试论语义悖论的弗完全理论

弗完全理论通过限制排中律的使用,弱化经典逻辑,采用非经典的三值语言来处理语义悖论,最终使得形式语言能够一致地包含自身的真谓词。文中我们讨论了弗完全理论的两种基本形式——基础的弗完全理论和高级的弗完全理论。基础的弗完全理论引入了＂真值空缺＂的思想,认为句子除了真假之外还有＂既不真也不假＂的第三值,像说谎者这样的语义悖论语句就落在真假之空缺中,该理论借助于对不动点的归纳构造过程证明了形式语言中真谓词的存在性。高级弗完全理论在前者的基础上引入一个适当的条件句,定义了一个＂更强的真＂,发展出了既满足真的素朴模式又具有不动点解释的、一致的高级弗完全理论。

On the Paracomplete Theory of Semantical Paradox

By restricting the universal applicability of Excluded Middle and thereby weakening the classical logic,a paracomplete theory shows that a formal language, such as a three-valued non-classical language,can consistently contain its own truth predicate and solve the truth-theoretical paradox.In this paper,we present two different paracomplete theories—a basic paracomplete theory and an advanced one.The basic paracomplete theory employs the idea of a ＂truth-value gap＂,and argues that some sentences,such as liar sentences,are neither true nor false but fall within the gap between truth and falsity.By proving the existence of fixed-points of the ＂jump function＂,the basic paracomplete theory also proves that a rich enough language can contain its own truth predicate.On the other hand,the advanced paracomplete theory adds a suitable conditional to the basic theory,defines a ＂stronger truth＂ or ＂determinately true＂ operator,and proves by giving fixed-point interpretation that a consistent theory containing the naive truth theory,a suitable condition,and a stronger truth operator is possible.