布尔悖论的雅布鲁展开式

Yabloseque Unwinding of Boolean Paradoxes

根据库克等人的提法,雅布鲁悖论可看作是说谎者悖论的“展开”。这种展开被证明保持了说谎者的悖论度,从而也保持了它的循环性,并且这种保持对n-卡片悖论及其展开也成立。将这个结论进一步推广到更大的一类悖论———布尔悖论上,利用语句网来表达布尔悖论及其展开可以证明,任何一个布尔悖论与其展开都具有相同的悖论度,还可证明两者依赖了相同的循环性。

According to the notions introduced by Cook et al., Yablo s paradox can be considered as an “unwinding” of the Liar. It has been proved that the unwinding preserves the degree of paradoxicality of the Liar, and thus the circularity of the Liar. Moreover, the above conclusion is also true for all n-card paradoxes and their unwindings. In this paper, the conclusion is extended to a larger class of paradoxes--Boolean paradoxes. Sentence net is applied to represent Boolean paradoxes and their unwindings. It is shown that any Boolean paradox has the same degree of paradoxicality as its Yabloseque unwinding. As a result, both of them depend on the same circularity.