The Kalam Cosmological Argument as Amended: The Question of the Metaphysical Possibility of an Infinite Temporal Series of Finite Duration (2004)

Arnold T. Guminski

Abstract: The Kalam Cosmological Argument (KCA) is standardly understood as being based upon the proposition that any infinite temporal series is metaphysically impossible. Embedded, however, in the writings of William Lane Craig and some other advocates of the KCA is an independent KCA-type argument which relies upon the Standard Big Bang Model, which is commonly understood to presuppose the metaphysical possibility of an infinite temporal series of indefinite finite duration (i.e., the duration backward from the present approaches a finite limiting value). This article shows why this Kalam Cosmological Argument As Amended (KCAAA) fails—given principles that are more plausible than their denials. But the rejection of the KCAAA has important consequences for both the theist and naturalist with respect to the metaphysical possibility of an infinite temporal series of indefinite finite duration.

1. The Kalam Cosmological Argument (hereafter KCA), as expounded by William Lane Craig[1], is designed to ultimately prove the existence of God (conceived as the personal Creator of the universe.[2]) The KCA is based upon the premises (1) that whatever begins to exist has a cause and (2) that the universe began to exist. To prove its second premise (SP-KCA), i.e., that the universe began to exist, the KCA includes two philosophical subarguments. The first purports to show that any denumerably infinite set of real entities is metaphysically impossible. The second purports to show (assuming for argument's sake that not all real infinites are metaphysically impossible) that any denumerably infinite temporal series of consecutive past events or temporal intervals (hereafter ITS) is metaphysically impossible.[3] The resulting philosophical subpremise of the KCA (hereafter MS-KCA) is that any ITS is metaphysically impossible. According to the KCA, the universe must be of finite duration and its beginning is a first event, state, or phase.[4] The MS-KCA means that it is metaphysically impossible for either (a) an ITS of finite duration, consisting of events (hereafter ITS-FD), or (b) an ITS of infinite duration (hereafter ITS-ID), to obtain. If the KCA is accepted as sound, then any alleged empirical confirmations of the SP-KCA, even if considered as an independent argument, are to be understood as being fully consistent with the MS-KCA. The KCA, therefore, is only consistent with such empirically plausible astrophysical cosmological models which assume or posit that the temporal series constituting or including the history of the universe has finitely many events and is of finite duration.

2. My first two articles on the KCA[5] addressed in turn two philosophical subarguments in support of the MS-KCA. The first philosophical subargument in support of the KCA (i.e., any infinite set of real entities is metaphysically impossible) primarily depends upon the purported showing that the application of Cantorian set theory[6] to the real world generates counterintuitive absurdities. The second philosophical subargument in support of the KCA, i.e., that any ITS is metaphysically impossible (even assuming that not all real entities are metaphysically impossible) primarily if not exclusively depends upon two propositions: (a) that it is impossible to form an actual infinite by successive addition and that any temporal series is formed by successive addition; and (b) a traversal of an infinite temporal series is indeed metaphysically impossible whether or not there is sometime an infinite yet to be traversed.[7]

3. My first article[8] shows that the general objections to any application of Cantorian set theory to the real world lack merit. More importantly, it shows that it is the application of the theory to the real world according to what I call the standard version (SV) which generates the counterintuitive absurdities that provide the basis for concluding that real infinites are metaphysically impossible. I propose what I call the alternative version (AV)[9] of the application of Cantorian set theory to the real world. My article shows that such application by AV does not generate counterintuitive absurdities. Given the foregoing, my article (so I think and hope) compellingly defeats the first philosophical subargument in support of the MS-KCA.[10]

4. My second article shows that the propositions upon which the second philosophical subargument depends are unwarranted because: (a) an infinite temporal series is a series neither formed by successive addition nor is it otherwise formed; and (b) a traversal of an infinite temporal series is indeed metaphysically possible unless there is sometime an infinite yet to be traversed.[11] Moreover, my second article also shows how, in his post-The Kalam Cosmological Argument-writings, Craig presented several grounds originally used in support of the first philosophical subargument in order to buttress his second philosophical subargument—a procedure which is unwarranted given my demonstration that the application of Cantorian set theory to the real world via the AV does not generate counterintuitive absurdities. The adherent of the KCA holds that any traversal of an infinite is metaphysically impossible; whereas my position is that this metaphysical impossibility obtains only in a case where there was at sometime an infinite yet to be traversed.[12] The metaphysical impossibility of a traversal of an infinite in such a case is something which I believe to be properly basic and incorrigible. Such a metaphysical impossibility entails that between any two events in any given temporal series there are either no intermediate events or only finitely many intermediate events. Rejection of the MS-KCA justifies the conclusion that (minimally at least) the adherents of the KCA have not shown that an ITS is metaphysically impossible, for both of the two philosophical subarguments in support of the MS-KCA have been compellingly defeated.[13]

5. My initial intention was to have continued my inquiry with a philosophical consideration of the so-called empirical confirmations of the KCA, given my refutation of MS-KCA. However, for some time I had failed to discern that the ITS-FD could be metaphysically impossible upon grounds that I had not explicitly considered in my first two articles. Eventually I came to realize that I must also evaluate what I have come to call the Kalam Cosmological Argument As Amended (KCAAA) before ever possibly addressing the probative value of the so-called empirical confirmations of the SP-KCA.

6. The KCAAA, as I define it, offers some astrophysical cosmological models as constituting the basis for an independent argument in support of the SP-KCA, but with the (at least implicit) qualification that it is hypothetically assumed (i.e., for argument's sake) that an ITS-FD is metaphysically possible. Thus (to use C. D. Broad's expression) the finite limiting value of the duration of this series can be taken to be coincident, but not identical, with the initial cosmological singularity (hereafter ics) posited in the Standard Big Bang Model of General Relativity Theory (SBBM). The SBBM is especially relied upon by Craig as providing an empirical confirmation of the SP (i.e., that the universe began to exist) of the KCA and the KCAAA. Because the SBBM is admittedly incomplete—if only because it does not take into theoretical account the Planck era (the first 10-43 sec. after the ics), during which quantum effects predominate—it will be useful for our purposes to speak of any empirically plausible Big Bang model which preserves the ics, with respect to an imperfectly homogenous and isotropic universe, and embodies an ITS-FD (hereafter any BBS:ITS-FD).

7. The KCAAA is something that requires careful scrutiny together with its core issue: the metaphysical possibility of an ITS-FD. But there is something about my project which makes me feel uneasy. I believe that the KCAAA is embedded in the writings of William Lane Craig, as I believe I can show. But he seems hardly aware (if at all) that the KCAAA is hopelessly incompatible with the KCA, as evidenced by the fact that his writings are frequently characterized by a conflation of some aspects of these two arguments. This is most puzzling because, despite my disagreements with him, I have a very great appreciation of his excellence as a philosopher, and of the courage of his convictions, intellectual hospitality, and his formidable analytical and dialectical skill. I acknowledge that I could be very wrong, but I do not think that I am, in what is the objective meaning of what he writes. However, it would not be the first time that an exceptionally able philosopher has managed to unwittingly fuse some incompatible components because of an overall commitment to some philosophical vision. In any event, it will be very easy for Craig to eventually set us all straight about what he actually means given this challenge. In the meantime I shall expound and criticize the KCAAA, as I understand it, because it involves most interesting issues and its consideration may be helpful to all of us. And I surely think this is worthwhile even if I am incorrect in claiming that the KCAAA is embedded in the writings of Craig.[14] However, I do not propose to evaluate the scientific merits of any BBM:ITS-FD detached from issues pertaining to its metaphysical possibility.

8. Eventually, I have come to realize that the rejection of the MS-KCA (considered in light of the alternative version (AV) of how Cantorian set theory applies to the real world) renders it more antecedently probable than not that an ITS-FD is indeed metaphysically impossible (at least per accidens)—given the (tensed or dynamic) A-theory of time, together with certain complementary doctrines concerning metaphysical time and related matters. If this conclusion successfully withstands criticism and if the universe has in fact a finite past, then its history is necessarily constituted by (or included as a part of) a finite temporal series, whether of events or temporal intervals.[15] But this would be contrary to the received understanding of the SBBM, according to which the universe is of finite duration but without a first event. On the other hand, it is possible that the history of the universe is necessarily constituted by (or included as a part of) an ITS-ID. But this too is contrary to the received understanding of the SBBM. The net result of our inquiry is that the metaphysically possible temporal series which includes the history of the universe is necessarily either (1) a FTS or (2) a ITS-ID. Further philosophical analysis would be required to show which of the two alternatives is more probable, if not reasonably certain to be true.

9. I have been writing of two kinds of ITS. The first is an ITS of infinite duration (ITS-ID); the second is an ITS of finite duration (ITS-FD). Frequently, the first is referred to as being topologically infinite, while the second is held to be metrically finite. Sometimes the former is described as a series that is temporally infinite, while the latter is described as temporally finite. Another usage is to refer to the former as a series having an infinite past, and the latter as having a finite past. And yet another usage is to refer to the former as a temporal series with an infinite past and the latter as one with a finite but open past. (A FTS, on the other hand, is one with a finite but closed past.) Sometimes I shall refer to a universe with an ITS-FD history as a universe of an indefinite finite duration; and sometimes I shall refer to a universe with a FTS-FD history as a universe of a definite finite duration.

10. A paradigm way of speaking of a temporal series with a finite but open past is to compare it with a continuous sequence of rational fractions in descending order of magnitude, with 1/2 as the last fraction, the penultimate fraction as 1/4, next with 1/8, then 1/16, and so on down with 0 as the limiting value to which the sequence converges (but never reaches). The limit to which a temporal series with a finite but open past regressively converges (but does not reach) can conveniently be called a finite limiting value of its duration (hereafter flvd). Thus one example of an ITS-FD is a TS of nonoverlapping, consecutive intervals of equal duration that consists of two parts. The second part consists of all intervals except the first—with each such interval encasing finitely many consecutive events. The first part of the series, the first interval, consists of a sequence of infinitely many consecutive events, each being of longer duration than the immediately preceding event in that sequence. The first part of this particular series of temporal intervals is comprised of denumerably infinite many temporal subintervals of unequal duration, each of which encases one and only one event. Here it is worth bearing in mind that to speak of a TS of finite duration is somewhat ambiguous. In the case of a series having a first event, the duration of the history of the universe from that first event to the present is indeed definite. In the case of an ITS of events of finite duration (thus having a flvd), the duration of that ITS during the first temporal interval bounded by the flvd in the earlier-than direction is indefinite since there is neither a first event nor a first subinterval which encases one and only one event.

11. An ITS-FD clearly appears to be logically possible. However, our inquiry is whether this series is per se or per accidens metaphysically possible. Whatever is metaphysically possible is logically possible; but the converse does not hold. To assert that it is metaphysically possible for an ITS to obtain does not entail that such a series necessarily obtains as a so-called brute fact. Thus neither the KCA nor the KCAAA itself is concerned with whether an ITS of events, whether of finite duration or not, is as a whole contingent upon God as its sustaining or conserving cause.[16] Neither the KCA nor the KCAAA is concerned with whether or not an ITS, as a whole, has been created (in a causally but not temporally prior sense) by God, nor whether or not it could possibly obtain without his creation—assuming for argument's sake that such a series is metaphysically possible. The KCA only purports to show that the universe of finite duration began to exist (in the sense of having a first event), and that the beginning of the universe was necessarily caused by God.[17] The KCAAA only purports to show that the history of the universe involves an ITS-FD, and that its actualization was necessarily caused by God. The philosophical arguments for the KCA were concerned with the metaphysical possibility of any ITS; because if any such series is metaphysically impossible, then not even an omnipotent God could create, sustain or conserve such series as a whole. Thus the SP-KCA is purportedly established on purely philosophical grounds. The SP-KCAAA will necessarily depend upon empirical grounds—absent showing why an ITS-ID, but not an ITS-FD, is metaphysically impossible.

12. Craig enumerated in his The Kalam Cosmological Argument three plausible alternatives (attributing them to C. D. Broad): "that the universe either (1) had no beginning and is temporally infinite, (2) had no first event but is temporally finite, being analogous to the series ... [1/8, 1/4, 1/2], or (3) had a first event and is temporally finite."[18] Immediately following this statement, Craig quotes the following passage from Broad:

Now ... I find no difficulty in supposing that the world's history had no beginning and that its duration backward from its present phase is infinite. Nor do I find any insuperable difficulty in supposing that the world's history had no beginning, but that its duration backward from its present phase does not exceed a certain finite limiting value. But I confess that I have a very great difficulty in supposing that there was a first phase in the world's history, i.e., a phase immediately before which there existed neither matter, nor minds, nor anything else.... I may say when I am trying to give Hume a run for his money, I cannot really believe in anything beginning to exist without being caused (in the old-fashioned sense of produced or generated) by something else which existed before and up to the moment when the entity in question began to exist.[19]

13. Note how Broad uses the term "the world's history had no beginning" in exactly the same sense: i.e., that the world had no first bounded phase, event, or state, whether or not of finite duration (in the sense of a duration backward from the present towards a finite limiting value). There is something else to note. The causal principle with respect to beginnings of existence (hereafter CPBE) stated by Broad can be paraphrased as follows: whatever begins to exist has been caused (either produced or generated) by something else which existed before and up to the moment when the entity in question began to exist. This is clearly much more precise than the causal principle as stated in the FP-KCA.

14. After quoting C. D. Broad, Craig then explained that "the first two alternatives [as Craig lists them] are untenable in the light of [his philosophical and empirical arguments in favor of the SP-KCA]."[20] This leaves Craig's third alternative (that the universe had a first event and is temporally finite) surviving the arguments in favor of the SP-KCA.[21] Given the causal principle embodied in the first premise of the KCA (hereafter FP-KCA), it follows that the beginning of the universe was caused since "no one ever questions the premise that if in the past nothing existed then nothing would exist now."[22] But note that in this context Craig also uses the phrase "the universe began to exist" in the same way as Broad, implying that there was a first event in the finite history of the universe.[23] In other words, as Craig uses the phrase, "the universe began to exist" does not apply to a universe whose history is included in or constituted by an ITS, whether it is of infinite duration or not. Thus within the meaning of FP and SP-KCA, the beginning of the universe of finite duration is the first event or moment of its history. But it is again worth noting here that Craig's statement of the causal principle concerning beginnings of existence in FP-KCA is verbally broader than that which Broad would have provided. The FP-KCA uses the term cause to refer to the something which causes (i.e., produces or generates) the beginning of an existence. But this could encompass the cause as existing before and up to the beginning of the existence of the entity in question; or it could encompass an atemporal being which did not exist before and up to the first moment of the existence of the created entity.

15. In The Kalam Cosmological Argument William Lane Craig presented two philosophical subarguments to show that our universe is of definite finite duration. The first was that an infinite set of real entities (which any ITS is) is metaphysically impossible. The second was that any ITS is metaphysically impossible[24] (despite assuming for argument's sake that an infinite set of real entities is metaphysically possible). Having made these two subarguments, Craig proceeds to buttress his case that the universe began to exist with empirical confirmations. He explains: "Some persons may be sceptical about philosophical arguments concerning the universe—what has been characterized as 'armchair cosmology'. They distrust metaphysical arguments, considering them to be misguided attempts to legislate for reality what can and cannot be. They are liable to be more impressed by empirical facts than by abstract arguments and are apt to ask for scientific evidence that the universe began to exist."[25] Such persons, therefore, are more likely than not to be agnostic or indifferent about the metaphysical possibility, or impossibility, of an ITS. For such people, Craig should have considered himself as having stopped himself from relying upon the MS-KCA.

16. By ostensibly condescending those who denigrate armchair philosophy, in The Kalam Cosmological Argument Craig appears to regard his empirical confirmations as being independent of his MS-KCA. Nevertheless, he asserts: "Besides, in our argument, the empirical evidence is simply confirmatory of a conclusion already reached by pure philosophical argument; it shows, if you will a harmony between theory and observation."[26] In other words, the empirical confirmation serves as the frosting on the cake. But whether considered simply as confirmation or as a separate argument, in The Kalam Cosmological Argument Craig clearly holds that so-called 'empirical confirmations' are not to be understood as supporting any thesis inconsistent with his conclusion that any ITS is metaphysically impossible.

17. The first empirical confirmation is provided by the Standard Big Bang Model (SBBM). According to this model, "the universe began with a great explosion from a state of infinite density.... [but] a condition of 'infinite density' is precisely equivalent to 'nothing.'"[27] Craig's second empirical confirmation is based upon the second law of thermodynamics—according to which, Craig contends, "eventually the universe and all its processes will, so to speak, 'run down', and the entire universe will slowly grind to a halt and reach equilibrium."[28] Craig concludes that the "scientific evidence concerning the expansion of the universe and the thermodynamic properties of closed systems indicates that the universe is finite in duration, beginning to exist about fifteen billion years ago."[29]

18. Ultimately, these 'empirical confirmations' are dispensable if Craig's theological commitments preclude them. As a theologically conservative Christian, Craig believes that it is a divinely-revealed truth that this world is of finite duration and that the beginning of the world was caused ex nihilo by God[30]; and this belief overrides whatever current or future scientific models and evidences conflict with it.[31] After all, it behooves us all to remember the dictum of St. Ambrose: Non in dialectica complacuit Deo salvum facere populum suum—It is not in dialectic that it pleases God to save his people.[32]

19. Fortunately for Craig and others, however, there do (arguably) appear to be empirical confirmations of the SP-KCA. Even more fortunately for them, the opponents of the KCA have generally been polemically handicapped, almost exclusively due to self-inflicted wounds which adversely affect their efforts to adequately respond. For example, we have seen that opponents of the KCA have generally agreed with Craig that the only plausible way of applying Cantorian set theory to the real world is via (what I call the) the standard version (SV)—which I thoroughly (and I think justly) criticized in my first Kalam article. Another example is the failure of critics of Craig's second argument to notice that an ITS cannot possibly be properly said to be a series formed by successive addition, or indeed in any other way. Moreover, there has been a general failure to discern that the proposition that any traversal of an infinite is metaphysically impossible is ambiguous—such that there is a frequent failure to appreciate that the impossibility of a traversal of an infinite applies only to the situation where at sometime there was an infinite yet to be gone through one-by-one. That the philosophical arguments in favor of the SP-KCA should be rejected as untenable does not preclude holding that a traversal of an infinite is metaphysically possible when there is no time that an infinite has yet to be gone through.

20. Since advocates and opponents of the KCA (including Craig) generally accept the standard version (SV) of how Cantorian set theory can possibly apply to the real world, if it can be applied at all, we have to be on the alert for the following. If Craig presents the so-called 'empirical confirmations' as an independent argument for the premise that the universe began to exist, he may be willing (if only implicitly) to assume—for argument's sake—that not every ITS is metaphysically impossible after all. In that case, he may very well be disposed to also (implicitly) assume—for argument's sake—that it is metaphysically possible to traverse an actual infinite yet to be gone through one-by-one. He may be so disposed because in his advocacy of the KCA he fails to make the critical distinction between the traversal of an infinite where (1) there is at sometime an infinite yet to be traversed and (2) where there is only a finite yet to be traversed. Or perhaps Craig may have, or eventually come to have, something else (at least implicitly) in mind. And so he might have come to distinguish between the traversal of an infinite which at any time is yet to be traversed consisting of (a) equal units and (b) an infinite number of unequal units ordered in a series converging to a finite limiting value. Almost needless to say, I do not see Craig as abandoning the KCA and replacing it with the KCAAA. Rather, he appears to be desperately offering both arguments—having it both ways—in order to appeal to two disparate kinds of readers.[33] On the one hand, he presents the KCA to intellectually satisfy readers who agree or come to agree that any ITS is metaphysically impossible; on the other, he presents the KCAAA for those readers, more likely to be impressed by empirical matters, who are open to the idea that the temporal series which includes (or constitutes) the history of the universe is (or might very well be) an ITS-FD. But by admitting (for the sake of argument) that an ITS-FD is metaphysically possible (i.e., accepting the KCAAA) he has deprived himself of any principled basis for successfully arguing that an ITS-ID is also metaphysically impossible. But perhaps he must give these people some epistemically respectable basis for believing that the cause of the universe is a personal Creator who is changeless and timeless sans creation, based upon the supposition that an ITS-FD, unlike an ITS-ID, is metaphysically possible.

21. In their book Theism, Atheism, and Big Bang Cosmology, Craig and Quentin Smith explore the KCA in light of an agreement to treat the SBBM as probably true. Craig was quite willing to do so since he considers each of the more plausible alternative empirical models to be seriously flawed.[34] Smith did so, almost in a spirit of bravado, because he argues that on the SBBM the beginning of the universe is not only uncaused but actually inconsistent with the theistic explanation.[35] Craig and Smith agreed to explore the issue of the probative value of the SBBM as evidence for creatio ex nihilo theism and for atheism, respectively. Incidentally, both appear to have consciously disregarded considerations based upon philosophical arguments for the MS-KCA.[36] Yet unless informed otherwise, the reader would naturally have supposed that Craig's independent empirical argument for the SP-KCA (that the universe began to exist) would at least be consistent with the MS-KCA. As we shall see, Craig never acknowledges that his independent empirical argument for the SP-KCA is radically inconsistent with the MS-KCA. To show this we must now proceed to lay the necessary foundations—or rather sap the foundations—of the KCAAA.

22. In Theism, Atheism, and Big Bang Cosmology, Craig initially presents what he describes as "an abridged excerpt" from his Kalam Cosmological Argument.[37] Thus he presents a condensed and amended version of his earlier book, but again with the two philosophical arguments supporting the MS-KCA and his empirical confirmations.[38] But he also includes some additional matter which will prove to be very relevant to our discussion. He addresses the issue of whether it is metaphysically possible for temporal instants to be events or moments. But he explains that "[s]ince an event is a change, there are no instantaneous events."[39] He submits, with G. J. Whitrow, that "'although the hypothesis that time is truly continuous has definite mathematical advantages, it is an idealization, and not an actual characteristic of physical time.'"[40] Indeed, Craig observes: "Treating instants as degenerate temporal intervals of zero duration does seem to land one in Zeno's clutches, since temporal becoming would require the actualization of consecutive instants, which is incoherent."[41] Accordingly, "it makes no difference whether we stipulate that the events at issue be equal in duration or not; even if we take events of progressively shorter durations, we shall never come up with an actual infinite number of them in any finite interval."[42] For this reason Craig explains that his "conclusion that an actually infinite temporal regress of events cannot exist rules out an infinite, but not a finite, past." Therefore," he declares, "the universe began to exist."[43] But then, according to Craig, the finite past cannot consist of infinitely many events or moments of progressively shorter duration towards the flvd since any ITS is metaphysically impossible. For this reason Craig initially confirms his conclusion in Essay I of Theism, Atheism, and Big Bang Cosmology, reached in The Kalam Cosmological Argument, that the metaphysical impossibility of an ITS, whether or not of finite duration, rules out every option except that the universe had a first event or moment.[44]

23. In Essay IV[45] in their book, Quentin Smith provides an admirably lucid and useful exposition of the SBBM, and of his reasons for affirming the reality of the initial cosmological singularity (ics) which preceded the Big Bang.[46] Smith also considers what should be regarded as the beginning of the universe and whether it took place at: "(1) the singularity; (2) after the singularity; or (3) neither at nor after the singularity."[47] Smith explains that the first alternative "would be relatively simple," provided that it were the case "that there exists a single point in which the entire universe is compressed, and the existence counts as the beginning of the universe"—and that this point exists for one instant before exploding in the Big Bang. But "the universe is imperfectly homogeneous and isotropic [and such] imperfect symmetry implies the universe began non-simultaneously at a series of points." Indeed, although "the universe is sufficiently symmetric so that all [past-directed timelike geodesices] do end in singularities," nevertheless "[t]he less dense parts of the universe exploded from points first, followed by the more dense parts."[48] However, Smith rejects the first proposed definition of what constitutes the beginning of the universe since the initial singularity cannot be regarded as a part of the universe, as it is not a point in the spacetime continuum.[49] Smith also considers the third alternative, but rejects it because "[t]he concept of a singularity, on this view, is a limiting concept that refers to nothing existent."[50]

24. Ultimately, the definition of the beginning of the universe that Smith adopts is that it is the first Big Bang, i.e., the first post-t0 (post-initial singularity) interval of length—the first 10-43 seconds (the first Planck era)—which should be deemed to constitute the first state of the universe.[51] Smith notes that, besides the explosion of four-dimensional spacetime out of the point(s) that exist(s) at t0, there are other explosions from points that exist at instants later than t0. Thus the Big Bang that explodes from the singularity at t0 is the first Big Bang, and can be designated as "the Big Bang1" since there are other Big Bangs which follow the the the Big Bang1. It is the Big Bang1 that is the beginning of the universe. He decides to "assume the second definition to be the correct one, as it treats the singularity as real and thus complies with the Hawking-Penrose singularity theorems."[52]

25. In Essay VII, Smith propounds his argument that classical Big Bang cosmology is inconsistent with theism in part due to the unpredictable nature of the Big Bang singularity. In this essay, Smith makes an effort to anticipate the counter-argument to the effect that the singularity is not real but is, instead, a mere mathematical idealization.[53] Indeed, Smith urges not only "that the description or definition of the Big Bang singularity as a mere idealization does not belong to Big Bang cosmology itself," but that moreover the "past-directed spacetime paths in the early universe are not modeled on half-open intervals that approach arbitrarily close to but never reach the ideal limit, but on closed intervals one of the end-points of which is the singularity."[54]

26. Responding in Essay VIII ("Theism and Big Bang Cosmology")[55] to Smith's argument about whether the Big Bang singularity is real rather than being a mathematical idealization, Craig makes the following significant point: "The initial cosmological singularity is not an existent."[56] He goes on to explain:

[T]he singularity has no positive ontological status: as one traces the cosmic expansion back in time, the singularity represents the point at which the universe ceases to exist. It is not part of the universe, but represents the point at which the time-reversed contracting universe vanishes into non-being. There is no first instant of the universe juxtaposed to the singularity. The temporal series is like a series of factions converging toward 0 as its limit: [1/2, 1/4, 1/8,...,0]. Just as there is no first fraction, so there is no first state of the universe.[57]

27. Accordingly, Craig announces that given his interpretation "the singularity is not the first created state of the universe after all."[58] This declaration by Craig should be considered in light of his opinion that "anything having positive ontological status would seem necessarily to exist for some temporal duration; to say it exists only for a durationless instant is to ascribe reality to a mathematical chimera."[59] Craig similarly says: "[A]n object which has no spatial dimensions and no temporal duration hardly seems to qualify as a physical object at all, but is rather a mathematical conceptualization."[60] Craig opines in conclusion: "it seems to me that the metaphysician is rational in interpreting the ontological status of the singularity as nothingness rather than as the first state of physical reality."[61]

28. In the course of responding to Smith's criticism of his analysis in Essay IX, Craig confirms his opinion concerning the ontological status of the ics (in Essay X[62]). Again urging that "points and instants have reality only in so far as they bound intervals," Craig submits: "[T]he universe did not begin at the singularity. Rather the universe, the spacetime manifold, does not possess a first temporal instant, but exists at any moment arbitrarily close to the initial cosmological singularity."[63]

29. In other writings Craig has sometimes expressed himself in a way seemingly contrary to the foregoing—perhaps when he was writing ad populum.[64] However, Craig has taken pains to explicitly set forth his professed position in response to a charge by Adolf Grünbaum. Grünbaum charged that Craig had maintained that the first temporal interval concerns a scenario in which the ics is treated as the first physical state of the universe.[65] Craig explained that he had simply "argued ex concessionis that the initial cosmological singularity, if ontologically real, requires a cause, whether or not any arbitrarily chosen initial temporal interval is closed or open in the earlier-than direction." However, he declared that his "own position has been to regard the initial cosmological singularity as ontologically equivalent to nothing, so that t = 0 is a mathematical idealization and any initial interval of time is open in the earlier-than direction [citing Craig and Smith (1993), pp. 43-44, 146-147. 224-227, 258-261]."[66]

30. But to show that Craig expressed himself in a fashion utterly inconsistent with the MS-KCA, I refer the reader to his statement in note 3 of his 1994 article "Prof. Grünbaum on Creation":

This conclusion [that if the universe did begin to exist, its origination must have been the effect of some transcendent cause] is not undermined by the query of an anonymous referee for this journal: "Why does the big bang imply that the universe begins to exist without a cause? In the standard big bang models, for every time t there is a t1, and the state at t1 is a cause of the state at t".... The referee cannot mean to deny the premise that whatever begins to exist has a cause, because he affirms that every instantaneous state of the universe has a cause in a prior state. So he is not claiming that the origin of the universe is uncaused and, hence, an exception to this principle. But neither does he appear to be denying the premise that the universe began to exist. For a beginning of time (and the universe) does not entail that a first instant of time existed. Time began to exist iff [if and only if] there is a finite interval of time which is such that every other congruent temporal interval is later than that interval, and prior to any finite interval of time there is at most a finite number of congruent temporal intervals. Hence, it is standard to regard the universe as having a beginning even though any initial temporal interval of arbitrary length is open in the past.[67]

31. What Craig is contending is that there must be a transcendental cause of an ITS-FD (constituting the history of the universe), notwithstanding that each event in the series has been caused by an earlier event. But the point of the MS-KCA is to show that the universe had a beginning in the sense that it had a first event in its history and is of finite duration. So what Craig is emphasizing is that the universe should be deemed to have begun to exist because it is of finite duration (in that its history is that of an ITS-FD). And so it is with a mine de rien (that is, as if it were nothing), without so much as the sound of the trumpet, or even a blinking of an eye, that Craig now explains what is presently the standard understanding of what constitutes the beginning of the universe. However, as we have seen, Craig's understanding of this matter in The Kalam Cosmological Argument and his two essays in the first part of Theism, Atheism, and Big Bang Cosmology was not at all standard in the same sense.

32. Other than in his replies to Grünbaum, Craig has never stated that his acceptance of the received understanding of the SBBM—that the universe (the spacetime manifold) does not possess a first temporal instant bounding a physical event in an earlier-than direction—was made simply for argument's sake, ex concessiones. If Craig had used this so-called standard interpretation to undercut an argument by Quentin Smith that Big Bang cosmology is actually inconsistent with theism, he could not have accepted the received understanding of the SBBM merely ex concessiones. However, in actually accepting the received understanding of the SBBM, Craig has (seemingly without realizing it) constructed a KCAAA utterly incompatible with the MS-KCA. However, having taken the position that Big Bang cosmology provides empirical confirmation of the SP-KCA, there was little he could have done without jeopardizing the ostensible persuasive value of his empirical argument—treating it as independent of the philosophical subarguments in support of MS-KCA. But then it follows that he implicitly acknowledged (if but for argument's sake) that it is metaphysically possible for there to be an ITS of finite duration. A fortiori, Craig does not appear have any principled basis for objecting to the metaphysical possibility of an ITS of infinite duration. In constructing the KCAAA he redefines the term beginning of the universe such that "[t]ime begins to exist just in case there is some finite interval of time which is not preceded by an interval of equal length"—whether or not it pertains to an ITS.[68] According to Craig: "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"—apparently in reference to physical rather than metaphysical time.[69]

33. Perhaps there is a clue to be found in Craig and Moreland's Philosophical Foundations for a Christian Worldview, which again expounds the KCA. According to Craig and Moreland, an ITS of physical events cannot be traversed. In response to the objection based upon the Tristram Shandy Paradox that the argument is "a sleight-of-hand trick like Zeno's paradoxes of motion," they write:

But such an objection fails to reckon with two crucial disanalogies of an infinite past to Zeno's paradoxes: whereas in Zeno's thought experiments the intervals are potential and unequal, in the case of the infinite past the intervals are actual and equal. The claim that Achilles must pass through an infinite number of halfway points in order to cross the stadium is question-begging, for it already assumes that the whole interval is a composition of an infinite number of points, whereas Zeno's opponents, like Aristotle, take the line as a whole to be conceptually prior to any divisions which we might make in it. Moreover, Zeno's intervals, being unequal, sum to a merely finite distance, whereas the intervals in an infinite past sum to an infinite distance. Thus his thought experiments are crucially disanalogous to the task of traversing an infinite number of equal, actual intervals to arrive at our present location.[70]

34. However, our authors remarkably fail to point out what is crucially analogous: the task of traversing at sometime a yet to be traversed infinite of unequal actual intervals (either in ascending or descending order of magnitude) to arrive at our present location. Craig and Moreland want to have it both ways. First, they want to deny (and rightly so) that Achilles has to traverse infinitely many points or intervals in order to cross the stadium. Second, they want to distinguish (1) Achilles having to traverse infinitely many unequal intervals in crossing the stadium from (2) his having to traverse infinitely many equal intervals to arrive at the present moment. After all, as Craig and Moreland explain: "from any given point in the past, there is only a finite distance to the present, which is easily 'traversed."[71] Given the foregoing, my guess is that Craig and Moreland have the following strategy implicit in their dialectic: First, they use the philosophical argument for the SP-KCA in order to preclude any alternative but that the universe is of definite finite duration. However, a tension obtains with respect to the so-called 'empirical confirmations' according to the SBBM, as there is no first event in the history of the universe even though its past is of indefinite finite duration. Second, in making an independent argument based upon 'empirical confirmations,' they assume (for argument's sake) the metaphysical possibility of an ITS in order to conform with the received interpretation of the SBBM. Thus the "temporal distance" between the ics and the present is finite, and intuitively we know that a finite distance may be "easily traversed." It is ironic that the KCAAA has effectively deprived the KCA simpliciter of its incisors if not all its teeth. To admit the metaphysical possibility of a universe with a finite but open past is inconsistent with the original conclusion that this alternative is precluded by the philosophical arguments in support of the KCA. What is interesting is that the KCA and the KCAAA are not just two independent arguments which mutually support each other; rather, they devour one another.

35. In discussing the question of the metaphysical possibility of a universe with a finite but open past, it is very useful to circumscribe the scope of our inquiry in the interest of economy—with the concomitant hope that the reader will be willing to at least go along for the ride for the sake of argument. Therefore, I am quite willing to express agreement with Craig upon some fundamental issues not simply ex concessiones but also because I do in fact substantially agree with him. It is, I think, quite unnecessary for me to burden this paper with an exposition of the reasons of why I agree with Craig upon numerous issues—and I hereby incorporate by reference all those sound arguments that support those basic, relevant propositions about which we agree.

36. First, like Craig, I adhere to some version of the dynamic or tensed A-theory of time—whereby "events are temporarily ordered by tensed determinations of past, present, and future, and temporal becoming is an objective feature of physical reality, [as distinguished from the] B-theory of time, according to which events are ordered by the tensiveless relations of earlier than, simultaneous with, and later than, and temporal becoming is subjective and mind-dependent."[72] According to Craig, "belief in the objective reality of tense and the reality of temporal becoming is a properly basic belief.... and enjoys such powerful positive epistemic status for us that not only can we be said to know that tense and temporal becoming are real, but also that this belief constitutes an intrinsic defeater-defeater which overwhelms the objections brought against it."[73] I agree with that assessment. In any case, the A-theory is presupposed by the second philosophical subargument of the KCA (i.e., that an infinite temporal series is metaphysically impossible).[74] And that is just fine with me.[75]

37. Furthermore, according to Craig and Moreland,

[T]he A-theory of time indicates a commitment to presentism, the doctrine that the only temporal entities that exist are present entities. According to presentism, past and future entities do not exist. Thus there really are no past or future events, except in the sense that there have been certain events and there will be certain others; the only real events are present events.[76]

On the other hand, past events or moments have a kind of actuality which future events or moments patently lack. And it is this actuality of past events or moments which makes it possible to speak of an actual infinite of the same.[77] But presentism does appear to me to be most consistent with the reality and objectivity of temporal becoming. Again, although some A-theorists disagree, I nevertheless ask the reader to accept presentism for argument's sake.

38. I also heartily concur with Craig that whatever constitutes the present moment (or any temporal interval) is not of zero duration, and that instants (which by definition are not of zero duration) are but the boundaries of temporal intervals. It is hence meaningless to speak of the present instant. We do, however, speak meaningfully of the present event or phase, or second, minute, hour, year, and so forth. Accordingly, every event or temporal interval in a finite temporal series (except the last member) is immediately followed by the next event or temporal interval. And I agree with him as to foregoing. Craig rightly insists that the A-theory requires that temporal intervals be of nonzero duration, otherwise "Zeno's paradoxes of motion and quantity seem to become inescapable."[78]

39. However, I part with Craig's rejection of the view "that time does in fact exist in physically minimal units, or time atoms called 'chronons.'"[79] According to the atomistic version of presentism, there are ultimately indivisible temporal intervals of nonzero duration that are consecutively sequenced one immediately after the other. Craig admits "[w]e instinctively feel that there must be some unique metric interval which is present absolutely." This notwithstanding, the principal reason for Craig's rejection of the theory of the atomicity of time appears to be based upon Zeno's paradox of the stadium.[80] According to Craig, the atomistic version of presentism leads to "some bizarre results" and thus "seems crazy."[81] He presents the stadium paradox as follows: Let us imagine two rows of spatial atoms moving in opposite directions along a row of atoms at rest at the rate of one atom per chronon. Doing so, however, discloses the startling anomaly that there are discontinuous jumps resulting in the total absence of some alignments as illustrated in the diagram shown in the accompanying note.[82]

40. Fortunately, Craig may be relieved of his scruples occasioned by Zeno's paradox of the stadium. This paradox obtains simply because it is uncritically assumed that the rows A and B of atoms move at the rate of one full atom-space per chronon. According to this assumption, there are finitely many nonoverlapping spaces which are consecutively occupied. But why make this assumption? Why shouldn't rows A and B of atoms move at the rate of one overlapping atom-space per chronon? Suppose, for example, that A moves at the rate one-half atom space per chronon such that any two consecutive atom-spaces overlap by half—as illustrated in the schema in the accompanying note.[83] Voilá! There is no problem of missing alignments! The undercutting defeater of Craig's objection is that the idea of the motion of an object involves the sequential occupation of finitely many consecutive overlapping spaces with a corresponding temporal sequence of as many successive nonoverlapping chronons—thereby successfully obviating Zeno's paradox of the stadium.

41. But having improvidently rejected the atomistic theory of time, Craig holds that the present temporal interval, such as the present minute, is "qua minute present simpliciter, but if we divide it into seconds, then only one second is qua second present simpliciter. If any sub-interval of an interval is present, then the whole interval is as such present."[84] According to Craig: "This process of narrowing can be continued indefinitely, with the present instant as a conceptual limit, so that there is no minimal temporal interval which is now."[85] He asserts that "[t]he present will be any arbitrarily chosen interval centered on a present instant." Nevertheless, "time is not composed of instants, [and] temporal becoming does not proceed by instants."[86] However, Craig candidly acknowledges that his nonmetricist account of presentism "is admittedly strange because it implies that there is no such thing as the present time." He goes on to lament: "None of the alternatives for understanding the extent of the present leaves one feeling entirely comfortable. But discomfort is not incoherence. It may be a reflection of how profoundly difficult time is to understand. It does not show that temporal becoming is unreal."[87] On the other hand, Craig's objection to the atomistic theory of time is unwarranted, and so there is hope that he will someday feel entirely comfortable with it. In the meantime, having duly noted my disagreement with him, we proceed on the shared assumption that some presentist version of the A-theory obtains (whether atomistic or nonmetricist) which excludes temporal intervals of nonzero duration.

42. With the A-theory we have absolute simultaneity rather than some operational definition for "simultaneity." If an event happens now there may well be other events also happening even though we may not be able to determine whether they happen now—as in a case in which we are in one inertial frame and the other events in question pertain to another inertial frame moving near the speed of light in some far distant region of space.[88] According to Craig, metaphysical time differs from physical time (the measured time pertaining to the physical world). Local physical time and space are determined by measurements made with one's own "clocks" and "rods," and are affected by motion relative to another inertial frame. By contrast, metaphysical time is independent of physical measurements. As Craig describes it: "[metaphysical time] is characterized by a universal and objective present and, hence, relations of absolute simultaneity."[89] The Special Theory of Relativity only concerns reference frames in a state of uniform motion. However, General Relativity Theory and developments in astrophysical cosmology have led to the recognition that there is a cosmic time based upon a unique fundamental reference frame provided by the global features of the universe itself. The cosmic time reliably approximates the true time because the former is measured by a clock at rest with respect to the fundamental reference frame—"in contrast to the multiplicity of local times registered by clocks in motion relative to the cosmological substratum."[90]

43. According to Craig, it is metaphysically possible for there to be two or more mutually discrete physical or space-time manifolds in addition to our own.[91] Even before the creation of any physical world, God could have created a supernatural world. Indeed, he could have eternally willed a temporal succession of his own mental events—albeit only finitely many given the MS-KCA. For example, God could be conceived "to be counting down toward the moment of creation: '...three ...two ...one ...Let there be light!'"[92] Moreover, it seems to me that God could have created one or more other universes which are not spatially related to each other. But there can only be one metaphysical time. As Craig explained the matter:

But while it makes sense, perhaps, to speak of a B-theory of branching metaphysical time, I can see no such sense of an A-theory of branching metaphysical time. For on an A-theory of metaphysical time, moments of time elapse successively one after another completely independently of what may be happening physically. Since such time is not wedded to space, even the formation of new universes would not cause time to 'branch': the same metaphysical time in which the wider space endures measures all the separate universes as well. This seems to me a coherent picture, and the theist who regards God as temporal would no doubt conceive of Him as existing in this metaphysical time, which would measure the succession of God's contents of consciousness.[93]

44. Along with other philosophers, Craig has made an impressively persuasive (if not convincing) case that God's being atemporally (or timelessly) eternal without qualification is inconsistent with the A-theory.[94] I concur with this assessment. Moreover, Craig candidly acknowledges that, although God is omnitemporal only in a rather limited sense (in that he exists at every moment of time), "[t]his might seem to imply that God has existed for infinite time in the past and will exist for infinite time in the future."[95] However, given the MS-KCA, time—insofar as it is conceived as consisting of temporal intervals of equal duration—must be considered as having a beginning, for it necessarily has a first interval. So Craig's thesis is 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."[96] He concedes that the argument that there was an undifferentiated time temporally prior to creation is plausible, although he ultimately rejects it.[97]

45. Given Craig's thesis that God is atemporal without creation but temporal with it, what is God's relation to metaphysical time and to that cosmic time of the space-time manifold of our universe? Let us suppose that God enters, as it were, metaphysical time with the creation of the universe. Craig declares:

Now God's metaphysical time cannot be said to be identical with cosmic time, since the former is capable of exceeding the latter, in that metaphysical time could precede physical time (recall God's counting down to creation). Nevertheless, since the inception of cosmic time, the moments of God's time would seem to coincide with the moments of cosmic time. When we reflect that God is causally related to the cosmos, sustaining it in being moment to moment, then it seems difficult to deny that the duration measured by cosmic time is also the duration of God's temporal being.[98]

However, as Craig reminds us, "cosmic time is physical time rather than metaphysical time." Moreover, "cosmic time and metaphysical time are presently coincident, though not identical.... In virtue of that coincidence, cosmic time may be quite properly said to be absolute in the sense that it gives the true time."[99]

46. As Craig writes: "God brought the universe into being out of nothing at some moment in the finite past and ... He sustains it immediately in being moment to moment."[100] Now when, pray tell, did God bring this "universe into being out of nothing at some moment in the finite past"? Recall that Craig says that "there were no instants of [physical] time prior to the initial cosmological singularity."[101] Given the SP of the KCA or the KCAAA, he insists that the cause of the universe's origin is not necessarily chronologically prior to that origin. For Craig the beginning of this universe (according to the KCAAA usage) is coincident with the ics. As he explains:

If nothing can be, technically speaking, "simultaneous" with the singularity, since it is not an instant of time, then we can substitute other locutions to convey the idea, like "coincidence," i.e., two incidents co-occurring, or occurring together. If this is not clear enough, we can say further that two incidents co-occur iff they both occur and there is no time between their occurrences. One might note furthermore that even though t = 0 is not an instant of time, nevertheless it functions logically like an instant of time, so that it makes perfectly good sense to say that God created the universe at t = 0.[102]

And to tell the truth, this does make good sense to me for our purposes. Accordingly, God created the universe at that instant of metaphysical time which was coincident with the putative ics and this coincidence can be said to constitute the beginning of the universe in the KCAAA sense of that term. More recently, Craig has confirmed his belief "that God exists timelessly sans creation and temporally at and subsequent to the moment of creation, so that His act of causing the beginning of the universe is simultaneous with the universe's beginning to exist."[103]

47. At this point I cannot go along with Craig regarding the form of a particular issue, although I can follow him as to the matter of it. This pertains to the FP and the SP of the KCA, and to the FP and the SP of the KCAAA, in connection with the meaning of begins to exist as applied, respectively, to a universe of a FTS-FD kind, and one of a ITS-FD kind. Recall that with respect to the FP and SP-KCA, the moment of creation is simultaneous with a corresponding first moment or first event of the existence of the universe in question. The universe of a FTS-FD kind begins to exist in a rather straightforward manner (one might say). In the case of the creation of the universe of an ITS-FD kind, there is no first moment or event corresponding to the moment of creation. The moment of creation has an initial instant which coincides with the flvd, which is the boundary of a degenerate temporal interval. Craig expands the meaning of begins to exist to encompass the creation of a universe with a history constituted by an ITS-FD. Although I do not find it useful to speak of such a universe as having a beginning in the sense of the KCA, for our purposes I am quite willing to go along with Craig as much as I can. Our purposes can be served by simply referring to the beginning of existence in the sense of the KCAAA.

48. The reason why I insist upon the verbal distinction is that the FP-KCA supposedly embodies a first principle—a belief which is properly basic and incorrigible.[104] But why water-down the principle by broadening it to encompass a problematical situation? However, assuming the truth of the FP-KCA, a fortiori it would be antecedently more probable than not that a universe of an ITS-FD kind also has a cause—provided, of course, that such a universe is metaphysically possible. With respect to a universe which begins to exist in the KCA sense, whatever event that constitutes the efficient cause of the beginning of the universe is either immediately temporally prior to or simultaneous with that beginning. With respect to a universe which begins to exist in the KCAAA sense, that event that constitutes the efficient cause of the actualization of the universe involving an ITS-FD is neither immediately temporally prior to nor simultaneous with the first moment or event in the history of the universe (since there is no such first moment or event). Surely that the causation of such a universe is so different from the causation of an universe of a FTS-FD kind is sufficient to justify our preference for speaking of entities which, respectively, begin to exist in either the KCA sense, or in the KCAAA sense, as the case may be.[105]

49. We are now finally ready to address the central issue: whether an infinite temporal series of finite duration is per se or per accidens metaphysically possible. First, let's address this issue as it pertains to the various species of theism. Recall that, notwithstanding the rejection of MS-KCA, the traversal of an infinite which at some time involves an infinite yet to be traversed is metaphysically impossible. This proposition holds true both for the supporters and opponents of MS-KCA. Hence there can be only finitely many events or temporal intervals between any two bounded events or intervals in an ITS. We will now consider the various principal kinds of theism in sequence.

50. According to the thesis that God is omnitemporally eternal, metaphysical time necessarily includes infinitely many successive events or temporal intervals in God's mental life. So that instant of metaphysical time coincident with the flvd of a universe that begins to exist in the KCAAA sense[106] is the boundary of some event or moment in metaphysical time. This boundary may be in the earlier-than or the later-than direction, depending upon whether the moment of God's creation is temporally prior to or simultaneous with the beginning of the universe in the sense of the KCAAA. Yet there are infinitely many events between the flvd and the present moment, which by hypothesis are mapped on or coincident with God's metaphysical time. But this is not possible: If an omnitemporally-eternal God exists, then an ITS-FD is metaphysically impossible.

51. Let us now consider the thesis that God exists sans creation in some undifferentiated time. That instant of metaphysical time, which both terminally bounds God's undifferentiated time and serves as the initial instant of the moment of creation of a universe which begins to exist in the KCAAA sense, is coincident with the flvd. Alas! But in this scenario there are also infinitely many events and bounded temporal intervals between the flvd and the present moment. By hypothesis, this is metaphysically impossible since it entails a traversal of an infinite such that at some time there is yet an infinite to be traversed. Therefore, an ITS-FD in the context of the foregoing scenario is also metaphysically impossible.

52. Next consider Craig's thesis that God is timeless without creation but temporal with creation. Let's assume there are no moments in metaphysical time before the moment of creation. According to Craig, God is temporal with the creation of a universe which begins to exist in the KCAAA sense. In this case metaphysical time begins at the moment in which its initial instant coincides with the flvd. Indeed, Craig has fairly recently clarified what he has in mind as follows:

[I]t is insufficient to account for the origin of the universe by citing simply God, His timeless intention to create a world with a beginning, and His power to produce such a result. There must be an exercise of His causal power in order for the universe to be created. That entails, of course, an intrinsic change on God's part that brings Him into time at the moment of creation.[107]

Nevertheless, this scenario is also metaphysically impossible because there is a first temporal interval in metaphysical time which includes the infinitely many events and temporal intervals constituting the ITS-FD which are mapped on to it. Again, this entails the polizeilich verboten (i.e., forbidden) traversal of an infinite which at some time involves an infinite yet to be traversed.

53. Finally, we have the scenario involving the creator-of-the-universe God who is absolutely atemporal. We have noted Craig's thesis that the existence of such a God is radically inconsistent with the A-theory. But I will prescind from raising this and other objections to the thesis that an absolutely atemporal God exists—especially one that creates a temporal world which begins to exist in either the KCA or the KCAAA sense. I shall therefore assume—for argument's sake—that the existence of an absolutely atemporal God with the power to create a temporal world is compatible with the A-theory.

54. To say that God is absolutely atemporal entails that his eternal now is neither earlier than, nor later than, nor even simultaneous (or coincident) with any physical event or quasi-event (such as the flvd of the ITS-FD). So God never is in metaphysical time—that master time common to all temporal universes (if there are any in addition to our own, whether natural or supernatural)—even in his creation of a temporal universe. However, in the case of a universe which begins to exist in the KCAAA sense, the A-theory presupposes metaphysical time. Therefore when God timelessly wills that a temporal world begin to exist in the KCA sense, the first moment of the existence of this world is simultaneous with the first moment of metaphysical time. But with respect to the timeless creation of a universe which begins to exist in the KCAAA sense, there is no first event or first moment encasing the first physical event. The first instant of this time is coincident with the flvd and bounds a temporal interval coincident with any degenerate interval in physical time which is defined in terms of the flvd. The first interval of metaphysical time then necessarily includes the infinitely many events and event-encasing moments which are mapped from physical time—and such inclusion is certainly not dreamt of in our philosophy. So again we conclude that the thesis that a temporal world involving an ITS-FD can be created by an absolutely atemporally-eternal God is metaphysically impossible even when we allow that an atemporal God with creative powers exists.

55. Whether or not some ITS-FD is per se metaphysically possible, it must nevertheless be the case that the SBBM or any other BBM:ITS-FD is metaphysically impossible. And this is true on either theist or nontheist assumptions. Recall that the SBBM (and any BBM:ITS-FD) posits an initial cosmological singularity and numerous other singularities non-simultaneous with the ics because the universe is imperfectly homogeneous and isotropic. So we have numerous ITS-FD.[108] On that scenario every spacetime path necessarily consists of infinitely many events or intervals. But the singularities are staggered such that the second singularity, for example, is coincident with the in-the-later-than-direction instant bounding the degenerate-temporal interval defined by the ics and the corresponding Planck era. This being the case, there is necessarily an interval of metaphysical time which unlawfully encompasses infinitely many events or intervals. So whether or not any ITS-FD is per se metaphysically impossible, it is per accidens metaphysically impossible for an ITS-FD to be encompassed within a finite temporal interval. Therefore, every BBM:ITS-FD is per accidens metaphysically impossible.

56. Let us now consider whether a universe whose history is constituted by a single ITS-FD is at least per accidens metaphysically possible (given the A-theory and the complementary assumptions about metaphysical time and related matters), or whether it is simply antecedently more improbable than not. Let's consider the latter first. C. D. Broad discussed the possibility of a universe of an indefinite finite duration with the following reservation: "For my own part I regard analogies between actual existents (such as events and their temporal relations) and abstract entities (such as pure numbers and their arithmetical relations) as an extremely shaky foundation for any conclusions about the former." The possibility of an ITS-FD was considered only because an analogy was made based upon a continuous sequence of rational fractions in order of magnitude. Whereas Broad declared that he found "no difficulty in supposing that the world's history had no beginning and that its duration backward from its present phase is infinite," he nevertheless did not "find any insuperable difficulty in supposing that the world's history had no beginning, but that its duration backward from its present phase does not exceed a certain finite limiting value."[109] Unlike Broad, I think that there is an insuperable difficulty about a universe of an indefinite finite duration. There is something about an ITS-FD which at bottom strikes me as counterintuitive and even absurd. I refer to the weird anomaly that the flvd is not an instant of time but, at best, its boundary, which allegedly coincides with an instant bounding an interval of metaphysical time. The antecedent improbability of a universe of a single ITS-FD kind is enhanced by the following consideration.

57. Recall that it is more antecedently probable than not that an entity whose history is constituted by or included in an ITS-FD is caused to exist by something else—assuming arguendo that an ITS-FD is metaphysically possible. If the temporal series which constitutes or includes the history of the universe is denumerably infinite, whether or not it is of infinite duration, it follows that each successive state in an ITS is causally explained by a prior state ad infinitum. What is also common to both an ITS-FD and an ITS-ID is the contingency of the series itself. But a scenario involving an ITS-FD has other contingent characteristics, i.e., the finiteness of its duration and that such finiteness is indefinite (in that the duration backward from the present has a finite limiting value). On the other hand, consider the two scenarios involving a temporal series of a finite duration: The first is an ITS of an indefinite finite duration, while the second is a FTS of definite finite duration. There are two important ways in which these two scenarios differ.[110] The first difference is that, with respect to the latter scenario, there is one member of the temporal series (i.e., the first member) which is not causally explained by another member of the series. The second difference is that the finiteness of the latter scenario differs from the former in being definite. Consideration of these various scenarios leads to the conclusion that the hypothesis that the ITS which constitutes or includes the history of the universe of infinite duration is simpler (in the Ockham's razor sense) than the hypothesis that the ITS which constitutes or includes the history of the universe is of indefinite finite duration. Moreover, the hypothesis that the temporal series which constitutes or includes the history of the universe is of definite finite duration is simpler than the hypothesis that the temporal series in question is denumerably infinite and is of indefinite finite duration. Given the foregoing, we are warranted in holding with some rational confidence that an ITS-FD is at least very much less antecedently probable than either of the competing scenarios. The theist, metaphysical naturalist, and nontheist who is not a naturalist are all epistemically equally entitled to hold this opinion. But we can do much better than this—at least for some metaphysical naturalists and some absolutely omnitemporalist theists.

58. As succinctly stated by C. D. Broad, the causal principle of the beginning of existences (CPBE)—which should have been embodied in FP-KCA—is that whatever begins to exist in the KCA sense has been caused to exist (in the old-fashioned sense of having been produced or generated) by something else which existed before and up to the moment when the entity in question began to exist. It is this principle (rather than the principle embodied in the KCA as stated and explained by Craig) which should be considered as properly basic and incorrigible. It is this principle which Craig should have described as being additionally confirmed as "an empirical generalization based on the widest sampling of experience"[111] and as an arguably reformulated neo-Kantian a priori principle applicable both to natural noumena and phenomena.[112] Therefore, assuming the metaphysical possibility of an ITS-FD, it is antecedently more probable than not that whatever entity begins to exist in the KCAAA sense was caused to exist (in the old-fashioned sense of having been produced or generated) by something else which existed before and up to the moment when the entity in question began to exist in the KCAAA sense, i.e., that instant of metaphysical time coincident with the flvd of the duration backward of the entity in question.

59. There is a broader (but equally properly basic and incorrigible) belief in the principle that every event is causally related to some prior event.[113] Neither the FP-KCA (per Craig), nor the CPBE (i.e., the FP-KCA per Broad), nor the principle of temporally prior causation (hereafter PTPC) entails any thesis about epistemic or ontic determinism in any domain.[114] The CPBE and the PTPC also do not presuppose the nonexistence of supernatural entities. However, the PTPC itself is a first principle—a properly basic and incorrigible belief which is presupposed in daily life as well as scientific and historical inquiry. Even many of those who are too timid to admit first principles into their philosophy are at least willing to concede, or to act upon, the principle that actually or presumptively every event is causally related to some temporally prior event.[115]

60. The per accidens metaphysical impossibility of a single ITS-FD can be rightly discerned by a metaphysical naturalist or an absolutely omnitemporalist theist who hold that both the CPBE and the broader PTPC are properly basic and incorrigible beliefs. Let us assume with Craig that the expression beginning of the universe should be understood to encompass a scenario involving a temporal series of a finite duration, whether or not definite. Given that the MS-KCA has been refuted (or assumed for argument's sake to have been refuted), every beginning of existence in the KCA sense must at least presumptively be deemed to have been caused (in the sense of produced or generated) by something which has existed up to and including the beginning of the existence of the entity in question. So whatever the substance is, natural or supernatural, that was the cause (i.e., the agent of causation) of the beginning of the universe in the KCA sense (assuming such is a fact), this cause must have been temporally prior to the beginning of the universe. So too, before the beginning of the universe, between some single event in the history of the cause of this beginning and the present moment, there can only have been finitely many other events or temporal intervals. A fortiori, it should also be held that it is more probable than not that the beginning of the universe in the KCAAA sense was temporally preceded by some events in the history of the agent of causation. But either scenario entails that an ITS-FD obtains between some event before the beginning in the KCA or the KCAAA sense (as the case may be) and the present moment. But this is metaphysically impossible for the now familiar reason concerning the disallowable traversal of an infinite which involves an infinite which at sometime was yet to be traversed. This conclusion is even more plausible given some atomistic version of presentism. What better reason is there to explain why there cannot be even a single ITS-FD than that this version of presentism obtains? Therefore both the metaphysical naturalist and the absolutely omnitemporalist theist who reject the MS-KCA but who nevertheless adhere to the CPBE and the PTPC (and perhaps also the atomistic version of presentism) can agree that it is antecedently more probable than not in excelsis that a single ITS-FD is per accidens metaphysically impossible given that their principles are much more probable than their denials. Quod erat demonstrandum.

61. In my first two articles I refuted the MS-KCA. In this article I have shown that the SBBM and any other BBM:ITS-FD must be deemed erroneous to the extent that any such model entails the obtaining of numerous infinite temporal series within one bounded temporal interval. I have also shown that an ITS-FD is at least antecedently less probable than either an ITS-ID or a FTS-FD. More crucially, I have shown that a single ITS-FD is per accidens metaphysically impossible given premises which are more plausible than their denials. In doing so I have shown that the KCAAA should be rejected. In accomplishing this I have rendered the adherents of the KCA a great service in eliminating one kind of ITS. However, the refutation of MS-KCA only leaves them one polemically feasible alternative: showing that the temporal series constituting the history of this universe is of definite finite duration as an empirically contingent truth. Assuming they make their case that the universe began to exist in the KCA sense, they must then undertake a further analysis in order to determine what characteristics the cause of the beginning of the universe (in the KCA sense) has. But in doing so the erstwhile adherents of the KCA are effectively disabled from depending upon the thesis that every infinite set of real entities, and every infinite temporal series, is metaphysically impossible.

62. No doubt some metaphysical naturalists will be displeased with the conclusions of this article about the metaphysical possibility or impossibility of an ITS-FD. Of course, the acceptance of these conclusions depends upon the acceptance of assumptions concerning the A-theory, metaphysical time, and related matters described in this article. Some readers will be especially troubled, if not annoyed, by my conclusions which are inconsistent with the received opinion that an ITS-FD is not only metaphysically possible, but assumed by the SBBM and some other astrophysical cosmological models. I would like to remind these readers of the highly speculative nature of the most relevant aspects of any present or future astrophysical cosmological model (if interpreted realistically and not instrumentally) concerning the alleged ultimate origins of this universe. For all practical purposes these aspects are well beyond the possibility of empirical confirmation or disconfirmation for the reasonably foreseeable future.[116] Therefore the antecedent net improbability of the ITS-FD (prescinding from the issue of its metaphysical impossibility) is not ever likely to be overridden by empirical evidence. Moreover, as E. A. Milne declared in his presidential address to the Royal Astronomical Society: "It is a good rule that however well a theory appears to fit the facts, it cannot be accepted as satisfactory if it is not philosophically satisfactory."[117]

 

INDEX OF ABBREVATIONS

BBM:ITS-FD: A Big Bang cosmological model which retains the initial cosmological singularity and posits that the history of the universe is constituted by an infinite temporal series of indefinite finite duration.

CPBE: The causal principle of beginnings of existence, which holds that whatever begins to exist has a cause as understood by C. D. Broad—that whatever begins to exist was caused (i.e., produced or generated) by something which existed before and up to the moment that the entity in question began to exist.

Flvd: The finite limiting value of duration backward from the present with respect to an infinite temporal series of indefinite finite duration—the limit to which the series of temporal intervals of unequal duration converges but never reaches.

FP-KCA: The first premise of the KCA to the effect that whatever begins to exist has a cause—originally understood by Craig to apply only to a FTS-FD.

FP-KCAAA: The first premise of the KCAAA—verbally similar to the FP-KCA but understood to encompass the possibility of an infinite temporal series of an indefinite finite duration.

FTS-FD: A finite temporal series of finite duration (e.g., a temporal series of temporal intervals of equal duration with a first member).

FTS-ID: A finite temporal series of infinite duration (e.g., a finite temporal series of temporal intervals all of equal duration except the first which is not bounded by an instant in the earlier-than direction—as in the case of the first event in the history of the universe preceded by a beginningless, undifferentiated changeless state).

Ics: Initial cosmological singularity—the initial boundary of spacetime according to the Standard Big Bang Model.

ITS: An infinite temporal series, i.e., a temporal series the cardinal number of which is aleph-zero (Ào) and not some natural number.

ITS-FD: An infinite temporal series of indefinite finite duration (i.e., a duration backward from the present to a finite limiting value).

ITS-ID: An infinite temporal series of infinite duration.

MS-KCA: The metaphysical subpremise of the KCA to the effect that any infinite temporal series is metaphysically impossible.

PTPC: Principle that every natural event is causally related to some other temporally prior event.

SBBM: The Standard Big Bang Model of General Relativity Theory which posits an initial cosmological singularity.

SP-KCA: The second premise of the KCA to the effect that the universe began to exist.

SP-KCAAA: The second premise of the KCAAA to the effect that the universe began to exist—but understood to encompass the possibility of an ITS-FD.


NOTES

[1] See chiefly his The Kalam Cosmological Argument (New York: Barnes & Noble, 1979) and his contributions in William Lane Craig and Quentin Smith, Theism, Atheism, and Big Bang Cosmology (Oxford: Clarendon Press, 1993). I use the term Kalam Cosmological Argument to refer to that version of the argument as expounded by Craig, which includes two philosophical subarguments pertaining to the issue of the metaphysical possibility of an infinite temporal series as an integral part. Cf. Theism, Atheism, and Big Bang Cosmology, at 3.

[2] According to Craig, further analysis discloses that the cause of the beginning of the universe is a "personal Creator ... who exists changelessly and independently prior to creation and in time subsequent to creation. This is a central core of what theists mean by 'God.'" Kalam Cosmological Argument, at 152. The KCA does not itself show that God is omniscient, omnipotent, morally good, and so forth. Ibid., at 152, 172-174 n. 170. In his "Naturalism and Cosmology," Naturalism: A Critical Analysis, ed. William Lane Craig and J. P. Moreland (New York: Routledge, 2000), at 244, Craig more fully explains that the ultimate conclusion is that the personal Creator of the universe "sans the universe is beginningless, changeless, immaterial, timeless, spaceless, and enormously powerful" (and very knowing). But see note 21 below for Craig's much more restrained thesis as to what the KCA ultimately shows if the universe is constituted by a temporal series of bounded events, states, or phases preceded by a temporal interval unbounded in the earlier-than direction (and thus consisting of one changeless state). What is necessary in order for the KCA to ultimately show, upon philosophical grounds, that the universe was created ex nihilo by a personal Creator is the metaphysical impossibility of a finite temporal series of bounded events, states, or phases preceded by a changeless phase unbounded in the earlier-than direction. The most Craig has been able to do has been to persuasively argue that this scenario is nomologically (i.e., physically) impossible with respect to this universe.

[3] Whenever I refer to an ITS I mean one which is denumerably infinite, i.e., its cardinal number is not some natural number but rather aleph-zero (Ào). On the other hand, when I refer to a temporal series of the universe of infinite duration (or having an infinite past), I mean to refer to a series composed of infinitely many consecutive temporal intervals of equal duration. A temporal series of a finite duration (or having a finite past) is one in which there are only finitely many equal temporal intervals. Unless otherwise indicated, temporal intervals are to be understood as being nonoverlapping and consecutive.

[4] By "event, state, or phase," unless otherwise indicated, I mean an event, phase, or state bounded in both the earlier- and later-than directions. An event is a change; a state is either an event or is eventless; a phase is a stage characterized by a process of change, development, or being eventless. Hereafter, I will usually only to refer to "event" or "events" (as the case may be) for the sake of convenience.

[5] My first paper on the KCA is "The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities" (hereafter Guminski KCA-I), Philo 5 (2002): 196-215. This article is available on Philo Online and on the Secular Web at /library/modern/arnold_guminski/kalam.html (with several minor corrections and the addition of paragraph numbers). Citations herein will be to the Secular Web version. My second paper is "The Kalam Cosmological Argument Yet Again: The Question of the Metaphysical Possibility of an Infinite Temporal Series" (2003) (hereafter Guminski KCA-II), and is available at /library/modern/arnold_guminski/kalam2.html.

[6] I define Cantorian set theory in a broad sense to include naíve set theory or any axiomatic set theory in pure mathematics (such as Zermelo-Fraenkel set theory) that accepts the notion of an actual mathematical infinite and includes the propositions that (1) a one-to-one correspondence between sets is the necessary and sufficient condition of the sets having the same cardinality, and (2) that every such infinite set has a least one proper subset with which it is in one-to-one correspondence.

[7] There is a tendency in Craig's writings to conflate the two propositions. They are, however, analytically distinct. See Guminski KCA-II, pars. 22-24.

[8] The abstract of my first article reads as follows: "This paper examines the Kalam Cosmological Argument, as expounded by William Lane Craig, insofar as it pertains to the premise that it is metaphysically impossible for an infinite set of real entities to exist. Craig contends that this premise is justified because the application of the Cantorian theory to the real world generates counterintuitive absurdities. This paper shows that Craig's contention fails because it is possible to apply Cantorian theory to the real world without thereby generating counterintuitive absurdities, provided one avoids positing that an infinite set of real entities is technically a set within the meaning of such theory. Accordingly, this paper proposes an alternative version of the application of Cantorian theory to the real world thereby replacing the standard version of such application so thoroughly criticized by Craig."

[9] Guminski KCA-I, at par. 19: "In place of SV, this paper proposes an alternative version (hereinafter referred to as AV) of the application of Cantorian theory to the real world. AV includes four principal propositions. The first (AV1) is that every real infinite and N (the set of all natural numbers) are equipollent because the members of the former correspond one-to-one with the members of the latter. Instead of a bridging rule, which intrinsically entails the equipollence of any real infinite with N because 'set,' as standardly used in Cantorian theory, is erroneously deemed by Craig to encompass real infinites, we have a bridging rule which extrinsically matches every member of any real infinite with one and only one member of N, and conversely. The second (AV2) is that the cardinal number of N is the cardinal number of every real infinite because each such infinite is equipollent with N. The third (AV 3) is that equipollence between two real infinites is a sufficient but not necessary condition for such two sets (as commonly understood) to have the same cardinality. The fourth (AV4) is that no real infinite is equipollent with any of its infinite proper subsets, although both have the same cardinality, i.e., Ào."

[10] In my first article, I (believe that I) showed, for example, that it is metaphysically possible for there to be infinitely many worlds, none of which is spatially related to another, but with each world only having finitely many entities. And, with somewhat less confidence, I (believe that I) also showed that it is metaphysically possible for there to be a world with infinitely many entities. At least I think that I showed that any metaphysical impossibility in the latter case could not be successfully grounded upon mathematical considerations based on Cantorian set theory.

[11] See Guminski KCA-II at par 41. I shall use the term "traversal of an infinite" (or kindred expressions) to also encompass the elapsing of an infinite (or kindred expressions). Strictly speaking, a traversal of events or temporal intervals is analytically distinct from the elapsing of events or temporal intervals.

[12] For a discussion of this matter, see Guminski KCA-II, at par. 41.

[13] Although I concluded in my second article that it is metaphysically possible for an ITS to obtain, I did not mean to say that it is metaphysically possible for any ITS to obtain. What I surely minimally meant to say was that it is not metaphysically impossible for some ITS to obtain based upon the ground that the application of Cantorian set theory to the real world generates counterintuitive absurdities, or upon the ground that an actual infinite cannot have been traversed even when it was never the case that there was an actual infinite yet to be traversed. However, I surely did mean to say that I believe that some ITS of infinite duration are metaphysically impossible.

[14] Davis S. Oderberg, a staunch ally of Craig with respect to the KCA, has recently written: "The first thing to note is that, as Grünbaum correctly insists, the closed model [according to which the initial singularity is the first physical state of the universe] is not a bona fide physical model of the 'Big Bang.' Contrary to the loose way in which many physicists and philosophers talk, the space-time singularity is not a point in space-time on the general relativistic cosmology.... The space-time singularity is not, on general relativity, an event or a point—it is a limit or boundary towards which density approaches infinity and volume approaches zero." "The Beginning of Existence," International Philosophical Quarterly 43 (2003), at 151. Oderburg's able essay proposes a technically improved definition of the "beginning of the universe" to conform with the foregoing. As he puts it: "My point is simply that the supporter of the Kalam argument should not be diverted by considerations of an infinite universe into thinking that a finite, open interval model deprives the argument of its bite in that case." Ibid., at 157. The finite, open interval model Oderberg refers to is what I call an infinite temporal series of finite duration. It is noteworthy that in the closing note to his paper, Oderberg writes (in part): "I am indebted to William Lane Craig for discussion of the issues raised in this article..." Ibid., at 157 n. 23.

[15] In the case of a FTS-ID, the first interval consists of a changeless state which is unbounded in the earlier-than direction. A FTS of equal temporal intervals of a finite duration is one in which the first interval is also bounded in the earlier-than direction. This article assumes that a temporal interval is of non-zero duration, and a non-degenerate instant is a boundary of an interval except as otherwise noted. A bounded temporal interval is bounded by two instants, in the earlier-than and later-than direction, respectively.

[16] As conceived by theologically conservative Christians, Jews, and Muslims, God is a one and only one purely spiritual personal being, omniscient, omnipotent, having libertarian free will, and all-good, who both creates and sustains (or conserves) the universe. However, Craig makes it abundantly clear that the central core of what 'God' means is the one and the same personal Creator of the universe—prescinding from whether he is omniscient, omnipotent, or even benevolent, and so forth. Kalam Cosmological Argument, at 152; and see Craig's statements in Five Views on Apologetics, ed. Steven B. Cowan (Grand Rapids, MI: Zondervan Publishing House, 2000), at 320.

[17] Craig, Kalam Cosmological Argument, at 141: "The phrase 'cause of its existence' needs clarification. Here I do not mean sustaining or conserving cause, but creating cause. We are not looking here for any continual ground of being, but for something that brings about the inception of another thing. Applied to the universe, we are asking, was the beginning of the universe caused or uncaused?"

[18] Ibid., at 142. For Broad's discussion of these alternatives, see Kant: An Introduction, ed. C. Lewy (Cambridge: Cambridge University Press, 1978), at 215-218 (cited in Craig as "Kant's Mathematical Antinomies," Proceedings of the Aristotelian Society 40 (1955), at 9-10). In his own words, Broad presents the three alternatives as follows: "(i) A first event and therefore a finite duration backward from the present. (ii) No first event, but a finite upper limit of duration backward from the present. (iii) No first event and an infinite duration backward from the present." Kant, at 217.

[19] Kalam Cosmological Argument, at 142.

[20] Ibid.

[21] Actually, Craig considers a fourth alternative which is not listed, i.e., that the history of the universe consists of an FTS of events but is of infinite duration. As he puts it: "the temporal sequence of events had a beginning, but that the universe did not, that is to say, the temporal series of events was preceded by an eternal, quiescent universe, absolutely still." Ibid., at 99. He discusses this alternative in ibid., at 99-102 and in his "The Kalam Cosmological Argument and the Hypothesis of a Quiescent Universe," Faith and Philosophy 8 (1991): 104-108. He dismisses this alternative as being metaphysically and nomologically impossible. Interestingly, in the article just cited (at 105-106) Craig states that "as I employ it the kalam cosmological argument's primary aim is to support theism, not creatio ex nihilo." He admits the possibility that jump-starting (my term) the quiescent universe can be attributed to "an eternal, changeless, uncaused, timeless, immaterial, spaceless, personal Prime Mover" (ibid., at 106). But he later postulates "a being who is also the sovereign Lord over all the universe and its every most minute operation" in order to explain the miraculous transformation of the universe from quiescence because the same "is simply physically impossible" (ibid., at 106-107). But we still do not have creatio ex nihilo. I too reject the fourth alternative upon the ground (natural enough for this conservative metaphysical naturalist) that I believe as properly and incorrigibly basic that it is metaphysically impossible for the entire temporal series pertaining to this universe to have had a first event. (Cf. the remarks on this issue by G. E. Moore, Some Main Problems of Philosophy (New York: Collier Books, 1962), at 193-194.) For a brief discussion of the nature of conservative metaphysical naturalism, see my paper "The Moral Argument for God's Existence, the Natural Moral Law, and Conservative Metaphysical Naturalism" (2004), at pars. 7-10 (listed at http://www.theologyforum.net/—click on media and then papers—and directly available at http://www.colorado.edu/philosophy/TheoForum/gum.pdf).

[22] Ibid., at 143.

[23] Ibid., at 142-143. Cf. ibid., at 157 n. 34: "It might be protested that we need not bring in the notion of actual infinity when speaking of past events; we may simply say that the series of temporal events is beginningless.... As G. E. Moore indicates, if we grant that events really occur in time, then only two alternatives are possible: either there was a first event or there has been an actually infinite series of events prior to the present one. For if there was no first event, then there must have been an event prior to any given event; since this one also could not be first, there must be an event prior to it, and so on ad infinitum. (George Edward Moore, Some Main Problems of Philosophy (London: George, Allen & Unwin, 1953), at 174-5.) Therefore, a beginningless series involves the existence of an actual infinite."

[24] Kalam Cosmological Argument, at 69-110.

[25] Ibid., at 110-111. Of course, it is much more difficult to mount a plausible argument that an atemporal-sans-creation God caused the universe to begin ex nihilo based upon empirical grounds, but prescinding from the two philosophical subarguments in support of the MS-KCA. Since such an argument assumes (for argument's sake) the metaphysical possibility of an ITS, it is antecedently more probable that the creator is absolutely omnitemporal, and it is even more plausible that at the time of the creation he was the last in a denumerably infinite series of successively instantiated temporally finite gods (each having great power and knowledge) existing throughout metaphysical time.

[26] Ibid., at 163 n. 80. Craig was even more explicit in Essay V of Theism, Atheism, and Big Bang Cosmology, at 157: "But as I have defined it in Essay I [which is an abridgment of his Kalam Cosmological Argument], divine creatio ex nihilo is grounded in revelation and philosophical argument, and the scientific evidence merely serves as empirical confirmation of that doctrine. The theist, after all, has no vested interest in denominating the Big Bang as the moment of creation. He is convinced that God created all of spacetime reality ex nihilo, and the Big Bang model provides a powerful suggestion as to when that moment was." This is truly a very modest assessment of the probative value of the so-called 'empirical confirmations' of the MS-KCA.

[27] Ibid., at 116. See also ibid., at 117, where Craig declares: "A literal application of the big bang model in which the universe originates in an explosion from a state of infinite density, that is, from nothing, provides a simple, consistent, and empirically sound construction of how the universe began."

[28] Ibid., at 132.

[29] Ibid., at 140.

[30] "A robust doctrine of creation therefore involves both the affirmation that God brought the universe into being out of nothing at some moment in the finite past and the affirmation that He thereafter sustains it in being moment by moment." William Lane Craig, God, Time, and Eternity (Boston: Kluwer Academic Publishers, 2001), at 253.

[31] "Should a conflict arise between the witness of the Holy Spirit to the fundamental truth of the Christian faith and beliefs based on argument and evidence, then it is the former which must take precedence over the latter, not vice versa." William Lane Craig, Reasonable Faith: Christian Truth and Apologetics, (Wheaton, IL: Crossway, 1994), p. 36.

[32] De Fide, 1. 42.

[33] Fortunately, Craig has solid scriptural warrant for his polemical methods. See 1 Cor. 9: 19-23.

[34] Theism, Atheism, and Big Bang Cosmology, at 44-56, 148-160.

[35] Ibid., at 234.

[36] Ibid., at vi, 108.

[37] Kalam Cosmological Argument, at 7.

[38] In so doing, Craig repeats his discussion of the three alternative scenarios discussed supra in paragraphs 12-14. Theism, Atheism, and Big Bang Cosmology, at 57-59.

[39] Ibid., at 37.

[40] Ibid., at 29.

[41] Ibid.

[42] Ibid., at 30 (emphasis added).

[43] Ibid.

[44] Ibid., at 58-59. See also Craig's Essay III, ibid., at 107: "These arguments [based on the impossibility of an actual infinite and on the impossibility of forming an actual infinite by successive addition] ... do seem to furnish philosophical grounds for holding to the finitude of the past and the beginning of the universe." This statement is made in the first part of the book, which does not consider the empirical confirmations independently of the MS-KCA. Essay III, "Time and Infinity," is a shorter version of an essay first published in International Philosophical Quarterly 31/4, Issue 124 (Dec. 1991): 387-401.

[45] Ibid., at 108: "Portions of this essay were first pub. in 'The Uncaused Beginning of the Universe', Philosophy of Science, 55 (1988), 39-57."

[46] Ibid., at 108-140.

[47] Ibid., at 115.

[48] Ibid.

[49] Ibid., at 115-116.

[50] Ibid., at 117.

[51] Ibid., at 116-117.

[52] Ibid., at 119. Smith conveniently summarizes the Hawking-Penrose singularity theorems as follows: "(1) Einstein's General Theory of Relativity holds true of the Universe. (2) There are no closed timelike curves (i.e., time travel into one's past is impossible and the principle of causality is not violated). (3) Gravity is always attractive. (4) The spacetime manifold is not too highly symmetric; i.e., every spacetime past of a particle or light ray encounters some matter or randomly oriented curvature. (5) There is some point p such that all the past-directed (or future-directed) spacetime paths from p start converging again. This condition implies that there is enough matter present in the universe to focus every past-directed (or future-directed) spacetime path from some point p. The solutions for the Hawking-Penrose theorems show ... that 'in the general case there will be a curvature singularity that will intersect every world line. Thus general relatively predicts a beginning of time.'" Ibid., at 139. Alas, what is overlooked is that the Hawking-Penrose theorems presuppose that an ITS-FD is metaphysically possible even where there were multiple Big Bangs following the ics. It is true enough that the theorems predict a beginning of physical time; but for the foreseeable future there is no possible way in which this prediction can be empirically tested or independently confirmed by particle physics.

[53] Ibid., at 207-212.

[54] Ibid., at 208. During his First Rebuttal in the course of his most recent debate with Craig on the existence of God, Smith reversed his position concerning the ontological status of the ics. He declared: "The Big Bang singularity is an ideal mathematical limit to a series.... [I]t doesn't exist! It's a part of the mathematical equations of Big Bang cosmology that physicists interpret as not corresponding to anything real." "The Craig-Smith Debate: Does God Exist?" (Veritas Forum—Harvard University, April 7, 2003), available online at http://www.leaderu.com/offices/billcraig/docs/craig-smith_harvard00.html.

[55] Theism, Atheism, and Big Bang Cosmology, at 218-231. This essay was first published in the Australasian Journal of Philosophy, 69/4 (1991): 492-503.

[56] Theism, Atheism, and Big Bang Cosmology, at 224.

[57] Ibid. Subject to correction, this appears to be the first time in his published writings that Craig adverts to the absence of a first physical event, state, or phase of the universe in the first post-t0 (initial singularity) interval. See his "Origin and Creation of the Universe: A Response to Adolf Grünbaum." British Journal for the Philosophy of Science 43 (1992): 233-240, where Craig displays a similar awareness and appears for the first time to define the beginning of the universe with a finite duration as not necessarily involving a first event in its history. To be sure Craig's later writings develop and refine what he considers to be empirical confirmations of his philosophical arguments. See, e.g., J. P. Moreland and William Lane Craig, Philosophical Foundations of a Christian Worldview (Downers Grove, IL: InterVarsity Press, 2003), at 477: "Sometimes objectors appeal to scenarios other than the standard model of the expanding universe in an attempt to avert the absolute beginning predicted by the standard model. But while such theories are possible, it has been the overwhelming verdict of the scientific community than none of them is more probable that the big bang model. The devil is in the details, and once you get down to specifics you find that there is no mathematically consistent model that has been so successful in its predictions or as corroborated by the evidence as the traditional big bang model." Craig has acknowledged that "[o]f course, quantum effects will become important prior to the Planck time, but it is pure speculation that these will serve to avert the initial singularity." Theism, Atheism, and Big Bang Cosmology, at 149. Cf. Craig, "Naturalism and Cosmology," at 228-230. See also Quentin Smith in his "Time was Created by a Timeless Point: An Atheist Explanation of Spacetime," in Gegansall and Woodruff, eds., God and Time (New York: Oxford University Press, forthcoming), where he declares that the "big bang singularity.... is posited by both classical general relativistic cosmology and by the new quantum gravity cosmology." He also writes: "Most philosophers believe that the hypothesis of the big bang singularity is inconsistent with quantum gravity cosmologies. However ... quantum cosmologies do postulate a big bang singularity"—clearly meaning an initial big bang singularity. Ibid. Given the foregoing, I believe I am justified in speaking of any empirically plausible BBM:ITS-FD as providing what Craig thinks is an empirical confirmation of the SP of the KCAAA, but not of the KCA. On the other hand, only an empirically plausible astrophysical cosmological model which involves an FTS-FD is to be deemed as confirming the KCA and thus being consistent with the MS-KCA.

[58] Ibid.

[59] Ibid., at 217. Craig also writes: "One could consistently maintain that the initial singularity is a state of non-being and that physical reality approaches arbitrarily close to it without having a first instant of existence." Ibid., at 226.

[60] Ibid., at 227.

[61] Ibid.

[62] Essay X is titled "A Criticism of the Cosmological Argument for God's Non-Existence." Craig states at 257: "This essay is an adaptation and expansion of 'God and the Initial Cosmology Singularity: A Reply to Quentin Smith', Faith and Philosophy, 9 (1992), 238-48."

[63] Ibid., at 260.

[64] For examples of this practice, see his "Naturalism and Cosmology" in Naturalism: A Critical Analysis, eds. William Lane Craig and J. P. Moreland (New York: Routledge, 2000), at 217; and Paul Copan and William Lane Craig, Creation Out of Nothing: A Biblical, Philosophical and Scientific Exploration (Grand Rapids, MI: Baker Academic, 2004), at 222-224; and William Lane Craig and J. P. Moreland, Philosophical Foundations, at 477. In these writings there is no intimation whatsoever that the ics is not, according to the received understanding of the SBBM, the initial boundary of a physical event but rather is the boundary of spacetime.

[65] "A Response to Grünbaum on Creation and Big Bang Cosmology," Philosophia Naturalis 31 (1994): 237-249 n. 2.

[66] Ibid. Craig's citation to pp. 43-44 of Theism, Atheism, and Big Bang Cosmology discloses a vague passage; and the citations to pp. 146-147. 224-227, 258-261 refer to passages in the second part of that book.

[67] Erkenntnis 40 (1994): 325-341 n. 2. See also William Lane Craig, "Prof. Grünbaum on the 'Normalcy of Nothingness' in the Leibnizian and Kalam Cosmological Arguments," Brit. J. Phil. Sci. 51 (2001), at 381 n. 5, where Craig confirms in substance what he asserts below in the quoted text.

[68] Craig has defined what constitutes the beginning of the existence of some entity as follows: "x comes into being at t ≡ x exists at t; t is either the first time at which x exists or is separated from any time t* < t at which x existed by a non-degenerate, temporal interval; and x's existing at t is a tensed fact." Craig, "Must the Beginning of the Universe Have a Personal Cause? A Rejoinder," Faith and Philosophy 19: 94-105, at 99. Craig presently holds: "[F]or any entity e and time t, e comes into being at t if and only if (i) e exists at t, (ii) t is the first time at which e exists, (iii) there is no state of affairs in the actual world in which e exists timelessly, and (iv) e's existing at t is a tensed fact." ("Question 168: Beginning to Exist")

[69] Time and Eternity: Exploring God's Relationship to Time (Wheaton, IL: Crossway Books, 2001), at 220.

[70] Philosophical Foundations, at 475. The authors refer to Achilles' crossing the stadium. He must first cross halfway; but before he does so, must cross a quarter of the way; but before this, he must cross an eighth of the way, and so forth on to infinity. Therefore, Achilles could not even move.

[71] Ibid., at 475-476.

[72] Craig, Theism, Atheism, and Big Bang Cosmology, at 94. Craig and Moreland succinctly describe the competing tenseless or static B-theory of time in their summa, Philosophical Foundations, at 379, as follows: "All moments of time are equally existent and are related by the tenseless relations of earlier than, simultaneous with and later than. The distinction between past, present and future is not an objective distinction, being merely a subjective feature of consciousness.... If there were no minds, there would be no past, present or future. There would be just the four-dimensional space-time universe existing as a block."

[73] The Tensed Theory of Time: A Critical Examination (Boston: Kluwer Academic Publishers, 2000), at 138.

[74] Craig in Five Views, at 51; William Lane Craig, God, Time, and Eternity: The Coherence of Theism II: Eternity (Boston: Kluwer Academic Publishers, 2001), at 260. Indeed, as Craig and Paul Copan emphatically state in their Creation Out of Nothing: A Biblical, Philosophical, and Scientific Exploration (Grand Rapids, MI: Baker Academic, 2004), at 161: "[C]reatio ex nihilo entails an A-theory of time."

[75] See Craig's Time and Eternity for an accessible discussion of the various versions of the A- and B-theories of time. For a more thorough scholarly presentation, see his Tensed Theory and the Tenseless Theory of Time: A Critical Examination (Boston: Kluwer Academic Publishers, 2000).

[76] Philosophical Foundations, at 388. There are various schools or versions of the so-called A-theory, but there is no need to adjudicate them here, as they involve differences of opinion upon a mixed bag of semantical and ontological issues. As described by Garrett De Weese, "Timeless God, Tenseless Time," Philosophia Christi 2 (2000) at 53: "Ontologically, A-theorists believe that the past and present are real (or, for the presentist version of the A-theory, only the present is real), while the future is not; that is, that there is a genuine ontological distinction between the past and present on the one hand, and future on the other, and that temporal becoming is real."

[77] Kalam Cosmological Argument, at 97, 103; Theism, Atheism, and Big Bang Cosmology, at 24-26; "A Swift and Simple Refutation of the Kalam Cosmological Argument?" Religious Studies 35 (1999), at 62-63. The version of presentism which Craig advocates, rejecting the theory of the atomicity of time, asserts "the non-degenerate interval of time, which is itself potentially infinitely divisible and may be analyzed into sub-intervals which are respectively past, present, and future." Tensed Theory, at 258.

[78] Ibid., at 231. For Craig's careful and helpful analysis of the relevant issues concerning the extent of the present, see ibid., at 228-248; Time and Eternity, at 157-160. He vindicates his theory of presentism in his paper "In Defense of Presentism," Time, Tense, and Reference, eds. Aleksander Jokic and Quentin Smith (Cambridge, MA: MIT Press, 2003), at 392-408.

[79] Tensed Theory, at 239.

[80] There are other reasons which Craig (in turn) analyzes and dismisses as unpersuasive. Tensed Theory, at 240-242. He does advert to one issue which is especially worthy of consideration. He urges that the atomistic theory of temporal becoming may apply to our measurements of time, but not to time itself. Ibid., at 244. But it seems to me that this point is not at all plausible since the issue of what constitutes the extent of the present—even in metaphysical time—cannot be evaded. For the theist the atomistic theory of temporal becoming may plausibly call for concluding that God wills whatever constitutes the extent of the chronon in metaphysical time.

[81] Ibid., at 158.

[82]

Chronon 1
Chronon 2
← A 1 2 3
A 1 2 3
.... S 1 2 3
.. S .. 1 2 3
......... B 1 2 3
..... B ..... 1 2 3

As Craig explains: "At chronon 1, A1 and B1 are aligned, then at chronon 2, A3 and B1 are aligned. But this seems crazy because it implies that there never was any event of the alignment of A2 with B1. But in order to move from being aligned with A1 to being aligned with A3, B1 must have passed A2 at some time. If we say that such an alignment did occur, it must have occurred in between chronons, which is impossible. Therefore, we have no choice but to say reality jumped discontinuously from one state to another. If we can find some way of avoiding this sort of weirdness, it would surely be preferable to do so!" Time and Eternity, at 158-159.

[83]

Chronon 1
Chronon 2
Chronon 3
← A | 1 | 2 | 3 |
A | 1 | 2 | 3 |
A | 1 | 2 | 3 |
.... S | 1 | 2 | 3 |
. S .. | 1 | 2 | 3 |
.... S .... | 1 | 2 | 3 |
......... B | 1 | 2 | 3 |
.... B .... | 1 | 2 | 3 |
.......... B ......... | 1 | 2 | 3 |

[84] Ibid., at 247 n. 108.

[85] Ibid., at 247.

[86] Time and Eternity, at 160.

[87] Ibid. As Tom Masterson has pointed out to me: the existence of an ITS-FD entails that there is no smallest possible temporal interval in the series; whereas the existence of an ITS-ID entails that there is a smallest possible temporal interval.

[88] What about the Special Theory of Relativity? It is exceptionally noteworthy that there are some theistic and nontheistic philosophers who, although disagreeing in detail, accept the reality of absolute simultaneity. Compare the exposition of their views on this subject by such theistic philosophers as Craig [Time and the Metaphysics of Relativity (Boston: Kluwer Academic Publishers, 2001)] and Richard Swinburne [Space and Time (Macmillan, 2d ed. 1981): 181-202] with those of nontheistic philosophers such as Quentin Smith ["Absolute Simultaneity and the Infinity of Time" ed. Robin Le Poidevin, Questions of Time and Tense (Oxford: Oxford University Press, 2001), at 135-183] and Michael Tooley [Time, Tense & Causation (Oxford: Clarendon Press, 1997), at 335-371]. As Swinburne succinctly puts it: "the [special and general] Theories of Relativity are perfectly compatible with the view that there are truths about which events are 'absolutely simultaneous' with which (i.e., that there is a unique frame of reference in which measurements of simultaneity are correct)—the so-called 'relativity of simultaneity' being a limit on our knowledge of simultaneity (our ability to discover that true frame), not a limit on its existence." The Christian God (Oxford: Oxford University Press, 1994), at 75 n. 4. Quentin Smith explains: "The observational data require us to accept the hypotheses that the laws of electrodynamics (and mechanics) appear to hold (with same form) relative to every inertial frame, and light appears to have a constant velocity c, independent of the state of motion of the emitting body, relative to every inertial frame." "Absolute Singularity," at 146.

[89] Craig, Time and the Metaphysics of Relativity, at 170. During his opening speech in "The Craig-Smith Debate: Does God Exist?," Smith confirmed that he agrees "with [Craig] and some philosophers and physicists that Einstein's relative time merely describes how time appears to us and that time in reality consists in successive states of absolutely simultaneous events."

[90] Craig, God, Time and Eternity, at 216. As Craig explains: "The existence of a unique fundamental reference frame also has important implications for our interpretation of SR as well. For the existence of a fundamental reference frame for light propagation implies that the speed of light is isotropic only with respect to observers which are stationary relative to the fundamental frame (the observers). With reference to an observer which is moving with a velocity v relative to the fundamental frame, light will approach such an observer with the speed of c + v in the line of v and overtake it with a speed of c - v in the line of v. These departures from c will not, however, be detectable to such observers due to length contraction and time dilation. Length contraction results from the endeavor of a moving system of particles to maintain its internal equilibrium. Time dilation follows as a result of the anisotropy of the velocity of light and length contraction. Einstein's Light postulate is now seen to concern the measurement of light's velocity in various inertial frames, and the relativity of simultaneity which results from his synchronization procedure becomes intelligible in view of observers who are in motion relative to the fundamental frames regarding their inertial systems as being at rest for the purpose of clock synchronization." Time and the Metaphysics of Relativity, at 218-219.

[91] God, Time, and Eternity, at 18.

[92] Time and Eternity, at 66. See Craig, God, Time, and Eternity, at 257: "[t]ime 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. Or God could have created angelic beings prior to the Big Bang which were undergoing a succession of mental states." Or, God could have created a physical universe not spatially related to our own but which temporally preceded it. As Quentin Smith points out in "Absolute Simultaneity," at 166: "Absolute temporal relations are not based on spatial relations; they are logically and metaphysically independent of spatial relations..."

[93] Theism, Atheism, and Big Bang Cosmology, at 153. I think Craig slips when he describes metaphysical time as measuring the succession of God's content of consciousness. Instead, the metaphysical time is much more aptly considered by an omnitemporalist theist as encompassing the successively occurring events, states, and phases in God's mental life.

[94] See Craig, Time and Eternity, and his God, Time, and Eternity for comprehensive discussions. For more accessible discussions, see "Timelessness and Omnitemporality," Philosophia Christi 2 (2000): 29-33, and his contributions in Four Views: God & Time, ed. Gregory E. Ganssle (Downers Grove, IL: InterVarsity Press, 2001). See also, inter alia, Nicholas Wolterstorff, "God and Time," Philosophia Christi 2 (2000): 5-10; Garrett De Weese, "Timeless God, Tenseless Time," Philosophia Christi 2 (2000): 53-59, and see also his God and the Nature of Time (Burlington, VT: Ashgate Publishing Co., 2004).

[95] Time and Eternity, at 216.

[96] Ibid., at 236.

[97] As Craig explains this concept: "[P]rior to creation there literally are no intervals of time at all. In such time, there would be no earlier and after, 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.'" Ibid., at 235.

[98] Craig, God, Time, and Eternity, at 217. "In God's 'now' the universe has (present tense) certain specific and unique properties, for example, a certain radius, a certain density, a certain background temperature, and so forth; but in the cosmic 'now' it has all the identical properties, and so it is with every successive 'now'.... [T]herefore ... God's time and cosmic time ought naturally to be regarded as coincident since the inception of cosmic time." Ibid., at 218.

[99] Ibid, at 242. As Craig later remarks: "God thus exists in metaphysical time per se, but He exists in cosmic time per accidens." Ibid., at 246.

[100] Ibid., at 255.

[101] Ibid., at 275.

[102] Ibid (emphasis added). I cannot complain that Craig does not cover all his bases, as this can be discerned in the following passage: "In standard Big Bang Cosmology, the initial cosmological singularity at which the universe, indeed spacetime itself, begins is not conceived to be an instant or any other part of time, but rather to constitute a boundary to time. Thus, it cannot be said technically to be earlier than the universe, and yet it is causally prior to the universe. It is clearly distinct from a terminal cosmological singularity, which represents the terminal boundary of a universe in gravitational self-collapse. Although the physical grounds for regarding such singularities as constituting boundaries to, rather than points of, spacetime are inapplicable to the notion of metaphysical time, nonetheless they do serve as an illustrative analogy to the state of God's existing sans the universe. Perhaps we could say that the envisioned state is a boundary of time which is causally, but not temporally, prior to the origin of the universe." God, Time, and Eternity, at 272. Therefore the ics is atemporal! Pace Craig, were Jeremy Bentham alive he would have found the foregoing, rather than the notion of natural rights, as a much more fitting target of his biting epithet: nonsense upon stilts.

[103] "Must the Beginning of the Universe," at 101. Craig was quite explicit during his debate with Quentin Smith in March, 1996, at Southern Methodist University: "My own view is that once the Creator creates the Big Bang and the first event occurs, then, in fact, God enters into time and is temporal from the beginning of time subsequently, so that while there is no time prior to the Big Bang or the creation event, God is, in fact, temporally related to the universe at, and subsequent to, the moment of creation.... I would say that God had a timeless intention to create a Big Bang, but in terms of the actual causal exercise of His power, the actual volition, 'Let there be...!' that would occur simultaneously with the Big Bang singularity." "The Craig-Smith Debate: Does God Exist?" (questions from the floor) (Southern Methodist University, March, 1996), available online at http://www.leaderu.com/offices/billcraig/docs/craig-smith0.html).

[104] Note that the FP-KCA (as construed by Craig) does not entail that the cause of the beginning of the universe in the KCA sense existed before and up to that moment or event which constitutes the beginning of the universe.

[105] I am inclined to think that Craig would prefer to say that the FP-KCA (to paraphrase him) is plausible in excelsis for something that begins to exist in the KCA sense, then even if its plausibility is significantly diminished when it comes to something that begins to exist in the KCAAA sense, that does not in any way show that the FP-KCA is implausible, much less no more plausible than its contradictory. Cf. Craig, "A Rejoinder," at 95.

[106] The ics of the SBBM is not analytically identical with the flvd. However, they are functionally equivalent for our purposes.

[107] "A Rejoinder," at 102. Craig's explication of this point was quite obviously due to being hard-pressed by Wes Morriston's "Must the Beginning of the Universe Have a Personal Cause?" Faith and Philosophy 17 (2000): 149-169. See also note 103 above and accompanying text.

[108] In all my papers on the KCA, I have been referring to the history of the universe as being constituted by or included in one temporal series. This was in the manner of a façon de parler for the sake of convenience, since surely the history of the universe is composed of numerous such series.

[109] C. D. Broad, Kant, at 217 (emphasis added).

[110] In what follows, I appreciatively borrow some insights from Oderberg's "The Beginning of Existence," at 155-157. Oderberg himself observes: "What this means (ironically) is that the open interval model [i.e., my ITS-FD], originally postulated to deprive the universe of the need for a cause, may in fact require more in the way of causal explanation than the other two models..." Ibid., at 156.

[111] Kalam Cosmological Argument, at 143.

[112] Ibid., at 145.

[113] Referring to the "principle of universal causation" as being "the general principle that every event is causally determined by some earlier event," Broad commented: "I do not believe for a moment that our belief in the principle of universal causation does in fact rest on induction, or that it could be established by induction in the sense in which particular causal laws can be." With reference to cases where cause and effect seem to be simultaneous, he appears to agree with Kant "that we have to consider order in time and not lapse of time. There is never [in such cases] any lapse of time between the completion of the causal conditions and the beginning of the effect." Kant, at 176-177. A fortiori, similar considerations apply to the principle of temporally prior causation (PTPC).

[114] The FP-KCA (whether per Craig or Broad) is proposed as stating a metaphysical truth ultimately based upon the purportedly indefeasible intuition ex nihilo nihil fit (out of nothing nothing comes). Craig has frequently been at pains to point out that the principle is not inconsistent with ontic indeterminacy in some domains, most recently in his Creation Out of Nothing. There Craig affirms again (at 254) "the principle that out of nothing nothing comes is a first principle of metaphysics as well as science." But again he emphatically insists (at 256) that the principle is not defeated by "an appeal to quantum indeterminacy," or because virtual particles allegedly "spring uncaused from the quantum mechanical vacuum." Thus, whether or not one agrees with the principle embodied in the FP-KCA (whether per Craig or Broad), it is not to be understood as a falsifiable nomological proposition. As Craig very helpfully explained elsewhere: "For if an event requires certain physically necessary conditions in order to occur, but these conditions are not jointly sufficient for its occurrence, and the event occurs, then the event is in principle unpredictable, but it could hardly be called uncaused in the relevant sense. In the case of quantum events, there are any number of physically necessary conditions that must obtain for such an event to occur, and yet these conditions are not jointly sufficient for the occurrence of the event. (They are jointly sufficient in the sense that they are all the conditions one needs for the event's occurrence, but they are not sufficient in the sense they guarantee the occurrence of the event.).... To be uncaused in the relevant sense of an absolute beginning, an existent must lack any non-logical necessary or sufficient conditions whatsoever." "The Caused Beginning of the Universe," Theism, Atheism, and Big Bang Cosmology, at 146. Despite such pains to avoid misunderstanding, it happens often enough that some critics of the KCA erroneously maintain that the FP-KCA (whether per Craig or Broad) is falsified by physical science. [For example, Victor J. Stenger, in his Has Science Found God? (Amherst, NY: Prometheus Books), at 173 (note omitted), declares about the FP-KCA: "Craig gives no real justification for [the FP-KCA] calling it 'intuitively obvious.' Perhaps it is intuitively obvious to him, but not to physicists like myself. Quantum phenomena, such as atomic transitions and radioactive decay of nuclei, seem to happen without prior cause. In fact, the highly successful theory of quantum mechanics does not predict the occurrence of these events, just their probabilities for taking place."] Like Craig, I also have taken pains in this endnote in an effort to avoid misunderstanding as to the meaning of the FP-KCA (per Craig or Broad). Implicit in my discussion in this paper is that the reader assumes, at least for argument's sake, the metaphysical truth (of either Craig's or Broad's version) of the FP-KCA in order to pursue our inquiry.

[115] Cf. Wes Morriston, "Causes and Beginnings in the Kalam Argument: Reply to Craig." Faith and Philosophy 19 (2002) at 237-238: "The only time-related intuition I can think of that is in any way relevant to the kalam argument is one that is anything but helpful to the case Craig wants to make. Some people have quite a strong resistance to the whole idea of a First Moment. The idea of a time prior to which there was no time—of an event before which there were no others—strikes them as profoundly counter-intuitive. Even when they try to imagine a 'timeless person' somehow producing a first event, a powerful sense of absurdity may remain. 'But where did it come from? What was there before it happened?' At the level of raw intuition, 'nothing at all' and 'there was no before, before the beginning' do not 'feel' to them like acceptable answers. This intuition may or may not be trustworthy, and it may or may not have been defeated by Craig's philosophical arguments against the infinite past, but I think it is clear that many people have it, and I suspect that this, rather than any special intuition about what does or doesn't need a cause, is what some of them really have in mind when they join in the refrain, 'from nothing, nothing comes.'"

[116] As to this point, see inter alia the comments of Quentin Smith in the Introduction to "The Black Hole Origin Theory of the Universe: Frontiers of Speculative, Current Physical Cosmology," a paper read at the Internal Conference on Physical Cosmology, Santa Barbara, 2000. Available online at: http://www.qsmithwmu.com/physical_cosmology.htm. See also Stanley L. Jaki, "The Intelligent Christian's Guide to Scientific Cosmology," Catholic Essays (Front Royal, VA: Christendom Press, 1990), 148-150; Robert Jastrow, "What Forces Filled the Universe with Energy Fifteen Billion Years Ago?," in Henry Margenau and Roy Abraham Varghese, eds., Cosmos, Bios, Theos: Scientists Reflect on Science, God, and the Origins of the Universe, Life, and Homo Sapiens, (La Salle, IL: Open Court, 1992), at 45-49. Even Craig acknowledges that "[i]t is true that an accurate physical description of the universe prior to the Planck time remains unknown and perhaps always will remain unknown, thereby affording room for speculations aimed at averting the origin of time and space implied in the expanding universe." Creation Out of Nothing, at 246. Incidentally, I find it puzzling (to say the least) that Craig's KCAAA so heavily depends upon the General Theory of Relativity (GTR), together with the Hawking-Penrose singularity theorems, notwithstanding Craig's endorsement of the view that the geometrical approach to the GTR, whereby gravity is understood not as a force but in terms of the curvature of space-time (in turn taken to be a four-dimensional continuum), is regarded as providing a merely instrumental model. Craig, Time and Eternity, at 178-180.

[117] Monthly Notices of the Royal Astronomical Society 104 (1944): 121 (as approvingly quoted in Craig. Time and the Metaphysics of Relativity, at 151. Davis S. Oderberg, Craig's ally, unexceptionably declares: "Metaphysics is not a mere epiphenomenon of physical theory: on the contrary, it is the base upon which any adequate physical theory must build. If a physical theory implies or is otherwise committed to metaphysical theses which are absurd, illogical, or repugnant to common sense, then that theory will find itself standing on foundations of sand." "Traversal of the Infinite, the 'Big Bang,' and the Kalam Cosmological Argument." Philosophia Christi 4 (2002), at 320-321.

I gratefully acknowledge the helpful comments and encouragement by Tom Masterson, as well as by Quentin Smith and Jeffrey Grupp, the editor and associate editor of Philo, respectively. Last, but not least, my many thanks to Keith Augustine for his excellent and much appreciated editing of this paper, and to Don Morgan for so ably facilitating the publication of my three Kalam papers on the Secular Web.


Copyright ©2004 Arnold T. Guminski and Internet Infidels, Inc.

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