Taylor - Theoretic Arithmetic.pdf - Platonic Philosophy

XX
INTRODUCTION
utility it administers to human concerns. If, however, it be
requisite to refer its utility to something else, it must be referred
to intellectual knowledge. For it leads us to this, and prepares
the eye of the soul for the knowledge of incorporeal
wholes, purifying it, and removing the impediments arising
from sensible objects. As therefore, we do not say that the
whole of cathartic or purifying virtue is useful, or the contrary,
looking to the utility of the sensible life, but regarding the
advantage of the contemplative life; thus also it is fit to refer
the end of the mathematical science to intellect, and the whole
of wisdom. Hence, the energy about it, deserves our most
serious attention, both on its own account, and on account of
an intellectual life.
It is also manifest, as Aristotle says, that this science is desirable
of itself to its votaries, because, though no reward was
proposed to its investigators, yet, in a short time, the mathematical
theory has received such an abundant increase. Besides,
all men who have in the smallest degree experienced its utility,
are willingly employed in its pursuit, and are desirous of being
at leisure for this purpose, omitting every other concern.
Hence, those who despise the knowledge of the mathematics,
have not tasted of the pleasures they contain. The mathematical
science, therefore, is not to be despised, because its thee
retic part does not contribute to human utility; for its ultimate
progressions, and such as energize in conjunction with matter,
consider as their end an advantage of this kind; but on the
contrary we should admire its immateriality, and the good
which it contains in itself alone. For in short, when men
were entirely disengaged from the care of necessary concerns,
they converted themselves to the investigation of the mathematical
disciplines; and this indeed, with the greatest propriety.
For things by which we are nourished, and which are connascent
with sensible objects, first employed the attention of man-