considered by Plato as imperfect and useless, and of no worth. For as
the true end of man according to his philosophy is an assimilation to
divinity, in the greatest perfection of which human nature is capable,
whatever contributes to this is to be ardently pursued; but whatever has
a different tendency, however necessary it may be to the wants and
conveniences of the mere animal life, is comparatively little and vile.
Hence it necessary to pass rapidly from things visible and audible, to
those which are alone seen by the eye of intellect. For the mathematical
sciences, when properly studied, move the inherent knowledge of the soul;
awaken 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