The recent publication of Jeffrey Johnson’s The Failure of Natural Theology: A Critical Appraisal of the Philosophical Theology of Thomas Aquinas, a critique of the alleged Aristotelian excesses of Aquinas’s natural theology, sparked a great deal of excited controversy in the theological circles I run in. I have no interest here in entering the lists on Aquinas’s behalf; others better equipped and more interested than I have already done so. What struck me about the book was rather what a brilliant piece of Thomistic propaganda it represented: not only for his enthusiasts, but even for his detractors, Aquinas has somehow come to stand as the paradigmatic natural theologian.
In point of fact, Aquinas was among the most fainthearted practitioners of natural or philosophical theology in the thirteenth century, and this precisely because of his Aristotelianism. In a recent piece I described how Aquinas’s Aristotelian empiricism led him to reject Augustine’s view that God is the first object of human intellection, and Anselm’s related view (expressed in his two “ontological arguments”) that God’s existence is demonstrable a priori and not merely by inference from creatures. By contrast, Bonaventure, Aquinas’s Franciscan contemporary and friendly rival, defended both of these theses, and saw their increasing unpopularity in his time as an unfortunate symptom of Aristotle’s growing influence.
In this essay, I would like to extend the case for the failure of Aquinas as natural theologian still further, by considering another of his arguments with Bonaventure, this time about the finitude of time. Here again, as we will see, Aquinas’s allegiance to Aristotle betrayed him into rejecting perfectly sound arguments—first developed in the sixth century by the Christian philosopher John Philoponus, and popularized in later centuries by Muslim theologians or mutakalamin, such as al-Ghazalī (d. 1111)—that an infinite temporal series is logically impossible. For Aquinas, as for Kant after him, pure reason is paralyzed in the face of antinomic arguments for and against the infinity of time; only divine revelation can settle the issue. By contrast, Bonaventure—probably with some influence, however indirect, from Philoponus—ingeniously hoisted Aristotle on his own petard, showing how the standard Aristotelian arguments against the possibility of an infinite regress of causes ruled out the possibility of an infinite regress of times.
Bonaventure’s begins from the conviction that creation is pervasively finite, displaying its dependence on God, and its own intrinsic bias toward the nothing whence it was drawn, in its every aspect. As he suggests in the very opening of his Sentences commentary, “The deep of creation,” which is plumbed in the second book, “is the vanity of created being,” which “consists in two things, namely in the change from being to non-being,” at creation, “and again in its reversion to non-being,” with sin. The chronic finitude of creation extends also, he insists, to its temporal duration: the discourse which creation is can only be an ordered, and so interpretable, whole, he thinks, if every successive moment in it is referred to an absolute temporal beginning. And so, an eternal creation, as he fiercely argued against both the anti-theological Aristotelians on the University of Paris’s Arts Faculty and the harmonizing Aristotelian Aquinas, is a logical impossibility.
Consider the standard arguments for the world's eternity. First, there is the original Aristotelian argument that the grammar of time-talk always requires that any selected moment be suspended between a prior moment (which is its past), and a posterior moment (which is its future). Any putative "first" moment of creation would still necessarily be thought as one member in a series which, like the set of integers, stretches back in(-de-)finitely in both directions. (The integers, for an Aristotelian at least, are not a realized infinity, but rather a set expanded indefinitely according to the rule “Add 1”.)
Bonaventure did grant that these arguments are at least possibly Aristotelian rather than Aristotle's. In the Sentences commentary, he flags a contemporary exegetical dispute about whether Aristotle intended to prove that the world could have had no beginning, or simply to prove that it could not have begun “by natural motion.” About this dispute, he simply shrugs: “Which of these [readings] is truer, I’ve no idea.” And in his last work, the Collationes in Hexaëmeron, he was even more willing to exculpate Aristotle on this score: “Aristotle can be excused regarding the eternity of the world, because he understood this as a philosopher, speaking as a naturalist (ut naturalis), namely that the world could not begin through nature.”
Arguments about the nature of time are arguments from below, but Bonaventure also considered an argument from above for the world's eternity, drawn from the nature of God's creative act: God is a necessary and sufficient cause of the creature from all eternity; but no reason could be given for the activation of that causality at this rather than that time, so creation must be eternal. Now, Bonaventure responds to each of these sets of arguments, attempting to show that the idea of an eternal temporal duration is incoherent, and also to show that it is inconsistent with creation ex nihilo. On the first score, he—strikingly like John Philoponus six centuries earlier—turns Aristotle’s arguments against the possibility of a realized infinite series against the Aristotelian argument for the world's eternity. For the sake of space, we will just consider the two most compelling of Bonaventure’s arguments against an eternal duration, each of which involves valid inferences from true premises, and each of which, as we will note in passing, are versions of the arguments earlier developed against the eternity of the world by Philoponus; some direct influence seems likely, but is tantalizingly difficult to trace); we will consider them in turn.
First, Bonaventure notes, “it is impossible for the infinite to be added to . . . but if the world is without beginning, it has endured an infinitely long time; and so its duration cannot be added to.” An infinitely-old world ought to be beyond the possibility of growing older; but the set of days (for instance) plainly is larger at any time t+1 than it was at t. Moreover, if the world is infinitely old, it is also true that, while the earth has completed an infinite number of revolutions around the sun, and the moon an infinite number of revolutions around the earth, the moon's revolutions are necessarily twelve times as numerous as the earth's, so that the eternity of time requires not only addition to the infinite, but actually existing infinite sets of greater and lesser magnitude.
This argument, of course, presupposes that the heavenly bodies themselves have existed for the entire duration of the world. Would extending generation and corruption to the heavenly bodies, so that the stars and even the atoms that compose them are all finitely old, neutralize this argument? Not necessarily. Say that the universe consists, as on one current cosmological model (“the bouncing universe”), of an infinite sequence of the following series: a “Big Bang,” followed by universal inflation and expansion, followed by universal contraction leading to a “Big Crunch,” which gives way in its turn to a new Big Bang. And say also that every universe so produced contains at least n of the subatomic particles (quarks, or muons, or whatever) which compose our world. On that model, the universal series will contain at least two infinities of differing magnitude: first, the infinity of universes themselves, and second, the infinity of subatomic particles contained in those universes, which will be n times greater than the number of universes themselves.
Aquinas responded to Bonaventure’s attempted proofs of time’s finitude in many of his works, including the early Commentary on the Sentences (1252-56), both Summas, and opuscula such as On the Eternity of the World. (There is not development across these discussions; there are interesting differences among them, but no significant changes of mind.) In the Commentary, Aquinas responds to Bonaventure’s argument that infinity cannot be added to by insisting that the world’s infinity does not require this: the world “is not actually infinite, nor is this necessary for the eternity of the world,” since “addition is not made to the infinite according to its total succession, which the infinite has merely the power of receiving, but to something finite taken in act: and nothing prevents that from becoming more or greater.”
Aquinas’s thought is that even an eternal world would not be infinite in act, since only a finite portion of it ever exists in the present moment. (Properly speaking, however, the “present” is not finite, but rather “infinitesimal,” in the sense of being extensionless; it is born over its own grave.) The objection depends on thinking of past time as a realized infinity of days lined up in a row, to which a new day is added with every stroke of midnight. This is incoherent, Aquinas agrees, but thinks that the eternity in view here is different, since it only ever requires a finite sum to which new time is added.
This is a curious response. To see why, consider the set of all sunrises up to and including yesterday, and the set of all sunrises up to and including today. (To simplify things, imagine a Ptolemaic cosmos, complete with unoriginated and incorruptible heavens, so that both sets are infinite.) Nothing in Aquinas’s response to Bonaventure allows him to escape the conclusion that the set of sunrises is larger at t+1 than at t; but, if the world’s duration is infinite, then that set is plainly infinitely large at both times. And so, in an eternal world, the infinite is being added to all the time.
And yet—a doughty eternalist might object – hasn’t Georg Cantor’s proof of the existence of “transfinite cardinals” demonstrated that there are in fact nested infinities of various magnitudes? Of course: but Cantor’s “diagonal argument” has nothing to do with the existence of a realized infinity in Aristotle’s sense. What Cantor showed is “that the cardinality of the real numbers [e.g., including irrational numbers] is larger than the cardinality of the integers [the counting numbers].” (“Two sets of numbers are equal (have the same cardinality) if the members of the first set can be put into a one-to-one correspondence with the members of the second set.”) Cantor demonstrated this by showing that, if every integer were paired with some real number, it would be possible to construct a real number which was not paired with any integer, whose “nth digit after the decimal point is chosen as any digit that is not the nth digit of the nth row.” But nothing about this proof requires that there actually be an infinitely-long list lying around somewhere (outside the divine intellect, at least!), from which the tell-tale decimal expansion was missing.
Bonaventure raises a further objection to the world’s eternity on the grounds that “infinites cannot be traversed,” here citing Aristotle’s own maxim in Posterior Analytics 1.18. "But if the world did not begin, there have been infinite revolutions, and so it is impossible to traverse them, and so impossible to have arrived at the present.” The intuition here is similar to the one at work in the first objection: if C presupposes the occurrence of B, and B the occurrence of A, then A's actuality is a necessary condition for C; but if A itself presupposes necessary conditions which stretch back indefinitely into the past, and those conditions presuppose conditions which regress still further, then the series never gets off the ground. This is why, in the prior paragraph, Bonaventure waves away the objection that this kind of resolution is only required in a “vertical” series of causes, rather than in the “horizontal” series of events: “If you say, that a state of order (statum ordinis) only need be posited in those things which are ordered causally, because in causes there is necessarily rest (status), I ask, why not in other [sequences] as well?”
In the Summa Theologiae, Aquinas again offers a rather lame response to this objection (“infinites cannot be traversed”), proposing, “Traversal is always understood from term to term. But whatever past day might be selected, there are only finite days from it to the present, which series can be traversed. But the objection proceeds as if, given the extremes, there are intermediate infinities.” Aquinas suggests that the problem vanishes if we focus on the distance between the present moment t and any moment t-n, which distance by definition is finite. But this begs the key question, which is whether the conditions are satisfied for the existence of t-n; and if the world is infinitely old, they cannot be, because those conditions comprise an infinite series, and “infinities cannot be traversed.”
It seems to me that Bonaventure’s arguments for the impossibility of an eternal (i.e., indefinitely-old) creation are simply correct. It is curious, then, that Aquinas not only found them not to be probative, but even attempted, in all his major works, to show them not to be so. Fernand van Steenberghen makes the interesting suggestion that Aquinas was emboldened in his defense of the philosophers by virtue of the weakness of Bonaventure's insistence that an eternal duration of creation is inconsistent with its existence ex nihilo: “It is impossible,” Bonaventure insisted, “that what has being after non-being should have eternal being.” As van Veldhuijsen notes, Bonaventure seems to have regarded this thesis as “evident like a first principle, so there is no need for [a] demonstration” of it.
This is the argument that seems most to have stuck in Aquinas’s craw: “The whole question consists in this, whether being created by God according to one’s whole substance and not having a beginning of one’s duration are mutually inconsistent.” In any case, when Aquinas introduces the position that the world’s finitude in time is demonstrable by reason in the corpus of his own discussion of this question in the Commentary on the Sentences, the only argument he mentions in support of it is the view creation ex nihilo requires a temporal transition from non-being to being. Aquinas rightly insisted that creation ex nihilo in no way implies a transition in time, but rather an a-temporal relation of dependence between uninflected being and the creaturely whats which borrow their thatness from it.
Aquinas granted to Bonaventure, of course, that creation ex nihilo and an absolute temporal beginning fit together nicely—a “transition” into spacetime that presupposes no spatio-temporal reality as its background (the first moment of creation’s existence, or as close to it as physicists can conceive) serves as a fitting synecdoche for the a-temporal origination of all of spacetime by God from nothing. Nonetheless, “creation” (at the putative beginning of spacetime, t=0) and “preservation” (at any time t > 0) differ only in that the latter presupposes a creaturely terminus a quo, while the former does not; but with respect to the LORD, every point of spacetime is equally dependent, equally a creature out of nothing. As George Berkeley nicely put it centuries later, “The divine conservation of things is equipollent to, and in fact the same thing with, a continued repeated creation: in a word, that conservation and creation differ only in the terminus a quo.”
The weakness of Bonaventure’s argument “from above” against the world’s eternity in no way detracts from the strength of his arguments against it “from below,” from the impossibility of a realized infinity. Aquinas was simply wrong to follow the Aristotelian tradition rather than the distinctively creationist tradition running back through the Islamic philosophers to Philoponus. Indeed, it is hard not to wonder if Aristotle himself had theological reasons for preferring an eternal world. After all, Aristotle rejected Plato’s notion of divine creation; his God was self-enclosed “thinking thinking of thinking,” with no regard for the world which arose from matter’s eternal if futile longing to imitate the divine perfection. As David Sedley argued in his Creationism and Its Critics in Antiquity, Aristotle took it that “if god must be a pure contemplator [as Plato’s own arguments in Republic might be taken to imply] he cannot be an administrator. There can therefore be no Demiurge, and no divine world-soul. In which case, the world is uncreated and functions without divine oversight” (170). Aristotle, Sedley observes, “reconciles these two apparently conflicting motifs (god as detached and god as causally supreme) by drawing on another Platonic idea: that god is the supreme object of emulation” (170, cf. Tht. 176: likeness to god). On this view, then, “the supreme divinity” is the world’s cause, but only as “an unmoved mover, a detached self-contemplator, whose activity is pure actuality,” while “everything else in the world functions by striving, in its own way, to emulate that actuality” (170). But this is only a coherent picture of the God-world relation on the assumption of an eternal universe. A finitely-old universe would have raised awkward questions which Aristotle’s theology left him ill-positioned to answer.
Many modern physicists from Newton through Einstein prided itself on having rescued Aristotle’s belief in the eternity of time from its theological critics. And indeed, the progress of the historical sciences, from astronomy to geology, revealed a universe vastly older than any of the ancients or medievals could have conceived. During this period, sound physics seemed to be in revolt against sound metaphysics. But as David Hart often quips, reason abhors a dualism; something had to give.
Happily, in the early twentieth century, physics began to cooperate with metaphysics, initially in the discovery, by the priest-scientist Georges Lemaitre, no less, that the universe appeared to be expanding out from a “primeval atom,” a singularity from which space and time itself took their beginning. Even after the discovery of the cosmic microwave background radiation provided striking empirical confirmation of the “Big Bang” theory, however, physicists sought new ingenious models for saving an eternal universe, as in theories of an infinite succession of “bouncing universes,” or of “eternal chaotic inflation,” with new universes branching off from old ones ad infinitum (for an accessible survey of these developments, cf. Stephen Meyer’s recent, The Return of the God Hypothesis).
Nonetheless, the walls are closing in around the eternalists. Recent work by the physicists Alan Guth, Arvind Borde, and Alexander Vilenkin has offered an apparent mathematical demonstration, the Borde-Guth-Vilenkin [BGV] theorem, of the fact that, as Meyer puts it, “the universe must have had a beginning.” Indeed, they have shown in a number of publications that “all cosmological models in which expansion occurs—Including inflationary cosmology, multiverses, and the oscillating and cosmic egg models—are subject to the BGV theorem.” Vilenkin has framed the implications in the starkest possible terms: “Cosmologists can no longer hide behind the possibility of a past-eternal universe . . . They have to face the problem of a cosmic beginning.”
Vilenkin has also vigorously argued against any “creationist” implications for this finding, insisting, “If all the conserved numbers of a closed universe are equal to zero, then there is nothing to prevent such a universe from being spontaneously created out nothing.” Though this is really beside my present point, it is worth noting that, as the Catholic physicist Stephen Barr once quipped, Vilenkin’s “quantum creation out of nothing” is akin to the transition in a bank account from the “zero-dollar state” to the “one-hundred dollar state”—there would still a emphatically be a complex structure of physical laws and constants obtaining in the background as Vilenkin’s universe quantum tunneled into existence. Nonetheless, Vilenkin is admirably clear about the extent to which physical and mathematical reasoning now converges with the metaphysical arguments “from below” for time’s finitude, which were advanced by creationist thinkers such as Philoponus, al-Ghazalī, and Bonaventure.
As we have seen, the late-ancient and medieval debate over time’s eternity or finitude remains highly relevant today, not least for the way it has been dramatically revived by physicists and cosmologists over the past century. This debate was at the heart of the thirteenth-century controversy over Aristotle’s rising influence on Christian theology. Within this dispute, Aquinas, here as elsewhere, took Aristotle’s part, insisting that while time’s finitude was revealed in Scripture, no rational demonstration of it could be given. Bonaventure, by contrast, was happy to follow Philoponus and his heirs in turning good Aristotelian philosophy against bad Aristotelian theology. He insisted that time was necessarily finite, and he was right. This is yet another case in which Bonaventure succeeds as a natural theologian by abandoning Aristotle, while Aquinas fails precisely by heeding him.
 For Philoponus, cf. his Against Aristotle on the Eternity of the World (trans. Christian Wildberg; Bloomsbury Academic 2013). For a survey of the classic formulations of this argument by Islamic philosophers in particular, cf. William Lane Craig, The Kalām Cosmological Argument (Wipf & Stock, 2000 ).
 Proemium in IV Sententiarum Libros I.1, 3b-4a. Unless otherwise noted, all translations are my own.
 Bonaventure, II Sent. d. 2, art. 1, q. 2, obj. 3; II, 20a, cf. Aristotle’s Physics IV, 219b.
 II Sent. d. 2, art. 1, q. 2, concl.; II, 21b-22a.
 Coll. In Hex. 7.2; V, 365b.
 II Sent. d. 2, art. 1, q. 2, concl.; II, 20a.
 Cf. e.g., Phys. 8.5, 255a-256b.
 Ibid., contra 1; II, 20b-21a.
 For the same argument in Philoponus, cf. his Contra Aristotelem VI, frag. 132, in Simplicius, In Phys. 1179,11-25; Wildberg, 145-46).
 II Sent. d. 2, art. 1, q. 2, concl.; II, 21a.
 Cf., e.g., Brandenberger and Peter, “Bouncing Cosmologies: Progress and Problems” (9 May 2016).
 For discussion of the differences among Aquinas’s various treatments of this problem, cf. Thomas Bukowski’s “An early dating for Aquinas’ De aeternitate mundi.”
 Super Sent. II, d. 1, art. 5, ad sc. 4.
 Quotations in this paragraph are from my personal correspondence with the mathematician Cliff Comisky.
 “Row 1: 0.4637362713536146...
Row 2: 0.1627083730270152...
Row 3: 0.8331312490101278...
Row 4: 0.7398241068392315...
Row 5: 0.2064910326775827...”
And so on…
 II Sent. d. 1, art. 1, q. 2, contra 3; II, 20b.
 Maimonides considers a similar kalām argument for creation, from the impossibility of an infinite number of transient individuals (Guide I.74, fourth arg.), but again, the clearest parallel is Philoponus in Contra Aristotelem VI, frag. 132, in Simplicius, In Phys. 117816-30; Wildberg, p. 144-45). For Maimonides’s awareness of Philoponus, if not his direct knowledge of his writings on the eternity of the world, cf. Guide I.71.
 II Sent. d. 1, art. 1, q. 2, obj. 2; II, 20a.
 ST 1.46.2 obj. 6.
 Ibid. ad 6.
 Bujdosó notes that Aquinas “does not answer the question whether infinity is traversable or not and how we can reach now from the infinite distance of creation” (“Difficulties in Defending Aristotle,” 125).
 II Sent. d. 1, art. 1, q. 2, contra 6; II, 22a. Cf. van Steenberghen’s "Éternité du monde," 277.
 P. van Veldhuijsen, “The Question on the Possibility of an Eternally Created World: Bonaventura and Aquinas,” 27.
 De aeternitate mundi.
 “The second position is of those who say that the world began to be after it was not, along with everything besides God, and that God could not make a world from eternity, but because he is impotent to do so, but because a world could not exist from eternity, precisely in being created” (Scriptum super Sententiis II, d. 1, art. 5, corp.).
 cf. Summa Theologiae 1.104.1.
 George Berkeley, Correspondence with Johnson in The Works of George Berkeley, v. 2, 280.
 Cf. Metaphysics Lambda, 1072b-1074b.
 The Return of the God Hypothesis, Kindle loc. 2252.
 Ibid., Kindle loc. 2314
 Vilenkin, Many Worlds in One, 176, quoted in Meyer, The Return of the God Hypothesis, Kindle loc. 2317.
 Alexander Vilenkin, “The Beginning of the Universe,” in The Kalām Cosmological Argument, v. 2: Scientific Evidence that the Universe Had a Beginning (ed. Paul Copan with William Lane Craig; Bloomsbury, 2018), 154.