悖论的自指性与循环性

Self-reference and Circularity of Paradoxes

本文使用语义网分析悖论与自指性和循环性。主要结论是证明了有穷悖论都是自指的,同时其矛盾性必定基于循环性。我们还证明存在非自指但基于循环性的(无穷)悖论,比如亚布鲁悖论及其一般变形;又证明了存在自指但不基于循环性的(无穷)悖论,比如超穷赫兹伯格悖论和麦基悖论。这表明自指性与循环性对悖论而言是两个不同的概念。

In the present paper, the sentence nets are used to determine the self-reference and circularity of paradoxes. The main result is that all finite paradoxes must be self-referential and they are also circularity-dependent in the sense that their paradoxicality is based upon some certain circularity. We also prove that there are non-self-referential but circularity-dependent （infinite） paradoxes, such as Yablo’s paradox and its variants;and there are also non-circularity-dependent but self-referential （infinite） paradoxes, such as the transfinite Herzberger’s paradoxes and McGee’s paradox. It suggests that the self-reference and the circularity are two different conceptions with respect to the paradoxes.