Zeno of Elea - Greek logician and philosopher, which is mainly known for his paradoxes, named in his honor.His life is not very much known.Hometown Zeno - Elea.Also in the works of the philosopher Plato mentioned meeting with Socrates.
Around 465 BC.e.Zeno wrote a book, which recounted their ideas.But, unfortunately, to this day she did not find a striker.According to legend, the philosopher died in battle with the tyrant (presumably head of Elea Niarchos).All information about Elea collected bit by bit: from the writings of Plato (born 60 years later, Zeno), Aristotle and Diogenes Laertes, who wrote three centuries later book biographies of the Greek philosophers.Mention of Zeno there are in the writings of the later representatives of the school of Greek philosophy: Themistius (4th century BC. E.), Alexander Afrodiyskogo (3rd century BC. E.), As well as Philoponus and Simplicius (both lived in the 6th century BC. E.).And data from these sources is so good agreement, that it is possible to reconstruct all the ideas of the philosopher.In this article, we will tell you about the paradoxes of Zeno.Let's get started.
Paradoxes sets
Ever since the era of Pythagoras, space and time were considered exclusively from the point of view of mathematics.That is, it was believed that they are composed of a plurality of points and points.However, they have the property that easier feel than determine, namely the "continuity".Some of the paradoxes of Zeno prove that it can not be divided into points or points.The reasoning philosopher is as follows: "Let's say that we had until the end of the division.Then, true to only one of the two choices: either we get a remainder of the smallest possible size or parts that are indivisible, but are infinite in their number, or the division lead us to pieces without value, since the continuity of being a homogeneous must be divisible under any circumstances.It may not be divisible into one part and the other - no.Unfortunately, both the result is quite ridiculous.Origin of the fact that the fission process may not end until there is a balance portion having value.And second, because in such a situation it would be initially integrally formed of nothing. "Simplicius attributed this argument Parmenides, but it is more likely that its author - Zeno.Come on.
Zeno's paradox about the movement
They are considered in most of the books on philosophy as enter into dissonance with the evidence of the senses Eleatics.With respect to the motion, Zeno's paradoxes are the following: "Boom", "Dichotomy", "Achilles" and "flock".And they came to us thanks to Aristotle.Let's examine them in detail.
«Boom»
Another name - quantum Zeno paradox.Philosophers have argued that any thing or standing still or moving.But nothing is in motion, if the space is occupied by the extent of it.At some point, the moving arrow is in one place.Therefore, it is not moving.Simplicius formulated this paradox in a concise form: "Flying object occupies an equal place in space, and that it takes an equal place in space, not moving.Therefore, the arrow rest. "Himalia and Felopon formulated similar options.
«dichotomy»
ranked second list "Zeno's paradox".It reads as follows: "Before the object that started the movement, will be able to go a certain distance, it must overcome the half of the way, then the remaining half, and so on. D. To infinity.Since the re-dividing the distance cut in half all the time becomes finite and the infinite number of pieces of data, it is impossible to overcome the distance in a finite time.And this argument is valid both for small distances and high speeds.Consequently, any movement is impossible.That is, the runner can not even start. "
This paradox is very detailed Simplicius said, pointing out that in this case, a finite time is necessary to make an infinite number of touches."He who regards anything, can lead the score, but you can not go through an infinite number or count."Or, as formulated Philoponus, an infinite number of indefinable.
«Achilles»
Also known as Zeno's paradox of the tortoise.This is the most popular argument of the philosopher.This paradox movement Achilles compete in the race with the turtle, which is given at the start of a small handicap.The paradox is that the Greek soldiers will not be able to catch up with the tortoise, as he first run so far to the place of its launch, and she'll be on the next point.That is, the tortoise will always be ahead of Achilles.
This paradox is very similar to the dichotomy, but there is an infinite division goes according progression.In the case of the dichotomy has been a regression.For example, the same runner can not start, because he can not leave his location.And in a situation with Achilles, even if the runner will get under way from a place, he still will not come running.
«Stages»
If we compare all the paradoxes of Zeno degree of difficulty, this would come out the winner.It is difficult to give in other presentation.Simplicius and Aristotle described this argument is fragmented and can not with 100% certainty to rely on its reliability.Reconstruction of this paradox is the following: Let A1, A2, A3 and A4 are fixed bodies of equal size, and B1, B2, B3 and B4 - a body of the same size as A. Body B moves to the right so that each B passesAnd for a moment, which is the smallest time interval of all.Let B1, B2, B3 and B4 - identical bodies A and B with respect to A and move to the left, overcoming each of the bodies in an instant.
Obviously, B1 overcome all four bodies B. Assume per unit time, the need for a single body in the passage of the body B. In this case, the movement took all four units.However, it was believed that the two points, the last for this movement to be minimal and therefore - are indivisible.From this it follows that the four indivisible unit are two indivisible units.
«place»
So now you know the basic paradoxes of Zeno of Elea.It remains to tell about the latter, which is known as "The Place."This paradox of Zeno ascribes to Aristotle.Similar arguments were cited in the writings of Philoponus and Simplicius in the 6th century BC.e.Here Aristotle says about this issue in his physics: "If there is a place, how to determine where it is located?The difficulty, which came Zenon, requires explanation.Since everything that exists is the case, it is obvious that at the place should be a place, and so on. D. To infinity. "According to most philosophers, there is a paradox here because none of the current can not be different from himself and contained in itself.Philoponus believes that by focusing on self-contradictory concept of "place" Zeno wanted to refute the theory of multiplicity.
