[Footnote 1: See De Morgan's _Essay on Probabilities_, c. vi.,
"On Common Notions of Probability".]

CHAPTER IX.

PROBABLE INFERENCE TO PARTICULARS--THE MEASUREMENT OF PROBABILITY.

Undoubtedly there are degrees of probability. Not only do we expect
some events with more confidence than others: we may do so, and our
confidence may be misplaced: but we have reason to expect some with
more confidence than others. There are different degrees of rational
expectation. Can those degrees be measured numerically?

The question has come into Logic from the mathematicians. The
calculation of Probabilities is a branch of Mathematics. We have seen
how it may be applied to guide investigation by eliminating what is
due to chance, and it has been vaguely conceived by logicians that
what is called the calculus of probabilities might be found useful
also in determining by exact numerical measurement the probability
of single events. Dr. Venn, who has written a separate treatise on the
Logic of Chance, mentions "accurate quantitative apportionment of our
belief" as one of the goals which Logic should strive to attain. The
following passage will show his drift.[1]

A man in good health would doubtless like to know whether he
will be alive this time next year. The fact will be settled
one way or the other in due time, if he can afford to wait,
but if he wants a present decision, Statistics and the Theory
of Probability can alone give him any information. He learns
that the odds are, say five to one that he will survive, and
this is an answer to his question as far as any answer can be
given. Statisticians are gradually accumulating a vast mass of
data of this general character. What they may be said to aim
at is to place us in the position of being able to say, in any
given time or place, what are the odds for or against any at
present indeterminable fact which belongs to a class admitting
of statistical treatment.

Again, outside the regions of statistics proper--which
deal, broadly speaking, with events which can be numbered or
measured, and which occur with some frequency--there is still
a large field as to which some better approach to a reasoned
intensity of belief can be acquired. What will be the issue of
a coming war? Which party will win in the next election? Will
a patient in the crisis of a given disease recover or not?
Tha