Page:Wittengenstein - Tractatus Logico-Philosophicus, 1922.djvu/101

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meaningless; in Frege (and Russell) it only shows that these authors hold as true the propositions marked in this way.

"|-" belongs therefore to the propositions no more than does the number of the proposition. A proposition cannot possibly assert of itself that it is true.)

If the sequence of the truth-possibilities in the schema is once for all determined by a rule of combination, then the last column is by itself an expression of the truth-conditions. If we write this column as a row the propositional sign becomes: "(T—T) (p,q)" or more plainly: "(T T F T) (p,q)".

(The number of places in the left-hand bracket is determined by the number of terms in the right-hand bracket.)

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 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.

4.461 The proposition shows what it says, the tautology and the contradiction that they say nothing.

The tautology has no truth-conditions, for it is