悖论的语言结构:递归否定

The Language Structure of Paradox:Recursive Negation

悖论是逻辑学、基础数学、哲学、语言学中的重要问题,从根本上看是一个认识论问题,因此仅仅从人工语言的角度来认识悖论是不充分的,因为人工语言不能解决元语言这一根本问题。自然语言是最根本的元语言,悖论更需要从自然语言的角度来认识,尤其是从自然语言结构的递归性来认识。通常把悖论分成逻辑悖论(集合悖论)和语义悖论两大类,但这种分类界限并不严格。实际上这两类悖论从语言生成的角度看都具有递归否定的特点,因此可以用递归否定这一语言结构性质来统一语法悖论和语义悖论。罗素的类型论和塔尔斯基语义理论主要涉及产生悖论的层阶性质,不能概括悖论的递归否定性质。自然语言和形式语言都是从有限规则和有限符号到无限句子的系统,不可能避免层阶循环或递归,因此悖论的消除不可能通过类型论或元语言层阶来解决,考虑递归否定的性质是消除悖论的一个途径。

Basically, language, Paradox is an important problem in logic, foundation of mathematics, philosophy and linguistics. paradox is a problem of epistemology. It is not enough to research on paradox on the line of formal because the problem of metalanguage can not be resolved on the base of formal language. Natural languages are most primitive metalanguages, and paradox needs to be studied more on the line of natural especially on the line of recursion of the structure of natural languages language. Paradox is usually divided into logic paradox and semantic paradox. However, the border is not clear. Both of them have the feature of recursive negation and can be explained generally by the feature. Both Russell＇s type theory and Tarski＇ s semantic hierarchy concern the hierarchy of paradox but fail to cover the recursive negation. Either the natural language or the language can produce infinite sentences by finite rules and symbols, thus the hierarchy and recursion of theory formal language can not be avoided, so the paradox can not be cleared only by the type theory and semantic hierarchy theory. It is one of the ways to clear paradox on the line recursive negation.