VARIOUS USES OF FACTORS 35

fallacy will be perpetrated. Our student's contention
would then reduce itself to this : " the a posteriori verifica-
tion of a consequence deducible from my hypothesis (or
' theory/ as he calls it) appreciably increases the probability
of a hypothesis that was already probable a priori" Note
that in such an argument the final probability must depend
on three things x : (i) the relatively high a priori probability
of the hypothesis to be proved ; (ii) the number of inde-
pendent conclusions that can be deduced from it in advance
and verified by experiment; (iii) the relatively low a priori
probability of those conclusions. The last point is con-
stantly overlooked or misunderstood. To argue, as our
investigator does/that the "hypothesis is improbable a priori
reduces the probability of the final conclusion. To argue
that the deducible consequences were improbable a priori
would increase its probability. We tend to believe a
speculative theory, not because it is surprising in itself,
but because it explains, or enables us to predict, facts that
would otherwise surprise us.

(2) The categorical syllogism could be validated if we
could add the premiss : " all school children owe their
progress to the same cause." Once again this is the kind of
sweeping assumption that most naive thinkers make, until
its obvious inaccuracy is pointed out. Later on, however,
we shall see reason to suppose that the assumption contains
a larger element of truth than the stickler for formalities
usually realizes. It implies a belief in homogeneous
populations—natural kinds, natural types, and the like.
Such a belief, no doubt, is untenable in its primitive form.
Nevertheless, some such postulate is essential to all attempts
to generalize from experience.2 And once again we can in

1 The c criteria of problematic inference ? are fully discussed by Keynes,
Broad, and Johnson in the volumes cited below.

2 This requirement is seen most clearly in an important type of inductive
argument which is rarely considered, viz. generalization from a single speci-
men. The physicist will argue : " All gold has the same atomic weight j this
specimen has an atomic weight of 197 : therefore all gold has that weight."
And, as I have already remarked, if he goes on to repeat his test with other
specimens, it is rather to eliminate experimental errors than to extend the
enumeration on which his induction is based. Ab uno disce omnes. But
why does this apply to the weight of gold, but not to the colour of swans or