'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.)


4.242 Expressions of the form 'a = b' are, therefore, mere representational
devices. They state 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 whether their meaning is the same or
different? Suppose I know the meaning of an English word and of a German
word that means the same: then it is impossible for me to be unaware that
they do mean the same; I must be capable of translating each into the
other. Expressions like 'a = a', and those derived from them, are neither
elementary propositions nor is there any other way in which they have
sense. (This will become evident later.)


4.25 If an elementary proposition is true, the state of affairs exists: if
an elementary proposition is false, the state of affairs does not exist.