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.
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