of them, according to vigilant perception." Hence too, as Proclus well
observes, it is evident that the soul does not collect her knowledge from
sensibles, nor from things partial and divisible discover the whole and
the one. For it is not proper to think that things which have in no
respect a real subsistence, should be the leading causes of knowledge to
the soul; and that things which oppose each other and are ambiguous,
should precede science which has a sameness of subsistence; nor that
things which are variously mutable, should be generative of reasons which
are established in unity; nor that things indefinite should be the causes
of definite intelligence. It is not fit, therefore, that the truth of
things eternal should be received from the many, nor the discrimination
of universals from sensibles, nor a judgment respecting what is good from
irrational natures; but it is requisite that the soul entering within
herself, should investigate herself the true and the good, and the
eternal reasons of things.

We have said that discipline awakens the dormant knowledge of
the soul; and Plato considered this as particularly effected by the
mathematical discipline. Hence, he asserts of theoretic arithmetic that
it imparts no small aid to our ascent to real being, and that it
liberates us from the wandering and ignorance about a sensible nature.
Geometry too is considered by him as most instrumental to the knowledge
of the good, when it is not pursued for the sake of practical purposes,
but as the means of ascent to an intelligible essence. Astronomy also is
useful for the purpose of investigating the fabricator of all things,
and contemplating as in most splendid images the ideal world, and its
ineffable cause. And lastly music, when properly studied, is subservient
to our ascent, viz. when from sensible we betake ourselves to the
contemplation of ideal and divine harmony. Unless, however, we thus
employ the mathematical discipline, the study of them is justly