as the classical cosmologies could, but it does not start at a Big Bang where physical quantities are infinite. . . .”⁷ Thus, the beginning of time is not avoided.

So today, in Hawking’s words, “almost everyone now believes that the universe, and time itself, had a beginning at the big bang.”⁸ This consensus seems to lend strong support to the view that neither events nor time existed prior to creation. As physicist David Park says, “It is deceptively easy to imagine events before the big bang . . . , but in physics there is no way to make sense of these imaginings.”⁹

The fly in the ointment, however, is Park’s phrase “in physics.” For we have been wont to emphasize throughout this study that time as it plays a role in physics is at best a measure of time, not time itself. It is perfectly coherent to imagine non-physical events prior to the Big Bang, whether mental events in God’s stream of consciousness or events in angelic realms created by God prior to the physical universe. At most, then, the physical evidence proves that physical time had a beginning at the Big Bang, not that time itself so began. In order to explore that question, we shall have to have recourse to metaphysical, rather than physical, arguments.

What reasons, then, might be given for thinking that past time is infinite? We have seen that Newton believed space and time to be infinite because they are the effects of an omnipresent and eternal God.¹⁰ Newton assumed that God cannot exist timelessly and spacelessly. But he gave no arguments at all for this presupposition. We have seen, to the contrary, that there is no reason to think that a personal being could not exist timelessly in the absence of any physical universe.¹¹ So long as God exists changelessly, He can, in the absence of a temporal world, exist timelessly.

Is there, then, some non-theological reason to think that time is infinite? Oxford University’s Richard Swinburne thinks so.¹² He argues that at every instant it is true that “There were swans or there were not swans.” Necessarily, one of these alternatives is true. But whichever alternative is true, there must be a past at that instant, since the statement is in the past tense. Thus, there cannot be an absolutely first instant of time. Time is unbounded and therefore infinite.

This argument, however, is multiply flawed. In the first place, at best all the argument proves is that every instant of time is preceded by another instant and that therefore there is no first instant of time. But there being no first instant of time is perfectly compatible with the finitude of the past. Compare the series of fractions converging toward zero as a limit: . . . 1/8, 1/4, 1/2. For any fraction you pick, there is always a fraction before it. There is no first fraction in such a series. Nonetheless, the distance covered by all the fractions is still finite. If we let each fraction represent an instant, then we can see that in, say, the first half-minute of time, any instant you pick is preceded by another instant, but the past is not for all that infinite—on the contrary, it is only thirty seconds long. In short, for time to have a beginning, it does not have to have a beginning point. Time begins to exist just in case there is some finite interval of time which is not preceded by an interval of equal length. Thus, if time had a beginning, there would be a first hour, or a first minute, or a first second, but there need not be a first instant.

In the second place, the argument fails in any case to show that there cannot be a first instant of time. Swinburne argues that the truth of past-tense statements requires that there be a past. But specialists in the logic of tensed sentences have shown that this is not correct. A statement such as “There were swans” can be analyzed logically as asserting, “It was the case that there are swans.” Such a statement does imply a past. But a negative statement such as “There were no swans,” when asserted at the first instant of time, should not be analyzed as asserting, “It was the case that there are no swans,” but rather as asserting, “It was not the case that there are swans.” Such a statement does not imply a past, for it denies that it was the case that swans exist. Hence, such a statement can be true at a first instant of time.

Thus, we have not seen any good reasons for thinking that the past is or must be infinite.

Are there any good reasons for thinking that the past is finite? There is a long tradition in Western philosophy of arguments for the finitude of the past, and while most philosophers today are skeptical of such proofs, it does seem to me that some of these arguments, at least, are quite plausible and that the standard refutations of them fail.¹³

The Impossibility of an Actual Infinite

Consider, for example, the argument based on the impossibility of the existence of an actual infinite. This argument may be formulated as follows:

1. An actual infinite cannot exist.

2. A beginningless series of equal past intervals of time is an actual infinite.

3. Therefore, a beginningless series of equal past intervals of time cannot exist.

But if there cannot be a beginningless series of equal past intervals of time, then time must have begun to exist.

In order to understand this argument, let us examine each step individually.

1. An actually infinite number of things cannot exist. In order to understand this first step, we need to understand what an actual infinite is. There is a difference between a potential infinite and an actual infinite. A potential infinite is a collection that is increasing toward infinity as a limit but never gets there. Such a collection is really indefinite, not infinite. For example, any finite distance can be subdivided into potentially infinitely many parts. You can just keep on dividing parts in half forever, but you will never arrive at an actual “infinitieth” division or come up with an actually infinite number of parts. By contrast, an actual infinite is a collection in which the number of members really is infinite. The collection is not growing toward infinity; it is infinite, it is “complete.” This sort of infinity is used in set theory to designate sets that have an infinite number of members, such as {1, 2, 3 . . . }. Now the argument is, not that a potentially infinite number of things cannot exist, but that an actually infinite number of things cannot exist. For if an actually infinite number of things could exist, this would spawn all sorts of absurdities.

Perhaps the best way to bring this home is by means of an illustration. Let me use one of my favorites, Hilbert’s Hotel, a product of the mind of the great German mathematician David Hilbert.¹⁴ 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 the new guest is turned away. 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 #1 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 rooms. “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 less person in the hotel? Not according to the mathematicians—but just ask Housekeeping! 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 less people in the hotel—but don’t talk to Housekeeping! 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 is absurd. As one person remarked, if Hilbert’s Hotel could exist, it would have to have a sign posted outside: no vacancy—guests welcome. The above sorts of absurdities show that it is impossible for an actually infinite number of things to exist. There is simply no way to avoid these absurdities once we admit the possibility of the existence of an actual infinite. Students sometimes react to such absurdities as Hilbert’s Hotel by saying that we really don’t 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, so that these absurdities result precisely because we do understand the notion of a collection with an actually infinite number of members.

Critics have raised various objections to premise (1). For example, the philosopher Wallace Matson objects that (1) must mean that an actual infinite is logically impossible; but it is easy to show that such a collection is logically possible. For example, the set of negative numbers { . . . , -3, -2, -1} is an actually infinite collection with no first member.¹⁵ Similarly, the Australian philosopher Graham Oppy insists that because infinite set theory is a logically consistent system, it must be possible for an actual infinite to exist.¹⁶

The error of these thinkers lies in their failure to distinguish between what philosophers have called “strict logical possibility” and “broad logical possibility.” Something is strictly logically possible if it does not involve a contradiction. Something may be strictly logically possible, however, without being capable of existing in reality. For example, there is no logical contradiction in asserting, “Something has a shape but not a size,” “An event occurs before itself,” or, “Something came into existence without a cause,” but all of these statements are plausibly broadly logically impossible. Broad logical possibility is thus usually identified with metaphysical possibility, that is to say, with what is possible in reality. Now infinite set theory is strictly logically consistent, granted its axioms and rules, but that does nothing to prove that such a system can exist in the real world. This fact is especially evident when it comes to mathematical operations such as subtraction and division, which transfinite arithmetic must prohibit in order to maintain logical consistency. While we can slap the hand of the mathematician who attempts such operations with infinite numbers, we cannot in reality prevent people from checking out of a Hilbert’s Hotel with all the attendant absurdities.

One should also note that even the mathematical existence of the actual infinite cannot just be taken for granted. For the small, but brilliant, school of intuitionist mathematicians denies even mathematical infinities. In their view the number series is merely potentially infinite, not actually infinite. So long as intuitionism remains a viable position in the philosophy of mathematics, one cannot justifiably appeal to mathematical infinites as counter-examples to premise (1).

Some critics have claimed that even the existence of a potential infinite implies the existence of an actual infinite. For example, Rucker states that in order for the intuitionist to regard the number series as potentially infinite via the operation of counting, there must exist a “definite class of possibilities” which is actually infinite.¹⁷ Similarly, Sorabji thinks that a line’s being potentially infinitely divisible implies that there is an actually infinite number of positions where the line could be divided.¹⁸

But these inferences are mistaken. Infinite divisibility does not imply an infinite number of pre-existing points unless one presupposes that a line is already composed of an infinite number of points. But if an extension is logically prior to any points one specifies in it, potential infinite divisibility does not imply the existence of points. From the truth that “Possibly, there is some point at which a line is divided,” it does not follow that “There is some point at which the line is possibly divided.” The same is the case for numbers and counting.¹⁹

The late Oxford University philosopher J. L. Mackie disputed premise (1) because the so-called absurdities of the existence of an actual infinite are resolved once we understand that for infinite groups Euclid’s axiom “The whole is greater than its part” does not hold as it does for finite groups.²⁰ Similarly, Quentin Smith comments that once we understand that an infinite set has a proper subset which has the same number of members as the set itself, then the purportedly absurd situations become “perfectly believable.”²¹ But far from being the solution, this is precisely the problem. Because in infinite set theory this axiom is denied, one winds up with all sorts of absurdities such as Hilbert’s Hotel when one tries to translate that theory into reality. The issue is not whether these consequences would result if an actual infinite were to exist; we agree that they would. The question is whether such consequences are metaphysically possible. That question is not resolved by reiterating that they would be possible if an actual infinite could exist. Moreover, not all the absurdities result from a denial of Euclid’s axiom: The absurdities illustrated by guests checking out of Hilbert’s Hotel result from subtraction of infinite quantities, which set theory must prohibit to maintain logical consistency.

Hilbert himself, who declared that Cantor’s infinite set theory is “one of the supreme achievements of purely intellectual human activity,” and that “No one shall drive us out of the paradise which Cantor has created for us,”²² nevertheless also believed that that paradise exists only in the realm of the intellect: “the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought. . . . The role that remains for the infinite to play is solely that of an idea. . . .”²³ The great philosopher Ludwig Wittgenstein agreed—though with considerably less enthusiasm for Cantor’s paradise. Reacting to Hilbert’s remark about the Cantorian paradise, Wittgenstein quipped, “I would say, ‘I wouldn’t dream of trying to drive anyone from this paradise.’ I would do something quite different: I would try to show you that it is not a paradise—so that you’ll leave of your own accord. I would say, ‘You’re welcome to this; just look about you.’”²⁴ Once we take a sober look about us at the absurd consequences of such a world, we shall not regret leaving it to exist only in the imagination.

Premise (2) seems pretty obvious. If time never had a beginning, then if one were to add up all the temporal intervals of some finite extent, say, seconds, then there will have existed an actually infinite number of seconds prior to the present second.

As I say, this seems pretty obvious. Nevertheless, some critics of the argument have denied premise (2), claiming that the past is a potential infinite only. Swinburne, for example, admits that it makes little sense to think that the past could have an end but no beginning, but he advises that we avoid this puzzle by numbering the events of the past by beginning in the present and proceeding to count backwards in time.²⁵ In this way the past is converted from a series with no beginning but an end, into a series with a beginning but no end, which is unobjectionable.

It seems to me that this solution is clearly wrong-headed. In order for the past to be a mere potential infinite, it would have to be finite, but growing in a backwards direction. This contradicts the nature of time and becoming. Swinburne confuses the mental regress of counting with the real progress of time itself. The direction of time itself is from past to future, so that if the series of past seconds is beginningless, then an actually infinite number of seconds have elapsed.

Thus it seems to me that the objections lodged against the argument’s premises are less plausible than those premises themselves. Given the truth of the two premises, it follows that a beginningless series of equal past intervals of time cannot exist. Thus, time must have had a beginning.

THE IMPOSSIBILITY OF THE FORMATION OF AN ACTUAL INFINITE

But suppose the above is altogether wrong. Suppose that an actual infinite can exist. That still does not imply that the past can be actually infinite. For we now must consider how an actual infinite can come to exist. And here we confront the argument for the finitude of the past based on the impossibility of the formation of an actual infinite by successive addition. This argument goes as follows:

1. A collection formed by successive addition cannot be actually infinite.

2. The series of equal past intervals of time is a collection formed by successive addition.

3. Therefore, the series of equal past intervals of time cannot be actually infinite.

Once again, if the series of equal, past temporal intervals is not actually infinite, then the past must be finite.

Premise (1) is the crucial step in this argument. One cannot form an actually infinite collection of things by successively adding one member after another. Since one can always add one more before arriving at infinity, it is impossible to reach actual infinity. Sometimes this is called the impossibility of “counting to infinity” or “traversing the infinite.” It is important to understand that this impossibility has nothing to do with the amount of time available: It belongs to the nature of infinity that it cannot be so formed.

Now someone might say that while an infinite collection cannot be formed by beginning at a point and adding members, nevertheless an infinite collection could be formed by never beginning but ending at a point, that is to say, ending at a point after having added one member after another from eternity. But this method seems even more unbelievable than the first method. If one cannot count to infinity, how can one count down from infinity? If one cannot traverse the infinite by moving in one direction, how can one traverse it simply by moving in the opposite direction?

Indeed, the idea of a beginningless series ending in the present seems absurd. To give just one illustration: Suppose we meet a man who claims to have been counting from eternity and is now finishing: . . . , -3, -2, -1, 0. We could ask, why did he not finish counting yesterday or the day before or the year before? By then an infinite time had already elapsed, so that he should already have finished by then. Indeed, at no point in the infinite past could we ever find the man finishing his countdown, for at any point he would already be done! In fact, no matter how far back into the past we go, we can never find the man counting at all, for at any point we reach he will have already finished. But if at no point in the past do we find him counting, this contradicts the hypothesis that he has been counting from eternity. This illustrates the fact that the formation of an actual infinite by successive addition is equally impossible whether one proceeds to or from infinity.

Sorabji has objected that, while it is true that at any point in the past someone counting down from infinity will have counted an infinity of negative numbers, there is no reason to think that he will have counted all the negative numbers.²⁶ David Conway also claims that there is no good reason to think that if someone had counted an infinite number of numbers by yesterday, then he would have finished his countdown of all the numbers by yesterday.²⁷ But these objections misunderstand the argument. At whatever number the countdown of the negative numbers ends—say, -17 or -3—an actual infinite will have been completed by successive steps, and we may ask why that task was not accomplished by yesterday. The central contention of the argument is not that if someone had counted an infinite number of numbers by yesterday, then he would have finished counting all the numbers by yesterday, but rather that if someone would have finished his countdown of the negative numbers by today, then he would have already finished that same countdown by yesterday. The defender of the infinite past claims that the seemingly impossible task of counting all the negative numbers is possible because for every negative number to be counted there is a corresponding moment of past time in which to count it. But that is true at every moment of the infinite past! Thus, if the task could be completed today, it becomes inexplicable why it was not already completed yesterday, or the day before yesterday, ad infinitum. On Sorabji and Conway’s position, it becomes inexplicable why the counter should finish at any number that he does.

Moreover, a deeper absurdity now surfaces: Suppose we have two counters, one man counting a negative number every second and the other counting a negative number every hour. Since the number of past seconds and the number of past hours is identical (if the past is infinite), both men complete their countdown at the same time. But this is absurd, since one man is counting down the numbers 3,600 times faster than the other!

Critics typically allege that premise (1) illicitly assumes an infinitely distant starting point in the past and then pronounces it impossible to travel from that point to today.²⁸ If we take the notion of infinity “seriously,” Mackie says, then we must say that in the infinite past there would be no starting point whatever, not even an infinitely distant one. Yet from any given point in the past, there is only a finite distance to the present.

But it seems to me that Mackie’s allegation that the argument presupposes an infinitely distant starting point in the past is entirely groundless. As I have explained it, the argument concerns the possibility of completing a task such as counting down all the negative numbers in succession, a series which has no beginning. Indeed, the fact that the past has no beginning at all, not even an infinitely distant one, makes it even more bewildering how the past could have been formed by successive addition. It is like trying to jump out of a bottomless pit! And Mackie’s observation that from any point in the past the distance to the present is finite is quite correct but simply irrelevant to the discussion. For the issue is how the whole infinite past can be formed by successive addition, not merely some finite portion of it. Does Mackie think that because every finite segment of the past can be formed by successive addition, the whole infinite past can be formed by successive addition? That is as logically fallacious as saying that because every part of an elephant is light in weight, therefore the whole elephant is light in weight.

It seems to me, therefore, that premise (1), despite the objections of its detractors, is more plausible than its denial.

As for premise (2), the only persons who deny this step of the argument are the proponents of a static conception of time. Since they reject the reality of temporal becoming, they deny that the past was formed by successive addition. All times exist tenselessly, and there is no lapse of time. But our lengthy inquiry into the nature of time in chapters 4 and 5 brought us to the conclusion that the static conception of time is wrong. Time is dynamic, and therefore the past has been formed sequentially, one moment elapsing after another. If the past is infinite, then God has lived through an infinite number of past temporal intervals one at a time in order to arrive at today. But such a traversal of the infinite past, as we have seen, seems absurd.

From the two premises of the argument it again follows that the series of equal past intervals of time cannot be actually infinite.

We thus have what seem to me to be two quite plausible, independent arguments for the finitude of time. The objections of the argument’s critics do not strike me as compelling, so that the premises of the argument remain more plausible than their denials.

WHY DID GOD NOT CREATE THE WORLD SOONER?

Moreover, there is a third, peculiarly theological argument for the finitude of past time which bedevils proponents of Newtonian eternity, namely, why did God not create the world sooner? Leibniz pressed this question in his famous correspondence with Newton’s follower Samuel Clarke.²⁹ On Leibniz’s relational view of time, time does not exist in the absence of events. Hence, time begins at the moment of creation, and it is simply maladroit to ask why God did not create the world sooner, since there is no “sooner” prior to the moment of creation. Time comes into existence with the universe, and so it makes no sense to ask why it did not come into being at an earlier moment. But on Newton’s view, God has endured through an infinite period of creative idleness up until the moment of creation. Why did He wait so long?

This problem can be formulated as follows (letting t represent any time prior to creation and n represent some finite amount of time):

1. If the past is infinite, then at t God delayed creating until t + n.

2. If at t God delayed creating until t + n, then He must have had a good reason for doing so.

3. If the past is infinite, God cannot have had a good reason for delaying at t creating until t + n.

4. Therefore, if the past is infinite, God must have had a good reason for delaying at t, and God cannot have had a good reason for delaying at t.

5. Therefore, the past is not infinite.

Premise (1) is obviously true, given a dynamic view of time. At t God could have created the world. But He did not. He deliberately waited until a later time. He self-consciously refrained from creating at t and delayed His action until t + n.

Premise (2) seems to be plausibly true. It does not depend for its truth on the validity of some broader Principle of Sufficient Reason (a controversial principle defended by Leibniz to the effect that everything has a reason why it is the way it is). Rather it states merely that in this specific case, God, in deciding to delay creating the world until some later time, must have had some good reason for doing so. Notice also that premise (2) does not presuppose either the finitude or the infinitude of the past. It merely asserts that if at some moment prior to creation God deliberately deferred creating until a later moment, then He must have had a reason for doing so. A perfectly rational person does not delay some action which he wills to undertake unless he has a good reason for doing so. Since God is a supremely rational being, premise (2) strikes me as eminently plausible.

That brings us to premise (3), which again seems obviously true. As Leftow points out in his interesting analysis of this problem,³⁰ if God comes to acquire at some moment a reason to create the world, this reason must be due to some change either in God or in the world. The only change going on outside God is the lapse of absolute time itself. But since all moments of time are alike, there is nothing special about the moment of creation which would cause God to delay creating at t until t + n had arrived. After all, at t God has already waited for infinite time to create the world, so why wait any longer? There is nothing about t + n that makes it a more appropriate time to create than t. As for God Himself, He has from time immemorial been perfectly good, omniscient, and omnipotent, so that there seems to be no change that could occur in Him that would prompt Him to create at some time rather than earlier. Thus, it seems impossible that God should acquire some reason to create which He did not always have; nor by the same token does it seem possible for Him to have always had a reason for singling out t + n as the moment at which to create.

Leftow tries to escape this reasoning by suggesting that God’s reason for delaying creation is the joy of anticipation of creating. Just as we find joy in the anticipation of some great good, so God can enjoy the anticipation of creation.

But why would God delay creating for infinite time? Having already at t anticipated for infinite time His creating the world, why would He yet delay even longer until t + n? Why did He quit anticipating at t + n instead of earlier or later? Leftow answers that there comes a point at which the joy of anticipating begins to fade. So God will not want to delay creating beyond that point. He knows from all eternity precisely when His anticipation peaks and so will not delay beyond that point. Leftow imagines a sort of pleasure curve charting God’s rising and falling anticipation of creation (Fig. 6.1).

Fig. 6.1: God’s anticipatory pleasure rises from a low at t = –∞ to a peak value before declining toward a low at t = +∞.

God will create the world at the moment when His anticipatory pleasure peaks.

We might be skeptical of such a portrayal of God’s anticipatory pleasure as grossly anthropomorphic; but never mind. The more serious problem is that Leftow’s scheme does not explain anything. For we may still ask, “Why does God’s anticipatory pleasure peak at t + n instead of at t?” Leftow answers that since the curve displayed in Fig. 6.1 extends infinitely into the past and future, it cannot be “shifted” in either direction. It is fixed in time and so must peak when it does.

This answer fails to appreciate the paradoxical nature of the actual infinite. Just as Hilbert’s Hotel can accommodate infinitely many new guests simply by shifting each guest into a room with a number twice his own, so God’s pleasure curve, though infinitely extended, can be shifted backward in time simply by dividing every value of the x-coordinate by two. Since the past is supposed to be actually infinite, there is no danger of “scrunching up” the earlier slope of the curve by such a backward shift. If such a shift seems impossible, this only calls into question once again the infinity of the past. But if the past is infinite, there is no problem. Therefore, Leftow has not provided a good reason for why God at t should delay creating until t + n. After all, by t God has already had eternity to anticipate creating the world.

But if premises (1)-(3) are true, then (4) and (5) logically follow. Accordingly, it seems to me that Leibniz was quite correct in opposing Newton with respect to the infinity of God’s past.

We thus seem to have three good arguments for denying the infinity of the past and holding to the beginning of time: the impossibility of the existence of an actual infinite; the impossibility of the formation of an actual infinite by successive addition; and the impossibility of God’s delaying creation from eternity. For all these reasons it is plausible to believe that time began to exist and that, therefore, God has not existed for infinite time.

But now we are confronted with an extremely bizarre situation. God exists in time. Time had a beginning. God did not have a beginning. How can these three statements be reconciled? If time began to exist—say, for simplicity’s sake, at the Big Bang—then in some difficult-to-articulate sense God must exist beyond the Big Bang, alone without the universe. He must be changeless in such a state; otherwise time would exist. And yet this state, strictly speaking, cannot exist before the Big Bang in a temporal sense, since time had a beginning. God must be causally, but not temporally, prior to the Big Bang. With the creation of the universe, time began, and God entered into time at the moment of creation in virtue of His real relations with the created order. It follows that God must therefore be timeless without the universe and temporal with the universe.

Now this conclusion is startling and not a little odd. For on such a view, there seem to be two phases of God’s life, a timeless phase and a temporal phase, and the timeless phase seems to have existed earlier than the temporal phase. But this is logically incoherent, since to stand in a relation of earlier than is by all accounts to be temporal.³¹

How are we to escape this apparent antinomy? One possibility is suggested by a re-examination of the three arguments we presented for the finitude of the past. Strictly speaking none of those arguments reached the conclusion, “Therefore, time began to exist.” Rather what they proved is that there cannot have been an infinite number of equal temporal intervals in the past. But if we can conceive of a time which is not divisible into intervals, a sort of undifferentiated time, then the arguments are compatible with the existence of that sort of time prior to creation. God existing alone without the universe would exist in an amorphous time before the beginning of divisible time as we know it. A number of philosophers associated with Oxford University have defended such a view of divine eternity, so that one could aptly speak of the Oxford school on this issue.³²

Members of the Oxford school tend to embrace the doctrine of metric conventionalism with respect to time. The metric of time has to do with the measure of time—whether two separate intervals of time can be said to be equal or unequal in extent. Conventionalism is the view that there is no objective fact about this matter. There is no objective fact that two separate temporal intervals are equal; it all depends on what measures we use. In the absence of any measures, there is no objective fact that one interval is longer or shorter than another distinct interval. Thus, prior to creation it is impossible to differentiate between a tenth of a second and ten trillion years. There is no moment one hour, say, before creation. Time literally lacks any intrinsic metric.

Such an understanding of God’s time prior to creation seems quite attractive. It enables us to speak literally of God’s existing before creation. And yet we seem to avoid the problematic claim that God has endured through infinite time prior to creating the universe.

Nevertheless, a closer inspection of the view reveals difficulties. Metric conventionalism is the view that there is no objective fact of the matter concerning the comparative lengths of separate temporal intervals. But metric conventionalism does not hold that there really are no intervals of time or that no intervals can be objectively compared with respect to length. Thus, even in a metrically amorphous time, there are objective factual differences of length for certain temporal intervals (Fig. 6.2).

Fig. 6.2: Intervals in a metrically amorphous time prior to the moment of creation t=0.

According to metric conventionalism, there is no fact of the matter concerning the comparative lengths dc and cb or db and ca. But there is an objective difference in length between da and ca or cb and ca, namely, da > ca and cb < ca. For in the case of intervals which are proper parts of other intervals, the proper parts are factually shorter than their encompassing parts.

But this implies that prior to creation God has endured through a beginningless series of longer and longer intervals. In fact we can even say that such a time must be infinite. For the past is finite if and only if there is a first interval of time. (An interval is first if there exists no interval earlier than it, or if there exists no interval greater than it but having the same end point.) The metrically amorphous past is clearly not finite. But is it infinite? The past is infinite if and only if there is no first interval of time and time is not circular. Thus, the amorphous time prior to creation would be infinite, even though we cannot compare the lengths of separate intervals within it. Thus, all the difficulties of an infinite past return to haunt us.

The shortcoming of the Oxford school is that it has not been radical enough. It proposes to dispense with the metric of time while still retaining the geometry of time as a line. Since on a geometrical line intervals can be objectively distinguished and, when included in one another, compared in length, time is not sufficiently undifferentiated to avoid the problems attending an infinite past. What must be done is to dissolve the geometrical structure of time as a line. One must maintain that prior to creation there literally are no intervals of time at all. In such a time, there would be no earlier and later, no enduring through successive intervals and, hence, no waiting, no temporal becoming, nothing but the eternal “now.” This state would pass away as a whole, not successively, at the moment of creation, when time begins. It would be an undifferentiated “before,” followed by a differentiated “after.”

The problem is that such a changeless, undifferentiated state looks suspiciously like a state of timelessness! It seems to have the topology of a point, the traditional representation of timeless eternity. The only sense in which such a state can be said to be temporal is that it exists literally before God’s creation of the world and the beginning of differentiated time.

Perhaps this realization ought to prompt us to reconsider the alternative that God is simply timeless without creation and temporal subsequent to creation. Detractors of this position simply assume that if God’s life lacks earlier and later parts, then it has no phases. But why could there not be two phases of God’s life, one timeless and one temporal, which are not related to each other as earlier and later? Critics have perhaps too quickly assumed that if any phase of God’s life is timeless, the whole must be timeless.

We have already seen that a state of undifferentiated time looks very much like timelessness. This impression is reinforced by recalling the dynamic theory of time. On a static theory of time, it is very tempting to picture the two phases of God’s life as equally existent, bounded by the moment of creation, the one earlier and the other later. But given a dynamic theory of time, this picture is a misrepresentation. In reality God existing without creation is changelessly alone, and no event disturbs this complete tranquility. There is no before, no after, no temporal passage, no future phase of His life. There is just God.

To claim that time would exist without the universe in virtue of the beginning of the world seems to postulate a sort of backward causation: The occurrence of the first event causes time to exist not only with the event but also before it. But on a tensed theory of time, such retrocausation is metaphysically impossible, for it amounts to something’s being caused by nothing, since at the time of the effect the retro-cause in no sense exists.³³

The impression that God without creation is timeless can be reinforced by a thought experiment. Imagine God existing changelessly alone in a possible world in which He refrains from creation. In such a world, God is reasonably conceived to be timeless. But God, actually existing alone without creation, is no different than He would be in such a possible world, even though in the actual world He becomes temporal by creating. Apart from backward causation, there seems to be nothing that would produce a time prior to the moment of creation.

Perhaps an analogy from physical time will be illuminating. The initial Big Bang singularity is not considered to be part of time, but to constitute a boundary to time. Nevertheless, it is causally connected to the universe. In an analogous way, perhaps we could say that God’s timeless eternity is, as it were, a boundary of time which is causally, but not temporally, prior to the origin of the universe.

It seems to me, therefore, that it is not only coherent but also plausible that God existing changelessly alone without creation is timeless and that He enters time at the moment of creation in virtue of His real relation to the temporal universe. The image of God existing idly before creation is just that: a figment of the imagination. Given that time began to exist, the most plausible view of God’s relationship to time is that He is timeless without creation and temporal subsequent to creation.

2. Timelessness without Creation