讀書筆記︰Alfred Tarski: Life and Logic
Alfred Tarski: Life and Logic
Anita Burdman Feferman & Solomon Feferman
2024-07-14按︰呢本書2014年暑假喺倫敦Judd Books買同睇，入面介紹到Tarski嘅學生（Solomon Feferman本身都係），當時寫咗幾個Facebook posts，主要係關於 Tarski 啲學生，因為佢都幾多學生成為邏輯學家，聽過個名但唔係好搵到相，結果喺呢本書見到。
講另一本書提到呢本，放埋呢啲字出嚟（部分會執少少同加返背景）。
改姓及改信天主教
話說 Tarski 原本姓 Teitelbaum，因為猶太裔身份被針對（教過兩年書，校長收到投訴話猶太人教數學而炒咗佢）而改信天主教同改埋姓。當時波蘭改姓需要無人反對，佢查到華沙得一個人姓Tarski，所以反對風險比較低而揀呢個姓。
雖然佢係無神論者，但改信波蘭主流嘅天主教時扮得好虔誠，書入面提到佢同同事（同樣改信天主教）Bronislaw Knaster 嘅一個故事︰
When Tarski, eager to display his erudition, discussed the details and fine points of the Catholic religion and its hierarchy, Knaster - a phisical opposite of Tarski, tall, slim, dark-eyed, and possessed of a flashy wit - would say, “Alfred, I am sure that one of these days you will write a book about all of this.” To which Alfred would reply: “Look. Don't be silly. It's just a hobby.” Years later when Tarski, by then long in the United States, published his book Cardinal Algebras, he received a telegram from Knaster, still in Poland, that read, “Congratulations! You see, I was right, after all.”
（簡單解釋一下︰呢度食咗 “Cardinal” 一字「樞機主教」同（集合論入面嘅）「基數」雙重意思。）
逃離波蘭
上回提到佢未揾到大學教職，1939 年 Quine 邀請佢去美國參考 Unity of Science Congress，咁啱當時有個空缺（佢老師死咗），又係全世界都覺得應該係佢填補（當時佢已經係波蘭最頂尖嘅邏輯學家，而嗰期波蘭都可算係邏輯重鎮），不過佢又驚去咗美國會有變數（畢竟佢係猶太人），所以一直猶豫去唔去。
最後佢決定唔理，由得波蘭嗰邊啲人自己搞掂，申請到 visa 搭船走。去同一個 congress 嘅仲有 Janina Hosiasson-Lindenbaum，科學哲學及邏輯學家，《維基百科》佢係最早寫文討論 Raven paradox 嘅人。（稍有接觸數理邏輯的話應該認得 Lindenbaum 呢個名，佢老公就係嗰個 Lindenbaum。）Janina 遲 Tarski 一班船，喺下一個星期去，結果 visa 已經唔批，走唔到，最後兩夫婦都俾納粹殺咗。而 Tarski 搭嗰架船，三個月之後亦被德國擊沉。
Tarski 落船時，波蘭已經落入納粹手上，佢都返唔到去波蘭，唯有出境再申請個 permanent visa（佢去嘅係古巴），當時 Quine、Ernest Nagel、Curry、Russell 等共十七個學者寫信幫佢入藉，所以幾順利。但佢一直想接屋企人過嚟都接唔到，甚至有個瑞典哲學家 Anders Wedberg 寫信畀佢阿爸——一個瑞典最高法院法官——求幫拖，可惜當時已經太遲，瑞典無船去到美國所以批唔到 visa。
C. C. Chang
（按︰呢部分係2020年寫，2014年未查到佢個名。）
C. C. Chang 中文名叫張晨鐘（但網上寫又叫「辰中」，唔肯定），著名嘅模型論專著 Model Theory 作者之一（好似有幾本都叫 Model Theory，呢本通常叫 Chang & Keisler），Peter Smith 稱之為「舊約」（「新約」係Wilfrid Hodges本A Shorter Model Theory）。
C. C. Chang 係 Tarski 學生之一（Keisler都係），Tarski本傳記有提到佢好似七八十年代左右就無做數學，轉去學佛定探索靈性之類，所以比較神秘。
話說早兩年有朋友FB問起 C. C. Chang係咪仲在生，之後留言見到有人貼個Geni（族譜網站）寫佢2014年過身，同時發現原來佢老豆係張彭春（曾任聯合國安全理事會中華民國代表、參與起草《世界人權宣言》，據稱「新月派」個名都同佢有關，但我需要再確認下）。
我透過個網站資料聯絡到佢個仔（花咗少少時間起底同撞中佢email），得到回覆確認真係C. C. Chang，問我想知啲乜，但我再追問之後就無覆我，所以暫時都無辦法知道C. C. Chang當年點解放棄數學同之後做咗乜了。
相關段落︰
“In the spirit of the zeitgeist of the seventies, while Wells was dropping out of the Ph.D. program, C. C. Chang had also gone on a spiritual quest and was soon to give up doing any serious work in mathematics. Chang, as a professor at UCLA, had done important research in a number of the fields of interest inspired by Tarski, and with Jerome Keisler he had written the first comprehensive expository text on model theory. Tarski was extremely upset at Chang's openly announced decision to forsake mathematics in favor of a deep exploration of and commitment to the Buddhist path.”
Robert Vaught
Robert Vaught，Tarski 學生，模型論奠基者之一。上 sem 透過 Tarski–Vaught test 聽過佢個名。佢讀博士時本來跟 John Kelley，不過時值麥卡錫年代，大學要求所有教授宣誓自己唔屬於共產黨或其他推翻美國政府嘅組織。John Kelley 拒絕（因為已宣誓效忠美國及加州憲法，咁係重複，幾年後呢個誓言亦被加州最高法院判違憲），結果俾大學炒咗（Leon Henkin 都因為咁而拒絕 UC Berkeley 當時嘅 offer，直到取消咗宣擱誓之後佢先去，Kelley 都返咗去）。
Tulane University 好快就請咗 Kelley，亦畀咗個位 Vaught 可以繼續完成論文。但 Vaught 當時精神狀態好差，抑鬱又狂躁，唔想跟 Kelley 去新奧爾良（因為嗰度無家人朋友）。佢留喺 UC Berkeley 就侷住要轉跟第二個，於是揾咗 Tarski（書中所述，Kelley 指 Tarski 認為宣誓一事應該簽完就唔理，費事煩；Henkin 就認為佢同情拒簽嘅人）。
Vaught 當時絕望到企圖自殺幾次，被送去強制治療，包括喺佢唔同意下電擊治療。於是佢提出開聽證會證明佢心智健全。佢叫佢啲朋友同教授去，但好多朋友都認為佢真係會對自己甚至其他人造成危險，其中一個原因係佢有次嘗試揸車撞樹自殺。
然後抄書︰
Vaught never forgot his professor's testimony at the hearing, recalling that Tarski spoke for about ten minutes and in the end said, “It isn't that his is so exceptionally good in mathematics [but of course he was!] but I admire his judgment,” and then he started to cry.
Throughout Vaught's many years of mental illness depression, and mania, in and out of various hospitals, Tarski remained a staunch ally even though Vaught, in his disturbed state of mind, sometimes insulted and attacked him verbally - as he did others. [...] He attempted to understand the mysteriousness of the illness, helped Vaught seek out doctors and psychiatrists, was interested in his treatment, and above all, encouraged him as a student and saw him through a successful Ph.D.
Richard Montague
Richard Montague，據稱對待學生嘅標準好跟 Tarski。David Kaplan 咁講︰
“I have enormous intellectual respect for Tarski and I always thought of him as an intellectual grandfather, because a huge amount of what I got from Richard, Richard got from Tarski.”
而家 Montague 最出名應該係 Montague grammar，不過我唔識。第一次聽呢個名係知道 Reflection principle (as a theorem in ZFC)︰對於任何有限嘅 formula，如果（喺 V 入面）成立就有 model（留意「對於任何」係後設的，唔可以放喺 ZFC 入面，唔係就可以用 compactness 證明 ZFC 本身有 model，違反 GIT）。用 Reflection principle 可以推論出 ZFC 唔可以寫成有限公理，否則可以串成一條 formula，又會證明 ZFC 有 model。好似係同 replacement schema 等價，但未有時間揾多啲嚟睇。
喺 Tarski 嘅 party 度，Tarski 會叫 Vaught 彈琴，然後到 Montague（唔知咩樂器）。Montague 都彈 Organ，會星期日去教堂度負責彈，甚至諗過做職業樂手。
按 Donald Kalish 所講︰
“On campus Richard was a model of decorum but off campus there was no risk that was too great for him. He would go to bars, “cruising”, and bring people home with him One time he picked up someone who brought along three “friends”. These guys proceeded to tie Richard up and strip the house of everything of value. This was nothing “kinky” or sexual. It was just a straight old robbery and the guys knew he was not going to call the police to explain how it happened.”
結果有另一次，三至四人上咗佢屋企，佢朋友發現時佢已經死咗，呢單謀殺案一直未破。
J.C.C. McKinsey
J.C.C. McKinsey，Tarski 其中一個好友，模態邏輯中嘅 McKinsey formula $ \Box \Diamond p \rightarrow \Diamond \Box p $ 就係以佢命名。
由於 McKinsey 公開自己係同性戀（嚴格嚟講應該只係無隱暪），即使研究同教學方面都唔錯，亦一直無 tenure。去過幾間大學教後又去咗 RAND 度做，但結果又被視為「高危」員工而要走。佢嘅反應係 “How can anyone threaten me with disclosure when everybody already knows?”。離開 RAND 後佢去咗 Stanford 教，後尾升咗佢做教授，1953 年自殺身亡。
佢同 Tarski 合寫篇長文 The Algebra of Topology 好似對 modal logic 影響深遠，不過我就唔多識了。
Mojzesz Presburger, Janina Hosiasson-Lindenbaum & Adolf Lindenbaum
上面講過 Hosiasson-Lindenbaum，當時波蘭嘅一位科學哲學家。今次講埋其餘兩個，都係 Tarski 喺華沙大學教書時嘅學生，兩個讀邏輯嘅人必定會遇上嘅名。
第一個係 Presburger。哥德爾 1931 年證明咗 Peano arithmetic——即係自然數連埋乘法、加法以及數學歸納法嘅系統——並非完備。而 Presburger 喺 1928 年則證明咗如果無乘法的話，個系統係 complete and decidable，後世稱為 Presburger arithmetic。
書中提到，呢個本來係 Tarski 畀 Presburger 嘅一道習題，結果成為 Presburger 嘅碩士論文，亦係喺邏輯方面唯一一篇論文。佢喺納粹入侵波蘭期間被殺。
第二個係 Lindenbaum，證明一階（或者命題）邏輯完備性時會用到嘅 Lindenbaum's lemma 嗰個 Lindenbaum（另一度會見佢個名，應該就係 algebraic logic 入面嘅 Lindenbaum-Tarski algebra）。
Tarski 喺 Cardinal Algebras 一書入面提到︰
“It would be impossible for me to conclude this introduction without mentioning one more name - that of Adolf Lindenbaum, a former student and colleague of mine at the University of Warsaw. My close friend and collaborator for many years, he took a very active part in the earlier stages of the research which resulted in the present work, and the few reference to his contributions that will be found in the book can hardly convey an adequate idea of the extent of my indebtedness. The wave of organized totalitarian barbarism engulfed this man of unusual intelligence and great talent - as it did millions of others.”
Lindenbaum 後來俾蓋世太保捉咗，如 Tarski 所言，兩夫婦同樣係納粹大屠殺死難者。
原來 UC Berkeley 嘅邏輯 Ph.D program 基本上係由 Tarski 一手搞出嚟。二十世紀嘅數理邏輯明顯受佢影響（最明顯應該係 model theory 同 algebraic logic），論地位論影響力，都算係數一數二。
不過呢本書其中一個主旨應該係揀論文導師要好小心，好多學生都俾佢捽得好勁（因為佢高要求，有時拖好耐唔肯簽名批個學生嘅 thesis），有啲本身好猛嘅就無乜嘢，甚至幾有用，但有啲都幾大創傷。同埋做佢 research assistant（多數係學生）都好慘，要跟佢作息時間（佢習慣通宵工作）、超高要求，又要幫佢做啲可能同自己題目無關嘅嘢，例如翻譯佢啲文（有個佢有事先警告的，做咗陣個學生先知中伏）同幫佢出書。
即使其中一個作者 Solomon Feferman 係佢學生，呢本傳記都無一面倒讚，反而幾呈現到 Tarski 嘅長短處。同埋兩個作者都應該花咗好多時間去訪談考證，資料幾充足（例如 Tarski 成日話自己中學邏輯得 B，佢哋都揾得返佢嘅中學成績出嚟，指 Tarski 有意無意講大話——可能係為咗講出嚟更吸引人）。
延伸閱讀
cky
