4.2
The sense of a proposition is its agreement and disagreement with the possibilities of the existence and non-existence of the atomic facts.

4.21
The simplest proposition, the elementary proposition, asserts the existence of an atomic fact.

4.211
It is a sign of an elementary proposition, that no elementary proposition can contradict it.

4.22
The elementary proposition consists of names. It is a connection, a concatenation, of names.

4.221
It is obvious that in the analysis of propositions we must come to elementary propositions, which consist of names in immediate combination.

The question arises here, how the propositional connection comes to be.

4.2211
Even if the world is infinitely complex, so that every fact consists of an infinite number of atomic facts and every atomic fact is composed of an infinite number of objects, even then there must be objects and atomic facts.

4.23
The name occurs in the proposition only in the context of the elementary proposition.

4.24
The names are the simple symbols; I indicate them by single letters (x, y, z).

The elementary proposition I write as function of the names, in the form "fx", " (x, y)", etc.

Or I indicate it by the letters p, q, r.

4.241
If I use two signs with one and the same meaning, I express this by putting between them the sign "=".

"a=b" means then, that the sign "a" is replaceable by the sign "b".

(If I introduce by an equation a new sign "b", by determining that it shall replace a previously known sign "a", I write the equation -- definition -- (like Russell) in the form "a=b Def.". A definition is a symbolic rule.)

4.242
Expressions of the form "a=b" are therefore only expedients in presentation: They assert nothing about the meaning of the signs "a" and "b".

4.243
Can we understand two names without knowing whether they signify the same thing o r two different things? Can we understand a proposition in which two names occur, without knowing if they mean the same or different things?

If I know the meaning of an English and a synonymous German word, it is impossible for me not to know that they are synonymous, it is impossible for me not to be able to translate them into one another.

Expressions like "a=a", or expressions deduced from these are neither elementary propositions nor otherwise significant signs. (This will be shown later.)

4.25
If the elementary proposition is true, the atomic fact exists; if it is false the atomic fact does not exist.

4.26
The specification of all true elementary propositions describes the world completely. The world is completely described by the specification of all elementary propositions plus the specification, which of them are true and which false.