超级任务:现代的芝诺悖论

Supertasks: Modern Zeno’s Paradoxes

超级任务是指在有限的时间间隔内依次序完成一个步骤的数量为无限大的序列。它指代了一系列与芝诺悖论相类似的问题。本文按照时间顺序梳理了超级任务从20世纪中叶诞生至今的历史脉络,主要介绍了超级任务概念产生的历史背景、前期的重要论题——汤姆森台灯、伊尔曼和诺顿对这一类问题总结性的解答和新时期超级任务与融入不同具体学科的新发展趋势。

Supertasks are processes which consist of infinitely many actions performed in a finite amount of time.They refer to a series of Zeno-like puzzles.This article combs the history of supertasks starting from mid 20th century and mainly introduces the historical context of origination of supertasks,Thomson’s Lamp,an important thesis at the early stage,Earman and Norton’s conclusive solution and the new tendency towards integration of supertasks and various research fields.