science, which previously fabricates for itself definite principles, from
which it evinces things consequent to such principles, does not tend to
the principle, but to the conclusion. Hence Plato does not expel
mathematical knowledge from the number of the sciences, but asserts it to
be the next in rank to that one science which is the summit of all; nor
does he accuse it as ignorant of its own principles, but considers it as
receiving these from the master science dialectic, and that possessing
them without any demonstration, it demonstrates from these its consequent
propositions.

Hence Socrates, in the Republic, speaking of the power of dialectic,
says that it surrounds all disciplines like a defensive enclosure, and
elevates those that use it to the good itself, and the first unities;
that it purifies the eye of the soul; establishes itself in true beings,
and, the one principle of all things, and ends at last in that which is
no longer hypothetical. The power of dialectic, therefore, being thus
great, and the ends of this path so mighty, it must by no means be
confounded with arguments which are alone conversant with opinion: for
the former is the guardian of sciences, and the passage to it is through
these, but the latter is perfectly destitute of disciplinative science.
To which we may add, that the method of reasoning which is founded in
opinion, regards only that which is apparent; but the dialectic method
endeavors to arrive at the one itself, always employing for this purpose
steps of ascent, and at last beautifully ends in the nature of the good.
Very different therefore is it from the merely logical method, which
presides over the demonstrative phantasy, is of a secondary nature, and
is alone pleased with contentious discussions. For the dialectic of Plato
for the most part employs divisions and analyses as primary sciences, and
as imitating the progression of beings from the one, and their conversion
to it again. It likewise sometimes uses definitions and demonstrations,