基于限制版第五基本定律的抽象主义集合论

Abstractionist Set Theory Based on Restricted Basic Law Ⅴ

布劳斯使用大小限制观念改造弗雷格的第五基本定律,由此引发了各种各样的限制第五基本定律的策略。我们的目的在于比较三种限制第五基本定律的策略,并对比基于限制版第五基本定律的两种集合论。我们的贡献在于:首先,我们找到了伯吉斯放弃达米特的不定可扩充性而坚持布劳斯路线的原因;其次,我们也找到了夏皮罗放弃复数逻辑重述集合论公理的原因;最后,我们察觉到夏皮罗改造伯奈斯—布劳斯集合论的关键要素。

George Boolos once used the idea of limitation of size to improve Gottlob Frege’s Basic Law Ⅴ,and then incurred different kinds of strategies of restricting the Basic Law Ⅴ.Our aim is to compare the three kinds of strategies of Restricted Basic Law Ⅴ,and contrast one set theory with another set theory.Our contributions are the following:first,we find the reason why Burgess abandoned Dummett’s indefinite extensibility and sticked to Boolos’s option;second,we also find the reason why Shapiro gave up on using plural logic to reformulate the axioms of set theory;third,we perceive the key ingredients that Shapiro used to reform Bernays-Boolos set theory.