集合论-泛逻辑悖论

对于一类 n(2≤n≤_n) 值逻辑可以给出一个一般形式的形式语言,通过一个六元组的模型,可以递归地定义出该形式语言中的公式的值.这构成了刻画这类逻辑的一个泛逻辑系统 UL ₁.在该系统中,可以定义出抽象否定、抽象蕴涵和抽象等值等联结词,它们分别是二值逻辑中的联结词否定、蕴涵和等值的一般化.利用这些联结词,可以给出Russell型造集谓词、Curry型造集谓词的一般形式.此外,还提出了一种新型造集谓词,这种造集谓词只包含等值联结词,而不涉及其它联结词.通过这3种造集谓词,利用该系统的逻辑工具,证明了在通常的有穷值逻辑、可数无穷值逻辑和不可数无穷值逻辑系统中,概括原则都将导致悖论.

Paradox of set theory-universal logic

A general formal language in which the value of formulas can be recursively defined can be given by a sextuple-model for n(2≤n≤_n )-valued logic. It constitutes a universal logic system UL ₁, which characterizes this kind of logic. Connectives like abstract negation, abstract implication and abstract equivalence can be defined in the system. They are the generalization of negation, implication and equivalence in two valued logic. Applying these connectives, the general forms of Russellian sets-making predicate and Curryian sets-making predicate were developed. In addition, a new type of set-making predicate which only contains equivalence was developed. Applying these three kinds of sets-making predicates, abstraction principle led to paradoxes in general system of finite valued logic, countable infinite valued logic and uncountable infinite valued logic.