# 丽贝卡-戈尔茨坦的《不完备性：哥德尔的证明和悖论》中的“阅读建议”

Jaakko Hintikka的《论哥德尔》（On GodelBelmont, CA: Wadsworth Thomson Learning, 2000）这本书非常薄（70页），也是为非专业人士提供的对哥德尔证明的清晰和简洁的介绍。与更著名的《哥德尔证明》一样，Hintikka的证明也是自成一体的，不需要以前的逻辑知识，他也有很好的幽默感。

John Dawson也有两篇关于哥德尔的论文，通俗而有趣。"Kurt Godel in Sharper Focus " "The Reception of Godel's Incompleteness Theorems"。这两篇论文都转载于Stuart Shanker编辑的《聚焦哥德尔定理》，以及其他有趣的文章，包括Solomon Feferman "Kurt Godel: 确信和谨慎（Kurt Godel: Conviction and Caution»

****

Incompleteness: The Proof and Paradox of Kurt Gödel

Like many before and after me, my first substantive exposure to Godel's incompleteness theorems came not by way of studying the famous 1931 paper itself but rather by reading, as an undergraduate, the celebrated Godel's Proof by Ernest Nagel and James R. Newman (New York: New York University Press, 1968). This is a popular exposition that yet manages to go into some detail concerning the substance of the proof. My world was rocked. On rereading it after all these years, I was impressed all over again. It's a wonderful little book, in its own way a classic.

Jaakko Hintikka's very slim (70 pages) book, On Godel (Belmont, CA: Wadsworth Thomson Learning, 2000), is also a clear and concise presentation of Godel's proof for the non-expert. Like the more expansive Godel's Proof, Hintikka's proof is self-contained, requiring no previous knowledge of logic. He also has a good sense of humor.

So far as the life of the logician is concerned, Logical Dilemmas: The Life and Work of Kurt Godel (Wellesley, MA: A K Peters, 1997) by John Dawson is definitive. As not only a logician but also GodePs archivist, whose wife learned to translate Godel's shorthand, Dawson was in an unrivaled position for presenting the life of Godel. I was told by Institute mathematician Armand Borel that Godel's literary remains, which had been donated to the Institute for Advanced Study by Godel's widow, were in utter chaos, piled helter-skelter into decaying boxes; and then "a young man" (Dawson) had offered to put it all into order. "He did a good job, I'm told." Indeed he did.

John Dawson also has two papers on Godel that are accessible and interesting: "Kurt Godel in Sharper Focus" and "The Reception of Godel's Incompleteness Theorems." Both are reprinted in Godel's Theorem in Focus, edited by Stuart Shanker, as are other interesting essays, including Solomon Feferman's "Kurt Godel: Conviction and Caution. »

Hao Wang produced three rather eccentric but intriguing books out of the pickings of Godel's mind: From Mathematics to Philosophy (New York: Humanities Press, 1974), Reflections on Kurt Godel (Cambridge, MA: MIT Press, 1987), and A Logical Journey (Cambridge, MA: MIT Press, 1996). The books recount conversations Wang had with Godel, interlaced with history of the logician's life and Wang's own views on the topics he and Godel discussed. What they lack in structure they compensate for in content.

There are several, memoirs of Godel, written by those who had first known him in Vienna, and they are fascinating and in their own way touching. There is first of all Georg Kreisl's "Kurt Godel: 1906-1978," Biographical Memoirs of Fellows of the Royal Society, Vol. 26 (1980), pp. 148-224. Kreisl, an eminent mathematical logician, is in a unique position, having known Wittgenstein quite well when Kreisl was a student, and then, later, having gotten to know Godel in Princeton. Karl Menger had been invited, together with Godel, to join the Vienna Circle as favored students of Hans Hahn and his invaluable first-hand reminiscences of Godel are recounted in "Memories of Kurt Godel," in Reminiscences of the Vienna Circle and the Mathematical Colloquium, ed. Louise Golland, Brian McGuinness, and Abe Sklar (Dordrecht: Kluwer, 1994). And then there is Olga Taussky-Todd, herself a number-theorist, who also had first come to know Godel in their student days. Her "Remembrances of Kurt Godel" is in Godel Remembered (Naples: Bibliopolis, 1987).

If the reader is interested in seeing how a contemporary polymath applies Godel's theorems in his own creative scientific thinking) then he is advised to read Roger Penrose's The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (New York: Penguin, 1989) and his Shadows of the Mind: A Search for the Missing Science of Consciousness (Oxford: Oxford University Press, 1994). Like Go'del, Penrose is a confirmed mathematical Platonist; he interprets the incompleteness theorems exactly as Godel did. There's lots of further fascinating mathematics that he discusses—-including Turing's contributions to the work Godel began, the Mandelbrot set, and Penrose's own work on the tiling of the plane—all argued, by him, as pointing in the direction of Platonism. Penrose's overall argument is that mathematical knowledge, the amazing fact that we have it, is evidence that the laws of physics are of a fundamentally different character than we have heretofore dreamt.

Douglas Hofstadter's Pulitzer-prize-winning Godel, Escher, Bach: The Eternal Golden Braid (New York: Basic Books, 1974) is a spirited romp through self-referentiality. Hofstadter does a wonderful job of braiding together ideas in logic, art, and music, just as the title promises. When, upon being asked what I'd been working on these past few years, I'd say "Godel," more often than not I got a blank stare in return. Then I'd mention the title of Hofstadter's bestseller, and the blank stare would give way to a smile and an "oh yes. »

Finally, there is the writing of Godel himself, his few published papers and his many unpublished works, in Collected Works, ed. Solomon Feferman et al. (Oxford: Oxford University Press, 1986-). There are three volumes to date.

https://m.sciencenet.cn/blog-2322490-1304173.html

## 全部精选博文导读

GMT+8, 2022-12-3 10:35