indeed, for the
purpose of discovering this Law that Observation, Classification, and
Induction are undertaken. It has been the triumphant boast of the
Inductive Method, that it guarded, by means of these preliminary steps,
in the most careful manner, against error in establishing its Laws. To
the extent of its capacity it has done so. But we have already seen,
that deriving its Principles, as it was obliged to, from less than _all_
the Facts which appertained to the Principles, these must inevitably
have been lacking in some particulars; it being impossible to make the
whole out of less than all its parts.

The Inductive Method has obtained an importance greatly exaggerated, for
the reason that it has been brought into comparison, for the most part,
with the Anticipative or Hypothetical, the bastard Deductive Method
only, and its superiority over this exhibited in the most detailed
manner, while the right application of the Deductive Method, except in
Mathematics, has not been considered possible. The reason of this can be
made obvious.

The immense superiority of _Mathematical_ Reasoning, as _Demonstration_
is often called, over all other kinds, is universally known and
recognized. For in this mode of reasoning there is no room for doubt or
uncertainty. It starts from Principles of whose truth there can be no
doubt, because it is impossible for _the human mind to apprehend them in
more than one way_, and proceeds by steps, every one of which can
likewise be apprehended in only one way. Hence all men arrive
_inevitably_ at the same conclusion at the close of the chain of
reasoning. It is, therefore, a Method of proof which sets out from a
precise, definite, universally established Law or Principle which really
contains the conclusion in itself, and which can be developed to the end
through a series of necessary and irresistible convincements; while in
the Inductive Method we are obliged to start from this or that admitted
Fact or Truth assumed after Observation, Classification, and Induction,
which may have been rigorously performed, but which, nevertheless, could
not, in the nature of the case, prove the Fact or Truth with complete
certainty, and which is not, perhaps, universally admitted, and proceed
by merely probable inferences drawn from various, diverse, and often
uncertain relations, until we reach a conclusion. Such reasoning may be
sufficient to incline the mind to a particular conclusion, as against
those