芝诺悖论的逻辑分析

A Logic Analysis of Zeno's Four Paradoxes

对芝诺悖论迄今尚未有全面、通俗而透彻的逻辑分析。这几个悖论的"神奇"之处在于,其结论的荒谬性不言而喻,但其论证却似乎难以挑出毛病:前提都好像是可接受的,而论证形式也仿佛没有违反逻辑规则。其实,它们的结论并非必然违背常识,一定条件下也可以成立。而在通常条件下,其结论之所以不可接受,实源于其论证中隐含着真正的逻辑谬误:把可带有统一度量单位的"无穷"与不可能有统一度量单位的"无穷"混为一谈,把相对于具体条件的现象(静止、运动、速度等)绝对化、无条件化,从而要么违反同一律,要么违反充足理由律。

Zeno’s four paradoxes have not yet been a comprehensive,popular and thorough logical analysis.Their conclusions are clearly absurd,but it is difficult to find fault from their argumentation.This is precisely the magic of these paradoxes.In fact,their conclusions are not necessarily contrary to common sense,and can also be correct under certain conditions.Under normal conditions,their conclusions are clearly unacceptable.But the real reason is the implied logical fallacies in their argumentation： two different ＂infinity＂ are confused,some phenomena relative to the specific conditions（such as stillness,movement,speed,etc.） are absolutized,and thus either the law of identity,or the principle of sufficient reason,is violated.