（奎因《短文集：一本不拘泥于分类学标准的哲学词典》，译者：翟玉章）
【（约束）变项在日常语言中的原型是关系代词，其目的是消除嵌套的关系从句的歧义性。变项标记一个语句中的不同位置并使之发生关联，以便将该语句对某个对象的述说整合成一个形容词短语。】
奎因哲学词条：函数
奎因哲学词条：类型与标记
Variable
变项
If the amount of some substance available for packaging at one time is different from the amount available at another, it is fairly usual and highly professional to speak of the amount as variable. It is as if there were those various amounts at the various times, 837gallons for example, and then, over and above all those amounts, some further amount that is simply called the amount and is said, unlike them, to vary from time to time. Of course this doesn’t fool anybody.
如果某种可用于打包的物质的量在某个时刻不同于另一个时刻，那么它就是一个变量；这是一个相当平常而又高度专业化的说法。这种说法似乎有一种弦外之音：除了各个不同时刻的固定的量（比如，837加仑）之外，还有一个可被称为量本身的东西，后者并不是固定的，而是随时间变化的。当然，这样的解读愚弄不了任何人。
The idiom is pressed farther. It has long been customary to use a letter, first and foremost the proverbial ‘x’, as if it were a name of that phantom number, on a par with numerals like ‘837’ that are names of genuine numbers.
这种习惯说法还可以被进一步发挥。很久以来，人们就习惯于使用字母（首先是众所周知的‘x’）来表示变量；正像数字‘837’是固定的数837的名称一样，‘x’也仿佛是那个捉摸不定的数的名称。
A somewhat different and more celebrated role of that same letter is as an unknown: something to solve for in high-school algebra. Variation is not the idea there; x is some fixed number, and the problem is to find out which one. It varies only from problem to problem. In both of these roles, however, and in further uses as well, ‘x’ and its fellow letters are called variables. We must acquiesce in the word, which is well entrenched, and let its etymology go. But the word is to be seen as referring to the letters themselves, in their pertinent uses, and not to some strangely unstable sort of number. Every number is simply what it is, as Bishop Butler might have said, and not another thing.
这同一个字母会扮演一个有些不同但更著名的角色，即用来表示未知数。未知数是待求解的某种东西，这一点我们在中学代数课上就已经知道了。这个用法与变化无关；x是某个固定的数，我们的任务是找出它是哪个固定的数。当然，答案会随着问题的变化而变化。但在这两种用法中，以及其他用法中，‘x’之类的字母都被称为变项（或变量、变数）。我们必须将这个根深蒂固的词接受下来，而不必计较它的词源。但“变项”一词在它的各种相关用法中指的就是‘x’之类的字母本身，而并不指某种奇怪的不稳定的数。正如巴特勒主教可能会说的那样，每一个数都只是如其所是，而不是别的东西。[1]
Numbers, indeed, are the least of it; variables in their various uses can range over objects of any sort. As for those various uses, they are not so various after all when we probe their inner nature. Variables are essentially pronouns. I shall make the connection by turning to pronouns and building out from that side.
数只是变项所涵盖的一类对象。广义上讲，变项可以涵盖任何种类的对象。但这些形形色色的变项从内在本性上讲都是一样的，它们其实都是代词。下面，我将从代词说起，并建立它们与变项之间的联系。
Pronouns are so called because they sometimes stand for a repetition of a singular noun as in ‘John took off his hat and hung it up’, which is to say ‘John took off John’s hat and hung John’s hat up’. Such are the pronouns of laziness, as Peter Geach calls them. They are of no logical or philosophical interest and of little interest even to linguistics. On the other hand ‘Sadie stole something and sold it’ tells us more than that Sadie stole something and sold something. The ‘it’ here is not a pronoun of laziness; it is serious business. Pronouns in their serious use are even a more serious business than the singular nouns themselves, as may be sensed in reading the pieces on PREDICATE LOGIC and UNIVERDALS. Charles Sanders Peirce quipped that nouns might more justly have been called pro-pronouns.
代词的全称是代名词，因为它们有时可用来避免单数名词的重复，就像下面的例句所表明的那样：‘约翰脱下他的帽子并把它挂了起来。’这句话不过是‘约翰脱下约翰的帽子并把约翰的帽子挂了起来’的缩写。这里的代词‘它’，用彼得·吉奇（Peter Geach）的术语来说，是懒散的代词。这样的代词不但没有什么逻辑上的或哲学上的价值，而且也没有多少语言学上的价值。但另一方面，‘萨迪偷了某个东西，而且卖掉了它’告诉了我们比‘萨迪偷了某个东西，而且卖掉了某个东西’更多的东西。因此，这里的‘它’并不是一个懒散的代词，而是一个严肃的代词。严肃的代词甚至比单数名词还要严肃，读者在阅读词条谓词逻辑和共相时当能感觉到这一点。查尔斯·桑德斯·皮尔士（Charles Sanders Peirce）曾机智地指出，名词被称为代代词也许是更公正的。
The true genius of the pronoun is manifested in the relative clause. This is a device for packaging what a sentence says about something. What the sentence ‘I bought Fido from a man who found him’ says about Fido can be packaged in the relative clause ‘that I bought from a man who found him’. In the relative pronoun ‘that’ here, and the pronoun ‘him’ that refers back to it, we see the logically fundamental role of pronouns. Our relative clause here can be thought of as an adjective phrase, and in effect our original sentence about Fido predicates this adjective phrase of Fido. A more succinct adjective phrase to the same effect is ‘bought from finder’, but the importance of the relative clause is that it is a uniform device for abstracting what any sentence says about anything.
代词的真正精髓体现在关系从句中。关系从句的功能是对一个句子中的关于某个对象的描述进行打包处理。句子“我从某个发现他的男人那里买下了菲多”对菲多的描述可以处理为关系从句‘我从发现他的人那里买下的’（that I bought from a man who found him）[2]。从关系代词‘that’和后面起着再次提及作用的代词‘him’那里，我们看到了代词的根本作用。我们的关系从句可以理解为一个形容词短语；实际上，我们关于菲多的原句就是用这个形容词短语来描述它的。当然，起相同作用的形容词短语可以是更紧凑的‘买自发现者’；但关系从句的重要性在于，它提供了从一个语句中提取出描述某个对象的形容词短语的统一手段。
The uniformity in the construction of relative clauses can be heightened and contortions in word order can be avoided, at some cost in stylistic elegance, by switching to the ‘such that’ idiom. We get ‘such that I bought him from a man who found him’. The recipe for constructing such a clause from a sentence is simple: just prefix ‘such that’ to the sentence and substitute a pronoun for the noun from which you are abstracting. The ‘such that’ idiom is helpful in coping with intricate contexts; hence its popularity in mathematical writing.
关系从句作为提取形容词短语的统一手段，可以借助习语‘如此以致’（such that）得到强化。我们无需打乱原句中的词序，只需为文体的优雅付出一些代价。在上面的例子中，如果我们转向习语‘如此以致’，我们将得到‘如此以致我从一个发现他的男人那里买下了他’。从一个语句中构造‘如此以致’从句的方法很简单：将‘如此以致’置于句首：如此以致我从某个发现他的男人那里买下了菲多，再用代词替换将要从中分离的名词（‘菲多’）：如此以致我从一个发现他的男人那里买下了他。习语‘如此以致’在处理复杂语境时很有用，所以在数学著作中很常见。
Our present example actually shows one relative clause nested within another. Converting the inner one likewise into the ‘such that’ idiom, we get ‘such that I bought him from a man such that he found him’. At this point a latent ambiguity is activated: who found whom?
我们现在的例子实际上是一个内部嵌套了另一个关系从句的关系从句。当我们对处于内层的另一个关系从句使用‘如此以致’习语来改写时，我们得到的整个关系从句将会是：‘如此以致我从一个男人（如此以致他发现了他）那里买下了他’。至此，一个潜在的含混性被激活了：谁发现了谁？
The mathematician settles matters by putting distinctive letters for his ambiguous pronouns and then labeling each ‘such that’ with its appropriate letter, thus: ‘x such that I bought x from a man y such that y found x’.
数学家的解决办法是用不同的字母来区别有歧义的代词，然后再将每一个‘如此以致’标记上适当的字母。经过这样的处理，上面的关系从句便成了：‘x如此以致我从一个男人（y如此以致y发现了x）买下了x。’
Here, I say, is the birth of the variable: in the disambiguation of nested ‘such that’ clauses, which is to say nested relative clauses. This is not true historically, but it could have been. It is a myth of origins that reveals the basic role and ultimate utility of the variable. The variable is a device for marking and linking up various positions in a sentence so as to encapsulate, in an adjective phrase, what a sentence says about something. Its business is linking and permuting.
我要说，变项就诞生于此，其目的是消除嵌套的‘如此以致’从句（从根本上说，是嵌套的关系从句）的歧义性。这从历史上看并不是真的，但从逻辑上是讲得通的。这个关于变项起源的神话揭示了变项的基本角色和根本功能。变项标记一个语句中的不同位置并使之发生关联，以便将语句对某个对象的述说整合成一个形容词短语。变项所做的事情就是关联和组合。
This is not just an example of the use of variable; it is the whole story. All use of variables is reducible to their use as the pronouns of ‘such that’ clauses. When we solve the equation ‘x+5=9’ the unknown x we are finding is the number x such that x+5=9. Most uses of variables, when written out explicitly, already exhibit the ‘such that’ construction in so many words: thus ‘the class of all objects x such that …’, ‘everything x is such that …’, ‘something x is such that …’. Incidentally the last two contexts listed, known as quantifiers, can be shown to suffice; all others can be paraphrased in terms of these. Indeed either of the two quantifiers suffices alone; the other can be paraphrased in terms of it.
以上所说的不是变项的用法之一，而是变项的全部用法。任何语境下的变项都可以化归为‘如此以致’从句中的代词。当我们解方程‘x+5=9’时，我们寻找的那个未知数x就是那个数x如此以致x+5=9。多数涉及变项的语境，如果明确地写出来，其中的‘如此以致’结构将昭然若揭，比如‘以（所有对象x如此以致…x…）为元素的类’，‘每个事物都是x如此以致…x…’，‘某些事物是x如此以致…x…’。附带说一下，可以证明最后两个语境（被称为量词）就已经足够了，因为所有其他涉及到变项的语境都可以用这两个量词加以解释。进一步地，这两个量词中的任何一个就已经足够；其中的一个可以用另一个来定义。
[1]巴特勒主教（Bishop Joseph Butler，1692——1752）是十八世纪英国著名的宗教哲学家。他的原话是“Everything is what it is and nothing else”（每个事物都如其所是，而不是别的东西。）——译者注
[2]英语中的关系从句是以语句形式呈现的，而起着形容词的作用。相比之下，对它的汉语翻译是以形容词形式出现的，语句的痕迹已经荡然无存。——译者注
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