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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 these.
This would be evident, if we were to change the order of such
definitions, e.g. of that of man, saying 'animal which is two-footed
and endowed with feet'; for 'endowed with feet' is superfluous when
'two-footed' has been said. But there is no order in the substance;
for how are we to think the one element posterior and the other prior?
Regarding the definitions, then, which are reached by the method of
divisions, let this suffice as our first attempt at stating their

Let us return to the subject of our inquiry, which is substance.
As the substratum and the essence and the compound of these are called
substance, so also is the universal. About two of these we have
spoken; both about the essence and about the substratum, of which we

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