数学的有效性问题初探

数学的有效性始终是数学史及哲学史上广为关注的重要问题之一,而要对之达到深刻的理解,还必须作出本源性思考,回到数学得以产生和发展的源头--人类能动的社会实践去.本文立足于对历史的深入考察,指出从人类现实的社会实践中抽象而来的"实体"范畴乃是数学的最根本的前提性预设,是理解问题的关键.进而对"实体"概念的现实基础及其理想化色彩作出了深入分析,由此揭示了数学乃至科学和现代技术的有效性及其限度,这将有助于我们更好地认识和把握与之相关的一系列科学哲学及技术哲学问题.

A Preliminary Study on the Effectiveness of Mathematics

As one of important problems in the history of science and philosophy, the effectiveness of mathematics has been discussed for a long time. In this paper, it is pointed out that the category "Entity" is the most important premise of mathematics ,and it's also the key to understand the effectiveness of mathematics and it's limitation.The analysis will help us to understand the effectiveness and limitations of science and technology,and it is good for us to understand the Questions of the Philosophy of Science and Technology.