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
奎因哲学词条：谓词逻辑
奎因哲学词条：知识
（《奎因短论：一本不拘泥于分类学标准的哲学词典》，译者：翟玉章）
【融贯论的荒谬性。符合论的空洞性。符合论的残余价值：去引号。融贯论和对理论真理性的评估。塔尔斯基对真理的递归定义。真理悖论及其根源。真理的等级及其问题】
本文提到的词条：真理、原子、预言、事物、悖论、谓词逻辑、递归、排中律
Truth
真理
Philosophy primers tell of two opposing doctrines as to the nature of truth: the coherence theory and the correspondence theory. Neither theory, when naively stated, can be taken seriously. The coherence theory would have it that the truths qualify as such simply by all hanging together as a logically consistent system. The correspondence theory would have it that they qualify as true by corresponding to reality.
真理的本性是什么？哲学入门书会讲到两种对立的学说：融贯论和符合论。两种理论的素朴形态都不值得认真对待。融贯论认为，真理之所以是真理，是因为所有的真理聚在一起是一个逻辑上一致的系统。符合论认为，真理之所以是真理，是因为它们是与实在相符合的。
The coherence theory, thus baldly stated, seems to rest on an irrational rationalism -- on the absurd idea that the infinite totality of possible statements admits of only one overall distribution of yesses and noes that is logically consistent. Moreover, the theory makes no visible demands on observation and experiment. On this showing we can receive it only as a dummy doctrine, a straw man or whipping boy.
如此直率地表述的融贯论，其基础似乎是一种非理性的理性主义：无穷多个可能陈述的总体只能允许一种在逻辑上一致的肯定和否定的指派[1]。此外，该理论对观察和实验没有提出任何明显的要求。根据这个表现，我们只能把它当作一个徒有虚名的学说、一个稻草人或一个替罪羊。
On the other hand the correspondence theory, as thus far stated, is vague or vacuous. What on the part of true sentences is meant to correspond to what on the part of reality? If we seek a correspondence word by word, we find ourselves eking reality out with a complement of abstract objects fabricated for the sake of the correspondence. Or perhaps we settle for a correspondence of whole sentences with facts: a sentence is true if it reports a fact. But here again we have fabricated substance for an empty doctrine. The world is full of things, variously related, but what, in addition to all that, are facts? They are projected from true sentences for the sake of correspondence.
另一方面，上面所说的那种符合论，则是不清楚或空洞的。真语句中的什么东西要与实在中的什么东西相符合？如果我们逐一为语句中的词寻找符合关系，我们将只好把一些捏造的抽象对象填充到实在中去，以便落实这种符合关系。或者，我们也可以选择让整个语句与事实相符合：如果一个语句报道了一个事实，那么这个语句就是真的。但这只不过是又一次为了一个空洞的学说而捏造材料。世界上充满了以各种不同的方式发生联系的事物，但除了这些事物之外，事实在哪里呢？它们是为了落实符合关系而从真语句中推断出来的。
But let us ponder this last maneuver for a moment. The truth of 'Snow is white' is due, we are told, to the fact that snow is white. The true sentence 'Snow is white' corresponds to the fact that snow is white. The sentence 'Snow is white' is true if and only if it is a fact that snow is white. Now we have worked the fact, factitious fiction that it is, into a corner where we can deal it the coup de grace. The combination 'it is a fact that' is vacuous and can be dropped; 'It is a fact that snow is white' reduces to 'Snow is white'. Our account of the truth of 'Snow is white' in terms of facts has now come down to this: 'Snow is white' is true if and only if snow is white.
但让我们在上面这个用事实来定义真理的做法上驻足片刻。语句“雪是白的”的真理性，据说就在于雪是白的这一事实（the fact that snow is white）。真语句“雪是白的”符合雪是白的这一事实（the fact that snow is white）。语句“雪是白的”是真的当且仅当这是一个事实：雪是白的（it is a fact that snow is white）。现在，我们终于把事实这个捏造出来的东西逼到了墙角。对它予以最后歼灭的时机到来了。“这是一个事实”（it is a fact that）这个语词组合是空洞的、可以删除的；“这是一个事实：雪是白的”可以简化为“雪是白的”。我们用事实对“雪是白的”的真理性的解释，到头来不过是说：“雪是白的”是真的当且仅当雪是白的。
Here, as Tarski has urged, is the significant residue of the correspondence theory of truth. To attribute truth to the sentence is to attribute whiteness to the snow. Attribution of truth to 'Snow is white' just cancels the quotation marks and says that snow is white. Truth is disquotation. An ignominious end, one may feel, to the correspondence theory of truth. But we shall see later that it is more ignominious than it looks.
正如塔尔斯基所主张的，这就是真理符合论的残余价值之所在。把真赋予语句“雪是白的”，就是把白赋予雪。说语句“雪是白的”是真的，就是去掉引号而直接说雪是白的。真理就是去引号。人们可能觉得，真理符合论到头来成了去引号论，真是没有面子。但更没有面子的事情还在后面呢。
A place remains also for something like the coherence theory. The significant contrast between the correspondence theory and the coherence theory, when we set the untenable details aside, is that correspondence looks to the relation of the true sentence to what it is about, such as the white snow, while coherence looks to the relations of the true sentence to other sentences. Some sentences, to begin with, we accept as true directly on the strength of observation; the essential mechanism here is a conditioning of strings of words to sensory stimulations. Further sentences are rated as true on the strength of systematic connections with the observation sentences. We work out the neatest world system we can that conforms to the record of observations, and we tighten the squeeze by multiplying the observations. (See ATOMS; PREDICTION; THINGS.) Here is the reasonable place to appeal to coherence, in a vaguer but richer sense than logical consistency.
融贯论也有它的一席之地。撇开那些站不住脚的细节不谈，符合论和融贯论各有侧重：符合论所关注的是真语句和它所谈到的事物（如白雪）之间的关系，而融贯论所关注的则是真语句和其他语句之间的关系。一开始，我们直接通过观察接受一些语句为真；这里的基本机制是：通过条件作用，我们在语词串和感官刺激之间建立起了联系。其他语句之被接受为真，是根据它们与观察句之间的系统联系。我们尽可能地制定出符合观察记录的最简洁的世界体系，并借助更多的观察结果使之更加紧凑。（参见原子、预言、事物）融贯性的用武之地就在这里；这里所说的融贯性，其含义要比逻辑融贯性更加含糊，也更加丰富。
Coherence and correspondence, properly considered, are not rival theories of truth, but complementary aspects. The coherence aspect has to do with how to arrive at truth, by the best of our lights. The correspondence aspect has to do with the relation of truths to what they are about.
适得其所的融贯论和符合论，并不是互相对立的真理理论，而是真理理论的两个方面。融贯论方面与获得真理的最佳方式有关。符合论方面与真理和它们所谈到的东西的关系有关。
We saw the correspondence theory dwindle to disquotation. The attribution of truth to a statement is equated to the statement itself. This has been called the disappearance theory of truth, but unjustly; the quotation marks are not to be taken lightly. What can justly be said is that the adjective 'true' is dispensable when attributed to sentences that are explicitly before us. Where it is not thus dispensable is in saying that all or some sentences of such and such a specified form are or are not true, or that someone's statement unavailable for quotation was or was not true, or that the libel laws do not apply to true statements, or that you will tell the truth, the whole truth, and nothing but the truth, so help you God. In such contexts, when paraphrased to fit PREDICATE LOGIC, what stands as subject of the truth predicate is not a quotation but a VARIABLE. It is there that the truth predicate is not to be lightly dismissed.
我们看到，符合论最终沦为去引号论。说一个陈述是真的，与说出这个陈述本身，这两者是等价的。这曾被称为真理消失论，但这个称呼其实是不恰当的；引号是不应该被忽视的[2]。恰当的说法是：“真”这个形容词在应用于明摆在我们面前的语句时，是可有可无的。但如果我们想说的是：具有某种具体结构的语句的全部或一些是或者不是真的；或者，某人无法引用的某个陈述是或者不是真的；或者，诽谤法不适用于真陈述；或者，愿上帝保佑你说真话，完全说真话，而且只说真话[3]，那么“真”这个形容词就不是可有可无的。当这些语境被改写以适合谓词逻辑时，真谓词的主语将不再是一个引语，而是一个变项[4]。在变项语境中，真谓词是不容易被消去的。
The disquotational account may be said still, in a sense, to define truth. It intelligibly demarcates all our intelligible truths, by rendering the truth of each sentence as intelligible as the sentence itself. But in a stricter sense it does not define truth. It does not tell us how to eliminate the adjective 'true', by paraphrase, from every context in which it can grammatically occur. It only tells us how to eliminate it when it is attached to a quotation. Definition in the strict sense is elimination, and this is not wholly forthcoming. We can be thankful, for we know at least one context where its definability would involve us in self-contradiction. See the final formulation of the Liar Paradox in the piece on PARADOXES. It is remarkable how nearly definable we just now found truth to be, and how trivially, and yet how lethal its genuine definability would be.
在某种意义上，去引号的解释可以看成是对真理的定义。根据这一解释，一个语句的真理性和这个语句本身有着同样程度的可理解性；所以，它划出了我们所有可以理解的真理的界线。但严格说来这一解释并不是对真理的定义。它并没有告诉我们如何通过改写把每一个语境中合乎语法地出现的“真”这个形容词消除掉，它只告诉我们如何在它被附加到引语的时候把它消除掉。严格意义上的定义是消除，但去引号的解释并不能完全实现这一点。我们应该感到庆幸，因为我们知道至少一个可定义性让我们陷入自相矛盾的语境。见悖论中对说谎者悖论的最终表述。值得一提的是，真理是多么地接近可定义，而且又是多么地微不足道，但真正的可定义性却是致命的。
Tarski undertook to press the definition of truth. The "object language," whose truths were to be covered, comprised the notation of PREDICATE LOGIC with an unspecified lexicon of predicates. His strategy was RECURSION: start by defining the concept in application to atomic sentences, and then show how the definition, when achieved for sentences of any given degree of complexity, can be extended to the next. But he could not define truth in this way, because of the variables. Atomic sentences are neither true nor false; 'Fxy', say 'x inhabits y',is true of certain pairs of objects as values of the free variables 'x'and 'y', and false of others. It is only when all the variables in a sentence have been bound by quantifiers that we have a closed sentence, true or false.
塔尔斯基着手制定真理的定义。“对象语言”（定义所要覆盖的就是其中的真语句）由谓词逻辑的符号系统和未具体指定的谓词词汇所组成。他的策略是递归：先定义如何把有关概念应用到原子句，再表明如何把定义从应用于某个级别的复杂性语句，扩展到应用于高一个级别的复杂性语句。但他不能用这种方式来定义真理，因为含有自由变项的原子句是谈不上真假的；模式“Fxy”的例句，例如“x居住于y”，并不是无条件地是真的，而只是对于某些作为自由变项x 和 y 的值的对象对是真的。只有当语句中的所有变项都被量词所约束时，我们才会得到有真假可言的闭语句。
What Tarski does define recursively is satisfaction of a sentence by an object or sequence of objects as values of its free variables. Truth falls out afterward, trivially; a closed sentence is true if it is satisfied by the sequence of length zero, so to speak.
塔尔斯基递归定义的是一个语句被作为自由变项的值的对象（或对象的序列）所满足。随后对真理的定义是微不足道的；可以这样来理解：一个闭语句是真的，如果它被长度为零的序列所满足。
It is a masterly construction when seen in detail, and it goes through. Why then does it not saddle us with the Liar Paradox after all? The answer emerges when we try to write the paradoxical sentence in the object language, using symbolic logic and whatever elementary devices go into talking about appending expressions to quotations (see end of PARADOXES). The word 'true' figures in the paradoxical sentence in such a way that in the explicit reconstruction it has the context 'x is true' where 'x' is subject to a quantifier. But the recursive definition of satisfaction and truth does not show how to eliminate 'satisfies x', or 'x is true'; it eliminates 'satisfies' and 'is true' only when these are predicated of explicitly given open or closed sentences. We are emphatically reminded of the gulf between recursive and direct definition.
塔尔斯基的定义很精湛，而且是一个成功的定义。但它为什么终于逃过了说谎者悖论呢？如果我们使用符号逻辑和那些用于谈论引语附加表达式的手段，来改写对象语言中那个悖论句（见悖论的结尾），那么答案将昭然若揭。“真”这个词在悖论句被改写后将出现在“x是真的”这样的语境中，其中x是量词所约束的变项。但关于满足和真理的递归定义并不告诉我们如何消去“满足x”或“x是真的”；它只能用来消去用来谓述明确给出的开语句或闭语句的“满足”和“是真的”。我们清楚地看到了递归定义和直接定义之间的鸿沟。
We know how to turn a recursive definition into a direct one (see RECURSION), but the method draws on resources of set theory which, in the present instance, the object language must be presumed incapable of supplying. Add them and you do get a language in which truth and satisfaction for the old object language can be directly and fully defined; but still further set theoretic resources would then be needed for direct definition of truth and satisfaction with respect to this strengthened language. We are headed up the hierarchy of levels of truth and denotation that was glimpsed under PARADOXES.
我们知道如何将递归定义转变为直接定义（见递归），但是这种方法要用到集合论中的资源，而这些资源必须被假定是当前的对象语言所无法提供的。把这些资源加入到当前的对象语言中去，你就得到一种增强了的对象语言，它可以用来直接和完全地定义应用于原对象语言的真理和满足；但这样一来，应用于这种加强了的语言的真理和满足，又需要进一步的集合论的资源，才能直接地加以定义。我们正沿着真理和指示的等级不断向上攀爬，这一点我们在悖论中已经见识过了。
I must end on a somber note by reporting that all is perhaps not well in the hierarchy. What if two men say of each other on a given day that everything he said that day was true? Each of these two statements, then, would have to rank higher in the hierarchy than the other. Saul Kripke argues[5] that quite casual and useful ascriptions of truth can get lodged crosswise in the hierarchy in similar but more complicated ways. He devises an alternative concept of truth that is univocal, rather than hierarchical, and yet can consistently be expressed within the language to which it applies. It avoids paradox by neither holding nor failing of certain sensitive sentences. Thus it suspends the law of EXCLUDED MIDDLE. Also it is discouragingly complex. Let me just say again that all is not well.
在结语中，我必须把自己在真理等级化方面的悲观看法报告出来：一切都不妙。设想两个人在某一天都说对方那天所说的是真的，那么这两个语句中的每一个都要求比另一个更高的等级。索尔•克里普克论证说，那些相当随意且有用的对语句真假做出断言的语句[6]，它们的等级会以类似的但更复杂的方式发生交叉。克里普克设计了另一种真理概念，这种真理概念是单一的，没有等级之分，而且可以在它所应用的语言中得到一致的表达。但它既不肯定也不否定某些敏感的语句；这样一来，它便悬置了排中律。此外，它的复杂性也令人沮丧。让我再说一遍，一切都不妙。
[1]如果语句组中只包含一个语句，它有两种可能的肯定和否定的指派，即要么肯定该语句，要么否定该语句。在绝大多数情况下，这两种指派都是融贯的。随着语句组中的语句增加，它可能有的肯定和否定的指派会以几何级数迅速增多。要说这众多的指派中只有一个是融贯的，这是非常不可信的。——译者注
[2]当“‘雪是白的’是真的”被简化为“雪是白的”时，与真谓词一起消失的还有引号。——译者注
[3]这句话是常见的宣誓证词。——译者注
[4]举例来说，排中律（任何形如“p或者并非p”的语句都是真的）用逻辑语言表示将是：每个对象都是如此这般的x：如果x是形如“p或者并非p”语句，那么x是真的。——译者注
[5]Journal of Philosophy, 1975.
[6]以下是克里普克的两个例子：Everything Dean says about Watergate is false. （迪恩关于水门事件所说的一切都是假的。）、All of Nixon's utterances about Watergate are false. （尼克松关于水门事件的所有言论都是假的。）——译者注
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