The issue of time and (one of) Zeno's Paradox(es)

One of the problems with the whole ESS fiasco, and the so-called recovery of the historic doctrine of God by people like Reformed Baptist James Dolezal, is its uncritical appropriation of Aristotelianism as mediated by Thomas Aquinas. To put it bluntly, these "confessional scholars" are philosophically stuck in the 16th century. They are reasonably well-versed in the Scholastic literature during the Reformed and Post-Reformed period, but they ignore or downplay the reasons why philosophy has dumped Aristotelianism as a whole.

One major issue has to do with the problem of time. Time is something that is hard to grasp, only because we are creatures of time. How do we go about thinking about time when we are bound by time itself? There is no place whereby we can be "objective" about time and the passage of time. It seems prima facie that time progresses, does it not? We can conceive of time moving faster or slower, because time can appear to move faster or slower (even when it does not do so objectively) when we labor at things we enjoy or things we dread. But to conceive of a stoppage of time, or timelessness, or reversal of time, or time loops, all of these are conjectures not available to us except by extrapolation and guesswork. We can deal with it mathematically, but numbers are abstract things which we cannot conceived how it may or may not work out in real life.

One ancient paradox concerning the issue of time in general is Zeno's paradox of Achilles and the Hare. In this paradox, the hare is ahead of Achilles by a certain distance (let's say 1 meter). As they race, both Achilles and the hare moved a certain distance in a certain time. In order for Achilles to overtake the hare, he must first cover the distance from him to the initial point of the hare. But during that time, the hare would have moved a certain distance (e.g. 0.1m). Achilles would then still be behind the hare, and must now race to where the hare is currently at. But at distance 1.1m, the hare would have moved 0.01m which Achilles needs to cover, but then the hare would move 0.001m, and so on. The paradox here asserts that if motion is possible, then Achilles would need to cover an infinite series of distances in order to catch up and overtake the hare. Since it is not possible to cover an infinite series of motions, the fact that Achilles can actually overtake the hare suggests that motion and change does not truly exist—they are illusionary.

For those from a scientific background, the "solution" to Zeno's Paradox of Achilles and the hare seemed easy enough. After all, it is a mere addition of a set to infinity of (1 + 0.1 + 0.01 + 0.001 +...). Or rather it can be expressed as follows:

Therefore Achilles will pass the hare at distance 1-1/9m. There, problem solved, but has the paradox actually been resolved?

We must remember that the key point of the paradox is not that Achilles will not overtake the hare. Rather, the key point of the paradox is that true motion, true change, cannot exist. The argument is a philosophical reductio ad absurdum concerning the nature of motion and time. It is not an empirical question at all. Just as in Plato's Allegory of the Cave, just because something is empirically seen does not necessarily imply that what is seen and what is perceived is indicative of true reality. Zeno's paradox is a question on reality itself, not empirically how things work. One might as well "disprove" Zeno by merely arranging a race between Achilles and a hare and showing that Achilles does in fact overtake the hare, easily, and it would still prove nothing. Why is the overtaking not a mere illusion, and that actually change is not real, but everything merely exists? Already, in modern physics under a B-series interpretation of space-time, time itself is a dimension and therefore nothing really changes, since the 4-D tesseract of space-time is "fixed" (in a universe without any higher dimensional beings or gods/God), and therefore space-time is determined right from "the start."

Science therefore cannot address Zeno's paradox. Since it deals with empirical reality, it cannot, until and unless there is a way to get us time-bound creatures out of the dimension of space-time (and I do not mean tunneling from one point of space-time to another point in space-time, but to be independent of space-time altogether). So how then should we deal with this paradox, but by rational philosophical inquiry?

One way, the way I think would address this paradox, is to point out how, as Achilles reached the next place of the hare, the time taken for each part in the series gets shorter and shorter. Let's say Achilles took 1 second to reach the hare's first position. He will then take 0.1 seconds to reach the hare's second position, and 0.01 seconds to reach the hare's third position. One would get a decreasing infinite series for the time traveled for Achilles to overtake the hare, and therefore it seems that we will never reach the "point" in time whereby Achilles overtake the hare. However, since there are two infinite series of time and distance, dividing the two infinite series gives us a finite (non-serial) speed of 1 m/s. One can therefore assert that the "infinite" aspect of the paradox is illusionary, since motion in terms of speed is not an infinite series but a finite number. Therefore, following Aristotle, I would say that seeing motion as a continuum instead of moving from point to point in space-time would solve the paradox quite nicely.

However Zeno's paradox of Achilles and the hare is solved, Zeno's paradox (not by itself) points to an even deeper issue concerning the nature of time itself (and thus indirectly opens the paradox again to mystery). We talk about time as "here," "before," and "after," or "now," "yesterday," and "tomorrow." But what exactly is this thing called "now"? John McTaggart has given an argument why time itself is not real. This is reflected in Zeno's paradox as one considers the infinite series of temporal instances Achilles must cover to overtake the hare. So while we can perhaps prove that motion seems real (since speed is a finite non-serial number), how do we, or can we, prove the reality of time? And if time is not real, then space is not real and motion becomes a mere mathematical number depicting the relation of two unreal things.

As with time, thus goes the notion of "eternity." "Eternity" is defined as an "infinity" with regards to time. When we say God is "eternal," what we mean is that God is infinite with respects to time But what does this mean when the notion of "time" itself gets questioned?

To untangle all these will not be easy, and this article is not meant to give all the answers to these questions, although I have suggested a preliminary approach here. The main point of this post rather is to show, by appeal to Zeno's paradox of Achilles and the Hare, that issues concerning time and eternity are so much more complicated than our modern "confessional theologians" make it out to be. Adopting Thomism as orthodoxy is not a virtue but a step backward in the wrong direction. If we are to be interested in truth, then we should wrestle with the actual issues involved when we talk about terms like "time" and "eternity," or even "temporal attributes," instead of going back to the "Golden Age" of "Reformed Scholasticism," which definitely has its strengths but many weaknesses also, chief among them its wholesale embrace of Aristotelianism.