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All these difficulties follow naturally, when they make the
Ideas out of elements and at the same time claim that apart from the
substances which have the same form there are Ideas, a single separate
entity. But if, e.g. in the case of the elements of speech, the a's
and the b's may quite well be many and there need be no a-itself and
b-itself besides the many, there may be, so far as this goes, an
infinite number of similar syllables. The statement that an
knowledge is universal, so that the principles of things must also
be universal and not separate substances, presents indeed, of all
the points we have mentioned, the greatest difficulty, but yet the
statement is in a sense true, although in a sense it is not. For
knowledge, like the verb 'to know', means two things, of which one
is potential and one actual. The potency, being, as matter,
universal and indefinite, deals with the universal and indefinite; but
the actuality, being definite, deals with a definite object, being a
'this', it deals with a 'this'. But per accidens sight sees
universal colour, because this individual colour which it sees is
colour; and this individual a which the grammarian investigates is
an a. For if the principles must be universal, what is derived from
them must also be universal, as in demonstrations; and if this is
so, there will be nothing capable of separate existence-i.e. no
substance. But evidently in a sense knowledge is universal, and in a
sense it is not.
Book XIV

REGARDING this kind of substance, what we have said must be
taken as sufficient. All philosophers make the first principles
contraries: as in natural things, so also in the case of
unchangeable substances. But since there cannot be anything prior to
the first principle of all things, the principle cannot be the
principle and yet be an attribute of something else. To suggest this
is like saying that the white is a first principle, not qua anything
else but qua white, but yet that it is predicable of a subject, i.e.
that its being white presupposes its being something else; this is
absurd, for then that subject will be prior. But all things which
are generated from their contraries involve an underlying subject; a
subject, then, must be present in the case of contraries, if anywhere.
All contraries, then, are always predicable of a subject, and none can
exist apart, but just as appearances suggest that there is nothing
contrary to substance, argument confirms this. No contrary, then, is
the first principle of all things in the full sense; the first
principle is something different.
But these thinkers make one of the contraries matter, some
making the unequal which they take to be the essence of
plurality-matter for the One, and others making plurality matter for
the One. (The former generate numbers out of the dyad of the
unequal, i.e. of the great and small, and the other thinker we have
referred to generates them out of plurality, while according to both
it is generated by the essence of the One.) For even the philosopher
who says the unequal and the One are the elements, and the unequal
is a dyad composed of the great and small, treats the unequal, or
the great and the small, as being one, and does not draw the
distinction that they are one in definition, but not in number. But
they do not describe rightly even the principles which they call
elements, for some name the great and the small with the One and treat
these three as elements of numbers, two being matter, one the form;
while others name the many and few, because the great and the small
are more appropriate in their nature to magnitude than to number;
and others name rather the universal character common to these-'that
which exceeds and that which is exceeded'. None of these varieties
of opinion makes any difference to speak of, in view of some of the
consequences; they affect only the abstract objections, which these
thinkers take care to avoid because the demonstrations they themselves

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