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  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 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. |