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greater and the less, it will be contrary to more things than one. But
if the unequal means the same as both the greater and the less
together, the equal will be opposite to both (and the difficulty
supports those who say the unequal is a 'two'), but it follows that
one thing is contrary to two others, which is impossible. Again, the
equal is evidently intermediate between the great and the small, but
no contrariety is either observed to be intermediate, or, from its
definition, can be so; for it would not be complete if it were
intermediate between any two things, but rather it always has
something intermediate between its own terms.
It remains, then, that it is opposed either as negation or as
privation. It cannot be the negation or privation of one of the two;
for why of the great rather than of the small? It is, then, the
privative negation of both. This is why 'whether' is said with
reference to both, not to one of the two (e.g. 'whether it is
greater or equal' or 'whether it is equal or less'); there are
always three cases. But it is not a necessary privation; for not
everything which is not greater or less is equal, but only the
things which are of such a nature as to have these attributes.
The equal, then, is that which is neither great nor small but is
naturally fitted to be either great or small; and it is opposed to
both as a privative negation (and therefore is also intermediate). And
that which is neither good nor bad is opposed to both, but has no
name; for each of these has several meanings and the recipient subject
is not one; but that which is neither white nor black has more claim
to unity. Yet even this has not one name, though the colours of
which this negation is privatively predicated are in a way limited;
for they must be either grey or yellow or something else of the
kind. Therefore it is an incorrect criticism that is passed by those
who think that all such phrases are used in the same way, so that that
which is neither a shoe nor a hand would be intermediate between a
shoe and a hand, since that which is neither good nor bad is
intermediate between the good and the bad-as if there must be an
intermediate in all cases. But this does not necessarily follow. For
the one phrase is a joint denial of opposites between which there is
an intermediate and a certain natural interval; but between the
other two there is no 'difference'; for the things, the denials of
which are combined, belong to different classes, so that the
substratum is not one.
6

We might raise similar questions about the one and the many. For
if the many are absolutely opposed to the one, certain impossible
results follow. One will then be few, whether few be treated here as
singular or plural; for the many are opposed also to the few. Further,
two will be many, since the double is multiple and 'double' derives
its meaning from 'two'; therefore one will be few; for what is that in
comparison with which two are many, except one, which must therefore
be few? For there is nothing fewer. Further, if the much and the
little are in plurality what the long and the short are in length, and
whatever is much is also many, and the many are much (unless,
indeed, there is a difference in the case of an easily-bounded
continuum), the little (or few) will be a plurality. Therefore one
is a plurality if it is few; and this it must be, if two are many. But
perhaps, while the 'many' are in a sense said to be also 'much', it is
with a difference; e.g. water is much but not many. But 'many' is
applied to the things that are divisible; in the one sense it means
a plurality which is excessive either absolutely or relatively
(while 'few' is similarly a plurality which is deficient), and in
another sense it means number, in which sense alone it is opposed to
the one. For we say 'one or many', just as if one were to say 'one and
ones' or 'white thing and white things', or to compare the things that
have been measured with the measure. It is in this sense also that
multiples are so called. For each number is said to be many because it

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