th-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.)

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 m