哥德尔证明
Gödel's proof
Ernest Nagel、James Roy Newman · 初版 1958 年
30人推荐
39位读者提及
45次提及
为什么值得读
- 篇幅仅为同类书的十分之一，直奔主题
- 剥离冗长寓言，清晰讲解不完备定理
- 平易近人，有效澄清对定理的哲学误读
1931年，Kurt Godel发表了他具有奠基意义的论文《On Formally Undecidable Propositions of "Principia Mathematica" and Related Systems》。这篇革命性的论文挑战了数学与逻辑学诸多前沿研究背后的某些基本假设。1951年，Godel凭借其在自然科学领域的卓越成就荣获首届Albert Einstein Award，其工作由此获得了学界与公众的高度认可——这或许是当时美国该领域的最高荣誉。评奖委员会盛赞他在数理逻辑方面的贡献是“近年来对科学界最伟大的贡献之一”。然而
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当我第一次对不完备性着迷时（在学完计算理论的初级课程之后），它在一段时间内几乎成了我的一种“信仰”。但正如许多数学家所感叹的那样，不完备性定理是有史以来被滥用最多的证明之一——被非专业人士用来鼓吹自己半生不熟的伪哲学（当然，量子力学也是同样的遭遇……
When I first became fascinated with incompleteness (following initial coursework in theory of computation), it kind of became my "religion" of sorts for a while. But as many mathematicians lament, the Incompleteness Theorem is one of the most popularly abused proofs of all time - used for non-experts to assert their own half-baked pseudo-philosophy (of course, the same goes for quantum mechanics a
我出于一种责任感硬着头皮从头读到尾，但结果非常失望。阿喀琉斯、乌龟和各种随机生物的寓言让人厌烦透顶，内容绕了半天才切入正题。对于任何对该证明感兴趣的人，我推荐内格尔（Nagel）的《哥德尔证明》（Gödel’s Proof）。它用大约十分之一的篇幅讲完了同样的材料。 （GEB里确实还有其他哲学探讨，
I read it cover to cover out of a sense of obligation but came away very disappointed. The Achilles-Turtle-Random Other Creature allegories got very tiresome, and the content took a very long time to get to the point. For anyone interested in the proof, I recommend Gödel’s Proof by Nagel instead. It covers the same material in about a tenth the space. (GEB has other philosophical discourses that
……哪怕只是对计算机科学的基础稍微有一点点在乎的人，都绝对应该读一读，尽可能精读。稍微相关的补充：虽然探讨得更偏技术/更深一些，但内格尔和纽曼合著的《哥德尔证明》[1]是该领域一本非常平易近人的入门书，解释了不完备性定理的许多方面。[1] http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814...
…even vaguely cares about fundamentals of computer science should definitely give it a read, and if possible a thorough read. Slightly related: Although a more technical/deeper discussion, but the book "Godel's Proof"[1] by Nagel and Newman is a very approachable text in this domain, and explains many aspects of the incompleteness theorems. [1] http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814...
对我来说，GEB纯粹是在浪费时间，对我理解智能或AI毫无帮助。那些时间花在别处会更有价值。如果你想理解哥德尔的证明，那我推荐欧内斯特·内格尔和詹姆斯·R·纽曼写的《哥德尔证明》：http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...。与其读侯世达的GEB，不如读读他的一些论文，比如《类比……
For me, GEB was a considerable waste of time and contributed nothing to my understanding of intelligence or AI. The time would have been be better spent elsewhere. If you want to understand Godel's proofs then I recommend "Godel's Proof" by Ernest Nagel and James R. Newman: http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837.... Instead of Hofstadter's GEB, read some of his papers, e.g., "Analogy…
……在人脑中运行的系统）其复杂度至少会与这套公理相当。另外，你真应该读读J·R·卢卡斯的材料——它把这个解释清楚了。而且，我建议读读内格尔和纽曼的《哥德尔证明》，作为不完备性定理的极佳入门解释。
…one running inside each human brain) is going to at least be as complex as this set of axioms. Also, you really should read the JR Lucas material-- it explains this. And, I'd suggest Nagel & Newman's _Godel's Proof_ for a great introductory explanation of the Incompleteness Theorems.
有一本很棒的小书叫《哥德尔证明》，作者是内格尔和纽曼[1]。确实需要集中注意力，但依然很通俗易懂。[1] https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081... 编辑：删掉了一行
There is a little great book called "Godel's proof" by Nagel and Newman[1]. And definitely requires some focus but readable nevertheless. [1] https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081... Edit : removed a line