5.5

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Every truth-function is a result of the successive application of the operation  (- - - - -T) ( xi ,....)  to elementary propositions.

This operation denies all the propositions in the right-hand bracket and I call it the negation of these propositions.

5.501 - 5.503

5.51 (5)   If  xi  has only one value, then N( xi-bar ) = ~p (not p); if it has two values then N( xi-bar ) = ~p.~q (neither p, nor q).

5.52 (6)   If the values of  xi  are the total values of a function fx for all values of x, then N( xi-bar ) = ~( EXISTS x).fx.

5.53 (03+5)   Identity of the object I express by identity of the sign and not by means of a sign of identity. Difference of the objects by difference of the signs.

5.54 (2)   In the general propositional form, propositions occur in a proposition only as bases of the truth-operations.

5.55 (7)   We must now answer a priori the question as to all possible forms of the elementary propositions.

The elementary proposition consists of names. Since we cannot give the number of names with different meanings, we cannot give the composition of the elementary proposition.