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figures, and the one would have been the triangle. And the same
argument applies to all other classes. Since, therefore, while there
are numbers and a one both in affections and in qualities and in
quantities and in movement, in all cases the number is a number of
particular things and the one is one something, and its substance is
not just to be one, the same must be true of substances also; for it
is true of all cases alike.
That the one, then, in every class is a definite thing, and in
no case is its nature just this, unity, is evident; but as in
colours the one-itself which we must seek is one colour, so too in
substance the one-itself is one substance. That in a sense unity means
the same as being is clear from the facts that its meanings correspond
to the categories one to one, and it is not comprised within any
category (e.g. it is comprised neither in 'what a thing is' nor in
quality, but is related to them just as being is); that in 'one man'
nothing more is predicated than in 'man' (just as being is nothing
apart from substance or quality or quantity); and that to be one is
just to be a particular thing.

The one and the many are opposed in several ways, of which one
is the opposition of the one and plurality as indivisible and
divisible; for that which is either divided or divisible is called a
plurality, and that which is indivisible or not divided is called one.
Now since opposition is of four kinds, and one of these two terms is
privative in meaning, they must be contraries, and neither
contradictory nor correlative in meaning. And the one derives its name
and its explanation from its contrary, the indivisible from the
divisible, because plurality and the divisible is more perceptible
than the indivisible, so that in definition plurality is prior to
the indivisible, because of the conditions of perception.
To the one belong, as we indicated graphically in our
distinction of the contraries, the same and the like and the equal,
and to plurality belong the other and the unlike and the unequal. 'The
same' has several meanings; (1) we sometimes mean 'the same
numerically'; again, (2) we call a thing the same if it is one both in
definition and in number, e.g. you are one with yourself both in
form and in matter; and again, (3) if the definition of its primary
essence is one; e.g. equal straight lines are the same, and so are
equal and equal-angled quadrilaterals; there are many such, but in
these equality constitutes unity.
Things are like if, not being absolutely the same, nor without
difference in respect of their concrete substance, they are the same
in form; e.g. the larger square is like the smaller, and unequal
straight lines are like; they are like, but not absolutely the same.
Other things are like, if, having the same form, and being things in
which difference of degree is possible, they have no difference of
degree. Other things, if they have a quality that is in form one and
same-e.g. whiteness-in a greater or less degree, are called like
because their form is one. Other things are called like if the
qualities they have in common are more numerous than those in which
they differ-either the qualities in general or the prominent
qualities; e.g. tin is like silver, qua white, and gold is like
fire, qua yellow and red.
Evidently, then, 'other' and 'unlike' also have several
meanings. And the other in one sense is the opposite of the same (so
that everything is either the same as or other than everything
else). In another sense things are other unless both their matter
and their definition are one (so that you are other than your
neighbour). The other in the third sense is exemplified in the objects
of mathematics. 'Other or the same' can therefore be predicated of
everything with regard to everything else-but only if the things are
one and existent, for 'other' is not the contradictory of 'the
same'; which is why it is not predicated of non-existent things (while

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