Zeno from Elea. Zeno of Elea, ancient Greek philosopher: biography, main ideas

Zeno the philosopher (5th century BC) - an Elean, the son of Televtogor, a favorite student of Parmenides, confirmed his doctrine of the unity and immobility of being with dialectical arguments, showing that the usual ideas about plurality and movement that were contrary to him disintegrate in internal contradictions. Aristotle calls him the inventor of dialectics. Here is the essence of Z.'s main arguments:
Against plurality: if everything consists of many things, or if the existent is really divided into separate parts, then each of these parts turns out to be both infinitely small and infinitely great at the same time, because, having an infinite set of all other parts outside of itself, it constitutes an infinitely small particle of everything, but, on the other hand, being itself composed of an infinite number of particles (being divisible to infinity), it represents an infinitely large quantity. So, it turns out if we recognize all particles as having magnitude and divisible; if, however, it is admitted that the many, that is, the particles of everything, have no magnitude and are therefore indivisible, then a new contradiction emerges: everything turns out to be equal to nothing. Indeed, that which has no magnitude cannot, by joining another, increase it (zero is not a term); therefore, everything that consists of indivisible, devoid of magnitude, itself has no magnitude, or is (materially) nothing. According to Hegel, "Zeno's dialectic of matter has not been refuted to this day" (see Matter).

B) Against the movement.

In order to pass through a certain space, a moving body must first pass through half of this space, and for this, first another half of this half, and so on ad infinitum, i.e., it will never move; on this basis, swift-footed Achilles can never overtake a slow tortoise. Another argument: a moving body, for example. a flying arrow, at each moment of movement, occupies a certain space, i.e., is at rest, and thus, the entire movement is decomposed into moments of rest, therefore, it represents an internal contradiction (since it is impossible to make a positive value from the zeros of the movement). Z.'s arguments are not the essence of sophism, but point to real contradictions in the concept of matter, space and time, as consisting of really separate parts; it was precisely this concept that Z. wanted to refute. On the positive doctrine that he proved in this negative way, see Parmenides, the Eleatic school; literature there.

encyclopedic Dictionary F. Brockhaus and I.A. Efron. - St. Petersburg: Brockhaus-Efron. 1890-1907 .

See what "Zeno the Philosopher" is in other dictionaries:

Zeno- Zeno, son of Mnases (or Demeus), from Kitia, in Cyprus, a Greek city with Phoenician settlers. He had a crooked neck (says Timothy of Athens in the Biographies), and he himself, according to Apollonius of Tyre, was thin, rather ... ... About the life, teachings and sayings of famous philosophers

- (lived c. 150 BC) Epicurean philosopher; stood at the head of the school in Athens (between 100 - 78 BC). Prod. it has not been preserved. Some of the Op. Cicero, who was his listener, "De natura Deorum", as well as much ... Philosophical Encyclopedia

Thinker, sage, wise man, cultural philosopher, thinker, wise man; Zeno, Kant, Pythagoras, Xenophanes, Spinoza, Schelling, Descartes, Schopenhauer, Aenesidemus, Bacon, Democritus, Hume, Galileo, Leibniz, Menippus, Helvetius, Locke, Chrysippus, Epicurus, Heraclitus, ... ... Synonym dictionary

Zeno of Elea, Lucania Zeno of Elea (ancient Greek Ζήνων ὁ Ἐλεάτης) (c. 490 BC c. 430 BC), ancient Greek philosopher, student of Parmenides. Born in Elea. Famous for its aporias (paradoxes), proving the impossibility of movement, ... ... Wikipedia

- (born c. 490, Elea, Lower Italy - d. 430 BC) the first ancient Greek. philosopher who wrote prose works. and who used the methods of indirect evidence, for which he was called the "inventor of dialectics", became famous for his paradoxes. ... ... Philosophical Encyclopedia

- (c. 336 264 BC) philosopher, founder of the Stoic school, born in Cyprus, studied and taught in Athens School teachers go crazy because they are always messing with boys. Only the one who constantly uses it has virtue. Everything… … Consolidated encyclopedia of aphorisms

ZENON (Ζήνων) from Elea (Southern Italy; according to Apollodorus, acme 464 461 BC; according to Plato, “Parmenides” 127e, c. 450, which is less likely) an ancient Greek philosopher, a representative of the Elea school, a student of Parmenides. In the dialogue “Sophist” (fr. 1 Ross) ... ... Philosophical Encyclopedia

ZENON Dictionary-reference to Ancient Greece and Rome, according to mythology

ZENON- (c. 336 264 BC) Greek philosopher, founder of Stoicism. Born in Kition, Cyprus. Organized his philosophical school ca. 300 BC e. Developed the basic principles of stoicism, namely: 1. The concept of space as a rational organism. 2.… … List of ancient Greek names

As you remember from the last lesson, Parmenides, the founder of the Eleatic school, came to conclusions that contradicted common sense. Naturally, this point of view could not but arouse objections. And these objections demanded a stricter and more detailed defense of Parmenides' propositions. His student Zeno undertook the development of such an argument.

Zeno (c. 490 - c. 430) also from Elea. Sources say that he was the adopted son of Parmenides. In general, there is very little information about his life. It is only known that he was a politician, a supporter of democracy and participated in the fight against the tyrant Nearchus. His struggle ended in failure. Zeno himself was captured, he was tortured for a long time so that he would betray his accomplices. Zeno, as Diogenes Laertes points out, pretended to succumb to torture and asked the tyrant, who was present during the torture, to come closer to him. The tyrant went up to Zeno, brought his ear to his mouth, Zenon grabbed the ear of the tyrant and held until the servants stabbed Zeno. According to others, Zeno bit off his tongue and spat it in the tyrant's face. And then he was crushed in a mortar into small pieces.

Zeno was a direct student of Parmenides. And if Parmenides proved his position directly, then Zeno resorted to another method of proof - from the contrary. Apparently, therefore, Aristotle considers Zeno the first initiator of dialectics. In ancient Greece, dialectics was understood not as it is now, not the doctrine of the struggle of opposites, not the doctrine of development, but the art of dispute (from the Greek words lego - I say, duo - two, that is, a conversation between two, a conversation). Indeed, each of you will agree that in a dispute there are often decisive arguments that prove the inconsistency of the point of view of the interlocutor from the inside. In the same way, Zeno tried to prove the validity of his teacher's statements about being, showing that the opposite point of view is absurd.

Zeno's argument boils down to this: assuming that movement and a plurality of things exist, we come to absurd conclusions. These reasonings of his were called "aporia"; in total there are about 47 of them. Only a few, about 9, have come down to us, and about 5 aporias are most often mentioned due to their unusual, paradoxical nature.

Aporias are divided into two groups. The first group are aporias against plurality, and the second - against movement. Arguing against the plurality of things, Zeno says: let us assume that beings are indeed plural, i.e. existence is made up of parts. If there are parts, then we can divide the existing into even smaller parts, and those, in turn, into even smaller ones, and so on. If we can divide them to infinity, then in the end we get that the existent consists of elements that are further indivisible. And if the further indivisible element is multiplied by infinity, then we get an infinite, infinitely large body, i.e. each body turns out to be infinite, which is impossible. And if, on the other hand, we divide to infinity, not to some definite, further indivisible things, not to atoms, but to infinity, then in the end we will decompose everything into non-existence, and non-existence does not exist, how about this the word itself says. Therefore, in any case, beings have no parts, i.e. there is no plurality of things, since it turns out that every quantity is either infinitely large or infinitely small. There can be no final thing. Aporia about space: if a thing exists, then it exists in space. This space exists, respectively, in another space. This space, in turn, exists in a third space, and so on. to infinity. But it is impossible to accept an infinite number of spaces. Therefore, it cannot be said that a thing exists in space.

However, it was not his aporias about the plurality of things that received the greatest fame, but his aporias against movement. There are four of these aporias, and each of them has its own title. These are Dichotomy, Achilles and the Tortoise, Arrow and Stages. The aporia "Dichotomy" says the following: the movement can never begin. Let's say the body needs to go some way. In order for him to reach the end, he must first reach half, and for this he must reach a quarter. To get to a quarter, you need to get to an eighth of the way, and so on. Dividing all time to infinity, we get that the body can neither reach the end nor even begin. After all, in a finite time it is impossible to go through an infinite section of the path, that is, a section consisting of an infinite number of points (cf. the aporia against multiplicity).

Another aporia - "Achilles and the tortoise", perhaps the most paradoxical, also indicates that movement does not exist. Assume that there is movement, and imagine that the fastest runner in Greece, Achilles, is trying to catch up with the tortoise. Achilles runs after the tortoise and comes to the point where the tortoise was at the moment he started moving. But the tortoise also traveled some distance during this time. Achilles again comes to the point where the tortoise was, but it goes even further. Achilles comes to this point, but the tortoise again moves forward, and so on. Achilles will never catch up with the tortoise in the end. He will always strive to the point where the turtle has just been, and she will go at a slower speed, but will leave.

The third aporia - "Arrow" claims that since a flying arrow at each moment of time occupies some place in space, i.e. at each moment of time rests in some place in space, then the state of motion is a change in states of rest. Therefore, we can say that during the entire flight the arrow rested, and did not fly.

And the fourth aporia - "Stages". Imagine that there are three bodies of the same length. One body moves in one direction, another in the other, and the third is at rest. For the same time, the moving bodies covered some distance, i.e. each point of the first body has traveled one distance relative to the stationary one and twice the distance relative to the moving one. That is, the body moves simultaneously with two different speeds. But this cannot be.

It is difficult to count how many works have been written on the theme of Zeno's aporias. Who has not thought about them! Indeed, Zeno groped for moments in our thinking that show the inconsistency of thinking about the sensible world. So the knowledge of the sensory world with the help of concepts is by no means so simple and not always an objective process. We know the refutation of aporias by Diogenes of Sinop, who did not say anything, but simply got up and walked around the room, showing that all arguments break down on this sensual indisputable fact. Pushkin wrote the following poem on this occasion:

“There is no movement,” said the bearded sage, The other was silent and began to walk before him. He could not have objected more strongly; All praised the convoluted answer.

But, gentlemen, this amusing case Another example gives me a reminder: After all, every day the Sun walks before us, However, the stubborn Galileo is right.

Thus, our Russian genius agrees with Zeno in the opinion that feelings should not be trusted in everything. Reason, no matter how paradoxical its statements (that the Earth moves, for a man of the Middle Ages was also a paradoxical statement), often turns out to be more right than feelings. And Zeno's conclusion about the paradox of movement is also not without foundation and has the deepest philosophical meaning. But do they have a physical meaning? If we divide a thing to infinity, then we will eventually go to the area of ​​the microcosm, in which other physical laws, other systems of measurements operate. And at very small distances, at very low speeds, the Heisenberg uncertainty relation works in quantum mechanics: Dp ´ Dq< ћ, где ћ - постоянная Планка. Если тело покоится, т.е. Dp=0, то Dq=¥, т.е границы тела размываются, что означает, что абсолютный покой невозможен. Таким образом, не зная квантовой механики, Зенон показал, что покой и движение противоречивы.

Regarding the aporia "Arrow", Aristotle made the following remark: Zeno unlawfully stops time. He says that there is a moment of time, but a moment of time does not exist, you can only talk about a period of time. But the concept of a moment of time, nevertheless, is still widely used, including in the exact sciences. Consequently, Zeno's aporia "Arrow" also finds real contradictions in knowledge.

Bibliographic description:
Solopova M.A. ZENON OF ELEA // Antique Philosophy: Encyclopedic Dictionary. M.: Progress-Tradition, 2008. S. 386-390.

ZENON OF ELEA (Ζήνων ὁ ’Ελεάτης ) (born c. 490 BC), other Greek. philosopher, representative Eleatic school, student Parmenides. Born in the city of Elea in Yuzhn. Italy. According to Apollodorus, acme 464–461 BC According to Plato's description in the dialogue "Parmenides" - c. 449: (cf.: Parm. 127b: "Parmenides was already very old ... he was about sixty-five. Zeno was then about forty"; the young Socrates, presumably not younger than twenty years old, participates in a conversation with them, - hence the date). Plato depicts Zeno as the famous author of the collection of arguments he compiled "in his youth" (Parm. 128d6-7) to defend the teachings of Parmenides.

Zeno's arguments glorified him as a skillful polemist in the spirit of the fashionable for Greece ser. 5th c. sophistry. The content of his teachings was supposed to be identical to the teachings of Parmenides, whose only "disciple" (μαθητής) of which he was traditionally considered (Empedocles's "successor" was also called). Aristotle, in his early dialogue The Sophist, called Zeno "the inventor of the dialectic" (Arist., fr. 1 Rose), using the term dialectics, probably in the sense of the art of proof from conventional premises, to which his own Op. Topeka. Plato in the Phaedrus speaks of the "Eleatic Palamedes" (a synonym for a clever inventor), who perfectly mastered the "art of debating" (ἀντιλογική) (Phaedr. 261d). Plutarch writes about Zeno using the terminology adopted to describe the practice of the sophists (ἔλεγξις, ἀντιλογία): "he knew how to skillfully refute, leading through counterarguments to aporia in reasoning." A hint of the sophistical nature of Zeno's studies is the mention in the Platonic dialogue "Alcibiades I" that he took a high tuition fee (Plat. Alc. I, 119a). Diogenes Laertius translates the opinion that “Zeno of Elea was the first to write dialogues” (D.L. III 48), probably derived from the opinion about Zeno as the inventor of dialectics (see above). Finally, Zeno was considered the teacher of the famous Athenian politician Pericles (Plut. Pericl. 4, 5).

Doxographers have reports of Zeno himself engaging in politics (D.L. IX 25 = DK29 A1): he participated in a conspiracy against the tyrant Nearchus (there are other variants of names), was arrested and, during interrogation, tried to bite off the ear of the tyrant (Diogenes recounts this story according to Heraclid Lembu, and that, in turn, according to the book of the peripatetic Satire). Messages about the firmness of Z. at the trial were transmitted by many ancient historians. Antisthenes of Rhodes reports that Z. bit off his tongue (FGrH III B, n ° 508, fr. 11), Hermippus - that Zeno was thrown into a mortar and crushed in it (FHistGr, fr. 30). Subsequently, this episode was consistently popular in ancient literature (it is mentioned by Diodorus Siculus, Plutarch of Chaeronea, Clement of Alexandria, Flavius ​​Philostratus, see A6–9 DK, and even Tertullian, A19).

Compositions. According to the Court, Z. was the author of Op. "Spores" (εριδας), "against philosophers" (πρὸς τοὺς φιλοσόφοςς), "On nature" (περὶ φύσεως) and "Interpretation of the EmPedocla" ('εξήγησις τῶν' εμπεδοκλέοςς), - it is possible that the first three in fact represent are variants of the titles of one composition; the last work called by the Court is not known from other sources. Plato in "Parmenides" mentions one work (τὸ γράμμα) by Z., written with the aim of "ridiculing" the opponents of Parmenides and showing that the assumption of plurality and movement leads to "even more ridiculous conclusions" than the assumption of a single being. Zeno's argument is known in the retelling of later authors: Aristotle (in " Physics”) and its commentators (primarily Simplicia).

The main (or only) work Z. apparently consisted of a set of arguments, the logical form of which was reduced to proof by contradiction. Defending the Eleatic postulate of a single immovable being, he sought to show that the adoption of the opposite thesis (of plurality and movement) leads to absurdity (ἄτοπον) and therefore must be rejected. Obviously, Z. proceeded from the law of the “excluded middle”: if one of two opposing statements is false, then the other is true. We know of two main groups of Z.'s arguments - against the multitude and against the movement. There is also evidence of an argument against place and against sense perception, which can be seen in the context of the development of the argument against set.

Arguments against set preserved by Simplicius (see: DK29 B 1–3), who quotes Z. in a commentary on Aristotle's Physics, and by Plato in Parmenides (B 5); Proclus reports (In Parm. 694, 23 Diehl = A 15) that Z.'s work contained only 40 such arguments (λόγοι).

1. "If there is a multitude, then things must necessarily be both small and large: so small that they have no magnitude at all, and so large that they are infinite" (B 1 = Simpl. In Phys. 140, 34). Proof: what exists must have some magnitude; being added to something, it will increase it, and being taken away from something, it will decrease it. But in order to be different from another, you need to defend yourself from him, to be at some distance. Therefore, between two beings there will always be given a third, by virtue of which they are different. This third, as being, must also be different from the other, and so on. On the whole, being will turn out to be infinitely large, representing the sum of an infinite multitude of things.

2. If there is a multitude, then things must be both limited and unlimited (B 3). Proof: if there is a set, there are as many things as there are, no more and no less, which means that their number is limited. But if there is a set, there will always be others between things, third things between them, and so on ad infinitum. So their number will be infinite. Since the opposite is proved at the same time, the original postulate is wrong, hence there is no set.

3. “If there is a set, then things must be both similar and unlike, and this is impossible” (B 5 = Plat. Parm. 127e1–4; this argument, according to Plato, began the book of Zeno). The argument involves considering the same thing as similar to itself and unlike others (different from others). In Plato, the argument is understood as a paralogism, because similarity and dissimilarity are taken in different respects, and not in the same one.

4. Argument against place (A 24): “If there is a place, then it will be in something, since every being is in something. But what is in something is in the place. Therefore, the place will be in the place, and so on ad infinitum. Therefore, there is no place” (Simpl. In Phys. 562, 3). Aristotle and his commentators referred to this argument as a paralogism: it is not true that "to be" means "to be in a place," because incorporeal concepts do not exist in any place.

5. Argument against sensory perception: "Millet grain" (A 29). If one grain, or one thousandth of a grain, makes no noise when it falls, how can the fall of a copper grain make noise? (Simpl. In Phys. 1108, 18). Since the fall of a copper grain on a grain produces noise, then the fall of one thousandth should produce noise, which in fact is not. The argument touches on the problem of the threshold of sense perception, although it is formulated in terms of part and whole: as the whole is related to the part, so the noise made by the whole must be related to the noise made by the part. In such a formulation, the paralogism consists in the fact that “the noise produced by the part” is being discussed, which in reality does not exist (but is possible, according to Aristotle).

Arguments against the movement. The most famous are 4 arguments against motion and time, known from the "Physics" of Aristotle (see: Phys. VI 9) and comments on the "Physics" of Simplicius and John Philopon. The first two aporias are based on the fact that any segment of length can be represented as an infinite number of indivisible parts (“places”) that cannot be traversed in a finite time; the third and fourth - on the fact that time also consists of indivisible parts (“now”).

1. "Stages"(other name "Dichotomy", A25 DK). A moving body, before overcoming a certain distance, must first pass half of it, and before reaching half, it must pass half a half, and so on. to infinity, because any segment, no matter how small, can be divided in half.

In other words, since the motion always occurs in space, and the spatial continuum (for example, the line AB) is considered as an actually given infinite set of segments, because any continuous quantity is divisible to infinity, then the moving body in a finite time will have to go through an infinite number of segments, which makes movement impossible.

2. "Achilles"(A26 DK). If there is movement, “the fastest runner will never catch up with the slowest one, since it is necessary that the one who is catching up first reaches the place from which the evader began to move, therefore the one running more slowly must always be slightly ahead” (Arist. Phys. 239b14; cf. Simpl. In Phys. 1013, 31).

In fact, to move means to move from one place to another. Fast Achilles from point A starts chasing the tortoise located at point B. He must first go half the whole way - that is, the distance AA1. When he is at point A1, the turtle will go a little further to a certain segment BB1 during the time he was running. Then Achilles, who is in the middle of the path, will need to reach point B1, which, in turn, needs to go half the distance A1B1. When he is halfway to this goal (A2), the turtle will crawl a little further, and so on ad infinitum. In both aporias Z. assumes that the continuum is divisible to infinity, thinking this infinity as actually existing.

In contrast to the aporia "Dichotomy", the added value is not divided in half, otherwise the assumptions about the divisibility of the continuum are the same.

3. "Arrow"(A27 DK). The flying arrow is actually at rest. Proof: at each moment of time, the arrow occupies a certain place equal to its volume (because otherwise the arrow would be "nowhere"). But to occupy an equal place with oneself means to be at rest. It follows from this that movement can only be thought of as a sum of states of rest (the sum of "advanced"), and this is impossible, because nothing comes from nothing.

4. "Moving Bodies"(other name "Stages", A28 DK). “If there is movement, then one of two equal quantities moving with equal speed into equal time will pass twice the distance, not equal, than the other” (Simpl. In Phys. 1016, 9).

Traditionally, this aporia was explained with the help of a drawing. Two equal objects (denoted by letter symbols) move towards each other along parallel straight lines and pass by a third object of equal size. Moving with equal speed, once past a moving, and another time past a resting object, the same distance will be covered simultaneously in a certain time interval t, and in a half interval t / 2.

Let row A1 A2 A3 A4 mean a stationary object, row B1 B2 B3 B4 - an object moving to the right, and C1 C2 C3 C4 - an object moving to the left:

A 1 A2 A3 A4

After the expiration of the same moment of time t, point B4 passes half of the segment A1–A4 (i.e., half of a stationary object) and the entire segment C1–C4 (i.e., an object moving towards). It is assumed that each indivisible moment of time corresponds to an indivisible segment of space. But it turns out that point B4 at one time t passes (depending on where to count from) different parts of space: in relation to a stationary object, it passes a shorter path (two indivisible parts), and in relation to a moving object, a larger one (four indivisible parts). Thus, an indivisible moment of time turns out to be twice as large as itself. And this means that either it must be divisible, or the indivisible part of space must be divisible. Since Z. does not allow either one or the other, he concludes that it is impossible to think of movement without contradiction, therefore, movement does not exist.

The general conclusion from the aporias formulated by Zeno in support of the teachings of Parmenides was that the evidence of the senses, which convinces us of the existence of multitude and movement, diverges from the arguments of the mind, which do not contain contradictions, therefore, are true. In this case, feelings and reasoning based on them should be considered false. The question of who Zeno's aporias were directed against does not have a single answer. There has been a point of view in the literature that Zeno's arguments were directed against the supporters of the Pythagorean "mathematical atomism", who constructed physical bodies from geometric points and accepted the atomic structure of time (for the first time - Tannery 1885, one of the last influential monographs emanating from this hypothesis - Raven 1948 ); at present this view has no adherents (for more details, see Vlastos 1967, pp. 256–258).

In the ancient tradition, it was considered a sufficient explanation for the assumption that goes back to Plato that Zeno defended the teachings of Parmenides and that his opponents were all those who did not accept the Eleatic ontology and adhered to common sense trusting feelings.

Fragments

• DK I, 247–258;
• Untersteiner M. (ed.). Zeno. Testimonianze e framementi. Fir., 1963;
• Lee H.D.P. Zeno of Elea. Camb., 1936;
• Kirk G.S., Raven J.E., Schofield M.(edd.). The Presocratic Philosophers. Camb., 1983 2 ;
• Lebedev A.V.. Fragments, 1989, p. 298–314.

Literature

• Raven J.E. Pythagoreans and Eleatics: An Account of the Interaction Between the Two Opposed Schools During the Fifth and Early Fourth Centuries B. C. Camb., 1948;
• Guthrie, HistGrPhilos II, 1965, p. 80–101;
• Vlastos G. Zeno's Race Course (= JHP 4, 1966);
• Idem. Zeno of Elea ;
• Idem. A Zenonian Argument Against Plurality ;
• Idem. Plato's Testimony Concerning Zeno of Elea, repr.:
• Vlastos G. Studies in Greek Philosophy. Vol. 1. The Presocratics. Princ., 1993;
• Grunbaum A. Modern Science and Zeno's Paradoxes. Middletown, 1967;
• Salmon W.Ch.(ed.). Zeno's Paradoxes. Indnp., 1970 (2001);
• Ferber R. Zenons Paradoxien der Bewegung und die Struktur von Raum und Zeit. Münch., 1981. Stuttg., 1995 2 ;
• Yanovskaya S.A.. Have you overcome modern science the difficulties known as the "Aporius of Zeno"? – Problems of logic. M., 1963;
• Koire A. Essays on the history of philosophical thought (translated from French). M., 1985, p. 27–50;
• Komarova V.Ya. The Teachings of Zeno of Elea: An Attempt to Reconstruct the System of Arguments. L., 1988.

Zeno of Elea (ancient Greek Ζήνων ὁ Ἐλεάτης). Born ca. 490 BC e. - died ca. 430 BC e. Ancient Greek philosopher, student of Parmenides, representative of the Eleatic school. Born in Elea, Lucania. He is famous for his paradoxes, with which he tried to prove the inconsistency of the concepts of motion, space and multitude.

Scientific discussions caused by these paradoxical arguments have significantly deepened the understanding of such fundamental concepts as the role of discrete and continuous in nature, the adequacy of physical movement and its mathematical model, etc. These discussions continue at the present time.

The works of Zeno have come down to us in the exposition of Aristotle's commentators: Simplicius and Philopon. Zeno also participates in Plato's dialogue "Parmenides", is mentioned by Diogenes Laertes, in the Court and many other sources.

Aristotle calls Zeno of Elea the first dialectician.

Son of Televtagoras, studied under Xenophanes and Parmenides. According to Diogenes Laertes, Zeno participated in a conspiracy against the then Eleatic tyrant, whose name Diogenes did not know for sure. Was arrested. During interrogation, when demanding to extradite accomplices, he behaved steadfastly and even, according to Antisthenes, bit off his own tongue and spat it in the face of the tyrant. The citizens present were so shocked by what had happened that they stoned the tyrant. According to Hermippus, Zeno was executed by a tyrant: he was thrown into a mortar and crushed in it.

Diogenes reports that Zeno was the lover of his teacher, but Athenaeus strongly refutes such a statement: “But what is most disgusting and most false is to say without any need that fellow citizen Parmenides Zeno was his lover.”

Contemporaries mentioned 40 aporia zeno, 9 have come down to us, discussed by Aristotle and his commentators. The most famous aporias about movement are: Achilles and the tortoise, Dichotomy, Arrow, Stadium.

The aporias “Dichotomy” and “Arrow” are reminiscent of the following paradoxical aphorisms attributed to the leading representative of the ancient Chinese “school of names” (ming jia) Gongsun Lun (mid-4th century BC - mid-III century BC): “ In the swift [flight] of an arrow there is a moment of absence and movement, and a stop”; “If a stick [length] of one chi is taken away daily from half, it will not be completed even after 10,000 generations.”

Nearchus (or Diomedont - the history of the Eleatic tyrants is unclear). They say that Zeno led a conspiracy against tyranny, but was captured, did not betray his friends under torture, but slandered the friends of the tyrant. Unable to withstand further torment, he promised to tell the truth, and when the tyrant approached him, he dug his teeth into his ear, for which he was immediately killed by servants. According to another version, Zeno bit off his own tongue, spat it out in the tyrant's face, was thrown into a large mortar and crushed to death.

Philosophy of Zeno of Elea

Diogenes Laertius(IX, 29) reports that “the opinions of [Zeno of Elea] are as follows: worlds exist, but there is no void; the nature of all things has come from warm, cold, dry and wet, turning into each other; people came from the earth, and their souls are a mixture of the above-mentioned principles, in which none prevails. If Diogenes did not confuse Zeno with someone else, then it can be assumed that the Elean considered it necessary to state not only "truth", but also an "opinion", similar to that of which Parmenides spoke. But the main thing in his teaching is that it substantiates the system of Parmenides "from the contrary." The ancients attribute to Zeno of Elea 40 proofs “against plurality”, that is, in defense of the doctrine of the unity of being, and 5 proofs “against movement”, in defense of its immobility. These proofs are called aporias, insoluble difficulties. Zeno's proofs against motion and four proofs against multiplicity survive, including both arithmetic, numerical, and spatial aspects.

The meaning of the aporias of Zeno of Elea is that he explores the logical structure of the “world of opinion”, in which number and movement dominate, and draws consequences from these concepts. Since the consequences turn out to be contradictory, the concepts themselves are reduced to absurdity and discarded. In other words, the discovery of a contradiction in the strictly logically deduced consequences of the basic concepts of ancient philosophy and ordinary consciousness is considered by Zeno as a sufficient basis for their removal from the realm of true knowledge, from the “path of truth”. The result is “negative dialectics”, based on the use of the laws of formal logic in the application to the existent. It is difficult to say to whom the explicit formulation of formal-logical laws belongs, but it is certain that Parmenides uses the laws of identity and contradiction, and Zeno also uses the law of the excluded middle. The aporias of Zeno of Elea quite obviously proceed from the idea that if A and not-A are given simultaneously, and if not-A is contradictory, then it is false, but A is true. Such is the structure of all aporias. Let's consider them separately.

Aporia of Zeno of Elea against the plurality of beings

“So if there is a multitude, then [things] must necessarily be both small and large: so small that they have no magnitude at all, and so large that they are infinite.” Zeno's aporia refers to the magnitude, and its justification, if we compare it with the well-known teaching of the Pythagoreans that a thing is the sum of material points ("things"), will be as follows. If to something that has a value is added another thing that has a value, then it will increase it. But in order to be different from another thing, the added thing must stand apart from it, i.e. (since Zeno does not recognize emptiness!) between any two things there must be one more thing, between it and the first two - also according to the thing, etc. d. to infinity. This means that a thing composed of extended things is infinite in size. If it is composed of unextended things, then it does not exist at all. One can also take this argument of Zeno from the quantitative point of view: if there are many things, then there are as many of them as there are, that is, a finite number. But if there are many of them, then, according to what was said above, a third is placed between each two of them, and so on ad infinitum. The source of the contradiction is the very concept of number or set: if there are many things, then the finite thing is both infinitely large and small, and the number of things in the world is both finite and infinite.