t statistics are lying here in the background, and are thus
indirectly efficient in producing and graduating our belief, I
fully hold; but there is such a large intermediate process
of estimating, and such scope for the exercise of a practised
judgment, that no direct appeal to statistics in the common
sense can directly help us. In sketching out therefore the
claims of an Ideal condition of knowledge, we ought clearly to
include a due apportionment of belief to every event of such
a class as this. It is an obvious defect that one man should
regard as almost certain what another man regards as almost
impossible. Short, therefore, of certain prevision of the
future, we want complete agreement as to the degree of
probability of every future event: and for that matter of
every past event as well.

Technically speaking, if we extend the name Modality (see p. 78) to
any qualification of the certainty of a statement of belief, what Dr.
Venn here desiderates, as he has himself suggested, is a more exact
measurement of the Modality of propositions. We speak of things as
being certain, possible, impossible, probable, extremely probable,
faintly probable, and so forth: taking certainty as the highest
degree of probability[2] shading gradually down to the zero of
the impossible, can we obtain an exact numerical measure for the
gradations of assurance?

To examine the principles of all the cases in which chances for and
against an occurrence have been calculated from real or hypothetical
data, would be to trespass into the province of Mathematics, but a few
simple cases will serve to show what it is that the calculus attempts
to measure, and what is the practical value of the measurement as
applied to the probability of a single event.

Suppose there are 100 balls in a box, 30 white and 70 black, all being
alike except in respect of colour, we say that the chances of drawing
a black ball as against a white are as 7 to 3, and the probability of
drawing black is measured by the fraction 7/10. In believing this we
proceed on the principle already explained (p. 356) of Proportional
Chances. We do not know for certain whether black or white will
emerge, but knowing the antecedent situation we expect black rather
than white with a degree of assurance corresponding to the proportions
of the two in the box. It is our degree of rational assurance that
we measure by this fraction, and t