Is the Past Finite? On Craig’s Kalam Argument
by George W. Shields
George W. Shields teaches philosophy at Indiana University Southeast, New Albany, Indiana. The following article appeared in Process Studies, pp. 31-40, Vol. 14, Number 1, Spring, 1984. Process Studies is published quarterly by the Center for Process Studies, 1325 N. College Ave., Claremont, CA 91711. Used by permission. This material was prepared for Religion Online by Ted and Winnie Brock.
William Lane Craig has authored a well-informed historical account and sophisticated modern defense of the cosmological argument for God’s existence which has its origin in the medieval Arabic practitioners of kalam (sometimes translated ‘scholastic theology’). The work (K) should be of special interest to process thinkers since the kalam cosmological argument challenges an important tenet of process metaphysics, namely, that the class of finite actualities has infinite members -- the infinitude of past events. In other words, Craig’s defense of the kalam argument upholds the position that the past of finite events had an absolute beginning a finite time ago.
In this essay I shall examine some of Craig’s arguments for this position, concurring with him that they have cogency; yet I shall also uncover a process theist’s rebuttal which appears to have equal cogency. I conclude that Craig and the process theist are at an impasse so that if a decision is to be made concerning the cognitive superiority of either the kalam or process theistic models, this must be made by appeal to issues in philosophical theology other than the question of the extension of the past.
Before I get into the body of my commentary and reflections, a few remarks on the programmatic structure of Craig’s book are necessary. Part I, "Historical Statements of the Kalam Cosmological Argument," presents various formulations of the argument found in al-Kindi, the Jewish thinker Saadia ben Joseph, and al-Ghazali. Part II, "A Modern Defense of the Kalam Cosmological Argument, is organized around Craig’s valid syllogistic formulation of the argument (K 63):
First Premise: Everything that begins to exist has a cause of its existence.
Second Premise: The universe began to exist.
Conclusion: Therefore the universe has a cause of its existence.
Since it is the Second and not the First Premise which is controversial, Craig devotes the larger portion of Part II to a discussion of it. The central chapter on the Second Premise (K 65-140) contains: (i) a refutation of the attempted application of Cantor’s transfinite mathematics to the domain of extramental reality, (ii) two philosophical arguments which attempt to show the conceptual absurdity of the notion of an infinite past of finite actualities, and (iii) two arguments from physics (concerning Big Bang and Thermodynamic theory, respectively) which attempt to show that probably the natural universe had an absolute beginning a finite time ago. Craig then briefly defends the First Premise (K 141-48), largely with respect to the classic objection of David Hume. (Hume’s objection is shown to commit a non sequitur.) He then concludes that the universe has a cause of its existence, which by definition transcends the whole realm of finite reality, and which must be a personal or psychic being. (In this latter respect he follows an old, but I think largely cogent, argument of al-Chazali’s.) In effect, for Craig, the existence of a personal Creator ex nihilo, and only that, is established by the argument.
In what is to follow I will examine those strands of Craig’s philosophical argument for the view that the universe began to exist which seem to be the strongest. I will not discuss his two arguments from physics for three reasons. (i) These arguments can at best establish some probability that the natural universe had an absolute beginning. They cannot remove the possibility of an uncompromised process theism. (ii) Craig’s argument from thermodynamics depends upon assuming that the natural universe is a closed system, and so it will have force only for those who make that assumption. But we need not make that assumption, especially if we have antecedent and independent grounds for theistic belief. That is to say, if theism is true, the natural universe might well be open to divine ordering and restoring influences which alter thermodynamic conditions. (iii) Most importantly, Craig has apparently overstated the extent to which cosmological physicists are agreed upon a finite Big Bang cosmology,1 so I am skeptical of his claims concerning the strength of the scientific evidence.
Craig validly schematizes the basic philosophical argument to be discussed as follows (translation into strict categorical and syllogistic form produces a valid EAE, figure 1 syllogism, K 103):
1. A temporal series of events is a collection formed by successive synthesis.
2. A collection formed by successive synthesis cannot be an actual infinite.
3. Therefore the temporal series of events cannot be an actual infinite.
First of all, unless one is to deny that there is a temporal series of events, premise (1) above is true. The temporal series of past events is not a collection of events which coexist simultaneously. For, some past events had not occurred when others did in fact occur, e.g., when the death of George Washington took place, the birth of Charles Hartshorne, twentieth century philosopher-theologian, had not taken place. Thus, the temporal series of past events is clearly "instantiated sequentially or successively" (K 103).
Yet the process theist is clearly committed to a denial of premise (2). For both Whitehead and Hartshorne (PR 345-51/ 523-33; CSPM l00f., 125f.), the divine consequent nature is everlasting or infinitely temporal, entailing that God has been interacting with the domain of finite actualities for an infinitely past time, and that God will continue to interact with finite actualities infinitely in the future. In turn this entails that, for Whitehead and Hartshorne, there is, at any arbitrarily designated present, a completed infinite collection of events which has been formed successively or in temporal sequence.
Premise (2) must be upheld, Craig argues, since (i) it is logically impossible to count or successively synthesize an infinite quantity, and (ii) the assumption of an infinite past destroys the contrast between actuality and potentiality.
The issue of ‘counting to infinity’ is relevant here, since it is a continuously repeatable, publicly accessible datum that each new event in the temporal series can be counted as it occurs. There is a real, not just imagined, correspondence between quality and definite event. Indeed, counting has just the asymmetrical character that the ocurrence of temporal events has. Counting "maps" the occurrence of events. Yet one could never reach a complete infinite set of events that is assumed to exist by infinitistic process theists prior to any given Present. This is the case since "for every element one adds, one can always add one more. Therefore one could never arrive at infinity. What one constructs is a potential infinite only, an indefinite collection that grows and grows as each new element is added" (K 104).
Process philosophers have a ready response to this. Charles Hartshorne has objected to this very same reasoning as we find it embodied in the thesis of Kant’s First Antinomy: "Counting to infinity is an incompletable process. Of course this is true if the process has a beginning. But that is the question at issue. Must it have a beginning?" (CSPM 126, my italics). In other words, a past process which ex hypothesi is infinite cannot have a beginning by definition. So nothing is really proven by appealing to the impossibility of counting to infinity, since any such count must have a beginning.
Craig, while not addressing Hartshorne explicitly, does offer a strong counter-argument to this kind of objection. An examination of it will take us to the heart of his case. The counter-argument resides in his citation and defense of G. J. Whitrow’s argument2 to the effect that an infinitist is committed to the idea of an infinite number of intermediary past events which ex hypothesi ought to be able to be counted or successively synthesized (but which everyone agrees cannot be), and that this very situation of infinite intermediaries obliterates the intuitively sound distinction between actual past and potential future.
The Whitrow argument can be reconstructed as follows (see K 200f). Assume that there are an infinite number of past events. Let E be the present event in some infinite, arbitrarily selected chain of temporal events. Now, on the infinitist assumption, E has both an finite past and infinite future, but with a difference. The infinite past of E is actual; the infinite future of E is potential. A potential future infinite has two defining characteristics: (i) for any event in the future of E there will be further future events, and (ii) any event in the future of E which becomes actualized is separated from B by a finite number of intermediary events in the temporal chain to which E belongs. We have already assumed that the infinite past is actual. But if that is so, then the chain of events antecedent of E is actually infinite, and there must be some actual event 0 that is separated from E by an infinite number of intermediaries. For to deny that there really is an infinitely distant actual event O is to give up either the actuality of the infinite past or the infinitude of the actual past. (On either alternative the infinitist assumption is undermined.)
But when in the temporal chain does O occur; when does there come an event, not finitely, but infinitely distanced from E? Of course this is impossible to answer in principle. No matter how far we mentally trace the events ensuing between E and O, we could never arrive at O since O is an infinite distance from E. The infinite distance of O requires that we never halt the regress in order to specify O. This establishes that the logical impossibility of specifying some infinitely remote past event O is equivalent to the logical impossibility of specifying some infinitely remote future event B’ (infinitely remote from E). Moreover, if ever we halt the regress of past events in order to specify O, then O functions in every way like a "future" or "potentially related" event of E, for: (i) there will always be events in the past of O, and (ii) there will be a finite number of intermediaries between O and E (and this satisfies the two formal criteria for O’s being in a "potential, future relation" to E). Thus the infinitist assumption obliterates the distinction between actual past and potential future by giving the past characteristics definitive of potentiality or futurity.
We can connect Whitrow’s argument with Craig’s intuitions about counting to infinity, but this time, we will run the sequence from the past to the present (indeed, the past is symmetrical). Since the infinitist must hold that there is an actual event O which is infinitely distant from any arbitrarily designated present B, we may take the existence of O as logically positing an infinite number of intermediaries between O and E, and we can then ask how an infinite series of’ intermediary events, one after another, could be instantiated and exhaustively enumerated so that we finally reach E.
It appears to me that the above argument concerning specifically the obliteration of the past and future is not effective, at least against counter-arguments of process philosophers. By holding that "there will always be events in the past of 0" and "there will be a finite number of intermediaries between O and E" is definitive of O’s being in a "potential" relation to E, one commits a subtle "fallacy of misplaced concreteness." For it can be argued plausibly that the real difference between the categoreal contrasts "past actuality" and "future potentiality" is not seen in abstract relations having to do with mere location in the extensive continuum, but is seen in the definiteness of the description (including inherited history) which can be discerned (at least in principle) for the event in question.
Thus, an actual and past sea battle is distinct from a potential and future sea battle in that the events constituting the actual sea battle can be specified (in principal or for an ideal knower) to any level of definiteness (including subatomic details), while the potential sea battle has no such definite particulars; it is the more or less general sea battle which, if actualized, will be particularized somehow.
If this is denied, then it seems that, as Bergson once put it, "potentialities" are just actualities taken over again; they are definite particulars somehow waiting to be actualized. The intuitive decision as to whether an event belongs to the past or future does not depend upon any aspect of quantity (i.e., whether the event belongs to a sequence having infinite or finite members), but does depend upon an aspect of quality (i.e., whether the content of the said event is sufficiently rich or particularized). Indeed, if the past is infinite, it must share certain abstract characteristics, such as are embodied in Whitrow’s two criteria, by virtue of its infinitude, with any other infinite sequence.
Nonetheless, Craig’s argument concerning specifically the logical impossibility of counting to infinity does have force, and it does so granting any principles of process philosophy. For consider: all that Craig requires his opponent to assume is that there is at least one actual or definite event which is infinitely past relative to some designated present event E. But any process philosopher who upholds the hypothesis of an infinite past actuality is committed to that much. For, if the past contains nothing but actual or definite events, as process philosophers assume, then any and every past event referred to is actual or definite. And, if the sequence of past events is infinite in extension and is always so relative to any designated present, as process philosophers assume, then, in conjunction with the above, there must be at least one actual event O which is infinitely past relative to some designated present event E.3
Note that the argument involves no circular "sneaking in" of the notion of a beginning of the past. It involves only the beginning of a sequence, O to E, which the hypothesis of an infinite past commits one to. In other words, the argument states simply that, if there is at least one actual event O infinitely in the past of a designated present event E, then we can legitimately ask how it is possible for there to be an enumeration, one event counted after another, of the sequence starting with O and ending with E.
Craig’s reasoning here leads to the recognition that an infinite collection is something which, to be thought of at all, must be thought of as given all-at-once or given in totality. In other words, such a collection must be simply posited, for it cannot be conceived as something which is formed item by item. There is only one way we can legitimately conceive a set which is actually infinite to which items are being successively added. That would be to conceive it as having "an infinite ‘core’ to which additions are made" (K 105). But this would not be a set formed by successive addition, since in this case there would always exist an unformed, surd infinite, namely, the infinite core to which additions are being made. And of course the temporal series of events cannot be depicted in this way, since every part of the series is formed by successive addition.
All of these arguments are quite compatible with Cantor’s transfinite mathematics, despite what some might erroneously think (see K 63-95). Cantor’s aleph-null, the first of the transfinite cardinals, has no immediate predecessor and thus cannot be arrived at by counting or successive synthesis. Aleph-null must be merely assumed to exist as a given totality. This means that Cantor’s "mathematical paradise" should be understood as follows: Let there be a mathematical universe such that sets constitutive of it have the defining feature that a part of the set is equal to the whole of the set. Given such sets, what would their formal relations be like? The response to this question is Cantor’s arithmetical operations. Indeed, the overwhelming consensus among mathematicians who work with transfinites is that transfinite mathematics entails no ontological commitment.4 In fact, when Platonic realism or Russellian logicism (which holds to the extra-mental reality of infinite sets) are employed as interpretations of infinite sets, we open the door to the very antinomies and problematics, such as the Burali-Forti antinomy and Russell’s difficulty with sets and impredicative definitions, which have led mathematicians and philosophers of mathematics to new interpretations of set theory such as the axiomatic. As Craig observes in concurrence with Pamela Huby (K 201),5 far from establishing the real possibility of actual infinite sets, the very existence of antinomies attaching to Cantorian type sets looms large as a mark against the view that an actual infinite set could be instantiated extra-mentally.
I think that Craig has submitted some formidable arguments. At present I see no fatal defects (other than where noted) in the reasoning examined here. In spite of this, it is my view that this does not mean that process theism must be considered either defeated or in need of drastic revision. The metaphysical-theological issue of infinity is a very special, queer one. For there may be considerations of equal cogency which show that a finite past is absurd. Indeed, I see one strategy open to the process theist which would force Craig to admit, on the basis of his own case, that a successive actual infinite could be instantiated.
At one juncture Craig admits that, "Some persons might be prone to reject the argument if they thought it involved a beginning to time, which they regard as an impossibility (K 106). His response to such persons is that the kalam proof is neutral as to the two competing theories of time, the absolute and the relational theory. That is to say, the proposition that ‘the universe of finite events had an absolute beginning a finite time ago’ is compatible with (a) an absolutist point of view in which the universe arose in an "undifferentiated" time which existed prior to the universe, and with (b) a relationist point of view in which time itself arose with the first finite event. For Craig, there is no obvious absurdity involved in either of these points of view, nor any obvious absurdity in combining either point of view with the kalam argument. The difficulty I see resides in Craig’s assumption that the absolute theory of time and the kalam argument are compatible. Indeed, this difficulty becomes fatal when compounded with the impressive case that can be made for an absolute theory of time, to which I now turn attention.
It seems that the absolute theory of time, in so far as it involves the proposition that ‘temporal duration cannot have a limit’ is sound. Inspired by Richard Swinburne’s Space and Time,6 the following argument for this proposition is compelling.
Grant that some unit interval of temporal duration has occurred, say, the first Planck time (10-43 second) of the physicist’s Big Bang event. (Anyone who chooses not to grant this -- that is, that unit intervals of time occur -- will pay the cognitive price of violating one of our most basic conceptual intuitions for the sake of an exotically speculative philosophical position.) For convenience, let us call this interval P. Now, since P is a unit interval of time, this logically entails that time can have no beginning. For suppose ex hypothesi that P is the "first" unit interval of time, contrary to the hypothesis that time has no beginning. We see at once that it would be an absurdity to say that P is (1) a unit interval of time, while also (2) a first unit interval having no predecessor. For, if P is a unit interval, then P is, by the meaning of "unit interval," bounded by an antecedent interval prior to P and an interval posterior to P. And since the interval prior to P is a unit interval (or a moment of eternal duration, which automatically grants our case), then it too has its antecedent unit interval, and so on ad infinitum. Thus, if P has occurred, time has no beginning. But P did occur, and so time has no beginning.
One might object that prior to the physicist’s first Planck time, there was an initial absolutely stationary state of the universe or (inclusive disjunction) of God, and that since time can only exist where there is change, time does not exist always, i.e., in case of a stationary state of affairs descriptive of the universe class. However, this objection not only depends upon the controversial thesis that there really could be an absolutely stationary state, but also upon the assumption that "time can only exist where there is change." Such a criterion for the existence of time can be shown to be very problematic. Thus, J. R. Lucas points out that such a criterion for time involves not only technical tense-logical difficulties,7 but also involves a denial of the basic intuition that time is a concomitant of consciousness -- we are aware of time even in the most tranquil of environments (TTS 13). (This is an intuition of such universal acknowledgement that it is granted even by the "skeptics" who deny that time is a feature of the external world, e.g., Grünbaum, Weyl, Costa de Beauregarde.) What is more, those who hold this criterion seem to be mistaking the "measure" for the "meaning." Simply because we measure time by the motion of clocks does not mean that time is not there to be measured if the motion of clocks is absent. "Time is not what the clocks say, but what they are trying to tell, are there to tell" (TTS 10).
A second objection might be that, however plausible our philosophical argument above, absolute time "went out with Newton" after the Einsteinian revolution. But this wide-spread assumption is at best a gross overstatement:
The relativity that Newton here rejected is not the relativity that Einstein propounded; and although the Special Theory of Relativity has shown Newton to be wrong in some respects, and in particular has shown that we should not think of time by itself in complete independence of everything external, time is related to space, and also to velocity, contrary to Newton’s opinion, it has not shown that time is relative in Newton’s sense, and merely some numerical measure of process. (TTS 90)
Newton’s position that time is "objective" and "rules" our measurement of time (not vice versa) is vindicated by the fact that we have a rational theory of clocks, i.e., we presuppose that all our clocks can and ought to be corrected, wherever we note irregularities.
Indeed, if Craig is to admit, as he does, that the kalam argument shows that a personal Creator exists, then this seems to amount to an argument that the Creator cannot on any condition be timeless. For, it cannot be true of a personal deity that it is timeless, since time is concomitant of consciousness whatever else it is, and a personal God is conscious, intelligent, etc.
Suppose then that time is a limitless constant. Further suppose for the sake of argument that the kalam argument is correct: no finite events exist prior to creation, although the Creator exists prior to creation. This means that the Creator has existed throughout an infinite duration of time.
Now Craig quickly sees the paradox arising here as suggested in a paper by Julian Wolfe,8 namely, that this very eternity of time prior to creation represents the instantiation of an actual infinite series. Craig attempts to purge the paradox by pointing out that the kalam argument contends only "that an infinite number of events cannot elapse, not that an infinite time cannot elapse" (K 172). However, clearly this will not do, because Craig leaves out of account the existence of a Creator who is, on his own admission, a personal spirit which by definition has experiences. Are the personal Creator’s thoughts, feelings, enjoyments to be excluded from the class of events in time, once we have admitted the reality of time prior to special creation? There is absolutely no reason I can conjure to think that they should be.
Will someone reply that prior to creation there is only a single divine event, not a number of divine events which might elapse? But surely a single, undifferentiated-yet-temporal, divine event would have the characteristic of asymmetry. For if the time of the precreation divine experience did not share the successive nature of postcreation divine experience (which entails asymmetry), how could we characterize it as time at all? How could it be said to differ from timelessness? This query seems to lead inescapably to the conclusion that, in this case, there would be a successive actual infinite, namely, the actual asymmetrical infinitude of divine experience -- not mere time -- prior to the hypothesized act of special creation.
But now we have shown the instantiation of an actual infinite process, and this undermines any confidence that the infinitistic process theist must be wrong.
At the present, my concluding estimation of the whole matter is this. The process theist’s best strategy with respect to Craig is to argue for the necessity of time, as I have done and as does Hartshorne (MVG 233f., PSG 60), and to go on to show the severe conundrums and paradoxes this necessity involves for the kalam proof with its claim that there can be no actual infinite process. We are then, it seems to me, faced with a choice between two paradoxical positions on the infinitude of God. God is either a unilateral or a processive infinite being, both views involving their respective paradoxes. However, a decision to adopt the process theistic model over the classical type kalam model could be supported by demonstrating process theism’s relative absence of paradox when other matters in philosophical theology are considered, such as the problem of evil, theory of omniscience, theory of omnipotence, etc. In other words, process theism might be judged cognitively superior, not because it involves no paradox, but because it involves least paradox in comparison with the formally possible theological alternatives, when all issues are considered.
I should add that I do not suppose that the "antinomy" of models of divine infinitude is real in the final analysis. For in that case, reality is inherently contradictory or irrational. I hold such a position to be itself irrational, since it collapses in order to be maintained as a consistent non-self-contradictory truth. Somehow one model or the other is fully consistent, even if I cannot presently see how this is so. Perhaps, as one suggested way out, Cantorian or Dedekindian proofs are applicable to the problem after all, as indeed J. R. Lucas thinks they are applicable to making sense out of the "destiny" of infinitesimal instants in his absolute theory of time (TTS 29-34).
Of course, the efficacy of the above strategy also depends upon showing that process theism forms an exclusive contrast with any theistic model which is a logical implicant of a special act of creation. In other words, the cognitive superiority of an uncompromised process theism could be maintained as long as there is no philosophically tenable via media model, such that God creates ex nihilo, but possesses the attributes of a dipolar, temporalistic God once there is something finite to be in relation to. For, in the case of a tenable via media, the theoretical advantages of process theism would not be its exclusive property. The investigation of such models, such as the one recently proposed by William P. Alston,9 is, I suggest, the next frontier for research in process philosophical theology.
CSPM -- Charles Hartshorne. Creative Synthesis and Philosophic Method. LaSalle: Open Court, 1970.
K -- William Lane Craig. The Kalam Cosmological Argument. Library of Philosophy and Religion Series, edited by John Hick. New York: Barnes and Noble, 1979.
LP -- Charles Hartshorne. The Logic of Perfection. LaSalle: Open Court, 1962.
MVG -- Charles Hartshorne. Man’s Vision of God and the Logic of Theism.
PSG -- Charles Hartshorne and William L. Reese. Philosophers Speak of God. Chicago: University of Chicago Press, 1953.
TTS -- J. H. Lucas. A Treatise on Time and Space. London: Metheun, 1976.
1Cosmologist Joseph Silk holds that Big Bang cosmology "cannot answer.. at all," the question, Did the universe exist prior to this moment [the moment of the initial Big Bang singularity]?" See his The Big Bang: The Creation and Evolution of the Universe (San Francisco: W. H. Freeman, 1980), p.61. Apparently the interpretations of currently available cosmological data are more controverted than one would surmise on the basis of Craig’s account of recent cosmology. Craig also claims that process theology requires a steady state universe (K 170), even though Hartshorne explicitly denies steady state theory on philosophical grounds (LP 214). The idea of ‘cosmic epochs’ seems to fit nicely with an oscillating model having repeated ‘hangs’ and contractions’.
2C. J. Whitrow, "Time and the Universe," in The Voices of Time (London: Penguin, 1968), pp. 567-68, and "On the Impossibility of an Infinite Past," British Journal for the Philosophy of Science 29 (1978), 39-45. In this same journal issue see Sir Karl Popper’s rejoinder, "On the Possibility of an Infinite Past: A Reply to Whitrow, 47f. Popper’s reasoning against Whitrow seems to me quite feeble. He argues that the set of past events is actually infinite, while the series of past events is potentially infinite. As Craig remarks, this is nonsense, because if the series of past events were potentially infinite, the past would have to be finite and growing in a backwards direction (K 204).
3I should point out that apparently not all philosophers who could be reasonably interpreted as "process philosophers" have held the infinitist hypothesis regarding the past. Henri Bergson is a case in point. As Milic Capek has argued, "taking into account all Bergson’s utterances relevant to this problem, it is clear that he, indeed, did accept the finitistic thesis." See Capek, "Appendix III: Bergson’s Thoughts on Entropy and Cosmogony," in his Bergson and Modern Physics (Dordrecht: D. Reidl, 1971), p. 37sf.
4Cf. A. A. Fraenkel, Abstract Set Theory (Amsterdam: North-Holland, 1961), especially p. 240, and B. Rotman and C. T. Kneebone, The Theory of Sets and Transfinite Numbers (London: Oldbourne, 1966), especially p. 60f.
5Pamela M. Huby, "Kant or Cantor? That the Universe, if Real, Must be Finite in Both Space and Time," Philosophy 46 (1971), 121-23.
6R. C. Swinburne, Space and Time (London: Macmillan, 1968).
7TTS 10-11. Also see A. N. Prior, Papers on Time and Tense (Oxford: Oxford University Press, 1948), p. 111.
8Julian Wolfe, "Infinite Regress and the Cosmological Argument, International Journal for Philosophy of Religion 2 (1971), 246-49.
9William P. Alston, "Hartshorne and Aquinas: A Via Media," presented November 4, 1981, at The University of Chicago’s conference in honor of Charles Hartshorne.