Page:Wittengenstein - Tractatus Logico-Philosophicus, 1922.djvu/115

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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 Tr is the number of the truth-grounds of the proposition "r", Tr the number of those truth-grounds of the proposition "s" which are at the same time truth-grounds of "r", then we call the ratio Trs:Tr the measure of the probability which the proposition "r" gives to the proposition "s".

5.151 Suppose in a schema like that above in No. 5.101 Tr is the number of the "T"'s in the proposition r, Trs the number of those "T"'s in the proposition 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 Trs: Tr.

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