文献类型：期刊文献

中文题名：阿基里斯与龟悖论诠释

英文题名：An interpretation of Achilles and turtle paradox

作者：林妹平[1];黄江[1];师文庆[1];谢玉萍[1]

机构：[1]广东海洋大学电子与信息工程学院物理与光电科学系

年份：2019

卷号：0

期号：12

起止页码：24

中文期刊名：黑龙江科学

外文期刊名：Heilongjiang Science

收录：国家哲学社会科学学术期刊数据库

基金：广东省自然科学基金(2015A030310354);广东海洋大学创新强校项目(GDOU2017052504);广东海洋大学优秀青年骨干教师项目(HDYQ2017005);广东海洋大学海南海青年学者项目,广东海洋大学大学生创新创业项目(CXXL2018177);广东省教育厅特色创新项目(Q18267)

语种：中文

中文关键词：阿基里斯悖论;龟悖论;无限操作;自然时间;芝诺时间

外文关键词：Achilles paradox;Turtle paradox;Infinite operation;Natural time;Zeno time

中文摘要：公元前5世纪,芝诺发表了著名的阿基里斯悖论,此悖论提出让乌龟在阿基里斯前面1 000 m处开始,与阿基里斯赛跑,并且假定阿基里斯的速度是乌龟的10倍,芝诺认为阿基里斯能够继续逼近乌龟,但决不可能追上它,这就是芝诺的阿基里斯悖论。几千年来,阿基里斯悖论成为一些智者,哲学家,语言学家甚至数学家研究和讨论的焦点。尽管如此,阿基里斯悖论到底'悖'在哪里说法不一。从逻辑推导分析了芝诺对阿基里斯悖论的语义理解过程。通过确立参数时间的本性即自然时间与芝诺时间的关系,重新对芝诺的阿基里斯悖论进行分析,试图理清阿基里斯悖论的脉络。通过数学理论计算,证明了阿基里斯只是在有限的时间内无法追上乌龟,并非永远追不上乌龟,揭示芝诺悖论的理论错误,得到阿基里斯悖论是在有限的时间内作无限次操作,但无限次操作并不意味着需要无限时间的结论。在阿基里斯悖论中阿基里斯追赶乌龟的过程是一个周期性的循环过程,而这些重复次数所用的时间总和是有限的。阿基里斯经过无限次这样的操作不能追上乌龟,但不能断论说阿基里斯经过无限的时间也不能追上乌龟,更不能因此就得出阿基里斯永远追不上乌龟的结论。通过定量分析得知重复进行无限个操作不一定要用无限的时间来完成,芝诺分析阿基里斯追乌龟的问题时就是因为看不到问题的本质,把无限的操作和无限的时间看作同一个概念而得出阿基里斯永远追不上乌龟的论断。

外文摘要：In the 5 th century B.C.,Zeno published the famous Achilles paradox,which proposed that the tortoise should start at 1 000 meters ahead of Achilles and race with Achilles.Assuming that Achilles was 10 times faster than the tortoise,Zeno believed that Achilles could continue to approach the tortoise,but could never catch up with it.This is the Achilles paradox of Zeno.For thousands of years,the Achilles paradox has become the focus of research and discussion by some intellectuals,philosophers,linguists and even mathematicians.Nevertheless,there are different opinions about where the Achilles paradox is.The process of Zeno’s semantic understanding of Achilles paradox is analyzed by logical deduction.By establishing the nature of parameter time,i.e.the relationship between natural time and Zeno time,this paper re-analyses Zeno’s Achilles paradox and tries to clarify the context of Achilles paradox.Through mathematical theoretical calculation,it is proved that Achilles can not catch up with the tortoise in a limited time,not forever.The theoretical errors of Zeno paradox are revealed.It is concluded that Achilles paradox is operated infinitely in a limited time,but infinite operation does not mean that it needs infinite time.In the Achilles paradox,Achilles’pursuit of turtles is a cyclical process,and the total time spent on these repetitions is limited.Achilles could not catch up with the tortoise after such operations for infinite times,but it could not be concluded that Achilles could not catch up with the tortoise after infinite time,let alone conclude that Achilles could never catch up with the tortoise.Quantitative analysis shows that repeated infinite operations do not necessarily take infinite time to complete.Zeno’s analysis of Achilles’pursuit of turtles is because he can’t see the essence of the problem and regards infinite operation and infinite time as the same concept,and concludes that Achilles will never catch up with the turtle.