by AlicetheCurious » Mon Feb 20, 2006 10:32 am
For those who want to dive into an intellectual black hole, be my guests: knock yourselves out...<br><br><!--EZCODE BOLD START--><strong>sophistry</strong><!--EZCODE BOLD END--><br><br>n : a deliberately invalid argument displaying ingenuity in reasoning in the hope of deceiving someone [syn: sophism, sophistication]<br><br><!--EZCODE BOLD START--><strong>ZENO'S PARADOXES</strong><!--EZCODE BOLD END--><br><br><!--EZCODE UNDERLINE START--><span style="text-decoration:underline">Introduction</span><!--EZCODE UNDERLINE END--><br><br>Zeno’s paradoxes are only known from manuscripts of others. His own writings are lost. The most explicit description is given by Aristotle in his Physics. He mentions four arguments of Zeno: the dichotomy argument, the Achilles (and the tortoise) argument, the stationary arrow argument and lastly the stadium argument.<br><br><!--EZCODE UNDERLINE START--><span style="text-decoration:underline">The dichotomy argument</span><!--EZCODE UNDERLINE END--> maintains that no motion is possible, because going from A to B, a mobile (object) has to cross half the distance between A and B first, and then half the distance remaining etc. Therefore, it can never reach B, because there is no end to the series of halved distances.<br><br><!--EZCODE UNDERLINE START--><span style="text-decoration:underline">The Achilles argument</span><!--EZCODE UNDERLINE END--> maintains that Achilles cannot overtake ‘the slowest’(tortoise), because at the moment he reaches the starting point of the tortoise, the tortoise is already somewhere else (no matter how small the distance travelled by the tortoise) etc.<br><br><!--EZCODE UNDERLINE START--><span style="text-decoration:underline">The stationary arrow argument</span><!--EZCODE UNDERLINE END--> maintains that, at any instant, an arrow flying through the air is in some place. And because it cannot be in more than one place at the same time, in must be at rest at any instant. Therefore the arrow is not moving at any time during its flight.<br><br><!--EZCODE UNDERLINE START--><span style="text-decoration:underline">The stadium argument</span><!--EZCODE UNDERLINE END--> maintains that if indivisible time units existed (infinitisimals), then two chariots, with the same speed and therefore each traversing the same distance in one indivisible unit time, in opposite directions, would have an approach speed of that distance in half a unit of time, which is impossible. Zeno (implicitly) assumes that if motion exists, there must be a minimal, indivisible unit of time. Because such a unit cannot exist, there cannot be motion, because motion depends on duration. <br><br><!--EZCODE AUTOLINK START--><a href="http://home.tiscali.nl/siemoppe/paradox/zeno/">home.tiscali.nl/siemoppe/paradox/zeno/</a><!--EZCODE AUTOLINK END--><br><br>For the rest of us, could we please get back to FourthBase's conspiracy class & term paper? <p></p><i></i>