its intelligence; purify its dianoetic power; call forth its
essential forms from their dormant retreats; remove that oblivion and
ignorance which are congenial with our birth; and dissolve the bonds
arising from our union with an irrational nature. It is therefore
beautifully said by Plato in the 7th book of his Republic, "that the soul
through these disciplines has an organ purified and enlightened, which is
blinded and buried by studies of a different kind, an organ better worth
saving than ten thousand eyes, since truth becomes visible through this
alone."

Dialectic, however, or the vertex of the mathematical sciences,
as it is called by Plato in his Republic, is that master discipline which
particularly leads us up to an intelligible essence. Of this first of
sciences, which is essentially different from vulgar logic, and is the
same with what Aristotle calls the first philosophy and wisdom, I have
largely spoken in the introduction and notes to the Parmenides. Suffice
it therefore to observe in this place, that dialectic differs from
mathematical science in this, that the latter flows from, and the former
is void of hypothesis. That dialectic has a power of knowing universals;
that it ascends to good and the supreme cause of all; and, that it
considers good as the end of its elevation; but that the mathematical
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 alo