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Does God Have a Beginningless Past?

On the Possibility of an Infinite Past

(Part 3 of the article series God and Time)

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Introduction

This article is the third part of the series God and Time, which explores the question of the relation between God and time. One of the important issues is how to understand God's eternal nature. There are two main views: (1) sempiternalism and (2) eternalism. According to the sempiternal view, God is infinite in time, i.e., He has a beginningless past and an everlasting future. On this view, one can say that God has always existed in the past, He exists now, and He will always exist in the future. However, according to eternalism, it is illegitimate to say that God has always existed in the past, and neither is it correct to say that God has an everlasting future, since this would imply that God is in time. An eternalist would argue rather that God is outside time, i.e., God's existence is timeless.

In our previous articles in the series, we have seen that the timeless eternity of God is a very dubious doctrine for both biblical and philosophical reasons. In the Bible, God is portrayed as someone who profoundly interacts with people: someone who is involved in personal relations. We have seen that God's relation to His created world makes Him essentially temporal. We have also argued that the idea of God's timeless eternity is conceptually incoherent.

However, there is one important issue concerning the intelligibility and coherence of the idea of an infinite past. Some eternalists maintain that the idea of an infinite past is logically incoherent.1 They argue that the supposition of a beginningless past would imply that an infinite number of time units, such as days, have passed to reach the present. The issue is whether it is possible for an infinite number of days to pass leading up to the present. The question of the coherence of an infinite past was a hotly disputed controversy in Arabic, Jewish and Christian medieval thought. Our goal is to show that this is quite possible.

In the recent history of this issue, William Lane Craig has offered a challenging argument worth exploring. He is one of the most vocal advocates for the Kalām Cosmological Argument for God's existence, the steps of which include an argument for the beginning of time. His argument is representative of temporal finitism, which is why we have chosen to discuss it. Our goal is to show how his arguments fail. Our exposition will also serve as a reply to other similar arguments, such as Kant's classic argument for the finitude of time, or more recent arguments such as by Steven B. Cowan.2

In our discussion of this issue, we will reserve the terms 'temporal finitism' and 'temporal infinitism' for the views that time is finite and infinite, respectively. A temporal finitist is someone who subscribes to temporal finitism, while a temporal infinitist subscribes to temporal infinitism. Sometimes we will shorten the terms to 'finitist' or 'infinitist,' although these particular terms have a different standard usage in the philosophy of mathematics and epistemology, respectively.3

In the discussion concerning God's relation to time, the term 'eternalism' refers to the theological view that God's eternal nature is timeless, while 'sempiternalism' refers to the view that God is essentially in time and that he has a beginningless past and an everlasting future, i.e., God is infinite in time with respect to both the past and the future. We will use the term 'eternalism' in the theological sense as outlined above, and not as a metaphysical view figuring in the philosophy of time, where all events in the past, present and future have equal ontological status.

Craig's Argument for the Impossibility of an Infinite Past

The Kalām Cosmological Argument

Craig is one of the most outspoken defenders of the Kalām Cosmological Argument, as evidenced by his many articles and books on the issue. For instance, in "The Existence of God and the Beginning of the Universe,"4 his argument is as follows:

The Kalam Cosmological Argument (KCA)

  • (KCA1) Whatever begins to exist has a cause of its existence.

  • (KCA2) The universe began to exist.

  • (KCA3) Therefore, the universe has a cause of its existence.

From a theistic perspective, the second premise is not so clear because of the obscurity of the term 'universe'. It can mean, for instance, the created physical universe, but can also mean the totality of everything, including God and His creation. In addition, from an eternalist5 perspective, although God is the creator of the physical universe, God did not exist before the creation: His existence is timeless rather than in time, and, accordingly, temporal characterizations with 'before', 'simultaneous,' or 'after' do not apply to God's existence. According to Craig, time began with the creation, and we can interpret the second premise as saying that time began to exist as well. On Craig's view about God's relation to time, God was timeless before the creation, but after the creation, when both time and space started to exist, God started to exist in time as well.6 In our article "The Timelessness of God," we have seen that such talk forbidding temporal characterizations of God's existence and his actions is absolutely unintelligible and incoherent. How can God initiate change with His act of creation and not be part of the creative process occurring in time? The creation of an object W is essentially an act where W did not exist before the creation, started to exist at the creation, and has continued to exist after the creation. However, under the eternalist assumption, it is incorrect to say that "W did not exist before the creation," since there is no "before" before creation, which is a highly dubious statement. How should we understand the statement "W did not exist before time," and how to understand "before" without presupposing time? Craig does not offer a good explanation of how to talk meaningfully about timeless creation; he simply takes it for granted that the world has come into existence through timeless creation, which is a metaphysically controversial idea. For instance, in his debate with Quentin Smith, he says:

[Kant] also believed that reason forced you to adopt the antithesis [that the past is beginningless] as well, but I think that the argument for the antithesis is simply a faulty argument. It erroneously assumes that time necessarily precedes the beginning of the universe; but on a non-Newtonian relational view of time, time begins simultaneously with the first event. So there's simply no problem about when the universe would have begun to exist in the empty time prior to the beginning of the universe. So again, it seems to me that this argument is a forceful and persuasive argument, which both Hume and Kant, in effect, concede.7

How does time begin simultaneously with the first event? Does this mean that time did not exist before time? How can one meaningfully and coherently understand the concept of time's non-existence before time? Those questions remain unanswered, as discussed in "The Timelessness of God." It makes more sense, therefore, to say that the world did not exist before the creation and started to exist at the creation and has continued to exist after the creation, where "before", "at" and "after" signify a temporal order that is necessary to presuppose when talking about processes and actions that involve substantial changes. For this reason, we believe that Kant's argument for the antithesis concerning time (which contends that time has a beginningless past) makes more sense than the opposite thesis, viz., that time has a beginning in the past. We will now examine the argument that purports to show that time necessarily has a beginning.

It is obvious that the second premise of the KCA is the crucial one and Craig offers two arguments for its support: (a) an argument on the basis of the impossibility of an actual infinite, and (b) an argument on the basis of the impossibility of the formation of an actual infinite by successive addition.8 The first argument tries to show that an actual infinite cannot exist, while the second one does not deny the possibility of the existence of an actual infinite, but rather the possibility of its being formed by successive addition. We are more interested in the second argument, which more closely resembles the classic arguments against an infinite past. However, for the sake of completeness, we will discuss the first argument, before proceeding to the classic argument against an infinite past. Discussions of these two arguments are independent, and one could skip the discussion of the first argument, and jump straight to the second one.

An Infinite Past as an Actual Infinite

Craig's first argument in support of the KCA's second premise goes as follows:9

Argument against an infinite past as actual infinity (ACT)

  • (ACT1) An actual infinite number of things cannot exist.

  • (ACT2) A beginningless series of events in time entails an actually infinite number of things.

  • (ACT3) Therefore, a beginningless series of events in time cannot exist.

The first argument tries to show that the past cannot be infinite by arguing for the impossibility of an actual infinite.

There are two concepts of infinity that is used by mathematicians and philosophers: actual and potential infinity. Actual infinity involves acceptance of infinite objects as a given, actual and completed collection (e.g., a set of all natural numbers). Potential infinity is conceived in terms of an unending procedure (such as “add 1 to a previous number”) producing a sequence with no last element, and where each individual result is finite and is achieved in a finite number of steps.

Craig's strategy of showing that actual infinity is impossible is based on certain thought-experiments which purport to show the absurdity of an actually infinite number of things existing. For instance, his favorite thought-experiment on this topic is Hilbert's Hotel--a hotel with an actually infinite number of rooms. He tries to show that such a hotel would have some absurd implications for the kind of world we live in. We will not go into detail about this first point for two reasons.

First, even if we accept Craig's argument that Hilbert's Hotel is really absurd, and that it therefore cannot exist, it does not follow that the infinite past is impossible. As Landon Hedrick notes:

Nevertheless, it is certainly not clear that [the first premise], 'an actually infinite number of things cannot exist,' follows from the absurdity of Hilbert's Hotel, at least if abstract objects count as 'things.' Consider numbers, for example. If a number is a thing, and if there are an actually infinite number of them, then [the first premise] is false. Of course, some philosophers have held that numbers are things, and that there are an actually infinite number of them. Let's call such a view about numbers 'Platonism'. In response to this worry, Craig reassures us that there are other views which hold that, for example, numbers don't really exist, or that there aren't an actually infinite number of them ... But surely this response misses the thrust of the worry. The obvious point to make is that if Platonism is correct, then it follows that the Hilbert's Hotel thought-experiment doesn't prove [the first premise]. So it's Craig's burden to show that Platonism must be false. Rather than merely point out that we need not be Platonists, Craig needs to give an argument against Platonism.10

The issue about the existence of an actual infinite remains quite a controversial one in mathematical philosophy and is far from being settled. Hence, it is very problematic to use a highly controversial premise in the context of a discussion about yet another controversial issue, i.e., the question of the infinity of the past; someone who believes in abstract mathematical infinite sets, e.g., the set of natural numbers, would not be convinced by his first argument. It is unclear whether Craig argues against the existence of an actual infinite that would rule out the existence of abstract mathematical objects, such as the set of natural numbers {1, 2, 3, ...}, numbers which we use pragmatically in our daily lives when we collect and count various things, pay our bills, go shopping, etc. If there is an infinite number of them, the first premise is false, and the argument against the impossibility of an infinite past fails. If Craig argues against Platonism in mathematics, Landon's point holds.

Moreover, on the basis of the first premise, Landon observes that we should rule out other metaphysical views. In addition to Platonism about numbers, one might believe in an infinite number of other abstract objects--e.g., propositions, properties, sets, possible worlds, etc. Moreover, some people believe that space is continuous and that there are an infinite number of points, but as Landon notes, the first premise seems to rule this out as well.11 Craig claims that the idea of continuous space is unproven.12 Apparently, he thinks that it is up to his opponent to prove it. However, Craig's premise seems to entail that space is not continuous, which is also an unproven claim. Hence, it is reasonable to expect him to prove it. As Landon observes:

We're beginning to see that in order for [Craig's argument] to go through, it has to settle a number of controversial metaphysical debates. And we're expected to think that these debates can be resolved by the Hilbert's Hotel thought-experiment, or parallel thought-experiments. It seems that there is plenty of room here to doubt that the absurdity of Hilbert's Hotel proves [the first premise]. ... But notice that there are really two distinct problems here. First, we can see that if any of these views are true, then Craig's premise is false. So Craig seems to have his work cut out for him in showing that all of these various views are false. But secondly, and perhaps more importantly, I want to claim that whatever else can be said against these metaphysical views, we should probably not think that the Hilbert's Hotel thought-experiment disproves all of them. So even if Craig does have good reasons to reject these views, this would not show us that Hilbert's Hotel provides us with a good reason to reject these views, and therefore to affirm [the first premise]. At the very least, we should probably be hesitant to accept [the first premise] on the basis of Hilbert's Hotel, given that it rules out a number of plausible metaphysical views that have been held by some very intelligent people.13

But why is Craig so adamant in his claim that an actual infinite cannot exist in the “real world”? Is there some principle presupposed in Craig’s thought experiments showing the impossibility of an actual infinite? Indeed there is a principle that Craig appeals to,14 namely the Euclid’s Maxim (EM), which is the Fifth Axiom of Euclid, not to be confused with the much discussed Fifth Postulate of Euclid.

EM: A whole is greater than any of its parts.

According to Craig, EM is not valid when dealing with infinite sets because of the Principle of Correspondence (PC).

PC: If two sets can be placed in one-to-one correspondence, they must have the same number of elements.

For instance, the set of all natural numbers {1, 2, 3, …} and the set of all even numbers {2, 4, 6, …} have the same numbers of its members, even though the second set is the proper subset of the first. They have the same numbers of its members because both sets can be placed in one-to-one correspondence:

1 <–> 2,
2 <–> 4,
3 <–> 6, etc.

Both principles EM and PC are intuitive plausible when dealing with finite sets. Given PC and EM, Craig thinks he can show that there are no actually infinite sets. For suppose there were. Then its members could be placed in one-to-one correspondence with a mere part (a “proper subset”15) of itself. By PC, it would then follow that the set has no more members than its part, contrary to EM.

Notice, how EM is interpreted in Craig’s argument. It is interpreted as EMN.

EMN: The number of elements in a set must be greater than the number of elements in any proper subset of that set.

It would be very instructive to see Wes Morriston’s comments on Craig’s argument.

There is, then, a fairly intuitive sense in which any set - even an infinite one - is ‘greater’ than any of its proper subsets. Not because the number of elements in the greater set is necessarily larger than the number of elements in the lesser one - but merely in virtue of the fact that it ‘contains’ all the elements in the lesser set plus some others that the lesser one does not contain. That, all by itself, and without any reference to the number of elements in either set, is sufficient to make one ’ greater’ than the other. When it is understood this way, an actually infinite set does not violate the principle that the ‘whole’ is greater than its ‘part.’16

It is true, of course, that the number of elements in any finite set is necessarily greater than the number of elements in any of its proper subsets. But why think this must hold for all sets in the ‘real world’? Euclid’s maxim about wholes and parts may be ‘intuitively’ obvious; but as we have just seen, this provides little, if any, support for EMN when dealing with infinite sets.

We will now turn our attention to Craig's second argument, which does not deny the existence of an actual infinite, but rather denies that the temporal regress of past events is such an actual infinite.

An Infinite Past as Successive Addition

Formulation of the Problem

Craig's second argument in support of the KCA's second premise goes as follows:17

Argument against an infinite past as successive addition (ASA)

  • (ASA1) A collection formed by successive addition cannot be actually infinite.

  • (ASA2) The temporal series of past events is a collection formed by successive addition.

  • (ASA3) Therefore, the temporal series of past events cannot be actually infinite.

His second argument looks more like Kant's famous first antinomy18 concerning time, where the idea of the impossibility of completion of an infinite series through successive addition is the crucial premise. However, the argument, at face value, is not so much an argument against time per se, but that the events, or the world, or the universe cannot have a beginningless past in time. It concerns the relation between the world (or universe) and time. Given Craig's eternalist view, the argument can be interpreted as opposing not only the idea of a beginningless universe, but also the idea that God's existence has an infinite past. Moreover, Craig says in his later writings that the argument "can be restated in time itself," by replacing the term "temporal series of events" with "temporal segments of equal duration, say hours."19 Thus, the ASA is an argument against the infinity of time per se and not just against the infinity of past events. Because we are more concerned with the question of God's beginningless past, we will interpret the argument with that objective in mind as follows: "past events" as figuring in the second premise can also be understood as past divine events--that is, events directly involving God. Among those events is the creation of the physical universe and the human world. Under such an interpretation, the argument tries to show that God has no infinite past, and, a fortiori, the temporal series of past divine events has a beginning in time. This would go against the sempiternalist view, which understands past divine events as beginningless simply because God has always existed.20

Let us first start with the second premise (ASA2) because, while it is not very questionable, it does have certain problems. It says that the events in the past have happened successively, one after another. However, the premise does not take into account overlapping events that do not occur successively one after another, but are partially simultaneous, i.e., when one event starts during another event. Moreover, the premise presupposes a discrete division of temporal units and not continuous temporal intervals, since successive addition makes sense when talking about a sequence of objects that are countable. We will, therefore, interpret the premise as stating that events in the temporal series do not overlap but rather occur one after another, where the temporal units are of a discrete kind, e.g., hours, days, months, years, etc.

Moreover, the premise presupposes a dynamic view of time, as Craig explains:

Premiss [(ASA2)] presupposes a dynamical view of time according to which events are actualized in serial fashion, one after another. The series of events is not a sort of timelessly subsisting world-line which appears successively in consciousness. Rather becoming is real and essential to temporal process. Now this view of time is not without its challengers, but to consider their objections in this article would take us too far afield. In this piece, we must rest content with the fact that we are arguing on common ground with our ordinary intuitions of temporal becoming and in agreement with a good number of contemporary philosophers of time and space.21

The dynamic view of time takes seriously the notion of temporal becoming, where the future becomes the present, and the present becomes the past. This is in contrast to the view of time as static, which maintains that the present is a matter of subjective experience rather than an objective feature of reality; on this view, there is no special privileged temporal location having the status of being the present. For the sake of argument, we will accept Craig's dynamic view of time.

Why does it make a difference for the argument whether we hold a dynamic view of time? Wes Morriston gives a good answer to the question:

The answer appears to be that if time really "passes" then an infinite series of events ending in the present would actually have been traversed, one at a time. In this process, an infinite series would have reached completion--something Craig believes to be absurd. "Since one can always add one more before arriving at infinity," he says, "it is impossible to reach actual infinity."22

This is one of the issues in the discussion about the coherence of the infinity of the past, viz., the problem of traversing the infinite. Another issue is the problem of the formation of an actual infinite collection by successive addition, which is addressed in the first premise. These two issues are different as we shall see below.

The first premise says that a collection that is formed by successive addition cannot be actually infinite. Craig explains his first premise:

[The first premise] is the crucial step in the 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 infinity." 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 by simply moving in the opposite direction?

Indeed, the idea of a beginningless series ending in the present seems to be absurd.23

This same analogy of counting is used in Craig's discussion with Quentin Smith:

Now if the past were infinite, it would be as though someone had claimed to have just finished counting down all the negative numbers ending in "0," and surely this is absurd. If you can't count to infinity, how can you count down from infinity? If you can't traverse an infinite distance by running in one direction, how can you traverse it by simply turning around and running in the opposite direction?24

Similarly, Gregory E. Ganssle explains why it is impossible for the past to be infinite by the analogy of counting natural numbers, {1, 2, 3, …}.25 One cannot finish counting all natural numbers; there is no last natural number. Since we cannot complete the counting to the last natural number, nor can we count from infinity, i.e., to count backward from infinity and arrive at zero (or frontward, from negative infinity to zero in the set of negative integers with zero {…, -3, -2, -1, 0}). It is further argued that since it is impossible to count from negative infinity to zero, so reaching the present from a beginningless past is equally impossible.

The explanations above are not so clear in explaining how the analogies of "counting to (or from) infinity" or "traversing the infinite" have to do with "successive addition" as figuring in the premise. What is actually meant by "counting from infinity" or "traversing infinity" as they figure in the analogies? If it means to count from an "infinite number" or to reach the present from an "infinite (temporal) distance," then surely a finitist requires an impossibility, since there is no such thing as an infinite number or an infinite distance. When counting numbers, each counted number is a finite number, although there are infinite numbers of them. Since there are infinite numbers of them, one cannot complete counting or finish the count of all natural numbers. The same goes with an "infinite (temporal) distance." Each moment in the past is a finite distance from the present, although there can be infinite moments in the past. The point is that a finitist, under such an interpretation, requires some sort of beginning that starts from, per impossibile, an "infinite number" or an "infinite distance," which is question-begging, since there is no such starting point.

However, if "traversing infinity" means "traversing from any past moment to the present," then this task is, in principle, possible, since any past moment has a finite temporal distance to the present. An omnipotent god, for instance, could traverse from any past moment to the present.

It should be noted that "counting from infinity" and "traversing infinity" are not the same analogies. A temporal infinitist can concede that counting from infinity is impossible, but deny that the analogy applies for understanding the concept of traversing infinity. The impossibility of counting from infinity does not entail that an actual infinite sequence of past temporal units, say days, does not exist. It rather entails that the beginning of these days does not exist. Nor does the impossibility of counting from infinity entail that one cannot count to zero from any of infinitely many negative integers.

Craig would object here and insist that he does not presuppose an infinitely distant starting point with "counting from infinity" or "traversing infinity." In his reply to Mackie, who gave a response similar to ours above,26 Craig says:

Mackie objects that the argument illicitly assumes an infinitely distant starting point in the past and then pronounces it impossible to travel from that point to today. But there would in an infinite past be no starting point, not even an infinitely distant one. Yet from any given point in the infinite past, there is only a finite distance to the present. Now it seems to me that Mackie's allegation that the argument presupposes an infinitely distant starting point is entirely groundless. The beginningless character of the series only serves to accentuate the difficulty of its being formed by successive addition. The fact that there is no beginning at all, not even an infinitely distant one, makes the problem more, not less, nettlesome. And the point that from any moment in the infinite past there is only a finite temporal distance to the present may be dismissed as irrelevant. The question is not how any finite portion of the temporal series can be formed, but how the whole infinite series can be formed. If Mackie thinks that because every segment of the series can be formed by successive addition therefore the whole series can be so formed, then he is simply committing the fallacy of composition.27

Mackie's reply is actually quite to the point. Craig's appeal to "counting from infinity" or "traversing infinity," understood as a finitist objection to an infinite past, can be plausibly interpreted as a challenge for temporal infinitists to count from or traverse from, per impossibile, an infinitely distant starting point. Mackie's further point shares the same insight as ours concerning the problem of traversing infinity, viz., any temporal point in the infinite past has a finite distance to the present. It should be noted here that Craig deems Mackie's point irrelevant, dismissing it on the grounds that it is founded on a logical error: just because all the segments of a series can be formed by successive addition does not mean that "the whole infinite series can be formed" that way. For Craig, it is the formation of the whole infinite series that matters. However, Mackie's point is not necessarily about the formation of a beginningless temporal series, but rather about the problem of traversing infinity. These two issues are related, but different. The problem of traversing infinity is the question of how the present is reached from the beginningless past. This is not the same as the problem of the formation of a beginningless temporal series by successive addition. We will deal with these two issues separately.

The Problem of Traversing Infinity

Mackie's point about traversing infinity is that any temporal point in the infinite past has a finite distance to the present. This reply is a standard, classic reply to temporal finitists that was even used by some eternalists, such as Thomas Aquinas. For instance, in Summa Theologica and Summa contra Gentiles, his replies are similar to Mackie's:

In Summa Theologica I, Q. 46, Art. 2, we read:

Objection 6: Further, if the world always was, the consequence is that infinite days preceded this present day. But it is impossible to pass through an infinite medium. Therefore we should never have arrived at this present day; which is manifestly false.28

Reply to Objection 6: Passage is always understood as being from term to term. Whatever bygone day we choose, from it to the present day there is a finite number of days which can be passed through. The objection is founded on the idea that, given two extremes, there is an infinite number of mean terms.29

In Summa contra Gentiles, Book 2, Ch. 38, we read:

Arg. 3. It is not possible to pass through infinity. But if the world always had been, infinity would have been passed through by this time, there being infinite days, or daily rounds of the sun, if the world always has been.30

Reply. An infinite quantity, though not existing in simultaneous actual realisation, may nevertheless be in succession, because every infinite, so taken, is really finite. Any given round of the sun could be passed, because so far the number of them was finite: but when they are all viewed together, on the supposition that the world had always existed, it would be impossible to fix upon any first day, and so to make any transition from that to the present day, since transition always requires two extreme points.31

In both places, Aquinas points out that the present can be reached from any distant temporal location in the past because the temporal distance is finite, and by this token, it is possible to reach the present from a beginningless past. A particular temporal location t in the past (e.g., a particular day or year in the past) is understood to be temporally reachable if and only if the temporal distance between the present and the temporal location t is finite. Aquinas points out that there is nothing impossible with the existence of infinitely many temporal locations in the past where each temporal location has a finite distance to the present. Since any moment in the past has a finite distance to the present, any moment in the past is reachable. This important insight can be proved by the following informal argument:

Informal Argument for a Beginningless Past

The present day is trivially reachable from the present, since the distance between them is trivially zero. What about yesterday? The present is also reachable from yesterday, since the temporal distance between them is a finite number, viz., one day ago. The same goes for the day before yesterday: the present is reachable from the day before yesterday, since the temporal distance is finite as well, viz., two days ago. We can continue to examine the days that are three, four, and five days ago, realizing that from these past days, the present is also reachable, since the temporal distances for these days are finite. The goal is to prove that the present day is reachable from infinitely many days in the past. Let us assume that the present is reachable from some arbitrarily chosen past day n, i.e., the temporal distance between the present and n is a finite distance of n days ago. Given the assumption that it holds for n, i.e., n is a finite number, it is obvious that the present would be reachable from one day earlier than n, viz., n + 1, since the distance between the present and the day n + 1 is finite as well, given that the sum of two finite numbers, such as n and n + 1, is a finite number. Thus, the present is reachable from any day in the past. However, can the present be reachable from infinitely many days? Obviously it can, since we can repeat the steps for n + 1, n + 2, ad infinitum. In other words, the present can be reachable from infinitely many days in the past. It follows that the idea of an infinite past is logically coherent, i.e., it is not impossible that a temporal regression of past events is infinite.

The Pseudoproblem of Traversing the Infinity

Assuming dynamic understanding of time, where "temporal becoming" is the essential feature of time, Craig maintains that it is an impossibility to reach the present day from a beginningless past. However, the idea of impossibility of reachinging the present day from infinity past is a very odd idea, since any day in the past was a present day.

Although past days are earlier than the present day, and we have to traverse (or live through) earlier days before the present day, we have to ask the following question: Why are the past days earlier than the present day? They are earlier precisely because they had the temporal status of being the present one, i.e., they were once the present day. They are now in the past because they ceased to be a present day. So the whole problem of reaching the present from “infinite past” is a pseudo problem because it ignores the very fact that each past day was once a present day. When we traversed the yesterday, the yesterday was the present at the time of its traversing. Traversing a particular day means simply that the particular day in question has the temporal status of being the present.

If the time is static, then the question of traversing the time makes no sense, since in the static view of time, the time is essentially a metric by which we coordinate the events along the time axis. Such understood, infinite past time is analogous to the negative numbers.

A Meaningful Talk About the Infinity of the Past

Given the foregoing, we can make an important observation:

There is a distinction between (1) finite distances of any day belonging to infinitely many days in the past, and (2) an "infinite distance" from a beginningless past. Let us dwell on this important distinction.

Temporal finitists seem to confuse these two different concepts, since they maintain that the present is not reachable if there are infinitely many past days, even though each of those infinitely many days has a finite distance to the present. A temporal finitist would contend that a temporal distance between day A and day B is a number of days between A and B. If there are infinitely many days between a beginningless past and the present, then the distance is infinite, and thus the present is unreachable. However, what does the term "beginningless past" actually mean? It means that there is an indefinite plurality of days and not a definite single day. Thus, we cannot talk meaningfully about a distance between the plurality of days and some definite temporal location. A temporal distance is between two definite temporal locations. A distance between any two definite temporal locations is finite, i.e., it has finitely many days between any two definite temporal locations. Hence, a finitist's talk about "infinite distance" does not make sense when dealing with a beginningless past. A meaningful way to describe a beginningless past is that it consists of infinitely many days where each day has a finite distance to the present. Therefore, the present is reachable from a beginningless past.

The Problem of the Formation of an Infinite Temporal Series

The classic problem of a temporal infinity is the problem of traversing infinity from the beginningless past to the present. From the foregoing, we have seen that the problem is solved. However, there is another related problem, seen in Kant's antimony concerning time, known as the problem of the formation of an infinite temporal series. The problem of traversing infinity and the formation of an infinite temporal series are two different kinds of problem, and should be distinguished one from the other.

In connection with Craig's reply to Mackie’s objection, the pertinent question is how the whole temporal series can be formed if there is no starting point. This question is precisely the problem of the formation of an infinite temporal series. Let us again take a look at Craig’s reply to Mackie’s objection:

The fact that there is no beginning at all, not even an infinitely distant one, makes the problem more, not less, nettlesome. And the point that from any moment in the infinite past there is only a finite temporal distance to the present may be dismissed as irrelevant. The question is not how any finite portion of the temporal series can be formed, but how the whole infinite series can be formed. If Mackie thinks that because every segment of the series can be formed by successive addition therefore the whole series can be so formed, then he is simply committing the fallacy of composition.32

As noted above, Mackie's point is not necessarily about the formation of a beginningless temporal series, but rather about the problem of traversing infinity. These two issues are related, but different. If Mackie's point was about the formation of the temporal series, Craig's charge would be valid.

Craig is correct in this matter: one may not validly infer that the whole infinite past has been formed by successive addition just because every finite segment of the past has been so formed. This would indeed be an instance of the fallacy of composition. But it is also logically fallacious to conclude that there cannot be an infinite series of past events itself not formed by successive addition simply upon the ground that every finite segment thereof has been formed by successive addition. This would indeed be an instance of the fallacy of division.33

Therefore, the pertinent question is: If a temporal series has no first member, how can it, as a whole, be formed? If each event is dependent on a previous one, ad infinitum, how can any event be generated if there is no first event that serves as a foundation for all subsequent events? In other words: How can a temporal series of past events be formed if there is no first founding member?

Reply to Craig's Challenge

In our theological context, we are most interested in the question of divine events, i.e., events that are directly related to the activity of God. The temporal series of divine events is infinite, since each event in the series does not necessarily depend on its predecessor, but rather on God's everlasting, self-sufficient existence alone. Divine events are associated with God's self-sufficient existence, and if God's existence is beginningless, the temporal series of divine events is beginningless as well. We will, therefore, turn our attention to the question of the temporal series of divine events in the next chapter.

The Beginningless Divine Events

Divine events are events that are directly related to the activity of God. Among those events is the creation of the physical universe and the human world. A sempiternalist would contend that there are divine events before the creation of the physical universe (cf. Psalms 90:2; 93:2),34 since God has always existed and His days are beginningless. Our limited human mind cannot fathom the nature of divine events and it will remain a mystery until there is a revelation unveiling its secret. Nevertheless, the mystery of beginningless past divine events is neither a logically nor metaphysically incoherent concept. To illustrate this, let us consider one important class of divine events: divine thoughts and communication between the Holy Persons of the Godhead. Divine thoughts can be understood as a stream of divine consciousness, where a divine thought can either spring from another thought, or it can be formed independently of other divine thoughts in God's mind.

God is not a solitary individual but rather the essence of a loving community manifested through the Holy Trinity. In the words of Clark Pinnock, God seen as Trinity is "God who is the ultimate in community, mutuality and sharing."35 God is not a metaphysical abstract principle but rather three relationally interconnected persons in its place. God manifests diverse persons united in a communion of love and freedom. In other words, God is the perfection of love and communion.

Communication between the Holy Persons of the Godhead can be understood as sharing divine thoughts between each other in the perfection of love and communion. There is nothing incoherent in supposing that such divine communication has always existed from a beginningless past. Divine communication remains, for our limited human minds, something we cannot completely comprehend, but we can catch a glimpse of it through the model of human communication. It is conceivable that divine communication is something wonderfully shared between the Holy Persons of the Godhead, i.e., a Holy Person's participation in divine communication is a beautifully blissful event that does not depend on having a created non-divine reality. For this reason, God could have decided not to create the physical universe. This line of reasoning can give an answer to the eternalist's question Q.

Q: Why did God not create the world sooner or later than He did?36

It nagged Augustine until he began to think of God as atemporal. It seems as though any point in the infinite past is as good as any other, since there is nothing that makes them different from each other. Did God arbitrarily pick out some point and decide "Now I will do it," as on a whim? Or did God have some reason to prefer one moment to all of the others? Either way of answering this question seems a bit strange.37

The question presupposes that all temporal points of the past are uniform and uneventful, something that is questionable given the eventful nature of divine communication (which, as argued above, could have existed prior to the world's creation in a beginningless past). Moreover, the eternalist's question is somehow odd, since God's act of creation is not a metaphysically necessary act, but rather a contingent one.38 There does not need to be any particular reason why God choose to create the world at the time He did. After God decided to create the world, the moment could indeed have been chosen randomly; indeed, it seems that God is very fond of randomness in our universe, given the evidence of quantum mechanics.39 On the other hand, God could have equally decided not to create the world, for the creation of the world is not a metaphysical necessity. His divine existence would be eventful without creating the world, since divine communication in the perfection of love and communion is a blissful form of divine existence that exceeds the human form of existence and communication.

The answer above does not entail that God's decision to create the world was made on a whim, since He certainly had some good reasons why He created the world. These reasons, however, are not metaphysically necessary reasons. It is important to note that the question Q is not a question of coherence, since there is no logical contradiction involved in the divine choice of the moment of creation.40 It is more incoherent to say that God did not exist before creation, as eternalists would have us believe, than to say that God decided to create the world at the time He did.

We can, therefore, conclude that the temporal series of past divine events has no beginning, since God has always existed by virtue of His everlasting beginningless nature.

Conclusion

In this article, we reply to an argument that purports to show that the infinity of the past is an incoherent idea. The issue of the coherence of an infinite past is important in connection with the sempiternalist's view of God's everlasting nature, where God is understood as someone who is essentially infinite in time: God has always existed, He exists and He will always exist. The sempiternalist's view is threatened by arguments against an infinite past that are known from Arabic, Jewish and Christian medieval philosophy.

In the recent history of this issue, William Lane Craig has offered a challenging argument worth exploring. The argument presents two problems: (1) the problem of traversing the infinite, and (2) the problem of the formation of an infinite temporal series of past events. These are two different problems and should not be conflated.

The problem of traversing infinity is a question of how the present can be reached if one first has to traverse infinitely many past days in order to reach the present. The problem of traversing infinity was already solved in medieval classical philosophy, as seen in Thomas Aquinas' treatment of the problem, which we have discussed in our article. Aquinas' solution involves an insightful observation that there is nothing impossible about the existence of infinitely many temporal units--days, for example--in the past, where each day has a finite distance to the present. Since any day in the past has a finite distance to the present, any day in the past is reachable. This important insight was also demonstrated by a proof of mathematical induction on a sequence of numbers representing the number of past days.

The problem of the formation of an infinite temporal series of events is a question of how a series of events can be formed by successive addition if there is no beginning with a first founding member of the series. In general, an infinite collection of objects is formed by applying a rule of a repeatable procedure that generates a member from its preceding member. If there is no first member that serves as a foundation for the generation of all subsequent members, how can such an infinite collection be formed? This question seems to presuppose that each event is dependent for its existence on its predecessor in the temporal series of events. In our theological context, we are most interested in the question of divine events, i.e., events that are directly related to the activity of God. The temporal series of divine events is infinite, since each event in the series does not necessarily depend on its predecessor, but rather on God's everlasting, self-sufficient existence alone. Divine events are associated with God's self-sufficient existence, and if God's existence is beginningless, the temporal series of divine events is beginningless as well.

Appendix: Does Science Show That the Time Has a Beginning?

Some would argue that the universe together with space and time had a beginning by appealing to the Big Bang hypothesis.41 The big bang hypothesis holds that the universe, including space and time itself, came into existence a finite amount of time ago, and shortly after the universe came into existence it was in a state of large energy density, and the energy density in the various regions of the universe has overall been decreasing. The Big Bang hypothesis is based on the general theory of relativity. By appealing to the Big Bang hypothesis, one argues that the metaphysical questions about space and time are settled by our most advanced scientific theories.

There are two problems with the above reasoning. First, science cannot settle our metaphysical questions, given that two most fundamental scientific theories (namely, theory of relativity and quantum mechanics) are incompatible. Second, the Bing Bang hypothesis is just that, a hypothesis, and we do not know if it is true.

1. Incompatibility Between the Theory of Relativity and Quantum Mechanics

There is a tension between general/special theories of relativity with quantum mechanics. This is seen in the phenomenon of quantum entanglement, when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance.

The particles appear to remain “connected” or “in communication” no matter how distantly separated they may become. The outcome of experiments performed on one member of the pair appears to depend not just on that member’s own intrinsic physical state but also on the result of experiments carried out on its twin.

Many features of this quantum connection are puzzling. It is, for example, entirely undiminished by distance. This distinguishes it from any connection mediated by a classical force, such as gravity or electromagnetism. But even more amazingly, the connection exists even when the observations carried out occupy positions in space and time which cannot be connected by light rays. The particles communicate faster than light.

It is this last feature which raises questions about the consistency of our fundamental theories. Relativity is commonly taken to prohibit anything from traveling faster than light. But if nothing can go faster than light, how can the particles continue to display the requisite correlations even when greatly separated? The two pillars of modern physics seem to contradict one another.

The predicted correlations have been experimentally confirmed. Indeed, they have been seen even in conditions where the communication between the particles would require superluminal velocities. So we are presented with the problem of determining whether Relativity has been violated, and, if so, whether our present account of space-time structure must be modified or abandoned.42

Because of these observations, some philosophers of science deem relativity theory and quantum mechanics as incompatible.

Our two best theories of physics, quantum theory and relativity theory, are incompatible. The evidence in favor of quantum theory suggest that relativity theory is false, and the evidence in favor of relativity theory suggests that quantum theory is false.

Here is an example of what I have in mind. Some of the evidence for quantum theory (from, for example, the two-slit experiment) suggests that a particle can be in a superposition of different positions. But in general relativity, where the curvature of spacetime is based on the distribution of matter, there is no way to have a superposition of spacetimes.43

Given this tension, we have to be cautious in basing our metaphysical claims on science alone.

2. We Do Not Know Whether There Was a Big Bang At All

As Bradley Monton observes, the Big Bang hypothesis is true given the assumption that general relativity is true, but we don’t know that the Big Bang hypothesis is true of the actual universe. “The Big Bang hypothesis is based on a theory (general relativity) that can’t accommodate evidence that supports quantum theory, and that gives us reason not to believe the Big Bang hypothesis.”44 Moreover, the theories of relativity (both general and special) are not the only theories that can accommodate all scientific data. “In fact, there is a theory that is not merely observationally equivalent to the Special Theory, but also observationally superior to it, namely Lorentzian or neo-Lorentzian theory,”45 which is consistent with the relations of absolute, instantaneous simultaneity, and as such has no incompatibility with quantum mechanics.

It is a commonly said in the popular media that the history of the universe can be traced back to a big bang that (according to current estimates) occurred about 13.7 billion years ago. As Wes Morriston points out, “Unfortunately matters are not that simple. At best, the extrapolated Hubble expansion takes us back to a time when the universe was in a state of extremely high energy and density. When energy levels are that high, quantum effects are extremely significant, physics is entirely speculative, and just about everything is up for grabs.”46

The Big Bang Hypothesis is just a speculation, and given our current state of inquiry in physics, we do not know if the Big Bang happened at all. Let me quote Monton,

If one were to watch the history of the universe going backwards in time, one would see the energies increasing. … As the energy increases to 100 GeV, the physics becomes speculative—we’re not really sure what happens at that point. As the energy increases to 1014 GeV (assuming it does increase to that point), the physics becomes extremely speculative, even unknown. In other words, we just don’t know what happens once the energies get that high. … But in fact our lack of knowledge is much more fundamental. Because the physics doesn’t tell us what happens once we trace the history of the universe backwards in time to these high energies, we don’t even know whether there’s a Big Bang at all.47

Another scientist maintains the same point about the speculative nature of our scientific theories on the early times of our universe.

I find it surprising that someone would claim . . . that the extrapolated Hubble expansion, back to “time zero” (13.7 billion years ago) was the start of everything. We know so little about the laws of physics at these times, small lengths, enormous energies, even the nature of space and the vacuum.48

Given the speculative nature of the Big Bang theory, it cannot serve as the foundation for our metaphysical claims about space and time.

Endnotes

  1. In recent discussions as to whether the past can be infinite, theologians such as William Craig, Steven Cowan and J. P. Moreland are examples of eternalists that maintain the view that the infinite past is incoherent. Not all eternalists share their view. For example, Aquinas, in his De Aeternitate Mundi, argues that the world could have always existed even if we suppose that God created it. Moreover, Summa Theologica I, Q. 46, Art. 2, ad. 6, and Summa contra Gentiles, Book 2, Ch. 34-37, Argument 3, are replies to the argument against an infinite past. We will use a similar reply in our text.↩︎

  2. Steven B. Cowan, "A Reductio Ad Absurdum of Divine Temporality," Religious Studies, Vol. 32, No. 3 (Sept. 1996). An excellent rebuttal of Cowan's argument is Nicholas Everitt, "Interpretation of God's Eternity," Religious Studies, Vol. 34, No. 1 (March 1998).↩︎

  3. Standard usage of "finitist" refers to someone who subscribes to finitism in mathematical philosophy, where one accepts the existence only of finite mathematical objects. Infinitism is a view in epistemology concerning the structure of epistemic justification of knowledge, where knowledge may be justified by a non-repeatable infinite chain of reasons.↩︎

  4. William Lane Craig, "The Existence of God and the Beginning of the Universe," Truth: A Journal of Modern Thought 3 (1991), (LeadershipU, http://www.leaderu.com/truth/3truth11.html, accessed 3 June 2017).↩︎

  5. As was explained in the introduction, "eternalism" refers to a theological view of timelessness of God, and not to the metaphysical view of time where events of the past, the present and the future have equal ontological status.↩︎

  6. Craig argues for his peculiar eternalist view in "Timelessness & Omnitemporality," God and Time--Four Views, ed. Gregory E. Ganssle (InterVarsity Press, Downers Grove, IL, 2001).↩︎

  7. Craig, "Does God Exist?", opening arguments in a debate between William Lane Craig and Quentin Smith, March 22, 1996 on the campus of Southern Methodist University. (A transcript of this debate can be found at http://www.leaderu.com/offices/billcraig/docs/craig-smith0.html, last accessed 10 April 2015.)↩︎

  8. In this context the term 'successive addition' signifies an order where a new member is formed by succeeding its former member. In mathematics, the formation is usually given by a formula showing how a new member is formed from a previous one.↩︎

  9. Craig, Reasonable Faith: Christian and Apologetics, 3rd ed., (Wheaton, IL: Crossway, 2008). The argument is discussed in Landon Hedrick, "Heartbreak at Hilbert's Hotel," Religious Studies, Vol. 50, Issue 1 (March 2014). The earlier version of Craig's argument appears in "The Existence of God and the Beginning of the Universe," where "an actual infinite" is used instead of "an actual infinite number of things" in the first premise, and "temporal regression of events" is used instead of "a beginningless series of events in time." There is yet another version in Time and Eternity: Exploring God's Relationship to Time (Crossway, Wheaton, IL, 2001), where "a beginningless series of equal past intervals of time" is used.↩︎

  10. Landon Hedrick, "Heartbreak at Hilbert's Hotel," Religious Studies, Vol. 50, Issue 1 (March 2014), p. 30.↩︎

  11. Ibid., p. 31.↩︎

  12. William Lane Craig & James D. Sinclair, "The Kalam Cosmological Argument," in The Blackwell Companion to Natural Theology, eds. William Lane Craig & J. P. Moreland (Wiley-Blackwell, Oxford, 2012), pp. 112-13.↩︎

  13. Hedrick, op.cit, p. 31.↩︎

  14. William Lane Craig & Quentin Smith, Theism, Atheism, and Big Bang Cosmology (Oxford: Oxford University Press, 1993), pp. 23ff.↩︎

  15. A set A is a proper subset of a set B if every element of A is an element of B, but not every element of B is an element of A.↩︎

  16. Wes Morriston, “Craig on the Actual Infinite” in: Religious Studies, Vol. 38, No. 2 (Cambridge University Press, 2002), p. 155.↩︎

  17. Craig, "The Existence of God and the Beginning of the Universe." The argument is discussed in Wes Morriston's papers: "Must the Past Have a Beginning?" Philo, Vol. 2, No. 1 (1999), pp. 5-19 (Wes Morriston's page at University of Colorado, http://spot.colorado.edu/~morristo/MustThePast.pdf, accessed 10 April 2015); and "Must Metaphysical Time Have a Beginning?" Faith and Philosophy, Vol. 20, No. 3 (July 2003), pp. 288-306 (Wes Morriston's page at University of Colorado, http://spot.colorado.edu/~morristo/metaphysical-time.pdf, accessed 10 April 2015).↩︎

  18. Antinomy (Greek anti, "against, in opposition to," and nomos, "law") literally means the mutual incompatibility of two laws. Here it is used as a contradiction between two apparently equally valid principles or between inferences correctly drawn from such principles. Kant's antinomies concerning time are two incompatible theses concerning the infinity/finitude of time. One thesis affirms the finitude of time, while the other maintains the infinitude of time. Kant gives two arguments for both theses.↩︎

  19. Craig, "Time and Infinity," in Theism, Atheism, and Big Bang Cosmology, p. 105, quoted in Arnold T. Guminski, "The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities," paragraph 16 (The Secular Web, Internet Infidels Inc., http://infidels.org/library/modern/arnold_guminski/kalam2.html, last accessed 10 April 2015).↩︎

  20. According to a sempiternalist, it does not make any sense to say that God has always existed if He has a beginning, since He would not have existed before (whatever "before" means) God's beginning.↩︎

  21. William Lane Craig, "The Existence of God and the Beginning of the Universe."↩︎

  22. Wes Morriston, "Must the Past Have a Beginning?" in: Philo Vol. 2 (1999) no. 1, p. 8.↩︎

  23. Craig, "The Existence of God and the Beginning of the Universe."↩︎

  24. Craig, "Does God Exist?", opening arguments in a debate between William Lane Craig and Quentin Smith, 22 March 1996 on the campus of Southern Methodist University. (A transcript of this debate can be found at http://www.leaderu.com/offices/billcraig/docs/craig-smith0.html, last accessed 10 April 2015.)↩︎

  25. Gregory E. Ganssle, "Introduction: Thinking About God & Time," God and Time--Four Views, pp. 17-18.↩︎

  26. J. L. Mackie, The Miracle of Theism (Clarendon Press, Oxford, 1982), p. 93, relying on Craig, "The Existence of God and the Beginning of the Universe."↩︎

  27. Craig, "Does God Exist?"↩︎

  28. Thomas Aquinas, Summa Theologica, Translated by Father Laurence Shapcote of the Fathers of the English Dominican Province, I, Q. 46, Art. 2, arg. 6, in: Great Books of the Western World, Vol. 17 (Encyclopædia Britannica, Chicago, IL, 1994).↩︎

  29. Summa Theologica I, Q. 46, Art. 2, ad. 6.↩︎

  30. Thomas Aquinas, Summa contra Gentiles, Translated by Joseph Rickaby, S.J. (The Catholic Primer, 2005, http://www.catholicprimer.org/aquinas/aquinas_summa_contra_gentiles.pdf), II.38, arg. 3.↩︎

  31. Ibid.↩︎

  32. Craig, "The Existence of God and the Beginning of the Universe."↩︎

  33. Arnold T. Guminski, "The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities," paragraph 20 (The Secular Web, Internet Infidels Inc., http://infidels.org/library/modern/arnold_guminski/kalam2.html, last accessed 10 April 2015)↩︎

  34. "Before the mountains were brought forth, or ever thou hadst formed the earth and the world, even from everlasting to everlasting, thou art God" (Psalms 90:2). "Thy throne is established of old: thou art from everlasting" (Psalms 93:2). Notice that the Bible speaks in temporal terms when describing God's existence before the creation of physical universe.↩︎

  35. Clark H. Pinnock, "Systematic Theology," The Openness of God (InterVarsity Press, Downers Grove, IL, 1994), p. 108.↩︎

  36. For example, see Craig, "Timelessness & Omnitemporality," p. 153.↩︎

  37. Gregory E. Ganssle, op. cit., p. 17.↩︎

  38. A contingent relation or truth is one that is not metaphysically necessary. For instance, one contingent truth is that the planet Earth has one natural moon. This truth is contingent because it is not metaphysically necessary: it is possible to imagine that the earth could have more than one moon. Notice that 'contingence' is defined in terms of metaphysical necessity, namely something that is not metaphysically necessary. Metaphysical necessity is understood as the strictest form of necessity, i.e., a relation of things, actions, or events that must obtain no matter what. In other words, a metaphysical relation of things, actions, or events is necessary if and only if the description of the relation is logically true. In modal logical terms, a logical true proposition is true in all possible worlds. A possible world, in modal logic, can be understood as a possible imagined situation, both real and not real, e.g., a situation where the planet Earth is the third planet from the sun, or where the grass is pink, etc.↩︎

  39. Quantum indeterminacy is the apparent necessary incompleteness in the description of a physical system, which has become one of the characteristics of the standard description of quantum physics. An example of quantum indeterminacy is Heisenberg's uncertainty principle, which states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position x and momentum p, can be known simultaneously. The uncertainty principle states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.↩︎

  40. The appeal to the Principle of Sufficient Reason (PSR) is questionable. The PSR is not a logical principle, but rather a controversial metaphysical principle. For instance, Kant has argued in his Critique of Pure Reason (in "Second Analogy of Experience") that a certain version of the PSR is valid for human experience, but not necessarily for a realm that is beyond human experience, such as a divine transcendent realm.↩︎

  41. For instance William Lane Craig and William Rowe; see William Lane Craig, The Kalam Cosmological Argument (The MacMillan Press, 1979), p. 140; William Rowe, “Cosmological Arguments”, in The Blackwell Guide to the Philosophy of Religion, ed. William Mann (Blackwell Publishing, 2005), p. 113.↩︎

  42. Tim Maudlin, Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics (Third edition, Wiley-Blackwell, Hoboken, New Jersey, 2011), p. 2.↩︎

  43. Bradley Monton, “Prolegomena to Any Future Physics-Based Metaphysics” in: Oxford Studies in Philosophy of Religion, Volume 3, ed. Jonathan L. Kvanvig (Oxford Scholarship Online, May 2011), p. 143-44.↩︎

  44. Ibid., p. 151-52.↩︎

  45. William Lane Craig & Quentin Smith, “Introduction” in: Einstein, Relativity, and Absolute Simultaneity, ed. William Lane Craig & Quentin Smith (Routledge, London, 2008), p. 5.↩︎

  46. Wes Morriston, “Doubts About the Kalam Argument” in: Debating Christian Theism, ed. J. P. Moreland, Chad Meister, and Khaldoun A. Sweis (Oxford University Press, 2013), pp. 20-21.↩︎

  47. Monton, op. cit.↩︎

  48. Michael Shull, professor of astrophysical and planetary sciences and College Professor of Distinction at the University of Colorado in Boulder, in his correspondence with Wes Morriston, as quoted in Morriston, op. cit., in the footnote 2, p. 30.↩︎

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