A proposition is the expression of agreement and disagreement with the truth-possibilities of the elementary propositions.

4.41 (1)    The truth-possibilities of the elementary propositions are the conditions of the truth and falsehood of the propositions.

4.42    With regard to the agreement and disagreement of a proposition with the truth-possibilities of n elementary propositions there are SUMMATION(kappa=0 to Kn, binom-coeff(Kn over kappa) = Ln possibilities.

4.43 (1)    Agreement with the truth-possibilities can be expressed by co-ordinating with them in the scheme the mark "T" (true).

Absence of this mark means disagreement.

4.44 (2)    The sign which arises from the co-ordination of that mark "T" with the truth-possibilities is a propositional sign.

4.45    For n elementary propositions there are Ln possible groups of truth-conditions.

The groups of truth-conditions which belong to the truth-possibilities of a number of elementary propositions can be ordered in a series.

4.46 (6)    Among the possible groups of truth-conditions there are two extreme cases.

In the one case the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological.

In the second case the proposition is false for all the truth-possibilities. The truth-conditions are self-contradictory.

In the first case we call the proposition a tautology, in the second case a contradiction.