公理化真与说谎者悖论

Axiomatized Truth and the Liar Paradox

公理化真理论把真看作一个原始谓词,并用一组公理和规则给出真谓词的意义,真首先是语形概念。在公理化真理论的标准模型中,一个定理可解释为真。因此模型真和语形真在概念上需要作出区分。通过不同的技术手段大部分公理化真理论都能较好地处理悖论,但DT和KF系统同时证明"说谎者语句λ"与"λ不是真的",此时语形真和模型真产生了冲突。莫德林和费弗曼等国外学者从哲学解释或技术上对此进行的辩护都存在不足之处,本文通过从语义视角入手建立起一种真对应关系后指出,这一受到质疑的结论既不应归结为形式技术问题,不是一个意外的推论,也不必从其他哲学角度进行辩护,问题是由克里普克语义真理论自身在处理强化说谎者悖论时失效所导致的。KF系统两种真的冲突,反而以形式方法揭示了当内、外逻辑不一致时,真理论所具有的性质。

In contrast to semantic theories of truth,axiomatic theories of truth treat truth as a primitive predicate and use certain axioms and rules to govern it.So truth is primarily a notion of syntax.The syntactic truth and model truth should be distinguished.Axiomatic theories of truth have enough resources to represent the liar sentenceλwhose truth value is either both true and false or neither true nor false.Most axiomatic theories of truth treat the liar sentenceλwell using different techniques.But the systems KF and DT prove the Liar Sentenceλand“λis not true”,and at this point the syntactic truth and model truth conflict.Previous attempts to justify this problem by philosophical explanation or technical interpretation are inadequate.On the basis of particular semantic analysis,this paper points out that the problem of KF should not be due to formal technique or accidental conclusion,and moreover the essential reason is the failure of Kripke's semantic truth theory to handle strengthened liar paradoxes.Instead,these problematic theorems reveal the properties of truth theories wherein the inner and outer logics are not coincident.