I have been puzzled by how Craig’s Aristotelian solution to Zeno’s paradoxes is consistent with presentism. I finally got around to reading the part of his book that explains this. If I am understanding his view correctly, it seems that his Aristotelian solution comes at the cost of (1) giving up on presentism, and (2) giving up on the supporting premise for the second premise of the Kalam cosmological argument. The Kalam, Craig says, depends on the A-theory of time where temporal becoming is real; presentism—the view that only the present exists—is the most popular version of A-theory.
What is the Aristotelian solution to Zeno’s paradox?
… before Achilles could cross the stadium, he would have to cross half-way; but before he could cross half-way, he would have to cross a quarter of the way; but before he could cross a quarter of the way, he would have to cross an eighth of the way, and so on to infinity. Therefore, Achilles could not arrive at any point. Zeno’s paradox is resolved by noting that the intervals traversed by Achilles are potential and unequal. Zeno gratuitously assumes that any finite interval is composed of an infinite number of points, whereas Zeno’s opponents, like Aristotle, take the interval as a whole to be conceptually prior to any divisions which we might make in it. Moreover, Zeno’s intervals, being unequal, add up to a merely finite distance. By contrast, in the case of an infinite past the intervals are actual and equal and add up to an infinite distance.
Craig makes two points here. First, against those who argument for actual infinities based on Zeno’s paradox, that there is a disanalogy between the infinities in Achilles’ case and the case with an infinite temporal past. Second, and more relevant, the Aristotelian solution is to take the whole to be conceptually prior to the parts. Think of a length of 1 meter. That meter is not composed of points; rather, the whole meter exists prior to the points, and any points within the meter are merely a result of our conceptual divisioning, our thinking of it. Furthermore, conceptual divisions don’t entail an actual infinity, because we can only go through the process of conceptually specifying a potential infinity.
What puzzled me was: How could this Aristotelian view be applied to presentism, given that, on presentism, only the present exists and the future and past do not exist. The question for Craig is: In the past 13.7 billion years, do we traverse an actual infinity of points? For the Aristotelian solution to work—for the whole to be prior to the parts—the whole has to exist. The Aristotelian solution couldn’t work because the only thing we could be conceptually dividing is the present instead of the whole 13.7 billion years. So, at this point, the Aristotelian solution does not seem to solve Zeno’s paradox applied to past time.
To see how Craig would reply, we need to go into his book A Tensed Theory of Time: A Critical Examination. A natural question arises for presentism: What is the extent of the present? Craig goes over three options: (1) instantaneous, (2) atomic, and (3) non-metric. I’ll go through each in turn.
An instantaneous present has been criticized “because a concrete object can no more exist with zero duration than with zero breadth and length” (Williams 1951). The idea is that it is puzzling how something with zero duration can exist. (Objectors think this isn’t problematic as they think that space is composed of an uncountably infinite number of extensionless points. The cosmological singularity, if real, would be an example of an extensionless point.)
Craig criticizes the instantaneous present view because of Zeno’s paradoxes of motion and plurality. Consider Zeno’s paradox of motion, given the continuity of time:
… let us suppose … that the basic parts of time are instants. In order for the present instant to elapse it must be succeeded by another. But there is no immediate successor to the present instant. Before the succeeding instant can become present, an infinite number of succeeding instants will have to become present first. … For no instant can immediately succeed the present. The present would therefore exist as the nunc stans of the classical doctrine of eternity, not the nunc movens of A-theoretic time. (Craig 2000, p.235-6)
and Zeno’s paradoxes of plurality:
If we conceive temporal becoming to proceed instant by instant, the length of time between some past event or moment and the present could never increase, since the lapse of durationless instants adds nothing to the interval between the past instant and the present instant. But then there is no “flow” of time at all, and we are left again with the nunc stans of the present instant, never able to recede into the past. The doctrine of the instantaneous present is thus incompatible with objective temporal becoming. (Craig 2000, p.236)
In sum, Craig sees two problems for instantaneous presents: (1) there cannot be ‘motion’, and (2) there cannot be duration since adding a series of zeros is still zero.
Consider how instantaneous presents affect the Kalam. Craig offers two philosophical arguments that the universe must have a beginning. The first argument argues against the metaphysical possibility of an actual infinite using thought experiments like Hilbert’s Hotel. The second argument grants the possibility of an actual infinite, but denies that an actual infinite can be formed by successive addition. (This second argument is dialectically stronger.) It is this second argument that seems to lead to problems for instantaneous presents. If Craig is right on his view of Zeno’s paradoxes, then not only can’t an infinite be formed by successive addition, but a finite can’t be formed either.
Alternatively, one might think of the present as having some minimal duration in time, called chronons. “One disturbing feature of such a model of temporal becoming, however, is that temporal becoming seems to be “jerky” rather than smooth (Craig 2000, p.242).”(Zeno’s stadium paradox is relevant here, but I’ll skip the details.)
The problem of jerkiness is enough for Craig to favor the next view.
We can maintain that the extent of the present depends upon the extent of the entity described as present. To quote again Andros Loizou: “… no event or state of affairs is ever present simpliciter—it is present by implicit or explicit reference to a kind of events or states of affairs, as when we speak of the present eclipse, or by reference to a time scale, as when we speak of the present hour or day, and so on.” … There is no such thing as “the present” simpliciter: it is always “the present ____,” where the blank is usually filled by a reference to some thing or event. The duration of the present will be as long or as short as the event or thing under discussion (italics mine). (Craig 2000, p.245)
Craig is saying that it makes no sense to speak of the present moment (the now), unless context is added. But surely our deciding to speak of the present hour in one context and the present day in another context does not affect the metaphysics of time: we don’t control what exists by deciding what to think. I think Craig would agree, but I don’t see how this odd view is not entailed by his non-metric view.
Craig brings up a worry about his non-metric view going back to Augustine.
The nerve of Augustine’s argument against some interval of positive duration’s being present is the assumption that in order to be present, the interval in question must be incapable of analysis into past, present, and future phases. But if what we have said so far is correct, this assumption is not incumbent upon the A-theorist. He may instead hold that an interval is present if any phase of it is present. (Craig 2000, p.247)
I share Augustine’s worry. The non-metric view entails that any interval can be present. Presentism is the view that only the present exists, but if the future and past can be in the present interval, then Craig’s view seems to be a quasi B-theory. On B-theory there is no privileged now, and all moments of time have equal ontological status, all moments are equally real. On the non-metric view, it seems the future and past can be said to exist in virtue of being contextually included in the present interval. Again, this seems to raise the same problem as before, where we can think things into existence.
What about the lower and upper limits on the “present ____?” As for lower limits:
… there need be no such minimum length or temporal duration because both space and time are potentially infinitely divisible. The duration stipulated to be present will be an arbitrary, finite duration centered on a conceptually specified instant (Craig 2000, p.246-7).
Here Craig is using the Aristotelian view applied to his non-metric view. Since, on the Aristotelian view, the whole is prior to the parts, and any parts are merely a result of our conceptualization, there won’t be a lower limit because we can always think of something smaller. Craig does not mention if there can be an upper limit on the duration of the present ____, and I don’t see how he could have a non-arbitrary upper limit. If this is right, nothing stops us from speaking about the present 13.7 billion years or the present actual infinity! So it seems one can adopt Craig’s own non-metric view and hold to actual infinities.
Stephen Puryear on Craig
Finally, Stephen Puryear (2014) has pointed out that Craig’s Aristotelian view can be equally used by the infinitist who believes in an actual infinite past, thus undermining the Kalam. The infinitist can say that the whole past infinite is prior to its parts, and since we can only conceptually divide a potential infinity there isn’t an actual infinity of events to traverse (even if there is an actual infinity in duration).
In addition, there seems to be a tension between the Aristotelian view and Craig’s argument for the impossibility of the formation of an actual infinite by successive addition—the stronger argument I was referring to earlier.
2.21 A collection formed by successive addition cannot be actually infinite.
2.22 The temporal series of past events is a collection formed by successive addition.
2.23 Therefore, the temporal series of past events cannot be actually infinite.
This argument does not seem relevant on the Aristotelian view. Given that the whole is prior to the parts, the duration of events does not consist of successive additions but conceptual divisions; successive additions presuppose that the parts are prior to the whole, contrary to the Aristotelian view.
This is not to say that there isn’t some mystery as to how an actual infinite duration can be traversed; rather, it’s that the non-metric view does not seem plausible, and that the Aristotelian view does not seem compatible with Craig’s view that the temporal series of past events is a collection formed by successive addition.
The other two options for presentism—the instantaneous and atomic presentist—seem more plausible to me, but I’ll leave that for another time.
Craig, William Lane, and James Porter Moreland. The Blackwell companion to natural theology. Vol. 49. John Wiley & Sons, 2012.
Craig, William Lane. The tenseless theory of time: A critical examination. Vol. 294. Springer Science & Business Media, 2000.
Puryear, Stephen. “Finitism and the Beginning of the Universe.” Australasian Journal of Philosophy 92.4 (2014): 619-629.
Williams, Donald C. “The myth of passage.” The Journal of Philosophy 48.15 (1951): 457-472.