Zeno of Elea is an ancient Greek philosopher who was a student of Parmenides, a representative of the Elea school. He was born around 490 BC. e. in southern Italy, in the city of Elea.
What was Zeno famous for?
Zeno's arguments glorified this philosopher as a skilled polemicist in the spirit of sophistry. The content of the teachings of this thinker was considered identical to the ideas of Parmenides. The Elean school (Xenophanes, Parmenides, Zeno) is the forerunner of sophistry. Zeno was traditionally considered the only "disciple" of Parmenides (although Empedocles also called him "successor"). In an early dialogue called "Sophist," Aristotle called Zeno the "inventor of dialectics." He used the concept of "dialectics", most likely, in the meaning of evidence from some generally accepted premises. It was to him that Aristotle's own topic, Topeka, was dedicated.
In Fedra, Plato speaks of a mastery of the "art of word-writing" of the "Eleamic Palamede" (which means "clever inventor"). Plutarch writes about Zeno, using the terminology adopted to describe the sophist practice. He says that this philosopher was able to refute, leading to aporia through counterarguments. A hint that Zeno’s studies were sophisticated is the mention in the Alcibiades I dialogue that this philosopher took a high fee for training. Diogenes Laertius says that for the first time Zeno of Elea began to write dialogues. This thinker was also considered the teacher of Pericles, the famous politician of Athens.
Politics Zeno
You can find reports from doxographers that Zeno was involved in politics. For example, he took part in a conspiracy against Notarch, a tyrant (there are other options for his name), was arrested and tried to bite his ear off during interrogation. This story is set out by Diogenes according to Heraclides Lemb, who, in turn, refers to the book of the peripatetics of Satyr.
Many historians of antiquity reported persistence at the trial of this philosopher. So, according to Antisthenes of Rhodes, Zeno of Elea bit his tongue. Hermippus says that the philosopher was thrown into a stupa in which he was interpreted. This episode was subsequently very popular in the literature of antiquity. Mention is made of him by Plutarch of Heronias, Diodir of Sicily, Flavius Philostratus, Clement of Alexandria, Tertullian.
Zeno's works
Zeno of Elea was the author of the compositions Against Philosophers, Controversy, Interpretation of Empedocles, and On Nature. It is possible, however, that all of them, except for the "Interpretation of Empedocles," were actually variants of the name of one book. In Parmenides, Plato mentions an essay written by Zeno in order to ridicule the opponents of his teacher and to show that the assumption of movement and multitude leads to even more ridiculous conclusions than the recognition of a single being according to Parmenides. The argumentation of this philosopher is known in the presentation of later authors. This is Aristotle (the work "Physics"), as well as his commentators (for example, Simplicius).
Zeno's arguments
The main work of Zeno was composed, apparently, from a set of a number of arguments. Proof from the contrary reduced their logical form. This philosopher, defending the postulate of an immovable single being, which was put forward by the Elean school (the aporia of Zeno, according to a number of researchers, were created in order to support the teachings of Parmenides), sought to show that the assumption of the opposite thesis (on motion and multitude) certainly leads to absurdity, therefore, must be rejected by thinkers.
Zeno, obviously, followed the law of the “excluded third”: if one statement of the two opposite is false, the other is true. Today, the following two groups of arguments of this philosopher (the aporia of Zeno of Elea) are known: against the movement and against the multitude. There is also evidence of arguments against sensory perception and against space.
Zeno vs. Argument
Simplicius retained these arguments. He quotes Zeno in a commentary on Aristotle's Physics. Proclus says that the composition of the thinker we are interested in contained 40 such arguments. Five of them we will list.
- Defending his teacher, who was Parmenides, Zeno of Elea says that if there is a multitude, then, therefore, things must be both large and small: so small that they have no size at all, and so large that they are infinite.
The proof is as follows . A certain value should have the existing one. When added to something, it will increase it and decrease it, when taken away. But in order to be different from some other one, one should stand up from it, be at a certain distance. That is, a third will always be given between two beings, thanks to which they are different. It must also be different from another, etc. On the whole, the existing will be infinitely great, since it is the sum of things, of which there are an infinite number. The philosophy of the Elean school (Parmenides, Zeno, etc.) is based on this thought.
- If there are many, then things will be unlimited and limited.
Proof : if there are many, there are as many things as there are, no less and no more, that is, their number is limited. However, in this case there will always be other things between things, between which, in turn, there will be third, etc. 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 Parmenides (Elean school) is developing. Zeno supports her.
- If there is a multitude, then things must simultaneously be dissimilar and similar, which is impossible. According to Plato, this argument began the book of the philosopher of interest to us. This aporia suggests that the same thing is seen as similar to itself and different from others. In Plato, it is understood as paralogism, since disagreement and similarity are taken in different respects.
- We note an interesting argument against the place. Zeno said that if there is a place, then it must be in something, since this applies to everything. It follows that the place will also be in place. And so on ad infinitum. Conclusion: there is no place. Aristotle and his commentators attributed this argument to paralogisms. It is not true that “to be” means to be in a place, since in some place disembodied concepts do not exist.
- Against sensory perception, the argument is called Millet. If a single grain or its thousandth part does not make noise during a fall, how can it be mediated in a fall? If the medima of the grain produces noise, therefore, this should apply to one thousandth, which is not really the case. This argument touches on the problem of the threshold of perception of our senses, although it is formulated in terms of the whole and part. The paralogism in this formulation is that we are talking about "noise produced by a part", which is not really (according to Aristotle, it exists in possibility).
Arguments Against Movement
The four aporias of Zeno of Elea against time and movement, known by the Aristotelian Physics, as well as the commentaries on it by John Philopon and Simplicius, became most famous. The first two of them are based on the fact that a segment of any length can be represented as an infinite number of indivisible "places" (parts). It cannot be completed at the final time. The third and fourth aporia are based on the fact that time consists of indivisible parts.
"Dichotomy"
Consider the "Stage" argument ("Dichotomy" is another name). Before overcoming a certain distance, the moving body must first go through half a segment, and before it reaches half, it needs to go half a half, and so on to infinity, since any segment can be halved, no matter how small it is.
In other words, since motion is always carried out in space, and its continuum is considered as an infinite number of different segments, this is relevant, since any continuous quantity is divisible to infinity. Consequently, a moving body will have to go through the number of segments, which is infinite, in a finite time. This makes movement impossible.
Achilles
If there is movement, the fastest runner will never be able to catch up with the slowest one, since it is necessary for the catcher to reach the place where the runner started to move. Therefore, if necessary, the runner more slowly should always be slightly ahead.
Indeed, moving means moving from one point to another. From point A, fast Achilles begins to catch up with the turtle, which is currently at point B. First, he needs to go half the way, that is, the distance AA. When Achilles is at point AB, during the time he made the movement, the turtle will go a little further to the segment BBB. Then the runner who is in the middle of his path will need to reach point Bb. For this, it is necessary, in turn, to go half the distance A1Bb. When the athlete is halfway to this goal (A2), a turtle will crawl a little further. Etc. Zeno of Elea in both aporias suggests that the continuum divides to infinity, thinking that this infinity is actually existing.
"Arrow"
In fact, the flying arrow is at rest, Zeno of Elea believed. The philosophy of this scientist has always been justified, and this aporia is no exception. The proof is as follows: the arrow at each moment in time occupies some place that is equal to its volume (since the arrow would otherwise be "nowhere"). However, to occupy a place equal to oneself means to be at rest. From this we can conclude that one can think of movement only as the sum of various states of rest. This is impossible, since there is nothing out of nothing.
"Moving bodies"
If there is movement, you can notice the following. One of two quantities, which are equal and move at the same speed, will travel twice the distance in equal time, and not equal to the other.
This aporia has traditionally been clarified by drawing. Two equal objects move towards each other, which are indicated by letter symbols. They go along parallel paths and at the same time pass by the third subject, which is equal in size to them. Moving with the same speed, once past a resting one, and another - past a moving object, the same distance will be traveled simultaneously both for a period of time and for half of it. The indivisible moment in this case will be twice as large as himself. This is logically incorrect. It must be either divisible, or the indivisible part of some space must be divisible. Since Zeno does not allow either one or the other, he concludes therefore that movement cannot be thought without a contradiction. That is, it does not exist.
Conclusion from all aporias
The conclusion that was drawn from all the aporias formulated in support of the ideas of Parmenides by Zeno is that the movements that convince us of the existence of a lot of evidence of feelings disagree with the arguments of the mind, which do not contain contradictions in themselves, and therefore are true. In this case, reasoning and feelings based on them should be considered false.
Against whom were the aporia directed?
The only answer to the question against whom the aporia of Zeno were directed does not have. A point of view was expressed in the literature, according to which the arguments of this philosopher were directed against the supporters of the "mathematical atomism" of Pythagoras, who constructed physical bodies from geometric points and believed that time had an atomic structure. This view currently has no supporters.
In the ancient tradition, the assumption dating back to Plato that Zeno defended the ideas of his teacher was considered a sufficient explanation. His opponents were therefore all those who did not share the doctrine that the Elean school (Parmenides, Zeno) put forward, and adhered to evidence based on common sense feelings.
So, we talked about who Zeno of Elea is. His aporia were briefly examined. And today, discussions about the structure of movement, time and space are far from complete, so these interesting questions remain open.