se; it is mere counting: and to carry out the syllogism
is a hollow formality. Accordingly, our definition of Induction excludes
the kind unfortunately called Perfect, by including in the notion of
Induction a reliance on the uniformity of Nature; for this would be
superfluous if every instance in question had been severally examined.
Imperfect Induction, then, is what we have to deal with: the method of
showing the credibility of an universal real proposition by an
examination of _some_ of the instances it includes, generally a small
fraction of them.

Sec. 4. Imperfect Induction is either Methodical or Immethodical. Now,
Method is procedure upon a principle; and if the method is to be precise
and conclusive, the principle must be clear and definite.

There is a Geometrical Method, because the axioms of Geometry are clear
and definite, and by their means, with the aid of definitions, laws are
deduced of the equality of lines and angles and other relations of
position and magnitude in space. The process of proof is purely
Deductive (the axioms and definitions being granted). Diagrams are used
not as facts for observation, but merely to fix our attention in
following the general argument; so that it matters little how badly they
are drawn, as long as their divergence from the conditions of the
proposition to be proved is not distracting. Even the appeal to
"superposition" to prove the equality of magnitudes (as in Euclid I. 4),
is not an appeal to observation, but to our judgment of what is implied
in the foregoing conditions. Hence no inference is required from the
special case to all similar ones; for they are all proved at once.

There is also, as we have seen, a method of Deductive Logic resting on
the Principles of Consistency and the _Dictum de omni et nullo_. And we
shall find that there is a method of Inductive Logic, resting on the
principle of Causation.

But there are a good many general propositions, more or less trustworthy
within a certain range of conditions, which cannot be methodically
proved for want of a precise principle by which they may be tested; and
they, therefore, depend upon Immethodical Induction, that is, upon the
examination of as many instances as can be found, relying for the rest
upon the undefinable principle of the Uniformity of Nature, since we are
not able to connect them with any of its definite modes enumerated in
chap. xiii. Sec. 7. To this subject we shall return in chap. xix.,