直觉主义解决集合论悖论的方案  

Intuitionism's Solutions to the Paradoxes of Set Theory

作　　者：李娜[1] 袁旭亮[1] LI Na;YUAN Xuliang(College of Philosophy,Nankai University,Tianjin,30035)

机构地区：[1]南开大学哲学院,天津300350

出　　处：《自然辩证法通讯》2018年第9期59-64,共6页Journal of Dialectics of Nature

基　　金：国家社科基金重点项目"基于哲学逻辑的集合论研究"(项目编号:16AZD036)

摘　　要：直觉主义者认为,集合论悖论的产生与接受实无穷、排中律和非直谓性有关。因此,为了解决集合论悖论,直觉主义者要求承认潜无穷、拒斥排中律、接纳直谓性。基于这种直觉主义思想建立的直觉主义集合论和构造性集合论,是直觉主义解决集合论悖论的两种方案。它们与逻辑主义学派的类型论方案和形式主义学派的公理化方案具有相同的地位。Intuitionists think that the origin of the paradoxes of set theory is connected with the actual infinite, the law of excluded middle and impredicativity. Therefore, in order to solve paradoxes, intuitionists have required admitting the potential infinite, rejecting the law of excluded middle and accepting impredicativity. Intuitionistic set theory and constructive set theory based on this intuitionism idea are two solutions of intuitionism to solve the paradoxes of set theory, and they have the same status as the type theory solution of logicism and the axiomatic solution of formalism.

关 键 词：集合论悖论 实无穷 恶性循环 直觉主义集合论 构造性集合论 

分 类 号：N0[自然科学总论—科学技术哲学]