d. Logical Atomism and Wittgenstein’s Tractatus
Ludwig Wittgenstein came to Cambridge to study mathematical logic under Russell, but he quickly established himself as his teacher’s intellectual peer. Together, they devised a metaphysical system called “logical atomism.” As discussed at the beginning of Section 2, qua total system, logical atomism seems to have been Wittgenstein’s brainchild. Still, this should not be seen as in any way marginalizing Russell’s significance for the system, which can be described as a metaphysics based on the assumption that an ideal language the likes of which was provided in Principia Mathematica is the key to reality.
维特根斯坦来到剑桥向罗素学习数学逻辑，但他很快变为了他老师在研究中的同伴。他们在一起设计了一种被称作是“逻辑原子主义”的形而上学系统。正如在第二节开头所讨论的，作为一个完整的系统，逻辑原子论似乎是维特根斯坦所思考出来的。然而，这不应该被认作是罗素在这个系统中所做出的卓越的贡献，他基于一个在数学原理中类似的理想语言是与现实相联系的关键的猜想，而形成了一种形而上学的体系。
According to logical atomism, propositions are built out of elements corresponding to the basic constituents of the world, just as sentences are built out of words. The combination of words in a meaningful sentence mirrors the combination of constituents in the corresponding proposition and also in the corresponding possible or actual state of affairs. That is, the structure of every possible or actual state of affairs is isomorphic with both the structure of the proposition that refers to it and the structure of the sentence that expresses that proposition—so long as the sentence is properly formulated in the notation of symbolic logic. The simplest sort of combination is called an atomic fact because this fact has no sub-facts as part of its structure. An atomic fact for some logical atomists might be something like an individual having a property—a certain leaf’s being green, for instance. Linguistically, this fact is represented by an atomic proposition: for example, “this leaf is green,” or, in logical symbolism “F(a).” Both the fact F(a) and the proposition “F(a)” are called “atomic” not because they themselves are atomic [that is, without structure], but because all their constituents are. Atomic facts are the basic constituents of the world, and atomic propositions are the basic constituents of language.
根据逻辑原子主义，命题是由那些与世界的基本组成部分相联系的元素所构成的，就像语言是由单词构成的一样。在一句有意义的话中，单词的组合反映了命题相应的组成部分，同时也是事态的可能或实在的组成部分。即是说，每个事态的可能或实在的结构是与指向其的命题或者表达这个命题的语句同构的——正如语句被恰当地被转化为符号逻辑那样。最简单的组合被称为原子事实因为这类事实没有子事实来作为它的构成部分。一个原子事实对一些逻辑原子主义者来说就是一些只具有一种性质的单独个体——例如，一片特定的叶子是绿色的。从语言学角度看，这个事实是一个原子论点：例如“这片叶子是绿色的”，或者用符号逻辑“F(a)”来表示。不论是事实F(a)还是命题“F(a)”都被叫做“原子的”不仅仅是因为他们是原子的（即没有结构的），也是因为它的组成部分也是原子的。原子事实是这个世界最基本的组成部分，同时，原子命题是语言最基本的组成部分。
More complex propositions representing more complex facts are called molecular propositions and molecular facts. The propositions are made by linking atomic propositions together with truth-functional connectives, such as “and,” “or” and “not.” A truth-functional connective is one that combines constituent propositions in such a way that their truth-values (that is, their respective statuses as true or false) completely determine the truth value of the resulting molecular proposition. For instance, the truth value of a proposition of the form “not-p” can be characterized in terms of, and hence treated as determined by, the truth value of “p” because if “p” is true, then “not-p” is false, and if it is false, “not-p” is true. Similarly, a proposition of the form “p and q” will be true if and only if its constituent propositions “p” and “q” are true on their own.
反映了更复杂的事实的复杂命题被称为分子命题和分子事实。这些命题利用像“and”，“or”和“not”这样的真值连词将原子命题联系起来。一个真值连词就是一个将组成命题的原子命题用一种方式串联起来的词，它使得分子命题的真值完全取决于原子命题的真值。例如，形如“not -p”的命题的真值可以按照，也由”p”的真值来决定，因为，当p为真时，“not -p”就是假，反之亦然。同样地，要使得”p and q”为真必须要组成这个命题的“p”和“q”同时为真。
The logic of Principia Mathematica is entirely truth-functional; that is, it only allows for molecular propositions whose truth-values are determined by their atomic constituents. Thus, as Russell observed in the introduction to the second edition of the Principia, “given all true atomic propositions, together with the fact that they are all, every other true proposition can theoretically be deduced by logical methods” (Russell 1925, xv). The same assumption—called the thesis of truth-functionality or the thesis of extensionality—lies behind Wittgenstien’sTractatusLogico-Philosophicus.
数学原理的逻辑就是一个完全真值表：即是，它只让分子命题的真实取决于组成它是原子命题。因此，当罗素在数学原理第二版的引言部分写道：“将所有为真的原子命题给出，和所有他们指向的原子事实，任何其他的真命题都可以利用逻辑方法推导出来”。同样的假设——被称作真值函数的论点或其外延性的论点——成为了维特根斯坦逻辑哲学论的基础。
As mentioned previously, Wittgenstein’s Tractatus proved to be the most influential expression of logical atomism. The Tractatus is organized around seven propositions, here taken from the 1922 translation by C. K. Ogden:
正如之前所提到的，维特根斯坦的逻辑哲学论被证明是在逻辑原子主义中最具影响力的著作。逻辑哲学论由骐达观点组成，这里采用了1922年C. K. Ogden翻译的版本：
The world is everything that is the case.
What is the case, the fact, is the existence of atomic facts.
The logical picture of the facts is the thought.
The thought is the significant proposition.
Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth function of itself.)
The general form of a truth-function is…. This is the general form of a proposition.
Where of one cannot speak, thereof one must be silent.
1.世界是所发生的一切事情的总和
2.事态和事实就是原子事实的存在
3.事实的逻辑图像就是思想
4.思考是最重要的命题
5.命题是基本命题的真值函数（一个基本命题就是它自己的真值）
6.真值函数的一般形式即是命题的一般形式
7.对于不可言说者，必须保持沉默