Zeno of Elea. The aporia of Zeno of Elea. Eleatic school

Zeno of Elea is an ancient Greek philosopher who was a pupil of Parmenides, a representative of the Eleatic school. He was born about 490 BC. E. In Southern Italy, in the town of Eley.

What did Zeno become famous for?

Zeno's arguments glorified this philosopher as a skilful polemicist in the spirit of sophistry. The content of the teachings of this thinker was considered identical with the ideas of Parmenides. Eleatic school (Xenophanes, Parmenides, Zeno) is the forerunner of sophistry. Zeno was traditionally considered the only "disciple" of Parmenides (although Empedocles was also called his "successor"). In an early dialogue called "Sophist" Aristotle called "inventor of the dialectic" Zeno. He used the notion of "dialectics", most likely in the sense of proof from some generally accepted premises. It is he who is dedicated to Aristotle's own work "Topeka".

In the Phaedrus, Plato speaks of a perfectly mastered "art of speech" "Eleatic Palamedes" (which means "clever inventor"). Plutarch writes about Zeno, using the terminology used to describe sophist practice. He says that this philosopher was able to refute, leading to aporia through counterarguments. A hint that Zeno's studies were sophistical is the mention in the dialogue of Alcibiades I that this philosopher took a high fee for teaching. Diogenes Laertius says that for the first time the dialogues began to be written by Zeno of Elea. This thinker was also considered the teacher of Pericles, a prominent politician of Athens.

Zeno politics

You can find reports from Doxographers that Zeno was engaged in politics. For example, he took part in a conspiracy against Neharkh, a tyrant (there are other variants of his name), was arrested and tried to bite his ear off during an interrogation. This story is presented by Diogenes in Heraclida Lemba, who, in turn, refers to the book of the peripatetic of Satire.

Many historians of antiquity transmitted reports of perseverance at the trial of this philosopher. So, according to Antisthenes of Rhodes, Zeno Eleajsky bit off his tongue. Hermippe says that the philosopher was thrown into the mortar in which he was extinguished. This episode was subsequently very popular in the literature of antiquity. They mention Plutarch of Hieronea, Diodir of Sicily, Flavius of Philostratus, Clement of Alexandria, Tertullian.

Works of Zeno

Zeno Eleiski was the author of the works "Against Philosophers", "Disputes", "Interpretation of Empedocles" and "On Nature". It is possible, however, that all of them, in addition to the "Interpretation of Empedocles," were in fact versions of the title of one book. In Parmenides, Plato mentions the work written by Zeno in order to ridicule the opponents of his teacher and show that even more absurd conclusions lead to the assumption of movement and set than the recognition of a single being in Parmenides. The argument of this philosopher is known in the account of later authors. This is Aristotle (the work "Physics"), as well as his commentators (for example, Simplic).

Zeno's arguments

The main work of Zeno was composed, apparently, from a set of a number of arguments. To prove from the contrary their logical form was reduced. This philosopher, defending the postulate of the immovable single being that the Eleatic school put forward (Zenon's aporias, as some scholars believe, were created in order to support the teachings of Parmenides), sought to show that the assumption of the opposite thesis (about motion and plurality) The absurd, therefore, must be rejected by the thinkers.

Zeno obviously followed the law of the "excluded third": in the event that one statement from the two opposite is not true, the other is true. Today we know about the following two groups of arguments of this philosopher (the aporia of Zeno of Elea): against the movement and against the set. There is also evidence that there are arguments against sense perception and against the place.

Arguments of Zeno against the set

Simplica retained these arguments. He quotes Zeno in a commentary on Aristotle's "Physics." Proclus says that the composition of the thinker of interest to us contained 40 similar arguments. Five of them we list.

1. Defending his teacher, who was Parmenides, Zeno of Eleia says that if there is a set, then, therefore, things must be necessary and great and small: they are so small that they do not have a value at all, and are so great that they are infinite.
   
   The proof is as follows . A certain value should have an existing one. Being added to something, it will increase it and reduce it, being taken away. But in order to be different from some other, it is necessary to defend against it, to be at a certain distance. That is, there will always be a third between the two beings, through which they are different. It must also be different from the other, and so on. On the whole, everything will be infinitely great, since it is the sum of things that are infinite. The philosophy of the Eleatic school (Parmenides, Zeno, etc.) is based on this thought.
   
   
2. If there is a set, then things will be limitless and limited.
   
   Proof : if there is a set, there are as many things as there are of them, no less and no more, that is, their number is limited. However, in this case there will always be others between things, between which, in turn, are third, and so on. That is, their number will be infinite. Since the opposite is proved at the same time, the original postulate is incorrect. That is, the set does not exist. This is one of the main ideas that develops Parmenides (Eleatic school). Zeno supports it.
   
   
3. If there is a multitude, then things must be simultaneously incomparable and similar, which is impossible. According to Plato, this argument began the book of the philosopher of interest. This aporia assumes that one and the same thing is regarded as similar to itself and different from others. In Plato, it is understood as a paralogism, since incompetence and similarity are taken in different ways.
   
   
4. We note an interesting argument against the place. Zeno said that if there is a place, then it must be in something, since it refers to everything that exists. It follows that the place will also be in place. And so on ad infinitum. Conclusion: there is no place. This argument Aristotle and his commentators referred to the number of paralogisms. It is wrong that "to be" means "to be in place," since in some place there are no incorporeal concepts.
   
   
5. Against sensory perception, the argument is called "The millet grain". If one grain or its thousandth part does not make a noise when falling, how can it be mediated by it during the fall? If the grain mediom produces noise, therefore, this should apply to one-thousandth, which is not really the case. This argument touches upon the problem of the threshold of perception of our sense organs, although it is formulated in terms of the whole and part. Paralogism in this formulation lies in the fact that it is a "noise produced by a part", which is not in fact (according to Aristotle's remark, it exists in possibility).

Arguments Against Motion

The most famous were the four aporias of Zeno of Elea against time and movement, known from the Aristotelian "Physics", as well as the comments of John Philopon and Simplicius on it. The first two of them are based on the fact that an interval of any length can be represented as an infinite number of indivisible "places" (parts). It can not be passed at the end time. The third and fourth aporias are based on the fact that time consists of indivisible parts.

"Dichotomy"

Consider the argument "Stages" ("Dichotomy" - another name). Before overcoming a certain distance, the moving body must first pass half the segment, and before reaching half, it needs to go half way, and so on ad infinitum, since any segment can be divided in half, no matter how small it is.

In other words, since motion always takes place in space, and its continuum is considered as an infinite set of different segments, it is actual given, since any continuous quantity is infinitely divisible. Consequently, the moving body will have to go through a finite number of segments, which is infinite. This makes motion impossible.

"Achilles"

If there is movement, the fastest runner will never be able to catch up with the slowest, as it is necessary for the former catching up to reach the place where the runaway starts to move. Therefore, if necessary, the running slower should always be a bit ahead.

Indeed, moving means moving from one point to another. From point A, the fast Achilles begins to catch up with the turtle, which is currently in point B. First, it needs to go half way, that is, the distance AAh. When Achilles is at the AL, during the time he made the movement, the tortoise will pass a little farther into the segment BB. Then the runner, who is in the middle of his path, will have to reach the Bb. For this, it is necessary, in turn, to pass half the distance ABB. When the athlete is halfway to this goal (A2), a little further the turtle will crawl away. And so on. Zenon of Eleus in both aporias suggests that the continuum is divided to infinity, thinking as the actual existing this infinity.

"Arrow"

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In fact, the flying arrow rests, thought Zeno of Elea. The philosophy of this scientist has always had a justification, and this aporia is no exception. The proof is as follows: the arrow at each time takes a place that is equal to its volume (since the arrow would otherwise be "nowhere"). However, to occupy a place equal to yourself means to be alone. Hence we can conclude that one can think of motion only as a sum of different states of rest. This is impossible, because nothing happens from nothing.

"Moving bodies"

If there is movement, you can notice the following. One of the two quantities that are equal and move at the same speed, will pass in an equal time twice the distance, and not equal to the other.

This aporia was traditionally clarified with the help of a drawing. Towards each other two equal objects move, which are denoted by letter symbols. They go along parallel paths and pass at the same time past the third object, which is equal to them in magnitude. Moving at the same speed, one time past the resting, and the other - past the moving object, the same distance will be traversed simultaneously both for a period of time and for half of it. Indivisible moment in this case will be twice as much of himself. This is logically incorrect. It must be either divisible, or the indivisible part of some space must be divisible. Since Zeno admits neither of these things, he concludes therefore that the movement can not be thought without a contradiction. That is, it does not exist.

The conclusion from all the aporias

The conclusion that was drawn from all the aporias formulated in support of Parmenides Zenon's ideas is that those who convince us of the existence of the movement and the set of evidence of feelings disagree with the arguments of reason, which do not contain contradictions in themselves, and therefore are true. False in this case should be considered reasoning and feelings based on them.

Against whom were the aporias sent?

The only answer to the question, against whom Zeno's aporias were directed, does not. There was expressed in the literature the point of view on which the arguments of this philosopher were directed against the supporters of the "mathematical atomism" of Pythagoras, which physical bodies constructed from geometric points and believed that time has an atomic structure. At present, this view has no supporters.

It was believed in the ancient tradition of a sufficient explanation of the assumption that goes back to Plato, that Zeno defended the ideas of his teacher. Its opponents therefore were all those who did not share the teaching that the Eleatic school (Parmenides, Zeno) put forward, and adhered to evidence-based senses of common sense.

So, we talked about who Zeno of Eleia is. His aporias were briefly examined. And today, discussions about the structure of the movement, time and space are far from complete, so these interesting questions remain open.