书籍介绍
这不是一本让你轻松翻完的科普书。它把哥德尔放在一个巨大的时代裂缝里书写：当相对论砸碎时空、量子力学动摇因果，数学这座理性最后的堡垒也被不完备性定理凿出一道无法弥合的裂痕——而亲手凿开它的人，自己却活成了裂痕。本书最耐人寻味的地方，恰恰是哥德尔身份的反讽：作为自亚里多德以来最伟大的逻辑学家，他毕生笃信数学对象独立于人类思维而存在（柏拉图主义），却用一条“系统内无法被证明的真命题”证明理性有其不可逾越的边界。作者以小说家的笔法，让这位偏执、孤独、与爱因斯坦晚年密切交往的天才重新开口说话。它适合两类人：一类是想听一段科学与命运相互撕扯的思想史，一类是愿意硬啃那段四十多页、四十六条定义的密集证明、并在读完后重新思考“真理”与“可证”究竟是否等同的人。
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。
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
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
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"
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