38 THE FACTORS OF THE MIND

characteristics. With a certain degree of probability,
which will increase not only with the number, but also with
the variety of the samples, he will then be justified in
generalizing from the instances examined to all instances,
examined and unexamined alike.

In such an argument, it will be seen, the cogency of the
final conclusion does not depend, as is popularly supposed,
on merely increasing the amount of agreement in the
relevant factors—the c positive analogy,'l as it has been
called. It depends far more on increasing what has been
called the ' negative analogy,'1 that is to say, on diminishing
the points of agreement2 that are to be ignored in the
conclusion, and so increasing the amount of difference in
all irrelevant factors. This may mean formally disproving
the chief rival explanations in special sections of the re-
search ; or it may mean planning the main research so that
the rival factors have no room to operate. In either case—
maior est vis instantiae negativae.

I do not suggest that this full procedure is always
indispensable. Different generalizations have different
antecedent probabilities, and so require different ranges of
favourable a posteriori evidence to attain an acceptable
degree of final probability. As we shall show in a moment,
some appeal to the a priori probabilities is inevitable.
Here, as we have already noted, our investigator, by his
initial claim that his hypothesis is * revolutionary,' and at
first sight ' scarcely credible,' has really made a convincing

1 These terms are introduced by J. M. Keynes [43], pp. 223 et stq* The
principles proposed would be clearer if, in addition to distinguishing, as his
terminology does, between (A) the positive and (B) the negative, and be-
tween (i) the total and (2) the known analogies, we also adopted technical
names for (a) the relevant and (£) the irrelevant analogies; and then, within
the relevant, known, positive analogy, distinguished between (i) the implying
or diagnostic analogy (Mill's c cause') and (ii) the implied or inferable analogy
(Mill's * phenomenon ' regarded as an ' effect'),

2 Points of agreement, it should be added, common not only to the entire
group, but also to sub-groups. The plausibility of the criticisms advanced
by Thomson and Thurstone against the advocates of a single general
factor largely depends on the fact that investigators, who may seem to
have eliminated all but one factor common to the entire group, do not
exclude the influence of a mixed set of (sub-) group-factors.