The Complete Aristotle (eng.)

contrary thing be found in the
contrary genus to that stated in the definition, and the thing
before you is not in that same genus, then it would clearly be in
the contrary genus: for contraries must of necessity be either in
the same genus or in contrary genera. The differentiae, too, that
are predicated of contraries we expect to be contrary, e.g. those
of white and black, for the one tends to pierce the vision, while
the other tends to compress it. So that if contrary differentiae to
those in the definition are predicated of the contrary term, then
those rendered in the definition would be predicated of the term
before us. Seeing, then, that both the genus and the differentiae
have been rightly rendered, clearly the expression given must be
the right definition. It might be replied that there is no
necessity why contrary differentiae should be predicated of
contraries, unless the contraries be found within the same genus:
of things whose genera are themselves contraries it may very well
be that the same differentia is used of both, e.g. of justice and
injustice; for the one is a virtue and the other a vice of the
soul: ‘of the soul’, therefore, is the differentia in both cases,
seeing that the body as well has its virtue and vice. But this much
at least is true, that the differentiae of contraries are either
contrary or else the same. If, then, the contrary differentia to
that given be predicated of the contrary term and not of the one in
hand, clearly the differentia stated must be predicated of the
latter. Speaking generally, seeing that the definition consists of
genus and differentiae, if the definition of the contrary term be
apparent, the definition of the term before you will be apparent
also: for since its contrary is found either in the same genus or
in the contrary genus, and likewise also the differentiae
predicated of opposites are either contrary to, or the same as,
each other, clearly of the term before you there will be predicated
either the same genus as of its contrary, while, of its
differentiae, either all are contrary to those of its contrary, or
at least some of them are so while the rest remain the same; or,
vice versa, the differentiae will be the same and the genera
contrary; or both genera and differentiae will be contrary. And
that is all; for that both should be the same is not possible; else
contraries will have the same definition.
    Moreover, look at it from the point of view of its inflexions
and coordinates. For genera and definitions are bound to correspond
in either case. Thus if forgetfulness be the loss of knowledge, to
forget is to lose knowledge, and to have forgotten is to have lost
knowledge. If, then, any one whatever of these is agreed to, the
others must of necessity be agreed to as well. Likewise, also, if
destruction is the decomposition of the thing’s essence, then to be
destroyed is to have its essence decomposed, and ‘destructively’
means ‘in such a way as to decompose its essence’; if again
‘destructive’ means ‘apt to decompose something’s essence’, then
also ‘destruction’ means ‘the decomposition of its essence’.
Likewise also with the rest: an admission of any one of them
whatever, and all the rest are admitted too.
    Moreover, look at it from the point of view of things that stand
in relations that are like each other. For if ‘healthy’ means
‘productive of health’, ‘vigorous’ too will mean ‘productive of
vigour’, and ‘useful’ will mean ‘productive of good.’ For each of
these things is related in like manner to its own peculiar end, so
that if one of them is defined as ‘productive of’ that end, this
will also be the definition of each of the rest as well.
    Moreover, look at it from the point of and like degrees, in all
the ways in which it is possible to establish a result by comparing
two and two together. Thus if A defines a better than B defines and
B is a definition of so too is A of a. Further, if A’s claim to
define a is like B’s to define B, and B defines B, then A too
defines a. This examination from the point of view of greater
degrees is of no use when a single definition is compared with two
things, or two definitions with one thing; for there cannot
possibly be one definition of two things or two of the same
thing.
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4
    The most handy of all the commonplace arguments are those just
mentioned and those from co-ordinates and inflexions, and