5.153 In itself, a proposition is neither probable nor improbable. Either
an event occurs or it does not: there is no middle way.


5.154 Suppose that an urn contains black and white balls in equal numbers
(and none of any other kind). I draw one ball after another, putting them
back into the urn. By this experiment I can establish that the number of
black balls drawn and the number of white balls drawn approximate to one
another as the draw continues. So this is not a mathematical truth. Now, if
I say, 'The probability of my drawing a white ball is equal to the
probability of my drawing a black one', this means that all the
circumstances that I know of (including the laws of nature assumed as
hypotheses) give no more probability to the occurrence of the one event
than to that of the other. That is to say, they give each the probability
1/2 as can easily be gathered from the above definitions. What I confirm by
the experiment is that the occurrence of the two events is independent of
the circumstances of which I have no more detailed knowledge.


5.155 The minimal unit for a probability proposition is this: The
circumstances--of which I have no further knowledge--give such and such a
degree of probability to the occurrence of a particular event.


5.156 It is in this way that probability is a generalization. It involves a
general description of a propositional form. We use probability only in
default of certainty--if our knowledge of a fact is not indeed complete,
but we do know something about its form. (A proposition may well be an
incomplete picture of a certain situation, but it is always a complete
picture of something .) A probability proposition is a sort of excerpt from