mething
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