Aristotle's thoughts on Zeno's Arrow Argument as represented in Chapter 9 of Aristotle's
Physics: A Guided Study can be understood in such a way that it might not be "next door
to madness". In this chapter, Aristotle interprets Zeno's argument of the Flying Arrow
as "missing the mark". There are four premises for this argument, and in Aristotle's
opinion, premise three can be rejected. He does not believe that time is composed of
indivisible nows, which he proves with laws of science. However, by evaluating the
falsity of premise three, you will find that premises one and two are also false. Almost
all opinions can be argued, however, and by evaluating the philosophy of both men, many
points can be reached about the validity and soundness of the argument. Though, by
finding the premises false, the argument is not sound, and therefore, Zeno's argument
leaves much to be said.
Deciphering from what we know of the argument by what Aristotle tells us in Chapter 9,
the premises are sketched out:
1. Everything is at rest when at a place equal to it;
2. The Flying arrow is at rest when at a place equal to it;
3. Time is composed of indivisible nows (instants).
4. Everything that changes place is doing so in the now.
5. Conclusion: The flying arrow doesn't move.
According to Zeno, time is composed of many indivisible nows, or instants. Aristotle
disagrees, stating in line 210 that no magnitude, including time, is composed of
indivisible nows. Exactly how long is an instant? Is time finite? As you start
dividing time, the smaller you get, the less movement occurs. But even when you do
divide it smaller and smaller, is there not at least some small amount of movement
occurring? When will time get so small that movement does not occur? This is
Aristotle's reasoning: that time will never get to a "smallest" point, as length will
never have a "smallest" division. Therefore, he is rejecting the third premise, stating
that time is not composed of indivisible segments.
Zeno, however, feels that time can be divided into a "smallest" part. After all, in
physics, you can determine an object's instantaneous velocity or acceleration at a
specific point in its journey, at a specific time. Wouldn't this make time indivisible?
Velocity and acceleration are given to mean motion, which means the object is moving at
this specific point in time. Therefore, according to Aristotle, this paradox would not
be so if it were not taken that time were composed of nows.
By rejecting this premise, and reevaluating the argument, you will read that premise one
and two do not match anymore. When you find that nothing is ever at rest because time is
never standing still, then the Flying Arrow is never at rest. This means that premises
one and two are not true either, and this further complicates Zeno's argument.
The reasoning from his standpoint makes sense, but by rejecting one premise using
Aristotle's rationalizing, we have now rejected two more. Zeno's argument has fallen
apart. The arrow is moving, and by following plain rules of science, we have found this
to be true.
Zeno's argument, as outlined in Aristotle's studies, is perfectly valid. He states that
everything is at rest when at a place equal to it, which qualifies the arrow as a part of
everything. Therefore, the arrow would be at rest when at a place equal to it. If the
arrow is flying, then it is changing place, and everything that changes place is doing so
in the now, so the arrow is changing place in the now. If you use Zeno's reasoning that
time is composed of indivisible nows, you find that premise three is a true statement.
But considering we have found, according to the laws of physics, Aristotle's views are
correct, then the premise is false, and the argument is not sound. We have gone over why
Zeno's reasoning about indivisible time segments is inaccurate, hence this will be the
case.
According to Aristotle, Zeno's theories "go beyond perception and pay no attention to it,
on the grounds that one is obliged to follow where the argument leads...", and because
Zeno seems to hold these opinions, Aristotle finds him "next door to madness." It seems
to be that one is tempted to follow the argument, because without consulting the laws
that hold true for motion and time, the argument will seem to be logical. At this point
in evaluating his argument, you must think into exactly what Zeno is stating and the
opinions he is holding. Certainly this is what Aristotle did, and what seems to be the
correct idea, for he has found the faults in Zeno's argument.
According to these points, both Zeno and Aristotle had the right ideas when formulating
their arguments. Zeno seemed to be neglecting many laws of science, and although
Aristotle corrected him on many of these points, he did not seem to prove him "next door
to madness", as he states in Gen/Corr 325a12-17. These seem to be points that Zeno had
very different opinions on, and even though they may be wrong, they do not seem to be so
inappropriate when you see where his argument leads, and where he wished it to go. He
had another way of interpreting what he saw. Zeno had a valid argument, we would have to
agree, but the soundness did "miss the mark" by just a bit. But this only rings true if
you are obliged to "follow where the argument leads".
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