The following is an excerpt from a manuscript in drafts, Searching for the Cosmos. It is from a chapter concerned with whether history is an essential property of the cosmos as a whole. Comments, criticism, and questions are welcome!
Does the cosmos have a beginning in time or is it temporally beginningless? Drawing on key insights from a medieval debate on the question of the so-called eternity of the world, I argue that, according to the lights of the philosopher of nature, both cosmic temporal inception and temporal beginninglessness are indemonstrable in an apodictic sense (§7.2.1). Still, the Thomistic natural philosopher can make sense of a relative temporal beginning of the world, and this claim can be defended with probability. This result is supported by considerations of the second law of thermodynamics and certain singularity theorems (§7.2.2). To be logically compatible with a cosmos with any sort of temporal beginning and historical innovation of form, hylomorphism must be compatible with a cosmos that has historical formal parts as well as the existence of temporally first substances (§7.2.3).
7.2.1: The Antinomy of Cosmic Time
We are wondering, then, whether on hylomorphic principles one can demonstrate either an absolute or relative temporal inception of the cosmos. An absolute temporal beginning means that there is a first moment of time without any prior moment or span of time. A relative temporal beginning cannot be as cleanly delineated—but I mean that there is some present epoch of order in the cosmos that is after a period of disorder. To focus the conversation even more, I consider a few selected arguments from St. Bonaventure and St. Thomas.[1] Their arguments for and against the beginninglessness of the world typically are grouped into arguments which proceed from the nature of God as Creator, or the nature of the world as created or subject to change, or the nature of production. In what follows, we consider a few of the arguments given for and against in the latter two categories, particularly as they relate to motion, time, and matter. This limits the range of the topic to natural philosophy, prescinding from metaphysics.[2] This limitation is more useful for our purposes, as natural philosophy’s methods are more proximate to cosmology’s and emphasizing this kinship helps to avoid certain mistakes.
Natural philosophy and the demonstrable undecidability of a cosmic beginning in time
Let us consider whether the cosmos is temporally beginningless (see Table 7.2).
| That the cosmos is temporally beginningless. | |||
| Arguments | Rebuttals | ||
| I | 1) All movement is motion preceded by a motion (either in the mover, as it must change to cause motion, or in the moved, which is now changed or has change); 2) all such motion is without a beginning; since 3) all movement needs mobile subjects, the cosmos of mobiles has always existed. | Premise (4) assumes that the subjects of motion have always been in existence, so it begs the question. See In Phys., lib. 8, lect. 2, n. 18 [988]: “The response is easy: for the mobiles were not previously in that disposition in which they now are because before they did not exist. | |
| II | 1) If time is perpetual, then motion must also be perpetual since time measures motion; 2) but time is perpetual, since the essence of the “now” is to have a time before and after (just as a point on a line); so, since 3) all motion needs mobile subjects, ∴ etc. | This does not follow because time exists only when motion does, and so this argument begs the question, in a way similar to argument (I). If the “now” does not relate to past and future essentially, a now without a past is possible (just as there can be an endpoint of a line). | |
| III | 1) If we must assume a thing’s existence while denying it, then that thing exists always; 2) denying time’s existence assumes it, because its existing must follow a duration of its non-existence; so, since 3) time is an accident of motion it needs mobile subjects, ∴ etc. | This argument proceeds from a fallacy of the imagination, as seen in examples of imagining a place outside a finite universe. Just so, one imagines time before that now prior to which there is not time. Note it also begs the question as in argument (I). | |
| IV | 1) All physical substance is either perpetual or comes into being; 2) if it comes into being, they do so from some subject or matter that preexists, for nothing comes from nothing (as all the philosophers say); so 3) all physical substance is either perpetual or supposes ones that are. | This applies only to things which arise by way of motion, and so it begs the question if things in fact can come into being ex nihilo: no becoming is before being for creatures. The axiom of the natural philosophers does not of itself reach the profundity of the principles of being as such. | |
In these arguments, (I) is from the priority and posteriority in motion, (II) and (III) take their start from the nature of time, while (IV) assumes the necessity of matter or a material substance to underlie change. As the rebuttals point out, all depend upon the Aristotelian contention that time is an accident of motion, and motion is an accident of a mobile subject, a physical substance. Thus, both Thomas and Bonaventure can point out that arguments of the sort as (I), (II), or (III) assume the point at issue, that physical substances always exist. As for (IV), it assumes that the only way in which substance can come into being is by way of motion, and this cannot be proven by assuming the priority in being of physical substances. At most,
these sorts of arguments are effective at showing that motion did not begin through a natural way [per viam naturae], as was posited by some [thinkers]. Yet such arguments cannot show that [motion] did not begin by things being produced, as it were, de novo from a first principle of things (as our Faith posits). . . . For when Aristotle asks whether movers and mobiles have always existed or not if motion did not always exist, he is to be answered by saying that the First Mover always existed, but all other things, whether they be movers or mobiles, did not always exist, but began to be due to the universal cause of the whole of being.[3]
Note three things. First is the key that these Aristotelian arguments are dialectically effective against positions which hold that the cosmos could come into being de novo by some sort of natural causal process. Second, for this very reason these argument cannot exclude the view that things are created ex nihilo, that is, by a causal power exceeding nature; all the less can they exclude creation ex nihilo with a beginning in time (which, Aquinas holds, must be believed on faith). Third, the distinction which these arguments fail to make is between particular agent causes of motion and a universal agent cause of being:
It does not follow that before the first change there is some other change. However, it would follow if movers and mobiles were produced de novo in being by some particular agent acting upon some preexisting subject which is changed from not being to being, or from privation to [having] form. For Aristotle’s reasoning proceeds with regard to this way of beginning.[4]
What about the proposition that the cosmos has a temporal beginning? Let us turn to another series of arguments between St. Bonaventure and St. Thomas.[5] Note, however, that it will beg the question—as the above arguments show—to assert that time or motion of substances coming into being have some absolutely first moment due to their nature. Some arguments avoid this by attempting to derive an impossibility from temporal beginninglessness (see Table 7.3).
| That the cosmos has an absolute temporal beginning. | ||||
| Arguments | Rebuttals | |||
| V | “It has been demonstrated that God is the cause of all things. However, the cause must precede in duration those things which come to be through its causal action.” Thus, the cosmos came into being temporally after not being, viz., with an absolute temporal beginning. | This temporal priority is true of agents acting through motion, but not of agents acting instantly, much less is it true of universal agent causes not acting in time. | ||
| VI | It is impossible either 1) to traverse what is infinite or 2) to add to what is infinite; but if the world is past-infinite, then 3) to see this sunrise today is (a) to attain to a point after traversing an infinite and (b) to also add to an infinite number of past sunrises; ∴ etc. | This argument is true concerning the infinite in act, not a successive infinite which exists in potency only. | ||
| VII | 1) It is impossible for a causally ordered series or system of things to be infinite; but 2) if the cosmos is past-infinite, then it is a system that is an actual infinite of causally ordered things, such as cosmological or other physical processes or animal generation; ∴ etc. | First, see above; this argument is true concerning causes which are essentially ordered, but not true of accidentally ordered, non-simultaneous causes. | ||
| VIII | If 1) the cosmos is past-infinite, and 2) the generation and corruption of its kinds is past-infinite, and 3) the human soul survives death, then there are actually in existence now an infinity of human souls. But 4) an actual infinity is impossible, and since (3) is true, (1) must be is false. | This argument supposes many things. Also, the valid conclusion here is that either (1) or (2) must be false, not (1) alone. | ||
Argument (V) begs the question in the way just described. It tacitly makes the assumption that agency is temporal, bringing things into being per viam naturae. Arguments (VI) and (VII) are typically found in defenses of the past finitude of the cosmos, and Aquinas frequently replies in the ways briefly described above. However, since he states of these arguments that “they do not conclude wholly of necessity, although they have some appearance of truth [probabilitatem],”[6] we discuss some finer points to (VI) and (VII) just below (##). Argument (VIII) has fascinations all its own (see §7.2.3, ##).
The general difficulty Aquinas sees in such arguments is due to the limitations of human reason. He argues this in two ways. First, resolving the debate would require knowing the specific will of God; the other is what I will call the argument from abstraction.
The newness of the world is unable to admit of demonstration on the part of the world itself. For the principle of demonstration is the what it is of a thing. However, each thing, according to the notion of its own species, abstracts from the here and now, on which account one says that universals are everywhere and always. Whence, one cannot demonstrate that a man, or a heaven, or a stone did not always exist.[7]
This argument hopes to head off all rebuttals by relying upon the core of Aristotelian scientific demonstration, proving that a certain property belongs to a subject in virtue of its essence as a cause. That is, in order to demonstrate apodictically that the cosmos had a beginning in time, one would have to show that due to the quod quid est (what it is) of the cosmos it must necessarily have a temporal beginning. However, because this mode of human knowledge abstracts from place and time (hic et nunc, “the here and now”), such an abstractly known essence cannot be used to demonstrate the reason why an individual must begin to exist here or now rather than there or then of necessity.
Aristotelian demonstration is a high bar. It is reserved for propositions which cannot be otherwise; hence, mathematics was ever Aristotle’s paradigm case.[8] Such necessities are grounded in the essences of things, for a thing cannot fail to be what it is when it exists. Thus, demonstration cannot be had of singular, concrete things, for they are not identical to their own essence and not only into being but can pass away.[9] However, even granting such background assumptions about demonstration, it does not follow that arguments grounding a certain assent and based upon the essences of things cannot be proposed about species of things—such as ‘man’ or ‘heaven’ or ‘stone’—or even singular things—this man or this heaven or this stone. Argument (VIII), about human beings, might be such a one, and Steno et alia would have things to say about stones.
Nonetheless, accepting Aquinas’s Aristotelian standards of demonstrative rigor, it seems that neither can one show that the world is eternal nor can one show that the world is temporally past-finite. Indeed, St. Thomas is well-known for defending this view, as well as the additional claim that a perpetual world is a metaphysical possibility.[10] However, ours has been a far more restricted case, that this question is demonstrably undecidable using the resources of natural philosophy, namely, the natures of physical substances and their natural causes. It is an antinomy of reason for the natural philosopher.[11]
Natural philosophy and the probable decidability of a cosmic beginning in time
One can grant this antinomy the strength of a true demonstration and still, however, insist that other lines of evidence lead to a probable inference motivating assent. The difference between the gold standard of Aristotelian demonstration and belief or assent is studied at length in St. John Henry Newman’s An Essay in Aid of a Grammar of Assent.[12] Complementary to the notional or universal modality of Aristotelian scientific demonstration, Newman articulates the idea of real inference or concrete reasoning: the illative sense. The logical architecture of this idea he expesses in a passage which I quote and examine at length due to the light it sheds on the question of knowledge of the cosmos through a historical natural science.
The principle of concrete reasoning is parallel to the method of proof which is the foundation of modern mathematical science, as contained in the celebrated lemma with which Newton opens his Principia. We know that a regular polygon, inscribed in a circle, its sides being continually diminished, tends to become that circle, as its limit; but it vanishes before it has coincided with the circle, so that its tendency to be the circle, though ever nearer fulfilment, never in fact gets beyond a tendency. In like manner, the conclusion in a real or concrete question is foreseen and predicted rather than actually attained; foreseen in the number and direction of accumulated premisses, which all converge to it, and as the result of their combination, approach it more nearly than any assignable difference, yet do not touch it logically (though only not touching it), on account of the nature of its subject-matter, and the delicate and implicit character of at least part of the reasonings on which it depends. It is by the strength, variety, or multiplicity of premisses, which are only probable, not by invincible syllogisms,—by objections overcome, by adverse theories neutralized, by difficulties gradually clearing up, by exceptions proving the rule, by un-looked-for correlations found with received truths, by suspense and delay in the process issuing in triumphant reactions,—by all these ways, and many others, it is that the practised and experienced mind is able to make a sure divination that a conclusion is inevitable, of which his lines of reasoning do not actually put him in possession. This is what is meant by a proposition being “as good as proved,” a conclusion as undeniable “as if it were proved,” and by the reasons for it “amounting to a proof,” for a proof is the limit of converging probabilities.[13]
Newman’s analogy in the first three sentences is clear: just as the sides of a series of regular polygons inscribed in a circle approach its curved circumference as a limit, so also do the lines of evidence and argument for a given singular proposition (about something concrete) approach the proof of its truth as a limit.
The analogy relies upon the idea of a limit as the terminus of a tendency, a mental motion towards (not a formalized delta-epsilon proof à la Weierstrass).[14] The mind sees where the evidence leads and can survey the conclusion in advance but cannot “touch it logically,” just as there is no lats polygon that becomes a circle. As there is no other line that the series approaches “more nearly than any assignable difference,” just so the conclusion. The mind assents to the conclusion not “by invincible syllogisms” bearing necessary causal insight but a type of reductio ad absurdum, a “the cumulation of probabilities, independent of each other, arising out of the nature and circumstances of the particular case which is under review.”[15] Thus, in the fourth sentence, Newman evocatively describes a process of investigation familiar to researchers, scholars, and scientists alike—the concrete landscape of personal knowledge about difficult subjects.[16] This habit of concrete reasoning of “the practised and experienced mind,” the faculty of the “illative sense,” Newman defines by comparison to Aristotelian prudence.[17] Just as prudence is the virtue of practical right reasoning about things to be done here and now, so also is the illative sense, more generally, is the virtue of right reasoning about things to be assented to here and now. We can assent to propositions whose reference to particulars precludes them from Aristotelian demonstrability.[18]
Such is the case with the question of the temporal finitude of the cosmos because it is this certain unity of order, a particular thing and not a notion. This very fact is assumed by the argument from abstraction. Nonetheless, Aquinas’s own rigor in arguing for his antinomy provides a clue as to the Newmanian answer to the question. If the abstract modalities through which essences are considered prescind from concrete or particular times and places, one must somehow show that the natures of things, even when known abstractly in this way, retain temporal or historical information in the abstract or in general.
With this in mind, let us consider Argument (VII) in Bonaventure’s version.
It is impossible for the infinite in number to be ordered. (VIIa) For every order flows from a principle toward a mean. Therefore, if there is no first, there is no order; but if the duration of the world or the revolutions of the heaven are infinite, they do not have a first; therefore they do not have an order, and one is not before another. But since this is false, it follows that they have a first. (VIIb) If you say that it is necessary to posit a limit [statum] to an ordered series only in the case of things ordered in a causal relation, because among causes there is necessarily a limit, I ask why not in other cases.[19]
Bonaventure assumes the notion of order implies a multitude of things related to each other in some species of priority and posteriority with reference to a first.[20] He contends in (VIIa) that without a principle an order among an infinite multitude of things cannot exist, because an actual infinite by definition has neither first nor last. He ans Aquinas agree on this much.
In (VIIb), Bonaventure attemps to avoid a rebuttal such as Aquinas’s, who thinks the argument “has no force,” because,
according to the philosophers, to proceed to infinity in agent causes is impossible in causes acting at once, because this would require the effect to depend upon an infinity of actions existing at once. Such are the causes which are essentially infinite, because their infinity is required for the thing caused. However, in causes not acting at once, this [to proceed to infinity] is not impossible, according to those who posit perpetual generation. However, this infinity accidentally belongs to causes, for it just so happens to the father of Socrates that he is the son of one man or another. However, it does not just so happen to a stick, insofar as it moves a stone, that it is moved due to a hand, for [the stick] moves [the stone] insofar as it is moved.[21]
The sticking point between Thomas and Bonaventure is whether causal order must always be finite. Aquinas replies that an essential causal order must be finite, whereas an accidental causal order can be infinite. To make this point, he supposes a case of causal order in which infinity is essential to its causality versus a causal order in which infinity is accidental to its causality. In the former series, each cause in it is dependent upon another in the series to act as a cause now. Thus, since the purportedly infinite series must by definition lack a first cause, each cause lacks its necessary condition for acting as a cause now, and so none of them can be causes. In the latter series, each cause in the series is not dependent upon another in the series to act as a cause now (although each cause may be dependent upon other causes essentially). Thus, since the existence of any other cause in such a series is not required for the occurent causality of this cause, were such a series to be infinite its infinity would be accidental to the causal efficacy members of the series and not such as to prevent causal action.[22]
Aquinas’s illustration might seem profoundly unclear, namely, that “it just so happens to the father of Socrates that he is the son of one man or another.” Without my grandfather, my father would not be my father, so how is this an accidental connection? Such is not Aquinas’s point. That this grandfather is required if this grandson is to bear a family resemblance through the grandson’s father is of course true as well as a per se genetic series. Rather, had a father a different father, he would still be able to be a father.[23] The father per se begets his son, but the grandfather is only per accidens the “begetter” of his grandson, namely, in virtue of his own son whom he begot. For the grandfather could die and his son still beget a son. Potency as a principle is crucial here, especially if one looks at the generations prospectively and not retrospectively. It is not necessary that a man beget a son at all, and in turn his son could potentially beget or not with any number of mates. Thus, the link from grandfather to grandson qua acts of generation is accidental. The example relies upon the indeterminacy of material agency.
However, Bonaventure has a rebuttal, the third part of the above argument. One “[does] not escape in this way.
(VIIc) For there has never been a revolution of the heaven without there being a generation of animal from animal. But an animal is certainly related causally to the animal from which it is generated. If, therefore, according to Aristotle and reason it is necessary to posit a limit among those things ordered in a causal relation, then in the generation of animals it is necessary to posit a first animal. And the world has not existed without animals: therefore etc.[24]
Thomas would not be moved by this reply. While the action of the spheres in medieval cosmology was a per se cause of the necessary conditions of animal generation, this causality was exercised over time—literally through the seasons of the year—and thus not an essential causal series existing all at once.[25] Aquinas assumes the indefinite character of potentiality, that over time it never “gives out,” and thus material generations in the terrestrial realm never fail on the material side even as the conservation of celestial motion is indefinite in the celestial regions as a background cause. The essential causal series is, rather, among the natures of the spheres and animal species as such. That one revolution of the sun is per se necessary to one animal generation is similarly related to subsequent revolutions as the series of grandfather, father, and son.
However, what if Bonaventure’s conception of a causal history is read differently, along the lines of the per se genetic series between familial generations? That is, while the connection between grandfather and grandson is per accidens in the sense that a grandfather is not occurently necessary for the father’s act of begetting, the grandfather’s individuality is necessary for certain genetic features of the grandson. In this, we might build upon Sylvester’s insight that substances, once their concrete existence is posited, can as such possess certain temporal properties per se, and those properties we can know abstractly and they may even have general causal conditions.
Let us reconsider Bonaventure’s argument, (VIIc) in particular. His could be read as asserting that the cosmological conditions for biological generation must exist prior not only in nature but also in time (Aquinas, of course, agrees with the former but not the latter). Consider a process of development: this newborn, Jack → this teenager, Jack → this adult, Jack. In Jack’s lifetime, the connections between these stages are per se to the individual.[26] That is, the teenage Jack is the individual that develops out of the newborn Jack, and this is not an accidental connection, and neither is the connetion between adult Jack and newborn Jack accidental. The individual process of maturation in an individual of a kind is not an accidental sequence, any more than the general type of that matural process for that species. Another example: carbon → organic compounds → human beings. That is, elemental carbon is a necessary constituent of organic compounds, which are in turn necessary constituents of human beings.[27] This sequence in material composition is atemporal, but each connection is per se and the essentiality of the connection is transitive (carbon is essential matter for human nature).
Aquinas’s accidental causal series trades on the concepts of the A-series of time. An A-series statement is one like this: “The meeting will happen two days from today.”[28] Here, the temporal relation two days from today does not fix when exactly the meeting is, unless one has further contextual information. As Feser notes, “This series is tensed, and events are constantly changing their position in the series.”[29] So too, to say that this man is someone’s son and another’s father is not to fix a generational reference point. By contrast, maturation as a temporal sequence trades more on B-series descriptions, such as the statement “The meeting will take place two days after July 22, 2003.” Here, the temporal relations are fixed, as July 22, 2003 is temporally before July 24, 2003, which day is temporally after it: “This series is tenseless, and events retain their position in it in a fixed way.”[30] So too, Jack’s being a teenager is always between his being a newborn and being an adult.
Now, the cases of newborn Jack (maturation) and carbon (material composition) cannot be infinite series. This is because maturation is a process teleologically determined according to a given species. Analogously, material composition cannot be infinite because it is an essentially ordered series (the man must have organic compounds now, while these must be composed of carbon now, which in turn . . . etc.). This applies to all four causes.[31] For example, an essence cannot have an infinite multitude of defining terms, for then there would be no first and, consequently, no real definitions.[32] Now, these material components are part of the essence of human nature. So, neither can they be infinite as contributing to the quiddity of human nature.
However, if the sequence carbon → organic compounds → human beings is not only one with a priority in nature but a temporal priority, then that sequence will contain relative temporal beginnings. That is, if carbon as a formal part of the cosmos (one of its species) exists in the cosmos without organic compounds or human beings, then when those formal parts come into being their species will begin to be absolutely in the cosmos, but this is a relative beginning within the cosmos overall. For Aquinas’s argument would require him to say that, for all we know, carbon has always existed. But what if such historically ordered, stage-like causal series characterized the history of the cosmos as such? Thus, the cosmos would have some fundamental type of substance composing it, which substance may or may not have always existed. However, what if the history of such causes cannot be past-infinite? If so, then one could propose an argument for historically-ordered hylomorphism:
- If human nature (or any hylomorphic nature)
(1) requires as necessary conditions types of historical orders of causes to bring individuals of such natures into existence, and
(2) such types of historical order are properties of this cosmos, and
(3) such a type of historical order cannot be past-infinite (for it is an essentially ordered causal system), - then this cosmos probably has a temporal beginning.
Note, first, that this is not an argument for evolution, cosmic, chemical, biological, or otherwise, because no agent causalty or mechanisms are proposed. Indeed, second, a difficulty with the argument is that the three conditions in this argument are themselves knowable only with probability. Furthermore, as I will discuss below, this temporal beginning is at best a relative one. Hylomorphic natures, conceived of in abstraction, of themselves need not be subject to historical stages of maturation. However, perhaps they are so subject. Natures conceived of in abstraction from the conditions of this cosmos contain only the priority of natural composition in being in their essences. However, in their determinate existence in this cosmos, investigation might reveal that this priority contains temporal information when one compares the natures of those substances in their relationships to the whole. Seeing such relationship in the concrete is what requires the cosmological exercise of a natural philophical illative sense.
7.2.2: Singular Beginnings of Time and Disorder (unfinished)
Conditions (1) and (2) of the argument for historically-ordered hylomorphism are treated in §7.3. I discuss condition (3) in this sub-section and the compatibility of Thomistic hylomorphism with a historically first kind or kinds of substances next (§7.2.3). As for condition (3), note that Aquinas assumes—above (###)—the indefinite character of potentiality, that over time it never “gives out,” and so material generations in the terrestrial realm never fail on the material side even as the conservation of celestial motion is indefinite in the celestial regions as a background cause.[33] This makes good sense, given his doctrine of prime matter as pure potency, a material infinity. Prime matter has no built-in “decay factor.” However, do the causal interactions of substances, according to their natures, have such decay factors? Perhaps there are global conditions which restrict the past history of the action of agent causes.
Cosmologists and philosophers alike propose such views. Some cosmologists are skeptical: “A start to the universe may have occurred a finite time ago, but a variety of alternatives are conceivable: eternal universes, or universes where time as we know it came into existence in one or another way. We do not know which actually happened, although quantum gravity ideas suggest a singularity might be avoided.”[34] By contrast, philosophers who defend the Kalām cosmological argument do so.[35] The argument is brief:
1. Whatever begins to exist has a cause of its beginning.
2. The universe began to exist.
C. Therefore, the universe has a cause of its beginning.
In a qualified sense, St. Thomas agrees with the Kalām argument, “for if the world and motion began to be de novo, it is plain that one must posit some cause which produces the world and motion de novo, because everything which comes to be de novo must take its origin from some innovating [cause], since nothing draws itself out from potency to act or from non-being to being.”[36] Aquinas thinks, however, that one cannot demonstrate the second premise. It cannot be proven philosophically, as we have seen above, by arguing that an actual infinity is impossible or that an actual infinite cannot be formed, and that a cosmos with an infinite past would be have to contain various such infinities.[37]
Yet the premise could be supported such that one can form a probable opinion or even assent to the past finitude of the cosmos. This logical possibility is opened by the argument for historically-ordered hylomorphism in response to Aquinas’s argument from abstraction. The second premise could be supported from cosmology, either from a physical interpretation of the mathematical models of cosmological expansion that imply an initial singularity or from the second law of thermodynamics (entropy).[38] Such investigations complete the argument for historically-ordered hylomorphism, allowing it to conclude with probability that the cosmos has a relative temporal beginning in the past.
[1] The medieval debate was truly vast. One can usefully consider Albert, Bonaventure, and Thomas on this question alone. Bonaventure’s text is found along with texts by St. Thomas Aquinas and Siger of Brabant in: On the Eternity of the World (De Aeternitate Mundi), trans. by C. Vollert, L. H. Kendzierski, and P. M. Byrne, Medieval Philosophical Texts in Translation, vol. 16 (Milwaukee: Marquette University Press, 1964). In what follows, we do not quote the Universal Doctor, and even from the texts of the Seraphic and Angelic Doctors I only select arguments relevant to natural philosophy and cosmology, as opposed to logical, metaphysical, or theological ones.
[2] A more complete consideration, inclusive of creation, is proposed in Chapters 10 and 11. Thus, our discussion currently prescinds from considering properly metaphysical claims about creation ex nihilo and properly theological or revealed truths.
[3] St. Thomas, In Phys., lib. 8, lect. 2, n. 15 [987].
[4] Ibid. I discuss the distinction between universal and particular agency in Chapters 10 and 11.
[5] See the world of Baldner and Walz concerning Bonaventure’s view of the philosophical success of such arguments.
[6] St. Thomas, ScG, II.38, n. 7 (Leon.13.355): “Hae autem rationes quia non usquequaque de necessitate concludunt, licet probabilitatem habeant, sufficit tangere solum, ne videatur fides Catholica in vanis rationibus constituta, et non potius in solidissima Dei doctrina.” Because of what Aquinas states in the remainder of the sentence (“it suffices barely to touch on them, lest the Catholic faith seem to be erected upon empty reasonings and not, rather, upon the most perfect teaching of God”), it is important to use another meaning of probabilitatem, “appearance of truth,” to avoid modern connotations and emphasize the arguments’s dialectical quality.
[7] St. Thomas, ST, Ia, q. 46, a. 2, c. The conclusion reads: “Unde demonstrari non potest quod homo, aut caelum, aut lapis non semper fuit.” Aquinas could say “a heaven” since in the geocentric cosmos there were many heavens (the sphere of the Moon, or of Mars, etc.). It is still a question I have as to whether the argument from abstraction is unique to Aquinas.
[8] It still is; see Jean W. Rioux, Thomas Aquinas’ Mathematical Realism (Cham: Palgrave Macmillan, 2023), and consider James Franklin, An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure (New York: Palgrave Macmillan, 2014).
[9] [citations later]
[10] Indeed, Aquinas thinks that, using the resources of philosophy tout court, one can demonstrate the following:
(1) An eternally created world is possible.
(2) A temporally finite world is possible.
(3) Whether God created the world as (1) or (2) is not demonstrable philosophically.
There are also subtler variations under which we could approach claim (1). Someone could hold the following views: (a) an eternally created world is possible; (b) it is not possible to demonstrate the impossibility of the eternity of the world; (c) it is not the case that the impossibility of the eternity of the world has been demonstrated yet. Option (c) is the weakest one, and (b) is stronger, while position (a) is the strongest position. That is, if one holds (a), one must defend (b) and (c); if you maintain (b) you must maintain (c) but can remain silent about (a); holding (c) obliges nothing in regard to (a) or (b). Throughout his career, St. Thomas clearly holds (c), and then, over his life, more and more clearly articulates his views regarding (b) and then (a). See John F. Wippel, Metaphysical Themes in Thomas Aquinas (Washington, DC: Catholic University of America Press, 1995), Ch. 8, “Thomas Aquinas on the Possibility of Eternal Creation,” 191–214, at 193.
[11] Of course, “antinomy” is not used in a Kantian sense, for the above arguments appeal to our limited understanding of real things. There are antinomies even for realists.
[12] It would be too far outside the scope of this book to investigate the question as to what extent Newman’s nascent epistemology is thoroughly Aristotelian and Thomistic.
[13] Newman, Grammar of Assent, 320–21.
[14] For helpful discussions, see Juvenal Lalor, “Notes on the Limit of a Variable,” LTP 1, no. 1 (1945): 129–49, as well as John Francis Nieto, “What Is a Limit?” The Aquinas Review 13 (2006): 81–92.
[15] Newman, Grammar of Assent, 288.
[16] See Michael Polanyi, Personal Knowledge: Towards a Post-Critical Philosophy (London: Routledge & Kegan Paul, 1978), and The Tacit Dimension (Chicago: University of Chicago Press, 2009); a helpful comparison is Martin X. Moleski, S.J., Personal Catholicism: The Theological Epistemologies of John Henry Newman and Michael Polanyi (Washington, DC: The Catholic University of America Press, 2000).
[17] See Newman, Grammar of Assent, 353–54.
[18] See Aristotle, Posterior Analytics, I.8, 75b24: “No attribute can be demonstrated nor known by strictly scientific knowledge to inhere in perishable things.” It is beyond the scope to analyze here the natural acts of belief, assent, and the intellectual grasp of singulars (see ST, Ia, q. 86, a. 1, c.) which would bear out the complementarity between Aristotle, Aquinas, and Newman.
[19] St. Bonaventure, In II Sent., d. 1, p. 1, a. 1, q. 2, in On the Eternity of the World, 107, emphases removed.
[20] This was previously discussed in Chapter 4, §4.3.2, ##.
[21] St. Thomas, ScG, II.38, 5th resp. See also the helpful analysis of Ferrariensis, III.2 (Leon.13.356).
[22] That such a series would not exist all at once—on the presentist view of time—avoids any problems with an actually existing infinite.
[23] There are of course the typical ceteribus paribus clauses one must attach to this (e.g., provided the son grows up, is not infertile, finds a wife, etc.).
[24] St. Bonaventure, In II Sent., d. 1, p. 1, a. 1, q. 2, in On the Eternity of the World, 107, emphases removed.
[25] Aristotle explains this view in the De Generatione et Corruptione.
[26] This involved the first and third (of four) senses of per se discussed by Aristotle, Posterior Analytics, I.4. See also St. Thomas, Exp. Po. An., lib. 1, lect. 10.
[27] The second sense of per se.
[28] See the discussions in Dainton, Time and Space, 10–11, and Feser, Aristotle’s Revenge, 237–38.
[29] Ibid., 237. Once three days pass, that meeting will no longer happen “two days from today,” as it happened yesterday.
[30] Ibid.
[31] See Aristotle, Metaphysics, II.2.
[32] See ibid., 994a10–18, 994b16–27. The necessity of real definitions is defended in Metaphysics, IV.4.
[33] [citations later]
[34] Ellis, “Issues in the Philosophy of Cosmology,” 1235.
[35] William Lane Craig, The Kalām Cosmological Argument (London: Macmillan Press, 1979).
[36] ScG, I.13.
[37] See Copan, “Introduction,” in Paul Copan and William Lane Craig, eds., The Kalām Cosmological Argument, 2 vols. (New York: Bloomsbury Academic, 2018), vol. 1, 5; this introduction is reproduced in both volumes, the first is subtitled Philosophical Arguments for the Finitude of the Past and examines these two philosophical arguments through a detailed debate.
[38] Ibid., vol. 2, 5. The second volume is entitled Scientific Evidence for the Beginning of the Universe and features an extensive debate about these two scientific arguments.
John G. Brungardt 