46	THE  FACTORS OF THE MIND
probability than an ^c induction' or a ' deduction ' resting
on an ' induction.'
The Relative Probabilities of Inductions and Eductions.—
To the student this point will doubtless be clearer if he
compares (a] the inductive-deductive procedure with
(b) the eductive at three stages of increasing difficulty :
(l) for verbal arguments of the traditional ^c class type/
based on complete generalizations ; (2) for statistical
arguments of the * attribute type,' based on proportions or
probabilities ; and finally (3) for statistical arguments of
the ^c variable type ' based on regressions.
(1)	In their simplest forms the two modes of reasoning
would follow some such schemes as these :
(a) Inductive-Deductive,—The samples examined show
that " (i) All children who succeed in this test are intelligent,
(ii) All children who are intelligent will gain scholarships."
But " (iii) Individual i has succeeded in this test* There-
fore, (iv) being intelligent, he will gain a scholarship."
(£) Eductive.—The sample examined shows that ^<£ (i)
the children who do well in this test will gain a scholar-
ship." But " (ii) i has succeeded in this test. Therefore,
(iii) he will gain a scholarship."
Is it not obvious that an appeal to premiss b (i) affords
a safer ground for the common conclusion than a twofold
appeal to premisses a (i) and a (ii) ? What woman, instead
of trying on a new hat at first hand, would be content to
send her dress to the milliner, and argue, " my dress matches
my complexion ; the hat matches my dress; therefore the
hat must match my complexion " ? Even the carpenter
who carries a foot-rule prefers to make a direct comparison,
instead of trusting to Euclid's first axiom.
(2)	But in an empirical science our initial observations
can hardly ever be comprised in complete and sweeping
generalizations.    Hence, instead of using categorical argu-
ments of the traditional type, we must fall back on statistical
arguments in terms of frequencies or probabilities.    At
this level, our premisses will take the form :   (i) Judging
by our sample, ^a Such and such a proportion of the children,
who succeed in the test will prove to be intelligent *^9 ;
from which we deduce, (ii) " if i has succeeded, the proba-