论集合概念的本质——一个案例考察

On the Nature of the Concept of Set:A Case Study

集合概念的演变和现状说明,迭代集合概念对理解集合概念的本质是不够的。我们提出了一种基于证据的认识方法,并以一些案例说明,使用集合论的成果作为证据来理解集合概念的本质如何可能。证据方法还表明,谢拉对投影可决定公理的反驳不能成立。相反,他的论证可以帮助我们理解集合概念的本质。此外,这种基于证据的认识方法得出的结论具有可错性和理论间的可对比性。

The evolution and current state of the concept of set suggest that the iterative concept of set is not sufficient for understanding the nature of the concept of set.Therefore,we proposed an evidence-based approach to show with some cases how it is possible to use the results of the set theory as evidence to understand the nature of the concept of set.The evidence-based approach also showed that S.Shelah's refutation of the axiom of projective determinacy cannot be sustained.Instead,his argument can help us to understand the nature of the concept of set.Moreover,this evidence-based approach leads to conclusions which are falsifiable as well as comparable between theories.