'judgement stroke' '|-' is logically quite meaningless: in the works
of Frege (and Russell) it simply indicates that these authors hold the
propositions marked with this sign to be true. Thus '|-' is no more a
component part of a proposition than is, for instance, the proposition's
number. It is quite impossible for a proposition to state that it itself
is true.) If the order or the truth-possibilities in a scheme is fixed
once and for all by a combinatory rule, then the last column by itself
will be an expression of the truth-conditions. If we now write this
column as a row, the propositional sign will become '(TT-T) (p,q)' or
more explicitly '(TTFT) (p,q)' (The number of places in the left-hand
pair of brackets is determined by the number of terms in the right-hand
pair.)

4.45 For n elementary propositions there are Ln possible groups of
truth-conditions. The groups of truth-conditions that are obtainable
from the truth-possibilities of a given number of elementary
propositions can be arranged in a series.

4.46 Among the possible groups of truth-conditions there are two
extreme cases. In one of these cases 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
contradictory. In the first case we call the proposition a tautology; in
the second, a contradiction.

4.461 Propositions show what they say; tautologies and contradictions
show that they say nothing. A tautology has no truth-conditions, since
it is unconditionally true: and a contradiction is true on no condition.
Tautologies and contradictions lack sense. (Like a point from which two
arrows go out in opposite directions to one another.) (For example, I
know nothing about the weather when I know that it is either raining or
not raining.)

4.46211 Tautologies and contradictions are not, however, nonsensical.
They are part of the symbolism, much as '0' is part of the symbolism of
arithmetic.

4.462 Tautologies and contradictions are not pictures of reality. They
do not represent any possible situations. For the former admit all
possible situations, and latter none. In a tautology the conditions of
agreement with the world--the representational relations--cancel one
another, so that it does not stand in any representational relation to
reality.

4.463 The tru