HOME TOP UP PREV NEXT 1 2 3 4 5 6 GERMAN MAP Tractatus Logico-Philosophicus 5.15
Two elementary propositions give to one another the probability 1/2.
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.)
So this is not a mathematical fact.
If then, I say, It is equally probable that I should d raw a white and a black ball, this means, All the circumstances known to me (including the natural laws hypothetically assumed) give to the occurrence of the one event no more probability than to the occurrence of the other. That is they give -- as can easily be understood from the above explanations -- to each the probability 1/2.
What I can verify by the experiment is that the occurrence of the two events is independent of the circumstances with which I have no closer acquaintance.
It involves a general description of a propositional form. Only in default of certainty do we need probability.
If we are not completely acquainted with a fact, but know something about its form.
(A proposition can, indeed, be an incomplete picture of a certain state of affairs, but it is always a complete picture.)
The probability proposition is, as it were, an extract from other propositions.