Zeno of Elea - the Greek philosopher, who was a disciple of Parmenides, a representative of the Eleatic school.He was born about 490 BC.e.in southern Italy, in the city of Elea.
The famous Zeno?
arguments that philosopher Zeno praised as a skillful polemicist in the spirit of sophistry.The content of the teachings of the philosopher Parmenides considered identical ideas.Eleatic school (Xenophanes, Parmenides, Zeno) is a forerunner of sophistry.Zenon is traditionally considered the only "disciple" of Parmenides (although Empedocles also called him "successor").In the early dialogue called "sophist" Aristotle called "the inventor of dialectics" Zeno.He used the term "dialectic" is likely to prove the value of certain common assumptions.That he dedicated his own works of Aristotle "Topeka".
In "Phaedrus", Plato talks about owning fine "art logomachies" "Elea screamers" (which means "clever inventor").Plutarch writes about Zeno using sophistical adopted to describe the practice of terminology.He says that this philosopher was able to refute, resulting paradoxes through the counter.Alluding to the fact that employment Zeno had sophistic character is mentioned in the dialogue "Alcibiades I" that the philosopher took the high tuition fee.Diogenes Laertes says that for the first time began to write the dialogues Zeno of Elea.This was regarded as a teacher and thinker Pericles, known politician of Athens.
Sport Policy Zeno
doxography can be found in reports that Zeno in politics.For example, he was involved in a conspiracy against Niarchos, Tirana (there are other variations of his name), he was arrested and tried during the interrogation he bite off an ear.This story presents Diogenes of Heracleides Lembo, who, in turn, refers to a book peripatetic Satire.
Many historians of antiquity passed reports of resistance in the court of the philosopher.Thus, according to Antisthenes of Rhodes, Zeno of Elea bit off his tongue.Germipp says philosopher thrown into the stupa in which his istolkli.This episode was later very popular in the literature of antiquity.Plutarch mentions it Heroneysky, Diodir Sicilian, Flavius Philostratus, Clement of Alexandria, Tertullian.
Works
Zeno Zeno of Elea was the author of works "against the philosophy", "Controversy," "interpretation of Empedocles" and "On Nature".It is possible, however, that all of them except the "interpretation of Empedocles", were in fact variants of the name of one book.In the "Parmenides" Plato mentions the essay written by Zeno to ridicule opponents of his teacher and show that even more absurd conclusions assumption leads the movement and sets than the recognition of being a single Parmenides.The reasoning of the philosopher known as presented by later writers.This Aristotle (essay "Physics"), as well as his commentators (eg Simplicius).
arguments Zeno
main product Zeno was written, apparently, of a set number of arguments.The proof by contradiction reduced their logical form.This philosopher, defending the postulate of a stationary single being, which put forward the Eleatic school (Zeno, according to some researchers, were created in order to support the teaching of Parmenides), sought to show that the assumption of the opposite thesis (on the motion and set) definitely leads toabsurd, therefore, should be rejected thinkers.
Zenon obviously follow the law "excluded middle": if one statement of two opposite is not true, it is a loyal friend.Today we know the following two groups of arguments that philosopher (Zeno of Elea) against the motion and against many.Also, there is evidence which indicate the presence of the arguments against the sensory perception and against the seat.
Zeno's arguments against a variety
Simplicius have preserved these arguments.He quotes Zeno in the commentary to Aristotle's "Physics".Proclus says that the work we are interested in a thinker has concluded 40 such arguments.Five of them we list.
- Defending his teacher, who is Parmenides, Zeno of Elea says that if there are many, then, consequently, things must be necessary and large and small: so small that they do not have any value and are so large that they areendless.
proof follows .Must have a certain value exists.Being added to the something, it will increase and decrease its being taken away.But in order to be different from some other, should defend him, to be at a certain distance.That is always between the two will be given to bring into being the third, thanks to which they are distinct.It must also be different from each other and so on.. In general, things will be infinitely large, as is the amount of things that are infinite.The philosophy Eleatic school (Parmenides, Zeno, and others.) Is based on this idea.
- If there are many, then things will be and endless and limited.
proof : if there is a set of things to eat as much as they have, no less and no more, that is, their number is limited.However, in this case, will always exist between other things, between which, in turn, - the third and so on. D. That is the number of them is infinite.Because while the contrary is proved, the original postulate is incorrect.That is set does not exist.This is one of the main ideas which develops Parmenides (Eleatic school).Zenon supports it.
- If you have set things at the same time must be dissimilar and the like, which is impossible.According to Plato this argument begins the book that interests us of the philosopher.Aporia This suggests that the same thing is seen as similar to itself, and different from others.In Plato it is understood as paralogism as unlikeness and likeness are taken in different ways.
- note an interesting argument against the seat.Zenon said that if there is a place, then it must be something, since it applies to all things.It follows that the seat will also in place.And so on to infinity.Conclusion: there is no place.This argument Aristotle and his commentators are among paralogisms.Improperly that "be" - means "to be in place" as in any place not exist disembodied concepts.
- Against sensory perception argument is called "millet grain."If one grain or its thousandth of a fall no noise as it can do it in the fall medimnov?If medimnov grain produces noise, therefore, it should also apply to one-thousandth of what does not exist in reality.This argument raises the problem of the threshold of perception of our senses, even though it is formulated in terms of the whole and the parts.Paralogism in this formulation is that it is about "the noise produced by a part," is not in fact (as noted by Aristotle, it exists the possibility).
arguments against the motion
The largest known were four Zeno of Elea against time and movement, known by Aristotle's "Physics", as well as comments to her John Philoponus and Simplicius.The first two of these are based on the fact that an infinite number of indivisible "places" (parts) can be represented by a segment of any length.It may not be the final time passed.The third and fourth aporia based on that of the indivisible part consists of time.
"dichotomy"
consider the argument of "Stages" ("dichotomy" - another name).Before overcome a certain distance, the moving body must first go through half of the segment and before the half to achieve, he must pass half the half, and so on to infinity, because any segment can be divided in half, no matter how he was small.
other words, since the motion is always carried out in space, and it is viewed as a continuum of an infinite number of different segments, this important, since divisible to infinity is any continuous quantity.Consequently, the moving body will have a finite time to pass the number of segments, which is infinite.This makes it impossible to move.
"Achilles"
If there is movement, the quickest runner can never overtake the slowest, since it is necessary to first catching reached the place where runaway began to move.Therefore, the need for running more slowly should always be slightly ahead.
Indeed, the move - meaning move from one point to another.From point A fast Achilles begins to catch up with the tortoise, which is currently at point B. At first, he must pass half way, ie the distance a ^.When Achilles would be the point Ab, for as long as he made the motion, the tortoise will be several more in the segment DDL.Then, being in the middle of the way the runner will need to reach the point Bb.To do this, in turn, pass halfway A1V.When an athlete would be toward this goal halfway (A2) have crawled a little farther turtle.And so on.Zeno of Elea in both aporias suggests that the continuum is divisible to infinity, is thought of as actually existing this infinity.
"Arrow"
actually flying arrow is at rest, believed Zeno of Elea.The philosophy of this scientific rationale has always been, and this is no exception aporia.The proof of it the following: the arrow at each time takes a place, which is equal to its volume (since the boom would otherwise be "nowhere").However, to take place, an equal - means to be alone.It can be concluded that can be thought of as the sum of only the movement of various states of rest.It is impossible, as there is no out of nothing is nothing.
"moving body"
If there is movement, it is possible to note the following.One of the two values are equal, and move at the same rate, it may take time for equal twice the distance, but not equal to the other.
this aporia traditionally clarified with the help of the drawing.Move towards each other two equal subjects that are designated by letter symbols.They are on parallel paths and tested at the same time by a third subject, they are equal in size.Moving thus with the same speed, once past the stationary, and the other - by a moving object it will be completed at the same distance at the same time and in the time interval, and its half.Indivisible moment thus will be twice as much himself.It is logically incorrect.He must be either divisible or should be divisible and indivisible part of a space.Since Zeno neither one nor the other does not allow, he concludes, therefore, that the movement can not be conceived without a conflict.That is, it does not exist.
conclusion from all the paradoxes
conclusion that was made of all the paradoxes formulated in support of the ideas of Parmenides, Zeno, is what convinces us of the existence of a plurality of motion and at odds with the evidence of the senses by reason that the contradictions in themselves do not contain,and therefore it is true.False in this case should be considered the arguments and feelings based on them.
Against whom were sent paradoxes?
only answer the question, against whom Zeno were sent, it has not.The views expressed in the literature point of view, the arguments on which this philosopher were directed against the supporters of the "mathematical atomism" Pythagoras, who constructed the physical body of geometric points and believed that the time has atomic structure.This view now has no supporters.
believed in the ancient tradition of a sufficient explanation suggested going back to Plato, that Zeno defended the ideas of his teacher.Opponents have it so everyone who did not share the doctrine which has put forward the Eleatic school (Parmenides, Zeno), and held based on the testimony of common sense.
So, we talked about who is Zeno of Elea.Briefly reviewed its paradoxes.Today, the debate about the structure of movement, time and space is far from complete, so these interesting questions remain open.
