（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）
奎因哲学词条：函数
奎因哲学词条：类型与标记
奎因哲学词条：变项
【谓词逻辑可以用来高效地解决从某个前提能否推出某个结论这样的问题。谓词逻辑的语法：“它的原子模式中的每一个都包含一个谓词字母，再在后面附上一个或多个变项作为它的主词，比如‘Fx’、‘Gxy’。这些原子模式通过“而且”、“或者”、“并非”和量词，可以形成无止境的复合模式。”谓词逻辑中的证明技术及其完全性。
相关词条：谓词逻辑、空时、单独词项。】
Predicate Logic
谓词逻辑
"Non sequitur," protested Tweedledum. "De contrario," countered Tweedledee, "sequitissimur!" His Latin, for all its faultiness, was not unimaginative. At any rate their logical bone of contention, whatever it may have been, would no doubt have crumbled in short order if they had had modern predicate logic at their disposal. Predicate logic markedly expedites the business of settling what follows from what and what does not.
“推不出来啊！”（"Non sequitur"）叮当兄抗议道。“反过来就推出来了！”（"De contrario, sequitissimur"）叮当弟抬杆说。[1]尽管叮当弟的拉丁语有误，但并非没有想像力。但是，如果他们掌握了现代谓词逻辑，他们便能看出，他们的争论（不论所争的具体内容是什么）将由于不合逻辑而在瞬间崩溃。[2]谓词逻辑可以用来高效地解决从某个前提能否推出某个结论这样的问题。
What follows from what is largely a question of the patterns formed within a text by various grammatical connectives and operators, and of the patterns in which the verbs, nouns, adjectives, and pronouns recur and interweave. Predicate logic abstracts those patterns from the embedding texts by substituting neutral letters 'F', 'G', and so on for the predicates-that is, for the verbs, nouns, and adjectives that bear all the burden of subject matter. Just one of the predicates is retained intact, namely, the two-place predicate '=' of identity, as a distinctively logical predicate.
从某个语句中能否推出某个语句，这大体上是一个关于模式的问题。这里的模式是从具体语句中提取出来的。具体语句中的语法联结词和算子在模式中被保留下来。具体语句中体现题材的谓词（也就是动词、普通名词和形容词）在模式中则被替换为‘F’、‘G’等中性的模式字母，只有表示等同关系的二位谓词‘=’，作为一个独特的逻辑谓词，在模式中被保留下来。
Pronouns are likewise retained as part of the abstracted pattern, for pronouns carry no subject matter beyond what would have been thrust upon them by the predicates that have gone by the board. The pronoun contributes rather to structure. It serves to mark different positions where some one and the same object is referred to, unspecified though the object now is.
代词在模式中也得到保留。代词所携带的题材都来自谓词，而谓词在模式中已被模式字母所取代。代词本身只有结构上的贡献；一个代词用以标出模式中的不同位置，这些位置指向某个未具体指定的惟一的对象。

In symbolic logic these pronouns are rendered as varibales, and serve for referring back to a quantifier: perhaps to '∃x', 'there is something x such that', or to '∀x', 'everything x is such that'.
在符号逻辑中，这些代词被称为变项，用‘x’、‘y’等字母来表示。它们可以往回指向量词：可以是全称量词‘∀x’（每个事物是如此这般的x以致），也可以是存在量词‘∃x’（有些事物是如此这般的x以致）。
Other structural members that are left standing after the dismantling of subject matter are the sentence connectives 'and' and 'or' and a sign for negation, as most of my readers know from a first course in logic. The grammar of the resulting predicate logic is familiar to them and readily stated. Its atomic formulas consist each of a predicate letter with one or more variables appended as subject or complement-thus 'Fx', 'Gxy'. These atomic formulas are compounded without limit by 'and', 'or', 'not', and the quantifiers.
拆除题材之后留下的结构性部件，除了变项和量词之外，还有语句联结词‘而且’和‘或者’，以及表示否定的‘并非’。所有这些，大家在初级逻辑中已经知道了。谓词逻辑的最终语法也是众所周知的，而且陈述出来也很容易。它的原子模式中的每一个都包含一个谓词字母，再在后面附上一个或多个变项作为它的主词，比如‘Fx’、‘Gxy’。这些原子模式通过“而且”、“或者”、“并非”和量词，可以形成无止境的复合模式。
Paraphrasing and trimming, we can coax vast reaches of language into this skimpy structure. A celebrated example of paraphrase is that of 'if p then q' into 'not (p and not q)', which is faithful enough for most purposes. Our identity predicate '=' comes to the fore in paraphrasing 'else', 'except', and the singular 'the'. A complex segment of discourse may, on the other hand, be swept into the framework of predicate logic as a seamless whole and be treated as atomic when its internal structure offers nothing to the logical argument in hand.
通过改写和整理，我们可以将大量的语言现象纳入到上述吝啬的结构中。改写的一个著名例子是将‘如果p那么q’解释为‘并非（p而且并非q）’。在大多数情况下，这都是一种充分忠实的改写。等同谓词‘=’可用来解释‘其他的’、‘除……之外’和单数的定冠词（‘the’）。另一方面，一段话语中的一个复杂部分，只要其内部结构对正在处理的逻辑论证没有影响，就可以一古脑儿地作为一个无结构的整体而纳入到谓词逻辑的框架中。[3]
Nouns, verbs, and adjectives are represented indiscriminately: 'Fx' might stand for 'x is a dog', 'x is fierce', or 'x bites'. Verbs are treated as tenseless; see SPACE-TIME.  Proper names and other SINGULAR TERMS can be taken in stride, as explained under the latter heading. Adverbs can be insinuated into the scheme, Donald Davidson has shown, by converting them to nouns or adjectives that denote events. Prepositions,on the other hand, are logically unproductive and can be left out of sight as fragments of unanalyzed predicates. Thus 'Fxyzw' might stand for 'x sold y to z for w'.
普通名词、动词和形容词被不加区别地处理为谓词：‘Fx’可以表示‘x是狗’，也可以表示‘x是凶猛的’，还可以表示‘x会咬人’。动词可以处理为无时态的表达式，见空时。专有名词和其他单独词项可以从容地被解释掉。唐纳德·戴维森指出，副词也可巧妙地纳入到谓词逻辑的框架中，方法是将它们转化为指示事件的普通名词或形容词。另一方面，介词在逻辑上并没有独立地位，可以处理为未分析的谓词的片段；比如，‘Fxyzw’可以解释为‘x为了w而将y卖给z’（‘xsold y to z for w'）。
Much remains, however, that cannot be regimented to fit the structure of predicate logic. 'Because' cannot, nor 'necessarily', nor 'possibly', nor the strong 'if-then' of the contrary-to-fact conditional. There is no place for the idioms of propositional attitude: 'x believes that p', 'x regrets that p', and so on. There is no place for 'shalt' and 'shalt not', nor for questions.
但是，也存在很多无法被纳入到谓词逻辑框架中的语言现象。‘因为’就无法纳入，‘必然’和‘可能’也无法纳入，反事实条件句中的‘如果……那么……’也无法纳入。另外，命题态度习语（‘x相信p’、‘x后悔p’，等等）、‘应该’和‘不应该’，还有问句，在谓词逻辑中都没有位置。
Despite such exclusions, all of austere science submits pliantly to the Procrustean bed of predicate logic. Regimentation to fit it thus serves not only to facilitate logical inference, but to attest to conceptual clarity. What does not fit retains a more tentative and provisional status.
但尽管有上述例外，所有的严格科学对这个谓词逻辑的框架都很顺从。把科学中的话语整合到这个框架中，不仅有助于逻辑推理，而且有助于澄清概念。拒绝这种整合的话语，只是科学发展过程中的暂时的和局部的现象。
Discourse fitted to predicate logic carries all its subject matter in its predicates. The rest is logical structure. The effect of the regimentation is to reduce grammatical structure to logical structure. One sentence logically implies another, in the regimented language, when their grammatical structures are such that no two sentences having those same structures are respectively true and false. Complete procedures have been in hand since 1879 (Frege) for proving logical implication in this sense, and their completeness has been known since 1930 (Gödel).
已经被谓词逻辑所整合的话语，其题材完全体现在其中的谓词上，谓词之外的一切都是逻辑结构。整合的作用就在于把语法结构化为逻辑结构。一个语句蕴涵另一个语句，如果任何两个依次具有这两个语句的逻辑结构的语句，都不会出现第一个为真而第二个为假的情况。弗雷格早在1879年就发现了据以证明上述意义上的逻辑蕴涵的方法；而哥德尔则在1930年向人们指出这个方法具有完全性，即只要两个语句具有逻辑蕴涵关系，就可以用这种方法加以证明。
These considerations make for a neat demarcation of logic from the rest of science, but the demarcation need not be insisted on. It is customary to reckon the business of logic as exceeding grammatical structure to the extent of claiming also one of the predicates, as we saw, namely '='. Less defensibly, some imperialistic logicians claim set theory as well, thus reckoning the predicate '∈' as logical where 'x∈y' means that x is a member of y. In either case the grammar stays the same; it is just a terminological question of whether to classify certain of the predicates, perhaps '=' or perhaps '=' and 'E', as logical along with the grammatical structure.
这样一来，我们便在逻辑和科学的其他部分之间划了一条整齐的界线：逻辑只管语法结构，科学的其他部分则向语法结构中填充血肉。但逻辑却不必拘泥于这条界线。有一个谓词，即前面提到过的表示等同关系的谓词“=”，人们习惯上也将它视为逻辑谓词。比较难于辩护的是有些霸气的逻辑学家的做法：他们将逻辑扩张到了集合论，主张谓词“∈”（“x∈y”的意思是x属于y，或x是y的元素）也是一个逻辑谓词。但无论是那一种情况，语法还是一样的。这只是一个术语问题，即要不要语法结构之外，将某些谓词（也许是“=”，也许是“∈”）也算做逻辑谓词。
But the name of logic is commonly extended also beyond what can be fitted within the grammatical structure of predicate logic at all. We encounter a logic of necessity and possibility, a logic of questions, of 'shalt' and 'shalt not', of propositional attitudes, and of strong conditionals. Insofar as the grammar of predicate logic is in principle adequate as a vehicle of austere scientific theory, these ulterior endeavors have no part to play in our theoretical system of the world. They can serve still as clarification of various other aspects of ordinary language.
但人们以逻辑的名义所做的扩展，常常会超出谓词逻辑的语法结构所能容纳的范围。于是，我们碰到了关于必然性和可能性的逻辑，关于问题的逻辑，关于“应该”和“不应该”的逻辑，关于命题态度的逻辑，关于强条件句的逻辑。只要谓词逻辑的语法在原则上足以成为严格的科学理论的载体，这些旁门左道在我们关于世界的理论体系中就不会有用武之地。当然，它们可以用来澄清日常语言的的诸多其他方面。
[1]作者在这里是在模仿爱丽丝童话中爱抬杆的兄弟俩的对话。——译者注
[2]不能因为一个语句推不出某个结论，就据此说其否定句就能推出这个结论。比如，无论是从“雪是白的”，还是从其否定句“雪不是白的”出发，都推不出“2+2=4”这个结论。――译者注
[3]比如，从“苏格拉底是哲学家而且柏拉图也是哲学家”可以推出“柏拉图是哲学家”，但由于其中的语句“苏格拉底是哲学家”和“柏拉图是哲学家”的内部结构并不影响上述推理的有效性，因此，在对这一推理做形式化说明时，可以忽略其内部结构，而简单地分别用一个语句模式字母‘p’和‘q’来表示。——译者注。
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