Probably everyone has come across such a word as "aporia". This is not surprising, because many studied philosophy at the university. However, not everyone knows the essence of this word and will be able to interpret it correctly.
The aporias of Zeno of Elea are an outstanding monument of human thought. This is one of the most interesting problems in the philosophy of ancient Greece, which shows how paradoxical things can be completely obvious at first glance.
Zeno: a brief biography of the sage
We know almost nothing about the pages of the life of the ancient Greek philosopher. And the information that has come down to us is very contradictory.
Zeno of Elea is a philosopher of ancient Greece, born in 490 BC in Elea. He lived for 60 years and died (presumably) in 430 BC. Zeno was a student and adopted son of another famous philosopher, Parmenides. By the way, according to Diogenes, he was also the lover of his teacher, but this information was strongly rejected by the grammarian Athenaeus.
The first dialectician (according to Aristotle) became famous thanks to his logical conclusions, which were called"Aporias of Zeno". The philosophy of Zeno of Elea - all consists of paradoxes and contradictions, which makes it even more interesting.
The tragic death of a philosopher
The life and death of the great philosopher are shrouded in secrets and mysteries. He is also known as a politician, because of which he died. Zeno, according to some sources, led the fight against the Eleatic tyrant Nearchus. However, the philosopher was arrested, after which he was repeatedly and subtly tortured. But even under the most terrible torture, the philosopher did not betray his comrades.
There are two versions of the death of Zeno of Elea. According to one of them, he was subtly executed - thrown into a huge mortar and crushed to death. According to another version, during a conversation with Nearchus, Zeno rushed at the tyrant and bit off his ear, for which he was instantly killed by the servants.
Aporias of Zeno
It is known that the philosopher created at least forty different aporias, but only nine of them have come down to us. Among the most popular aporias of Zeno are Arrow, Achilles and the Tortoise, Dichotomy and Stages.
The ancient Greek philosopher, whose aporias are still puzzled by more than a dozen modern researchers, questioned the existence of such unshakable categories as movement, multitude and even space! The discussions provoked by the paradoxical statements of Zeno of Elea are still ongoing. Bogomolov, Svatkovsky, Panchenko and Maneev - this is not a complete list of scientists who de alt with this problem.
Aporia is…
So what is the point of thisconcepts? And what is the paradoxical aporia of Zeno of Elea?
If you translate the Greek word "aporia", then aporia is "a hopeless situation" (literally). It arises from the fact that a certain contradiction is hidden in the subject itself (or in its interpretation).
One could say that aporia is (in philosophy) a problem that is very difficult to solve.
With his conclusions, Zeno significantly enriched the dialectic. And although modern mathematicians are sure that they have refuted Zeno's aporias, they still conceal many more mysteries.
If we interpret the philosophy of Zeno, aporia is, first of all, the absurdity and the impossibility of the existence of movement. Although the philosopher himself, most likely, did not use this term at all.
Achilles and the tortoise
Let's consider in more detail the four most famous aporias of Zeno of Elea. The first two jeopardize the existence of such a thing as movement. These are the aporia "Dichotomy" and the aporia "Achilles and the tortoise".
Aporia "Dichotomy" at first glance seems absurd and completely meaningless. She claims that any movement cannot end. Moreover, it cannot even begin. According to this aporia, in order to cover the entire distance, one must first cover half of it. And to overcome half of it, you need to go half of half of this distance, and so on ad infinitum. Thus, it is impossible to go through an infinite number of segments in a finite (limited) period of time.
More famousis the aporia "Achilles and the tortoise", in which the philosopher emphatically asserts that the fast hero can never catch up with the tortoise. The thing is that while Achilles runs through the section separating him from the turtle, she, in turn, will also crawl some distance from him. Further, while Achilles will overcome this new distance, the tortoise will be able to crawl a little further. And so it will continue to infinity.
"Arrow" and "Stages"
If the first two aporias cast doubt on the existence of movement as such, then the aporias "Arrow" and "Stages" protested the discrete representation of time and space.
In his Arrow aporia, Zeno states that any arrow fired from a bow is motionless, that is, at rest. How does the philosopher argue this seemingly absurd assertion? Zeno says that a flying arrow is motionless, because at each individual moment of time it occupies a place in space equal to itself. Since this circumstance is true for absolutely any moment in time, it means that this circumstance is also true in general. Thus, says Zeno, any flying arrow is at rest.
Finally, in his fourth aporia, the extraordinary philosopher managed to prove that the recognition of the existence of movement is, in fact, the recognition that one equals its half!
Zeno of Elea suggests imagining three identical rows of riders on horseback lined up. Suppose that two of them moved in different directions, and with the same speed. Soon the last riders of these lines will be in line with the middle of the line, which has remained standing in its place. Thus, each line will pass by half of the line that is standing and by the whole line that is moving. And Zeno says that the same rider in one period of time will cover both the whole path and half of it at the same time. In other words, a whole unit is equal to its own half.
So we figured out this difficult, but very fascinating philosophical problem. Thus, aporia is, in philosophy, a contradiction that lurks in the subject itself or in the concept of it.
