§ 106. The demonstrative method, in order to bring about its proof of
necessity, has a choice of many different ways. But we must not imagine,
either that there are an unlimited number, and that it is only a chance
which one we shall take; or that they have no connection among
themselves, and run, as it were, side by side. It is not, however, the
business of Pedagogics to develop different methods of proof; this
belongs to Logic. We have only to remember that, logically taken, proof
must be analytic, synthetic, or dialectic. Analysis begins with the
single one, and leads out of it by induction to the general principle
from which its existence results. Synthesis, on the contrary, begins
with a general which is presupposed as true, and leads from this through
deduction to the special determinations which were implicit in it. The
regressive search of analysis for a determining principle is
_Invention_; the forward progress of synthesis from the simple elements
seeking for the multiplicity of the single one is _Construction_. Each,
in its result, passes over into the other; but their truth is found in
the dialectic method, which in each phase allows unity to separate into
diversity and diversity to return into unity. While in the analytic as
well as in the synthetic method the mediation of the individual with the
general, or of the general with the individual, lets the phase of
particularity be only subjectively connected with it in the dialectic
method, we have the going over of the general through the particular to
the individual, or to the self-determination of the idea, and it
therefore rightly claims the title of the genetic method. We can also
say that while the inventive method gives us the idea (notion) and the
constructive the judgment, the genetic gives us the syllogism which
leads the determinations of reflection back again into substantial
identity.
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