The aporia of Zeno is a proof of the impossibility of Rukh. Paradox to Zenon of Elei - description, meaning and facts. Historical significance of Zeno's aporias

Zeno of Elea and yoga aporia

On the eve of the day, look Parmenides against the hanging bars, taking the guilt of Parmenides’ friend and friend Zeno*. Vin was born on the cob 5 tbsp. to the sound e. (480) and died at 430 p. BC e. Zenon maw glory as a talented teacher and orator. Youth having lived in a quiet, self-sufficient vchenni, highly appreciating the victory of rosy malt - the only malt, as if they never crossed. When Parmenida learned to know the rozkish. Yogo city was the voice of his heart, which was evenly beating at the witness of his rightness. All yoga life is a struggle for truth and justice. Vaughn died tragically, but was not without reason. In this work, there were only a few numerical ones, but only a few, for the sake of complete knowledge, enriched by the best ancient writers. From them, at the first place, Aristotle's note can be placed in the "Physics", as well as the note of Simplicy, commentator of Aristotle's "Physics". They give the opportunity to characterize the new things that Zeno introduced in Greek science, equal to Parmenid, for all the simplicity of his argumentation in detail.

Zeno having raised low arguments against Parmenid's defense. Method, zastosovaniya him at tsikh arguments, zgod gave Aristotle the opportunity to call Zeno the ancestor of dialectics. Under the "dialectic" Aristotle at the time of understanding the mysticism of the truth is revealed by the path of internal protirich, like the thoughts of the enemy, and by the path of the adoption of these protirich.

Zeno's method is similar to what is called in mathematics "proof of the contrary." Zeno accepts - mentally - the theses of the opponents of Parmenides. Vіn accept, (1) that the expanse can be as slender as an empty one, as if it were clear in speech, that it is more spacious; (2) what is the basis of impersonal speeches; (3) What can we do? Having mentally accepted three omissions, Zenon bring, nibi їhnє vede z nebhіdnіstyu to protirіch. Tim himself brought up, scho pupuschennya pardon. But if you stink of pardon, then it is necessary to be guilty of being true firmness, which supersede them. And tse є Parmenid's firmness. Otzhe, the firmness of Parmenide is true: empty, faceless and ruh unacceptable.

Let's take a look at Zeno's arguments okremo z tsikh trokh pitan. Let's talk about food forgiveness empty, i.e., open space, water-reinforced speech. As we allow the foundation of such space, then you gain ceremoniality at the onset of peace. Everything is known here in space. Ale shob; іsnuvati, expanse tezh maє buti “here”, so іsnuvati from another space. Whose other expanse, at his own place, is guilty in the third expanse, and so on to inexhaustibility. Ale ce є absurd. Otzhe, expanse like okremy in the speech of the inexorable.

Other food - about many times. Let's say that it's more possible. Todi blame food: 1. What is the need to think about the skin around the element of the multiplier? 2. What is the need to think about the total number of elements in a multiplier: what will be the sum of the last number of chi inexhaustible? Zeno's investigation shows that both of these foods are superbly viable. From the first point of view - it is to blame for the thought of the skin as an element of the multiplicity - it is shown that such an element must be confirmed about the skin, that the wine is instantly and cannot be of equal magnitude and infinitely great in magnitude. From another food - what is the fault of the sum of the elements of the multiplier - it is shown that it is the fault of the mind and like the number of the last, and like the infinite number.

Follow-up from the third meal - about forgivability- so it is very necessary to bring to superb hardness. Zeno's arguments for this reason became especially popular and gained wide popularity. Zeno, having developed a few such arguments, from which the Chotiri have come before us: “Dichotomy (divided into two)”, “Achilles”, “Arrow to fly” and “Stage”. Zagalna їх scheme - those same prostuvannya "in the form of an unacceptable". It is permissible, together with the opponents of Parmenid, nibi ruh mislimy. Talk about a body that is collapsing, but about a crumbling body, it is necessary to be able to speak superbly one to one firmness: 1) that the ruh is able and 2) that the wine is not strong. For help, some of Zeno's arguments to prove that the Rukh is unbearable. It’s impossible, in a way, like the collapse of one single body, which moves along a straight line from one point to another. To go a long distance, which would make point A from point B,

* Do not follow the other Greek philosophers who wore the name, for example, the staunch Zeno from Kition in Cyprus.

it is possible to walk forward half of the distance; to go halfway, it can go forward half or half, etc. to infinity. As a result, this body can not only go from point A to point B, but can’t navigate to leave point A, so the flow from point A to point B can’t just end, having started, but it can’t start. Such a sensational argument "Dichotomy".

The unacceptability of the movement of a single, well-taken body is also brought up for an additional argument. Arrow to fly". For the release, the arrow to fly, then it collapses in the open. But about her at the same time it is necessary to harden, that she will occupy the space, that the health of the hair is good, that she will be in the midst of part of the space, “to mean” to the new one is not bad. To go out, what an arrow, what to fly, and collapse, and not collapse. In an aporia "Strela" Zeno to bring that, collapsing, the arrow at the skin moment takes up space given the space. So, as it is impossible to touch the skin (it’s only on the square of the dot in the hour), then the arrow cannot change its position in this boundary. And if it is not broken in the skin for one hour, it is not broken even during the whole period of yoga. The body that collapses does not collapse either in that place, as it borrows, nor in that, as it does not occupy. Shards of an hour are folded out of a few moments; Tse so unbearable ruh. Shards of an arrow in the skin point of its path occupy a full space, equal to its own volume, and the movement is immobile, as if it takes a body equal to its own space (for the movement, the object will require space, more for itself), then the body rests in the skin space. In a word, from that mirkuvannya, that the arrow is constantly resting with the singing ones, but the unblighted “here” and “now”, cry out, that the position of the arrow is also inconspicuous: there you rest.

Ale ruh is unacceptable and like ruh two bodies one but one. It’s unacceptable, like a collapse along a straight two bodies, separated by a certain distance, and at once collapse into the same straight line, moreover, the body that collapses behind, collapses more for those that collapse in front. Zenon to bring up that for these minds the body, which collapses with a greater swedishness, is no better than what comes with a smaller swedishness. Achilles, Which is famous for the speed of its big, never mind the tortoise, which is ticking in the sky. Let Achilles live for the turtle, but after the end of the hour, even if it’s not maly wine, the turtle won’t be able to go through, yak, as if it weren’t vaguely out, no way will it be zero. Henceforth, peace Zenon, at one moment the whole distance, which makes Achilles look like a turtle, does not turn to zero, and to that Achilles can’t help the turtle in any way.

Argument "Stage" simple mistrust of the rush, with one of the adopted half-hours of Zenon’s rethinks, the rush is an admission that the expanse is made up of inconsistent parts (windows), and the hour is also from inconsistent parts (moments). Let's kill the allowance. It is also possible that from the opposite sides the parallel lines are collapsing according to the size of the body. It is acceptable, nareshti, that the body of the body should pass along the third body of the same size, the scarlet of the indestructible (divine little ones).

A1 A2 A3 A4 B4 B3 B2 B1 ---><--- С1 С2 С3 С4

A1 A2 A3 A4 B4 B3 B2 B1 C1 C2 C3 C4

Then go out, that one and the same point, which collapses with equal swedishness, go through one and the same place not at the same time, or go through yoga in one fall at half an hour, and in another - at a sub-hour. At one and the same hour, the extreme points of the skin from the crumbling rows B4 B3 B2 B1 and C1 C2 C3 C4 pass over the point of the next row that is collapsing. However, at the same time, the stink will pass more than half the points in a row, which is filled with indestructible under the hour of this rush. Such a different result is stale, in addition, the stars are visible to us її ruh. Ale, as a result, we come to superbness, half of the shards appear as an equal whole. In other words, in the “Stage” argument, the incomprehensibility of the movement is brought to light by the hour, how much is conveyed, how wine, like space, is formed from impersonal discrete, but not a bit of essential elements.

We have gone overboard, that in all Zeno’s baptisms, food should be put not about those that we can take ruh through a little, or we can’t. The one who takes the ruh by the senses, neither Parmenides nor Zeno doubts. Nutrition is based on the fact that it is possible to think ruh, like, mislyachi ruh, we allow it when it’s open, in which the bodies collapse, it is formed from the impersonal structures of one type of one part, and it’s allowed, at the hour, in which all manifest there is a movement that is formed from the impersonal waters of the Kremlin one in one moment. Inevitably, super-evidents, such as when thinking about it, a thought comes, to bring, after Zeno, that the folly of impersonality is impossible to be confirmed by the opponents of Parmenides. The very same sense can scatter the mistrust of the empty space. The essence of Zeno's argument zovsіm not in proving that, nibi space is not true. Zeno to bring further. Vin to bring that space cannot be thought of as an empty space, like space, which is in its own part, okremo like speech.

Zeno's arguments gave a strained impulse to the further development of ancient mathematics, ancient logic and ancient dialectics. Numerous arguments have been debunked in the understandings of the modern Parmenidus and Zenon of science - in the understandings of space, about unity and richness, about the whole and the part, about the peace and calm, about the interruption and interruption. The aporias of Zeno spurred the idea of shukati allowing them to mark the difficulties. The threat of unresolved protyrіch that hung over mathematical knowledge was thwarted by the atomistic materialism of Leucippus and Democritus.

The aporia of Zeno is connected with the dialectic of shot and uninterrupted rush (as well as the space-hour itself). Analyzing the hypothetical shock of Achilles and the tortoise, Zenon imagines the displacement of the skin of them in the sight of the agglomeration of the okremikh kіntsevih displacement: cob vіdrіzka, which spreads the tortoise and tortoise, that vіdrіzka, like a propovse tortoise, but Achilles' valley of the other. Whom "poki" and pokaє zamina uninterrupted rush on the okremi "croki" - really not Achilles, not a tortoise checks one to one and collapses independently in the face of a mental breakdown of their path on a windy wind. Todі slyakh, which is to lay down the hem of Achilles, to add the sum of an inexhaustible number of dodankіv, the stars of Zenon and to rob the wisps, so as not to sew on the next (kintsev) hour.

Just remember that the time to fight a lot of winds, then the visnovok is just. Sound, however, to show that Zenon simply did not know how to understand the sum of the inexhaustible series; .

In this rank, the Elates were not able to tell that there was no rush. The stinks with their subtle mirkuvannyam showed those who osmislyuvav some of their co-workers - what is ruh? The stench themselves, in their thoughts, raised a high raven of philosophical quips in the cryptic movement. Prote stinks could break the tangle of historical obmezhenosti development of philosophical views. Aporia of Zeno "Achilles" and "Strela" expose deeply the mystery of how, from the unruliness, the visible presence of vimiriv ("the arrow rests in the skin moment"), the movement is born. Needed some special thoughts. The founders of atomism were waving to walk.

For the sake of Diogenes the Cynic, to challenge the argument of Zeno, straightened out against the ground, he got up and began to walk. A.S. Pushkin said it like this:

No Ruhu!

Saying the wise man of bradat,

The youngest zmovchav,

Ale standing in front of him to walk.

Kriz, viklikana with the aporias of Zeno, was more than deep; if you want to do it often, you will need some special, non-violent ideas. Tse far away from the long-standing atomists, the most prominent among those boules Leucippusі Democritus. Analysis of Zeno's aporias by revealing their "painful" points: bezmezhny podіl (vіdrіzka shlyakhu tіl). Atoms were allowed, scho speech, expanse, the hour at the principle cannot be extended indefinitely, more than more, gave them fragments - atoms of speech, ameri (atoms of space), chrononi (atoms of the hour). Those more bodies are folded from a single number of atoms, leather from some ending volumes, more or less ending volumes can be folded from atoms. Arrow to fly, more, for appointments, ruh є podannja sing nіdstanі, scho folded from the sing number of amerіv, for the sing hour, which is formed from the sing amount of its quanti (chrononiv). So once and for all it will be difficult to change the minds of the minds, it was allowed, that the atoms are immutable, it may be the same absolute vigor, that the parmenidian buttya, the stench is inconsistent and uniform. Atoms like bi "zveli" the change to the imminent, to the atoms.

Zenon's aporias were called a lot of times, simply pointing out the facts: And having caught up, C, fly, etc. However, such "simpling" arguments of the great philosophers are not richly varied. Adzhe Eleati to put food right in a scientific way: if it is ruh, then it is necessary to comprehend it. Obviously, from an unreasonable turn, the multiplicity does not scream, but there are none of them. Ale and write especially nothing, as if you don’t have a good understanding of the scientific positions, you need to make obvious speeches, mechanical movement, a different kind of change. Heraclitus to that and dratuvav eleativ, without giving an explanation for the fact of the change. Understandably, the eleati did not bring that there was no rush, the stench showed the co-workers that they could hardly understand the wreck. The eleati themselves, in a rosy rush, were on the right peak, glancing in the current era. It is immediately obvious that modern times anew and anew turn up to the aporias of Zeno, knowing in them new impulses for the development of a scientific thought. With this, obviously, the stench modifies the logic of the mirroring of the eleativs. It has long been clear: in order to understand the aporias of eleativs, it is necessary to turn to the most advanced philosophical, mathematical and physical theories. Come out, scho eleati continue to the singing world, buti and doninі our teachers. What did the stink teach and teach us to us in front of? The roles and meanings of logical evidence, the need to consider - the order of the light of the earth - the intelligible level of reality, without falling "to deceive you." Eleati posed the problem of single and multiple, uninterrupted and intermittent, and peace of mind.

Zenon of Eleisky(Blizko 490-430 BC)-Learning Learning I Parmenida Madming. "VIN, Logika Yak Dialektika. Nyibilsh viddanniy, cuhri-aor-know, Yakik Aristotle, named the vinosa. (single and unruly), it’s impossible to think, the whole area of thought, having crossed over the possibility of thinking, to analyze, and those who can’t think, don’t know.

The internal contradictions about the roc are clearly seen in the famous aporia "Achilles": the shvid-legged Achilles can never overtake the tortoise. Why? Shorazu, with all the speed of his big and with all the breadth of the space that spreads them, like only a few wines to step on the ground, like a turtle occupied before him, there will be a troch to push forward. As if the expanse between them did not change, even if it was not limited in its authenticity, it was necessary for them to go through everything, and for which it would take an endless hour. І Zenon, we miraculously know that not only Achilles with short legs, but even a lame-footed one, will immediately heal a tortoise. But for the philosopher, nourishment was placed above the plane of the empirical foundation of the rush, and the plans of the mind to bridge the system’s super-smartness, in the dialectic of the mind of space and hour.

Aporia "Dichotomy": an object that collapses to the bone is guilty of going half the way to it, and to go half way, it is guilty of going half the way, etc., to infinity. Otzhe, the body is within reach, because way of yoga is unskinned.

Aristotle shows that Zeno is infinitely far away from the infinitely great. Zeno looks at the space like a sum of windy winds, and it opposes it to an endless uninterrupted hour. At the "Turtle" the impossibility of the rush winds from the fact that it is impossible to pass at the end of the hour an endless number of halves of the path. Zenon simply didn’t know how to understand the sum of the inexhaustible series, otherwise he poached the bi, that the inexhaustible number of dodankiv gave all the same the final path, like Achilles, collapsing with the steady swedishness, without a doubt, podolay for the overdue (final) hour.

In this rank, the Elates were not able to tell that there was no rush. The stench with their subtle mirkuvannyam showed those who are unlikely to have understood from their co-participants that such a ruh? The stench themselves, in their thoughts, raised a high raven of philosophical quips in the cryptic movement. Prote stinks could break the tangle of historical obmezhenosti development of philosophical views. Needed some special thoughts. The founders of atomism were waving to walk.

The main power of the world- Not speech, but yakіst (post-yna vіchnіst, you can think) - such a visnovok of eleatіv.

16. Philosophy of atomism: the concept of the atom and causality.

№6 Vchennya Democritus. The understanding of the atom is empty.

Atomism- The movement of ancient thought to the philosophical unification of the first principles of buttya. The hypothesis was developed by Leucippus and especially by Democritus (460-370 BC).

In the basis of the inexhaustible diversity of the world is a single arche, there is an inexhaustible number of elements (atoms). Potential inconsistency -Before you buy a dog, you can add one more dog. Current indistinctness - The presence of an inexhaustible number of elements in the exchanged contract. For the help of a simple idea, it is not possible to explain yoga.

The buttya is borderline simple, far beyond, impenetrable-atom. Atoms are impersonal, the stench is eternal, imminent, they do not blame and do not abide. Atoms of water-kremlin are one like one empty; atom-buttya, empty-nebuttya. Atoms are forever rushing around in the empty space, as if they can’t top, or bottom, or end, or edge, zishtovhuyuchis, zchipleyayuchis and roses. Half of the atoms satisfy all the diversity of nature. Atoms create the power of self-rule: such is their same nature. Atoms are folded at different changes, yakі spriymaєmo like okremikh speeches, different structures of these changes, tobto. like a roaming world, to lie in different types of interaction between atoms

A person-a bunch of atoms, vіdіznyaєtsya vіd іnshih istot nayavnіstі soulі. Soul-speech, which is made up of the most crumbling, fiery atoms.

The democrat was talking about the nature of the gods, but he was firm in knowing the butt of God. Behind the Democrat, the gods are composed of atoms, and God is the cosmic mind.

Atomism to become one of the biggest sciences. On the basis of all ideas that hung dosі, on the cob, the idea of the atom to take revenge on oneself, krіm ugogo іnshoy, the principle of interdilimarity of matter: the atom was thought like the smallest part, like it came out like the rest of the creation and the rest of the speech. And tse - ingenious zlіt thoughts on the principle of a new riven of the philosophical understanding of existence.

The basis of knowledge-observation. “Vidiki” - material forms of speeches, rush from all sides in an empty space and penetrate to the organs through the pores. If you look at the size and shape of the "vidiks" that penetrate them, then you blame the image of the object, which is similar to the object itself. That. already in mind we take the correct image of the object. Prote іsnuyut objects, yakі z svoєї small size inaccessible to the senses, so the authority of speeches is touched by reason, and tse pіznannya also m.b. trustworthy.

Causality. The development of the all-world, the harmony of the world, everything is essentially appointed (determined) by the mechanical movement of the atoms. That is why there is no place in the system for the objective. іsnuvannya "vipadkovostі". And the "vipadness" itself is explained in the context of a causal explanation, ignorance of the causes of the singing manifestation. In Demokrit, like Diogenes Laertsky, "everything is blamed for the need: the reason for any blame is a tuft, and this tuft of wine calls the need." Tse understanding of the need and the consequences of the singing metaphysical absolutization of causality, which is mechanically understood. (The very moment was the main subject of criticism of one of the prominent representatives of ancient atomism - Epicurus.) Democritus's understanding of causality, as an absolute necessity, cannot, prote, like Aristotle's admonishment, nothing wrong with teleology and directing itself against teleological precedence. "The democrat comes out of the fact that he talks about meta and translates everything that is victorious nature, to the point of necessity."

Similar information.

Now we turn to specific sophistry and problems, how to stand behind them.

The famous mirkuvannya of the old Greek philosopher Zeno "Achilles and the tortoise", "dichotomy" and іn. The very idea to bring that the world is one and the same and so unruly, we see it as marvelous today. That marvelous woman was respected and long ago. The marvelous floorings, which “prove” that Zeno suggested, were immediately brought to simple cunning, moreover, they were spared especially cunning. Such stench and vozvazhalis two thousand more than a thousand years, and іnоdі vvazhayutsya th now. Marvel, reader, how the stench is formulated, and show respect for the modern simplicity and uncomplicated wisdom.

Nayshvidsha іstota is not able to overtake naypovіlnіshe, shvidko-legged Achilles is not in any way able to nazdozhena poіlnu tortoise. As long as Achilles reaches the turtle, it will stick out a little ahead. Vіn shvidko podolaє i tsyu vіdstan, ale tortoise goes more threes forward. And so to infinity. Shchoraz, if Achilles is within reach of the mist, de bula in front of it is a tortoise, it will oppose itself, wanting b troch, but in front.

The "dichotomy" develops respect that a rumpled object can reach half of its path, the first one is within the reach of one's kintsya. Then we are guilty of going through half of the half that was left out, then half of the fourth part, and so on, until the end. The subject is constantly approaching to the end point, but in no way can it be reached.

Qiu mirkuvannya can troch pereіnakshiti. In order to pass half of the way, the subject is guilty of passing half of the half of the half, and for which it is necessary to pass half of the quarter, etc. As a result, the subject must not be destroyed in the same way.

Hundreds of philosophic and scientific works are dedicated to simple-looking mirkuvannyam. There are dozens of different ways to prove that the absurdity of being able to move is absurd, that the science of geometry is free from paradoxes and that mathematics is able to describe the movement without super-exactness.

There is a great number of chanted arguments of Zenon showing. I don’t understand why they themselves have to prove qi that they bring the stench. Didn’t realize how “should” be brought and what here є vzagalі prove? It’s less obvious that there are problems and difficulties. First, ask Zenon, you need to tell me what to say to yourself, and how to prove your thesis. He himself did not directly formulate any problems, nor his own solutions to their problems. E, zokrema, it’s more than a short rozpovіd, like Ahiles unsuccessfully trying to catch up with the tortoise.

The moral lies, naturally, in view of that wide background, against which it is seen and changed against the changing background.

The consecration of Zeno at once, the need to think, is left to be seen from the category of cunning cunning. The stench, following B. Russell's words, "in that chi іnshіy form torkayutsya pіdstav vіdzhe vіhіh teorіy expanse, і neskіchennosti, scho proponuvalsya from 12:00 o'clock to the present day."

The spіlnіst tsikh mirkuvan e іnshimi sophіzms drevnіh is undoubted. І tі y іnshі may take the form of a short description of the simple description of the basic situation, so as not to have any particular problems. However, the description presents a remarkable phenomenon in such a way that it appears clearly insane with tired statements about the new one. Mіzh tsimi zvichaynymi vyavlennyy pojasche that description їх at aporії chi sophіzmі vinikaє rіzke razbіzhnіst, navit protirіchchya. As soon as it is pointed out, the rozpovid is tracing the appearance of a simple and innocent statement. Behind him, an inconspicuous and unrecognized depth is seen, in which it is inconspicuously guessed like a food, or to bring a rich food. It is important to say with a song, in which the food itself is blamed, it is still possible to see them formulate, but it is obvious that the stench is. It is necessary to stand out from roses like before, as morality is drawn from life's parables. And like a parable, the results of thinking about the rose of an important rank lie not only in itself, but in the context in which the rose is looked at. Through chains they appear not so placed, as inspired by opinions. The stench changes from person to person and sometimes until one o'clock. And there is no more reason to believe that the devil's pair of "nutrition - advice" has exhausted all the money of explanation.

"MEDIMNE GRAIN"

Zenon uttered one more sophism - "medimn of grain" (approximately a bear of grain), which served as a prototype for the famous sophisms of Evbulid "kupa" and "fox".

A great mass of dry, millet, for example, grains, when they fall on the ground, will always make a noise. Wine is added to the noise of about the grains, and, later, the skin grain and the skin of the least part of the grain are to blame, falling, making noise. Prote okreme grain falls to the ground noiselessly. It means that even the median grains that fall to the ground are not to blame for the sound of noise, even if the wines are made up of impersonal grains, the skin of them falls silently. Ale, all the same, the grain's medimin falls with noise!

In the last century, experimental psychology began to take shape. "Medimn grains" having begun to gloomy - for a quarter of an hour - as it is not clear before the introduction of the foundation of a well-founded spring threshold. Tse tlumachennya richly we are going to reconsider and today.

A person can feel the sounds in full, they can hardly reach the singing power. The fall of the sown grain makes a noise, but the vines of the flooring are weak, which lie beyond the boundaries of human hearing. Falling rich grains make a noise that people are falling for. “Jacby Zeno knows the theory of sound,” wrote the German philosopher T. Brentano, “I didn’t know, obviously, my argument.”

As if, with such an explanation, one simple, ale, the whole furnishing on the right was not rushed: the sophism of “medium grain” is strictly analogous to the sophisms of “kupa” and “fox”. But don't wait for a hundred years, neither to the theory of sound, nor to the psychology of hearing.

So, for them, you need more explanation.

Tse is obviously inconsistent. The same type of sophistry may be virishuvatisya however. In addition, the principle of prompting similar sophisms has been grasped, which can be tempted to formulate skilki. Bulo would be naїvno, however, for skin shukati, it’s your own solution.

Enriched with the glib є їхній analysis, given by G. Hegel. Nutrition: “What do you create an addition to one grain of kupu?”, “What is the tail of a horse we’re naked, how do we virvati from a new hair alone?” - naїvnimi. It is new to know one's own expression, the test of the ancient Greeks to reveal at first glance the super-fluidity of a change.

Postupov, incomprehensible, purely calculus change of such an object cannot be repeated indefinitely. At the singing moment, it reaches its own boundary, it is sharply changed, and the object passes into a different one. For example, at temperatures from 0° to 100°C, water is native. In the course of heating, it ends up, that at 100 ° C it boils and sharply, the strobkom goes into another yakіsny camp - it turns into a steam. “If Kilkіsna Zmin, - write G. Hegel, - it’s possible to cling to the spockey absolutely immune, Ale for the cinquefoil of the chronhe, I. Zmin Kilkishny, and it is a pagan, and for the pre -pile of the bun .

Sophistry like "medimn of grain", "kupa", "fox" is also an accurate butt of quiet difficulties, to some extent inaccurate or "explained" to understand. Ale about it already went to the third branch.

the most famous for aporiїv:
1) achilles if you need a turtle, because won in the rest of the moment you can work ahead
2) arrows do not fly, because at some point, the stench will perebuvayut at a calm moment
3) from point A, if we can get to point B, because we will walk half way back, then half way, then more, etc., but we will not reach point B, but we will get as close as possible to the new one.

APORIA (from Greek a - dumb and poros - way), restlessness, impossibility, shortness; zdaetsya non-searchable logic. aggravation, wiping out the problem. Other Greeks. Philosophy was particularly popular with Zeno's aporias (which were revealed by rubbing in the understanding of the ruin, the hour and space)" ... ("Glossary of Antiquity" M., SP "Zovnishsigma", 1992, page 42).
Zenon of Eleisky (bl. 490 - bl. 430 BC) Greek. philosopher, student of Parmenides. Having vanished under the hour of a nearby rebellion against the tyrant. Zenon, trying to warmly bring the truth of his teacher's testimony, which was sharply criticized, about the impossibility of the revolution and the multiplicity of speeches ... Vіdoma yogo aporia "Achilles": Achilles can not overtake the tortoise, as if it were ruined earlier for the new one. Aporiya polygaє in the indiscretion of mathematical. understanding inconsistency.
Yogo aporia, for example, "Strela" ("arrow, to fly, rest"), sown the development of logic. myslennia (there, page 213).
From the aporia of Zeno, the most famous are: "Mira", "Dichotomy", "Achilles", "Strila", "Stadion" and "Prosyane Grain". So mi about the aporia "Strela".
The essence of її zahal sounds like this: an arrow, let out of the bow, no matter how far it reaches its mark. Why? The one who, if it’s like a mit (in Zenonov’s way, it’s like “now”), the arrow’s goodness is resting, and the shards are all the time long and are made up of sumi moments, then it means – from sumi peace. Father - from one great peace. And all those who are resting do not collapse. Later, without interrupting Russia, the arrow is by no means within reach of its own goal. Її Rukh - ІLUZІYA real Rukh.

Zenon was one of the representatives of the Eleian school. We have developed famous proofs that confirm the ideas of Parmenides about those that ours seem to deceive us, and I can only paint a better picture of the world with reason. Zeno became famous for this, having created the rank of aporia, tobto. firmness, for those who have two super-judgments at the same time, it is true. For the help of such aporias, Zenon tried to bring out that the ruh, which we are afraid of, is not really true, since if we start about a new mirkuvat, then we use it for inexhaustible difficulties and rub it.

Below are the most important aporias of Zeno.

1. Achilles and the turtle
Admissible, Achilles lives ten times closer, lower than a tortoise, and stays behind her for a thousand rocks. For that hour, for a kind of Achilles, to pass through the distance, a turtle in the same bіk propovs a hundred rokіv. If Achilles walks a hundred miles, the tortoise prophesies ten more miles, if you walk one step, the turtle prophesies a tenth part of a crochet. The process continues to inexorable, Achilles so no way can the tortoise be cured.

It seems that one time Zenon raised his aporia at the gatherings of his colleagues, and one philosopher at the same time, having just begun to move around the room, they said to themselves: “Surprise, I’m collapsing, and Zenon is stverzhu, it’s impossible!”. However, this is not a simple aporia of Zeno, even if the aporia will not be so on a sensitive (zore) mind, but in a mind. Dosі richly vchenih try to prostuvati tsyu aporіyu, but it's good to prostuvati such a logically vіrnu aporіyu more smoothly.

2. Dichotomy
It is acceptable, the body can move from point A to point B. To hem the way, on the back, you can hem half the way, and before the qim - a quarter. The first is to go through a quarter, the body has passed the eighth part of the way, before the tsim - sixteen and so on. To go out, the body needed to go through the impersonal servants on their way, but it was impossible to go through indistinctness. That body will never move.

It is obvious, we know, that bodies can really move in the open, even if it is possible to guard against the ruins of life bodies, but Zeno’s aporia will hesitate to think about the truth of our caution.

3. Flying arrow
The flying arrow is unruly, to that at the skin moment it will rest for an hour, and the shards will rest at the skin moment of the hour, it will always rest.
Aristotle urged to prostuvati tsyu aporia. Vin wrote this:

“Zeno, the world is wrong. Forever, even wine, every body is resting, if it is in its equal place, and the body that moves, at the moment “now” is in its equal place, then the arrow, to fly, is not broken. But it’s not right, because the hour doesn’t add up to the inappropriate “now”, and also no other value.

However, the position of Aristotle is clearly not without reason, even if you have not been able to know the logical pardons from the courts of Zeno. True, even yoga aporia from the look of the logic of the bezdogann!

The philosophy of the Eleian school (Xenophanes, Parmenides, Zeno, Melissus) is close to the traditions of spontaneous, elemental materialism, which opposes the "spontaneous dialectics" of the older philosophical schools. The controversy of eleativs with the dialectic of Heraclitus, although it seems paradoxical, leads to the exasperation of real, objectively valid contradictions. Forbidding the movement, seeing through the rethinking of the minds of the yogi foundation - zokrema, at the viklady of Zeno - becomes a stimulus for the further development of dialectical thought. The great introduction of eleativs is the exercise of comprehension of action for the help of the conceptual apparatus. For the help of the main ones to understand the current philosophies, they started to imagine, to comprehend the objectively clear light. At the head of the eleativs, we speak with clear words about the butt and singing approaches to the nourishment of the knowledge of the world.

Zgidno with eleats, buttya - tse those who zavzhd є: it’s so very single and inconsistent, like a thought about it, against the multiplicity and authenticity of all the speeches of a sensible world. Buttya - those who can be known only with the mind. Myslennya and buttya - the same. Myslennya - tse building osyagat unity, even as a sensitive spryyattyu vіdkrivaєtyu vіdkrivаієє, raznomanіtya in speeches and appearances. Awareness of the nature of thought is a little far-reaching evidence for reflections of ancient Greek philosophers. Invariably, in Parmenides, the yogi of Zeno, and in Plato and the yogi of the school, the understanding of the one and the same is seen at the center of respect, and the discussion of the spontaneity of the one and richly something, the one and the same butt stimulates the development of ancient dialectics. Zeno undertook to bring up, that there is no rush with his "aporias": 1) Dichotomy - podіl navpіl. To pass yakus vіdstan, it is necessary to go halfway through the yogo half. Look at what you have lost, so share navpil, etc. Whether it’s a windfall, it’s impossible for an hour to cheer up for the end of the wind. 2) Ahiles is the tortoise. This aporia is also based on the admitted actual inconsistency of the elements of an uninterrupted magnitude. Zeno to bring, scho Ahiles be-if the tortoise is cured, tk. the turtle is still rushing forward. 3) Arrow. Arrow, scho to fly, really resting. Vіn podіlyaє hour into parts and at the skin moment the arrow rests for an hour. In vipadku Zeno to bring, scho theoretically ruh cannot be revealed.

The aporia is based on the fact that any wind can be divided into impersonal points.

Zeno to kill the visnovok - neither the faceless nor the ruh can be misunderstood without superficialities. In the aporias of Zeno, the problems of continuity and inconsistency are first discussed. Eleati in such a way razumili buttya: 1) Buttya є, no buttya. 2) Buttya alone, inappropriate 3) Buttya known, not known but not known. Zeno of Eleisky (about 490-430 BC) - the student and successor of Parmenides. buttya (single and unruly), it is not possible to think, the whole area of \u200b\u200bthought, having crossed over the possibility of thinking, to analyze, and those who cannot think.

In this rank, the Elates were not able to tell that there was no rush. The stench with their subtle mirkuvannyam showed those who are unlikely to have any of their co-participants osmislyuvav, what is Rukh? The stench themselves, in their thoughts, raised a high raven of philosophical quips in the cryptic movement. Prote stinks could break the tangle of historical obmezhenosti development of philosophical views. Needed some special thoughts. The founders of atomism were waving to walk.

The main power of the navkolish world is not speech, but yak_st (steady vichnist, you can think) - such a visnovo eleativ