Wittg.–
It is easy to suppose a contradiction in the fact that on the one hand
every possible complex proposition is a simple

ab-function of simple propositions, & that on
the other hand the repeated application of one

ab-function suffices to generate all these
propositions.
If e.g. an affirmation can be generated by double
negation, is negation in any sense contained in affirmation?
Does “p” deny “not-p” or assert
“p”, or both?
And how do matters stand with the definition of
“ ⊃ ” by
“ ⌵ ” &

“~”
“.”, or of
“ ⌵ ” by
“.” &
“ ⊃ ”?
And how e.g. shall we introduce
p ∣ q (i.e.
~p ⌵ ~q), if not by saying
that this expression says something indefinable about all arguments

p
&

q?
But the

ab-functions must be introduced as
follows: The function p ∣ q is
merely a mechanical instrument for constructing all possible

symbols of

ab-functions.
The symbols arising by repeated application of the symbol
“❘” do

not contain
the symbol “p ∣ q”.
We need a rule according to which we can form all symbols of

ab-functions, in order to be able to speak of the class
of them; & we now speak of them e.g. as those
symbols of functions which can be generated by repeated
application of the operation “❘”.
And we say now: For all

p's &

q's,
“p ∣ q” says something indefinable
about the sense of those simple propositions which are contained in

p
&

q.

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