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 *L _{n}*
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