TRACTATUS LOGICO-PHILOSOPHICUS

formal series, the second the form of an arbitrary
term *x* of the series, and the third the form
of that term of the series which immediately
follows *x*.

5.2523 The concept of the successive application of an operation is equivalent to the concept "and so on".

5.253 One operation can reverse the effect of another. Operations can cancel one another.

5.254 Operations can vanish (*e.g.* denial in "~ ~ *p*".
~ ~ *p = p*).

5.3 All propositions are results of truth-operations on the elementary propositions.

The truth - operation is the way in which a truth - function arises from elementary propositions.

According to the nature of truth-operations,
in the same way as out of elementary propositions arise their truth-functions, from truth-functions arises a new one. Every truth-operation
creates from truth-functions of elementary propositions another truth-function of elementary
propositions, *i.e.*, a proposition. The result of
every truth-operation on the results of truth-operations on elementary propositions is also
the result of *one* truth-operation on elementary
propositions.

Every proposition is the result of truth-operations on elementary propositions.

5.31 The Schemata No. 4.31 are also significant, if
"*p*", "*q*", "*r*", etc. are not elementary propositions.

And it is easy to see that the propositional
sign in No. 4.42 expresses one truth-function of
elementary propositions even when "*p*" and
"*q*" are truth-functions of elementary propositions.

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