哥德尔自指命题与悖论

On Gdel's Self-Reference Proposition and Paradox

"可证"的算子用法与谓词用法是严格区分概念层次的结果。"可证"的算子用法是从命题外部来理解"可证"的,而它的谓词用法则是从命题内部来理解的。哥德尔自指命题是否导致悖论,关键在于如何理解"可证"概念。如果把"可证"理解为语句算子,那么哥德尔自指命题就不会导致悖论。否则,如果把它理解为谓词,那么哥德尔自指命题就会导致悖论。

The operator and the predicate uses of ＂provable＂ are the results of distinguishing levels strictly. The operator use of ＂provable＂ looks ＂provable＂ outside a proposition, while its predicate use inside. Whether Godel＇ s Self-Reference Proposition leads to paradox depends on how to under- stand the essential concept improvable. In normal inference, if concept improvable is taken as a sen- tential operator, G^del＇ s Self-Reference Proposition can not lead to a paradox. Otherwise, if it is taken as a predication, Gt^del＇ s Self-Reference Proposition can lead to a paradox.