Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/123

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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.

5.32 All truth-functions are results of the successive