The Complete Aristotle (eng.)

their essences, nor are accidental unities like that of
‘Socrates’ and ‘musical’; for these are the same only by
accident.
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    div id="section87" class="section" title="12">
12
    Now let us treat first of definition, in so far as we have not
treated of it in the Analytics; for the problem stated in them is
useful for our inquiries concerning substance. I mean this
problem:-wherein can consist the unity of that, the formula of
which we call a definition, as for instance, in the case of man,
‘two-footed animal’; for let this be the formula of man. Why, then,
is this one, and not many, viz. ‘animal’ and ‘two-footed’? For in
the case of ‘man’ and ‘pale’ there is a plurality when one term
does not belong to the other, but a unity when it does belong and
the subject, man, has a certain attribute; for then a unity is
produced and we have ‘the pale man’. In the present case, on the
other hand, one does not share in the other; the genus is not
thought to share in its differentiae (for then the same thing would
share in contraries; for the differentiae by which the genus is
divided are contrary). And even if the genus does share in them,
the same argument applies, since the differentiae present in man
are many, e.g. endowed with feet, two-footed, featherless. Why are
these one and not many? Not because they are present in one thing;
for on this principle a unity can be made out of all the attributes
of a thing. But surely all the attributes in the definition must be
one; for the definition is a single formula and a formula of
substance, so that it must be a formula of some one thing; for
substance means a ‘one’ and a ‘this’, as we maintain.
    We must first inquire about definitions reached by the method of
divisions. There is nothing in the definition except the
first-named and the differentiae. The other genera are the first
genus and along with this the differentiae that are taken with it,
e.g. the first may be ‘animal’, the next ‘animal which is
two-footed’, and again ‘animal which is two-footed and
featherless’, and similarly if the definition includes more terms.
And in general it makes no difference whether it includes many or
few terms,-nor, therefore, whether it includes few or simply two;
and of the two the one is differentia and the other genus; e.g. in
‘two-footed animal’ ‘animal’ is genus, and the other is
differentia.
    If then the genus absolutely does not exist apart from the
species-of-a-genus, or if it exists but exists as matter (for the
voice is genus and matter, but its differentiae make the species,
i.e. the letters, out of it), clearly the definition is the formula
which comprises the differentiae.
    But it is also necessary that the division be by the differentia
of the diferentia; e.g. ‘endowed with feet’ is a differentia of
‘animal’; again the differentia of ‘animal endowed with feet’ must
be of it qua endowed with feet. Therefore we must not say, if we
are to speak rightly, that of that which is endowed with feet one
part has feathers and one is featherless (if we do this we do it
through incapacity); we must divide it only into cloven-footed and
not cloven; for these are differentiae in the foot;
cloven-footedness is a form of footedness. And the process wants
always to go on so till it reaches the species that contain no
differences. And then there will be as many kinds of foot as there
are differentiae, and the kinds of animals endowed with feet will
be equal in number to the differentiae. If then this is so, clearly
the last differentia will be the substance of the thing and its
definition, since it is not right to state the same things more
than once in our definitions; for it is superfluous. And this does
happen; for when we say ‘animal endowed with feet and two-footed’
we have said nothing other than ‘animal having feet, having two
feet’; and if we divide this by the proper division, we shall be
saying the same thing more than once-as many times as there are
differentiae.
    If then a differentia of a differentia be taken at each step,
one differentia-the last-will be the form and the substance; but if
we divide according to accidental qualities, e.g. if we were to
divide that which is endowed with feet into the white and the
black, there will be as many differentiae as there are cuts.
Therefore it is plain that the definition is the formula which
contains the differentiae, or, according to the right method, the
last of