" In endeavouring, therefore, to fix the degree of
strictly formal probability that is present in any given case, our method
of procedure should be, first to ascertain the ultimate ratios on which the
probability depends, and then to estimate the comparative value of these
ratios. Now I think there can be no doubt that the value of any probability
in this its last analysis is determined by the number, the importance, and
the definiteness of the relations known, as compared with those of the
relations unknown; and, consequently, that in all cases where the sum of
the unknown relations is larger, or more important, or more indefinite than
is the sum of the known relations, it is an essential principle that the
value of the probability decreases in exact proportion to the decrease in
the similarity between the two sets of relations, whether this decrease
consists in the number, in the importance, or in the definiteness of the
relations involved. This rule or canon is self-evident as soon as pointed
out, and has been formulated by Professor Bain in his "Logic" when treating
of Analogy, but not with sufficient precision; for, while recognising the
elements of number and importance, he has overlooked that of definiteness.
This element, however, is a very essential one--indeed the most essential
of the three; for there are many analogical inferences in which either the
character or the extent of the unknown relations is quite indefinite; and
it is obvious that, whenever this is the case, the value of the analogy is
proportionably diminished, and diminished in a much more material
particular than it is when the diminution of value arises from a mere
excess of the unknown relations over the known ones in respect of their
number or of their importance.
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