不完全性定理对人类思想的影响

The Influence of Incompleteness Theorem upon Human Thinking

哥德尔不完全性定理是数理逻辑中的一个定理,1931年奥地利逻辑、数学家克尔特.哥德尔(Kurt Godel)发现并证明。这个定理彻底粉碎了希尔伯特的形式主义理想,从根本上澄清了作为一个整体的数学不可形式化的本质。而且哥德尔定理产生的影响已远远超出数学的范围,他从根本上改变了我们对"真理"的认识和对世界的认识,不了解哥德尔就不了解人类已达到的智力水平与人类智力奋斗的历程,也就无法了解我们这个世界在思想观念上已经发生或正在发生的深刻变化。

Godel＇s incompleteness theorem falls into the category of Mathematical Logic, which was discovered and proved by the Austrian logician and mathematician Kurt Godel in 1931. The theorem thoroughly smashes the ideal of Hilbert＇s formalism, and basically clarifies the essence that mathematics as a whole can＇t be formalized. Furthermore, the influence of Godel＇ s incompleteness theorem has far exceeded the category of mathematics, and fundamentally altered our idea of ＂truth＂ and of the world. Hence, without getting to know Godel we can＇t understand the intelligence level achieved by mankind and the journey of mankind＇s striving for intelligence progress, neither can we apprehend the profound changes of thought that have taken place or are taking place in this world.