Sabtu, 23 April 2011

Zeno's Paradoxes

Zeno was Parmenides' pupil. Zeno defended his teacher's position on the illusion of change. Like Parmenides, Zeno took the view that common sense led to absurd conclusions. Our senses fail to provide any evidence about reality but only about appearances. Therefore, what our senses reveal to us is deceiving.

Zeno's Paradoxes

To illustrate these differences, Zeno came up with several paradoxes. Paradoxes are statements that appear contrary to common sense but are in fact true.
  • In the paradox of The Racecourse the runner will try to finish the course. But if the course is, say, 100 yards, the runner must first reach the 50-yard marker. And in order to reach the 50-yard marker, he must reach the 25-yard marker. To reach that marker, he needs to reach half that distance, and so on, with the halfway distances being infinitely subdivisible. But since an infinite series of points cannot be traversed in a limited time frame, the race can never really be finished, despite all appearances that tell us that that runners finish races all the time. Thus, motion cannot exist; it is illusory.
  • In Achilles and the Tortoise the point is similar. In order for the swift Achilles to overcome the tortoise, he must reach a point that the tortoise has already left. The distance between the two can be infinitely subdivided and so Achilles can never really overtake the tortoise. Motion cannot exist at all.
  • The Paradox of the Arrow also illustrates that motion is impossible. An arrow shot at a target cannot reach its destination, for at every moment, the arrow has to occupy a specific position in space equal to its length. But this is the definition of an object at rest. So the arrow does not move.
In all of these examples, Zeno is showing that a pluralistic universe is impossible. Parmenides had shown that variety and change were illusions of the senses. In his paradoxes Zeno showed the same thing about motion. Parmenides was right.

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Sabtu, 23 April 2011

Zeno's Paradoxes

Zeno was Parmenides' pupil. Zeno defended his teacher's position on the illusion of change. Like Parmenides, Zeno took the view that common sense led to absurd conclusions. Our senses fail to provide any evidence about reality but only about appearances. Therefore, what our senses reveal to us is deceiving.

Zeno's Paradoxes

To illustrate these differences, Zeno came up with several paradoxes. Paradoxes are statements that appear contrary to common sense but are in fact true.
  • In the paradox of The Racecourse the runner will try to finish the course. But if the course is, say, 100 yards, the runner must first reach the 50-yard marker. And in order to reach the 50-yard marker, he must reach the 25-yard marker. To reach that marker, he needs to reach half that distance, and so on, with the halfway distances being infinitely subdivisible. But since an infinite series of points cannot be traversed in a limited time frame, the race can never really be finished, despite all appearances that tell us that that runners finish races all the time. Thus, motion cannot exist; it is illusory.
  • In Achilles and the Tortoise the point is similar. In order for the swift Achilles to overcome the tortoise, he must reach a point that the tortoise has already left. The distance between the two can be infinitely subdivided and so Achilles can never really overtake the tortoise. Motion cannot exist at all.
  • The Paradox of the Arrow also illustrates that motion is impossible. An arrow shot at a target cannot reach its destination, for at every moment, the arrow has to occupy a specific position in space equal to its length. But this is the definition of an object at rest. So the arrow does not move.
In all of these examples, Zeno is showing that a pluralistic universe is impossible. Parmenides had shown that variety and change were illusions of the senses. In his paradoxes Zeno showed the same thing about motion. Parmenides was right.

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