Introduction: Why Revisit the Big Bang and Theism?

One might view this article as an instance of analytic theology or perhaps analytic philosophy of religion. Much of it addresses a deductive argument made by William Lane Craig and how to evaluate it. Seeking more precision in various areas is therefore important.

The article revisits a case made about seventeen years ago that there is no good theistic argument from the Big Bang singularity (Pitts 2008). Like that earlier paper, this one has very little to say about cosmic fine-tuning, a fascinating topic that has inspired interesting work.¹ While I remain largely content with the original paper, it did have a flaw (as Joshua Rasmussen first convinced me), a readily fixable one, I believe, but I have had no simple way to say how.² Response to the paper has been largely positive, but critics have latched onto the flaw while mostly ignoring the important points motivating it (Monton 2009; Craig and Sinclair 2012b; Craig and Sinclair 2018). This article aims to fix the flaw and address other issues discussed by William Lane Craig and James Sinclair in their response. Further issues are also addressed involving the question of past maximal extension, a criterion now proposed for lacking a beginning.³

Craig (1979, 63) formulates the kalām cosmological argument along these lines:

1. Everything that begins to exist has a cause of its existence.

2. The universe began to exist.

3. Therefore, the universe has a cause of its existence.

This argument is valid—that is, the premises, if true, would ensure the truth of the conclusion—assuming it is unproblematic to treat the universe as a thing and assuming no equivocation on “beginning,” on which more later. If “beginning” and its relatives are allowed to mean different things in different premises, then the argument will be subtly fallacious.

My 2008 paper’s remarks on the relevance of quantum gravity—the sought but possibly not yet achieved merger of gravity (perhaps as described by general relativity) and quantum mechanics (more strictly, quantum field theory)—still apply: one should have little confidence, I think, that the Big Bang singularity will persist once quantum gravity is achieved, so something like an eternal universe model is likely to result. Those who embrace scientific realism without qualification will thus likely feel pressure to accept that the universe is eternal. A good expression of these expectations and careful evaluation of what precisely they should mean and how plausible the various precise candidates are has been given recently by Karim Thébault (2023).

On the other hand, one should be wary of too-quick claims, such as Stephen Hawking’s no-boundary appeal to imaginary time as having already removed the singularity. If such a claim were taken very seriously among physicists (as opposed to being an instrumentally useful mathematical trick or one possible avenue within one possible program), there would be much less ongoing work in quantum gravity than there is.

Beginning as (Not) Requiring a First Moment

Craig and Sinclair devoted much of a chapter to refuting the 2008 paper (Craig and Sinclair 2012b; Craig and Sinclair 2018). Most of their critique focuses on the first moment criterion for a beginning.

The fixable flaw in the paper is the claim that a beginning in the sense relevant to making the kalām cosmological argument work, avoiding conventionality and modal provincialism,⁴ requires a first moment. Instead, there might be some more general feature that is also nonconventional and more modally robust that applies in more of, or one hopes all of, the cases that intuitively imply a beginning. In 2008, such a thing did not come to mind, while others seem not to have been looking for it.

The fix envisaged relaxes having a first moment in favor of lacking maximal extension toward the past—one might say, being past-extendible. In other words, a universe with a beginning could have had more of a past than it actually has, having all the same past as well as some earlier events. One could say a “longer past,” but that suggests a metric exists (and is probably unique) and is used as the standard of length, which is just what is to be avoided. This informal condition (with some unspecified conditions of differentiability assumed) is inspired loosely by notions used in global general relativity literature, but it does not assume either the existence of a metric or its uniqueness. If the universe actually came into existence five minutes ago, c. 7,000 years ago, three minutes “after the Big Bang,”⁵ or at any other time later than t = 0 (the “time” of the extrapolated singularity), then it could have had more of a past than it actually has. Such possibilities permit versions with a first moment and versions without. The point of requiring a first moment was to avoid conventionality (a familiar issue in this debate) while also pursuing modal robustness (on which more later). Note that “more of a past” makes sense given multiple metrics or given conformal invariance, in which one has only 90% of a metric, a notion of space-time shape without size (4-volume) and hence without length, including temporal length.

If one entertains the failure of maximal extension toward the past, one might want to expand one’s idea of the possibilities using notions of simultaneity that have become popular in numerical relativity, such as hyperboloidal simultaneity slices (Frauendiener 2000). Informally, the present started earlier in distant locations than it did here, making it possible to see further than one would have expected. Nothing requires the universe’s front edge of existence to make spatial homogeneity manifest; the front edge could be curved or wiggly.

Modality and Beginnings

Perhaps the least satisfactory aspect of Craig and collaborators’ argumentation involves the modal status and univocity of “beginning.” For assessing the validity of an argument, the use of a term must be univocal, having the same meaning in all instances. As the argument is presented, there is no “necessarily” in premise 1 that whatever begins to exist has a cause. But why not? The considerations Craig et al. employ are intended to be true outside the actual world or even worlds much like it. “Does anyone in his right mind really believe that, say, a raging tiger could suddenly come into existence uncaused, out of nothing, in this room right now?” (Craig 2008, 113). If not, could a tiger pop into existence in similar possible world, one in which I wear a blue shirt instead of a gray one while typing this sentence? Surely not: premise 1 is intended to apply beyond the actual world. This issue occupied much of an exchange between Craig and Wes Morriston some time ago (Morriston 2000; Craig 2002; Morriston 2002). The premise, according to Craig and Sinclair (2012a, 182), is based on a metaphysical intuition that ex nihilo nihil fit (out of nothing, nothing comes). Thus, this causal principle is a necessary truth, holding in all possible worlds. So Craig holds, a view that strikes me as plausible enough, though I do not know that doubters are insincere or out of their right minds, as he claims.

Reasoning about duration and causation should not essentially rely on physical assumptions that could easily be false. Suppose a scalar-tensor theory of gravity (or any other bimetric or multi-metric theory) is true (or the best classical theory, ignoring quantum gravity). The Brans-Dicke (1961) scalar-tensor theory of gravity—which has an additional scalar field (an extra number at each place and time, here relating to the effective gravitational constant G), along with the usual space-time metric of general relativity—was the most visible rival theory for some time, and so was a somewhat plausible idea when Craig started writing. A scalar-tensor theory can be viewed as having two different (but conformally related, giving the same shapes and angles but different lengths and volumes) metrics, known as the Jordan frame (in which the dynamics of gravity itself feature this scalar field) and the Einstein frame (in which the dynamics of gravity itself look like Einstein’s general relativity but matter also couples explicitly to a new scalar field). These different metrics define different ages. Which age is relevant for a beginning? Perhaps it does not matter if they are both finite or both infinite. But what assurance is there of that agreement? Either there is no assurance or it depends on detailed study of a great variety of bimetric/multi-metric theories, considerations Craig et al. have generally neglected in assuming that the actual world has a unique metric. Supposing some bimetric or multi-metric theory is empirically satisfactory and permits one age to be finite and one to be infinite, can tigers plausibly pop into existence in that theory? Of course not. Plausibly, our expectation that tigers cannot pop into existence is a modally robust a priori intuition on which we would insist even if we learned that the space-time metric is not unique and the age of the world is ambiguous between infinity and some finite value. Given the protracted failure to solve David Hume’s problem of induction (Howson 2000; Pitts 2023), a solution that would assure of the exceptionless uniformity of nature, our high confidence that tigers cannot just pop into existence is not merely inferred from experience.

If massive, slow-moving particles/fields fit with conformally invariant theories such as the Bach-Weyl theory—at first glance they do not, but perhaps some clever symmetry-breaking idea is possible—then our world could lack volumes and lengths and hence ages, at least fundamentally, yet we would remain confident that tigers could not pop into existence. In short, our confidence that whatever begins to exist has a cause is modally robust, unaffected by the possibilities that age is either radically ambiguous or meaningless. These considerations motivated seeking a non-metrical notion of a beginning (Pitts 2008).

Furthermore, premise 1 does not seem to be equivocal in content— meaning one thing (finite age) in some worlds (perhaps the actual world) and something else in others—or inhomogeneous in warrant, credible for one reason in one possible world and another reason in another world. If we make a serious effort to sort this question out, we will seek a modally robust notion of “beginning” that fits at least all these classical field theory cases. Having a first moment was modally robust enough and nonconventional but too strict: a tiger that suddenly exists for all moments after some given moment is as surprising as a tiger that suddenly exists starting at that given moment. But a metrical notion of beginning that fails to apply to many possible worlds describable in classical field theory, especially some that seem epistemically possible (might be real for all we know), simply does not suffice. Craig (2002) is apparently less committed to the a priori nature of the causal principle than to its metaphysical necessity: “It could well be that only logically posterior to our experience of reality do we intuitively grasp the necessary truth of the causal principle.” But necessity is the key feature that motivated my search for a modally robust notion of beginning. Since the causal principle is a necessary truth (Craig holds), it must be meaningful in all possible worlds. My own effort has merely been to require it to make sense in all classical field theory worlds, a lower bar than all possible worlds (or even all worlds conceivable with current mathematical physics) but an obvious place to start and a higher bar than Paul Copan and Craig (2004, 199) reached in defining “beginning” in terms of metrical time. If one is making key use of a claimed necessary truth, one would want to know what it means and have that meaning and the warrant be the same in all possible worlds.

Craig and Sinclair (2012b, 102), however, apparently disagree:

Pitts’ presumption seems to be that Copan and Craig take, not only the premises of the kalām argument, but more particularly their proffered criterion for there being a beginning of the series of past events to be metaphysically necessary truths….Pitts recognizes, as mentioned, that the actual world is characterized by an objective metric; but he insists that “a doctrine of creation needs to be modally rich enough to accommodate the possibility of God’s creating worlds with physical laws without a unique or preferred metrical structure to license an answer of ‘finite’ or ‘infinite’ age” (Pitts 2008, 681).

Pitts’ presumption is wrong. The proffered criterion was intended to apply only to the actual world. There is no intention or need to seek its application to other metaphysically possible words [sic] governed by different laws of nature.

Why Craig and Sinclair (2012b, 99) think that despite my “flirtation with metric conventionalism, [I] recognize that our universe is characterized by an objective temporal metric” is not entirely clear, though it would be useful to them in a debate. An aside on my other work is called for given Craig and Sinclair’s attempted ad hominem argument. Perhaps they misinterpreted this line: “It turns out that the actual universe probably does not behave in accord with a scalar-tensor theory, given the empirical confirmation of the various principles of equivalence in gravity (Will 1993), which make it difficult for theories empirically distinguishable from GTR in weak or moderate gravitational fields to be empirically viable” (Pitts 2008, 681). This sentence, while recognizing that scalar-tensor theories (at least the ones studied by Clifford Will) tend to differ from general relativity in weak and moderate fields, by no means excludes all bimetric or multi-metric theories. Some theories inspired by particle physics (Ogievetsky and Polubarinov 1965; Freund, Maheshwari, and Schonberg 1969; Pitts and Schieve 2007; Pitts 2011b, 2016c), namely massive spin-2 gravity, differ from general relativity only in strong fields (Visser 1998)—or at least do so if certain devils in the details can be handled (Boulware and Deser 1972; van Dam and Veltman 1972), a topic on which optimism grew considerably in the 2000s (though it has not remained as high). It would be odd for someone who sympathizes with conventionalism, particle physics, and massive gravity (as even the 2008 paper showed); emphasizes the need to pay attention to physical theories outside the “canon” of single-geometry theories (Pitts 2016b, 2019); and derives bimetric massive gravity theories from universal coupling (Pitts and Schieve 2007; Pitts 2011a, 2012, 2016c) to “recognize that our universe is characterized by an objective temporal metric,” because that would be practically a profession of faith in general relativity as the true theory in the classical limit. My confidence in general relativity, though fairly high, is not that great, as a glance at the works I cite and produce suggests. A massless spin-2 field is a natural animal in the particle physics zoo of masses and spins (Pauli and Fierz 1939) (due to representations of the Poincaré group of special relativistic symmetries) and yields Einstein’s equations using some rather compelling arguments, starting from flat space-time (Deser 1970; Pitts and Schieve 2001; Pitts 2016a). But why assume that the graviton mass is exactly zero instead of merely small? This is a natural question to ask for those influenced by particle physics. I am of course happy to try to interpret Einstein’s equations properly; I claim the theory makes better sense of energy conservation (Pitts 2010) and change in the Hamiltonian formalism (Pitts 2014, 2017) than is commonly held, if one listens to the mathematics without introducing interpretive postulates. But in my view, it is not implausible that the metrical criterion for a beginning fails even in the actual world.

Regardless of whatever I supposedly conceded, the need for a modally robust notion of beginning comes from attempting to make sense of Craig’s view that the causal principle is a necessary truth. I find his notion of a necessary truth that means radically different things in different possible worlds, such that one need not bother with its meaning in most possible worlds, unintelligible. The cause of careful argumentation cannot be served by this opportunism. If my presumption of Copan and Craig’s intention was incorrect, at least I saw a need for something modally robust. Once one takes seriously the project of understanding the notion of beginning in a modally robust way, as Craig’s necessarily true premise 1 requires, one rejects the metrical notion, seeking something that does not assume the existence or uniqueness of a metric. If the criterion of a first moment was too strict, the criterion of lacking maximal extension toward the past appears to do the job (at least in the realm of classical field theories). Conventionality and gross modal provincialism are avoided, as one would expect in a serious metaphysical argument.

However, once one defines beginning in terms of lacking past maximal extension, the Big Bang no longer counts as a beginning. Hence, removing the equivocation on a “beginning” achieves validity at the cost of making premise 2 unsupported by Big Bang cosmology. Craig has presented his case as a deductive argument but tends to avoid the usual standards for assessing deductive validity, standards I am to reinstate.

Cosmic Destroyer Argument Vindicated

Craig and Sinclair’s (2012b, 100, 133) response to my Cosmic Destroyer argument (Pitts 2008) pits it against the notion of beginning as requiring a first moment, so correcting the first moment criterion tends to vindicate the argument. The Cosmic Destroyer argument is intended as a reductio ad absurdum of the kalām argument’s use in the context of Big Bang cosmology. Noting that the mathematics of the Big Bang are the same as the mathematics of a simple homogeneous model of a collapsing star (Misner, Thorne, and Wheeler 1973, 846–59)—apart from the fact that the star is surrounded by empty space (which one can choose as a variant of the Big Bang if one wishes; references besides Charles Misner, Kip Thorne, and John A. Wheeler are in the earlier article) and apart from the direction of time—I inferred by parity of reasoning that stars collapsing into black holes call for a Destroyer God. Granting that Abrahamic theists generally take matter to persist due to continuous divine upholding as opposed to some kind of deistic existential inertia, one can infer (absurdly?) the need for special divine action. Much as the sudden disappearance of my desk would involve special divine action, even if it only required God to stop upholding my desk, the disappearance of a star due to singularity formation would involve special divine action. The time reversal of God’s creating (all or part of) a Robertson-Walker solution in gravitational collapse requires special divine action if God’s creating (all or part of) a Robertson-Walker solution requires special divine action in cosmology. But that time reversal, applied on a suitable distance scale (recalling the surrounding empty space option), is mathematically identical to the destruction of a star in the formation of a singularity. So, if the Big Bang requires God as Creator, continued stellar collapse requires God as Destroyer—perhaps welcome in Hinduism but an unwelcome innovation in Abrahamic religions.

Once the nonconventional, modally robust notion of a beginning has been generalized from having a first moment to lacking past maximal extension, the Cosmic Destroyer argument implies that a star that ceases to exist without a last moment of existence still needs God as Destroyer. While one could bite the bullet and simply accept that God destroys stars that collapse into black holes, the comparatively mundane nature of stellar collapse—it is just one of those things that happens from time to time, like bread getting moldy and unlike the creation of the universe—makes it peculiar to infer special divine action in a context calling for ordinary divine providence (and probably quantum gravity).

Is Gravitational Thermodynamics Mature?

Craig’s appeals to thermodynamics as heavily constraining eternal universe models are longstanding, reducing dependence on the singularity. On the other hand, until recently, gravitational thermodynamics was quite immature, and it was difficult to be confident in results that did not take the thermodynamics of both matter and gravity into account. One can compare that assessment to Craig’s (2008, 150) remark, plausible about non-gravitational thermodynamics: “Indeed, thermodynamics is so well established that this field is virtually a closed science.”

Plenty of challenges remain in gravitational thermodynamics. Two distinctive features of gravity are that it spontaneously leads to clumpiness rather than uniform distribution and that it makes certain quantities proportional to area rather than volume, blurring the textbook binary distinction between extensive (proportional to volume) and intensive (independent of volume) quantities (Oppenheim 2003). Energy also plays a crucial role in thermodynamics, but gravitational energy has been controversial for more than a century. Recent decades have seen substantial progress in gravitational thermodynamics on various fronts, so perhaps thermodynamic arguments made today are more credible than older ones.

Two recent sources of doubt might add to the older doubts, however. First, physical theories with funny minus signs in various places have come to be entertained since 2000: “ghosts” (fields with negative energy or negative probability) (Hawking and Hertog 2002; Mukohyama and Volkov 2018), “phantoms,” etc. Some are not as automatically disastrous as previously believed. Hence, there is a greater prospect that even bounded quantities (such as energy) are not so constraining if they might contain both positive and negative contributions. Perhaps monotonic behaviors found in the thermodynamics of matter can be counteracted when gravity is included? The fact that in general relativity the total energy equals zero apart from boundary terms (in some cases themselves equal to zero) is a precedent for gravitational compensation of the positive energy contribution of matter. (Naturalists sometimes invoke zero total energy as implying that universes can pop into being spontaneously, though I am not convinced the local conservation laws can be ignored.) Maybe entropy does something similar? Second, it is not clear yet even how many energies there ought to be in general relativity; perhaps the most principled answer based on the Noether symmetry-conservation law link—uncountably infinitely many (one for each vector field) (Bergmann 1958; Pitts 2010)— has rarely been entertained and has not been systematically explored. Clearly gravitational thermodynamics is a lively area to watch carefully. Making arguments based on a predicted outcome, however, still seems rather speculative.

On the Justification of Maximal Extension toward the Past: Empiricism or Rationalism?

The question of maximal extension is potentially interesting both in terms of scientific considerations (such as whether the universe existed “before” the “Big Bang”) and in terms of philosophical–theological considerations, to which this section now more fully turns. Maximal extension turns out to be more difficult to justify than one might have thought.

This section comments on a recent thread in the philosophy of science involving roughly the condition I propose as an analysis of “beginning.” It reflects both how philosophers of science are inclined to deny premise 2 (that the universe began to exist) and their limited success in justifying that denial. If these grounds are weaker than expected, that could make premise 2 easier to accept.

Given that philosophers of science are generally very pro-science as well as naturalistic in views, it is noteworthy that the justification of maximal extension toward the past has recently been a topic of puzzlement. The passages are sufficiently remarkable as to justify quoting at some length. Some time ago, John Earman (1977) pondered the question of what it would be for time to have a beginning or end. The discussion soon was restricted to “relativistic space-times,” by which he meant that there is a unique metric and, at least in physically interesting cases, Einstein’s equations hold (Earman 1977). (Clearly Earman was not concerned about modal robustness.) Here are some relevant excerpts:

[A]re there good reasons for believing that actual spacetime cannot be truncated?

If one holds that there are no good reasons, then one would be wise to receive extreme unction as soon as possible, since time may run out any second now. Moreover, such a position implies a profound skepticism with respect to our knowledge of the past and future; it implies that we do not in fact know the great bulk of the things we ordinarily claim to know about the past and future. (Earman 1977, 118, 119)

One’s initial reaction to such skepticism is apt to be that it is too absurd to be taken seriously. Whether or not this reaction can be sustained remains to be seen.

On the other hand, if one holds that there are good reasons to reject [truncated space-times] as a model for actual spacetime, then these reasons must be supplied. We shall see that this order is less simple to fill than one might think at first glance. (Earman 1977, 119)

At this point, common sense cries out: “If my world line cannot be extended backwards in time from now more than five seconds, then most of my memory impressions are mistaken. But this is absurd.” But exactly where does the absurdity lie? There is no logical contradiction, nor—apparently—any inconsistency with the basic laws of physics. Of course, it does seem that the likelihood that the universe switched itself on, so to speak, a few seconds ago in such a way that people are endowed with the memory impressions they in fact have, is very low. But this estimate of likelihood is surely not an estimate of probability based on either observed relative frequencies or on the implications of the laws of physics . . . The estimate of low likelihood in this case seems simply an expression of our unwillingness to accept a certain kind of explanation. But whether or not this unwillingness can be backed by philosophically respectable reasons is the question at issue. (Earman 1977, 121)

Earman later took up the question in a book-length treatment, becoming more explicit about metaphysical, or even theological, considerations.

Metaphysical considerations suggest that to be a serious candidate for describing actuality, a spacetime should be maximal. For example, for the Creative Force to actualize a proper subpart of a larger spacetime would seem to be a violation of Leibniz’s principles of sufficient reason and plenitude. If one adopts the image of spacetime as being generated or built up as time passes then the dynamical version of the principle of sufficient reason would ask why the Creative Force would stop building if it is possible to continue. However, this image does not sit well with the four-dimensional way of thinking, and in any case it runs into trouble in its own terms: since extensions of spacetime are generally non-unique there may be many ways to continue building and the Creative Force may be stymied by a Buridan’s ass choice (see Clarke 1993, 8–9). Some readers may be shocked by the introduction of metaphysical considerations in the hardest of the “hard sciences.” But in fact leading workers in relativistic gravitation, though they don’t invoke the name of Leibniz, are motivated by such principles (see, for example, Geroch 1970, 262; Penrose 1969, 253). The intrusion of metaphysics will also be evidenced in all of the chapters to follow. (Earman 1995, 32, 33)

So, does rationalist metaphysics (theology?) justify scientific claims in this area? Given how induction is related to the uniformity of nature, one might hope that philosophers of induction have finally delivered the goods; surveying three significant works will be illuminating. Colin Howson (2000) argues otherwise: Bayesianism gives us a good framework for updating our opinions using evidence, period; nothing requires that you and I have similar initial opinions, so we can still have differing current opinions. Recently, Gerhard Schurz (2019) has argued persuasively for the optimality of meta-induction, roughly, the idea that whatever predictive method has been most successful so far is the best choice for making future predictions. However, it is unclear that induction uniquely follows from meta-induction and the evidence (as he had claimed (Schurz 2008)) once one recognizes that it is question-begging to filter the evidence using induction when induction is in question (Pitts 2023).

John Norton’s work, addressing both induction and space-time philosophy, requires more discussion. Norton (2021), finding all induction to be local and fact-based in his material theory of induction, diagnoses various shortages of the requisite facts. In particular, facts are scarce in justifying the past maximal extension of space-time, oddly enough (Norton 2011).

What is troublesome from the material perspective is the absence of warranting facts for the inductions in the spacetime case. Take the case of extendability. It seems natural to infer inductively to the fully extended Minkowski spacetime rather than the extendable half Minkowski spacetime; or, more generally, to avoid admitting holed spacetimes that are created from other spacetimes by excising even quite small parts. However it is very hard to specify just what facts ground the inference. That we have never seen holes in spacetime does not settle the matter. By their construction, there cannot be an observable trace of holes, if that is what our spacetime has. That remains true even if our world tubes pass directly through the hole. We would cease to be for the portion of our world tubes coinciding with the excision. However the portion of our world tubes in the future of the hole would be reconstituted precisely with all the memories and other traces of the excised spacetime. If observed facts do not ground the inductive inference, what of physical laws? We could cite the common postulate in relativity texts that spacetimes are inextendable. However that postulate is merely the supposition of precisely what is at issue and is distinctive as being dispensable from a physical perspective. It is present as much for mathematical convenience

One cannot help but be struck by how tenuous the grounding has become. We are now to secure our inductions in abstract metaphysics. (Norton 2011, 173)

We routinely dismiss as desperate zealots those who tell us our universe was created last Wednesday complete with all records of an ancient past.

Yet, when we try to display the proper warrant of those inductive inferences we favor, whether the warrant is in general principles or material facts, the ground crumbles around our feet. (Norton 2011, 174)

To summarize, inductive logic has not solved the problem; it lets us repackage our opinions in more impressive language and revise them systematically using evidence but never free ourselves wholly of their influence. Bayesian convergence-of-opinion theorems (claiming that evidence eventually causes disagreeing initial subjective prior probabilities to wash out, leaving agreement on which theory is best) assume there are no theories with identical empirical consequences (Hawthorne 1993). Thus, we remain free to adhere to widely shared intuitions but struggle to turn them into a compelling argument.

The most sustained attention to the question of justifying past maximal extension evidently has been paid by John Manchak in a quest to understand what counts as a reasonable space-time (for example, see Manchak 2009, 2011, 2016b, 2016a). Manchak quotes or cites global general relativity authorities such as Roger Penrose, Robert Geroch, and C. J. S. Clarke, making Leibniz-like metaphysical proposals to justify maximal extension, much as Earman indicated. (Geroch seems the most explicit.)

Apparently, when one removes naive or intuitive (largely tacit) plausibility judgments about large scale space-time features in favor of a rigorous deductive evaluation of many possibilities, one gets a taxonomy of often startling possibilities and no way to close Pandora’s box. This situation resembles philosophers’ efforts to address skeptical arguments, often unsuccessfully. Perhaps the lesson is, as some ancient skeptics as well as Blaise Pascal (Merlan 1967), Bishop Huet ([1723] 1725, 184), Hume (Hume 1978, 269), and Thomas Reid (as a basic thrust of Scottish Common Sense) taught, that nature rather than reasoning leads away from skepticism.

A more explicit argument might take these hints at rationalistic theology more seriously. According to rationalistic theism, rationalistic theism is truth-conductive: it is a coherent and self-recommending belief system positing that a reasonable God has designed our minds to believe various things, including in a reasonable God and a lawful natural order. Rationalism’s being self-recommending means that according to rationalism, rationalism is a good way to gain knowledge. Such a feature will not impress non-rationalists but does provide a measure of reassurance to rationalists. In comparison to medieval nominalists, most modern Westerners are rationalists to some degree. Most readers of Zygon: Journal of Religion and Science are probably less scandalized than most philosophers of science by the idea that rationalistic theology would provide the justification for certain scientific claims; after all, rationalistic theology played a role in the shift from Leibniz’s view, which still accepted creation in the finite past (Alexander 1956, 76), to Friedrich Schleiermacher’s lack of attachment to the initial creation event (Russell 1996; Copan and Craig 2004, 150, 151) as well as motivated Darwin (Dilley 2012). The idea that empiricism might not lead readily to naturalism is hardly novel, having been suggested by rationalistic anti-supernaturalists such as F. H. Bradley, who advised filtering the evidence to match prior understanding (Bradley [1874] 2011; Vincent 1995, 13, 14), and advocated for by empiricist non-naturalists (Broad 1916–1917; Merlan 1967; Swain 1967; Stoller and Olkes 1987; Redmond 1987; Graubner 1989; Popkin 2003; Turner 2006). However, philosopher of biology Elliott Sober (2008, 127, 128) has cautioned against using rationalistic theology in scientific argument in biology; his reasoning might generalize to other sciences. Admittedly, being self-recommending is not unique to rationalistic theism; traditional orthodox theology, insofar as it posits divine grace in epistemology (as in Alvin Plantinga’s (2000, chapt. 8 and 9) internal testimony of the Holy Spirit), is also self-recommending. If the religious believer is correct that religious faith is caused by the Holy Spirit, then this faith is also true and warranted. While these two beliefs (rationalistic and orthodox theisms) vied for acceptance a few centuries ago, they have much in common, differing partly in a wholesale versus retail appeal to divine assistance. Given that rationalism is usually considered the antithesis of enthusiasm (the old name for disreputable belief that one is personally divinely inspired), it is illuminating that René Descartes’s rationalist epistemology was accused of enthusiasm (Heyd 1995, chapt. 4). By contrast to these theisms (existing perhaps on a spectrum rather than as two discrete rivals), naturalism is not self-recommending; indeed, sometimes roughly the opposite is argued (such as by Plantinga): that naturalism is self-defeating, so that it is an unwarranted belief if true and therefore cannot be knowledge, whether true or not (Beilby 2002).

Though one may believe in the maximal extension of cosmic history, some might not. Craig’s argument apparently uncovers people who doubt the causal premise 1, namely, Quentin Smith and J. L. Mackie (Craig 2008, 112). It seems to me that if one doubts premise 1, one could think the world popped into existence at some stage “after” the Big Bang rather than “at” the Big Bang. If universes can pop into existence, who knows, why not? If the universe popped into existence too recently, it could be awkward if our memories are false, for example. But if it is merely rock layers or cosmic nuclear abundances that lack their expected origin, those things, lacking truth values, cannot be false—though they might have some comparable defect, especially if too recent. The issue bears some resemblance to Boltzmann brains, which supposedly arise due to statistical fluctuations and have illusory experiences (assuming something like physicalism in the philosophy of mind). There also exist people who accept Criag’s premise 2 on scriptural grounds and think God created the world such that space-time did not maximally extend to the past;⁶ such people might consider the kalām argument sound but dialectically ineffective because they use the conclusion, accepted on other grounds, to motivate premise 2. While this view does not cohere well with the spirit of Enlightenment, it can be empirically adequate, which is better than what one sometimes sees. Derek Turner (2007) has discussed how to be relaxed about realism in the historical sciences, such as by holding the natural historical attitude, according to which one does not know or care—not his favorite view but a contender. For critique and leads into the discussion of (anti)realism about the past, one might see Sophie Botros (2017) and Efraim Wallach (2022). This seems not to be primarily a scientific question.

A striking example of how rationalistic theology can justify past maximal extension has appeared recently in the science–theology literature (Klose 2021). Joshua Klose (2021) apparently aimed to drive yet another nail into the coffin of young-Earth creation science, thinking hard about creation with apparent age (such as whether a circumscribed set of examples justified by functionality can be identified) but ultimately finding it unbelievable and entailing the “absurd position that much of the universe’s apparent history never occurred.” I confess finding the argument obscure. The implication of non-actual history is right there on the surface, not requiring the amount of reflection invested; on the other hand, finding something resembling a problem of evil or a philosophical skeptical puzzle is not automatically decisive. A problem of evil might be answered by some greater good, perhaps even one not yet articulated or articulated long ago. Descartes inaugurated early modern naturalistic historical science, anti-realistically construed, in terms of epistemic convenience (Descartes and Reynolds 1988, 37, 38). Michael Murray (2008, chapt. 3, 5, 6), in considering the question of animal suffering, finds that because criteria with apparent age have the advantage of avoiding pre-Adamic animal pain and suffering, he has to work fairly hard to find an alternative theodicy (or something weaker) consistent with scientific realism back to the Big Bang. A skeptical worry might be everyone’s problem (or, in this case, everyone who does not accept the eternity of the world, which was condemned by the fourth and fifth Lateran Western church councils) (McMullin 1981; Tanner 1990, 606). Hence, it seems Klose has more work to do before declaring another victory.

Given the unclear logic, I have relied on statements that seem clear; Klose offers what he considers an internal critique, concluding that efforts to avoid drawing unsavory conclusions from creation with apparent age all fail. One might wonder, however, whether Klose’s case proves too much, effectively a priori forbidding God from creating in the finite past (no matter how far back) and ensnaring most of the Christian tradition (and Jewish and Islamic traditions as well, Aristotle’s eternity of the world versus scriptures being a long-lasting trans-confessional controversy involving mutual influence). No matter when God created the world in the finite past (ignoring general relativity for the moment, given that Klose’s argument is not related to cosmology, and recalling that quantum gravity might permit eternal worlds again), doing so presumably would have involved creating it such that “much of the universe’s apparent history never occurred.” There is perhaps a difference in degree only, a degree that cannot even be expressed in terms of fractions, because any finite age is negligible compared to infinity. What it would be appropriate for God to do presumably aligns closely with what it would be appropriate for humans to claim God did. If an effort to address creation science appears to tar St. Augustine, John Philoponus, al-Ghazali, Moses Maimonides, St. Bonaventure, Thomas Aquinas, Martin Luther, John Calvin, etc., and two Western church councils with the same brush, one might want to reflect on that implication. Perhaps some other measure could make a difference, distinguishing intended from unintended targets, given that evidence about the more remote past is harder to find?

Creation science in any case can be criticized for misunderstandings of general relativity involving the question of energy conservation (Pitts 2004a, 2004b, 2009). This issue highlights the importance of making as much sense of energy conservation as general relativity will admit, emphasizing its similarity to other field theories and the symmetries of its laws (Pitts 2010).

If one is an empiricist and hence struggles to justify past maximal extension, one is of course still free to believe it. I personally believe we see stars because light left them, propagated across space, and reached our eyes. Perhaps the issue of past maximal extension pertains more to typical questions of epistemology, such as how to address skepticism (many versions of which are acknowledged by most philosophers as irrefutable though also incredible), than to science.

Conclusion

While Big Bang cosmology remains an excellent physical model far enough from the singularity and general relativity remains an excellent theory of space-time and gravity (albeit calling for quantum gravity), the Big Bang still seems not to support a good kalām theistic argument. Understanding “beginning” in a nonconventional and modally robust way in terms of past extendibility seems necessary to produce a valid argument with sufficiently broad modal scope. The justification of past maximal extension proves surprisingly difficult to find empirically, though one might justify it to oneself as a rationalist or simply believe it if it seems very plausible.

Acknowledgments

Thanks to Hans Halvorson for encouragement to be involved in this thematic section, David Wilkinson, an anonymous referee for useful comments, and M. Krauze for bibliographic assistance.