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being straight' not being of a certain quality, 'not being three
cubits long' not being of a certain quantity. What sort of being and
non-being, then, by their union pluralize the things that are? This
thinker means by the non-being the union of which with being
pluralizes the things that are, the false and the character of
falsity. This is also why it used to be said that we must assume
something that is false, as geometers assume the line 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

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