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differentia has an equal or a wider denotation than the species.
Moreover, see whether he has placed the genus inside the differentia,
by making 'colour' (e.g.) to be a thing that 'pierces', or 'number' a
thing that is 'odd'. Also, see if he has mentioned the genus as
differentia: for it is possible for a man to bring forward a statement
of this kind as well, e.g. that 'mixture' is the differentia of
'fusion', or that change of place' is the differentia of 'carriage'.
All such cases should be examined by means of the same principles: for
they depend upon common rules: for the genus should have a wider
denotation that its differentia, and also should not partake of its
differentia; whereas, if it be rendered in this manner, neither of the
aforesaid requirements can be satisfied: for the genus will both have
a narrower denotation than its differentia, and will partake of it.
Again, if no differentia belonging to the genus be predicated of the
given species, neither will the genus be predicated of it; e.g. of
'soul' neither 'odd' nor 'even' is predicated: neither therefore is
'number'. Moreover, see whether the species is naturally prior and
abolishes the genus along with itself: for the contrary is the general
view. Moreover, if it be possible for the genus stated, or for its
differentia, to be absent from the alleged species, e.g. for
'movement' to be absent from the 'soul', or 'truth and falsehood' from
'opinion', then neither of the terms stated could be its genus or its
differentia: for the general view is that the genus and the
differentia accompany the species, as long as it exists.
Part 3
Look and see, also, if what is placed in the genus partakes or could
possibly partake of any contrary of the genus: for in that case the
same thing will at the same time partake of contrary things, seeing
that the genus is never absent from it, while it partakes, or can
possibly partake, of the contrary genus as well. Moreover, see whether
the species shares in any character which it is utterly impossible for
any member of the genus to have. Thus (e.g.) if the soul has a share
in life, while it is impossible for any number to live, then the soul
could not be a species of number.
You should look and see, also, if the species be a homonym of the
genus, and employ as your elementary principles those already stated
for dealing with homonymity: for the genus and the species are
synonymous.
Seeing that of every genus there is more than one species, look and
see if it be impossible that there should be another species than the
given one belonging to the genus stated: for if there should be none,
then clearly what has been stated could not be a genus at all.
Look and see, also, if he has rendered as genus a metaphorical
expression, describing (e.g. 'temperance' as a 'harmony': a 'harmony':
for a genus is always predicated of its species in its literal sense,
whereas 'harmony' is predicated of temperance not in a literal sense
but metaphorically: for a harmony always consists in notes.
Moreover, if there be any contrary of the species, examine it. The
examination may take different forms; first of all see if the contrary
as well be found in the same genus as the species, supposing the genus
to have no contrary; for contraries ought to be found in the same
genus, if there be no contrary to the genus. Supposing, on the other
hand, that there is a contrary to the genus, see if the contrary of
the species be found in the contrary genus: for of necessity the
contrary species must be in the contrary genus, if there be any
contrary to the genus. Each of these points is made plain by means of
induction. Again, see whether the contrary of the species be not found
in any genus at all, but be itself a genus, e.g. 'good': for if this
be not found in any genus, neither will its contrary be found in any
genus, but will itself be a genus, as happens in the case of 'good'
and 'evil': for neither of these is found in a genus, but each of them
is a genus. Moreover, see if both genus and species be contrary to
something, and one pair of contraries have an intermediary, but not
the other. For if the genera have an intermediary, so should their