Zeno of Elea, a Greek philosopher, lived some 2500 years ago. Zeno’s Paradoxes dealt with a type of argument called reductio ad absurdum which is also known as proof by contradiction. He argued against plurality due to the fact that he believed that for an object there must be a point that protrudes out more than the rest and another point on that point would then further protrude out more than the rest this would go on ad infinitum. Therefore, this would lead to an infinite mass.
Zeno’s arguments against motion included the race course, Achilles and the tortoise, the flying arrow and the stadium. Many were baffled by his ideas, although they were never convinced that it was true, they had to accept the conclusion due to the fact that it was a proof by contradiction and some have yet to find a reasonable fault or premises to refute the deductive argument.
The idea of the race course paradox was that Zeno believed it was not possible to traverse a race course. He believed that in order to run a race course, one has to first run to the midpoint, half the distance, before eventually getting to the end of the race course. However, in order to reach the midpoint, one has to travel half the midpoint. This will eventually lead to an infinite number of half distances. Zeno believed that it was impossible to complete an infinite task in a finite time; hence he concluded it that movement was not possible in light of that.
Zeno’s second argument was the Achilles and the tortoise. He believed that the slower runner would never be overtaken by the faster in a race if the slower runner has a head start. He reasoned that in order for the faster to overtake the slower, he has to first catch up to the slower before being able take a lead. However, when he catches up to the point the slower runner was at, the slower runner has already moved a short distance forward in the time taken to catch up. This continues and the faster runner will never be able to catch up with the slower runner, because the former will always be behind the latter, albeit by a small distance each time.
Zeno’s arrow argument states that an arrow that is flying is actually stationary. He believed that it is at rest as it is not shifted by any degree out of place equal to its own dimension. At any particular instant, the arrow is in the place it occupies at that particular instant. He then drew the conclusion the arrow is not moving at any time during the flight, since the so called movement of the arrow consists of an infinity number of instants.
Through modern science and mathematics, we have been able to prove that movement is indeed possible. Common sense tells us that motion is possible. After all, Zeno himself probably walked home everyday. What he left for us is probably the idea that reasonable assumptions can lead to absurd conclusions, as his paradoxes did. He contributed much to logic and philosophical research today, but personally, I don’t find his stories very moving.
Zeno’s arguments against motion included the race course, Achilles and the tortoise, the flying arrow and the stadium. Many were baffled by his ideas, although they were never convinced that it was true, they had to accept the conclusion due to the fact that it was a proof by contradiction and some have yet to find a reasonable fault or premises to refute the deductive argument.
The idea of the race course paradox was that Zeno believed it was not possible to traverse a race course. He believed that in order to run a race course, one has to first run to the midpoint, half the distance, before eventually getting to the end of the race course. However, in order to reach the midpoint, one has to travel half the midpoint. This will eventually lead to an infinite number of half distances. Zeno believed that it was impossible to complete an infinite task in a finite time; hence he concluded it that movement was not possible in light of that.
Zeno’s second argument was the Achilles and the tortoise. He believed that the slower runner would never be overtaken by the faster in a race if the slower runner has a head start. He reasoned that in order for the faster to overtake the slower, he has to first catch up to the slower before being able take a lead. However, when he catches up to the point the slower runner was at, the slower runner has already moved a short distance forward in the time taken to catch up. This continues and the faster runner will never be able to catch up with the slower runner, because the former will always be behind the latter, albeit by a small distance each time.
Zeno’s arrow argument states that an arrow that is flying is actually stationary. He believed that it is at rest as it is not shifted by any degree out of place equal to its own dimension. At any particular instant, the arrow is in the place it occupies at that particular instant. He then drew the conclusion the arrow is not moving at any time during the flight, since the so called movement of the arrow consists of an infinity number of instants.
Through modern science and mathematics, we have been able to prove that movement is indeed possible. Common sense tells us that motion is possible. After all, Zeno himself probably walked home everyday. What he left for us is probably the idea that reasonable assumptions can lead to absurd conclusions, as his paradoxes did. He contributed much to logic and philosophical research today, but personally, I don’t find his stories very moving.
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