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A Critical Examination of Mark R. Nowacki's Novel Version of the Kalam Cosmological Argument (2008)

Arnold T. Guminski


[Note: This article was first published in Philosophia Christi, Vol. 10, No. 2, pp. 377-391 (2008) (© 2008). This electronic version (© 2010) is published with the permission of both Philosophia Christi and the author. More information about Philosophia Christi can be found at Although the formatting of this electronic version differs from that of the print version, the content is the same.]

[p. 377]


Professor Mark R. Nowacki's book, The Kalam Cosmological Argument for God (hereafter TKCAFG),[1] purports to be a thorough examination of the Kalam Cosmological Argument (KCA) insofar as that argument sounds in philosophy rather than in the natural sciences.[2] Accordingly, the author generally prescinds from those real or supposed deliverances of the natural sciences, such as big bang cosmological models, when offered to confirm the philosophical KCA, or to independently provide the basis for the premise affirming the finitude of the past history of this physical universe.[3] Incident to his examination, he sets forth the major objections and responses to contemporary versions of the KCA, particularly that exposited by William Lane Craig.[4] However, the primary object of his work is to set forth [p. 378] a metaphysical theory of substances, and a complementary modal theory of what he calls factual possibility or necessity pertaining to substances, in order to provide a better framework in which to construct an improved KCA.

Nowacki's version of the KCA sufficiently differs from that of William Lane Craig to warrant respectively designating the two versions as the Craig-KCA (C-KCA) and the Nowacki-KCA (N-KCA).[5] Of course, both the C-KCA and the N-KCA have some important principles and doctrines in common. The most important way in which the N-KCA is novel is that Nowacki affirms the following:
   (1) "[M]y position [is] that the substances that exist now bear the marks of their entire history; these temporal marks correspond to and ultimately are grounded in distinct real features of the substances."
   (2) "If the past were actually infinite, then there would be an actual infinity of significant real features (temporal marks) in what exists now."
   (3) "[I]t is impossible for there to exist substances with an actual infinity of significant temporal marks."
   (4) "Therefore, the universe cannot have existed eternally."[6]
I shall first review some preliminary matters before discussing the N-KCA insofar as it is most significantly novel.

Nowacki and Argument (A) of the C-KCA

What Nowacki calls argument (A) of the C-KCA reads:
   "(i) An infinite temporal regress of events would constitute an actual infinite."
   "(ii) An actual infinite cannot exist."
   "(iii) Therefore an infinite temporal regress of events cannot exist."[7]

Nowacki explains[8]:

[A]rgument (A) has as its goal the elimination of the possibility of an actual infinite of past events, and events (past or present) are concrete in a way that mathematical abstracta are not. So what a defender of the KCA might find useful is a notion of existence that distinguishes between the abstract mode of existence proper to mathematical entities (and other abstracta such as propositions) and the concrete (i.e., nonabstract) mode of existence enjoyed by nonabstract beings.

I fully agree with Nowacki in this matter.

According to the C-KCA and the N-KCA, Cantorian transfinite arithmetical theory cannot be instantiated in a real world consisting of concrete objects because such instantiation would generate counter- [p. 379] intuitive absurdities. Applying Cantorian transfinite arithmetical theory in toto to the real world means that any denumerably infinite set of concrete entities is to be treated as having the same relevant properties as a mathematical infinite set. This entails that any two denumerably infinite sets of concrete entities (each set necessarily equipollent to the set of natural numbers) are mutually equipollent.[9] My own writings amply disclose that I reject argument (A) of the KCA.[10] However, for the purposes of this paper, I shall assume for argument's sake that it is metaphysically (and, therefore, factually) impossible for there to obtain a denumerably infinite set of coexisting concrete entities in the real world.

The C-KCA predicates the metaphysical impossibility of an actual infinite of coexisting concrete entities based almost exclusively upon transfinite mathematical considerations. Nowacki's professed goal, on the other hand, is to construct an argument based upon a metaphysical theory of substances, and of modality pertaining to factual necessity/possibility focused upon this universe. Nevertheless Nowacki also in fact depends upon transfinite mathematical considerations in the exposition and defense of his novel argument. And in so doing, Nowacki appears to fully accept Craig's (at least implicit) assumption that the only arguably plausible way in which Cantorian theory can apply to the real world of concrete objects is to posit that any actual infinite set of real entities is to be treated as a mathematical set, with all its relevant properties—instead of merely postulating the equipollence between any such real infinite and the set of all natural numbers. Thus, because of the counterintuitive absurdities generated by total, systematic application of the principle of correspondence to the real world, Nowacki admonishes us not to project Cantorian theory of transfinite mathematics onto the real world of concrete objects.[11][p. 380]

Nowacki and Argument (B) of the KCA

Argument (B) in the C-KCA may be presented thus:[12]
   "(a) The temporal series of events is a collection formed by successive addition."
   "(b) No collection formed by successive addition can be an actual infinite."
   "(c) Therefore the temporal series of events cannot be an actual infinite."

As far as I can see, nowhere in his book does Nowacki explicitly question the soundness of argument (B) if that argument is understood not to presuppose that the existence of any denumerably infinite set of concrete entities is metaphysically possible.[13] However, just as Craig did in his post-TKCA writings, Nowacki appears to also rely upon transfinite mathematical considerations to buttress the cogency of argument (B).[14]

Perhaps apprehensive that many persons might find argument (B) (considered independently of argument (A)) to be unpersuasive, the N-KCA (unlike the C-KCA) insofar as it is novel does not assume for argument's sake that some actual denumerable infinite can be instantiated in reality.[15] On the contrary, the factual impossibility of an actual infinite of coexisting concrete entities is essential to a correct understanding of N-KCA insofar as it is novel.[16][p. 381]

Nowacki's Theory of Substances and Factual Possibility

Nowacki expounds a metaphysical theory of substances and of factual possibility calculated, so he maintains, to enhance the persuasive power of the KCA.[17] He explicates a notion of substance as a subject of predication but which itself is not predicated of other things, and which is the locus of active causal powers. According to him, the notion of possibility stronger than that of logical possibility is that of factual possibility. Now substantial possibility is a subdomain of factual possibility that holds for substances. According to Nowacki, the nature of a substance is "the intrinsic character of a substance that makes the substance to be what it is."[18]

Nowacki "formally characterize[s] substantial modality [as follows:] Substantial possibility is that subdomain of factual modality that is delimited by the naturally possible causal relations open to substances as a function of the particular natures they possess. Substantial impossibility is the negation of substantial possibility. Substantial necessity is that subdomain of factual modality that is delimited by the naturally necessary causal relations open to substances as a function of the particular natures they possess."[19]

Nowacki maintains that the KCA should be principally directed to what is factually possible with respect to this physical universe alone. Nowacki holds that it is neither necessary nor useful to consider what is metaphysically necessary/possible in the sense intended by Craig in order to construct a more persuasive KCA[20]—which, he insists has a "this-worldly focus."[21] The "this-worldly focus" of the N-KCA is essential to Nowacki's theory of temporal marks.[p. 382]

Nowacki's Theory of Temporal Marks

This leads us now to the most controversial aspect of the N-KCA insofar as it is most significantly original. I refer to the topic of temporal marks.[22] Nowacki claims that "the features currently found in substances bear the marks of their entire causal history," and submits that his substance-based metaphysics "leaves room for the articulation of a theory of temporal marks."[23] He expounds his theory thus: "for the purposes of the KCA events are to be identified with (pragmatically) significant, causally connected, real changes in substances.... [C]hange is as metaphysically real as the substances that do the changing, and all substances bear the marks of the entire series of prior changes that lead up to their being in their present condition."[24] Nowacki defines "a temporal mark as a metaphysically real feature possessed by a substance that belongs to that substance because of some particular, real causal relation that the substance (or some causal predecessor of the substance) entered into during its successive historical existence. Each substance bears the temporal marks of its entire causal history. No event in the history of a substance is ever completely lost, and no event is utterly devoid of consequence."[25] "[T]emporal marks must be distinct from each other [because otherwise] the successive elapsing of one event after another could erase one mark and replace it with a new one."[26] Nowacki explains that "[t]he claim that temporal marks are permanent should not be interpreted as the claim that temporal marks always persist in the same form."[27] He asserts that temporal marks "are metaphysically ordered in a way that parallels the temporal ordering of events in the substance's history."[28]

Nowacki's Arguments for His Theory of Temporal Marks

Nowacki presents two arguments for the existence and characteristics of temporal marks. The first appears to consist of extrapolations from empirical data. In this respect, the plausibility of his inference that each event [p. 383] leaves a temporal mark on a then existing substance, and that such a temporal mark is distinct, permanent (although changeable in form), and passed on to causal descendents, far exceeds its evidential basis.[29] At best, his empirical argument supports a very speculative metaphysical hypothesis, which is very improbable because of its radical scope.

Consider a set of twin brothers. These two substances have each finitely (yet so superlatively numerous) many temporal marks which pertain not only to their own persons proper, but pertain as well to all their causal ancestors. Are the temporal marks pertaining to the brothers' causal ancestors numerically identical, or only qualitatively identical? Are all temporal marks physical? Are all temporal marks spatially located on a physical substance? Are all spatially located temporal markers on physical substances spatially extended? What about spiritual substances (such as the angels or souls)? If they have temporal marks, how are these grounded and ordered upon a spiritual substance? And, one may inquire, what about a microorganism?—an entity just as substantial as a donkey. Despite its minute size, it too bears the multitude of temporal marks of its numerous causal ancestors. If a temporal mark constituting a real feature of a microorganism must be spatially extended, how small a temporal mark can there be in this universe? Similar remarks can be made mutatis mutandis about submicroscopic physical entities.[30] Moreover, Nowacki appears to admit the factual possibility of there being concrete entities other than substances —which are defined in terms of existence over time.[31] What about the factual possibility of concrete entities existing for a moment or for an extremely brief duration? The empirical data purporting to establish there are temporal marks appear to pertain only [p. 384] to concrete entities that are at least microscopic and are not of brief duration. Thus it is an extravagant extrapolation to infer that concrete entities, however minute and short-lived, bear temporal marks.

The second argument, which he attributes to DeWitt Parker and upon which he chiefly relies to construct his N-KCA, is "that permanent temporal marks are required to explain how there can be true propositions about the past."[32] Parker, Nowacki approvingly remarks, "is ... arguing that temporal marks of the past, existing as real features within the present, are the truth makers for historical propositions."[33] We are now at the essential part of the N-KCA. Nowacki declares:[34]

One who adopts a presentist ontology (i.e., an ontology wherein all that can be said to truly exist exists now) would be hard-pressed to avoid Parker's argument.... [I]t may be asked: What else but real marks existing now could justify our use of the past tense? ... The presentist asserts: "Only the present is actual." Fine; let this be granted. But if our presentist then proceeds to argue that temporal marks are not part of the ontological furniture of the present, it is difficult to see how ordinary discourse about past events can be justified. It is one thing to assert that talk about the past involves covert references to the present; it is another to flatly deny that there is no metaphysical foundation for discourse about the world's past to be found in the world itself.

The advantage of this version of presentism, according to Nowacki, is that "If ... there is a temporal mark left for each past event, the correlation between infinite past events and a presently existing actual infinite would be established metaphysical fact."[35] Thus Nowacki, perhaps thinking that a temporal series of successively occurring events or moments is not per se an actual infinite in sensa strictu,[36] nuances the problem by concluding:[37] "[I]t is substantially necessary that an actually infinite past should result in an actual infinite of presently existing temporal marks. The events of the past are actual precisely insofar as they have left indelible, distinct, and ordered marks of their passing upon substances existing now."[p. 385]

So it appears that Nowacki thinks that a set of infinitely many past events constitute an actual infinite in a rather Picwickian sense. But, he also writes, "it is impossible for there to exist substances with an actual infinity of significant temporal marks."[38] "Therefore," he concludes, "the universe cannot have existed eternally."

What are we to think of Nowacki's argument about temporal marks and presentism? Well, I profess to share with Craig a commitment to a presentist version of an A-theory of time.[39] But neither he nor I would feel "hard-pressed to avoid Parker's argument." The A-theory of time, in asserting the objective reality of temporal becoming, also asserts (according to Craig) the reality of tensed facts about the past, present, and future. Tensed facts about past and future events are present now; although past and future events are not present now. The truth-makers for propositions concerning past, present, and future events are tensed facts about such events. Therefore, there is no need to posit the existence of at least as many temporal marks as there have been past events in order to insure that there are truth-makers for truth-bearing propositions about past events.[40]

In his essay, "In Defense of Presentism," Craig expounds a presentist theory which obviates the difficulty raised by Nowacki. Craig explains:[42]

[F]ollowing the modal of modality di dicto and de re, it seems that tense taken de dicto would be tense as a feature of one's truth bearers, either the propositional content expressed by tensed sentences or the sentences themselves. Tense taken de re would hold that tense is an objective feature of concrete reality. These are not mutually exclusive views of tense; presentists typically hold that there are tensed truth bearers and tensed facts correspondent to them.

Addressing the question "whether one who holds to a view of truth as correspondence cannot be a presentist," Craig rhetorically answers: "Well, why not?"[43] He proceeds to answer an objection against presentism posed [p. 386] by Quentin Smith in terms similar to those he could also use with respect to Nowacki's bold version of presentism:[44]

The presentist may plausibly claim that a view of truth as correspondence requires only that the entities referred to in a true past- or future-tense proposition either did or will exist at the indicated times....

What such an account of the truth of past- and future-tense propositions requires is that there are tensed facts corresponding to tensed propositions, and the A-theorist is only to eager to affirm this conclusion. Thus the proposition Plato wrote The Republic is true, on a view of truth as correspondence, because this event did occur; that is, a man named Plato did exist and wrote the work entitled The Republic. These are tensed facts that (depending on what one takes a fact to be) exist or obtain or are true now, but were not so in, say, 5,000 B.C. So a view of truth as correspondence requires the objective reality of tensed facts, facts about what was or will be the case.

Craig thus holds that "a fact is a state of affairs that obtains.... [T]he A-theorist holds that there are tensed states of affairs that obtain at various times."[45] In terms of possible-worlds semantics, Craig explains: "A view of truth as correspondence requires that corresponding to the presently true proposition Hegel used to be alive is a tensed fact, which I have taken to be the tensed state of affairs Hegel's having been alive that presently obtains."[46]

The C-KCA like the N-KCA presupposes the A-theory of time but, unlike the N-KCA, it does not presuppose presentism —albeit that Craig is a presentist.

The N-KCA however, is wedded to a version of presentism that is radically defective in that it presupposes a version of the A-theory of time in which tensed facts as to past or future events lack ontological reality. Nowacki's presentism is advocated upon the basis that unless every temporal mark continues to exist in some form then there are no truth-makers for truth-bearing propositions about past events. I fail to see why the presence of some supposed real feature of a substance which Nowacki calls a [p. 387] temporal mark constitutes a truth-maker of a proposition. The temporal mark does not bear its characteristic as being a truth-maker upon its sleeve, as it were. All we have at best is "the correlation of past events with physical substances [as] a metaphysical fact."[47] Furthermore, although the Craig-type presentist theory gives an account of how future-tensed facts presently obtaining are the truth makers of propositions about the future, the Nowackian account fails to provide a sufficient basis whatsoever for saying there are any truth makers for propositions about the future. As he tersely puts it: "Whereas past events leave their mark on what exists now, future events do not enjoy a similar perch on what presently exists."[48]

Although I hold that Nowacki's theory of temporal marks is fatally flawed insofar as it affirms that all past events correspond to presently existing temporal marks, it might be urged that he could have made essentially the same points were he to have argued instead that tensed facts about past events presently obtain and that the total application of Cantorian theory to the real world hypothetically containing infinitely many tensed facts about past events generates counterintuitive absurdities. But perhaps the reason why he does not adopt this approach is because he apprehends that he would be obliged to concede that tensed facts about future events also presently obtain, and therefore there can be only finitely many future events since there can only be finitely many tensed facts about future events. This solution would be unsatisfactory for the Christian theist whose beliefs about life everlasting for humans standardly presuppose an endless succession of events.[49] So Nowacki arguably has a theologically driven reason why he maintains his version of presentism with its doctrines concerning temporal marks about past events being truth makers.

Another reason why Nowacki perhaps relies upon his particular version of presentism (based upon the necessity of temporal marks as truth-makers) is because otherwise his theory of substances and substantial possibility precludes him from arguing that something about this universe itself entails that it is of finite duration. Thus he writes[50]:[p. 388]

[I]t is worth emphasizing that giving an analysis of events in term of past changes in substances is metaphysically well grounded. As previous philosophers (most notably Aristotle) have argued, it is substantially necessary that change has been present in the universe for as long as the universe has existed. Since we observe change occurring now, it follows that there has always been change, and hence substances undergoing change, for as long as the universe has existed. Now the KCA obliges us to rule out the factual possibility of the quantity of prior events being actually infinite....

I disdain putting words in Nowacki's mouth, so we should hope for some clarification from him. It suffices to say that his book is strikingly flawed in that absent from his exposition and defense of his theory of temporal marks is any consideration of versions of the A-theory of time other than his own. For example, another plausible model neglected by Nowacki is that present and past-tensed facts now obtain but not (at least) some future-tensed facts; thus allowing a modified version of presentism consistent with an "open future view [according to which] the future cannot be completely and truly described in terms of what will or will not happen, but must also include reference to what might and might not happen."[51]

The N-KCA insofar as it is novel proposes that "an actually infinite quantity of past events cannot have elapsed in our universe [because]"[52]: (1) "the features currently found in substances bear the marks of their entire causal history [which includes those of their causal ancestors]"[53]; (2) "[I]t is substantially necessary that an actually infinite past should result in an actual infinite of presently existing temporal marks"[54]; (3) "[I]t is impossible for there to exist substances with an actual infinity of significant temporal marks."[55] Nowacki promises in effect that he will argue for his premise (3) in chapter 5 of his book.[56][p. 389]

What Nowacki does in chapter 5 is to try to show that it is substantially impossible in this universe to have infinitely many physical substances. And from this he evidently infers that it is substantially impossible for there to be infinitely many temporal marks. But this inference, insofar as we prescind from transfinite mathematical considerations, requires the premise that all temporal marks (of spatio-temporal entities) must be spatially located and extended. And Nowacki, whose hypothesis concerning the permanence (in some form or another) of all temporal marks is (to put it mildly) already rather far-fetched, would be indeed more rash in supposing (if he indeed does so) that all temporal marks on physical substances are spatially extended. But assuming that it is substantially impossible for there now to be infinitely many spatially extended substances in this universe, Nowacki cannot justly infer that there cannot have been have been infinitely many events in a temporal series unless, necessarily, all temporal marks are spatially extended. And if, as I suppose Nowacki believes, there are temporal spiritual substances, then whatever temporal marks they have cannot be spatially extended unless (as in the case of the post-resurrection spiritual body) the substances themselves are spatially extended. Accordingly, it does not seem incoherent to suppose that not all temporal marks of substances are spatially extended.

Nowacki and his Thought Experiments

Nowacki presents several thought experiments in order to show that it is substantially impossible to have infinitely many physical substances.[57] Nowacki has promised in effect "that thought experiments be translatable into this-worldly terms." He asks: "How could the KCA's reductio proofs ever get their bite unless they were somehow intimately related to our actual world?"[58] So it is no small wonder that Nowacki chooses to present us with thought experiments involving such fantasia as: hyperlumps;[59] two scenarios about Theseus, who for as long as the universe has eternally existed, "wanders lost through a vast labyrinth";[60] the case of the "four rocks, labeled A through D, [which] have existed for as long as the universe has [eternally] existed ... receding from each other at a constant rate for as long as they have existed";[61] the case of "two rocks ... separated by ℵo [aleph-zero] astronomical units [which] have traveled another astronomical unit in opposite [p. 390] directions";[62] and the case of "filling a two liter container with two liters of homogenous physical gunk."[63]

Since this paper assumes arguendo the premise that it is factually impossible for a denumerably infinite sets of concrete entities to actually exist, I shall discuss no thought experiment unless it purportedly pertains to the doctrine of temporal marks.

It appears that there is only one thought experiment that satisfies this criterion; and that is the second Theseus scenario. This scenario supposes that Theseus eternally wanders through a labyrinth without unwinding a ball of twine. According to Nowacki, this "Theseus thought experiment would parallel other traditional thought experiments that have a fixed quantity of matter moving eternally through empty space."[64] Nowacki asks whether it might be substantially possible for Theseus to have walked throughout the infinite past composed of denumerably infinite moments through the labyrinth. Nowacki has a remarkably lame response. He first remarks that "[t]he effects of the past are always carried forward into the present and what exists now bears the indelible marks of its total causal history." Accordingly, "[a]n actual body that travels through space always leaves something of itself behind; some token or sign of its passage always remains in its wake." Therefore, Nowacki rhetorically asks, "[s]ince it is not substantially possible for Theseus's infinite twine to exist, why should we suppose that the path described by that hypothetical twine represents a substantially possible travel path?"[65] His accompanying note protests that to "accept the substantial possibility of Theseus's walking the path described by that hypothetical twine is to adopt the position that seems to make a covert appeal to the erasability of temporal marks."[66] But he rejects the possibility that temporal marks are erasable. Thus the unacceptability for Nowacki of the scenario in question presupposes that all temporal marks survive to the present in some form.


The N-KCA proposes that the temporal series that constitutes the history of this universe must have denumerably finite members because otherwise there would now be denumerably infinite coexisting entities (i.e., temporal marks)—a state-of-affairs deemed factually impossible for this universe. According to the N-KCA, every substance bears temporal marks —which are permanent, distinct and indelible real features of that substance caused by all the events in the history of that substance and all its causal ancestors. All [p. 391] presently existing temporal marks of any given substance thus correspond one-to-one with all the events that have occurred in its history (including those of its causal ancestors). The N-KCA presupposes that a denumerably infinite set of coexisting entities is factually impossible because it is assumed that Cantorian theory can arguably apply to this universe only if every real infinite is treated as a mathematical set. The N-KCA is radically defective in that it includes a doctrine about temporal marks that involves a rather preposterous extrapolation from empirical data to all concrete entities of whatever size or duration. The argument also appears to presuppose that all temporal marks on physical substances are spatially extended. Moreover it is based upon a version of presentism which denies that tensed facts about past and future events obtain now and thus have ontological reality just as present events do. The N-KCA errs in making temporal marks (instead of tensed facts) the truth-makers of propositions.

Thus my final conclusion is that the N-KCA, insofar as it is novel, does not constitute an improved version of the KCA. Indeed, those persons (whether theists or not) who reject or are disposed to reject the KCA are very likely to conclude after due reflection that the N-KCA is much less plausible than that version of that cosmological argument so ably expounded and defended by William Lane Craig —whose writings on the subject have succeeded in having awakened so many of us from our dogmatic slumbers.[68]


[1] (Amherst NY: Prometheus Books, 2007).

[2] Nowacki initially refers to the KCA as an argument which "runs thus: 1. Whatever comes to be has a cause of its coming to be. 2. The universe came to be. 3. Therefore, the universe has a cause of its coming to be." TKCAFG, 13. Further argument establishes that God is the "transcendent cause [that] brought the universe into existence ex nihilo." Ibid., 14. In endnote 1 to his book's introduction, Nowacki writes: "In this introduction I will use KCA as shorthand for the entire family of arguments that attempt to prove the existence of God from the finitude of the past. In the remainder of the book I will focus exclusively upon contemporary variants of the argument that either arise from or make reference to Craig's work." Ibid., 20.

[3] I discuss scientific versions of the KCA in my paper "The Kalam Cosmological Argument as Amended: The Question of the Metaphysical Possibility of an Infinite Temporal Series of Finite Duration" (2004, updated 2005)

[4] Nowacki refers to Craig's early presentation of the argument in his The Kalam Cosmological Argument (London: MacMillan, 1979) (hereafter TKCA), and to Theism, Atheism, and Big Bang Cosmology (New York: Oxford University Press, 1993), as well as "an impressive number of articles and book contributions that elaborate and defend his position" (TKCAFG, 14), listed in the book's bibliography.

[5] It is to avoid confusion that I shall distinguish between the C-KCA and the N-KCA, and use KCA to only refer to the minimal sense of that term as described in note 2 supra.

[6] TKCAFG, 147n68.

[7] Ibid., 55.

[8] TKCAFG, 55.

[9] A denumerably infinite set, whether of concrete (e.g., dogs, atoms, spirits, bacteria) or abstract entities (numbers, propositions, points), is one the members of which correspond one-to-one to the members of the set of all natural numbers. Two sets are said to be equipollent if their respective members correspond one-to-one with each other.

[10] I thoroughly explore argument (A) in TKCA (and as considerably augmented in Craig's later writings) in my article, "The Kalam Cosmological Argument: The Question of the Metaphysical Possibility of an Infinite Set of Real Entities," Philo 5 (2002) 196-215. My Philo article was electronically published, with several changes, on the Secular Web (2003, updated 2005) My position, in a nutshell, is that any two denumerably infinite sets of concrete entities are necessarily equipollent to the set of all natural numbers but they are not necessarily equipollent to each other. See my post "A Brief Comment on Mark Nowacki's Recent Book on the KCA" (August 26, 2007) for my account of how Nowacki grossly misunderstands the thesis of my Philo article as to how Cantorian set theory could be applied to the real world without thereby generating counterintuitive absurdities.

[11] TKCAFG, 248-49.

[12] Ibid., 66.

[13] TKCAFG, 66: "It is useful to note that argument (B) takes no position on the question of whether an actual infinite can exist." In presenting what Nowacki calls Argument (B), Craig wrote: "Here we do not assume that an actual infinite cannot exist." TKCA, 103.

[14] See Nowacki, TKCAFG, 130-35, and accompanying endnotes. I thoroughly explore argument (B) in TKCA (as expounded in Craig's KCA and in his later writings) in my second Secular Web paper, "The Kalam Cosmological Argument Yet Again: The Question of the Metaphysical Possibility of an Infinite Temporal Series" (2003, updated 2005)

[15] Nowacki appears to have concern about the issue whether any infinite temporal series is per se factually impossible. See TKCAFG, 97n143, where he (after noting that "Craig is oddly terse regarding what he means by the reality of past events") comments: "My discussion of temporal marks in chapter 5, section 21.2, is intended to help alleviate the problem." See also ibid., 86n 67: "A natural objection to this claim [i.e., "if the universe were supposed to exist eternally a parte ante, then the events that make up its past would constitute an actually infinite totality" (ibid., 43)] is that past events cannot constitute an actually infinite totality because past events no longer exist." After referring to "Craig address[ing] this concern in the course of his presentation of the KCA," Nowacki refers the reader to chapter 5, section 21 ("Events and Temporal Marks," pages 235-42) "for more on how Craig's thesis might be defended."

[16] TKCAFG, 264: "The factual impossibility of instantiating an actual infinite in turn implies that the quantity of past events in the history of the universe is finite, a result congenial to a positive assessment of the KCA."

[17] Nowacki sets forth his explanation and justification of his metaphysical theory of substances and substantial necessity/possibility in chapter 4 of his book (pp. 198-231).

[18] Ibid., 199.

[19] Ibid., 220.

[20] Ibid., 233-34: "[T]the KCA ... talks only about the impossibility of this universe having existed forever. The question before us is not whether some possible universe or other could have existed eternally; the question, rather, is whether this universe of ours has existed eternally.... The question ... is whether the actual infinite described by Cantor might be instantiated in our universe.... It is this universe, with the particular concrete things that furnish it, that cannot have an eternal past existence." On the contrary, I believe that the KCA, especially as formulated by Craig, is concerned with the metaphysical possibility of denumerably infinite sets of concrete entities, rather than with just what is factually possible only with respect to this physical universe. But I need not discuss this matter for our purposes.

[21] Ibid., 237.

[22] Nowacki acknowledges (ibid., 237) that he "derive[s] [his] understanding of temporal marks from DeWitt [H.] Parker, who speaks of 'echoes' and 'traces' of past events that are inevitably and indelibly carried forward into the present as real features of existing things" (citing, at ibid., 257-58n14, Parker's Experience and Substance: An Essay in Metaphysics [Westport CT: Greenwood, 1970], 157).

[23] TKCAFG., 234.

[24] Ibid., 235.

[25] Ibid., 237. "Even if past events cannot be said to exist now, they have determinately existed and have left determinate marks of their passing on what exists now." Ibid., 107.

[26] Ibid., 240.

[27] Ibid., 238.

[28] Ibid., 236. Not only are all temporal marks permanent and indelible, but there is also "a natural order that exists among temporal marks copresent in a substance existing now." Ibid., 241.

[29] The grounds, or examples, are: (1) slight changes in the microstructure of substances due to changes in its position; (2) "temporal marks now present, can be used to distinguish two similar objects of the same kind." (3) detection of forgeries is possible because they "betray themselves because they inevitably—and indelibly—embody the history of their moment of creation." Ibid., 238-39.

[30] It is not altogether clear whether Nowacki regards submicroscopic physical entities, especially so-called virtual particles (if real), as substances. See KCAFG, 112-13, 208, 225 n33. It seems to me that his statement, "that there has always been change, and hence substances undergoing change, for as long as the universe has existed" (ibid., 235-36), indicates that he thinks that the stuff of the early universe according to big bang cosmology was substance-like.

[31] Nowacki's claim that there have always been substances is open to a serious flanking attack armed with his own admissions: "There may be other subdomains of factual possibility. For instance, physics recognizes other entities besides substances as exercising active causal power, the chief example of this being fields. Fields are not plausibly treated as substances, although they are locatable in time and space. Now, it may be the case that fields are ultimately explainable in terms of substances. (What is a magnetic field without a magnet?) Yet it seems prudent to leave open the possibility that another domain of factual possibility, corresponding to fields or other peculiar entities, may one day be distinguished." TKCAFG, 186n4. Do such concrete entities (locatable in time and space with active causal powers but that are not substances) also bear temporal marks?

[32] Ibid., 239.

[33] Ibid., 240.

[34] Ibid.

[35] Ibid., 242.

[36] In presenting his response to the objection to the KCA that "[t]he past cannot be said to be actually infinite because past events do not exist simultaneously," (Ibid., 115), Nowacki appears to adopt Robert Prevost's opinion that "'even though the past moments no longer exist, the permanent record of their existence would. Hence, if there were an infinite number of past moments, there would be an infinite number of permanent records.'" Ibid., 116.

[37] Ibid., 242. See also Ibid., 147n68: "If the past were actually infinite, then there would be an actual infinity of significant real features (temporal marks) in what exists now "

[38] Ibid., 147n68. This quotation begins with: "However, as I argue in chapter 5."

[39] For an accessible account of Craig's A-theoretic presentism and how it accords with a correspondence theory of truth, see his Time and Eternity, 115-65, 250-53.

[40] Interestingly, Nowacki makes a passing reference to facts, a term which he parenthetically defines as "what makes a true proposition true." TKCAFG, 117. But he does so in the course of rejecting the contention that facts are "elements or real features of substantial reality." Ibid. However, tensed facts about past events may plausibly be regarded by a presentist as a part of reality without being a part of substantial reality.

[41] William Lane Craig, "In Defense of Presentism," in Time, Tense, and Reference, ed. Alexandar Jokić & Quentin Smith (Cambridge: MIT Press, 2003), 391-408.

[42] Ibid., 392.

[43] Ibid., 396.

[44] Ibid., 396-97. I should note that Smith objected to presentism whereas Nowacki adheres to what Craig would think to be a defective version of presentism.

[45] Ibid., at 397.

[46] Ibid., 400. Craig says similar things about future-tensed facts: "If tense is an objective feature of reality ... then there are tensed facts which are every bit as much a part of any actual world's history as are entities. In possible worlds semantics tense is necessarily neglected because, as we learn from McTaggart's Paradox, there can be no maximal description of a world in tensed language.... In any instantiation of a temporal world there will be tensed states of affairs that obtain in addition to the entities that exist (e.g., Its being presently tn). If, then, future contingent propositions are bivalent, to what do they correspond? Even if we say that their truth is ultimately grounded in the future truth of their respective present-tense versions, they do not correspond to those present-tense states of affairs. Rather a view of truth as correspondence requires that they correspond to future-tense states of affairs which obtain right now." "Adams on Actualism and Presentism." Philosophia 25 (1997): 403.

[47] TKCAFG, 121.

[48] TKCAFG, 258n18. Nowacki approvingly quotes Parker: "'If the future does not have the reality of the event, neither does it have the reality of the trace.'" Ibid. However, Nowacki also affirms: "What exists now bears the marks of the past in a determinate way, whereas the marks of future happening are present in what exists now in an indeterminate way." Ibid., 124.

[49] Nowacki considers an objection to the KCA based upon God's omniscience encompassing infinitely many true propositions about potentially infinite future events. But his response is essentially that God's knowledge is nonpropositional. TKCAFG, 119-20, 149-50n78. Although he cites Wesley Morriston's "Must Metaphysical Time Have a Beginning?" Faith and Philosophy 20 (2003) 288-306, as containing a discussion of related issues, Nowacki fails to address Morriston's point (ibid., 301-02) that there is a complete and determinate set of true propositions about future events, and hence this set constitutes an actual infinite.

[50] TKCAFG., 235-36. See also ibid., 257n11; 136, 161n147.

[51] Alan R. Rhoda, Gregory A. Boyd, and Thomas G. Belt, "Open Theism, Omniscience, and the Nature of the Future," Faith and Philosophy 23 (2006), 432. See ibid., 446-50, for the authors' discussion of the A-theory and the correspondence theory of truth vis-à-vis presentism with respect to the future. À propos this version of presentism consistent with the open future view, the authors explain: "[T]he present bears upon the future in the manner of a cause upon its effect. For example, it is now true that the Sun will arise tomorrow. Why? Because the world in its present state is governed by nomic regularities that, barring a miracle, guarantee the Sun's rising tomorrow. It would appear, then, that the future-tense state of affairs the Sun's going to rise tomorrow consists in the present state of reality tending inexorably in that direction. The future is in that respect already present in its causes." Ibid., 447 (emphasis in original).

[52] Ibid., 234.

[53] Ibid. "[C]hange is as metaphysically real as the substances that do the changing, and all substances bear the marks of the entire series of prior changes that lead up to their being in their present condition." Ibid., 235.

[54] Ibid., 242.

[55] Ibid., 147n68.

[56] Ibid.

[57] Ibid., 121, 243-55.

[58] Ibid., 237.

[59] Ibid., 249-53.

[60] Ibid., 253-54. In the first scenario, Theseus unwinds a ball of twine as he wanders through the labyrinth; in the second he wanders without the twine.

[61] Ibid., 254.

[62] Ibid., 260n29.

[63] Ibid., 121, 151-52n87.

[64] Ibid., 253-54.

[65] Ibid., 254.

[66] Ibid., 260n28.

[67] My overall assessment of Nowacki's book appears to be very negative given my sharp disagreement with his novel version of the KCA for reasons of which only some have been given in this paper. I hasten to add, however, that Nowacki's book has scholarly value with many interesting and intellectually provocative insights. In fine, it should also be said that having his work ignored is much worse for a philosopher than having it sharply criticized.

[68] I wish to express my gratitude to Judge Dino J. Fulgoni, my learned friend and former colleague in the Los Angeles District Attorney's Office, for his careful review of and helpful comments about an earlier version of this paper. I also thank this journal's referees for their suggestions as to how to materially abridge this paper without prejudice to its dominant purpose.