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| Pythagoras' Duality of Substances; His “Categories.”
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Chapter
XIX.—Pythagoras’ Duality of Substances; His
“Categories.”
There are, then, according to Pythagoras, two
worlds: one intelligible, which has the monad for an originating
principle; and the other sensible. But of this (latter) is the
quaternion having the iota, the one tittle,656
a perfect number. And there likewise
is, according to the Pythagoreans, the i, the one tittle, which
is chief and most dominant, and enables us to apprehend the substance
of those intelligible entities which are capable of being understood
through the medium of intellect and of sense. (And in this
substance inhere) the nine incorporeal accidents which cannot exist
without substance, viz., “quality,” and
“quantity,” and “relation,” and
“where,” and “when,” and
“position,” and “possession,” and
“action,” and “passion.” These, then, are
the nine accidents (inhering in) substance, and when reckoned with
these (substances), contains the perfect number, the i.
Wherefore, the universe being divided, as we said, into the
intelligible and sensible world, we have also reason from the
intelligible (world), in order that by reason we may behold the
substance of things that are cognised by intellect, and are incorporeal
and divine. But we have, he says, five senses—smelling,
seeing, hearing, taste, and touch. Now, by these we arrive at a
knowledge of things that are discerned by sense; and so, he says, the
sensible is divided from the intelligible world. And that we have
for each of these an instrument for attaining knowledge, we perceive
from the following consideration. Nothing, he says, of
intelligibles can be known
to us from sense. For he says neither eye has seen, nor ear
heard, nor any whatsoever of the other senses known that (which is
cognised by mind). Neither, again, by reason is it possible to
arrive at a knowledge of any of the things discernible by sense.
But one must see that a thing is white, and taste that it is sweet, and
know by hearing that it is musical or out of tune. And whether
any odour is fragrant or disagreeable, is the function of smell, not of
reason. It is the same with objects of touch; for anything rough,
or soft, or warm, or cold, it is not possible to know by hearing, but
(far from it), for touch is the judge of such (sensations).
Things being thus constituted, the arrangement of things that have been
made and are being made is observed to happen in conformity with
numerical (combinations). For in the same manner as, commencing
from monad, by an addition of monads or triads, and a collection of the
succeeding numbers, we make some one very large complex whole of
number; (and) then, again, from an amassed number thus formed by
addition, we accomplish, by means of a certain subtraction and
re-calculation, a solution of the totality of the aggregate numbers; so
likewise he asserts that the world, bound by a certain arithmetical and
musical chain, was, by its tension and relaxation, and by addition and
subtraction, always and for ever preserved incorrupt.E.C.F. INDEX & SEARCH
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