—(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 or 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.
4.27 With regard to the existence of n atomic facts there are possibilities.
It is possible for all combinations of atomic facts to exist, and the others not to exist.
4.28 To these combinations correspond the same number of possibilities of the truth—and falsehood—of n elementary propositions.
4.3 The truth-possibilities of the elementary propositions mean the possibilities of the existence and non-existence of the atomic facts.