Paradoksy ruchu

Abstract

Strangely enough, antinomies of Zeno of Elea are still discussed among philosophers. Some of the thinkers claim that all antinomies of motion were resolved by the invention of calculus; some other object that mathematics, being a purely formal discipline, cannot deal neither with motion nor with time. The view of Henri Bergson is well known according to which in order to grasp the passing instant of time and the fluent stream of motion human consciousness must be taken into account. All empirical sciences spatialize time and freeze motion, and consequently they must be supplemented by philosophical investigations. The author of the paper agrees that mathematics as such is neutral with respect to problems of time and motion, but emphasizes that mathematical structures can model physical situations. He argues that Zeno’s antinomies are completely resolved if calculus is used to model motion. The rate of instantaneous change is effectively modelled by the concept of derivative.