书籍介绍
《不完备性:哥德尔的证明和悖论》是对哥德尔的生活、工作及其世界的重要新礼赞。20世纪早期见证了经典物理和数学的基础假设遭受的几次打击。相对论颠覆了约定俗成的时空观念，量子世界的研究挑战因果效应的基本观念。最为惊人的是，对于一切科学的基础——数学，不完备性定理揭示了将数学理性系统化的一切尝试中都藏有不可弥合的裂痕，这个结果简直是悖论式的。藏在这个发现背后的天才就是哥德尔，他自身就是一个悖论式的人物。他是自亚里士多德以来最伟大的逻辑学家，同时还是爱因斯坦晚年最亲密的思想伙伴。但他行事又极为古怪，惯于偏执狂推理，并最终因此悲剧性地死去。他深受失去理性的困扰，仍然对理性深具信心。通过天才的证明。他得以揭示在任何足够复杂的系统中——简单地说，任何数学家想要使用的系统——都存在不能被证明的真命题。一些思想家对此感、到绝望。另一些，如令人敬畏的维特根斯坦，一直不能接受它。还有一些人将其误解为对理性的破坏。然而对于哥德尔，这是永恒客观的真理存在的证据。它们独立于人类思想，只能被人类思维不完美地理解。
丽贝卡·戈德斯坦，通过她的小说家技巧和作为一名科学哲学家的洞见，使得哥德尔的定理以及其隐含意义通俗易懂，同时让这位古怪、痛苦的天才形象生动。
AI导读
核心看点
- 揭示哥德尔不完备性定理的深刻内涵
- 讲述天才逻辑学家哥德尔的传奇生平
- 探讨理性、真理与客观实在的哲学命题
适合谁读
- 对数学史与逻辑学感兴趣的科普读者
- 关注科学哲学与理性危机的思考者
- 喜爱传记文学与科学名人轶事的读者
读前提醒
- 本书侧重人物传记，定理证明细节较少
- 部分专业术语及翻译可能影响阅读体验
- 建议结合数学史背景知识辅助理解
读者共识
- 文笔生动幽默，将艰深理论通俗化
- 哥德尔与爱因斯坦的友谊令人动容
- 缺乏专业背景者阅读可能感到吃力
本导读基于书籍简介、目录、原文摘录、短评和书评生成，不等同于全文精读。
精彩摘录
- "More specifically, Einstein's and Gödel's meta convictions were addressed to the question of whether their respective fields are descriptions of an objective reality--existing independent of our thinking of it--or, rather, are subjective human projection, socially shared intellectual constructs."
- "The first of these problem revolving around Cantor's continuum hypothesis. What is Cantor's continuum hypothesis? The great nineteenth-century mathematician Georg Cantor had proved that (roughly speaking) there are more real numbers than there are natural numbers, even though there are an infinite n"
- "The First Incompleteness Theorem: The Overall Strategy The twenty-odd pages of Godel's famous proof are densely compact. There are 46 preliminary definitions. There are also preliminary theorems that must be proved before the main event can take place: the construction of an arithmetical proposition"
- "By tradition, the liar's paradox is attributed to the Cretan Epimenides, who reputedly said something implying: All Cretans are liars. This sentence, in itself, isn't paradoxical, except insofar as it suggests that what Epimenides was saying was something like this: This very sentence is false."
- "Now that sentence, as we've already seen, is true if and only if it's false—not a good situation, logically speaking. Godel's strategy involves considering an analogue to that paradoxical sentence, viz. the proposition:"
- "This very statement is not provable within this system."
- "Let's call this sentence G. G, unlike its analogue, isn't paradoxical, though it is, like all self-referential propositions, somewhat strange. (Even the nonparadoxical self-referential This very statement is true is mystifyingly strange. What's it saying? Where's its content?)"
- "Through the system of encoding we have come to call "Godel numbering" (of course self-effacing Godel didn't name it so) G can be rendered in arithmetical notation, so that it also makes an arithmetical statement. Here is one of the places where the hard work comes in, and a bit later on in this chap"
作者简介
丽贝卡·戈德斯坦著有五本书，包括《心脑问题》（The Mind-Body Problem）和《光的特性》（Propertise of Light）以及一本短篇小说集《奇怪吸引子》（Strange Attractors）。作为一位哲学教授，她因她的小说和学术成果记赢得了许多荣誉，她还是麦克阿瑟学会成员。
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