查询词典 incompleteness theorem

Incompleteness Theorem indicates that any formal system rich enoughis an incomplete theory, in which proof can be verified mechanically.

不完全性定理表明任何足够丰富的形式系统都是不完全的理论，而有机械的证明验证是对形式系统的基本要求。

The Incompleteness Theorem states that any consistent mathematical theory must contain one or more premises that cannot be proved within the theory.

哥德尔不完备定理是说：当一个演绎系统是自足的，总有至少一个或几个前提是在系统内不能证明的。

But the third mathematical crisis and Godel's Incompleteness Theorem provide obvious philosophical significance: It proclaims and proves that human mind is not infinite and we must maintain a humble attitude in front of the mysterious nature.

但第三次数学危机和哥德尔不完备定理，在哲学的意义上是明显的：它宣告并且证明人的理性、理智不是无限的，人类必须在大自然的秘密面前保持谦逊的态度。

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.

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。

Gdel's first incompleteness theorem states that:Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete.

第一，他证明了，对于任意的数学系统，如果其中包含了算术系统的话，那么这个系统不可能同时是完备的和一致的。

It is not my intention to introduce a mathematical crisis into religious arguments, although an American mathematician, when speaking of Godel's Incompleteness Theorem, did call mathematics a branch of theology.

我并不想把数学的危机问题引入宗教问题的争论中来，尽管一个美国数学史家，在谈到哥德尔不完备定理时，乾脆称"数学，神学的一个分支。"

In this paper, the author queried a few conclusions in [1] , and elaborated different views on several problems, such as relations between non-Euclidean geometry and real space, relations between mathematical logic and thinking, the significance of Godel s second incompleteness theorem, and so on.

本文对文〔1〕的几个论断提出一些疑问，并在"非欧几何与现实空间"、"数理逻辑与思维"、"哥德尔不完备性定理的意义"等若干问题上表述了与《数学是什么》一文中不同的观点。

It was not until Godel, the great mathematician who proposed the famous Incompleteness Theorem, that the philosophical significance more fully revealed itself in fundamental mathematical research.

直到再后来，大数学家哥德尔发现了著名的"哥德尔不完备定理"，将数学基础研究的哲学意义，揭示得更加明显。

Del's incompleteness theorem , the availability of complete information that omics data potentially represents might not be sufficient to understand all the underlying principles that govern the functions of biological systems.

拿歌德尔不完备定理作个类比，就算获得了完整的"组学"数据信息也并不意味着我们就可以理解生命系统中所有的潜在法则。

Gdel's second incompleteness theorem can be stated as follows: For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, T includes a statement of its own consistency if and only if T is inconsistent .

第二，他证明了，对于任意的数学系统，如果其中包含了算术系统的话，那么我们不能在这个系统内部证明它的一致性。这就是希尔伯特第二问题答案的一部分。

Continuously improve the production mechanism, to provide customers with better quality products and services.

不断的完善生产机制，给客户提供更优质的产品及服务。

B:Yes, he was the very prize-winner in the court tennis ten years ago?

是的，他是十年前的世界网球冠军。