A Revenge-Immune Solution to the Semantic Paradoxes
A Revenge-Immune Solution to the Semantic Paradoxes
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语义悖论的免疫报复解决方案
DOI：
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发表时间：
2003
影响因子：
1.5
通讯作者：
Hartry Field
中科院分区：
文献类型：
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作者：
Hartry Field
本文提出了一种解决语义悖论的方法，即(1)保留无限制的真(A)↔A图式，(2)对象语言可以包含它自己的元语言。由于第一个特征，经典逻辑必须受到限制，但完全经典推理适用于“普通”环境，包括标准集合论。取代经典逻辑的更一般的逻辑包括等价物的替代性原则，该原则与真值图式一起导致了语言中True(A)与A的一般互替性。该逻辑还被证明具有所需的资源来表示在经典逻辑中导致悖论的句子(如说谎句和Curry句)是有缺陷的。事实上，我们可以在语言中定义“缺陷”谓词的层次结构。与任何悖论的解决方案只会滋生涉及缺陷谓词的进一步悖论(“报复问题”)的说法相反，有一个普遍的一致性/保守性证据表明，谈论真理和各种“缺陷程度”都可以在一种单一的对象语言中连贯在一起。
The paper offers a solution to the semantic paradoxes, one in which (1) we keep the unrestricted truth schema “True(A)↔A”, and (2) the object language can include its own metalanguage. Because of the first feature, classical logic must be restricted, but full classical reasoning applies in “ordinary” contexts, including standard set theory. The more general logic that replaces classical logic includes a principle of substitutivity of equivalents, which with the truth schema leads to the general intersubstitutivity of True(A) with A within the language.The logic is also shown to have the resources required to represent the way in which sentences (like the Liar sentence and the Curry sentence) that lead to paradox in classical logic are “defective”. We can in fact define a hierarchy of “defectiveness” predicates within the language. Contrary to claims that any solution to the paradoxes just breeds further paradoxes (“revenge problems”) involving defectiveness predicates, there is a general consistency/conservativeness proof that shows that talk of truth and the various “levels of defectiveness” can all be made coherent together within a single object language.