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原创 Zeno's Paradox

2017-5-29 23:18 498 0 分类: 机器人/ AI

「芝诺毕竟曾经以非数学的语言,记录下了最早同连续性和无限性格斗的人们所遭遇的困难。」

— E.T.Bell



芝诺 (Zeno of Elea) 在其著名的芝诺悖论 (Zeno's Paradox) 中探讨了动和静,无限和有限,连续和离散之间的关系。从这个角度这些悖论本身并不仅仅是诡辩,至少它对当时数学和哲学的发展起到了推动作用。


比如芝诺悖论中的二分法悖论(The dichotomy's Paradox),翻译过来是说,「一个人从A走到B,要先走完路程的1/2,再走完剩下的路程的1/2即1/4,再走完剩下的路程的1/2即1/8,以此类推。。。无限循环下去,永远不能到达终点」。中国古代哲学家庄子在「庄子·天下篇」中也曾描述过无穷的思想:「一尺之锤,日取其半,万世不竭」。


In「 The dichotomy's Paradox 」, Zeno stated that to complete a infinite number of finite distances, one must take an infinite time. I.e., the total distance could never be completed. Here Zeno discussed the relationships bewteen infinite and finite, discrete and continuous, with respect to space and time.

An ancient Chinese philosopher Zhuang Zhou also mentioned the similar concept in his book「Zhuang Zi」:「一尺之锤,日取其半,万世不竭」(不好意思没找到翻译)。

Such kind of discussions contributed the development of mathematics and philosophy at that time and even up to now. And in this sense, Zeno's Paradoxes is not simply an sophism, but an attempts to the exploration of metaphysical world.


References:

1.「芝诺悖论」百度百科

2.Stanford Encyclopedia of Philosophy, Zeno's Paradoxes https://plato.stanford.edu/entries/paradox-zeno/#Dic


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