解决集合论悖论的模态方法研究

A Modal Solution to the Paradoxes of Set Theory

ZFC集合论等经典的集合论悖论解决方案,一般是通过限制康托尔不受限概括原则中的给定性质的“任意性”来解悖的。但是弗莱茨等人认为,除了这一路径外,还可以通过限制元素满足给定性质的方式的“任意性”来解决集合论悖论,并建议利用模态算子刻画元素满足给定性质的“特殊方式”。弗莱茨等人给出的这种模态解悖方法本质上是一种修正康托尔不受限概括原则的新方法。

Classical set theories such as ZFC solve the paradoxes of set theory by restricting the“arbitrariness”of the properties given in Cantor’s unrestricted comprehension principle. But Fritz et al. think that,instead of restricting the properties,we can also restrict the ways in which the elements satisfy a given property. Fritz et al. propose making use of a modal operator to formalize “a special way”,so that the set is formed by collecting those elements that satisfy the given property in a special way. In essence,the modal solution presented by Fritz et al. is a new method to modify Cantor’s unrestricted comprehension principle.