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. For it is evident that, in the latter case,
however little value the analogy may possess, the exact degree of such
value admits of being _determined_; while it is no less evident that, in
the former case, we are precluded from estimating the value of the analogy
at all, and this just in proportion to the indefiniteness of the unknown
relations.

Sec. 38. Now the particular instance with which we are concerned is somewhat
peculiar. Notwithstanding we have the entire sphere of human experience
from which to argue, we are still unable to gauge the strictly logical
probability of any argument whatsoever; for the unknown relations in this
case are so wholly indefinite, both as to their character and extent, that
any attempt to institute a definite comparison between them and the known
relations is felt at once to be absurd. The question discussed, being the
most ultimate of all possible questions, must eventually contain in itself
all that is to man unknown and unknowable; the whole orbit of human
knowledge is here insufficient to obtain a parallax whereby to institute
the required measurements.

Sec. 39. I think it is desirable to insist upon this truth at somewhat greater
length, and, for the sake of impressing it still more deeply, I shall
present it in another form. No one can for a single moment deny that,
beyond and around the sphere of the Knowable, there exists the unfathomable
abyss of the Unkn