Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/93

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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 connexion, 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 connexion 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”, “ϕ(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