As Aristotle realized, the Dichotomy Paradox is just the Achilles Paradox in which Achilles stands still ahead of the tortoise. In his Progressive Dichotomy Paradox, Zeno argued that a runner will never reach the stationary goal line on a straight racetrack.

What is the basic argument of Zeno’s paradox of motion Achilles and the tortoise?

Zeno’s argument rests on the presumption that Achilles must first reach the point where the tortoise started, by which time the tortoise will have moved ahead, even if but a small distance, to another point; by the time Achilles traverses the distance to this latter point, the tortoise will have moved ahead to another, …

What is the paradox of Achilles and the tortoise?

Achilles and the tortoise

In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.

What is Aristotle’s solution to the paradox of the runner?

Then Aristotle’s full answer to the paradox is that the question of whether the infinite series of runs is possible or not is ambiguous: the potentially infinite series of halves in a continuous run is possible, while an actual infinity of discontinuous half runs is not—Zeno does identify an impossibility, but it does …

What did Aristotle say about Achilles?

Aristotle refers to Homer’s portrayal of Achilles as a character with bad traits who is still depicted as a good person; Aristotle argues that such character (morality) should be a poet’s aim. Achilles kills Hector, but Homer still manages to make Achilles look like a good and moral man overall.

What is the point of Zeno’s paradox?

This is the resolution of the classical “Zeno’s paradox” as commonly stated: the reason objects can move from one location to another (i.e., travel a finite distance) in a finite amount of time is because their velocities are not only always finite, but because they do not change in time unless acted upon by an outside …

What is Zeno’s paradox simplified?

In its simplest form, Zeno’s Paradox says that two objects can never touch. The idea is that if one object (say a ball) is stationary and the other is set in motion approaching it that the moving ball must pass the halfway point before reaching the stationary ball.

What is the solution to Zeno’s paradox?

Or, more precisely, the answer is “infinity.” If Achilles had to cover these sorts of distances over the course of the race—in other words, if the tortoise were making progressively larger gaps rather than smaller ones—Achilles would never catch the tortoise.

Does Achilles overtake the tortoise?

Achilles must then reach the new position. But, again, the tortoise reaches a new point during this time; and so on. Whenever Achilles reaches a point, the tortoise reaches a further point and Achilles never overtakes the tortoise.

Why was the tortoise named Achilles?

According to Greek mythology, when Achilles was born, his mother held him up by his heel and dipped him in the river Styx so that he could live forever. After surviving many battles, Achilles finally died after an arrow struck him on his heel. In this story, the author has named his pet tortoise as Achilles.

Why is Zeno’s arrow paradox false?

The argument falsely assumes that time is composed of “nows” (i.e., indivisible instants). There is no such thing as motion (or rest) “in the now” (i.e., at an instant).

Are Zenos paradoxes solved?

The Zeno’s paradoxes lack that quality, so from the mathematical viewpoint, there is nothing to “solve”. The Achilles and the Tortoise “paradox” presents no problem to the modern mind.

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