The paradox of the Arrow and Aristotle’s solution

As citizens of the modern times, we understand motion as a result of inertia exerted upon that object that gives it the energy to move through space. However, that theory is more or less a book-keeping device to explain why motion take places, but it still cannot specifically clarify how things move. This same phenomenon has puzzled many scholars of ancient times, such as Zeno, who addressed four famous paradoxes concerning motion, with the most basic being the paradox of the Arrow. Aristotle, a famous Greek philosopher, attempted to provide a solution to this paradox but his solution was not completely satisfactory. This is because Aristotle did not directly solve Zeno’s paradox of the Arrow. Instead, he recreated a new set of conditions and assumptions that allows him to explain why the arrow can move over time.

First, Aristotle denounces Zeno’s assumption that the “now” is indivisible. In Book VI of the Physics, he explains that “parts of the now will be the past and part of it will be future” (234a16). To Aristotle, time is a continuum and that by definition means that there can never be an indivisible “now”. For the “now” by definition, means the time between the past and the future. The word “between” confirms the divisibility of the “now”, because “what is between limits in a continuum has the same name as the continuum itself” (234a10). This is contrary to what Zeno assumed. In his paradox of the Arrow, Zeno assumed that “now” is indivisible. So at each “now” during the arrow’s flight from the bow to the target, it is essentially at rest because nothing moves in a “now”. This, then, means that if you add up a series of “now” in which the arrow is at rest, then the arrow is still at rest and cannot be moving. This would contradict with the fact that locomotion exist and makes it difficult to explain how the arrow move from the bow to the target. Aristotle, by redefining the concept of “now”, has modified the most crucial element of this paradox and thus reconstructing the problem into a different one.

Next, Aristotle emphasizes that the arrow’s motion is a change. “Since every change is in time and there is no time in which change cannot occur” (234b20), it does not make sense that Zeno assumed that the arrow is at rest at that moment and no change could take place. Zeno’s logic does not work in this case because there is always the possibility that change can occur at any time. Hence, the argument that the arrow is completely at rest at a moment in time with absolutely no chance of moving and producing a change in space is invalid.

With that, Aristotle uses his theory of change to explain why it is “impossible for there to be a rest in the now” (234a31), which makes it impossible for the arrow to have a series of “now” in “at rest” position and generating no motion as Zeno claimed. Aristotle argues that something can only be considered to be at rest when it has the potential to move but is not moving. Potentiality and actuality only exist when there is a period of time over which the potentiality can be actualized. In the case of the arrow then, it cannot be at rest “now” if the “now” is indivisible because then it is impossible for the potentiality and actuality of the arrow to exist at the same time. Here, Zeno’s assumption of the arrow being at rest during the flight is rejected by Aristotle. Once again, this would only contribute to the explanation of the arrow’s motion over time; it does not solve the problem stated in Zeno’s paradox.

Finally, Aristotle draws the conclusion for the paradox of the Arrow after he has reconditioned the assumption of the problem, which is no longer the same problem that Zeno addressed. Based on the new assumptions, Aristotle explained that the arrow’s motion is the actualization of its potential. Before the arrow is shot, it has the potential to hit the target and as soon as it leaves the bow, that potential is being actualized. The time that it takes for the arrow to move is part of the actualization process and it is a period of continuous time rather than a series of indivisible instants. Hence motion exists as a continuous process of change in space over change in time. This conclusion fits reality because the new theory can now be applied to reality and it holds true that motion does exist. Nevertheless, it is not a direct solution to Zeno’s paradox of the arrow because we do not have evidence to prove whether time consist of indivisible instants or divisible time periods. This means that both Zeno’s and Aristotle’s assumption about the concept of “now” could be right or wrong and so the paradox remained unsolved.

In addition, Aristotle has only explained the “change in time” part of Zeno’s problem; he did not explain the other part about the “change in space”. Aristotle presented time and space as parallel continuums and briefly mentioned that an object moving through these two parallels will result in motion. However, this does not explain what cause an object to travel from one place to another over time. Therefore we cannot understand the arrow’s shift from the bow to the target. Motion in terms of change in space is not explained.

Overall, Aristotle did not provide a satisfactory solution to Zeno’s paradox. The paradox of the Arrow remains one of the most controversial and incomprehensible phenomenon until this day, over two millenniums later. Modern time’s scientists and philosophers are still struggling to clarify precisely how motion is created. Both Aristotle’s and Zeno’s work are still being studied and digested by many scholars in hope of strengthening that understanding of the connection between space, motion, matter, and time. Nonetheless, we are approaching closer and closer to the answer as more knowledge are gathered and more scientific tools are being developed. Perhaps with the increasing advancement in technology, we will soon arrive at the solution to Zeno’s paradox and enlighten ourselves with the wonders behind locomotion.