跳跃说谎者悖论与布尔悖论

Jump Liars and Boolean Paradoxes

作为说谎者悖论的推广,n-跳跃说谎者悖论是这样一种悖论,其中的语句在关系框架中每隔n个点真值都发生改变。利用布尔悖论的语义封闭性等特性,证明当n大于1时,n-跳跃说谎者悖论不可能通过布尔悖论来进行表达。同时,对任意的n,给出构造一类布尔悖论的方法,使得它们在比n-跳跃说谎者悖论规定稍弱的意义下,满足所谓的弱n-跳跃说谎者悖论的规定。这部分地解决了n-跳跃说谎者悖论的可定义性问题。

The n-jump liar,being the generalization of the liar paradox,is a paradox whose sentences change their truth values every n points in any relational frame. It is proved that whenever n>1,then the n-jump liars cannot be represented by any Boolean paradox owing to the semantic closeness of the Boolean paradoxes. However,for any number n,we can construct a Boolean paradox,that is,the so-called weak n-jump liar,satisfying the condition for the n-jump liar in some weak sense. These results provide a partial solution to the definability problem of the n-jump liar.