3.25 A proposition cannot be dissected any further by means of a definition:  it is a primitive sign.

3.261 Every sign that has a definition signifies via the signs that serve to define it; and the definitions point the way.  Two signs cannot signify in the same manner if one is primitive and the other is defined by means of primitive signs.  Names cannot be anatomized by means of definitions. (Nor can any sign that has a meaning independently and on its own.)

3.262 What signs fail to express, their application shows.  What signs slur over, their application says clearly.

3.263 The meanings of primitive signs can be explained by means of elucidations.  Elucidations are propositions that stood if the meanings of those signs are already known.

3.3 Only propositions have sense; only in the nexus of a proposition does a name have meaning.

3.31 I call any part of a proposition that characterizes its sense an expression (or a symbol). (A proposition is itself an expression.) Everything essential to their sense that propositions can have in common with one another is an expression.  An expression is the mark of a form and a content.

3.311 An expression presupposes the forms of all the propositions in which it can occur.  It is the common characteristic mark of a class of propositions.

3.312 It is therefore presented by means of the general form of the propositions that it characterizes.  In fact, in this form the expression will be constant and everything else variable.

3.313 Thus an expression is presented by means of a variable whose values are the propositions that contain the expression. (In the limiting case the variable becomes a constant, the expression becomes a proposition.) I call such a variable a ‘propositional variable’.

3.314 An expression has meaning only in a proposition.  All variables can be construed as propositional variables. (Even variable names.)

3.315 If we turn a constituent of a proposition into a variable, there is a class of propositions all of which are values of the resulting variable proposition.  In general, this class too will be dependent on the meaning that our arbitrary conventions have given to parts of the original proposition.  But if all the signs in it that have arbitrarily determined meanings are turned into variables, we shall still get a class of this kind.  This one, however, is not dependent on any convention, but solely on the nature of the pro position.  It corresponds to a logical form—­a logical prototype.

3.316 What values a propositional variable may take is something that is stipulated.  The stipulation of values is the variable.

3.317 To stipulate values for a propositional variable is to give the propositions whose common characteristic the variable is.  The stipulation is a description of those propositions.  The stipulation will therefore be concerned only with symbols, not with their meaning.  And the only thing essential to the stipulation is that it is merely a description of symbols and states nothing about what is signified.  How the description of the propositions is produced is not essential.