4.1273 If we want to express in conceptual notation the general proposition, ‘b is a successor of a’, then we require an expression for the general term of the series of forms ‘aRb’, ‘(d :  c) :  aRx . xRb’, ’(d x,y) : aRx . xRy . yRb’, ... , In order to express the general term of a series of forms, we must use a variable, because the concept ’term of that series of forms’ is a formal concept. (This is what Frege and Russell overlooked:  consequently the way in which they want to express general propositions like the one above is incorrect; it contains a vicious circle.) We can determine the general term of a series of forms by giving its first term and the general form of the operation that produces the next term out of the proposition that precedes it.

4.1274 To ask whether a formal concept exists is nonsensical.  For no proposition can be the answer to such a question. (So, for example, the question, ‘Are there unanalysable subject-predicate propositions?’ cannot be asked.)

4.128 Logical forms are without number.  Hence there are no preeminent numbers in logic, and hence there is no possibility of philosophical monism or dualism, etc.

4.2 The sense of a proposition is its agreement and disagreement with possibilities of existence and non-existence of states of affairs. 4.21 The simplest kind of proposition, an elementary proposition, asserts the existence of a state of affairs.

4.211 It is a sign of a proposition’s being elementary that there can be no elementary proposition contradicting it.

4.22 An elementary proposition consists of names.  It is a nexus, a concatenation, of names.

4.221 It is obvious that the analysis of propositions must bring us to elementary propositions which consist of names in immediate combination.  This raises the question how such combination into propositions comes about.

4.2211 Even if the world is infinitely complex, so that every fact consists of infinitely many states of affairs and every state of affairs is composed of infinitely many objects, there would still have to be objects and states of affairs.

4.23 It is only in the nexus of an elementary proposition that a name occurs in a proposition.

4.24 Names are the simple symbols:  I indicate them by single letters (’x’, ‘y’, ’z’).  I write elementary propositions as functions of names, so that they have the form ‘fx’, ‘O (x,y)’, etc.  Or I indicate them by the letters ‘p’, ‘q’, ‘r’.

4.241 When I use two signs with one and the same meaning, I express this by putting the sign ‘=’ between them.  So ‘a = b’ means that the sign ‘b’ can be substituted for the sign ‘a’. (If I use an equation to introduce a new sign ‘b’, laying down that it shall serve as a substitute for a sign a that is already known, then, like Russell, I write the equation—­ definition—­in the form ‘a = b Def.’  A definition is a rule dealing with signs.)