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
奎因哲学词条：真理
奎因哲学词条：指称、实体化
（《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）
【从日常语言的角度看，含有空名“珀伽索斯”的语句，除了断言珀伽索斯存在或不存在的语句之外，都是没有真假可言的。这个做法违背了排中律。从逻辑的角度看，有一个更好的处理单独词项的方法，其要点是把单独词项吸收进谓词。名字。单独摹状词及其他复杂的单独词项。单独词项在理论上是多余的，但从操作（特别是数学操作）的角度看实际上是不可或缺的。】
本文提到的词条：单独词项、非直谓性、排中律、谓词逻辑、空时。
Singular Terms
单独词项
Asked whether Pegasus flew, whether he had horns, and whether he had pin feathers, we are apt to say that the first is true, the second false, and the third neither. This is an elliptical way of saying that the ancient myths affirm the first, that they rule out the second, and that they take no stand on the third.
当被问到珀伽索斯[1]会不会飞，有没有角，没有没针羽时，我们会倾向于回答：“珀伽索斯会飞”是真的，“珀伽索斯有角”是假的，“珀伽索斯有针羽”既不真也不假。这是一种缩略式的回答；完整的回答将是：古代神话肯定了第一个语句，否定了第二个语句，而对第三个语句没有观点。
But what then are our own verdicts on the three statements, speaking for ourselves and not for our fanciful forebears? Presumably that none of the three is either true or false, there being no such creature as Pegasus. Still we hesitate to reject them as meaningless. We understand the word 'Pegasus', after all, and we even recognize some statements as true that contain it, notably the statement 'There is no such creature as Pegasus'.
但是，如果只代表我们自己，而不代表我们的耽于幻想的祖先，那么我们会怎么回答呢？我们大概会说这三个语句都无所谓真假，因为根本就不存在珀伽索斯这样的生物。尽管如此，我们并不愿意把这些语句斥为无意义。毕竟，我们是理解“珀伽索斯”这个词的，甚至还知道有些含有这个词的语句是真的；显然，“不存在珀伽索斯这样的生物”就是这样一个语句。
There is a clear reason not to opt for meaninglessness, and it becomes evident when we move from Pegasus to such examples as Camelot and Prester John. We know there never was Pegasus, but are less sure whether there was or was not such a place as Camelot or such a man as Prester John; and it is undesirable to let the question of meaningfulness of sentences of our language hinge on such unsettled questions of nonlinguistic fact.
一个语句是否有意义不应取决于超语言的存在问题的答案。当我们从珀伽索斯转向卡米洛特和祭司王约翰这样的例子时，这一点将是显而易见的。我们知道珀伽索斯根本不存在，但我们并不知道卡米洛特[2]或祭司王约翰[3]是否存在。如果只有在卡米洛特存在的情况下，含有“卡米洛特”的语句才是有意义的，那么，含有“卡米洛特”的语句是否有意义对于我们来说将是悬而未决的；这一做法显然并不可取。
A better line, evidently, is to reckon all the above sentences about Pegasus as meaningful, but still to reckon the first three as neither true or false. The question what sentences about Camelot or Prester John are true or false, then, and what ones are neither, will hinge on the factual question of existence of such a place or person. This is better, since truth and falsity, unlike meaningfulness, normally do hinge on matters of fact and commonly do remain open questions.
显然，更好的做法是认为上面提到的所有关于珀伽索斯的语句都是有意义的，但同时认为前三个语句是没有真假的。至于关于卡米洛特或祭司王约翰的语句中哪些是有真假的，哪些是没有真假的，将取决于事实上有没有这样一个地方或这样一个人物。之所以说这样的做法是更好的，是因为一个语句有没有真假这个问题，与一个语句有没意义的问题不同，确实取决于超语言的事实，而且也常常是悬而未决的。
We had to give 'There is no such creature as Pegasus' special status. Similarly for its contradictory, 'Pegasus exists', and other sentences equivalent to these; they do qualify unequivocally as true or false. I pause here for a theological interlude. An old argument for the existence of God, known as the ontological argument, was that God is by definition perfect. Failure to exist would be an imperfection, so God exists. Kant was no more impressed than we by the argument, and his rebuttal was that existence is not a predicate. We have now noticed again the special status of singular existence statements, however their status be phrased.
语句“不存在珀伽索斯这样的生物”被给予了特殊地位，即它是有真假的。同样地，它的矛盾句“珀伽索斯存在”，以及与这两个语句等价的其他语句，也享有这样的特殊地位。行文至此，我想加入一段神学插曲。上帝的存在性有一个古老的论证，被称为“本体论的论证”。这个论证把上帝定义为完美的对象。它接着说，如果一个对象不存在，那么它是不完美的，。所以上帝存在。康德，和我们一样，并没有被这个论证所打动。他的反驳是说：存在并不是一个谓词。我们现在又一次注意到了单数存在陈述的特殊地位，尽管我们刚才对特殊地位的表述是和康德不一样的[4]。
As for other statements about Pegasus -- ones that might in a Kantian spirit be called "predicative" if that word were not preempted (see IMPREDICATIVITY) -- we concluded that the most natural way of representing everyday language is to regard them as neither true nor false. This means taking a negative stand in the matter of the EXCLUDED MIDDLE, q.v. But when for purposes of logical analysis we are concerned to regiment scientific language along logically economical lines, as in PREDICATE LOGIC, there is a better way of dealing with names and other singular terms. It conforms to the law of the excluded middle, and it is more explicit on matters of existence and uniqueness.
至于关于珀伽索斯的其他语句（本来我可以顺着康德的意思，将它们称为“谓词性的”（predicative），但这个词已另有它用了（见非直谓性（IMPREDICATIVITY））[5]，我们的结论是：从日常语言的角度看，最自然的方法是把它们看作无真假可言的语句。这一做法违背了排中律。但如果我们是在做逻辑分析，即，以逻辑上节俭的思路来整合科学语言（就像在谓词逻辑词条中所看到的那样），那么就有一种更好的处理名字和其他单独词项的方法。这种方法不违背排中律，而且在存在性和惟一性的问题上更加明确。
It is a matter of absorbing singular terms into predicates. 'Pegasus', 'Napoleon', and the rest are treated as inseparable fragments of the predicates 'is Pegasus', 'is Napoleon', and so on. 'Pegasus flies' becomes:
(1) ∃x(x is Pegasus and x flies),
that is, 'Something is Pegasus and flies'. See PREDICATE LOGIC. This sentence is simply false, along with '∃x(x is Pegasus)' itself. The three sentences about Pegasus that we accounted neither true nor false now turn out false.
这个方法就是把单独词项吸收进谓词。“珀伽索斯”、“拿破仑”等名字被处理成“是柏伽索斯”、“是拿破仑”等的不可分割的片段[6]。在这一做法下，“珀伽索斯会飞”成了：
（1）∃x(x是珀伽索斯而且x会飞)，
即，“某些东西是珀伽索斯而且会飞”。见谓词逻辑。这句话，就像“∃x(x 是珀伽索斯)”本身一样，根本就是假的。那三个曾被认为没有真假可言的关于珀伽索斯的语句，根据现在的方法，都成了假的。
Might we not have simply ruled them false at the outset, without paraphrasing? Might we not have agreed to account all sentences about Pegasus as false outright, except for ones like 'There is no such thing as Pegasus'? No, this line would have led to trouble. It would account 'Pegasus flies' and 'Pegasus does not fly' both as false, contrary to logic. The point of the paraphrasing is to sort out such conflicting cases. 'Pegasus does not fly' admits of two opposite paraphrases; for it is true that
not ∃x(x is Pegasus and x flies)
but false that
∃x(x is Pegasus and x does not fly).
Sentences formerly deemed neither true nor false, thus do not all get paraphrased as false. Distinctions emerge.
我们可以不诉诸改写而在一开始就把它们径直判定为假吗？我们可以同意将所有关于珀伽索斯的语句（“不存在珀伽索斯这样的东西”之类的语句除外）都直接解释为假吗？不可以，这样做会带来麻烦。它会把“珀伽索斯会飞”和“珀伽索斯不会飞”都解释为假，这是违背逻辑的。改写的目的就是要将这些相互矛盾的情况区别开来。“珀伽索斯不会飞”可以有两种改写。如果被改写为
并非∃x(x是珀伽索斯而且x会飞)，
它便是真的；而如果被改写为
∃x(x是珀伽索斯而且x会飞)，
它便是假的。过去被一律认为既不真也不假的语句，现在有了区别，并不都是假的。
A singular term connotes uniqueness. It purports to designate just one thing. On the present approach uniqueness, like existence, gets separate attention. When wanted it is expressly stated:
(2)∀x∀y(ifx is Napoleon and y is Napoleon then x = y),
that is, only one thing is Napoleon. First and last, thus, the effect of absorbing names into predicates is an explicit sorting out of logically pertinent features. It is reminiscent of what happens to tense under logical regimentation; see SPACE-TIME.
单独词项意味着惟一性。它旨在指定惟一的事物。在目前的方法中，惟一性，就像存在性一样，也得到了单独的关注。如果需要的话，它可以被明确地表达出来：
（2）∀x∀y(如果x是拿破仑而且y是拿破仑，那么x = y),
也就是说，只有一个事物是拿破仑。因此，将名字吸引收进谓词所要达到效果是：将有关逻辑特征明确地区别开来。这让人想起了对时态的逻辑处理；见空时。
Complex singular terms can be similarly absorbed. The dominant form of complex singular term is singular description, for example, 'the author of Waverley'. This is the ever recurring example, stemming from Bertrand Russell's pioneer work in paraphrasing singular terms. Here again the term gives way to a predicate -- in this case 'wrote Waverley'.Then, just as 'Pegasus flies' became (1), so 'The author of Waverley is Scottish' becomes:
∃x(x wrote Waverley and x is Scottish).
Again, as in (2), we can add a stipulation of uniqueness when we need it.
Similarly for the idiom of singular description generally. Its general form is 'the object x such that Fx'; and to ascribe any further predicate 'G' to the object thus described we have merely to write '∃x(Fx and Gx)'. Again we can stipulate uniqueness of the described object when we need to:
∀x∀y(if Fx and Fy then x = y).
复杂的单独词项，也可以如法炮制地被吸收。复杂单独词项的主要形式是单独摹状词；“《韦弗利》的作者”就是一个例子，它反复出现在伯特兰·罗素关于单独词项的解释的开创性著作中。在这里，单独词项再次让位于谓词：“《韦弗利》的作者”让位于“写《韦弗利》”。然后，正如“珀伽索斯会飞”变成了（1）一样，“《韦弗利》的作者是苏格兰人”则变成了：
∃x(x写《韦弗利》而且x是苏格兰人)。
同样地，如果我们需要，可以仿照（2），添加一个关于惟一性的条款。
所有的单独摹状词都可以这样处理。单独摹状词的一般形式是“那个如此这般的x：x是F”[7]。如果我们想说它所指称的对象可以用另一个谓词“G”来描述，只需这样来表达：“∃x(Fx 而且Gx)”。当然，如果我们需要，也可以添加关于这个对象的惟一性条款：
∀x∀y(如果Fx而且Fy，那么x= y)。
Singular terms in forms other than singular description are ubiquitous in mathematics -- thus 'z + w', 'zw', 'z2’. But they can all be disposed of in essentially the way we have been seeing. Thus 'z + w' gets absorbed into a three-place predicate '∑', meaning 'is-the-sum-of-... -and... '. A sentence about z+ w, say 'G(z + w)', becomes '∃x(∑xzw and Gx)'. A theorem or postulate of uniqueness, again, can be cited as needed:
∀x∀y∀z∀w(if∑xzw and∑yzw then x =y).
Such is the elimination of singular terms. It is part of the process of paraphrasing ordinary language into the straitjacket of PREDICATE LOGIC, in the narrow form in which I have sketched it under that heading. It makes for a streamlining of logic and for a reconciliation, as we have seen, of EXCLUDED MIDDLE with questions of nonexistence.
除了单独摹状词之外，其他形式的单独词项在数学中也很常见，例如“z + w”、“zw”、“z2”。但它们本质上也可以用我们刚刚看到的方式来处理。因此，“z + w”可以被吸收进三位谓词“Σ”（即“是……以及——的和”）。一个关于z + w的语句，例如“G(z + w)”，可以被改写为“∃x(Σxzw而且 Gx)”。同样，也可以根据需要援引关于惟一性的定理和假设：
∀x∀y∀z∀w（如果Σxzw而且Σyzw，那么x = y）[8]。
这便是对单独词项的消除。它是日常语言被改装从而穿上谓词逻辑狭义形式这一紧身衣的过程的一部分（我在该词条中概述过这个狭义形式）。它使逻辑更加简练了，而且正如我们所看到的，它使空名不再构成对排中律的挑战。
Its practical drawbacks, however, must be noted and heavily stressed. Substitution of polynomials and other complex singular terms directly for variables and for one another is the very life of computation and algebraic manipulation. Mathematics would be immobilized by the straitjacket of predicate logic without singular terms. In principle the work can all be done in the paraphrased idiom, but the clumsiness and the resulting barrier to intuition would be prohibitive. The dilemma has a happy solution, however, in the reversibility of the rules of paraphrase. We can switch back and forth, enjoying the best of both worlds. Logical elegance and clarity of analysis this side, efficient practice that.
然而，它在操作层面上的缺点必须引起注意并予以强调。计算和代数操作的生命力正在于：多项式（以及其他复杂的单独词项）可以为变项所替换，也可以为彼此所替换。如果没有单独词项，数学将会被谓词逻辑的紧身衣弄得寸步难行。理论上，单独词项能做到的事情，也能由用来改写的设施做到。是的，但那样做的代价——既笨拙又造成直觉理解上的障碍——足以令人望而却步。幸运的是，多亏了改写规则的可逆性，我们可以来回切换，从而享受到两边的好处：一边是分析带来的逻辑简练性和清晰性，一边是操作层面上的高效性。
[1]古希腊神话中的一个奇幻生物，也被意译为“飞马”或“天马”。——译者注
[2]英国民间传说中的亚瑟王的宫殿。——译者注
[3]传说中的中世纪亚洲的一个信奉基督教的国王。——译者注
[4]对康德来说，“珀伽索斯存在”或“珀伽索斯不存在”的特殊性在于：“存在”或“不存在”并不是对珀伽索斯的描述；对于奎因来说，这两个语句的特殊性在于：它们是有真假的。——译者注
[5]形容词predicative的原意是“谓词性的”或“表语的”，但它后来成了有着不同用法的专门术语（被翻译为“直谓的”）。现在，“珀伽索斯会飞”通常被称为谓述句（sentence of predication），而“珀伽索斯存在”则被称为存在句。所谓的谓述句，是指形如“S是P”的语句，其中“是”是起语句标记的系词，“S”是单独词项或概括词项，“P”是概括词项。——译者注
[6]此处的“是”不是谓述之“是”，而是等同之“是”，可以替换为“等于”（=）。——译者注
[7]“《韦弗利》的作者”可以被写成这个一般的形式：“那个如此这般的x：x写《韦弗利》”（或者：“那个如此这般的x：x是《韦弗利》的作者”）。——译者注
[8]这句话翻译成日常语言就是：任何四个对象都是如此这般的x、y、z和w：如果x=z+w而且y=z+w，那么x=y。——译者注
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