Gödel's Proof 在线电子书 图书标签: 数学 逻辑 哲学 哥德尔 mathematics 分析哲学 数理逻辑 philosophy
发表于2025-04-04
Gödel's Proof 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2025
我试图努力看懂,当时以为看懂了,现在回想不起来。应该再读一遍。因为任何不能融汇和提炼成抽象知识体系的知识点都是没有用的。
评分1973 version. Saw it in the bookstore. Seemed quite interesting. Then borrowed in the library. For me it's a revision of elementary logic. I'm not talented in Maths but I can follow it. Clear logic, nice english and detailed explanation.
评分such a genius
评分As long as you understand Cantor's diagonalization, you know where it leads to from very early on. But there's still an "aha" moment when Gödel's formalization of the problem finally lands. The intuition answers more wonders than I expected. Fortunate discovery, fortunate read.
评分"A little masterpiece of exegesis." ----Nature. Funny, this comment itself is a little awkward piece of exegesis. (Acquired from Brattle Book Shop, Boston, and read, in March 2010)
欧内斯特·内格尔(Ernest Nagel) (1901—1985)
内格尔出生于现在捷克共和国的首都布拉格(当时是奥匈帝国的一部分),十岁时随家庭移居美国。1923年获纽约城市学院学士学位,1925年获哥伦比亚大学数学硕士学位,1930年获该校哲学博士学位。此后除了在洛克菲勒大学工作过一年之外,一直在哥伦比亚大学任教:1946年起任教授,1956年至1966年任杜威讲座哲学教授,1967年至1970年退休前成为校级教授。其间,1940年至1946年任《符号逻辑》杂志编委;1939年至1956年担任《哲学杂志》编委;1956年至1959年任《科学哲学》杂志编委。曾任美国哲学和科学方法研究会主席,美国符号逻辑协会主席,美国哲学协会东部分会主席。他于1961年出版的《科学的结构》(The Structure of Science)被公认为科学分析哲学的开山之作,是逻辑实证主义运动的领军人物之一。内格尔是美国科学院院士,英国科学院的通讯院士。
詹姆士·R· 纽曼(James R. Newman)(1907—1966)
律师、数学家和数学史家。二战前后及期间曾担任美国驻伦敦大使馆首席情报官,战时副国务卿特别助理,美国参议院原子能问题顾问等重要敏感职务。战后从1948年起,成为《科学美国人》杂志的编委会成员。他曾用十几年的时间编辑出版了四卷本的《数学世界》丛书,其中收集了从古到今的重要数学文献,具有极大参考价值,曾多次再版。
In 1931 Kurt Godel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems". This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Godel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences - perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times". However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Godel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. Marking the 50th anniversary of the original publication of Godel's Proof, New York University Press is proud to publish this special anniversary edition of one of its bestselling and most frequently translated books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
太多关于哥德尔定理的讨论,都是就着一点感性认识随意发挥,实在太不着边际。我们都不是逻辑学专家(就我自己而言,在朝着专家的方向努力,能否成功还得两说,但至少现在肯定不是),要完全搞清哥德尔的工作然后再去讨论,既无可能也无必要。但在讨论之前,至少要了解哥德尔的...
评分所谓数的不完备性,即哥德尔证明:存在无穷多个真的算数命题,无法用一套封闭的演绎规则和一组公理推导出来。也就是说,数理无法推知一切。这篇东西不过是思路整理加上自己的一些想法,前面是对哥德尔论证的梳理,自然不能入专业人士的眼;后面就有点脑洞大开了,和哥德尔没啥...
评分0 高中时期翻过大半本,想来书的语言足够有趣也还算是易「懂」的 0.1 缺乏足够强的 motivation 却因各种原因「被迫」读书,是否学得好自是一方面,此外,慢慢丧失了对趣味性的追求。就好比此前看 GEB 时会觉得形式化几句就说得清楚的事情,何必大费周折玩得如此文雅呢?如此这...
评分强烈推荐!很难想象一本诠释如此艰深的理论的科普书籍可以写得那么通俗易懂,值得任何关心数学喜欢数学或者想从数学获取乐趣的人阅读。这次的译文也非常负责严谨,阅读起来较顺畅。你可以花一天的时间来享受一次神秘的数学之旅。
评分Gödel's Proof 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2025