摘要
数学基础的研究,形成了逻辑主义、形式主义和直觉主义三大学派,其运用理性主义构造数学,认为数学是一个欧几里得系统.拉卡托斯通过对三大学派所做工作分析之后,认为数学是一个拟经验系统,数学的真理性是被"说明",而不是被"证明"的,它的发展模式是:问题———猜测———反驳,数学理论具有可证伪性.由理性主义到经验主义是现代数学哲学研究的历史走向,这种走向表明数学在不断追求完美与和谐.
The research of the foundations of mathematics falls into three schools of thought: logicism, formalism and intuitionism. They constitute mathematics by means of rationalism and maintain that mathematics is a Euclidean system. After analyzing the results of the three schools of thought, Lakatos holds that mathematics is a pseudo-empirical system. Its truthfulness is explained rather than proved, and its development mode is: problem-conjecture-refutation. And the mathematical theories have falsifiability. The historical trend of mathematical philosophy is from rationalism to empiricism, which indicates that mathematics is going on pursuing perfection as well as harmony.
出处
《河南大学学报（自然科学版）》
CAS
2003年第4期50-53,共4页
Journal of Henan University:Natural Science
基金
河南省教育厅人文社会科学基金项目(018-2K-720)
河南大学教学改革项目(BW-0309)
关键词
理性主义
经验主义
数学基础
历史走向
rationalism
empiricism
the foundations of mathematics
historical trend
