♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣ We may say a thing is at rest when it has not changed its position between now and then, but there is no ‘then’ in ‘now’, so there is no being at rest. Both motion and rest, then, must necessarily occupy time. (Aristotle, 350 BC) ♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣♣ ★★★★★★★ Zeno s Paradox ★★★★★★★ The great Greek philosopher Zeno of Elea (born sometime between 495 and 480 B.C.) proposed four paradoxes in an effort to challenge the accepted notions of space and time that he encountered in various philosophical circles. His paradoxes confounded mathematicians for centuries, and it wasnt until Cantors development (in the 1860s and 1870s) of the theory of infinite sets that the paradoxes could be fully resolved. Zenos paradoxes focus on the relation of the discrete to the continuous, an issue that is at the very heart of mathematics. Here we will present the first of his famous four paradoxes. Zenos first paradox attacks the notion held by many philosophers of his day that space was infinitely divisible, and that motion was therefore continuous. ●●●●●●●●●●●●●●●●●●●●●●●●● Paradox : The Motionless Runner ●●●●●●●●●●●●●●●●●●●●●●●●● A runner wants to run a certain distance - let us say 100 meters - in a finite time. But to reach the 100-meter mark, the runner must first reach the 50-meter mark, and to reach that, the runner must first run 25 meters. But to do that, he or she must first run 12.5 meters. Since space is infinitely divisible, we can repeat these requirements forever. Thus the runner has to reach an infinite number of midpoints in a finite time. This is impossible, so the runner can never reach his goal. In general, anyone who wants to move from one point to another must meet these requirements, and so motion is impossible, and what we perceive as motion is merely an illusion. Where does the argument break down? Why? ■■■ Note: ■■■ A paradox is a statement or proposition which, despite sound (or apparently sound) reasoning from acceptable premises, leads to a conclusion that seems logically unacceptable or self-contradictory.
Posted on: Sun, 10 Aug 2014 07:54:12 +0000
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