Lago Ladoga

The paradoxes of Zénon form a whole of Paradoxe S imagined by Zénon d' Élée to support the doctrines of Parménide, according to which any obviousness of the directions is fallacious, and the movement is impossible.

Several of the eight paradoxes of Zénon crossed time (paid by Aristote in the Physique and by Simplicius de Cilicie in a comment on this subject) and are basically equivalent one to the other. Some were considered, even during ancient time, like very easy to refute. Three of most famous and difficult are the paradox of Achille and the tortoise , that of the stone launched towards a Arbre , and that of a arrow in flight .

The paradoxes of Zénon represented an important problem for the ancient and medieval philosophers, who did not find any solution satisfactory until the 17th century, with the development in Mathématiques of results on the infinite continuations and of the analysis.

Paradoxes of Zénon d' Élée

Achilles and the tortoise

In the paradox of Achilles and tortoise, it is known as that one day, the Greek hero Achille disputed a race on foot with the slow reptile. As Achille was famous being a very fast runner, it had granted gracefully to the tortoise an advance of cent meters. Zénon affirms whereas it fast Achille forever who been able to catch up with the tortoise. “Indeed, let us suppose to simplify the reasoning that each competitor runs at constant speed, one very quickly, and the other very slowly; at the end of some Time, Achille will have filled his cent meters of delay and reached the starting point of the tortoise; but during this time, the tortoise will have traversed a certain distance, certainly much shorter, but nonnull, let us say one meter. That will require then of Achille an additional time to traverse this distance, during which the tortoise will advance even further; and then another duration before reaching this third point, whereas the tortoise still progresses. Thus, all the times where Achille reaches the place where the tortoise found, it is found even further. Consequently, it fast forever who been able Achilles and will be able to never catch up with the tortoise”.

Stone launched towards a tree

This paradox is similar to the Paradoxe of Achilles and the tortoise.

The following paradox, that of the stone launched towards a tree, is an alternative of the precedent. Zénon is held with huit meters of a tree, holding a stone. It launches its stone in the direction of the tree. Before the stone can reach the tree, it must cross first half of the huit meters. It takes a certain time, not no one, with this stone to move at this distance. Then, there remain to him still quatre meters to traverse, of which it achieves initially half, deux meters, which takes a certain time to him. Then the stone advances of one meter, progresses after a half-meter and still of a quarter, and so on AD infinitum and each time with a time not no one. Zénon concludes from it that the stone will be able to strike the tree only at the end of an infinite time, i.e. never.

The arrow in flight

Other interpretations

One can note that several philosophers whose Kant, Hume, and Hegel proposed other solutions with these paradoxes. A solution even simpler, initially suggested by Leucippe and Démocrite, contemporaries of Zénon, is to deny that space is divisible ad infinitum. The atomic theory indeed enables us to move from one point to another without resorting to the infinite mathematical series.

See too

Dialectical Paradox

External bonds

Analysis of the paradoxes of Zénon
Modernity of the paradoxes of Zénon

Simple: Zeno' S paradoxes

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