It is of the essence of truth-
operations that, just as elementary propositions yield a truth-function of
themselves, so too in the same way truth-functions yield a further truth-
function. When a truth-operation is applied to truth-functions of
elementary propositions, it always generates another truth-function of
elementary propositions, another proposition. When a truth-operation is
applied to the results of truth-operations on elementary propositions,
there is always a single operation on elementary propositions that has the
same result. Every proposition is the result of truth-operations on
elementary propositions.
5.31 The schemata in 4.31 have a meaning even when 'p', 'q', 'r', etc. are
not elementary propositions. And it is easy to see that the propositional
sign in 4.442 expresses a single truth-function of elementary propositions
even when 'p' and 'q' are truth-functions of elementary propositions.
5.32 All truth-functions are results of successive applications to
elementary propositions of a finite number of truth-operations.
5.4 At this point it becomes manifest that there are no 'logical objects'
or 'logical constants' (in Frege's and Russell's sense).
5.41 The reason is that the results of truth-operations on truth-functions
are always identical whenever they are one and the same truth-function of
elementary propositions.
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