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哥德尔不完全性定理与悖论有着耐人寻味的不解之缘。涉及描述自身规定的悖论本身就是描述边界的界碑,此界碑表明了形式系统本身的不完全性。哥德尔不完全性定理根源于规定的不完备性,它从形式上证明了,任何封闭的描述体系都是不完全的;悖论是走向新领域的门枢。在人类理性的边界处做出的规定,正是形式系统甚至所有封闭的理论体系不完全性的根源,从而正是哥德尔不完全性定理的根据。哥德尔不完全性定理的悖论关联,具有极为深刻的哲学意蕴。
Gödel’s incompleteness theorem and paradox have an intriguing indissoluble bond. The paradox involved in describing its own provisions is itself a boundary monument, which shows the incompleteness of the formal system itself. Gödel’s incompleteness theorem stems from the incompleteness of the rules. It formally proves that any closed description system is incomplete; the paradox is the pivot to the new domain. Provisions made at the boundary of human rationality are precisely the root causes of the incompleteness of the formal system and even of all closed theoretical systems and are therefore the basis for Gödel’s incompleteness theorem. The paradoxical connection of Gödel’s incompleteness theorem has extremely profound philosophical implication.