What is wrong with Zeno's paradox of Achilles and the tortoise? (2024)

What is wrong with Zeno's paradox of Achilles and the tortoise?

The faulty logic in Zeno's argument is often seen to be the assumption that the sum of an infinite number of numbers is always infinite, when in fact, an infinite sum, for instance, 1 + 1/2 + 1/4 + 1/8 + 1/16 + 1/32 +...., can be mathematically shown to be equal to a finite number, or in this case, equal to 2.

(Video) Zeno's Paradox - Achilles And The Tortoise
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What is the answer to Achilles and the tortoise?

Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Achilles must reach infinitely many points where the tortoise has already been before he catches up, so, as Aristotle said, he can never overtake the tortoise!

(Video) Achilles and the Tortoise - 60-Second Adventures in Thought (1/6)
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What is the answer to Zeno's paradox?

The paradoxical conclusion then would be that travel over any finite distance can be neither completed nor begun, and so all motion must be an illusion.

(Video) This Paradox Proves Motion is a Lie (Achilles and the Tortoise)
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What is the paradox of Achilles vs 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, ...

(Video) Zeno's Paradox - Numberphile
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What is the standard solution to the Achilles and the tortoise paradox?

According to the procedure proposed by Zeno, Achilles will never reach the tortoise, as every time Achilles reaches the point where the tortoise was, the tortoise has moved further ahead. This is not a difficult problem to solve, and it is easy to calculate the time it will take for Achilles to reach the tortoise.

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Who won Achilles or the tortoise?

Logically, this would carry on forever. However small the gap between them, the tortoise would still be able to move forward while Achilles was catching up. Meaning that Achilles could never overtake.

(Video) Zeno's Paradox: Achilles and Tortoise Race
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What is the point of what the tortoise said to Achilles?

In Carroll's dialogue, the tortoise challenges Achilles to use the force of logic to make him accept the conclusion of a simple deductive argument. Ultimately, Achilles fails, because the clever tortoise leads him into an infinite regression.

(Video) What is Zeno's Dichotomy Paradox? - Colm Kelleher
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What is Zeno's paradox simplified?

Any moving object must reach halfway on a course before it reaches the end; and because there are an infinite number of halfway points, a moving object never reaches the end in a finite time.

(Video) Zeno's Paradox: Achilles and the Tortoise (90 Second Philosophy)
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Are Zeno's paradoxes based on a mistake?

More specifically, in the case of the paradoxes of motion such as the Achilles and the Dichotomy, Zeno's mistake was not his assuming there is a completed infinity of places for the runner to go, which was what Aristotle said was Zeno's mistake.

(Video) Zeno's Paradox: Achilles and the Tortoise - Will Achilles Catch the Tortoise?
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What is paradox answers?

A paradox is a statement or idea that seems to contradict itself. And, to be fair, they can be confusing. Think about the statement, 'This sentence is false.

(Video) Zeno's dichotomy paradox and its solution.
(ScienceWorld)

Why is Achilles flawed?

It can be argued that Achilles's fatal flaw is that of hubris, excessive pride and overconfidence. This is what prevents Achilles from making amends with Agamemnon when he steals Briseis from him, refusing to accept his offer of recompense for the humiliations he inflicted upon him.

(Video) The Paradoxes of Zeno
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Is Achilles paradox real?

Yes, and it's the same flaw as in the simpler Dichotomy paradox, where Achilles can't reach the destination in the first place because if you keep breaking his motion up into smaller and smaller pieces, eventually they're infinitely small, and no matter how many 0s you add up, you only get 0.

What is wrong with Zeno's paradox of Achilles and the tortoise? (2024)
How would you describe Achilles the tortoise?

Achilles is a small, young tortoise that Gerry purchases from the Rose-Beetle Man. He very quickly becomes tame enough to be given the run of the garden at the strawberry-pink villa. He adores both strawberries and grapes, and if he finds someone sunbathing outside, he tries to climb them.

Who designed the paradox on Achilles and the tortoise?

Zeno of Elea (c. 450 BCE) is credited with creating several famous paradoxes, and perhaps the best known is the paradox of the Tortoise and Achilles.

Who eventually kills Achilles?

Achilles is killed by an arrow, shot by the Trojan prince Paris. In most versions of the story, the god Apollo is said to have guided the arrow into his vulnerable spot, his heel. In one version of the myth Achilles is scaling the walls of Troy and about to sack the city when he is shot.

Why was the tortoise named Achilles?

It's interesting to speculate why the boy in the story named his pet tortoise Achilles. Perhaps the tortoise possesses qualities that remind the boy of the legendary Greek hero Achilles, such as strength, resilience, or determination.

Has Achilles ever lost?

According to legend, the Trojan prince Paris killed Achilles by shooting him in the heel with an arrow. Paris was avenging his brother, Hector, whom Achilles had slain. Though the death of Achilles is not described in the Iliad, his funeral is mentioned in Homer's Odyssey.

What is Zeno's most famous paradox?

It is useful to begin with the most well-known of Zeno's paradoxes: the Achilles. The idea is that Achilles and a Tortoise are having a race. Since Achilles is very fast, and the Tortoise is very slow, the Tortoise is given a head start. The idea is that Achilles and a Tortoise are having a race.

What the tortoise said to Achilles Amazon?

Achilles had overtaken the Tortoise, and had seated himself comfortably on its back. “So you've got to the end of our race-course?” said the Tortoise. “Even though it does consist of an infinite series of distances? I thought some wiseacre or other had proved that the thing couldn't be done?”

What is the message of the story about the tortoise?

The tortoise continues to move very slowly but without stopping and finally it wins the race. The moral lesson of the story is that you can be more successful by doing things slowly and steadily than by acting quickly and carelessly.

Is Zeno's paradox a paradox?

Quite often, things only seem inconsistent because we inadvertedly make an additional assumption, which turns out to be wrong. In the case of Zeno's paradox, that is the assumption that infinite sums cannot yield finite results. This is* a (pseudo)paradox of infinite divisibility.

What is the simplest paradox?

The paradox arises for any sentence that says or implies of itself that it is false (the simplest example being “This sentence is false”). It is attributed to the ancient Greek seer Epimenides (fl.

What are Zeno's paradoxes supposed to prove quizlet?

Zeno's paradoxes show that common sense itself is contradictory (self-contradictory): assuming common sense to be true, that truth generates irresolvable contradictions. Thus, it is said about Zeno's response to Parmenides' critics that Zeno is "repaying them in the same coin with something to spare."

How does Aristotle solve Zeno's paradox?

Aristotle, by contrast, solves the paradox by denying that the flight of the arrow is composed of instants; rather, on my reading, he holds that the flight is a unity which is ontologically prior to the temporal parts that may be abstracted from it.

What was Zeno's main idea?

Zeno believed that for all things that exist, they must exist in a certain point in physical space. For a point in space to exist, it must exist in another point in space. This space must in turn exist in another point in space, and so on.

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