数学原理
Principia mathematica
Alfred North Whitehead、Bertrand Russell · 初版 1910 年
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为什么值得读
- 奠定现代数学基础并确立数理逻辑推导的严格形式
- 展现将数学公理体系步步推演至极致的皇皇巨著
- 深刻影响数理逻辑与哥德尔不完备定理的后续发展
Principia Mathematica 被誉为人类历史上最伟大的学术成就之一。它试图将数学严格归约为逻辑。除其他成果外，它还界定了数的概念。显而易见，这是一部极其晦涩且抽象的著作；随着近年来逻辑概念符号化表述的发展，阅读这部作品变得更加困难。对于该书的任何新版本而言，若能提供对书中思想的反响与发展的总结、勘误表、参考书目以及等价表，都将大有裨益
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这里补一本漏掉的经典巨作：《数学原理》（Principia Mathematica，常缩写为 PM），这是由阿尔弗雷德·诺思·怀特海和伯特兰·罗素合著的一部关于数学基础的三卷本著作，分别出版于1910、1912和1913年。https://en.wikipedia.org/wiki/Principia_Mathematica
Here is a classic which is lacking: The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. https://en.wikipedia.org/wiki/Principia_Mathematica
……在某局具体的国际象棋里，难道象会突然被允许横着走吗？话说回来：如果你真对把算术还原为纯逻辑感兴趣，去看看罗素和怀特海的《数学原理》（Principia Mathematica）吧——或者更好的选择是，去读读图像小说《逻辑人生》（Logicomix），它面向非专业读者，把这个领域讲得极其精彩。
…some particular game of chess, the bishop won't suddenly be allowed to move sideways? Anyway: if you are really interested in the reduction of arithmetic to pure logic, check out Russell and Whitehead's Principia Mathematica-- or better yet, read the graphic novel "Logicomix" which does a wonderful job of covering the domain for non-specialists.
……也值得读一读，算是对古希腊思想的总结。还有芝诺悖论。* meaningness.com 可以作为了解广义佛教哲学的切入点。* 《逻辑人生》（Logicomix）可以作为了解罗素及其在《数学原理》中那项宏大工程的入门读物。* 政治、历史和经济方面，可以读密尔的《功利主义》、汉娜·阿伦特的《人的境况》和亨利·乔治的《进步与贫困》，顺便再加点罗尔斯。席勒的《强盗》也非常……
…worth reading about too, to summarise the Greeks. And Zeno's paradoxes. * meaningness.com as an entry-point to Buddhist philosophy in general. * Logicomix as an introduction to Russell & his project in Principia Mathematica. * Mill's Utilitarianism, Hannah Arendt 'The Human Condition', and Henry George 'Progress & Poverty' for politics, history and economy, throw in a bit of Rawls. Schiller's 'The Robbers' is also very…
……如果有更多人能看懂《数学原理》，人类就会进步发展吗？把“历史重要性”和“对大多数人理解的重要性”区分开来是很关键的。怀特海和罗素的《数学原理》（PM）在历史上的存在本身就是一个非常重大的历史事件。在至少一份书单里，它都是20世纪最重要的著作之一。PM彻底粉碎了所谓数学不可能拥有严密……的论调。
…progress and advance if more people understood Principia Mathmatica? It's important to separate historical importance from importance to understanding by most people. The presence of Whitehead & Russell's Principia Mathematica (PM) in history is a very important historical event. In at least one list, it's one of the most important books in the 20th century. PM shattered any argument that mathematics couldn't have rigorous…
……TED那种浮于表面的光鲜，而那个真实的世界是要去查阅原始文献才能发现的。别看了维基百科上哥德尔不完备定理的词条就浅尝辄止。去读《〈数学原理〉及相关系统中的形式不可判定命题 I》（On Formally Undecidable Propositions in Principia Mathematica and Related Systems I）。虽然很难啃，但绝对超屌。别看了一个酷炫的TED演讲就立马转发给所有朋友：去查查演讲者引用的期刊论文，真正去……
…TED's glossy sheen, and that world is found by looking up original sources. Don't read the Wikipedia article on Gödel's incompleteness theorem and stop there. Read On Formally Undecidable Propositions in Principia Mathematica and Related Systems I. It will be hard, but it will be awesome. Don't watch a cool TED talk and immediately show it to all your friends: look up the journal paper the presenter was referencing and actually…
……现有的数学技巧，这样大家才会信他，才会立马接受它。”苏布拉马尼扬·钱德拉塞卡，这位20世纪伟大的天体物理学家，其实专门为普通读者写过一本《数学原理》（Principia Mathematica）的解读版。如果你真想搞懂牛顿在他的传世巨作《自然哲学的数学原理》（Principia）里到底在搞什么鬼，我建议你既别买拉丁语原版也别买英译本，去买钱德拉塞卡这本……
…existing mathematical techniques so people would believe him, so people would accept it right away. "Subrahmanyan Chandrasekhar, who is a great 20th century astrophysicist, actually wrote a version of the Principia Mathematica for the common reader. If you ever want to know what Newton was actually up to in the in his great masterwork the Principia I would advise not buying either the original Latin or English but buying Chandrasekhar's…