摘要
数学中的“柏拉图主义”历史悠久,影响深远.现代柏拉图主义的重要观点主要表现在本体论与认识论两个方面.从科学反映论的观点来看,应对新柏拉图主义作两点较重要的修正和补充.一是,随着数学对象的不断被创造,与之相关的“数学真理”也是可以不断地诞生出来的.这个修正的要义是,有些数学真理是被创造出来的,而新、老柏拉图主义的数学发现观,必须融入数学发明观.二是,现代柏拉图主义者只是宏观地认识到了数学真理认识的不完全性.而事实上,人脑所能进行的概念思维,都只能是“单相性”的抽象思维.每一个数学概念都必然是“单相性抽象”的产物.故从本体论着眼,数学理念世界是不可能完全的.现代柏拉图主义很接近科学反映论,故对数学教育工作者也有重要启示作用.
In this paper various view-points of the neoplatonism had been reviewed and disussed. The well-known question concerned with the so-called isomorphism between the human thinking process and the real relations of the objective world had been illustrated with a few mathematical examples. Other related questions had been also mentioned with brief comments.
出处
《数学教育学报》
2004年第3期1-5,共5页
Journal of Mathematics Education
关键词
数学真理
现代
柏拉图主义
本体论
认识论
抽象思维
neoplatonism
idea world
mathematics entity
model truth
isomorphic relation
incomplete principle of abstract thought
predeterminate harmonization
practice inspection rule
