6.124 The propositions of logic describe the scaffolding of the world, or rather they represent it.  They have no ‘subject-matter’.  They presuppose that names have meaning and elementary propositions sense; and that is their connexion with the world.  It is clear that something about the world must be indicated by the fact that certain combinations of symbols—­whose essence involves the possession of a determinate character—­are tautologies.  This contains the decisive point.  We have said that some things are arbitrary in the symbols that we use and that some things are not.  In logic it is only the latter that express:  but that means that logic is not a field in which we express what we wish with the help of signs, but rather one in which the nature of the absolutely necessary signs speaks for itself.  If we know the logical syntax of any sign-language, then we have already been given all the propositions of logic.

6.125 It is possible—­indeed possible even according to the old conception of logic—­to give in advance a description of all ‘true’ logical propositions.

6.1251 Hence there can never be surprises in logic.

6.126 One can calculate whether a proposition belongs to logic, by calculating the logical properties of the symbol.  And this is what we do when we ‘prove’ a logical proposition.  For, without bothering about sense or meaning, we construct the logical proposition out of others using only rules that deal with signs .  The proof of logical propositions consists in the following process:  we produce them out of other logical propositions by successively applying certain operations that always generate further tautologies out of the initial ones. (And in fact only tautologies follow from a tautology.) Of course this way of showing that the propositions of logic are tautologies is not at all essential to logic, if only because the propositions from which the proof starts must show without any proof that they are tautologies.

6.1261 In logic process and result are equivalent. (Hence the absence of surprise.)

6.1262 Proof in logic is merely a mechanical expedient to facilitate the recognition of tautologies in complicated cases.

6.1263 Indeed, it would be altogether too remarkable if a proposition that had sense could be proved logically from others, and so too could a logical proposition.  It is clear from the start that a logical proof of a proposition that has sense and a proof in logic must be two entirely different things.

6.1264 A proposition that has sense states something, which is shown by its proof to be so.  In logic every proposition is the form of a proof.  Every proposition of logic is a modus ponens represented in signs. (And one cannot express the modus ponens by means of a proposition.)

6.1265 It is always possible to construe logic in such a way that every proposition is its own proof.

6.127 All the propositions of logic are of equal status:  it is not the case that some of them are essentially derived propositions.  Every tautology itself shows that it is a tautology.