无限问题与数学的统一性

The Infinite Problem and Unity of Mathematics

无限问题曾引发了数学史上三次著名的危机,它们是:(1)由无公度几何量的发现与芝诺论证引发的危机;(2)无限小量悖论导致的危机;(3)由“康托尔悖论”引发的危机。三次危机都涉及到了数学的基础,其成因均统一在无限性矛盾之中。本文认为数学的统一性问题内含广泛,它不仅是数学工作者研究的对象,而且应当成为数学哲学工作者研究、探讨的对象。

The problem of infinite once evoked three great crises in the history of mathematics, which are concerned with mathematic fundament and which are, (1) Zeno of Elea's paradox as well as the discovery of incommeasurable geometric quantity by Pythagorean school, (2) paradox made by Newton and Leibniz about infinitely small quantity and; (3) G. Cantor's paradox. The author attributes the crises to unity of mathematics.