January/February 2004
Did the World have a Beginning?
by Mark Goldblatt
The signature cosmological debate of the last century concerned the origin of the universe. Two principal views contended for the hearts and minds of professionals and amateurs alike: the Big Bang Theory and the Steady State Theory. The former, triumphant nowadays, holds that the world began at a single moment with a cataclysmic blast of matter and space; the latter, now largely abandoned, holds that the world had no beginning in time, that it always has and always will exist.
Curiously enough, the Big Bang-Steady State controversy had a philosophical corollary in a medieval Scholastic debate between Saint Bonaventure and Saint Thomas Aquinas. Well, sort of. Both Bonaventure and Thomas were Big Bangers in the sense that each accepted as true the first line of Genesis–“In the beginning, God created the heavens and the earth.” Nevertheless, Thomas devotes an entire treatise, De Aeternitate Mundi, to maintaining that the world’s beginning cannot be demonstrated logically; revelation alone compels us to believe that the world didn’t always exist. By contrast, Bonaventure contends that the beginning of the world is logically demonstrable since the opposite view–that the world has always existed–can be shown to be absurd. In this essay, I’m going to argue that Bonaventure was correct, that the beginning of the world is indeed demonstrable, and that Thomas’s position is undermined by his own logic.
But at the outset, and perhaps counter-intuitively, it’s necessary to clarify what both thinkers meant by “the world.” Bonaventure, for example, identifies the world as a thing that “has being after non-being” (II Sent d.1, p.1, a.1, q.2, fm.6). Thus, he effectively rules out a priori the possibility that it could have always existed. What’s critical to note, however, is that he’s described the world as identical with created being. Likewise, Thomas designates creation as “the emanation of all being” (ST 1a.45.1) and continues:
Hence if the emanation of the whole universal being . . . be considered, it is impossible that any being should be presupposed to this emanation. Now nothing is the same as no being. Therefore . . . creation, which is the emanation of all being, presupposes the non-being which is nothing. (ibid.)
If we accept Bonaventure’s and Thomas’s notion of the creation of the world as the creation of being, it follows that “being” can be predicated of any and all things. In other words, the “thing-ness” of things, including things that don’t actually exist, renders them beings. For example, unicorns don’t actually exist, but they’re still beings since they’re things capable of existing. Bonaventure and Thomas derive this idea of being from Aristotle who states that being encompasses whatever exists “in complete reality” or “potentially” (Metaph V.7.1017a.35). That is, being is the totality of what is or can be. Non-being, in turn, must encompass whatever is not and cannot be; hence, Thomas refers to non-being, in the passage above, as “no being” or “nothing.”
But the distinction between what can be and what cannot be is meaningless except in light of the laws of thought–which Thomas, in a discussion of self-evidentiality, refers to as “the first principles of demonstration”:
A proposition is self-evident because the predicate is included in the essence of the subject: e.g. man is an animal, for animal is contained in the essence of man. If, therefore, the essence of the predicate and subject be known to all, the propositions will be self-evident to all; as is clear with regard to the first principles of demonstration, the terms of which are certain common notions that no one is ignorant of, such as being and non-being, whole and part, and the like. (ST 1a.2.1)
Contemporary philosophers include among these first principles the laws of Identity, Non-Contradiction and Excluded Middle; Thomas’s point it that such laws must be presupposed for rational demonstration to proceed–and Bonaventure would no doubt concur. They are “first principles” because they’re invoked in all meaningful propositions. For example, the affirmation “Socrates is mortal” has meaning only if it’s a simultaneous denial of “Socrates is not mortal.” Moreover, it’s only with reference to these first principles that being can be described, as Thomas describes it, as a function of possibility. For instance, a sentient stone isn’t possible; thus, it cannot be. It’s a contradiction in terms: a stone, by definition, is a non-sentient being–which means that a sentient stone would be “a sentient, non-sentient being.” The fact that its definition is self-contradictory, a predicate simultaneously affirmed and denied, renders a sentient stone inconceivable, denying it even the possibility of being. But how do we know that a sentient stone doesn’t exist in an undiscovered place? What if a space probe someday sets down on a distant planet and a stone cries out in pain? The answer is that the moment a “stone” registers a sensation, it has ceased to be non-sentient; by definition, it has ceased to be a stone. The contradiction, thus, can never be reconciled.
According to the first principles, whatever cannot be in a logical sense, whatever is literally inconceivable, cannot be in an actual sense. This linkage of logical possibility and actual being effectively draws the horizon of the intelligible world on our eyes. Contradictory predicates cannot be simultaneously affirmed and denied; even as the rational mind rejects contradiction, so too the rational continuum of being rejects it. Clearly, this is what Thomas is thinking when he says that “everything is knowable in as far as it has being” and that “being cannot be understood except because being is intelligible” (ST 1a.16.3).
Whatever cannot be conceived, whatever violates the first principles, cannot be.
***
When Thomas argues that the question of the world’s beginning is a matter of faith, “not of demonstration or science,” his rationale is that the world might be as old as God, since creation wasn’t an act of motion:
. . . we must consider that an efficient cause which acts by motion precedes its effect in time. . . . But if the action is instantaneous and not successive, it is not necessary for the maker to be prior in duration to the thing made, as appears in the case of illumination. Hence it does not follow necessarily that if God is the active cause of the world, He must be prior to the world in duration; because creation, by which He produced the world, is not a successive change . . . (ST 1a.46.2)
It’s at least conceivable, Thomas argues, that the world has coexisted from eternity with God in that His very existence might summon into being the created world–in much the same way that a light’s existence produces immediate illumination. Paradoxically, however, Thomas doesn’t want to attribute eternity to the world, for this is an attribute of God alone. Following Boethius, Thomas thinks of eternity as “the simultaneously-whole and perfect possession of interminable life” (ST 1a.10.1). So described, eternity can be attributed only to a thing in which there is no change, no succession, “no before and after.” Yet in the world, there is, obviously, “before and after” (ibid.). Hence, strictly speaking, the world cannot be eternal. Yet Thomas’s point, remember, isn’t the possible eternity of the world, which he denies (ST 1a.10.3), but its possible existence from eternity, which he accepts . . . or, rather, accepts as a rational possibility, albeit one that must be rejected based on the first sentence of Genesis.
It’s here, then, that Thomas and Bonaventure differ: though both deny the possibility of the world’s existence from eternity on the basis of revelation, Bonaventure denies the possibility on the basis of reason also. The suggestion that the universe has always existed, Bonaventure contends, is logically absurd. For if the world is lacking a beginning, its duration must, de facto, be infinite (II Sent. d.1, p.1, a.1, q.2 fm.1). And it is against the prospect of the infinite duration of the world that Bonaventure frames his three main arguments:
1) According to Bonaventure: “It is impossible to add to the infinite.” The infinite duration of the world would entail an infinite number of revolutions of the sun and moon, and every new day or month would add another revolution (ibid.).
2) According to Bonaventure: “It is impossible for the infinite in number to be ordered.” An infinite past would mean no first revolution, and if no first, then no second, and if no second, then no third, and so on. Still, at present, we observe an ordered sequence of days and months (ibid. fm.2).
3) According to Bonaventure: “It is impossible to traverse what is infinite.” Likewise, an infinite past would mean that an infinite number of revolutions have come and gone before we arrived at the present one. Yet we have arrived at the present revolution, the present day and month (ibid. fm.3).
Thomas addresses the first two of these questions in the Summa Contra Gentiles. To Bonaventure’s contention that an infinite sequence cannot be ordered because it lacks an initial term–for example, a first revolution–Thomas responds that this is a difficulty only if infinity is viewed as existing all at once; time, however, doesn’t exist all at once but successively. “Understood in this sense,” Thomas asserts, “any infinite is finite.” That is, each successive lunar revolution (let’s say) requires only that a previous revolution be completed in order to come into existence. The new revolution doesn’t depend on there having been an initial revolution, only a preceding one. An initial revolution would be required to “order” the infinite sequence only if the totality of revolutions existed simultaneously (SCG 2.38).
To Bonaventure’s argument that infinity cannot be added to, Thomas responds, “There is nothing to prevent an addition to the infinite on the side which is finite.” That is, the infinite duration of the world implies an infinite past; an infinite past entails an infinity in only one direction, not both. Whenever, for example, new revolutions of the moon are added to the age of the world, they are added to the finite side, to the side that terminates in the present moment, the now of our experience (ibid.).
Thomas’s reply to the third objection raised by Bonaventure, that the infinite cannot be traversed, is found back in the Summa Theologica. “Passage,” he asserts, “is always understood as being from term to term. Whatever by-gone day we choose, from it to the present day there is a finite number of days which can be traversed” (ST 1a.46.1). Once again, therefore, the infinite is rendered finite. Thomas’s response here is, in essence, a recap of his responses to the previous two objections; it comprises a dogged refusal to consider the concept of infinite duration in its entirety. Thomas has, so to speak, refused to enter Bonaventure’s ballpark. Whether this refusal is justified logically, or merely strategically, is the issue I’ll now attempt to address.
***
Suppose, for the sake of argument, the world had no beginning, had always existed. Necessarily, then, the age of the world would be infinite; that is, its age as measured by any definite unit–whether minute or hour, year or millennium, could not come to a total. For Bonaventure, this constitutes a prima facie case to the contrary: the suggestion that the world’s age, divided into definite units, can never comprise a totality, strikes him as absurd. The absurdity of this suggestion, or at least his sense of its absurdity, is what underlies his arguments that infinity cannot be added to, ordered or traversed–and, therefore, cannot be attributed to the world. Thomas’s finesse of Bonaventure’s three arguments is, in effect, to chop infinity down to size, to insist that we re-conceive it in finite sections and treat the sections themselves as discrete units.
But in so doing, have we altered the concept of infinity?
The justification Thomas relies on is that time doesn’t exist all at once but successively; infinity, thus, is never simultaneously actualized; it’s never all here at once. Still, the world has an age–whatever has duration also has age since age is just the sum of whatever units duration is divided into. Therein, I think, lies the initial flaw in Thomas’s logic: in his refusal to treat the duration of the world as an infinite whole, Thomas denies that the world has a rationally expressible age.
The reason infinity can never be predicated as a quantitative measure is because it is a numeric plural, a hypothetical sequence of ever-increasing values. It isn’t a single amount, an extremely large number, x, but an endless series of extremely large numbers: x, x+1, x+2, x+3, and so on. To predicate infinity of a thing, as a quantitative measure, is thus to attribute to it the values of x and x+1 simultaneously. But x+1 is also, by definition, not-x; the predication of infinity, therefore, becomes the predication of x and not-x simultaneously–which, if we remember the first principles, violates the law of Non-Contradiction. Yet it is only on the basis of the absolute inviolability of that law that Thomas is able to use the criterion of possibility to distinguish being from non-being: that which is conceptually possible, that which is or can be, describes being; that which isn’t and cannot be describes non-being. Thomas himself maintains that God, “although He has infinite power, cannot make a thing to be not made (for this would imply that two contradictories are true at the same time)” (ST 1a.7.2). Again, that which is made cannot simultaneously be not-made. That which is sentient cannot simultaneously be not-sentient. That which is x cannot simultaneously be not-x. As Thomas notes, “Affirmation and denial cannot be simultaneously true . . . not even God could make such a thing, because it is nothing” (De Aeternitate 2). And nothing is the same as non-being.
To illustrate this idea in a more familiar way, consider that it’s impossible for one person to be two ages at the same time. Even if he’s getting older, he can never be, say, 32 and 33 years old simultaneously. The reason is that 33 is, by definition, not-32 . . . thus rendering his age simultaneously 32 and not-32, which would affirm and deny the same predicate, thereby violating the law of Non-Contradiction. Infinity, since it’s a numeric plural, x and not-x, cannot be ascribed of an actual thing. It would be, as we’ve seen, a contradiction.
It’s worth noting that Thomas himself rules out the possibility of an infinite magnitude (ST 1a.7.3) or infinite multitude (ST 1a.7.4) in actual existence at a given moment, though a potential infinite is possible. For example, a line potentially may be divided an infinite number of times, but at no point will the actual multitude of divisions total infinity. Likewise a line potentially may be extended an infinite distance, but at no point will its actual magnitude stretch to infinity.
Similarly, future time may be thought of as a potential infinite. We may even think of future time as either a kind of potential magnitude (extended through temporal rather than spatial units) or a potential multitude (counted in successive rather than simultaneous units). Revolutions of the moon, for example, can be added one by one ad infinitum, but at no point in the future, regardless how distant, will the actual number of revolutions come to infinity.
But how, then, should we respond to Thomas’s contention that past time mustn’t be viewed as a simultaneous existence of such units (SCG 2.38)? The answer is that the divisibility of past time compels us to view it as a simultaneous existence–an accumulation of units. That’s the nature of arithmetic. To calculate a sum is always to posit a simultaneous existence of units. Whether the units are temporal (hours, years or millennia) or physical (marbles, melons or moons), the mental act of adding them together for the sake of measurement presupposes that the units accumulate rather than replace one another. Past time, therefore, must be measured as a simultaneous existence–whether that past time stretches back to a well-known point, say, the last time the New York Jets won the Super Bowl, or that past time encompasses the entire duration of the world. And if we object that, in the latter case, such a duration cannot be “encompassed,” then we’re left with an actual infinity which violates the law of Non-Contradiction. Such a duration cannot be.
Duration simply cannot be infinite if it is comprised of a succession of definite units. The same logic by which Thomas rules out an infinite magnitude and an infinite multitude can be used to rule out an infinite duration. The world’s beginning in time is, therefore, demonstrable, as Bonaventure claims, and not simply a matter of faith.