逻辑哲学论-中英对照//5.5

5.5 每个真值函项是将运算

（……真）（ξ，……）

连续应用于原初命题的结果。

这个运算否定右面括弧中的一切命题，我把它称为这些命题的否定。

5.501 When a bracketed expression has propositions as its terms—and the order of the terms inside the brackets is indifferent—then I indicate it by a sign of the form ‘()’. ‘ξ’ is a variable whose values are terms of the bracketed expression and the bar over the variable indicates that it is the representative of all its values in the brackets.

(E.g. if ξ has the three values P, Q, R, then

() = (P, Q, R)

What the values of the variable are is something that is stipulated.

The stipulation is a description of the propositions that have the variable as their representative. /58/

How the description of the terms of the bracketed expression is produced is nor essential.

We can distinguish three kinds of description: 1. direct enumeration, in which case we can simply substitute for the variable the constants that are its values; 2. giving a function fx whose values for all values of x are the propositions to be described; 3. giving a formal law that governs the construction of the propositions, in which case the bracketed expression has as its members all the terms of a series of Forms.

5.501 一个用括弧括起来而其诸项都是命题的表达式，如果括弧内诸项的顺序并不重要，我就用一个具有“（）”形式的指号来表示。“ξ”是一个变项，括弧内诸项是它的值；这个变项上面的横线表示它代表括弧里的一切值。

（因此，例如，如果ξ有三个值：P，Q，R，那么

（）＝（P，Q，R）

变项的值是被规定了的。

这种规定就是对由变项代表的命题的描述。

对括弧表达式的那些项的描述是如何产生的，并不重要。

我们可以将描述区分为三类：1. 直接列举。在这种情况下，我们可以直接用变项的常值置换变项。2. 举出一个函项fx，对于x的一切值来说，它的值都是要加以描述的命题。3. 指定一个形式规则，那些命题就是根据这个规则构成的。在这种情况下，【236】括弧内表达式的诸项就是一个形式系列的全部的项。

5.502 So instead of ‘(----T)(ξ, ….)’, I write ‘N()’

N() is the negation of all the values of the propositional variable ξ.

5.502 因此，我不写“（……真）（ξ，……）”，而写成“N（）”。

N（）是命题变项ξ的一切值的否定。

5.503 It is obvious that we can easily express how propositions may be constructed with this operation, and how they may not be constructed with it; so it must be possible to find an exact expression for this.

5.503 关于命题如何能通过这种运算被构造出来和如何不能通过它构造出来，显然是不难表达的，因此这种情况也必能找到一种精确的表达。

5.51 If I has only one value, then N() = ~p (not p); if it has two values, then N() = ~p . ~q (neither p nor q).

5.51 如果ξ只有一个值，那么N（）~~p（非p）；如果有两个值，那么N（）＝~p.~q（非p亦非a）。

5.511 How can logics—all-embracing logic, which mirrors the world—use such peculiar crotchets and contrivances? Only because they are all connected with one another in an infinitely fine network, the great mirror.

5.511 无所不包、反映世界的逻辑何以会使用如此特殊的手段和操作法？只是因为这一切都在一个无限精细的网络中，一面巨大的镜子中，互相联系着。

5.512 ‘~p’ is true if ‘p’ is false. Therefore, in the proposition ‘~p’, when it is true, ‘p’ is a false proposition. How then can the stroke ‘~’ make it agree with reality?

But in ‘~p’ it is not’-’ that negates; it is rather what is common to all the signs of this notation that negate p.

That is to say the common rule that governs the construction of ‘~p’, ‘~~~~p’, ‘~p v ~p’, ‘~p.~p’, etc. etc. (ad inf.). And this common factor mirrors negation.

5.512 如果“p”是假的，那么“~p”就是真的。因此在真命题“~p”中，“p”是一个假命题。那么“~”这一道线如何能使之符合于实在呢？

但是，在“~p”中被否定的并不是“~”，而是这个记法中否定p的一切指号所共有的东西。

因而这就是“~p”，“~~~p”，~p V~p，~p•~p”等等，等等（以至无穷）按照它被构造出来的那个共同规则。而这个共同的东西又反映否定。

5.513 We might say that what is common to all symbols that /59/ affirm both p and q is the proposition ‘p.q’; and that what is common to all symbols that affirm either p or q is the proposition ‘p v q’.

And similarly we can say that two propositions are opposed to one another if they have nothing in common with one another, and that every proposition has only one negative, since there is only one proposition that lies completely outside it.

Thus in Russell’s notation too it is manifest that ‘q:p v ~p’ says the same thing as ‘q’, that ‘p v ~p’ says nothing.

5.513 我们可以说：既肯定p又肯定q的一切符号的共同的东西是命题“q•p”。肯定p或q的一切符号的共同的东西是命题“p或q”。

而且我们同样可以说：两个命题如果彼此没有共同的东西，它们就是彼此相反的；而且每个命题只有一个否定，因为只有一个命题完全外在于它。【237】

因此，在罗素的记法中。也明显地看出：“q：p V ~p”与“q”所说的是相同的；“p V ~p”没有说任何东西。

5.514 Once a notation has been established, there will be in it a rule governing the construction of all propositions that negate p, a rule governing the construction of all propositions that affirm p, and a rule governing the construction of all propositions that affirm p or q; and so on. These rules are equivalent to the symbols; and in them their sense is mirrored.

5.514 一种记法如被确定下来，那么在这种记法里就有一条据以构成一切否定p的命题的规则，一条据以构成一切肯定p的命题的规则，一条据以构成一切肯定p或q的命题的规则，等等。这些规则相当于一些符号，而这些符号的意义又反映在这些规则中。

5.515 It must be manifest in our symbols that it can only be propositions that are combined with one another by ‘v’, ‘.’, etc.

And this is indeed the case, since the symbol in ‘p’ and ‘q’ itself presupposes ‘v’, ‘~’, etc. If the sign ‘p’ in ‘p v q’ does not stand for a complex sign, then it cannot have sense by itself: but in that case the signs ‘p v p’, ‘p.p’, etc., which have the same sense as p, must also lack sense. But if ‘p v p’ has no sense, then ‘p v q’ cannot have a sense either.

5.515 从我们的符号就应看出，通过“V”、“.”等等而互相结合起来的东西必然是命题。

而且情形也确是这样，因为符号”p”和“q”本身就假定了“V”、“~”等等。如果在“p V q”中指号“p”不代表一个复合符号，那么它单独地就不可能具有意义；但这样一来，与“p”具有相同意义的指号“p V p”、“p•p”等等也就都是没有意义的了。但是如果“p V p”没有意义，那么“p V q”也不可能具有意义。

5.5151 Must the sign of a negative proposition be constructed with that of the positive proposition? Why should it not be possible to express a negative proposition by means of a negative fact? (E.g. suppose that ‘a’ does not stand in a certain relation to ‘b’; then this might be used to say that aRb was not the case.) /60/

But really even in this case the negative proposition is constructed by an indirect use of the positive.

The positive proposition necessarily presupposes the existence of the negative proposition and vice versa.

5.5151 负命题的指号是否一定要用正命题的指号构成？

为什么我们不能以一负事实来表达一负命题？（例如，如果“a”和“b”没有某种关系，那么我们就可以把这表述为：aRb不是发生的事情。）

但是即使在这里，负命题也是间接地由正命题构成的。

正命题必然预先设定了负命题的存在，反之亦然。

5.52 If ξ has as its values all the values of a function fx for all values of x, then N() = ~(x).fx.

5.52 如果的值是一个函项fx对于x的所有值而具有的全部的值，那么N（）＝~（x）.fx。

5.521 I dissociate the concept all from truth-functions.

Frege and Russell introduced generality in association with logical product or logical sum. This made it difficult to understand the propositions ‘(x) .fx’ and ‘(x).fx’ in which both ideas are embedded.

5.521 我把所有这个概念与真值函项分开。

弗雷格和罗素是将概括性与逻辑积或逻辑和联系在一起引进的。【238】这样就很难理解含有这两个观念的命题“（x）.fx”和“（x）.fx”了。

5.522 What is peculiar to the generality-sign is first, that it indicates a logical prototype, and secondly, that it gives prominence to constants.

5.522 概括性指号的特点是：第一，它指示一种逻辑的元图像，其次，它突出了常项。

5.523 The generality-sign occurs as an argument.

5.523 概括性指号是作为主目出现的。

5.524 If objects are given, then at the same time we are given all objects.

If elementary propositions are given, then at the same time all elementary propositions are given.

5.524 如果一些对象被给出了那么所有的对象从而也就被给出了。

如果一些原初命题被给出了，那么所有的原初命题从而也就被给出了。

5.525 It is incorrect to render the proposition ‘(x).fx’ in the words, ‘fx is possible’, as Russell does.

The certainty, possibility, or impossibility of a situation is not expressed by a proposition, but by an expression’s being a tautology, a proposition with sense, or a contradiction.

The precedent to which we are constantly inclined to appeal must reside in the symbol itself.

5.525 像罗素那样，将命题“（x）.fx”用语词表述为“fx是可能的”，是不正确的。

一个事况的确实性，可能性或不可能性，不是由一个命题表达的，而是由一个表达式之为一个重言式，一个有意义命题或一个矛盾式来表达的。

我们会经常引用的先例必已存在于符号本身中。

5.526 We can describe the world completely by means of fully generalized propositions, i.e. without first correlating any name with a particular object.

Then, in order to arrive at the customary mode of /61/ expression, we simply need to add, after an expression like, ‘There is one and only one x such that . . .’, the words, ‘and that x is a’.

5.526 我们通过完全概括化的命题，亦即无须从一开始就将某个名字归之于某个对象，就可以完全地描述世界。

于是，为了达到通常的表达方式，我们只须在“有一个且只有一个x，其……”这个表达式之后说：而且这个x是a。

5.5261 A fully generalized proposition, like every other proposition, is composite. (This is shown by the fact that in ‘(x, Φ), Φx’ we have to mention ‘Φ’ and ‘x’ separately. They both, independently, stand in signifying relations to the world, just as is the case in ungeneralized propositions.)

It is a mark of a composite symbol that it has something in common with other symbols.

5.5261 一个完全概括化的命题，像所有其他的命题一样，都是复合命题。（下面这个事实就说明了这一点，即在“（x，Φ），Φx”中，我们必须分别提到“Φ”和“x”。正如在非概括化命题中一样，二者对世界有独立的指称关系。）

组合符号的特征是：它与其他符号有某种共同的东西。【239】

5.5262 The truth or falsity of every proposition does make some alteration in the general construction of the world. And the range that the totality of elementary propositions leaves open for its construction is exactly the same as that which is delimited by entirely general propositions.

(if an elementary proposition is true, that means, at any rate, one more true elementary proposition.)

5.5262 每个命题的真或假对世界的一般结构都有某种改变。而且原初命题的总和留给世界结构的范围恰恰是完全概括的命题所限定的范围。

（如果一个原初命题是真的，那么无论如何同时还有一个原初命题是真的。）

5.53 Identity of object I express by identity of sign, and not by using a sign for identity. Difference of objects I express by difference of signs.

5.53 对象的等同，我用指号的等同而不用等同的指号（等号）来表达。对象的差异则以指号的差异来表达。

5.5301 It is self-evident that identity is not a relation between objects. This becomes very dear if one considers, for example, the proposition ‘(x):fx..x = a’. What this proposition says is simply that only a satisfies the function f, and not that only things that have a certain relation to a satisfy the function f.

Of course, it might then be said that only a did have this relation to a; but in order to express that, we should need the identity-sign itself.

5.5301 同一显然不是对象间的关系。例如，看一下命题

“（x）:fx..x = a”，这一点就变得非常清楚了。这个命题所说的不过是：仅有a满足函项f，而不是仅有对a有某种关系的那些事物才满足函项f。

当然我们可以说，恰恰只有a对a具有这种关系，但是要把这表达出来，我们则需要等号本身。

5.5302 Russell’s definition of ‘=’ is inadequate, because according to it we cannot say that two objects have all their properties in common. (Even if this proposition is never correct, it still has sense.) /62/

5.5302 罗素关于“＝”的定义是不适用的；因为根据他的定义，我们不能说两个对象共有一切特性。（即使这个命题决不是正确的，但它毕竟是有意义的。）

5.5303 Roughly speaking, to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing at all.

5.5303 顺便说一下，说两个事物是同一的，是无意义的，而说一个事物是自身同一的，则全然无所说。

5.531 Thus I do not write ‘f(a,b).a = b’, but ‘f(a,a)’ (or ‘f(b,b)’); and not f(a,b).~a = b’, but ‘f(a,b)’.

5.531 因此，我不写“f（a，b）a＝b”，而写做“f（a，a）”（或“f（b，b）”）；不写“f（a，b）.~a＝b”，而写做“f（a，b）”。

5.532 And analogously I do not write ‘(x,y).f(x,y) .x = y’, but ‘(x).f(x,x)’; and not ‘(x,y) .f(x,y) .~x = y’ but ‘(x.y).f(x,y)’.

(So Russell’s ‘(x,y).fxy’ becomes

(x,y).f(x,y).v.(x).f(x,x)’.)

5.532 同样地，我不写“（x，y）.f（x，y）.x＝y”，而写做“（x）.f（x，x）”；不写“（x，y）.f（x，y）~x＝y”，而写做“（x，y）.f（x，y）”。

（于是罗素的“（x，y）.fxy”就被代之以“（x，y）.f（x，y）.V（x）.f（x，x）”。）

5.5321 Thus, for example, instead of ‘(x):fxx = a’ we write ‘(x).fx. .fa : ~(x,y).fx.fy’.

And the proposition, ‘Only one x satisfies f ( )’, will read ‘(x).fx : ~(x,y).fx.fy’.

5.5321 因此，我们不写“（x）：fxx＝ a”，【240】而写做例如“（x）.fx.fa：~（x，y）.fx.fy”。

而且命题“仅有一个。满足f（）”要读作：“（x）.fx：~（x，y）.fx.fy”。

5.533 The identity-sign, therefore, is not an essential constituent of conceptual notation.

5.533 因此，等号不是概念文字的一个本质的成分。

5.534 And now we see that in a correct conceptual notation pseudo-propositions like ‘a =a’, ‘a=b.b=c. a = c’, ‘(x).x - x’, ‘(x).x = a’, etc. cannot even be written down.

5.534 现在我们看到，在一种适当的概念文字中，是根本不能写类如“a＝a”，“a＝b.b＝c. a＝c”，（x）.x＝x，“（x）.x＝a”等等似是而非的命题的。

5.535 This also disposes of all the problems that were connected with such pseudo-propositions.

All the problems that Russell’s ‘axiom of infinity’ brings with it can be solved at this point.

What the axiom of infinity is intended to say would express itself in language through the existence of infinitely many names with different meanings.

5.535 由此一切与这样似是而非的命题相关的问题也就消除了。

罗素的“无穷公理”引起的一切问题在这里终究可以解决了。

无穷公理要说的东西会通过无穷多具有不同意谓的名字的存在而表达在语言中。

5.5351 There are certain cases in which one is tempted to use expressions of the form ‘a = a’ or ‘p p’ and the like. In fact, this happens when one wants to talk about prototypes, e.g. about proposition, thing, etc. Thus in Russell’s /63/ Principles of Mathematics ‘p is a proposition’—which is nonsense—was given the symbolic rendering ‘p p’ and placed as an hypothesis in front of certain propositions in order to exclude from their argument-places everything but propositions.

(It is nonsense to place the hypothesis ‘p p’ in front of a proposition, in order to ensure that its arguments shall have the right form, if only because with a non-proposition as argument the hypothesis becomes not false but nonsensical, and because arguments of the wrong kind make the proposition itself nonsensical, so that it preserves itself from wrong arguments just as well, or as badly, as the hypothesis without sense that was appended for that purpose.)

5.5351 在某些情况下，人们很想使用具有“a＝a”或“pp”以及诸如此类形式的表达式。在人们想谈论元图像：命题、事物等等的时候，就有这种情况。因此，罗素在《数学的原理》中曾用“pp”将“p是一个命题”这种无意义的话复述在符号中，井且把它作为假设放在某些命题之前，以使其主目位置只能为命题所占有。

（把pp这个假设放在一个命题之前以保证其主目具有适当的形式，这已经就是无意义的了，因为对于作为主目的一个非命题来说，这个假设不是假的，而是无意义的，而且这个命题本身由于不适当的主目种类也成为无意义的，因而这个命题较之为此目的而附加的这个缺乏意义的假设对防止那些不适当的主目并不更好些或更糟些。）

5.5352 In the same way people have wanted to express, “There are no things’, by writing ‘~(x).x = x. But even if this were a proposition, would it not be equally true if in fact ‘there were things’ but they were not identical with themselves?

5.5352 同样，人们想通过“~（x）.x＝x”来表达“没有任何事物存在”。【241】但是即使这是一个命题，——即使的确“有事物存在”，虽然这些事物并非与自身同一，这个命题不也会是真的吗？

5.54 In the general prepositional form propositions occur in other propositions only as bases of truth-operations.

5.54 在普遍命题形式中，命题只是作为真值运算的根据才出现在其他命题中。

5.541 At first sight it looks as if it were also possible for one proposition to occur in another in a different way.

Particularly with certain forms of proposition in psychology, such as ‘A believes that p is the case’ and ‘A has the thought p’, etc.

For if these are considered superficially, it looks as if the proposition p stood in some kind of relation to an object A.

(And in modern theory of knowledge (Russell, Moore, etc.) these propositions have actually been construed in this way.)

5.541 乍一看，一个命题似乎也能以其他方式出现在另一命题中。

尤其在某些心理学的命题形式中，如“A相信p是发生的事情”，或者“A认为p”，等等。

因为在这里表面看来，似乎命题p与对象A有某类关系。

（而且在现代的知识论（罗素、穆尔等人）中，对这些命题也就是这样解释的。）

5.542 It is clear, however, that ‘A believes that p’, ‘A has the /64/ thought p’, and ‘A says p’ are of the form ‘“p” says p’: and this does not involve a correlation of a fact with an object, but rather the correlation of facts by means of the correlation of their objects.

5.542 但是，显然，“A相信p”，“A认为p”，“A说p”都是具有“‘p’说p”这种形式的命题；而且这里并不涉及一个事实和一个对象的相互配置，而是关于一些事实由于其对象的配置而成的配置的。

5.5421 This shows too that there is no such thing as the soul— the subject, etc.—as it is conceived in the superficial psychology of the present day.

Indeed a composite soul would no longer be a soul.

5.5421 这也表明，像如今肤浅的心理学所了解的那种灵魂——主体，等等——乃是一个子虚乌有。

一个复合的灵魂就不复是一个灵魂了。

5.5422 The correct explanation of the form of the proposition, ‘A makes the judgement p’, must show that it is impossible for a judgement to be a piece of nonsense. (Russell’s theory does not satisfy this requirement.)

5.5422 对“A判断p”这个命题的形式的正确说明必须指出，判断一个子虚乌有的东西是不可能的。（罗素的理论没有满足这个条件。）

5.5423 To perceive a complex means to perceive that its constituents are related to one another in such and such away.

This no doubt also explains why there are two possible ways of seeing the figure

as a cube; and all similar phenomena. For we really see two different facts.

(If I look in the first place at the corners marked a and only glance at the b’s, then the a’s appear to be in front, and vice versa).

5.5423 感知一个复合物即感知其诸成分彼此处于这样那样的关系中。

这或许也就说明了，对于下面这个图形何以可以两种方式看成立方形；而且这也可能说明一切类似的现象。因为我们的确就是看到了两个不同的事实。[see above]【242】

（如果我首先注视诸a角，对诸b角只是匆匆一瞥，那么诸a角就似乎在前，而诸b角居后，反之则似乎诸b角在前，而诸a角居后了。）

5.55 We now have to answer a priori the question about all the possible forms of elementary propositions. /65/

Elementary propositions consist of names. Since, however, we are unable to give the number of names with different meanings, we are also unable to give the composition of elementary propositions.

5.55 现在我们对原初命题的一切可能的形式问题应当给以先天的回答。

原初命题是由名字组成的。但是由于我们不可能指出具有不同意谓的名字的数目，我们也就不可能指出原初命题的组合。

5.551 Our fundamental principle is that whenever a question can be decided by logic at all it must be possible to decide it without more ado.

(And if we get into a position where we have to look at the world for an answer to such a problem, that shows that we are on a completely wrong track.)

5.551 我们的原则是：凡是完全可由逻辑判定的问题，都必可立即作出判定。

（而如果我们陷入了必须根据对世界的观察来回答这样问题的地步，那么这就表明我们走上了一条根本错误的道路。）

5.552 The ‘experience’ that we need in order to understand logic is not that something or other is the state of things, but that something is: that, however, is not an experience.

Logic is prior to every experience—that something is so. It is prior to the question ‘How?’, not prior to the question ‘What?’

5.552 我们为了解逻辑而需要的“经验”，不是某物情况如何，而是某物存在：然而这恰恰不是经验。

逻辑是先于一切经验的——先于某物之为如此情况的。

逻辑先于“如何”，而非先于“是何”。

5.5521 And if this were not so, how could we apply logic? We might put it in this way: if there would be a logic even if there were no world, how then could there be a logic given that there is a world?

5.5521 如果不是如此，我们怎能使用逻辑呢？我们可以说：如果纵然世界不存在，也会有一个逻辑，那么既然有了一个世界，【243】又怎么会有一个逻辑呢？

5.553 Russell said that there were simple relations between different numbers of things (individuals). But between what numbers? And how is this supposed to be decided?—By experience?

(There is no pre-eminent number.)

5.553 罗素说，在事物（个体）的不同数目之间有简单的关系。但是在什么数目之间？而且如何来判定这一点呢？——通过经验来判定吗？

（没有特异的数。）

5.554 It would be completely arbitrary to give any specific form.

5.554 举出任何特殊的形式，都会是完全任意的。

5.5541 It is supposed to be possible to answer a priori the question whether I can get into a position in which I need the sign for a 27-termed relation in order to signify something.

5.5541 我是否可能，例如，陷入一种必须用27位关系的指号来指称某物的境地，对此应可先天地予以确定。

5.5542 But is it really legitimate even to ask such a question? /66/ Can we set up a form of sign without knowing whether anything can correspond to it?

Does it make sense to ask what there must be in order that something can be the case?

5.5542 但是我们究竟可不可以提出这样的问题呢？我们是否可能提出一种指号形式，却不知道有无某物与之相应呢？

下面这个问题有无意义，即为使某物能够成为发生的事情，必须有何物存在？

5.555 Clearly we have some concept of elementary propositions quite apart from their particular logical forms.

But when there is a system by which we can create symbols, the system is what is important for logic and not the individual symbols.

And anyway, is it really possible that in logic I should have to deal with forms that I can invent? What I have to deal with must be that which makes it possible for me to invent them.

5.555 显然，除了其特殊的逻辑形式之外，我们对原初命题还是有某种概念的。

但是，在我们能按照一个系统来构造符号的地方，在逻辑上重要的东西就是这个系统，而不是一些个别的符号。

而且不论我是否可能在逻辑上处理我所能创造的形式，但是我必须处理使我可能创造它们的东西。

5.556 There cannot be a hierarchy of the forms of elementary propositions. We can foresee only what we ourselves construct.

5.556 不可能有一个原初命题形式的等级系统。我们只能预见我们自己构造的东西。

5.5561 Empirical reality is limited by the totality of objects. The limit also makes itself manifest in the totality of elementary propositions.

Hierarchies are and must be independent of reality.

5.5561 经验的实在为对象总和所限定，这个界限又显现于原初命题的总和中。

等级系统是而且必然是独立于实在的。

5.5562 If we know on purely logical grounds that there must be elementary propositions, then everyone who understands propositions in their unanalysed form must know it.

5.5562 如果我们根据纯粹逻辑的理由，知道必然有原初命题，那么凡是在其未分析的形式上了解了命题的人，一定都知道这一点。【244】

5.5563 In fact, all the propositions of our everyday language, just as they stand, are in perfect logical order. —That utterly simple thing, which we have to formulate here, is not a likeness of the truth, but the truth itself in its entirety.

(Our problems are not abstract, but perhaps the most concrete that there are.) /67/

5.5563 实际上，我们日常语言的一切命题，就像现在的样子，是有完全的逻辑次序的。——我们在这里应该说明的最简单的东西，不是真的一种类似物，而是整个的真本身。

（我们的问题不是抽象的，而也许是现有的最具体的问题。）

5.557 The application of logic decides what elementary propositions there are.

What belongs to its application, logic cannot anticipate.

It is clear that logic must not dash with its application.

But logic has to be in contact with its application.

Therefore logic and its application must not overlap.

5.557 逻辑的应用决定有哪些原初命题。

逻辑不能预见到包含在它的应用中的东西。显然，逻辑必不与其应用相冲突。

但是，逻辑必然涉及它的应用。

因此，逻辑与其应用不能互相重叠。

5.5571 if I cannot say a priori what elementary propositions there are, then the attempt to do so must lead to obvious nonsense.

5.5571 如果我不能先天地给出原初命题，那么要想给出它们就必然导致明显的无意义的话语。

5.6 The limits of my language mean the limits of my world.

5.6 我的语言的界限意谓我的世界的界限。

5.61 Logic pervades the world: the limits of the world are also its limits.

So we cannot say in logic, ‘The world has this in it, and this, but not that.’

For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well.

We cannot think what we cannot think; so what we cannot think we cannot say either.

5.61 逻辑充满世界：世界的界限也是它的界限。

因此我们在逻辑上不能说：世界上有这个东西，而没有那个东西。

因为这似乎就要以排除某些可能性为前提，而这种情况是不可能的，因为否则逻辑就必须超出世界的界限，以便也能从世界之外的那一边来观察这些界限。

我们不能思我们不能思的东西；因此我们也不能说我们不能思的东西。

5.62 This remark provides the key to the problem, how much truth there is in solipsism.

For what the solipsist means is quite correct; only it cannot be said, but makes itself manifest.

The world is my world: this is manifest in the fact that the limits of language (of that language which alone I understand) mean the limits of my world.

5.62 这段议论为判定唯我论在多大程度上是一个真理的问题提供了一把钥匙。

这就是说，唯我论的命意是完全正确的，只是它不可说，而是显示出来。

世界是我的世界，这一点就显示在语言（惟一能为我所理解的语言）的界限意谓我的世界的界限。【245】

5.621 The world and life are one.

5.621 世界与人生是一回事。

5.63 I am my world. (The microcosm.) /68/

5.63 我是我的世界。（小宇宙。）

5.631 There is no such thing as the subject that thinks or entertains ideas.

If I wrote a book called The World as I found it, I should have to include a report on my body, and should have to say which parts were subordinate to my will, and which were not, etc., this being a method of isolating the subject, or rather of showing that in an important sense there is no subject; for it alone could not be mentioned in that book.—

5.631 不存在能思维、能表象的主体。

如果我写一本名为《我所看到的世界》的书，那么在书中也会谈到我的身体，而且会说明哪些肢体部分服从我的意志，哪些不服从，等等。这就是使主体离析出来的一种方法，或者更确切地说，是指主体在一个重要的意义上并不存在的方法：也就是说，在这本书里惟独不能谈到主体。——

5.632 The subject does not belong to the world: rather, it is a limit of the world.

5.632 主体不属于世界，但是它是世界的一个界限。

5.633 Where in the world is a metaphysical subject to be found?

You will say that this is exactly like the case of the eye and the visual field. But really you do not see the eye.

And nothing in the visual field allows you to infer that it is seen by an eye.

5.633 要在世界何处去发觉一个形而上学的主体呢？

你说，这完全有类乎眼之与视野的情形。但是你实际上看不见眼。

而且从视野中的任何东西都不可能推出它是由一只眼看到的。

5.6331 For the form of the visual field is surely not like this

5.6331 因为视野绝不具有下面这样的一种形式：[see above]

5.634 This is connected with the fact that no part of our experience is at the same time a priori.

Whatever we see could be other than it is. Whatever we can describe at all could be other than it is.

There is no a priori order of things.

5.634 这与下面这个事实有联系，即我们的经验没有任何部分也是先天的。

我们所看到的一切都可能又是另外的样子。

我们一般能描述的一切都可能又是另外的样子。【246】

不存在先天的事物次序。

5.64 Here it can be seen that solipsism, when its implications are followed out strictly, coincides with pure realism. The self of solipsism shrinks to a point without /69/ extension, and there remains the reality coordinated with It.

5.64 在这里我们看到，严格贯彻的唯我论与纯粹的实在论是一致的。唯我论的自我缩成一个无广延的点，而与之同格的实在则保持不变。

5.641 Thus there really is a sense in which philosophy can talk about the self in a non-psychological way.

What brings the self into philosophy is the fact that ‘the world is my world’.

The philosophical self is not the human being, not the human body, or the human soul, with which psychology deals, but rather the metaphysical subject, the limit of the world—not a part of it.

5.641 因此，的确在某种意义上，在哲学中可以非心理学地谈论自我。

自我之进入哲学，是由于“世界是我的世界”。

哲学的自我并不是人，既不是人的身体，也不是心理学讨论的人的心灵，而是形而上学的主体，是世界的界限——而非世界的一部分。