The Complete Aristotle (eng.)

which is not
a foot long to be a foot long. But this cannot be so. For neither
do geometers assume anything false (for the enunciation is
extraneous to the inference), nor is it non-being in this sense
that the things that are are generated from or resolved into. But
since ‘non-being’ taken in its various cases has as many senses as
there are categories, and besides this the false is said not to be,
and so is the potential, it is from this that generation proceeds,
man from that which is not man but potentially man, and white from
that which is not white but potentially white, and this whether it
is some one thing that is generated or many.
    The question evidently is, how being, in the sense of ‘the
substances’, is many; for the things that are generated are numbers
and lines and bodies. Now it is strange to inquire how being in the
sense of the ‘what’ is many, and not how either qualities or
quantities are many. For surely the indefinite dyad or ‘the great
and the small’ is not a reason why there should be two kinds of
white or many colours or flavours or shapes; for then these also
would be numbers and units. But if they had attacked these other
categories, they would have seen the cause of the plurality in
substances also; for the same thing or something analogous is the
cause. This aberration is the reason also why in seeking the
opposite of being and the one, from which with being and the one
the things that are proceed, they posited the relative term (i.e.
the unequal), which is neither the contrary nor the contradictory
of these, and is one kind of being as ‘what’ and quality also
are.
    They should have asked this question also, how relative terms
are many and not one. But as it is, they inquire how there are many
units besides the first 1, but do not go on to inquire how there
are many unequals besides the unequal. Yet they use them and speak
of great and small, many and few (from which proceed numbers), long
and short (from which proceeds the line), broad and narrow (from
which proceeds the plane), deep and shallow (from which proceed
solids); and they speak of yet more kinds of relative term. What is
the reason, then, why there is a plurality of these?
    It is necessary, then, as we say, to presuppose for each thing
that which is it potentially; and the holder of these views further
declared what that is which is potentially a ‘this’ and a substance
but is not in itself being-viz. that it is the relative (as if he
had said ‘the qualitative’), which is neither potentially the one
or being, nor the negation of the one nor of being, but one among
beings. And it was much more necessary, as we said, if he was
inquiring how beings are many, not to inquire about those in the
same category-how there are many substances or many qualities-but
how beings as a whole are many; for some are substances, some
modifications, some relations. In the categories other than
substance there is yet another problem involved in the existence of
plurality. Since they are not separable from substances, qualities
and quantities are many just because their substratum becomes and
is many; yet there ought to be a matter for each category; only it
cannot be separable from substances. But in the case of ‘thises’,
it is possible to explain how the ‘this’ is many things, unless a
thing is to be treated as both a ‘this’ and a general character.
The difficulty arising from the facts about substances is rather
this, how there are actually many substances and not one.
    But further, if the ‘this’ and the quantitative are not the
same, we are not told how and why the things that are are many, but
how quantities are many. For all ‘number’ means a quantity, and so
does the ‘unit’, unless it means a measure or the quantitatively
indivisible. If, then, the quantitative and the ‘what’ are
different, we are not told whence or how the ‘what’ is many; but if
any one says they are the same, he has to face many
inconsistencies.
    One might fix one’s attention also on the question, regarding
the numbers, what justifies the belief that they exist. To the
believer in Ideas they provide some sort of cause for existing
things, since each number is an Idea, and the Idea is to other
things somehow or other the cause of their being; for let this
supposition be granted them. But as for him who does not hold this
view because he sees the inherent objections to the Ideas (so that
it is not for this reason that