Pre-Socratic philosopher Zeno, who was 20 years older than Socrates, was born around 490 BC according to Plato’s Parmenides. Again according to Plato, Parmenides and Zena were lovers. While Parmenides was attacking Heraclitus’ philosophy by rejecting pluralism and the reality of any kind of change and arguing that all is one indivisible, unchanging reality, and any appearances to the contrary are illusions, to be dispelled by reason and revelation, Zena was defending his lover with his paradoxes against technical doctrine of the Pythagoreans.

Zena wrote a book of paradoxes dedicated to defend Parmenides’ philosophy, where he was opposing common-sense notions of plurality and motion. However neither this book nor his 40 paradoxes about plurality have survived. Four of his surviving paradoxes, which are the main topic of this essay, have kept us paralyzed for more than two and a half millenniums.

This essay aims to show absurdities of the four paradoxes “Dichotomy, Achilles, Arrow and Stadium” which on the other hand have been forcing us to question and find the truth about time, space, finity, infinity, velocity, since Zena wrote them.

According to Dichotomy, a moving object first has to complete half way of its goal. When it completes the first half then it hast to complete the half of the remaining distance in order to be able to reach the end. However in order to be able to get the end it has to complete the other half of the remaining space and that continues infinitely…Therefore says Zena, the moving object can never complete infinite number of task in finite time.

However one can find it hard not to think not only twice but thousand times before criticising Zena’s dichotomy paradox only if one exclude the time from it. Of course that does not mean we should deny significance of the paradox which made us work hard to define finity, infinity, time and space for two and a half millenniums. Have we managed to define them yet? No! But we defined the relativities between them and we are still working on them.

Zena seems to miss one point that is the existence of every infinitesimal part of the finite space in infinitely finite time. Zena mistakenly separates the time from space which is not possible. When the moving object moves in space it also move in time. Therefore as soon as Zena divides the space he also divides the time, which takes the object to move from one point to another.(But he deliberately does not divide the time.) If the distance gets shorter and shorter every time he divides it, time also gets shorter and shorter. In this case the answer to Zena’s paradoxes is that time is as divisible and infinite as space is. Therefore the moving object can complete infinitely finite task in infinitely finite time.

In Achilles paradox, Zena gives us a scenario where Achilles and tortoise are in a race. The slow runner tortoise begins the race before the fast runner Achilles who has to catch up and surpass his slow rival. However he never manages and he can never manage, says Zena. How? Well, if Achilles really wants to beat his rival, he needs to get to the point where tortoise started to run. But by the time, please pay special attention to the word time here, yes by the time he catches up with tortoise, slow runner tortoise is no longer at the same point waiting for Achilles to catch him, he has moved. And when Achilles reaches where tortoise has moved, tortoise has moved again. That repeats infinitely and Achilles never overtakes the tortoise as he has infinitely has to catch up with tortoise in finite space of race. Therefore says Zena, fast runner never gets ahead of slow runner in this race. How? Shouldn’t we ask why Zena decides to break up Achilles’ motion as soon as he gets to the point where tortoise has started? Why does he reduce the velocity of Achilles’ as soon as he gets to that point? If velocity is the division of finite given space by finite given time, and if Achilles’ velocity is already higher, shouldn’t dividing the space cause Achilles to take even shorter time to overtake tortoise? And again the distance between runners gets shorter and shorter infinitely as in dichotomy.

Although this paradox is identical to dichotomy in the way it infinitely divides the space between runners, this time Zena makes us search and find velocity without, maybe deliberately, mentioning the word velocity.

Zena denies the existence of motion more straightforwardly in arrow paradox. Time is composed of infinite moments (nows).An arrow occupies a space which is equal to its size at any moment of its motion. This is by definition what it means to be at rest. Therefore, the arrow does not move since it is at any given moment at rest. How?

In order to be able to say that say that an object say Zena’s arrow is in motion first of all we have to be given finite distance which has start and end point and where we can observe the object’s motion. It is indisputable that time is composed of nows , in fact this not a news or new information which Zena can use to support his assumption of motionlessness. And no object can occupy any more space than its size. This is neither a news, nor is it a piece of information which Zena can build his assumption on. There is no object on earth which can occupy any more space than its size. However that does not mean that no object can move. In order to be able to say that Zean needs more evidence than this foggy premises which can satisfy Velocity= Distance/time. And no one ever needs more information like length or weight of the object to satisfy this formula.

Therefore I can clearly say that Zena’s assumption of motionlessness of arrow is based on not even false but irrelevant premises which have no connection with his conclusion at all. The arrow moves in given finite of infinite time and space like every other moving object.

And Finally Zena’s stadium paradox where this time he divides the task by two and says half the time is equal to its double.

According to Aristotle’s interpretation of the argument, there are say four stable bodies called As.And four moving bodies which move in opposite direction in a stadium, called Bs and Cs. When Bs and Cs start moving in the same speed in opposite direction they reach the end of As at the same time. And the question is this how can Bs traverse only two As which are equal to Cs in size, but traverse 4 Cs, which are moving in opposite direction to Bs and equal in size to Bs, at the same time? This question includes its answer without forcing the reader to read between lines.What can be more expected than this? Because Bs moved only distance equals to 2 As and the other 2Cs which equal to As in size, were passed by Cs themselves. In other words , Bc and Cs shared the task. Since their speed and the distance they had move were equal, there is only one thing here which is the task that is equally shared.

Does Zena really succeed to show us that all is one? No! Why? Because dividing any finite object in to infinite part doesn’t mean that there is not infinite number of the same object. I can divide a piece of finite iron into infinite parts but that doesn’t mean that all infinite amount of iron on earth, which we cannot even manage to add up to see their length, is one.