The Complete Aristotle (eng.)

but they do not; for ‘double’ and ‘a
multiple of’ do not signify the same thing.
    Inquire also not only if some impossible consequence results
directly from the statement made, that A and B are the same, but
also whether it is possible for a supposition to bring it about; as
happens to those who assert that ‘empty’ is the same as ‘full of
air’: for clearly if the air be exhausted, the vessel will not be
less but more empty, though it will no longer be full of air. So
that by a supposition, which may be true or may be false (it makes
no difference which), the one character is annulled and not the
other, showing that they are not the same.
    Speaking generally, one ought to be on the look-out for any
discrepancy anywhere in any sort of predicate of each term, and in
the things of which they are predicated. For all that is predicated
of the one should be predicated also of the other, and of whatever
the one is a predicate, the other should be a predicate of it as
well.
    Moreover, as ‘sameness’ is a term used in many senses, see
whether things that are the same in one way are the same also in a
different way. For there is either no necessity or even no
possibility that things that are the same specifically or
generically should be numerically the same, and it is with the
question whether they are or are not the same in that sense that we
are concerned.
    Moreover, see whether the one can exist without the other; for,
if so, they could not be the same.
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2
    Such is the number of the commonplace rules that relate to
‘sameness’. It is clear from what has been said that all the
destructive commonplaces relating to sameness are useful also in
questions of definition, as was said before:’ for if what is
signified by the term and by the expression be not the same,
clearly the expression rendered could not be a definition. None of
the constructive commonplaces, on the other hand, helps in the
matter of definition; for it is not enough to show the sameness of
content between the expression and the term, in order to establish
that the former is a definition, but a definition must have also
all the other characters already announced.
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3
    This then is the way, and these the arguments, whereby the
attempt to demolish a definition should always be made. If, on the
other hand, we desire to establish one, the first thing to observe
is that few if any who engage in discussion arrive at a definition
by reasoning: they always assume something of the kind as their
starting points-both in geometry and in arithmetic and the other
studies of that kind. In the second place, to say accurately what a
definition is, and how it should be given, belongs to another
inquiry. At present it concerns us only so far as is required for
our present purpose, and accordingly we need only make the bare
statement that to reason to a thing’s definition and essence is
quite possible. For if a definition is an expression signifying the
essence of the thing and the predicates contained therein ought
also to be the only ones which are predicated of the thing in the
category of essence; and genera and differentiae are so predicated
in that category: it is obvious that if one were to get an
admission that so and so are the only attributes predicated in that
category, the expression containing so and so would of necessity be
a definition; for it is impossible that anything else should be a
definition, seeing that there is not anything else predicated of
the thing in the category of essence.
    That a definition may thus be reached by a process of reasoning
is obvious. The means whereby it should be established have been
more precisely defined elsewhere, but for the purposes of the
inquiry now before us the same commonplace rules serve. For we have
to examine into the contraries and other opposites of the thing,
surveying the expressions used both as wholes and in detail: for if
the opposite definition defines that opposite term, the definition
given must of necessity be that of the term before us. Seeing,
however, that contraries may be conjoined in more than one way, we
have to select from those contraries the one whose contrary
definition seems most obvious. The expressions, then, have to be
examined each as a whole in the way we have said, and also in
detail as follows. First of all, see that the genus rendered is
correctly rendered; for if the