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. (Application of this
to tautology and contradiction.)