unconditionally true; and the contradiction is on no condition true.

Tautology and contradiction are without sense.

(Like the point from which two arrows go out in opposite directions.)

(I know, *e.g.* nothing about the weather, when
I know that it rains or does not rain.)

4.4611 Tautology and contradiction are, however, not nonsensical ; they are part of the symbolism, in the same way that "0" is part of the symbolism of Arithmetic.

4.462 Tautology and contradiction are not pictures of
the reality. They present no possible state of
affairs. For the one allows *every* possible state
of affairs, the other *none*.

In the tautology the conditions of agreement with the world — the presenting relations — cancel one another, so that it stands in no presenting relation to reality.

4.463 The truth-conditions determine the range, which is left to the facts by the proposition.

(The proposition, the picture, the model, are in a negative sense like a solid body, which restricts the free movement of another: in a positive sense, like the space limited by solid substance, in which a body may be placed.)

Tautology leaves to reality the whole infinite logical space; contradiction fills the whole logical space and leaves no point to reality. Neither of them, therefore, can in any way determine reality.

4.464 The truth of tautology is certain, of propositions possible, of contradiction impossible.

(Certain, possible, impossible: here we have an indication of that gradation which we need in the theory of probability.)

4.465 The logical product of a tautology and a pro-