逻辑数学悖论及其解决

Logic & Mathematics Paradox and Its Solution

逻辑——数学悖论是指仅借助于逻辑和数学的符号而得以构造的悖论。从历史发展看,其主要是指布拉里——福蒂(Burali-Forti)悖论,康托悖论和罗素悖论,它们分别是在1897、1899及1902年提出的。逻辑——数学悖论的出现,明确地表明素朴集合论中包含有逻辑矛盾。解决逻辑——数学悖论,必须对康托的素朴集合论加以限制,特别是必须抛弃前面所提到的概括原则。按策梅罗的研究成果,只须对公理适当地加以选择,就可做到既能使新建立的集合论能成为数学的基础,同时又能确保新的理论不会导致悖论。

Logic and Mathematics Paradox refers to the paradox formed with the help of logis and mathematic symbols. The major paradoxes are Burali - Forti Paradox, Cantor Paradox and B. Russell Paradox, which was proposed in 1897, 1899 and 1902 respectively. Logic and Mathematics Paradox clearly indicates that the simple set theory includes logic contradictions. To settle down the Logic and Mathematics Paradox needs to put some restrictions on Cantor＇s simple set theory, especially to discard the generalized principle previously mentioned. According to Zermelo＇ s research achievements, one should properly select the axioms, which can not only make the newly built set theory become mathematical foundation, but also ensure that the new theory result in paradox.