Table of contents:
- What made Zeno famous?
- Engaging in Zeno's politics
- Zeno's writings
- Zeno's Arguments
- Zeno's arguments against the multitude
- Arguments against the move
- Moving bodies
- Conclusion from all aporias
- Against whom were the aporias directed?
Zeno of Elea - 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 made Zeno famous?
Zeno's arguments glorified this philosopher as a skilled polemist in the spirit of sophistry. The content of the teachings of this thinker was considered identical to the ideas of Parmenides. The Eleatic school (Xenophanes, Parmenides, Zeno) is the forerunner of sophistry. Zeno has traditionally been regarded as the only "disciple" of Parmenides (although Empedocles has also been called his "successor"). In an early dialogue called The Sophist, Aristotle called Zeno the "inventor of the dialectic." He used the concept of "dialectic", most likely in the sense of proof from some generally accepted premises. It is to him that Aristotle's own work "Topeka" is dedicated.
In "Phaedra" Plato speaks of the "Eleatic Palamedes" (which means "clever inventor"), who is fluent in "the art of debating". Plutarch writes about Zeno using the terminology accepted to describe sophistic practice. He says that this philosopherhe knew how to refute, leading to aporia through counterarguments. A hint that Zeno's studies were of a sophistical nature is the mention in the dialogue "Alcibiades I" that this philosopher took high fees for education. 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.
Engaging in Zeno's politics
You can find reports from doxographers that Zeno was involved in politics. For example, he took part in a conspiracy against Nearchus, a tyrant (there are other variants of his name), was arrested and tried to bite off his ear during interrogation. This story is told by Diogenes after Heraclides Lembu, who, in turn, refers to the book of the Peripatetic Satire.
Many historians of antiquity relayed reports of steadfastness at this philosopher's trial. So, according to Antisthenes of Rhodes, Zeno of Elea bit off his tongue. Hermippus says that the philosopher was thrown into a mortar, in which he was pounded. This episode was subsequently very popular in the literature of antiquity. Plutarch of Chaeronea, Diodirus of Sicily, Flavius Philostratus, Clement of Alexandria, Tertullian mention him.
Zeno of Elea was the author of the works "Against the Philosophers", "Disputes", "The Interpretation of Empedocles" and "On Nature". It is possible, however, that all of them, with the exception of the Commentaries of Empedocles, were in fact variants of the title of the same book. In "Parmenides" Platomentions a work written by Zeno in order to ridicule the opponents of his teacher and to show that the assumption of movement and plurality leads to even more absurd conclusions than the recognition of a single being according to Parmenides. The argument of this philosopher is known in the presentation of later authors. This is Aristotle (composition "Physics"), as well as his commentators (for example, Simplicius).
Zeno's main work was composed, apparently, from a set of a number of arguments. Their logical form was reduced to proof by contradiction. This philosopher, defending the postulate of a fixed unified being, which was put forward by the Elea school (Zeno's aporias, 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 (about movement and multitude) inevitably leads to absurdity, therefore, must be rejected by thinkers.
Zeno, obviously, followed the law of the "excluded middle": if one of the two opposite statements is false, the other is true. Today we know about the following two groups of arguments of this philosopher (the aporias of Zeno of Elea): against movement and against multitude. There is also evidence that there are arguments against sense perception and against place.
Zeno's arguments against the multitude
Simplicius preserved these arguments. He quotes Zeno in a commentary on Aristotle's Physics. Proclus says that the workthe thinker we are interested in contained 40 such arguments. We list five of them.
Defending his teacher, who was Parmenides, Zeno of Elea says that if there is a multitude, then, consequently, things must necessarily be both great and small: so small that they have no size at all, and so great which are infinite.
The proof is as follows. Existing must have some value. When added to something, it will increase it and reduce it when taken away. But in order to be different from some other, one must be separated from it, to 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, and so on. In general, the existent will be infinitely great, since it is the sum of things, of which there is an infinite number. The philosophy of the Elean school (Parmenides, Zeno, etc.) is based on this thought.
If there is a set, then things will be both unlimited and limited.
Proof: if there is a set, there are as many things as they are, 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, there are third ones, etc. That is, their number will be infinite. Since the opposite is proved at the same time, the original postulate is wrong. That is, there is no set. This is one of the main ideas developed by Parmenides (Eleatic school). Zeno supports her.
If there is a set, then thingsmust be similar and similar at the same time, which is impossible. According to Plato, the book of the philosopher we are interested in began with this argument. This aporia suggests that the same thing is seen as similar to itself and different from others. In Plato, it is understood as a paralogism, since unlikeness and likeness are taken in different ways.
- Note an interesting argument against space. Zeno said that if there is a place, then it must be in something, since this applies to everything that exists. It follows that the place will also be in the place. And so on ad infinitum. Conclusion: there is no place. Aristotle and his commentators referred this argument to the number of paralogisms. It is wrong that "to be" means "to be in a place", since in some place there are no incorporeal concepts.
- An argument against sensory perception is called "Millet Grain". If one grain, or a thousandth of it, does not make noise when it falls, how can its copper do when it falls? If the medimna of the grain produces noise, therefore, this must also apply to one thousandth, which is not 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 the part. The paralogism in this formulation lies in the fact that we are talking about "the noise produced by the part", which does not exist in reality (according to Aristotle, it exists in the possibility).
Arguments against the move
The four aporias of Zeno of Elea againsttime and motion, known from the Aristotelian "Physics", as well as comments on it by John Philopon and Simplicius. 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 end time. The third and fourth aporias are based on the fact that time also consists of indivisible parts.
Consider the "Stages" argument ("Dichotomy" is another name). Before reaching a certain distance, a moving body must first cover half of the segment, and before reaching half, it needs to cover half of the half, and so on ad infinitum, since any segment can be divided in half, no matter how small.
In other words, since the movement is always carried out in space, and its continuum is considered as an infinite number of different segments, it is actually given, since any continuous value is divisible to infinity. Consequently, a moving body will have to go through a number of segments in a finite time, which is infinite. This makes movement impossible.
If there is movement, the fastest runner can never catch up with the slowest runner, because it is necessary that the runner first reaches the place from which the evader began to move. Therefore, by necessity, the one who runs more slowly must always be a littleahead.
Indeed, to move means to move from one point to another. From point A, fast Achilles begins to catch up with the tortoise, which is currently at point B. First, he needs to go half the way, that is, the distance AAB. When Achilles is at point AB, during the time that he made the movement, the tortoise will go a little further to the segment BB. Then the runner, who is in the middle of his path, will need to reach the point Bb. To do this, it is necessary, in turn, to cover half the distance A1Bb. When the athlete is halfway to this goal (A2), the turtle will crawl a little further. Etc. Zeno of Elea in both aporias assumes that the continuum is divisible to infinity, thinking of this infinity as actually existing.
In fact, the flying arrow is at rest, Zeno of Elea believed. The philosophy of this scientist has always had a rationale, and this aporia is no exception. The proof is as follows: the arrow at each moment of time occupies a certain place, which 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 it is possible to think of motion only as a sum of various states of rest. This is impossible, because nothing comes from nothing.
If there is movement, you can notice the following. One of two quantities that are equal and move at the same speed will pass in equal time twice as muchdistance, not equal to the other.
This aporia was traditionally clarified with the help of a drawing. Two equal objects are moving towards each other, which are indicated by letter symbols. They go along parallel paths and at the same time pass by a third object, which is equal in size to them. Moving at the same time with the same speed, once past a resting, and the other past a moving object, the same distance will be covered simultaneously in a period of time and in half of it. The indivisible moment will then be twice as large as itself. This is logically incorrect. It must either be divisible, or an indivisible part of some space must be divisible. Since Zeno admits neither of these, he therefore concludes that motion cannot be conceived without the appearance of 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 convincing us of the existence of movement and a lot of evidence of feelings diverge from the arguments of reason, 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 aporias directed?
There is no single answer to the question against whom Zeno's aporias were directed. A point of view was expressed in the literature, according to which the arguments of this philosopher were directed against the supporters of the "mathematicalatomism" of Pythagoras, who constructed physical bodies from geometric points and believed that time has an atomic structure. This view currently has no supporters.
It was considered in the ancient tradition as a sufficient explanation for the assumption, dating back to Plato, that Zeno defended the ideas of his teacher. His opponents, therefore, were all who did not share the doctrine that the Eleatic school put forward (Parmenides, Zeno), and adhered to common sense based on the evidence of feelings.
So, we talked about who Zeno of Elea is. His aporias were briefly considered. And today, discussions about the structure of movement, time and space are far from over, so these interesting questions remain open.