TIDY PARSIMONY
整齐的节俭
Willard Van Orman Quine
威拉德·范·奥曼·奎因
（1996年，奎因以88岁高龄获得日本稻盛财团设立的“京都奖”（相当于日本的诺贝尔奖）。这是他随后发表的纪念演讲。顺便说一下，著名科学哲学家波普是1992年的京都哲学奖的得主。）
We happy honorands were encouraged, in these commemorative lectures, to talk about ourselves. I remember myself as a small child sprawled on the floor and poring over my mother’s old geography book. I aimlessly pondered North and South America, Europe, Africa. I neglected Asia, for the name was unfamiliar. Then one day I did happen to take a proper look at Asia, and the scales fell from my eyes. There were all those romantic names―Arabia, Jerusalem, Bagdad, Persia, India, China, Japan. Somehow I hadn’t noticed their absence from the maps I had studied. They evidently had occupied the fairly-tale half of my brain. Now suddenly my world was one, and a rich one.
我们这些喜获殊荣的人会被鼓励在纪念演讲中谈谈我们自己。我记得还是个小孩的时候，我会趴在地板上专注地看我母亲的旧地理书。我漫无目的地对着北美洲和南美洲、欧洲、非洲出神。我会略过亚洲，因为我不认识“亚洲”这个词。终于有那么一天，我居然正视了一下亚洲地图，我一下子豁然开朗了。上面全是一些浪漫的地名：阿拉伯半岛、耶路撒冷、巴格达、波斯、印度、中国、日本。我过去从未注意到我所研究的地图上没有这些名字，原来它们一直只在我大脑另一半的童话世界里。突然，我的世界合二为一了，并一下子丰富了起来。
It was a purposeless pondering of boundaries, place names, and relative positions. It foreshadowed a taste for decisive distinctions and structure, as well asan almost but not quite insatiable wanderlust. In those early days I was given also to compiling lists, geographical and otherwise, to no better purpose than indulgence of a taste for tidy orderliness. It was a taste that was to favor mathematics and analytical philosophy over less disciplined disciplines.
我对界限、地名和相对位置的专注并没有什么目的性。但它预示了我对决定性的差别和结构的兴趣，也预示了我对旅游的近乎痴迷的爱好。在我的少年时代，我还汇编地理和其他方面的表格，同样也没什么目的性，只是表现了我对整齐秩序的追求。这种对整齐秩序的追求使我日后爱上了数学和分析哲学，而对条理性较差的学问敬而远之。
It was a taste that took to algebra and geometry in school, and to the diagramming of English sentence, and to Latin. My responsiveness to languages had been whetted by stamp collecting, a hobby traceable to my interest in geography. German was unavailable until college because of the World War I, but I studied French.
对整齐秩序的追求，使我在学校里喜欢上了代数和几何，喜欢上了分析英语句子，喜欢上了拉丁语。此外，我也喜欢集邮，这可以追溯到我对地理的兴趣。集邮增强了我对语言的敏感性。由于第一次世界大战的缘故，我在上大学前无法学习德语，但我学习了法语。
Religion was not oppressive in my home, but it was there, and by the age of ten my doubts had prevailed over it. This surely is how many modern philosophers started up or down the philosophical path. Also I had, at about that age, a more specifically philosophical thought. Unfriendly remarks about Jews were not uncommon in my neighborhood, and two of my friends were Jews, which I regretted. Then it dawned on me that we should judge a class by its members.
我家里有一种宗教气氛，虽然并不令人压抑。我10岁左右的时候，开始对宗教产生怀疑。这当然也是很多哲学家一开始走向哲学之路的情形。大概也是在这个时候，我还有了另一个更具体的哲学思想。在我生活的环境里，对犹太人的不友好的评价并不罕见，我的两个朋友是犹太人，我为他们感到难过。这时我突然想到，我们应该根据对其成员的表现来评价一个类。
【《奎因自传》中的相关文字：I may have been nine when I began to worry about the absurdity of heaven and eternal life, and about the jeopardy that I was incurring by those evil doubts. Presently I recognized that the jeopardy was illusory if the doubts were right. My somber conclusion was nonetheless disappointing, but I rested with it. I said nothing of this to my parents, but I did harangue one or another of my little friends, and I vaguely remember a parental repercussion. Such, then, was the dim beginning of my philosophical concern. Perhaps the same is true to the majority of philosophers.
大约在我9岁的时候，我开始担忧天堂和永生的荒谬性，也担忧这些不敬的怀疑给我带来的危险。不久我认识到，如果怀疑是正确的，危险就是虚幻的。我的冷峻的结论仍然是令人失望的，但我还是坦然接受了它。我从没有向父母说起过这个话题，但我确实对我的某个小伙伴高谈阔论过，我还依稀记得他父母的不满反应。我对哲学的关注就是隐隐约约地从这里开始的。也许多数哲学家的情况都是这样的。
The air I breathed was mildly anti-Semitic. I think of Bob Goldsmith, Al Green, and Herb Rose, school mates of mine and kindred sprites in stamp collecting. Little Herb, indeed, was the Acorn Stamp Co.: “Great oaks from little acorns grow, and so do stamp collections.”I liked these boys. What a pity, I thought, that they are Jews. Then I had a flash of philosophical insight, as memorable as the one that had paid to my religious faith some years before. Why, I asked myself, is it a pity that they are Jews, rather than its being a credit to the Jews? It was my first implicit appreciation of the principle of extensionality by which I have set such store down the decades: the universal is no more than the sum of its particulars.
我周围的环境有轻微的反犹气息。我想到了鲍勃•戈德史密斯、艾尔•格林和赫伯•罗斯，它们都是我的同学和集邮爱好者。小赫伯还成立了橡子邮票公司：“参天橡树长自小小橡子，集邮也是如此。”我喜欢这些孩子们。我曾经想，他们不幸生为犹太人，这是多么可惜啊。后来，我的脑海里闪现出一个哲学的洞见，一个和几年前关于我的宗教信仰的洞见一样值得纪念的洞见。我自问：“为什么要为他们是犹太人而可惜呢？为什么不认为他们的优秀表现是犹太人的自豪呢？”这是我第一次对外延性原则隐隐地表现出欣赏，在此后的几十年间我一直很重视这个原则：共相不过是其殊相的总和。】
My philosophical bent remained inarticulate, however, until college. I was just vaguely curious. I became actively interested rather in word origins and the history of language. I borrowed a book from the library on the subject and devoured it eagerly. I have been speculating and checking on etymologies ever since.
不过，我对哲学的爱好在上大学之前并不明确。我的哲学求知欲还很模糊。我主动感兴趣的领域是词源和语言史。我从图书馆借来了这样一本书，并如饥似渴地钻研了起来。自那以后，我养成了猜测并验证词源的习惯。
At Oberlin College, consequently, I had to choose among three competing fields for my major subject: philosophy, philology, and mathematics. A friend told me that Bertrand Russell had something called mathematical philosophy, and that settled it. I majored in mathematics and arranged for honors reading in mathematical philosophy. Philology was outnumbered, two to one.
后来，在我就读于奥伯林学院期间，我需要在三个不同的领域中选择我的专业：哲学、语言学和数学。一个朋友告诉我伯特兰罗素有一种被称为数学哲学的学问，这帮助我作出了决定。我选择了数学，并将数学哲学作为我的优等生学习内容。语言学以1：2的劣势而出局。
Mathematical philosophy turned out to be mathematical logic. It was not taught at Oberlin nor much elsewhere in America, but my professor got to me a reading list.
数学哲学其实也就是数理逻辑。那时，奥伯林和多数美国学校并不教授这个科目，但我的教授给我制定了一份阅读书目。
Practical mathematicians scoffed at mathematical logic as pedantic formalism. Mathematical logicians scoffed back fifteen years later, when their discipline had spawnedgeneral computer theoryand become indispensable in programming. Meanwhile, in 1931, mathematical logic had enabled Kurt Gödel in Vienna to prove a theorem that revolutionized the philosophy of mathematics. By applying mathematical logic to itself, he proved that no explicit set of rules of proof can cover all mathematical truths, or cover even so limited part of mathematics as the theory of whole numbers. A proof procedure can always be strengthened but never enough, without getting some falsehoods. Before Gödel’s discovery, we all thought each truth of mathematics could be proved, and proved by methods already at hand, though the proof might elude us. This, we thought, was what was distinctive about mathematics: truth is demonstrability. But not so.
那时，实用数学家看不起数理逻辑，将它嘲笑为学究气十足的形式主义。15年后，数理逻辑进入了通行的计算机理论，并为编程所不可或缺，于是数理逻辑学家得到了反唇相讥的机会。与此同时，在维也纳，库尔特·哥德尔于1931年运用数理逻辑证明了一条对数学哲学产生了革命性后果的定理。他将数理逻辑运用于自身，得出结论说：不存在覆盖所有数学真理（甚至只是作为数学一个有限部分的关于整数的理论中的真理）的一套明文规则。当然，我们总是可以通过强化规则使之覆盖所有数学真理，但在做到这一点的同时会不可避免地将一些数学谬误包括进来。在哥德尔的发现之前，我们都认为每一条数学真理都可以运用现成的方法得到证明，尽管我们未必能找到具体的证明。我们认为这是数学的一大特色：真理性就是可证明性。但事实并非如此。
It was two years before Gödel’s theorem that I was at Oberlin reading Whitehead and Russell’s greatPrincipia Mathematica, where they show in three volumes that all of classical mathematics can be translated into a few symbols of mathematical logic. The objects that made up the universe ofPrincipiawere predominantly class. A class, for mathematics, is just any lot, finite or infinite, of objects of any sort, however unlike or remote from one another. In subsequent improvements on Whitehead and Russell’s work, all the objects dealt with in pure classical mathematics end up as classes.
哥德尔定理问世两年前，我开始在奥伯林攻读怀特海和罗素的《数学原理》。他们在这部三卷本的伟大著作中表明：所有的经典数学都可以运用少数几个数理逻辑的符号加以改写。《原理》中谈到的对象主要是类。数学中的类可以任意一组对象（数目上可以是有限的，也可以是无穷多的）为元素，这些对象间不必彼此相似或彼此靠近。通过后来对怀特海和罗素工作的改进，我们可以进一步看清，纯粹的经典数学中所处理的所有对象都可以归结为类。
The numbers 0, 1, 2, etc. are an example. Each can be construed, however arbitrarily, as the class of all earlier ones. This makes 0 the empty class, 1 the class whose sole member is 0, 2 the class with the two members 0 and 1, and so on up. 0 has no members, 1 as one, 2 has two, and so on.
以0、1、2等等的数为例，其中每一个数都可以被人为地看成是之前的数的类。于是0就是空集，1则是以0为元素的类，2则是以0和1为元素的类，如此等等。
【这里的定义来自于冯·诺伊曼（1923）。另一种来自弗雷格（1884）的定义是：0是以空集为元素的集合，1是以所有单元集为元素的集合，2是以所有由两个元素组成的集合为元素的集合，如此等等。】
The three volumes ofPrincipiawere mostly in logical symbols. I reveled in the clarity, rigor, and elegance of the formulas and proofs and above all in the spectacular economy of the ideas that proved to suffice for the whole bewildering realm of classical mathematics. It was an achievement in tidy parsimony. A subsequent refinement by Gödel, and independently by Alfred Tarski in Poland, further enhanced the economy. They reduced the basic vocabulary to just the following. There are the adverb ‘not’ for negating a sentence and the conjunction ‘and’ for joining sentences. There is a generality prefix, with auxiliary variables, for saying that everything is thus and so. And finally, fourth, there is a verb ‘is a member of’ relating members to classes. I reduced these four basic devices to two equally simple ones. One is class inclusion, as in ‘Dogs are animals.’ The other is an abstruction prefix with auxiliary variables: ‘the class of all objects such that.’
三卷《原理》主要是逻辑符号。我对书中清晰、严谨而优雅的公式和证明推崇备至，我特别推崇全书在概念上的不可思议的节俭性：少数几个概念就足以表达令人眼花缭乱的经典数学中的一切。哥德尔后来的精致化工作（在波兰，阿尔弗雷德•塔尔斯基也独立地完成了这项工作）进一步增强了节俭性。他们将基本词汇进一步减少到下面四个：用来否定一个语句的副词“并非”、用来联结语句的连词“而且”、表示概括性的前缀加辅助性变项（意思是：每一个如此这般的事物x）、用来表示元素和类之间关系的动词“x是y的元素”。我将这四个设施减少为同样简单的两个。一个是类包含（比如“狗是动物”可以解释为狗类包含在动物类中）。另一个是抽象前缀加辅助性的变项：“以每一个满足如此这般条件的对象x为元素的类”）。
Whitehead and Russell took on the task inPrincipia not only of defining the various notions of classical mathematics, but also of framing axioms from which, along with the definitions, classical mathematics could be derived. At this point classes presented a deep problem: the paradoxes, the simplest of which is known as Russell’s Paradox. It proceeds from the principle, which had long gone without saying, that every membership condition you can formulate determines a class, the class of all objects fulfilling the condition. Very well, says Russell, try this condition: ‘x is not a member of x.’ This does not determine a class. There can be no such thing as the class of all non-self-members. It would belong to itself if and only it was a non-self-member. So we must rescind that obvious old rule. There are membership conditions that do not determine classes. This is one, and there are others.
怀特海和罗素在《原理》中的任务并不只是定义各种各样的经典数学概念，另一个任务是构造公理，并根据这些公理和定义推导出经典数学。但类在这一点上构成了障碍；更具体地说，成为障碍的是关于类的悖论，其中最简单的被称为罗素悖论。这个悖论是从一个一直以来不言而喻的原理（每一个可以明确表达的元素条件都决定一个类，它以满足条件的所有对象为元素）中推出来的。罗素发现了这个原理的一个反例。试试下面这个条件：x不是x的元素。这个条件并不决定一个类。并不存在以不属于自身的对象为元素的类，这样的类属于自身当且仅当它不属于自身。所以我们必须取消这个看上去显然的旧规则。存在着并不决定类的元素条件。不属于自身就是这样一个条件，但并不是这类条件中的惟一的一个。
But Russell did not rescind the old rule. He rejected the very words ‘x is not a member of x’ from the language, along with other paradoxical membership conditions, by complicating the grammar. Such was his theory of types, which governedPrincipia Mathematica. Individuals comprised his lowest type, classes of individuals his second type, classes of such classes his third, and so on. Formulas were meaningless that affirmed membership otherwise than between objects of consecutive types.
但罗素并没有取消这个旧规则。他采取的方案是取消“x不是x的元素”以及其他带来悖论的元素条件表达式，从而使语法复杂化了。这就是他的类型论，它支配了整个《数学原理》。个体构成了最低等级的对象，以个体为元素的类则处于第二等级，以类为元素的类则处于第三等级，如此等等。断言不相连的两个等级中的对象之间的属于关系的公式是无意义的。
A drawback of this expedient was that it saddled us with an infinite reduplication of arithmetic and the rest of mathematics, and of the logical class algebra itself, up the hierarchy of types. Each succeeding type had its universe class, its empty class, its numbers, all its mathematical ontology. With my predilection for tidy parsimony I deplored all this and sought less extravagant measures. I found that we could enjoy the protection conferred by Russell’s high-handed restraints on grammar, and by his infinite reduplication of the mathematical world, while paying neither of these prices. Instead I gave up what Russell was preserving, namely the law that every membership condition determines a class. Then I noted what membership conditions had been rendered meaningless by Russell’s restrictions on grammar, and just declared those sentences ineligible as membership conditions.
类型论的一个缺陷是，它使算术和数学的其他部分，包括关于类的逻辑代数本身，都有着无限多套的本体论，以适应无穷多的类型等级；每个类型都有它自身的全类、空类和元素。出于对整齐的节俭性的爱好，我并不认同类型论，而是转向寻求不那么奢侈的方案。我认为我们无需借助于罗素的强制式语法，无需借助于对数学世界的无限分层，就能享受到它们所带来的保护。我放弃了每一个元素条件都决定一个类这一罗素力图保全的规则。我也注意到了根据罗素的限制而成为无意义的元素条件，但我并不认为它们是无意义的，而只是宣布它们并不是真正的元素条件。
Along with its gains in simplicity, my system turned out to be stronger than Russell’s in its production of classes. This raised suspicions of some lingering paradox in my system. I have since been busy with other things, but a number of bright mathematicians in Belgium, Switzerland, England, and America have sought paradox in it without success, while turning up various surprises along the way.
我的系统除了更简单外，在产生类的能力上也要强过罗素的系统。这使人疑心我的系统里残存了悖论。我提出我的系统后一直忙于别的事情，但很多优秀的逻辑学家（来自比利时、瑞士、英国和美国）确实曾经试图在我的系统里找出悖论来，但并没有找到，反而发现了更多的优异之处。
Ernst Zermelo in Germany had long since had his own way around the paradoxes, devised independently of Russell’s and in the same year, 1908. Like me at my later date, he took the straightforward line of dropping the law that every membership condition determines a class. The laws that he then provided for existence of classes showed no kinship, as mine did, to Russell’s theory of types. Zermelo’s system, subsequently improved, is today’s standard. The search down the years for a contradiction in my system has been coupled with counter-effort to establish its consistency by constructing a model of it within Zermelo’s presumably consistent system. But this again has not succeeded.
在德国，恩斯特·策梅罗早就有了自己的解决悖论的方案。它和罗素的方案于1908年同时提出，但却是互相独立的。他像后来的我一样，直接取消了每个元素条件决定一个类这一定律。他提出的类存在定律，和我的一样，与罗素的类型论毫无亲缘关系。策梅罗的系统在经过后来的改进后成了今天标准的集合论。多年来，人们除了试图在我的系统内找出矛盾外，也曾经做过相反的工作，即试图在策梅罗的看上去一致的系统内，构造出我的系统的一个模式，从而证明我的系统的一致性，但这同样也没有成功。
A word now about the philosophical significance of the reduction of mathematics to logic, or to what has been called logic. It is a startling claim, for mathematics is proverbially mind-boggling whereas logic is proverbially obvious and trivial. The source of the confusion is the existence of classes, as is brought out by Russell’s Paradox and the others. The paradoxes reveal class theory as by no means trivial, and rather as a desperate challenge; and mathematics depends on the existence of classes at almost every turn, with or withoutPrincipia Mathematica. The gulf between little old traditional logic and the theory of classes, known as set theory, is borne out also by Gödel’s theorem, for that theorem applies to set theory along with number theory and higher branches.
现在来谈谈将数学还原为逻辑（或一直被称为逻辑的东西）这一方案在哲学上的意义。这里的主张是令人吃惊的，因为众所周知，数学是难以充分理解的，而逻辑却是自明的和微不足道的。罗素悖论和其他悖论让我们看清了混乱的根源在于类的存在性。悖论表明关于类的理论绝不是微不足道的，而毋宁是智力上的极大的挑战；数学在每一个节点上（不管是否包括《数学原理》）都依赖于类的存在。另外，有着悠久传统的狭义上的逻辑与关于类的理论（或集合论）之间的鸿沟，也得到哥德尔定理的支持，因为这个定理不但适用于数论，也适用于集合论和更高端的数学分支。
The place to draw the boundary between logic and the rest of mathematics is at classes. What lies below that boundary is indeed as easy and trivial as the name suggests. What classical mathematics is reducible to is set theory, a formidable branch of mathematics in its own right. The reduction of mathematics to set theory is illuminating and exciting for the tidy parsimony that it yields, but there is no trivialization.
逻辑和数学中的其他部分的分野在于是否涉及到类。处于类之下的逻辑确实如它的名字所提示的那样，易于理解而且微不足道。经典数学可以被还原，但只能被还原为集合论（逻辑加集合论），而集合论本身就是一个令人望而生畏的数学分支。这一还原是有启发价值的，也是激动人心的，因为它是体现了整齐的节俭，但这并不意味着数学归根到底是微不足道的。
There are and have long been philosophers, called nominalists, who balk at the very existence of classes. There are sticks, stones, and all the other concrete objects, but nominalists draw the line at abstract objects, and classes are indeed abstract objects. Our abstract words contribute to the sentences in which they occur, the nominalists say, but are not names of abstract objects.
一直都有拒绝承认类的哲学家，他们被称为唯名论者。唯名论者对棍子、石头和所有具体对象的存在性没有异议，但他们在抽象对象面前止步了，而类确实是抽象对象。他们承认抽象语词对包含它们的语句作出了贡献，但他们同时认为这些抽象语词并不是抽象对象的名称。
Another philosophical view of the matter is that once we get beyond words for concrete objects there is no real difference between viewing the word as naming and as not naming. I hold that both views come of looking in the wrong place. Where existence makes a difference is ordinarily not where we refer to a specific purported object, but where we are speaking of an unspecified object of a specified sort―some rabbit or other, some prime number―or every rabbit, every prime number. It is these repeated references to an identical but unspecified instance that introduce texture into our discourse and structure into our scientific theory. I go into detail in my workshop lecture.
这方面，还有一种哲学观点认为，语言中确实存在着表示具体对象的语词，但抽象语词有没有命名抽象对象是没有关系的。我认为这两种观点都来自于看问题的错误角度。一般说来，只有在我们谈到某个特定种类的未特指的对象或每个对象，比如谈到某个兔子或每个兔子、某个素数或每个素数时，而不是在意指某个特定对象时，存在与否才是一个真正的差别。正是这些对同一个未特指的对象的重复指称，才使我们的谈话或科学理论触及到了存在的本质或结构。在研讨会上我将对此详加说明。
【我们对单独词项的使用并不预设它们所指的对象的存在性，只有量词习语（“每一个”、“某个”）的使用才涉及到不存在或存在。奎因的名言是：存在就是成为变项的值。】
Mathematics leans heavily on existence when existence is thus identified, and the existence leaned on is existence of numbers and other abstract objects, ultimately classes. Natural science in turn leans heavily on mathematics. Some philosophers profess nominalism by not heeding the commitments of their own day-to-day or scientific discourse: not considering what constitutes reference to abstract objects.
数学严重地依赖于如此界定的存在，更具体地说，依赖于数和其他抽象对象的存在，最终则是依赖于类的存在。自然科学严重地依赖于数学。某些哲学家之所以能声称自己是唯名论者，是因为他们并没有认识到他们在日常话语和科学话语中所作出的承诺，他们并没有认识到这些话语指称了抽象对象。
My recognition of abstract objects was a bit melancholy at first, but I have been fully reconciled to them on gaining a clearer view of the nature of the assuming of objects and the service they perform in the structure of scientific theory. However, my abstract objects are classes and only classes. They work wonders, providing, as I said, for numbers and everything else in mathematics. I do not concede existence to properties or to meanings, for these are in trouble over identity and difference. Two properties, it seems, can be properties of all and only the same things and yet be called different properties. Nor is there a clear account of what it takes in general for two expressions to count as having the same meaning. Tidy parsimony makes short shrift of all that.
我一开始承认抽象对象时是有点沮丧的，但考虑到承认它们会让我们获得对对象设定过程的本性的更清楚的理解，考虑到它们在科学理论的结构中所发挥的作用，我也就感到释然了。但是我所承认的抽象对象是类，而且只是类。它们能够创造奇迹，能够帮助我们构造出数（如前所述）和数学中的其他对象。我并不承认性质和意义的实在性，问题出在识别标准上。两个性质可能适用的对象正好一样，但仍可能被称为不同的性质。同样地，两个语言表达式在什么条件下具有相同的意义，也是并不清楚的。缺乏整齐的节俭性，使我对这些所谓的抽象实体相当冷漠。
There is an obvious confusion, carelessness basically, that has plagued thinkers even of the stature of Whitehead and Russell. It is confusion of the written word or sign with the object referred to. It happens only when the object is abstract. In expository parts ofPrincipia Mathematica it muddies the thought of the authors and engenders needless complexities and obscurities. It is an evil―the confusion of use and mention―against which I have crusaded down the decades, with some success. I suspect that traces of it linger in the acquiescence of philosophers and layman in the notions of properties and meanings despite their infirmities in connection with identity. The philosopher who is out to clarify reality is ill advised to use notions as obscure as those he is trying to clarify. With classes, on the other hand, despite their abstractness, all is in order. They are as clearly identified as their members, for they are identical if they have the same members.
还有一个混淆，一个基本上产生于粗心的混淆，甚至使像怀特海和罗素这样的大师级思想家都深受其害。这就是在语词或符号与它们所指的对象之间的混淆。这种混淆只发生在当所指对象为抽象对象的场合。在《数学原理》的解释性段落中，作者便表现出这样的混淆，并因此使他们的著作产生了不必要的复杂性和含混性。我几十年来一直在与这个魔鬼——在使用和提及之间的混淆——作斗争，并取得了一些成效。我怀疑这一混淆的根源在于哲学家和普通人对性质和意义这些在同一性标准上不稳固的概念的默认。那些以澄清真相为己任的哲学家不慎使用了这些与他要澄清的概念同样隐晦的概念。如果他们使用类，情况就会大不相同；类虽然是抽象的，但却是一个清楚明白的概念。它们可以被清楚地识别的程度与它们的元素一样，因为如果它们具有相同的元素，它们就是同一个类。
My own work in and about mathematical logic occupied most of my next twenty years after college and a few more recent ones. From mathematics at Oberlin I had proceeded to graduate work in philosophy at Harvard because of my admiration of Whitehead, who had been brought there as professor of philosophy after his retirement from mathematics in London. I found that the Harvard philosophers back then were happier than I with properties, meanings, propositions, necessity.
在我从大学毕业后的20年间，我的大部分时间是在从事数理逻辑的研究或与之相关的研究；此外，再后来我也曾从事过几年这方面的研究。我从奥伯林数学专业毕业后，成了哈佛大学的哲学研究生，这是因为我对怀特海的仰慕的缘故。他那时已经从伦敦的数学专业退休，成了哈佛的哲学教授。我发现，那时的哈佛哲学家们对性质、意义、命题、必然性等概念采取了与我不同的容忍态度。
It was rather in Prague, on a postdoctoral fellowship two years later, that I first worked with an eminent philosopher who saw those matters as I did. He was Rudolf Carnap. I was similarly gratified on proceeding to Poland. I think it significant that both Carnap and the Poles were deep in mathematical logic. Sharpness of criteria and economy of assumptions―tidy parsimony―had guided them, as me. This is perhaps a basic contribution of mathematical logic to the philosophy of science, along with its direct and conspicuous contribution to the philosophy of mathematics. Whitehead and Russell, ironically, were perhaps too early to gain the full benefit of their own contribution.
直到两年后，当我在布拉格做博士后研究时，我才第一次遇到了与我看法一致的著名哲学家。他就是卡尔纳普。随后的波兰之行同样令我高兴。我想这里的关键在于，无论是卡尔纳普，还是那些波兰人，都有很深的数理逻辑方面的造诣。引导他们和我的都是整齐的节俭，即标准的清晰性和假设的经济性。
My first five books, along with three later ones, were devoted to logic and set theory. I kept striving for shortcuts, for streamlining, for clearer formulations, with a view to making modern logic a routine acquisition of the general student. One minor venture to that purpose did prove useful to computer theory and has brought my name into computer manuals, though oddly enough I have never been lured to computers myself, even to the word processor.
我的最早的五本书，以及后来的三本书，都是关于逻辑和集合论的。我希望现代逻辑能够成为普通学生的必修课，为此我一直在简化和完善我的思想，以便找到更清晰的表述。为着这个目的所做的一次小小的历险，确实也产生了一件对计算机理论有用的成果，这使得我的名字被列在了计算机工具书上。但奇怪的是，我对计算机的诱惑从不心动，甚至没有接触过文字处理机。
Around age 45 I began to feel that I had done what I wanted to do in logic and set theory, though three of those eight logic books and three revised editions were still to come. I had been teaching a course in philosophy of science, inspired largely by Carnap, for fourteen years along with my teaching of logic and set theory. So my mind for the past forty years has been primarily on the philosophy of science.
大约在45岁的时候，我觉得我已经做完了在逻辑和集合论领域里我想做的工作，尽管我的8本逻辑书中的3本是后来问世的，另外5本书中的3本在后来出了修订本。在随后的14年里，我除了继续从事逻辑和集合论的教学外，还开设了一门科学哲学方面的课程，这主要是受了卡尔纳普的鼓舞。所以从那以后的40年里，我基本上是在做科学哲学。
【奎因的8本逻辑书：《序列的逻辑》（1934）、《数理逻辑》（1940、1951）、《基本逻辑》（1941、1965、1980）、《新逻辑的含义》（1944、1996）、《逻辑方法》（1950、1959、1972、1982）、《集合论及其逻辑》（1963、1969）、《逻辑论文选》（1966、1995）、《逻辑哲学》（1970、1986）】
I am concerned with our knowledge of the external world. Our intake from the world, in the way of information about what is going on around us, is just the triggering of our sensory receptors by the impact of light rays and molecules, plus some negligible kinaesthetic data. It is not much to go on. But we come out in the fullness of time with a torrential account of the world around us, out to the farthest nebula and down to the humblest quark.
我关注我们关于外间世界的知识。我们从世界中所摄入的正在发生的信息，只限于光线和分子对我们的感受器的作用，加上一些其他微不足道的转瞬即逝的资料。这一摄入是很贫瘠的，但经过一段时间，我们据此产出的却是对我们周围的世界——从最遥远的星系到最微末的夸克——的丰富的认识。
Much of the intervening process was already prepared for by elaborate instincts, which are themselves accountable to natural selection down the generations. Instinctive standards of similarity implement the learning process. There is the development of language to account for, and the framing of hypotheses, and the testing of them by experiment. This is the domain of my workshop lecture.
这中间的过程很多是由精密的本能所完成的，这些本能自身可以由代际相承的自然选择得到说明。学习过程离不开天生的相似性标准。我们还要解释语言是如何发展的，假说是如何构造的，假说又是如何被实验检验的。这些我都会在研讨会上详细展开。
The canons of neat precision and economy of assumptions―tidy parsimony―are as much to the point here in the philosophy of science as in the philosophy of logic and mathematics, and indeed they apply equally within natural science itself. What is so striking about the foundations of mathematics is just that it is there that those canons find the least impediment.
无论是在科学哲学的领域，还是在逻辑哲学和数学哲学的领域，甚至在整个自然科学的领域，整齐的节俭性都是根本的要求，我们构造的假说应该既精确又经济。这个要求之所以在数学基础中如此引人注目，只是因为在这个领域实现这个要求的阻力是最小的。
