5.141 If *p* follows from *q* and *q* from *p* then they are
one and the same proposition.

5.142 A tautology follows from all propositions: it says nothing.

5.143 Contradiction is something shared by propositions, which *no* proposition has in common with
another. Tautology is that which is shared by
all propositions, which have nothing in common
with one another.

Contradiction vanishes so to speak outside, tautology inside all propositions.

Contradiction is the external limit of the propositions, tautology their substanceless centre.

5.15 If *T _{r}* is the number of the truth-grounds of the
proposition "

*r*",

*T*the number of those truth-grounds of the proposition "

_{r}*s*" which are at the same time truth-grounds of "

*r*", then we call the ratio

*T*the measure of the

_{rs}:T_{r}*probability*which the proposition "

*r*" gives to the proposition "

*s*".

5.151 Suppose in a schema like that above in No.
5.101 *T _{r}* is the number of the "T"'s in the proposition

*r*,

*T*the number of those "T"'s in the proposition

_{rs}*s*, which stand in the same columns as "T"'s of the proposition

*r*; then the proposition

*r*gives to the proposition

*s*the probability

*T*

_{rs}: T_{r}.5.1511 There is no special object peculiar to probability propositions.

5.152 Propositions which have no truth-arguments in common with one another we call independent.

Two elementary propositions give to one another the probability ½.

If *p* follows from *q*, the proposition *q* gives
to the proposition *p* the probability 1. The
certainty of logical conclusion is a limiting case
of probability.

(Application to tautology and contradiction.)

5.153 A proposition is in itself neither probable nor