On Concept and Object

Vierteljahrsschrift fur wissenschaftliche Philosophie 16 (1892), pp. 192-205. 
“论概念和对象”（刊于《科学哲学季刊》16，（1892年）192—205页）
In a series of articles in this Quarterly on intuition and its psychical elaboration, Benno Kerry has several times referred to my Foundations of Arithmetic and other works of mine, sometimes agreeing and sometimes disagreeing with me. I cannot but be pleased at this, and I think the best way I can show my appreciation is to take up the discussion of the points he contests. This seems to me all the more necessary, because his opposition is at least partly based on a  misunderstanding, which might be shared by others, of what I say about concepts; and because, even apart from this special occasion, the matter is important and difficult enough for a more thorough treatment than seemed to me suitable in my Foundations. 
贝诺·克里（Benno Kerry）在这本季刊上发表的一系列有关直觉及其心理形成过程的文章中，多次谈到我的《算术基础》和其他一些著作，他有时同意我的观点，有时反对我的观点。对此我只能感到非常高兴，并且我认为，我最好是对他所反驳的观点进行讨论，以此表示我的感谢。由于他的反对至少在某种程度上是基于曲解了我关于概念的表述，并且其他人也可能有这样的曲解，而且即使不考虑这种特殊的原因，由于对这个问题进行比我在《算术基础》中看来是恰当的那样的探讨更为深入的探讨是十分重要的并且是相当困难的，因此我觉得讨论他所反驳的那些观点就更有必要。
The word 'concept' is used in various ways; its sense is sometimes psychological, sometimes logical, and sometimes perhaps a confused mixture of both. Since this licence exists, it is natural to restrict it by requiring that when once a usage is adopted it shall be maintained. What I decided was to keep strictly to a purely logical use; the question whether this or that use is more appropriate is one that I should like to leave on one side, as of minor importance. Agreement about the mode of expression will easily be reached when once it is recognized that there is something that deserves a special term. 
“概念”一词有不同的使用，有时在心理学意义上使用，有时在逻辑意义上使用，有时也许是二者混淆不清地使用。这种已经存在的任意性自然受到下述要求的限制：一种使用方式一旦被采用，就要保留下来。我现在决定严格地在逻辑意义上使用这个词。这样还是那样使用才恰当，我认为这个问题不重要，而不予考虑。如果人们已经承认某物存在，它应该得到一个特定的名称，那么对表达方式就很容易形成一致的意见。
It seems to me that Kerry's misunderstanding results from his unintentionally confusing his own usage of the word 'concept' with mine. This readily gives rise to contradictions, for which my usage is not to blame. “
我认为，导致克里的曲解是由于他不自觉地混淆了他自己对“概念”这个词的使用方式和我对“概念”这个词的使用方式。由此确实容易产生矛盾，但这种矛盾不应由我的使用方式负责。
Kerry contests what he calls my definition of 'concept'. I would remark, in the first place, that my explanation is not meant as a proper definition. One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance. What is simple cannot be decomposed, and what is logically simple cannot have a proper definition. Now something logically simple is no more given us at the outset than most of the chemical elements are; it is reached only by means of scientific work. If something has been discovered that is simple, or at least must count as simple for the time being, we shall have to coin a term for it, since language will not originally contain an expression that exactly answers. On the  introduction of a name for something logically simple, a definition is not possible; there is nothing for it but to lead the reader or hearer, by means of hints, to understand the word as is intended. 
克里否定他所谓的我对’概念’的定义。这里我首先要说，我的解释不是指真正的定义。正如不能要求化学家分析所有物质一样，人们也不能要求对所有东西进行定义。简单的东西不能被分析。对逻辑上简单的东西不能进行真正的定义。逻辑上简单的东西同大多数化学元素一样，不是从一开始就给出的，只有通过科学研究才能获得。如果现在发现了简单的或至少暂时必须被看做简单的东西，那么就要为它制定一个名称，因为在语言中本来并没有一个严格相应的表达。定义不可能为逻辑中简单的东西引入名字。因此，只有通过提示来指导读者或听者理解这个词表达的意思。
Kerry wants to make out that the distinction between concept and object is not absolute. 'In a previous passage', he says, 'I have myself expressed the opinion that the relation between the content of the concept and the concept-object is, in a certain respect, a peculiar and irreducible one; but this was in no way bound up with the view that the properties of being a concept and of being an object are mutually exclusive. The latter view no more follows from the former than it would follow, if, e.g., the relation of father and son were one that could not be further reduced, that a man could not be at once a father and a son (though of course not, e.g., father of the man whose son he was)’. 
克里希望概念和对象之间的区别不被看做绝对的。他说：“前面我们已经表达了这种看法，概念的内涵和概念的对象之间的关系在某些方面是奇特的，不可化归的；但是这和下面这种观点绝没有关系：是一个概念和是一个对象，这两种性质相互排斥。后一种观点不是从前一种观点得出的，就像从父子之间的关系是不能进一步化归的关系得不出某人不能同时是父又是子（当然他不会是同一个人的父和子）一样。
Let us fasten on this simile. If there were, or had been, beings that were fathers but could not be sons, such beings would obviously be quite different in kind from all men who are sons. Now it is something like this that happens here. A concept (as I understand the word) is predicative1. On the other hand, a name of an object, a proper name, is quite incapable of being used as a grammatical predicate. This admittedly needs elucidation, otherwise it might appear false. Surely one can just as well assert of a thing that it is Alexander the Great, or is the number four, or is the planet Venus, as that it is green or is a mammal? If anybody thinks this, he is not distinguishing the uses of the word ‘is’. In the last two examples it serves as a copula, as a mere verbal sign of predication. (In this sense the German word ist can sometimes be replaced by the mere personal suffix: cf. dies Blatt ist gruen and dies Blatt gruent.) We are here saying that something falls under a concept, and the grammatical predicate means this concept. In the first three examples, on the other hand, 'is' is used like the 'equals' sign in arithmetic, to express an equation2.
让我们从这个比喻出发。如果有或有过一些生物，它们尽管是父，却不能是子，那么这样的生物与是儿子的人显然是完全不同的种类。现在，这里出现相似情况。概念——如同我对这个词的理解——起谓词作用1。相反，一个对象的名称，一个专名绝不能用作语法谓词。不过这需要加以解释，以免出现错误。人们在表达一事物时，难道不能像说这是绿的，或这是一个哺乳动物那样说这是亚历山大大帝，或这是数4，或这是金星吗？如果这样考虑问题，就没有区别“是”字的使用方式。在前两个例子中，“是”用作系词，用作命题的纯形式词。作为这样的词，它有时可以通过纯人称词尾来表现。例如，比较“这片叶子是绿的”（dieses Blatt ist grün）和“这片叶子变绿了”（dieses Blatt grünt）。于是我们说，某物处于一概念之下，在这里语法谓词意谓这个概念。而在后三个例子中，“是”的应用如同算术中的等号，表达一个等式2。
In the sentence 'The morning star is Venus', we have two proper names, 'morning star' and 'Venus', for the same object. In the sentence 'the morning star is a planet' we have a proper name, 'the morning star', and a concept-word, 'planet'. So far as language goes, no more has happened than that 'Venus' has been replaced by 'a planet'; but really the relation has become wholly different. An equation is reversible; an object's falling under a concept is an irreversible relation. In the sentence 'the morning star is Venus', 'is' is obviously not the mere copula; its content is an essential part of the predicate, so that the word 'Venus' does not constitute the whole of the predicate3. One might say instead: 'the morning star is no other than Venus'; what was previously implicit in the single word 'is' is here set forth in four separate words, and in 'is no other than' the word 'is' now really is the mere copula. What is predicated here is thus not Venus but no other than Venus. These words stand for a concept; admittedly only one object falls under this, but such a concept must still always be distinguished from the object4. 
在“晨星是金星”这个句子中，我们有两个表达同一对象的专名“晨星”和“金星”；在“晨星是一颗行星”这个句子中，我们有一个专名“晨星”和一个概念词“行星”。尽管这在语言上不过是用“行星”替代了“金星”，但是事实上，关系却变得完全不同。一个等式是可逆关系，而一个对象处于一个概念之下是不可逆关系。“晨星是金星”这个句子中的“是”显然不是纯粹的系词，从内涵上说它是谓词的一个本质部分，因此“金星”这个词不包括全部谓词3。对此，人们可以这样说，“晨星不过就是金星”。这里，我们把前面简单的“是”中所表达的意思用四个分开的字表达。“不过就是”中的“是”实际上确实仅仅是系词，因此这里表达的不是金星，而是不过就是金星。这些字意谓一个概念，在这个概念下当然只有一个唯一的对象。但是这样一个概念必须时刻与对象区别开4。
We have here a word 'Venus' that can never be a proper predicate, although it can form part of a predicate. The meaning 5of this word is thus something that can never occur as a concept, but only as an object. Kerry, too, would probably not wish to dispute that there is something of this kind. But this involves admitting a distinction, which it is very important to recognize, between what can occur only as an object, and everything else. And this distinction would not be effaced even if it were true, as Kerry thinks it is, that there are concepts that can also be objects. 
 我们这里有一个词“金星”，它实际上绝不能是真正的谓词，尽管它可以构成谓词的一部分。因此这个词的意谓5绝不能作为概念出现，而只能作为对象出现。大概克里也不愿否认有这种东西。但这样就承认了只能作为对象出现的东西和所有其他东西之间的一种区别。认识到这一点非常重要。即使克里所考虑的是真的，即存在着也可以是对象的概念，这种区别也不会消失。
•	Note1: It is, in fact, the meaning of a grammatical predicate.
•	Note2: I use the word 'equal' and the symbol ' = ' in the sense 'the same as', 'no other than', 'identical with'. Cf. E. Schroeder, Vorlesungen ueber die Algebra der Logik (Leipzig, 1890), Vol. 1, §1. Schroeder must however be criticized for not distinguishing two  fundamentally different relations; the relation of an object to a concept it falls under, and the subordination of one concept to another. His remarks on the Vollwurzel are likewise open to objection. Schroeder's symbol does not simply take the place of the copula.
•	Note3: Cf. my Grundlagen der Arithmetik [the Foundations of Arithmetic], §66, footnote.
•	Note4: Cf. Foundations, §51. 
•	Note5: Cf. my paper, ‘Ueber Sinn und Bedeutung' ['On Sense and Meaning'], shortly to appear in the Zeitschrift fur Philosophie und philosophische Kritik [this volume pp. 157— 77]. 
（1） 这实际上是语法谓词的意谓。
（2） 我在“与……相同”，“与……没有不同”，“与……同一”的意义上使用“相等”一词和“＝”这个符号。参见E.施罗德的《逻辑代数讲义》（莱比锡，1890年）第一卷§1，但是该书中有一点应该受到批评，它没有区别一个对象处于一个概念之下和一个概念从属于另一个概念这两种情况的根本不同的关系。他对Vollwurzel的意见也是令人怀疑的。他用的符号
 根本不能代替系词。
（3） 参见我的《算术基础》§66，注释。
（4） 参见我的《算术基础》§51。” “
（5）参见我的论文《论涵义和意谓》，即将在《哲学和哲学批判杂志》上发表。
There are, indeed, cases that seem to support his view. I myself have indicated (in Foundations §53, ad fin) that a concept may fall under a higher concept - which, however, must not be confused with one concept's being subordinate to another. Kerry does not appeal to this; instead, he gives the following example: 'the concept "horse" is a concept easily attained', and thinks that the concept 'horse' is an object, in fact one of the objects that fall under the concept 'concept easily attained'. Quite so; the three words 'the concept "horse"' do designate an object, but on that very account they do not designate a concept, as I am using the word. This is in full accord with the criterion I gave - that the singular definite article always indicates an object, whereas the indefinite article accompanies a concept-word6. 
现在确实有似乎支持这个观点的情况。我本人（在《算术基础》§53结尾之处）也已指出，一个概念可以在一个更高的概念之下，然而这不应与把一个概念归属于另一个概念混淆起来。克里没有依据这一点，而是给出下面的例子：“‘马’这个概念是一个易于获得的概念”，并认为“马”这个概念是对象，而且是处于“易于获得的概念”这个概念之下的对象之一。完全正确！“‘马’这个概念”这五个字表示一个对象，但是正因为这样，它们不表示我所使用的意义下的概念。这与我所给出的特征完全一致，根据这种特征，单数定冠词总指示一个对象，而不定冠词伴随一个概念词6。
Kerry holds that no logical rules can be based on linguistic  distinctions（日常语言）; but my own way of doing this is something that nobody can avoid who lays down such rules at all; for we cannot come to an understanding with one another apart from language, and so in the end we must always rely on other people's understanding words, inflexions, and sentence-construction in essentially the same way as ourselves. 
尽管克里认为，人们不能基于语言的区别来建立逻辑规则，但是正像我做的那样，任何制定逻辑规则的人实际上都不能避免根据语言的区别来建立规则。因为没有语言，我们就不能相互理解。并且因此我们最终也依赖于这样一种信念：别人对这些词、形式和句子构造的理解和我们自己的理解基本一样。
As I said before, I was not trying to give a definition, but only hints; and to this end I appealed to the general feeling for the German language. It is here very much to my advantage that there is such good accord between the linguistic distinction and the real one. As regards the indefinite article there are probably no exceptions to our rule at all for us to remark, apart from obsolete formulas like  Ein edler Rath ['Councillor']. The matter is not so simple for the definite article, especially in the plural; but then my criterion does not relate to this case. In the singular, so far as I can see, the matter is doubtful only when a singular takes the place of a plural, as in the sentence ‘the Turk besieged Vienna ‘, ‘the horse is a four-legged animal’. These cases are so easily recognizable as special ones that the value of our rule is hardly impaired by their occurrence. It is clear that in the first sentence ‘the Turk’ is the proper name of a people. The second sentence is probably best regarded as expressing a universal judgement（全称判断）, say 'all horses are four-legged animals' or 'all properly constituted horses are four-legged animals'; these will be discussed later7. Kerry calls my criterion unsuitable; for surely, he says, in the sentence 'the concept I am now talking about is an individual concept,' what the name composed of the first eight words means is a concept; but he is not taking the word 'concept' in my sense, and it is not in what I have laid down that the contradiction lies. But nobody can require that my mode of expression shall agree with Kerry's. 
如上所说，我不想定义，而只是提示一下，因为我在这里是根据德语的一般语感。然而，语言上的区别与事实上的区别相当一致，这对我极为有用。在不定冠词的情况下，我们的规则大概不会出现例外的情况，除非那些旧式用语，例如“ein edler Rat”（一个参议员）。而在定冠词的情况下，尤其是复数时，问题则不是这样简单。但是我给出的特征与这种情况无关。据我看，在单称情况下，只有在它代替了复数时，比如在“土耳其人包围维也纳”（“der Türke belagerte Wien”）、“马是四足动物”（“das Pferd ist ein vier beinige Tier”）这样的句子中，才是有问题的。这些情况很容易被看做特殊情况，因而它们的出现不损害我们的规则的价值。十分清楚，在第一个句子中，“土耳其人”是一个民族的专名。也许最好把第二个句子理解为表达一个全称判断，比如“所有马都是四足动物”或者“所有体魄强健的马都是四足动物”。后面还要谈到这一点7。当克里说我给出的特征不合适的时候，即当他说，在“我正说的这个概念是一个个体概念”这个句子中前面八个字所组成的名字肯定意谓一个概念时，他不是在我的意义上理解“概念”一词，而且矛盾不是在我的规定之中。然而谁也不能要求我的表达方式必须与克里的相一致。
•	Note 6: Foundations, §51; §66, footnote; §68, footnote on p. 80. 
•	Note 7: Nowadays people seem inclined to exaggerate the scope of the statement that different linguistic expressions are never completely equivalent, that a word can never be exactly translated into another language. One might perhaps go even further, and say that the same word is never taken in quite the same way even by men who share a language. I will not enquire as to the measure of truth in these statements; I would only emphasize that nevertheless different expressions quite often have something in common, which I call the sense, or, in the special case of sentences, the thought. In other words, we must not fail to recognize that the same sense, the same thought, may be variously expressed; thus the difference does not here concern the sense, but only the apprehension, shading, or colouring of the thought, and is irrelevant for logic. It is possible for one sentence to give no more and no less information than another; and, for all the multiplicity of languages, mankind has a common stock of thoughts. If all transformation of the expression were forbidden on the plea that this would alter the content as well, logic would simply be crippled; for the task of logic can hardly be performed without trying to recognize the thought in its manifold guises. Moreover, all definitions would then have to be rejected as false. 
（6） 《算术基础》§51，§66注释，§68注释，80页。
（7） 现在人们似乎很愿意夸大以下说法的范围，认为不同的语言表达绝不是完全等价的，一个词在另一种语言中也绝不会确切地复述出来。也许人们还可以走得更远说，一种语言的同一个词也从未被人完全同等地理解。我不研究这些句子有多少合理性，而只是强调，尽管如此，在各种不同的表达中常常还是有一些共同的东西，我称这些东西为涵义，尤其是在句子中我称它们为思想；换言之，应该承认，人们可以以不同的方式表达同一种涵义，同一个思想，因此这里的差异不是涵义的差异，而只是对涵义的理解、说明、修饰的差异，是逻辑不予考虑的。可能一个句子给出的信息比另一个句子既不多也不少；尽管语言多种多样，人类却有共同的思想财富。如果人们认为表达的改变会使内容也发生变化，因而想要禁止表达的改变，那么这恰恰使逻辑陷于瘫痪；因为如果人们不努力重新认出具有多种多样表达的思想，逻辑的任务大概是无法完成的。即使各种定义也会被看做假的而予以抛弃。
It must indeed by recognized that here we are confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept8, whereas, e.g., the city of Berlin is a city, and the volcano Vesuvius is a volcano. Language is here in a predicament that justifies the departure from custom. The peculiarity of our case is indicated by Kerry himself, by means of the quotation-marks around 'horse'; I use italics to the same end. There was no reason to mark out the words 'Berlin' and 'Vesuvius' in a similar way. In logical discussions one quite often needs to say something about a concept, and to express this in the form usual for such predications - viz. to make what is said about the concept into the content of the grammatical predicate. Consequently, one would expect that what is meant by the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object9, or, more precisely, an object must go proxy for it. We designate this object by prefixing the words 'the concept'; e.g.: 
人们不会看不出来，如果我们声称马这个概念不是一个概念8，而柏林这个城市是一个城市，维苏威火山是一座火山，那么这里确实就有一种不可避免的语言困难。这里语言处于一种困境，它表明偏离习惯是正当的。我们的情况是特殊的，克里本人通过在马这个词前后加上引号（“马”）指明了这一点。我在这个词下加重点也是为的同一目的。人们没有理由以类似的方式标出“柏林”和“维苏威”这些词。在进行逻辑研究时，常常要求表达一个概念的某种情况并且要求以这种表达的通常形式来表达它。就是说，表达成为语法谓词的内涵。由此人们要期待着概念成为语法主词的意谓；但是这个概念由于具有谓词性质而不能直接这样表现，必须先变成一个对象，或者更严格地说，它必须由一个对象来体现
9 。我们借助在后面加上的“这个概念”这个词来表示这个对象。例如：
'The concept man is not empty'.
“人这个概念不是空的”。
Here the first three words are to be regarded as a proper name10, which can no more be used predicatively than 'Berlin' or 'Vesuvius.' When we say 'Jesus falls under the concept man,'' then, setting aside the copula, the predicate is: 
这里，前面五个字应理解为专名10，它就像“柏林”或“维苏威”一样不能用作谓词。如果我们说：“耶稣处于人这个概念下”，那么（不考虑系词）谓词就是
'someone falling under the concept man'
“处于人这个概念下”，
and this means the same as:
'a man'.
But the phrase 
'the concept man'
 is only part of this predicate. 
这与
“一个人”
意谓相同的东西，但是，
“人这个概念”
这种词组只是这个谓词的一部分。
•	Note 8: A similar thing happens when we say as regards the sentence ' this rose is red': The grammatical predicate 'is red' belongs to the subject 'this rose'. Here the words, 'The  grammatical predicate "is red"' are not a grammatical predicate but a subject. By the very act of explicitly calling it a predicate, we deprive it of this property.
•	Note 9: Cf. my Foundations, p. x. 
•	Note 10: I call anything a proper name if it is a sign for an object. 
（8） 如果我们以“这朵玫瑰是红色的”这个句子说：“是红色的”这个语法谓词属于“这朵玫瑰”这个主词，就出现类似情况。在这里，“‘是红色的’这个语法谓词”这个短语不是语法谓词，而是主词。恰恰由于我们明确称它为谓词，所以我们取消了它的这种性质。
（9） 参见我的《算术基础》。
（10） 我称每个代表一个对象的符号为专名。
Somebody might urge, as against the predicative nature of concepts, that nevertheless we speak of a subject-concept. But even in such cases, e.g. in the sentence 
人们可能会反对概念的谓词性质，认为可以谈论主词概念。但即使在这样的情况下，例如在
'all mammals have red blood'
“所有哺乳动物都有红血”
we cannot fail to recognize the predicative nature11 of the concept; for we could say instead: 
这个句子中，不会认不出概念的谓词性质11，因为对此也可以说，
'whatever is a mammal has red blood'
“凡是哺乳动物的东西，都有红血”
or:
或者，
'if anything is a mammal, then it has red blood’.
“如果某物是哺乳动物，那么它有红血”。
•	Note 11: 'What I call here the predicative nature of concepts is just a special case of the need of supplementation, the 'unsaturatedness', that I gave as the essential feature of a function in my work Funktion und Begriff (Jena, 1891). It was there scarcely possible to avoid the expression 'the function f (x)', although there too the difficulty arose that what this expression means is not a function. 
（11） 我这里称为概念的谓词性质的东西只是需要补充性和不饱和性的一种特殊情况，我在论文《函数和概念》（1891年）中说明这种性质对于函数是至关重要的。在那里确实不能避免“f（x）这个函数”这个表达，尽管那里也出现困难，即这个短语的意谓不是函数。
When I wrote my Foundations of Arithmetic, I had not yet made the distinction between sense and meaning12; and so, under the expression 'a content of possible judgement', I was combining what I now designate by the distinctive words 'thought' and 'truth-value'.  Consequently, I no longer entirely approve of the explanation I then gave (Foundations, p. 77), as regards its wording; my view is, however, still essentially the same. We may say in brief, taking 'subject' and  'predicate' in the linguistic sense: A concept is what is meant by a predicate; an object is something that can never be the total meaning of a predicate, but can be what a subject means. It must here be remarked that the words ‘all’, ‘any’, ‘no’, ‘some’, are prefixed to concept-words. In universal and particular affirmative and negative sentences（全称特称肯定否定）, we are expressing relations between concepts; we use these words to indicate the special kind of relation. They are thus, logically speaking, not to be more closely associated with the concept-words that follow them, but are to be related to the sentence as a whole. It is easy to see this in the case of negation. If in the sentence 
在我写《算术基础》的时候，我还没有区别涵义和意谓12 ，这样，“可判断的内容”这一表达式也概括了我现在以“思想”和“真值”所区别表达的东西。因此，就文字表述而言，我不再完全同意那里77页所做出的解释，尽管我基本上仍持相同观点。我们可以简要地说，我们在语言的意义上理解“谓词”和“主词”：概念是谓词的意谓，对象是这样一种东西，它绝不能是谓词的全部意谓，却可能是主词的意谓。这里应该注意，“所有”，“每个”，“没有”，“有些”，这些词位于概念词之间。我们以全称和特称的肯定和否定的句子表达概念之间的关系，并且通过这些词指示这种关系的特殊的种类，因此这些词在逻辑上不应该与其后联接的概念词紧密结合，而应该与整个句子联系在一起。在否定时，很容易看出这一点。
'all mammals are land-dwellers’
“所有哺乳动物都是陆地居住者”，
 the phrase 'all mammals' expressed the logical subject of the predicate are land-dwellers, then in order to negate the whole sentence we should have to negate the predicate: 'are not land-dwellers'. Instead, we must put the 'not' in front of 'all'; from which it follows that 'all' logically belongs with the predicate. On the other hand, we do negate the sentence 'The concept mammal is subordinate to the concept land-dweller' by negating the predicate: 'is not subordinate to the concept land-dweller'. 
如果这个句子中的“所有哺乳动物”这个词组表达了都是陆地居住者这个谓词的逻辑主语，那么为了否定这整个句子，就必须否定谓词：“都不是陆地居住者”。如果不这样，而把“不”放在“所有”前面，那么“所有”就逻辑地属于谓词。相反，我们否定了谓词“不下属于陆地居住者这个概念”，也就否定了“哺乳动物这个概念下属于陆地居住者这个概念”这个句子。”
•	Note 12:  my essay, 'On Sense and Meaning'.
（12） 参见我的论文《论涵义和意谓》，刊于《哲学和哲学批判杂志》。
If we keep it in mind that in my way of speaking expressions like ‘the concept F’ designate not concepts but objects, most of Kerry’s  objections already collapse. If he thinks (cf. p. 281) that I have identified concept and extension of concept, he is mistaken; I merely expressed my view that in the expression ‘the number that applies to the concept F is the extension of the concept like-numbered to the concept F’ the words ‘extension of the concept’ could be replaced by ‘concept’. Notice carefully that here the word ‘concept’ is combined with the definite article. Besides, this was only an incidental remark; I did not base anything upon it. 
如果我们确定，在我的谈论方式中，像“F这个概念”这样的表达式不表示概念，而表示对象，那么克里的大部分反驳就站不住脚了。如果他认为（281页），我把概念等同于概念的外延，他就错了。我只是表达了我的意见：在“适合于F这个概念的数是与F这个概念等数的 概念的外延”这个表达，也可以用“概念”替代“概念的外延”这个用语。这里大概可以看到，这个用语与定冠词结合在一起。此外，这只是附带的说明，我并没有在它的基础上建立任何东西。
Thus Kerry does not succeed in filling the gap between concept and object. Someone might attempt, however, to make use of my own statements in this sense. I have said that to assign a number involves saying something about the concept13; I speak of properties ascribed to a concept, and I allow that a concept may fall under a higher one14. I have called existence a property of a concept. How I mean this to be taken is best made clear by an example. In the sentence 'there is at least one square root of 4', we are saying something, not about (say) the definite number 2, nor about -2, but about a concept, square root of 4; viz. that it is not empty. But if I express the same thought thus: 'The concept square root of 4 is realized', then the first six words form the proper name of an object, and it is about this object that something is being said. But notice carefully that what is being said here is not the same thing as was being said about the concept. This will be surprising only to somebody who fails to see that a thought can be split up in many ways, so that now one thing, now another, appears as subject or predicate. The thought itself does not yet determine what is to be regarded as the subject. If we say 'the subject of this judgement', we do not designate anything definite unless at the same time we indicate a definite kind of analysis; as a rule, we do this in connection with a definite wording. But we must never forget that different sentences may express the same thought. For example, the thought we are considering could also be taken as saying something about the number 4: 因此，克里没能填平概念和对象之间的鸿沟，而在这种意义上人们却可以利用我自己的表达。我说过13，数的给出包含着对概念的表述。我谈到关于一个概念所表达的性质并且让一个概念处于一个更高的概念之下14 。我称存在为一个概念的性质。用一个例子可以最清楚地说明我这是什么意思。在“至少有一个4的平方根”这个句子中，既不是对一个确切的数2，也不是对-2有所表达，而是对一个概念，即4的平方根有所表达，说它不是空的。但是如果我以下述方式表达相同的思想，“4的平方根这个概念被满足”，那么前九个字就构成一个对象的专名，并且表达了这个对象的某些东西。但是，人们大概会看到，这里表达的与关于概念表达的不是相同的东西。只有对那些认不清一个思想可以有各种各样的分析，因而有时此为主词彼为谓词，有时彼为主词此为谓词的人来说，这才是奇怪的。思想本身还确定不了什么应理解为主词。如果人们说，“这个判断的主词”，那么，只有当同时指出某种确切分析时，才表示确定的东西。人们这样做时，通常联系到一定的具体用词。但是不能忘记，不同的句子可以表达相同的思想。因此在我们的思想中也可以找到一个关于4这个数的表达：
'The number 4 has the property that there is something of which it is the square'.
“4这个数有这样的性质，即存在某物，4是它的平方”。
•	Note 13: Foundations, § 46. 
•	Note 14: Foundations, § 53.
   （13）《算术基础》§46。
   （14）《算术基础》§53。
Language has means of presenting now one, now another, part of the thought as the subject; one of the most familiar is the distinction of active and passive forms. It is thus not impossible that one way of analysing a given thought should make it appear as a singular judgement; another, as a particular judgement; and a third, as a universal judgement. It need not then surprise us that the same sentence may be conceived as saying something about a concept and also as saying something about an object; only we must observe that what is being said is different. In the sentence 'there is at least one square root of 4' it is impossible to replace the words 'square root of 4' by 'the concept square root of 4'; i.e. what is suitably said of the concept does not suit the object. Although our sentence does not present the concept as a subject, it says something about it; it can be regarded as expressing that a concept falls under a higher one15. But this does not in any way efface the distinction between object and concept. 
We see to begin with that in the sentence 'there is at least one square root of 4' the predicative nature of the concept is not belied; we could say 'there is something that has the property of giving the result 4 when multiplied by itself. Hence what is here said concerning a concept can never be said concerning an object; for a proper name can never be a predicative expression, though it can be part of one. I do not want to say it is false to say concerning an object what is said here concerning a concept; I want to say it is impossible, senseless, to do so. The sentence 'there is Julius Caesar' is neither true nor false but senseless; the sentence 'there is a man whose name is Julius Caesar' has a sense, but here again we have a concept, as the indefinite article shows. We get the same thing in the sentence 'there is only one Vienna'. We must not let ourselves be deceived because language often uses the same word now as a proper name, now as a concept-word; in our example, the numeral indicates that we have the latter; 'Vienna' is here a concept-word, like 'metropolis'. Using it in this sense, we may say: 'Trieste is no Vienna'. If, on the other hand, we substitute 'Julius Caesar' for the proper name formed by the first six words of the sentence 'the concept square root of 4 is realized', we get a sentence that has a sense but is false; for that so-and-so is realized (as the word is being taken here) is something that can be truly said only concerning a quite special kind of objects, viz. such as can be designated by proper names of the form 'the concept F’. Thus the words 'the concept square root of 4' have an essentially different behaviour, as regards possible substitutions, from the words 'square root of 4' in our original sentence; i.e. the meaning of the two phrases is essentially different. 
语词具有一些手段，可以有时使思想的这一部分、有时使思想的那一部分作为主词出现。人们最熟悉的一种情况是主动式和被动式的区别。因此，同一个思想在一种分析中表现为单称的，在另一种分析中表现为特称的，在第三种分析中又表现为全称的，这不是不可能的。所以，同一个句子可以理解为对一个概念的表达，也可以理解为对一个对象的表达，这不应令人感到奇怪，只不过必须看到，这些表达是不同的。在“至少有一个4的平方根”这个句子中，不可能用“4的平方根这个概念”替代“一个4的平方根”这个用语，就是说，适合于概念的表达不适合于对象。尽管我们的句子没有使这个概念作主词出现，却表达了它的某些东西。人们可以这样理解，这里表达了一个概念处于一个更高的概念之下15 。但是对象和概念的区别不因此而消失。首先我们看到，“至少有一个4的平方根”这个句子的概念并未掩盖自己的谓词性质，人们可以说，“存在某物，它具有与自身相乘得4的性质”。因此，这里关于概念所表述的东西绝不能是关于对象的表述。因为一个专名绝不能是一个谓词表达式，尽管它可以是这样一个表达式的部分。我不是要说，这里就一个概念所表达的东西是关于一个对象的表达，这种说法是假的；而是要说，这是不可能的，这是无意义的。“有朱利叶·凯撒”这个句子既不真，也不假，而是无意义的，尽管“有一个名叫朱利叶·凯撒的人”这个句子有涵义。但是这里我们又有一个概念，正如从这个不定冠词可以看出的那样。“只有一个维也纳”这个句子的情况也是同样。人们一定不要因为语言中相同的词常常有时用作专名、有时用作概念词而受欺骗。例中的数词说明存在着后一种情况。在这个句子中，“维也纳”是概念词，就像“帝都”一样。在这种意义上可以说，“的里雅斯特不是维也纳”。而如果我们把“4的平方根这个概念被满足”这个句子中前九个字所组成的专名代之以“朱利叶·凯撒”，我们就得到一个句子，它有涵义，但是假的，因为这里所理解的被满足一词在真的情况下只能表达某种完全特殊的对象，即以具有“F这个概念”这一形式的专名可以表达的对象。而“4的平方根这个概念”这个用语就其可替代性来说，与我们原初的句子中“一个4的平方根”这个用语根本不同，就是说，这两个词组的意谓根本不同。
•	Note 15: In my Foundations I called such a concept a second-order concept; in Function and Concept I called it a second-level concept, as I shall do here. 
（15） 我在《算术基础》中称这样一个概念为二阶概念，在《函数和概念》中称它为第二层概念，这里我也要这样做。
What has been shown here in one example holds good generally; the behaviour of the concept is essentially predicative, even where something is being said about it; consequently it can be replaced there only by another concept, never by an object. Thus what is being said concerning a concept does not suit an object. Second-level concepts, which concepts fall under, are essentially different from first-level concepts, which objects fall under. The relation of an object to a first-level concept that it falls under is different from the (admittedly similar) relation of a first-level to a second-level concept. (To do justice at once to the distinction and to the similarity, we might perhaps say: An object falls under a first-level concept; a concept falls within a second-level concept.) The distinction of concept and object thus still holds, with all its sharpness. 
这里用一个例子所表达的乃是普遍有效的：概念本质上是作谓词，即使在关于它做出一些表达的地方也是这样。因此它在那里也只能用一个概念代替，而绝不能用一个对象代替。所以，关于一个概念的表达绝不适合于一个对象。有概念处于其下的第二层概念与有对象处于其下的第一层概念有本质的不同。对象和它所处于其下的第一层概念之间的关系与第一层概念和第二层概念之间的关系虽然类似，却不相同。为了能够同时进行这种类似性的区别，我们大概可以说，一个对象处于一个第一层概念之下 ，一个概念处于一个第二层概念之中 。因而概念和对象的区别泾渭分明。
With this there hangs together what I have said (Foundations §53) about my usage of the words 'property' and 'mark'; Kerry's discussion gives me occasion to revert once more to this. The words serve to signify relations, in sentences like Ф is a property of Г and ' Ф is a mark of Ω'. In my way of speaking, a thing can be at once a property and a mark, but not of the same thing. I call the concepts under which an object falls its properties; thus 
我在《算术基础》中（§53）关于我对“性质”和“标志”这些词的使用方式所做的说明也与概念和对象的区别联系在一起。克里的论述促使我再一次回到这个问题上来。这些词在“Φ是Γ的性质”和“Φ是Ω的标志”这样的句子中表示关系。根据我的陈述方式，某物可以同时是性质和标志，但不能是同一事物的性质和标志。我称有一个对象处于其下的概念为这个对象的性质。因此，
'to be Ф is a property of Г'
‘是Φ’是Γ的一个性质”
is just another way of saying:
不过是
'Г falls under the concept of a Ф'.
“Γ处于Φ这个概念之下” 的另一种说法。
If the object Г has the properties Ф, X, and Ψ, I may combine them into Ω; so that it is the same thing if I say that Г has the property Ω, or, that Г has the properties Ф, X, and Ψ. I then call Ф, X, and Ψ marks of the concept Ω, and, at the same time, properties of Г. It is clear that the relations of Ф to Г and to Ω are quite different, and that consequently different terms are required. Г falls under the concept Ф; but Ω, which is itself a concept, cannot fall under the first-level concept Ф; only to a second-level concept could it stand in a similar relation. Ω is, on the other hand, subordinate to Ф. 
如果对象Γ有性质Φ、X和Ψ，我就可以把这些性质概括为Ω，这样无论我说Γ有性质Ω，还是说Γ有性质Φ、X和Ψ，都是一样的。在这种情况下，我称Φ、X和Ψ为概念Ω的标志，同时又是Γ的性质。显然，Φ与Γ的关系和Φ与Ω的关系完全不同，因此要求不同的命名。Γ处于概念Φ之下，但本身是一个概念的Ω却不能处于第一层概念Φ之下，而只能与一个第二层概念有相似的关系。相反，Ω下属于Φ。
Let us consider an example. Instead of saying: 
为此让我们来看一个例子，我们不说
'2 is a positive number' and
'2 is a whole number' and
'2 is less than 10'
“2是一个正数”并且
“2是一个整数”并且
“2是小于10的”，
we may also say 
我们可以说
'2 is a positive whole number less than 10'.
2是一个小于10的正整数”。
Here 
这里，
to be a positive number,
to be a whole number,
to be less than 10,
是一个正数，
是一个整数，
是小于10的，
appear as properties of the object 2, and also as marks of the concept 
表现为2这个对象的性质，但同时又作为
positive whole number less than 10. 
小于10的正整数这个概念的标志。
 This is neither positive, nor a whole number, nor less than 10. It is indeed subordinate to the concept whole number, but does not fall under it. 
这个概念既不是一个正数，也不是一个整数，也不是小于10的。尽管它下属于整数
 这个概念，却不处于它之下。
Let us now compare with this what Kerry says in his second article (p. 224). 'By the number 4 we understand the result of additively combining 3 and 1. The concept-object here occurring is the numerical individual 4; a quite definite number in the natural number-series. This object obviously bears just the marks that are named in its concept, and no others besides - provided we refrain, as we surely must, from counting as propria of the object its infinitely numerous relations to all other individual numbers; "the" number 4 is likewise the result of additively combining 3 and 1'. 
现在我们比较一下克里在第二篇论文（424页）所说的：“人们把4这个数理解为3和1相加的那个结果。以此给出的这个概念的概念对象是4这个个体的数，即自然数系列的一个完全确定的数。这个对象本身显然恰恰带有在它的概念中提到的标志，并且——如果像人们大概一定会做的那样，不把它与所有其他个体数的无穷多的关系看做是它所固有的话，——再没有其他标志：‘这个’4同样是3和1相加的那个结果。
We see at once that my distinction between property and mark is here quite slurred over. Kerry distinguishes here between the number 4 and 'the' number 4. I must confess that this distinction is  incomprehensible to me. The number 4 is to be a concept; 'the' number 4 is to be a concept-object, and none other than the numerical individual 4. It needs no proof that what we have here is not my distinction between concept and object. It almost looks as though what was floating (though very obscurely) before Kerry's mind were my distinction between the sense and the meaning of the words 'the number 4'16. But it is only of that which the words mean that we can say: this is the result of additively combining 3 and 1. 
人们马上看出，我所做的性质和标志之间的区别在这里完全消失了。克里在这里区别4这个数和4“这个”数。我必须承认，这个区别对我来说是不可理解的。4这个数应该是概念；4“这个”数应该是概念对象并且就是4这个个体的数。这里说的不是我对概念和对象的区别，这一点不必论证。看上去好像克里的眼前——尽管十分含混地——浮现了我对“4这个数”这个用语的涵义和意谓所做的区别16。但是只有对意谓才能说，它是3和1相加的那个结果。
•	Note 16: Cf. my essay, 'On Sense and Meaning'.
    （16）参见前面提到的论文《论涵义和意谓》。
Again, how are we to take the word 'is' in the sentences 'the number 4 is the result of additively combining 3 and 1' and '"the" number 4 is the result of additively combining 3 and 1’? Is it a mere copula, or does it help to express a logical equation? In the first case, 'the' would have to be left out before 'result', and the sentences would go like this:
 那么应该如何理解“4这个数是3和1相加的那个结果”和“4‘这个’数是3和1相加的那个结果”这些句子中的“是”呢？它是一个纯系词，还是帮助表达一个逻辑等式呢？在前一种情况下，“结果”前面必须没有“那个”，句子应该这样说：
'The number 4 is a result of additively combining 3 and 1’;
'"The" number 4 is a result of additively combining 3 and 1'.
“4这个数是3和1相加的结果”，
“4‘这个’数是3和1相加的结果”。
In that case, the objects that Kerry designates by 
这样我们就有下面的情况；即克里以
'the number 4' and '"the" number 4'
“4这个数”和“4‘这个’数”
would both fall under the concept 
所表示的对象处于
result of additively combining 3 and 1.
“ 3和1相加的结果 ”这个概念之下。
And then the only question would be what difference there was between these objects. (I am here using the words 'object' and 'concept' in my accustomed way.) I should express as follows what Kerry is apparently trying to say:
因此唯一的问题就会是：这些对象怎样区别？这里我用我常用的方式使用“对象”和“概念”这些词。对克里似乎想表达的东西，我将会如下表达：
'The number 4 has those properties, and those alone, which are marks of the
concept: result of additively combining 3 and 1.
“4这个数有并且只有以‘3和1相加的结果 ’这个概念作标志的东西作性质。”
I should then express as follows the sense of the first of our two sentences: 
因此我对我们那两个句子中第一句的涵义要表述如下：
'To be a number 4 is the same as being a result of additive combination of 3 and 1'.
“‘是一个数4’与‘是3和1相加的结果’是相同的”；
In that case, what I conjectured just now to have been Kerry's intention could also be put thus: 在这种情况下，我刚才推测的克里的看法则可如下表述：
'The number 4 has those properties, and those alone, which are marks of
the concept a number 4'
“4这个数有并且只有以数417这个概念作标志的东西作性质”。
（17） 德文“Zahl 4”。字面翻译为“4数”，但不符合中文习惯。同样，“4这个
数”的德文为“die Zahl 4”。定冠词“die”在词头，而中文只能以“这个”表
示，并且位置也有区别。——译注
(We need not here decide whether this is true.) The inverted commas around the definite article in the words '"the" number 4' could in that case be omitted. 
这里不需要确定这是否真。我们可以把“4‘这个’数”这个用语中的定冠词去掉。
But in these attempted interpretations we have assumed that in at least one of the two sentences the definite articles in front of 'result' and 'number 4' were inserted only by an oversight. If we take the words as they stand, we can only regard them as having the sense of a logical equation, like: 
但是，在试图进行这样解释的时候，我们已经假定，在这两个句子中，至少有一个句子中的“结果”和“数4”前面的定冠词是仅仅由于疏忽而加上的。如果我们按照这些用语的本身看，则只能把它们的涵义理解为逻辑等式，譬如：
'The number 4 is none other than the result of additively combining 3 and 1’.
“4这个数不过就是3和1相加的那个结果”。
The definite article in front of 'result' is here logically justified only if it is known (i) that there is such a result; (ii) that there is not more than one. In that case, the phrase designates an object, and is to be regarded as a proper name. If both of our sentences were to be regarded as logical equations, then, since their right sides are identical, it would follow from them that the number 4 is 'the' number 4, or, if you prefer, that the number 4 is no other than 'the' number 4; and so Kerry's distinction would have been proved untenable. However, it is not my present task to point out contradictions in his exposition; his way of taking the words 'object' and 'concept' is not properly my concern here. I am only trying to set my own usage of these words in a clearer light, and incidentally show that in any case it differs from his, whether that is consistent or not.
这里，只有承认，1）有这样一个结果，2）至多有一个结果，才能证明“结果”前面的定冠词是逻辑上正确的。在这种情况下，这种词组表示一个对象，应该被理解为专名。如果我们的两个句子都应该理解为逻辑等式，那么由此就会得出，这里右边是等同的，4这个数是4“这个”数，或者，如果愿意，4这个数不过就是4“这个”数，因此证明克里做出的区别是无效的。然而，指出他的论述矛盾，并不是我现在的任务。他对“对象”和“概念”这些词的理解实际上与我毫不相干。我只想以此更清楚地阐明我自己对这些词的使用方式，并且同时表明，我的使用方式与克里的使用方式肯定是不同的，无论它们在这里一致还是不一致。
I do not at all dispute Kerry's right to use the words 'concept' and 'object' in his own way, if only he would respect my equal right, and admit that with my use of terms I have got hold of a distinction of the highest importance. I admit that there is a quite peculiar obstacle in the way of an understanding with the reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thought; I mention an object, when what I intend is a concept. I fully realize that in such cases I was relying upon a reader who would be ready to meet me half-way - who does not begrudge a pinch of salt. 
我绝不否认克里有权以他的方式使用“对象”和“概念”这些词。但是我要捍卫我的同等权利并且声明，我以我的用词表达了一个最重要的区别。当然，对于读者的理解来说存在着一种特殊的障碍，就是说，由于某种语言的必然性，我的表达若是完全从字面理解，有时没有能够准确表达思想；因为当说到一个对象时，意谓的却是一个概念。我自己完全清楚，在这样的情况下，就要有赖于读者愿意接受我的观点，而且不遗余力。
Somebody may think that this is an artificially created difficulty; that there is no need at all to take account of such an unmanageable thing as what I call a concept; that one might, like Kerry, regard an object's falling under a concept as a relation, in which the same thing could occur now as object, now as concept. The words 'object' and 'concept' would then serve only to indicate the different positions in the relation. This may be done; but anybody who thinks the difficulty is avoided this way is very much mistaken; it is only shifted. For not all the parts of a thought can be complete; at least one must be 'unsaturated', or predicative; otherwise they would not hold together. For example, the sense of the phrase 'the number 2' does not hold together with that of the expression 'the concept prime number' without a link. We apply such a link in the sentence 'the number 2 falls under the concept prime number'; it is contained in the words 'falls under', which need to be completed in two ways - by a subject and an accusative; and only because their sense is thus 'unsaturated' are they capable of serving as a link. Only when they have been supplemented in this twofold respect do we get a complete sense, a thought. I say that what such words or phrases mean is a relation.We now get the same difficulty for the relation that we were trying to avoid for the concept. For the words 'the relation of an object to the concept it falls under' designate not a relation but an object; and the three proper names 'the number 2', 'the concept prime number', 'the relation of an object to a concept it falls under', hold aloof from one another just as much as the first two do by themselves; however we put them together, we get no sentence. It is thus easy for us to see that the difficulty arising from the 'unsaturated-ness' of one part of the thought can indeed be shifted, but not avoided. 'Complete' and 'unsaturated' are of course only figures of speech; but all that I wish or am able to do here is to give hints. 
也许有人认为，这种困难是人为的，根本不需要考虑我称之为概念的那种不切实用的东西，可以像克里那样把一个对象处于一个概念之下看做是一种关系，在这种关系中，这一次可以作为对象出现的东西，下一次又作为概念出现。这样，“对象”和“概念”这两个词只用来指示关系中的不同位置。人们可以这样做，但谁若是相信以此可以避免这种困难，那就大错特错了。这种困难只是被转移了，因为一个思想的部分不能都是完整的，肯定至少有一部分或多或少是不饱和的或者起谓词表述作用，否则它们就不能相互结合在一起。例如，没有联结的东西，“2这个数”这个词组的涵义就不会与“素数 这个概念”这个表达式的涵义联系起来。在“2这个数处于素数这个概念之下”这个句子中，我们就应用了这样的联结的东西，它包含在“处于……之下”这个用语之中。这个用语需要双重的补充：即以一个主词和一个谓词来补充，并且只是由于它的涵义的不饱和性，它才能用作联结的东西。只有当它得到这种双重的补充，我们才有一个完整的涵义，我们才有一个思想。我现在说的是这样的用语或词组，即它们意谓一种关系。我们在这种关系条件下也有在概念条件下所要避免的同样困难。因而，以“对象处于一个概念之下这种关系”这个用语并不表示关系，而是表示一个对象，而且“2这个数”、“素数这个概念”、“一个对象处于一个概念之下这种关系”这三个专名相互的关系与仅前两个专名的相互关系同样难以形成。我们无论怎样排列它们，都不会得到句子。因此，我们很容易认识到，由于一个思想部分的不饱和性而形成的困难尽管可以转移，却不可能避免。“完整的”和“不饱和的”尽管只是形象的表达，但是我愿意在这里给以提示并且只能给以提示。
It may make it easier to come to an understanding if the reader compares my work Function and Concept. For over the question what it is that is called a function in Analysis, we come up against the same obstacle; and on thorough investigation it will be found that the obstacle is essential, and founded on the nature of our language; that we cannot avoid a certain inappropriateness of linguistic expression; and that there is nothing for it but to realize this and always take it into account. 
如果读者对照我的《函数和概念》，就可能更容易理解。因为在数学分析中称为函数的东西是什么这个问题上，也遇到相同的障碍；经过深入的研究，人们将发现，这种障碍是由事物本身和我们的语言性质造成的，语言表达的某种不适当性是不可避免的，我们除去认识到这一点并且总是考虑到这一点之外别无良途。