真谓词的不可定义性问题的根源

On Cause of the Problem of the Indefinability of Truth

塔斯基的真之定义理论确定了“实质的恰当性”与“形式的正确性”标准,进而蕴涵了语言分层原则、组合性原则和本质上的丰富性原则。虽然为了证明无穷阶的普遍类理论语言或一阶皮亚诺算术语言的真谓词的不可定义性定理,塔斯基借助了循环性悖论,但真谓词的不可定义性定理并不局限于悖论性或循环性的语言。造成其真谓词不可定义的真正根源在于它们的元语言不符合真之定义理论的标准,尤其是“本质上的丰富性”原则。

Tarski provided the criterion of formal correctness and of material adequacy with his theory of definition of truth,which implies further three principles:that of hierarchy,of compositionality and of essential richness.Although Tarski proved the undefinability theorem,which asserts directly that the truth predicate of LGTC(or LPA)is undefinable in itself,with the circular paradox.However,what is asserted in the theorem is not only applicable to paradoxical or circular languages.The real cause of the undefinability of truth is that their meta-language cannot satisfy these criterions and principles,especially that the meta-language is not essentially richer than its object language.