论紧缩真理论的保守性困境

On the Dilemma of Conservativity in Deflationism

紧缩真理论认为"真"是非实质的概念,并得出保守性承诺,即真理论不能比基础理论证明更多的不包含真概念的事实。已有结论则表明,大部分充分的公理化真理论对作为基础理论的形式算术是不保守的,因此紧缩论陷入了保守性困境。但事实上,紧缩论的反对者将讨论局限在形式算术的句法保守性,且做了跳跃论证。通过分析,"PA系统是一致的"和"哥德尔语句G"并不能被视作新的实质算术知识。因此,如果将对句法的保守性扩展到对算术知识的保守性上,可以给夏皮罗论证有力的反驳,那么真理论对算术知识来说依然是保守的,已有困境将得到解决。

Deflationism holds that truth is a light and insubstantial notion.This leads to the conservativity commitment of deflationism,that is,the truth theory should not prove more facts that do not contain the truth concept than the base theory.However,the existing formal results show that most sufficient axiomatic theories of truth are not conservative over Peano Arithmetic as the base theory,so deflationism falls into the dilemma of conservativity.In effect,the existing argumentations are confined to the syntactic conservativity of formal Peano Arithmetic by the opponents of deflationism,and they make a jumping argument.Through our analysis,"PA system is consistent"and"G9 del sentence G"cannot be regarded as new substantial arithmetic knowledge.Therefore,if the syntactic conservativity is extended to the conservativity of arithmetic knowledge,then we can give a refutation to the classical Shapiro argument,so that the theories of truth are still conservative over arithmetic knowledge and the dilemma of conservativity will be solved.