Reflections on Kurt Gödel by Hao Wang (PDF)

Description

Newton/Descartes. Einstein/Gödel. The seventeenth century had its scientific and philosophical geniuses. Why shouldn’t ours have them as well? Kurt Gödel was indisputably one of the greatest thinkers of our time, and in this first extended treatment of his life and work, Hao Wang, who was in close contact with Gödel in his last years, brings out the full subtlety of Gödel’s ideas and their connection with grand themes in the history of mathematics and philosophy. The subjects he covers include the completeness of elementary logic, the limits of formalization, the problem of evidence, the concept of set, the philosophy of mathematics, time, and relativity theory, metaphysics and religion, as well as general ideas on philosophy as a worldview. Wang, whose reflections on his colleague also serve to clarify his own philosophical thoughts, distinguishes his ideas from those of Gödel’s and on points of agreement develops Gödel’s views further. The book provides a generous array of information on and interpretation of the two main phases of Gödel’s career – the years between 1924 and 1939 at the University of Vienna, which were marked by intense mathematical creativity, and the period from 1940 to his death in 1978, during which he was affiliated with the Institute for Advanced Studies in Princeton, a time in which Gödel’s interests steadily shifted from questions of logic to metaphysics. And it also examines Gödel’s relations with the Vienna Circle, his philosophical differences with Carnap and Wittgenstein, the intimate and mutually fruitful friendship with Einstein, and the periodic bouts of depression for which Gödel was hospitalized a number of times over the course of his life.A Bradford Book.

User’s Reviews

Editorial Reviews: About the Author Hao Wang is Professor of Logic at The Rockefeller University and author of scores of articles and several books on logic, computers, and philosophy, including From Mathematics to Philosophy (extensively discussed with Gödel and containing contributions by him) and Beyond Analytic Philosophy: Doing Justice to What We Know (MIT Press Bradford Books). He is currently preparing a companion volume, Conversations with Kurt Gödel which will concentrate on Gödel’s unpublished ideas.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I found this book to be extremely ‘painful’ to read, primarily, because of all the abbreviations.One thinks that since there is a page dedicated, at the beginning, to the ABBreviationsthat one need only slip an eXtra bookmark there for ‘flip-back’ reference.Nice try. ~ Within the text, there occurs a plethora of abBREViations for terms which are,not only ‘not’ listed on that ‘beginning dedicated page’; but are not eVen listed, or spelled out,within the text, itself-!- I honestly felt like I was purposely being lead into a thicker and darker forest by a guide who,himself, did not know the way 0ut. It is very sad, too, because the book has “its moments”, and thetopic is [for me] incredibly interesting; i.e. I, oh so, wanted it to be good and lucid; …too bad.

⭐Anything Godel is good.

⭐Wang has been an important source in compiling information on Godel and bringing it to public attention. This volume contains a variety of material about Godel- biographical facts, personal recollections, chronologies, Godel’s philosophical ideas, the impact and historical setting of his mathematical work, his relationship with Einstein, comparisons to other prominent intellectuals, and more. It assumes a basic understanding of Godel’s theorems. The bulk of the book is a presentation of some of Godel’s (largely unpublished) philosophical activity. There is also quite a bit on Wang’s own views as he contrasts them with Godel’s. Some of these sections require more background in philosophy than most students of mathematics possess (myself included).Wang supplies lots of interesting historical and biographical material as well. The 75 page chronology of Godel’s life and work is very informative. Contains 11 photographs of Godel and company. The book ends with some useful commentary on selected publications of Godel. If you’re looking just for a biography get Dawson’s excellent book, but anyone seriously interested in Godel will want this as well.

⭐On Pages 1 and 2, Wang tells us that Godel, the master of the incomplete, suggests the possibility of philosophy as an exact theory emerging within the next hundred years or even sooner. There will be, he believes, scientific disproofs of what he calls’ mechanism in biology’ and of the proposition that ‘there is no mind separate from matter’; moreover he thinks it practically certain that the ‘physical laws, in their observable consequences, have a finite limit of precision. In his conversations, he recommends the important project of finding what might be called a ‘rational religion.’I conclude that exact philosophy already exists because theological statements are being proven, even though the ultimate truth will always be incomplate. This prediction means that the scientific method cannot be used to prove worlds, which is a box in which we live. Thus, universe cannot be measured without measure standards. So the universe is relativistic and can never be known exactly. I also agree with Godel that mechanisms will never be found in living things. This is why US medical care is so bad. I agree with Godel that minds will never be without bodies because only organizations exist in Nature. I also agree with Godel that a rational religion is coming because theological statements are being proven.

⭐Depoimento fundamental para entender Gödel.

⭐その昔にクルト・ゲーデルの上記の言葉に出会って感動しただけのシロートが読んでいい本ではなかった。専門家の方どうぞ。評価しようがないので五つ星（白旗）。しかしワン先生に文句も言いたい。冒頭で「専門家以外の読者にもご理解頂けるよう」努めた本だとおっしゃる。ワン先生自身、著名なロジシャンであらされる。ロジシャンならば「ノンスペシャリスト」をもっと厳格に定義すべきざます。有限主義（finitism）とか、原始帰納算術（primitive recursive arithmetic）とか構成主義（constructivism）とかとか、微塵の解説もなくドンドン登場する文章が「ノンスペシャリスト」向きなんでせうか…と、蹴り出されたシロートは一発くらい愚痴ってもよろしかろうと。以下、それでも完読してしまった懲りない読者の雑感レビュー。本書は、晩年のゲーデルと交流のあった中国育ちのロジシャンによる資料集的な伝記＆論考。当時未発表の遺稿（Nachlass）から広く引用しつつ、ワン先生個人の回想や見解も交えつつ、ゲーデルの業績（数学基礎論、純粋数学、哲学、形而上学）を振り返る。テクニカルを無視しても読めなくはないが、読んでいいものかは微妙である。後半のゲーデル定理の含意と意義についての考察はシロートでも読めることは読めるし、トリビア部分もそれなりに興味深い。ゲーデル餓死の報を受けたワン先生のドライさと（少なくとも記述の上では）、チューリングの自殺を聞いたゲーデルの超天然な反応が重なったりなんかする。ゲーデルの人となりには焦点が当てられていないにしても、アドバイスを求める同僚や後輩を決して無下にしない生真面目さと誠実さが伝わる。「プラトン主義者」とラッセルに言われ、「貴方だって昔はそうだったではないか。ウィトゲンシュタインに影響される以前までは」と反論をしたためた手紙が未投函のまま遺稿の中に眠っていたりする。投函すれば良かったのに。「ゲーデル」が一貫して「G」と表記されるのはまあイイとしても、頻出用語が意味不明に省略表記なので無用な混乱が生じ、英訳なしのドイツ語引用が多発し、読み手を徹底的に考慮しない雰囲気が漂う少々不気味な本だ。やはりロジシャンはクレイジーなのだろうか。場所や住所、そして日付を逐一執拗に確認する感覚も何となく独特やなぁと感じたが、資料的価値はあるのだろう。という訳で、専門家の皆さん、どうぞ。

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