5.143 Contradiction is that common factor of propositions which no
proposition has in common with another. Tautology is the common factor of
all propositions that have nothing in common with one another.
Contradiction, one might say, vanishes outside all propositions: tautology
vanishes inside them. Contradiction is the outer limit of propositions:
tautology is the unsubstantial point at their centre.
5.15 If Tr is the number of the truth-grounds of a proposition 'r', and if
Trs is the number of the truth-grounds of a proposition 's' that are at the
same time truth-grounds of 'r', then we call the ratio Trs : Tr the degree
of probability that the proposition 'r' gives to the proposition 's'. 5.151
In a schema like the one above in
5.101, let Tr be the number of 'T's' in the proposition r, and let Trs, be
the number of 'T's' in the proposition s that stand in columns in which the
proposition r has 'T's'. Then the proposition r gives to the proposition s
the probability Trs : Tr.
5.1511 There is no special object peculiar to probability propositions.
5.152 When propositions have no truth-arguments in common with one another,
we call them independent of one another. Two elementary propositions give
one another the probability 1/2. If p follows from q, then the proposition
'q' gives to the proposition 'p' the probability 1. The certainty of
logical inference is a limiting case of probability.
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