applied to
Mathematics, the Inductive stage is so short and so slight that it is
performed instinctively by all people and the Deductive stage at once
reached. The other branch of the Hypothetical Method, that used by
Aristotle and the Greek Scientists, was, as we have seen, in reality a
first and imperfect attempt to use the Inductive Method. In this Method
itself, on the other hand, the main Process is the _Induction_ or
derivation of a Principle or Law from accumulated Facts, while
_Deduction_, or the bringing in of new Facts under the Law, is a
subordinate or Secondary Process.

In reality, there is but ONE Method, having several stages or
_Processes_, which Processes, preponderating at different epochs, have
not been clearly apprehended as necessary complements of each other, and
have, hence, been regarded as different Methods. In one phase of the
Anticipative or Hypothetical stage,--the assumption of basic Principles
as points to reason from,--the Observation and Collection of Facts, and
the Induction therefrom, were processes so imperfectly performed, that
they appeared to have no existence; in another phase, that employed by
Aristotle, these Processes were apparent, but still imperfectly
conducted, and hence, in both cases, the Law or Principle employed for
the _Deductive_ Process was liable to be defective, and therefore
insufficient as a guide to the acquisition of certain knowledge. In the
Inductive stage or Method, on the other hand, the Processes thus
defectively employed in the former stage, the Hypothetical, are
preeminently and disproportionately active, while the Deductive Process
is given a very inferior position. The establishment of the just,
reciprocal activity of these two Processes in intellectual investigation
would secure the perfection of the _one true Scientific Method_.

The Inductive Method--preserving the term Method to avoid confusion--in
which the mode of procedure from Facts to Principles predominates, and
which is hence sometimes called the Empirical, or the Experimental, or
the Positive, or the _a posteriori_ Method, is that which now prevails
in the world, which is extolled as if it were the only legitimate
Method, and the only possible route to Scientific Discovery. That the
just claims of the Inductive Method are very great is universally
admitted, but let us not stultify ourselves by assuming a position in
its defence which is in direct violation of the teachings of the Method
i