奎因的学生时代
（高中至博士后，1922—1933）
选自《我生命中的时光：奎因自传》
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译者：翟玉章
页码为英语原版页码
目录
7. High School（高中）…36
【职业选择中的荣誉动机和兴趣动机。文艺少年。“我发现了”和了解宇宙的欲望。对词源的兴趣。打零工。“致意者”滑稽俱乐部。】
8. Civilized Society（文明生活）…42
【青春萌动：与异性约会、香烟和酒。国务、战争和海军大楼。认识弗雷德和哈罗德·卡西迪兄弟。弗雷德的壮举。划船冒险旅行（啊，青春！）。纽约嘉年华上的Boid Goil。】
9. Freshman（大一）…49
【大学宿舍。搭便车。青春叛逆和烟酒。专业选择：主修数学，数学哲学作为优等生的学习内容。初恋。《鲁拜集》和旅途中自命不凡的青年。】
10. Sophomore and Junior（大二和大三）…54
【宿舍有了新名字“接合点”。埃德·哈斯卡尔搭便车的奇遇。奥伯林大三商人协会、灰泥、猫和金丝雀。罗素通俗著作的吸引力。沃森的行为主义心理学。钻研《数学原理》。】
11. Wild West（西大荒）…60
12. Europe and After（欧洲及以后）…68
13. Transplanted（迁居）…75
14. Graduate Study（研究生学业）…82
15. Sheldon Fellow（谢尔登研究员）…86
16. Vienna（维也纳）…92
17. Prague and After（布拉格及以后）…96
18. Warsaw and After（华沙及以后）…101
奎因的学生时代（连载之一）：高中
奎因的学生时代（连载之二）：文明生活
奎因的学生时代（连载之三）：大一
7. High School（高中）…36
【职业选择中的荣誉动机和兴趣动机。文艺少年。“我发现了”和了解宇宙的欲望。对词源的兴趣。打零工。抗上症。“致意者”滑稽俱乐部。】
8. Civilized Society（文明生活）…42
【青春萌动：与异性约会、香烟和酒。国务、战争和海军大楼。认识弗雷德和哈罗德·卡西迪兄弟。弗雷德的壮举。划船冒险旅行（啊，青春！）。纽约嘉年华上的Boid Goil。】
9. Freshman（大一）…49
【大学宿舍。搭便车。青春叛逆和烟酒。专业选择：主修数学，数学哲学作为优等生的学习内容。初恋。《鲁拜集》和旅途中自命不凡的青年。】
10. Sophomore and Junior（大二和大三）…54
[1927] Fred Cassidy joined us in the Hock Shop in September 1927; Harold waited a year. Three seniors were there from the year before: Ed Trethaway, Dave Hoffman, and Heimi. A fourth senior, my absent brother’s close friend Larry Kiddle, moved in with us from another house. Larry was a snappy and good-looking little fellow with a quick wit and ready{55} laugh. He had a gift for impersonation and foreign accents. His destiny lay in Ann Arbor as a professor of Spanish.
[1927]弗雷德·卡西迪于1927年9月住进了我所住的当铺，哈罗德一年后也加入了进来。三个高年级学生：埃德·特莱塞威、戴维·霍夫曼，还有海咪，一年前就住在这里了。另一个高年级学生拉里·基德从另一个屋子里搬来，他是已经离开这里的我哥哥的好朋友。拉里是一个活泼而漂亮的小个子，为人风趣，很爱笑。他模仿能力强，尤其擅长模仿外国口音。他最后成了安娜堡的西班牙语教授。
We felt that the name of the Hock Shop could be improved. I proposed “Αρθρον, “Arthron,”“Joint.”Fred elegantly painted the Greek word, using the back of the old sign. In later years it has adorned my Boston study, a sacred relic.
{55}我们觉得“当铺”这个名称还可以改进。我把它改成“接合点”，并提出了“Αρθρον”、 “Arthron”、 “Joint”等书写方案。弗雷德在旧标志的背面优雅地涂上了其中的希腊词。在后来的岁月中，我在波士顿的书房里也饰以这个标志，它成了一个神圣的遗产。
One Sunday that fall Heimi and I hitchhiked to Erie, Michigan, and back, sending postcards to “Αρθρον from that alien state. Later that fall we retraced those miles and extended them to a circuit Lake Erie, 630 miles. It was a holiday weekend that had been declared to the inauguration of Ernest Hatch Wilkins as president of Oberlin. We spent the first night in the YMCA in Windsor, Ontario, after a burlesque show in Detroit. Next we hitchhiked across Ontario to Niagara Falls and on to Buffalo. There we went to the police station with a view to sleeping in the courtroom or jail, but were directed to the DeGink Institute. The kind old policeman in charge there did not make us put our clothes in the fumigator and sleep in the big room with the ordinary tramps. He gave us a little room to ourselves. “You don’t need to be afraid,”he said. “The place is clean. It’s run by the mayor.”
那年秋天的一个星期天，我和海咪搭便车到密歇根的伊利并返回，从这个外州向“接合点”发了明信片。这个秋天的晚些时候的一个周末，奥伯林学院要举行欧内斯特·哈奇·威尔金斯的院长就职仪式，因此算是节假日。我和海咪又重温了一遍老路并在伊利湖绕了一圈（630英里）。我们第一天在底特律观看了滑稽歌舞剧，晚上宿在安大略省温莎市的基督教青年会招待所。第二天我们搭便车穿过安大略省到达尼亚加拉瀑布，并前往布法罗。我们去了那里的警察局，希望能在法庭或监狱里过夜，但被带到了德金克研究所。主管警察是个和蔼的老头，他不让我们把衣服放在消毒柜里并和普通流浪汉睡在一个大房间里，而是给了我们一个小单间。“你们不用害怕，”他说，“这个地方很干净，是市长开的。”
[1928] Fred, I subsequently learned, had never seen Niagara. Between winter examinations we hitchhiked thither, arriving at night. Canadian officials at the bridge made us fill out forms and then ruled that Fred, as a British subject, could not enter Canada without his original passport into the States. They were further put off by my indicating my religion as atheist. “You mean to say you’re an agnostic?”Settling finally on a simple ground for exclusion, they found our funds inadequate for support. So we walked back into Niagara Falls, New York, and requested lodging at the jails. We were given a big, well-ventilated cell. Next day we crossed the bridge from Buffalo to Fort Erie, Ontario, without incident. Then we crossed back and hitchhiked as far as Erie, Pennsylvania, where again we applied to the jail. It was full except for the basement, where there were said to be lice, so {56}we found a fifty-cent hotel. Erie retained a certain character: bedbugs in 1914, lice in 1928.
[1928]我后来了解到，弗雷德没有去过尼亚加拉。在冬季考试的间隙，我们搭便车去那里，一直到夜里才到达。桥上的加拿大官员让我们填写了表格，然后裁定，作为不列颠臣民的弗雷德，由于没有携带进入美国的护照原件，是不能进入加拿大的。另外，因为我表示我是无神论者，他们对我也失去了信任。“你的意思是说你是一个不可知论者吗？”最后，他们找到了一个拒绝我们入境的简单理由，那就是我们的川资不够。于是我们折回纽约州一侧的尼亚加拉瀑布，并且请求寄宿在监狱里。他们给了我们一间通风不错的大狱室。第二天，我们选择从布法罗到安大略省伊利堡的桥通过，没有遇到什么问题。后来我们再从这座桥回来，再搭车至宾夕法尼亚的伊利，并再次申请在监狱过夜。但监狱的房间已经满了，只有地下室可住，但地下室里据说有虱子，所以我们只好花50美分住进了一家旅馆。{56}伊利给我留下了某种印象：1914年的臭虫和1928年的虱子。
Larry and I hitchhiked to low haunts in Sandusky. He passed for a French Canadian who could not speak English; I interpreted. We slept in the courtroom that Joe Weller and I had initiated a year earlier. On an Oberlin holiday called the Day of Prayer, Larry and I made a similar trip to Detroit and Windsor. Having blown our small resources, we repaired to the MacGregor Institute and slept in a big room filled with dozens of cots. “Youse is lucky not to have to put your clothes in de fumigator.”“Do yez tink dey’d get sore if I din’t put me collar in de fumigator?”Such from either side of us. The man on duty had a black beard and looked like a steel engraving in Harper’s Weekly. His deep voice was in keeping: “It’s a warm night, men.”
拉里和我搭便车去桑达斯基游人不多的地方玩。他冒充成英语说不好的法裔加拿大人，我则充当翻译。我们夜里睡在法庭里，就是乔·韦勒和我一年前过夜的那个法庭。在奥伯林的一个被称为祷告日的假日，拉里和我还如法炮制地去过底特律和温莎。在挥霍完我们本就少得可怜的给养后，我们去了格雷麦戈研究所，睡在一个有几十张帆布床的房间里。“你不用把衣服放在消毒柜里真是幸运。”（Youse is lucky not to have to put your clothes in de fumigator.）“如果我不把衣领放到消毒柜里，你认为他们会生气吗？”（Do yez tink dey’d get sore if I din’t put me collar in de fumigator?）我们故意说着这样的话。值班的那个人有着黑色的山羊胡，看上去像《哈珀周刊》的钢板雕刻，而他深沉的声音也正与此相协调。“伙计们，这是一个温暖的夜晚。”
I signed up for a dinner a week at Oberlin’s French House. Fred Cassidy earned his meals there washing dishes. It was there that he met Hélène Monod, with whom he was destined to spend decades of connubial and collegial felicity on the Wisconsin faculty at Madison. It was also at the French House that Fred met Ed Haskell, a fellow dishwasher.
我在奥伯林的法国饭店订了每周一次的晚餐。弗雷德·卡西迪在那里靠洗盘子挣来他的饭食。就是在那里他认识了埃莱娜·莫诺，他们后来在威斯康星大学麦迪逊分校度过了几十年的夫妻兼同事的幸福生活。同样也是在法国饭店，弗雷德认识了当时同为洗碗工的埃德·哈斯克尔。
Ed was born in Bulgaria, son of an American missionary and a Swiss mother. He learned English, Swiss German, and Bulgarian concurrently—a matter, as he then saw it, of talking like a scholar, a woman, and a peasant. When at length he had grown up to be a freshman at Oberlin, he had a lucky hitchhike. A rich old lady, traveling with her daughter and chauffeur in her limousine, picked him up. She had been intrigued by his violin, which he was carrying, and she became further intrigued by his discourse. She settle a modest living on him, a hundred a month, in perpetuity.
埃德出生在保加利亚，父亲是美国传教士，母亲是瑞士人。他同时学会了英语、瑞士德语和保加利亚语；他那时认为，学会它们不过就是分别像学者、女人和农民说话而已。当他后来成了奥伯林的新生时，经历了一次幸运的搭便车。一个坐在豪华轿车里的有钱老太太（车上还有她女儿和司机）载了他一程。她被他随身携带的小提琴迷住了，更为他的谈吐所倾倒。她决定永久性地给予他每个月100美元的资助，这可以维持一个起码的像样生活。
Ed was ambitious, opinionated, contentious in the classroom, and rather shunned as an eccentric by conventional students. Fred proposed that he be invited to move into “Αϱθϱον. Happily it was done. It marked a turning point in Ed’s life and was a boon to the rest of us. Ed has long been my closest friend. It was he, indeed, who taught me to say, {57}in schwiezer dütsch, “Bischt z’kstabet ‘m füwafüfzk z’säge”(“You are too clumsy to say ‘fifty-five’”).
埃德在课堂上爱出风头、固执己见、喜欢争辩，一般学生视他为怪人，对他敬而远之。弗雷德建议他接受邀请，搬到接合点来住。令人高兴的是，他接受了这个建议。这是埃德生活的转折点，对于我们也是个福音。埃德一直都是我的密友。{57}他教会了我说瑞士德语的句子：“Bischt z’kstabet ‘m füwafüfzk z’säge”（你说“五十五”太别扭。）
[1928] Ed moved into “Αϱθϱον in the fall of 1928, my junior year. Fred and Harold Cassidy were there, and also Dave Hoffman, who was staying for a master’s degree. Loesch moved in with us and shared my little single, but he failed and left Oberlin after a term. There were other newcomers, notably Jim Sell.
[1928]埃德于1928年秋天搬进接合点，那时我刚上大三。弗雷德和哈罗德·卡西迪已经在那儿了，戴维·霍夫曼开始攻读硕士学位，也仍然住那儿。洛希搬进来加入了我们，住在我的小单间里，但一个学期下来因考试不及格而离开了奥伯林。另外还有一些新入住者，特别是吉姆·赛尔。
Jim had majored in classics and then switched to zoology. He was from Allentown, and was given to caricaturing the Pennsylvania Dutch. “Who iss making doce noices, pleece?” One of his stories will suffice to set the tone. He said he had been invited to the home of his Greek professor, Lofberg. He put on his new brown suit and tie, his brown shoes and sock, his tan shirt and brown hat, and appeared at the professor’s door. “Well, well,”the professor said, “you are very ensemble.”“Ahnsahmbel?”Jim pretends to have asked. “Vat meence ‘ahnsahmbel,’ pleece?”“Well, your suit is brown, and your tie, and shoes, and hat…”“Oh, I see. ‘Ahnsahmbel’ meence ‘all ofer bhown.’”In later years Jim took a Ph.D., occupied a high post in a pharmaceutical laboratory and died in his early sixties.
吉姆原来主修古典学，后来转至动物学。他来自阿伦敦，会夸张地模仿德裔宾州人说话。“请问是谁弄出来的声音？”（Who iss making doce noices, pleece?）他的一则故事足以说明他的这项才具。他说他有一次被邀至他的希腊语教授洛夫伯格家。他穿戴着新的棕色西装和领带、棕色的鞋袜、棕黄色的衬衫和棕色的帽子，出现在教授家的门口。“好，你穿着全套服装（ensemble）嘛，”教授说。“全套服装？”吉姆假装不懂地问，“‘全套服装’是什么意思？”（Ahnsahmbel? Vat meence “ahnsahmbel,”pleece?）“你看，你的西装是棕色的，还有领带，还有鞋子，还有帽子……”“哦，我明白了。‘全套服装’的意思是‘清一色的棕色。’”（Oh, I see. “Ahnsahmbel”meence “all ofer bhown.”）在后来的岁月里，他获得博士学位，在一个制药实验室里担任了高级职位，在刚六十开外的年龄上死去。
Jim’s roommate was Walt Hoy of Napoleon, Ohio. He ended up as a banker in Napoleon. Among other housemates during that year and the next there was Townsend Lodge, psychologist, who for a brief period many years later became Ed Haskell’s father-in-law. Another, Merbert to us, was Herbert Morse. But Fred, Harold, Ed, Jim, Walt, and I were the firm nucleus, along with Loesch for his brief term. We had meal tickets at Martin Inn, whither we would regularly troop down Main Street. After a time we were accorded a back room to ourselves in the inn, and thenceforward styled ourselves the Oberlin Junior Business Men’s Association. One of our usual waitresses was an unattractive but good-hearted young woman whom we referred to among ourselves as Stucco. “Beneath that rough exterior there beats a heart of gold.”Other waitresses were two pretty and merry little girls, matched in size and in the yellow of their waitress {58}uniform; whom we called the Cat and the Canary. They lived next door to “Αρθρον at Mrs. Hakes’s, a rooming house for business-school girls. That house was a cynosure for Arthric window watchers, despite lack of encouragement.
吉姆的室友沃尔特·霍伊来自俄亥俄的拿破仑，后来成了拿破仑的银行家。在这一学年和下一学年间，我们的屋里还住过心理学家汤森·洛奇，他很多年以后在一个很短暂的时间里成了埃德·哈斯克尔的岳父。还有一个房客是赫伯特·莫尔斯，我们都叫他莫伯特。但是，弗雷德、哈罗德、埃德、吉姆、沃尔特和我，还有退学前的洛希，是接合点的死党。我们有马丁餐厅的餐券，经常结伴从那儿在曼恩街上溜达。过了一段时间，餐厅给了我们一个包间，从此以后，我们便将自己命名为奥伯林大三商人协会。通常服务我们的那位年轻女招待没有外表上的吸引力，但心地很好，我们内部叫她灰泥。“在粗糙的外表下跳动着一颗金子般的心。”还有两名招待是漂亮而欢乐的小女孩，她们身材差不多，着装也差不多，都穿着黄色的女招待制服；我们分别呼为猫和金丝雀。{58}她们住在接合点隔壁的哈克斯夫人的屋子里，那是商业学校女生的公寓。尽管缺乏鼓励，这个公寓还是成了接合点的窗口观察家们的焦点所在。
Hilarity and horseplay at “Αρθρον gave way occasionally to music of a sort, what with Ed’s fiddle and my mandolin and sundry voices. It was mostly popular and ill-rendered, but Ed played well and came through rewardingly with Bulgarian and Swiss folk songs. We often played poker, drawing friends from other houses. There was serious talk on the part of Ed, Fred, Harold, and me. Ed would conjure up scenes and events of his life in distant places, telling of the ways of Swiss mountaineers and Bulgarians, and would hold forth in a more theoretical vein on the ills of society and on things he had been learning in psychology. I would tell of my adventures on freight trains, q. v. infra, and would hold forth on word origins and on what I had been reading in Russell.
接合点里的欢闹和嬉戏偶尔会让位于某种音乐：埃德的小提琴和我的曼陀林，还有大家音色不一的腔调。它属于流行音乐的范畴，但表演得很差，只有埃德的小提琴拉得不错，他的保加利亚和瑞士民歌大受赞赏。我们经常玩扑克牌，其他屋子的朋友也会被吸引进来。在埃德、弗雷德、哈罗德和我之间有过严肃的谈话。埃德会联想到他在遥远地方的生活场景和事件，介绍瑞士登山者和保加利亚人的生活方式，像个理论家似的滔滔不绝地议论社会的弊病和他刚从心理学课程里学到的东西。我则会介绍我在货运列车上的冒险经历（见下一章），并对词源和我刚阅读的罗素的东西侃侃而谈。
Already as a sophomore, having decided in my choice of a mathematics major that Russell was going to be important for me, I had turned to him for leisure reading, Marriage and Morals disposed me kindly to my new master. I read Skeptical Essays, Philosophy, Our knowledge of the External World, A-B-C of Relativity, and Introduction to Mathematical Philosophy. It was these books, and not my two survey courses in philosophy, that further whetted my appetite for cosmic understanding.
还在上大二的时候，已经选择了数学专业的我，由于深知罗素对我未来学业的重要性，于是他的一般性著作也成了我的休闲读物。《婚姻和道德》使我对这位刚刚进入我视野的大师大有好感。我也读了他的《怀疑论文集》、《哲学》、《我们关于外间世界的知识》、《相对论入门》和《数学哲学导论》等书。正是这些书，而不是我那两门关于哲学的概论性课程，进一步增进了我想要了解宇宙的欲望。
Though my linguistic interest had bowed to mathematics and philosophy in my choice of a major, it had not subsided. I once took Fred to task for coining a hybrid word from Greek and Latin. He asked me for guidelines, and the outcome was our collaboration on a compilation of English suffixes, etymological and semantical, for our amusement. Unwittingly I influenced the course of Fred’s career. He became an Anglo-Saxon scholar and a great lexicographer, the authority on Jamaican English and the creator of the monumental Dictionary of American Regional English, whole first volume will soon be off the press. He might have taken a different turning and have delighted us with more verse and sketches in a Bab Ballad vein.
我对语言学的爱好，虽然在选择专业时让位给了数学和哲学，但却不曾减退。我曾严厉批评过弗雷德从希腊语和拉丁语生造出来的一个混合词。他希望我能给予指导，结果，为了娱乐，我们共同编写了一份兼顾词源和语义的英语后缀表。我不知不觉地影响了弗雷德的职业生涯。他成了研究古英语的学者和杰出的词典编纂学家，他是牙买加英语的专家和大部头的《美国英语方言词典》的发起人，其中第一卷将在近期出版[1]。他也曾贡献过不同的方式，用类似《巴布民谣》风格的诗文和素描来为我们的娱乐助兴。
{59}I took a year of Greek and more French. My mathematics courses brought high marks but often imperfect understanding. I got more pleasure from Stetson’s course in psychology, where we read Watson on behaviorism, and from Thornton’s in Old French. In playful consequence of a mathematics class I compulsively computed e, the base of natural logarithms, to forty-five places and then memorized it for the dubious entertainment of my friends. I can still recite it.
{59}我上了一年的希腊语课，与此同时继续上法语课。我的数学课程得分很高，但在对内容的理解上仍有不足。我从斯泰森的心理学课程——我们被要求阅读沃森关于行为主义的著作——和桑顿的古法语课程中得到更多的乐趣。在一门数学课上，我出于闹着玩的心态，强迫自己计算自然对数e，一直算到45位，并应我的朋友们可疑的娱乐要求，记住了它。直到现在我仍能背得出来。
My literary leaning did not lapse altogether. I took literature courses and contributed to the college magazine. With a misguided sense of tongue in cheek I even wrote a horrid thriller for the pulps, not one of which was so undiscriminating as to accept it.
我对文学的爱好没有完全消失。我选修了文学课程并向学院的杂志投稿。我甚至还写过一篇惊险小说，自以为很有幽默感，但没有一家通俗杂志缺乏辨别力而愿意刊登。
Much contentment with my mathematics major came in my junior year, with my honors reading. Nobody at Oberlin knew modern logic; however, the chairman of the mathematics department, William D. Cairns, made inquiries and got me the books. They were Venn’s Symbolic Logic, Peano’s Formulaire de mathematiques, Couturat’s Algebra of Logic, Whitehead’s Introduction to Mathematics, Keyser’s Mathematical Philosophy, Russell’s Principles of Mathematics, and the crowning glory, Whitehead and Russell’s Principia Mathematica.
我在数学专业上的求知欲，直到我上大三时才在优等生阅读中开始得到满足。奥伯林没有人懂现代逻辑；但数学系主任威廉·D·凯恩斯做了查询并为我搞来了书。它们是文恩的《符号逻辑》、皮亚诺的《数学形式》、库蒂拉的《逻辑代数》、怀特海的《数学导论》、凯泽的《数学哲学》、罗素的《数学的原理》，还有，这个领域的最高荣耀：怀特海和罗素的《数学原理》。
Peano’s symbolic notation took Russell by storm in 1900, but Russell’s Principles, 1903, was still in unrelieved prose. I was inspired by its profundity and baffled by its frequent opacity. In part it was rough going because of the cumbersomeness of ordinary language as compared with suppleness of a notation especially devised for these intricate themes. Rereading it years later, I discovered that it had been rough going also because matters were unclear in Russell’s own mind in those pioneer days.
虽然皮亚诺的符号系统在1900年强烈震撼了罗素，但这在罗素1903年出版的《数学的原理》中并无反映。我既为它的深刻性所激励，但同时也对其中经常出现的晦涩段落感到困惑。这里的部分原因在于棘手的日常语言和顺手的符号系统（就是专门为处理这些复杂事情而设计的）之间的反差。多年后重读这本书，我发现它的费解之处也来自罗素本人，作为拓荒者，他那时对所讨论的事情也是不够清楚的。
Keyser came off badly in my eyes because of a chapter on “Korzybski’s concept of man”in which Keyser misapplied a logico-philosophical idea of Russell’s, the theory of types. When I remarked this to Cairns, he pointed Korzybski out in a group photograph and told of his buttonholing mathematicians {60}at meetings and holding forth on man as a time-binding animal. This was before Korzybski’s Science and Sanity.
我对凯泽的印象不佳，因为他在“科尔兹布斯基关于人的概念”这一章中，滥用了罗素的一个逻辑哲学思想——类型论。当我和凯恩斯谈起此事时，他在一张集体照中指出了科尔兹布斯基，并说起他的一个情况。他在会议中会强拉住数学家不放，长篇大论地谈他关于人是能连接时间的动物的观点。{60}这是科尔兹布斯基的《科学和理智》出版之前的事。
Principia Mathematica, 1910-1913, is devoted to showing in its three formidable volumes how the various concepts of classical mathematics, or concepts to the same purpose, can be expressed in symbols purely of logic and the theory of classes, or set theory, and how the laws of mathematics can then be deduced from laws of logic and set theory. The basic symbols assumed amount to ‘not’, ‘or’, ‘every’, ‘is’, pronominal cross-reference, and somehow more. Long derivations, rigorously carried out step by formal step, issue in definitions of numbers and functions, and in proofs of even such obvious laws as that x+y=y+x. but Whitehead and Russell’s purpose was not to persuade us of obvious truths; it was to show that these truths and their more recondite suite can be generated from such slim beginnings in logic and set theory, and how.
出版于1910—1913年的《数学原理》，是一部三卷本的皇皇巨著，其宗旨是要表明经典数学中的概念，或者服务于同一目的的概念，都可以只用逻辑和类理论（即或我正行进在大坝通往高速公路之间的蜿蜒曲折的小路上，这时ep under the car. 集合论）中的符号来表达，并进而表明数学规律可以从逻辑和集合论的规律中推导出来。它所采用的基本符号实际上相当于“并非”，“或者”，“每个”，“属于”，还有用来表示交叉指称的代词，以及其他一些不易说清楚的词。对数和函数的定义，对像x+y=y+x这样明显的规律的证明，都是通过很长的推导过程实现的，其中每一步都很严格。但是怀特海和罗素的用意，并不是要说服我们接受明显的真理，而是要表明，这些明显的数学真理，以及其他更深奥的数学真理，都可以从逻辑和集合论中很少的几个出发点中产生出来，以及产生的方法。
[1929] At the end of my junior year my mother bought me the three volumes of Principia ($16, $14, $8). She had made an equally inspired gift on Christmas: Skeat’s etymological dictionary, which I persistently consulted and explored over the succeeding half century.
[1929]大三学年结束时，我母亲给我买了三卷本的《数学原理》（16、14、8美元）。而到了圣诞节，她又送给我一件同样令我振奋的礼物：斯基特的词源词典[2]，在后来的半个多世纪里，我一直查阅和探索它。
[1]《美国英语方言词典》（Dictionary of American Regional English）第一卷出版于1985年。——译者
[2] Walter W. Skeat, ed. An Etymological Dictionary of the English Language (1879). Oxford: Oxford University Press, 1924. ——译者
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