that those who define in this way cannot show the essential nature
of the term they define, unless it so happens that the same thing is
more intelligible both to us and also absolutely, since a correct
definition must define a thing through its genus and its differentiae,
and these belong to the order of things which are absolutely more
intelligible than, and prior to, the species. For annul the genus
and differentia, and the species too is annulled, so that these are
prior to the species. They are also more intelligible; for if the
species be known, the genus and differentia must of necessity be known
as well (for any one who knows what a man is knows also what
'animal' and 'walking' are), whereas if the genus or the differentia
be known it does not follow of necessity that the species is known
as well: thus the species is less intelligible. Moreover, those who
say that such definitions, viz. those which proceed from what is
intelligible to this, that, or the other man, are really and truly
definitions, will have to say that there are several definitions of
one and the same thing. For, as it happens, different things are
more intelligible to different people, not the same things to all; and
so a different definition would have to be rendered to each several
person, if the definition is to be constructed from what is more
intelligible to particular individuals. Moreover, to the same people
different things are more intelligible at different times; first of
all the objects of sense; then, as they become more sharpwitted, the
converse; so that those who hold that a definition ought to be
rendered through what is more intelligible to particular individuals
would not have to render the same definition at all times even to
the same person. It is clear, then, that the right way to define is
not through terms of that kind, but through what is absolutely more
intelligible: for only in this way could the definition come always to
be one and the same. Perhaps, also, what is absolutely intelligible is
what is intelligible, not to all, but to those who are in a sound
state of understanding, just as what is absolutely healthy is what
is healthy to those in a sound state of body. All such points as
this ought to be made very precise, and made use of in the course of
discussion as occasion requires. The demolition of a definition will
most surely win a general approval if the definer happens to have
framed his expression neither from what is absolutely more
intelligible nor yet from what is so to us.
One form, then, of the failure to work through more intelligible
terms is the exhibition of the prior through the posterior, as we
remarked before.' Another form occurs if we find that the definition
has been rendered of what is at rest and definite through what is
indefinite and in motion: for what is still and definite is prior to
what is indefinite and in motion.
Of the failure to use terms that are prior there are three forms:
(1) The first is when an opposite has been defined through its
opposite, e.g.i. good through evil: for opposites are always
simultaneous by nature. Some people think, also, that both are objects
of the same science, so that the one is not even more intelligible
than the other. One must, however, observe that it is perhaps not
possible to define some things in any other way, e.g. the double
without the half, and all the terms that are essentially relative: for
in all such cases the essential being is the same as a certain
relation to something, so that it is impossible to understand the
one term without the other, and accordingly in the definition of the
one the other too must be embraced. One ought to learn up all such
points as these, and use them as occasion may seem to require.
(2) Another is-if he has used the term defined itself. This passes
unobserved when the actual name of the object is not used, e.g.
supposing any one had defined the sun as a star that appears by
day'. For in bringing in 'day' he brings in the sun. To detect
errors of this sort, exchange the word for its definition, e.g. the
definition of 'day' as the 'passage of the sun over the earth'.
Clearly, whoever has said 'the passage of the sun over the earth'
has said 'the sun', so that in bringing in the 'day' he has brought in
the sun.
(3) Again, see if he has defined one coordinate member of a division
by another, e.g. 'an odd number' as 'that which is greater by one than
an even number'. For the co-ordinate members of a division that are
derived from the same genus are simultaneous by nature and 'odd' and
'even' are such terms: for both are differentiae of number.
Likewise also, see if he has defined a superior through a
subordinate term, e.g. 'An "even number" is "a number divisible into
halves"', or '"the good" is a "state of virtue" '. For 'half' is
derived from 'two', and 'two' is an even number: virtue also is a kind
of good, so that the latter terms are subordinate to the former.
Moreover, in using the subordinate term one is bound to use the
other as well: for whoever employs the term 'virtue' employs the
term 'good', seeing that virtue is a certain kind of good: likewise,
also, whoever employs the term 'half' employs the term 'even', for
to be 'divided in half' means to be divided into two, and two is even.
5
Generally speaking, then, one commonplace rule relates to the
failure to frame the expression by means of terms that are prior and
more intelligible: and of this the subdivisions are those specified
above. A second is, see whether, though the object is in a genus, it
has not been placed in a genus. This sort of error is always found
where the essence of the object does not stand first in the
expression, e.g. the definition of 'body' as 'that which has three
dimensions', or the definition of 'man', supposing any one to give it,
as 'that which knows how to count': for it is not stated what it is
that has three dimensions, or what it is that knows how to count:
whereas the genus is meant to indicate just this, and is submitted
first of the terms in the definition.
Moreover, see if, while the term to be defined is used in relation
to many things, he has failed to render it in relation to all of them;
as (e.g.) if he define 'grammar' as the 'knowledge how to write from
dictation': for he ought also to say that it is a knowledge how to
read as well. For in rendering it as 'knowledge of writing' has no
more defined it than by rendering it as 'knowledge of reading':
neither in fact has succeeded, but only he who mentions both these
things, since it is impossible that there should be more than one
definition of the same thing. It is only, however, in some cases
that what has been said corresponds to the actual state of things:
in some it does not, e.g. all those terms which are not used
essentially in relation to both things: as medicine is said to deal
with the production of disease and health; for it is said
essentially to do the
latter, but the former only by accident: for
it is absolutely alien to medicine to produce disease. Here, then, the
man who renders medicine as relative to both of these things has not
defined it any better than he who mentions the one only. In fact he
has done it perhaps worse, for any one else besides the doctor is
capable of producing disease.
Moreover, in a case where the term to be defined is used in relation
to several things, see if he has rendered it as relative to the
worse rather than to the better; for every form of knowledge and
potentiality is generally thought to be relative to the best.
Again, if the thing in question be not placed in its own proper
genus, one must examine it according to the elementary rules in regard
to genera, as has been said before.'
Moreover, see if he uses language which transgresses the genera of
the things he defines, defining, e.g. justice as a 'state that
produces equality' or 'distributes what is equal': for by defining
it so he passes outside the sphere of virtue, and so by leaving out
the genus of justice he fails to express its essence: for the
essence of a thing must in each case bring in its genus. It is the
same thing if the object be not put into its nearest genus; for the
man who puts it into the nearest one has stated all the higher genera,
seeing that all the higher genera are predicated of the lower. Either,
then, it ought to be put into its nearest genus, or else to the higher
genus all the differentiae ought to be appended whereby the nearest
genus is defined. For then he would not have left out anything: but
would merely have mentioned the subordinate genus by an expression
instead of by name. On the other hand, he who mentions merely the
higher genus by itself, does not state the subordinate genus as
well: in saying 'plant' a man does not specify 'a tree'.
6
Again, in regard to the differentiae, we must examine in like manner
whether the differentiae, too, that he has stated be those of the
genus. For if a man has not defined the object by the differentiae
peculiar to it, or has mentioned something such as is utterly
incapable of being a differentia of anything, e.g. 'animal' or
'substance', clearly he has not defined it at all: for the aforesaid
terms do not differentiate anything at all. Further, we must see
whether the differentia stated possesses anything that is
co-ordinate with it in a division; for, if not, clearly the one stated
could not be a differentia of the genus. For a genus is always divided
by differentiae that are co-ordinate members of a division, as, for
instance, by the terms 'walking', 'flying', 'aquatic', and 'biped'. Or
see if, though the contrasted differentia exists, it yet is not true
of the genus, for then, clearly, neither of them could be a
differentia of the genus; for differentiae that are co-ordinates in
a division with the differentia of a thing are all true of the genus
to which the thing belongs. Likewise, also, see if, though it be true,
yet the addition of it to the genus fails to make a species. For then,
clearly, this could not be a specific differentia of the genus: for
a specific differentia, if added to the genus, always makes a species.
If, however, this be no true differentia, no more is the one
adduced, seeing that it is a co-ordinate member of a division with
this.
Moreover, see if he divides the genus by a negation, as those do who
define line as 'length without breadth': for this means simply that it
has not any breadth. The genus will then be found to partake of its
own species: for, since of everything either an affirmation or its
negation is true, length must always either lack breadth or possess
it, so that 'length' as well, i.e. the genus of 'line', will be either
with or without breadth. But 'length without breadth' is the
definition of a species, as also is 'length with breadth': for
'without breadth' and 'with breadth' are differentiae, and the genus
and differentia constitute the definition of the species. Hence the
genus would admit of the definition of its species. Likewise, also, it
will admit of the definition of the differentia, seeing that one or
the other of the aforesaid differentiae is of necessity predicated
of the genus. The usefulness of this principle is found in meeting
those who assert the existence of 'Ideas': for if absolute length
exist, how will it be predicable of the genus that it has breadth or
that it lacks it? For one assertion or the other will have to be
true of 'length' universally, if it is to be true of the genus at all:
and this is contrary to the fact: for there exist both lengths which
have, and lengths which have not, breadth. Hence the only people
against whom the rule can be employed are those who assert that a
genus is always numerically one; and this is what is done by those who
assert the real existence of the 'Ideas'; for they allege that
absolute length and absolute animal are the genus.
It may be that in some cases the definer is obliged to employ a
negation as well, e.g. in defining privations. For 'blind' means a
thing which cannot see when its nature is to see. There is no
difference between dividing the genus by a negation, and dividing it
by such an affirmation as is bound to have a negation as its
co-ordinate in a division, e.g. supposing he had defined something
as 'length possessed of breadth'; for co-ordinate in the division with
that which is possessed of breadth is that which possesses no
breadth and that only, so that again the genus is divided by a
negation.
Again, see if he rendered the species as a differentia, as do
those who define 'contumely' as 'insolence accompanied by jeering';
for jeering is a kind of insolence, i.e. it is a species and not a
differentia.
Moreover, see if he has stated the genus as the differentia, e.g.
'Virtue is a good or noble state: for 'good' is the genus of 'virtue'.
Or possibly 'good' here is not the genus but the differentia, on the
principle that the same thing cannot be in two genera of which neither
contains the other: for 'good' does not include 'state', nor vice
versa: for not every state is good nor every good a 'state'. Both,
then, could not be genera, and consequently, if 'state' is the genus
of virtue, clearly 'good' cannot be its genus: it must rather be the
differentia'. Moreover, 'a state' indicates the essence of virtue,
whereas 'good' indicates not the essence but a quality: and to
indicate a quality is generally held to be the function of the
differentia. See, further, whether the differentia rendered
indicates an individual rather than a quality: for the general view is
that the differentia always expresses a quality.
Look and see, further, whether the differentia belongs only by
accident to the object defined. For the differentia is never an
accidental attribute, any more than the genus is: for the
differentia of a thing cannot both belong and not belong to it.
Moreover, if either
the differentia or the species, or any of the
things which are under the species, is predicable of the genus, then
he could not have defined the term. For none of the aforesaid can
possibly be predicated of the genus, seeing that the genus is the term
with the widest range of all. Again, see if the genus be predicated of
the differentia; for the general view is that the genus is predicated,
not of the differentia, but of the objects of which the differentia is
predicated. Animal (e.g.) is predicated of 'man' or 'ox' or other
walking animals, not of the actual differentia itself which we
predicate of the species. For if 'animal' is to be predicated of
each of its differentiae, then 'animal' would be predicated of the
species several times over; for the differentiae are predicates of the
species. Moreover, the differentiae will be all either species or
individuals, if they are animals; for every animal is either a species
or an individual.
Likewise you must inquire also if the species or any of the
objects that come under it is predicated of the differentia: for
this is impossible, seeing that the differentia is a term with a wider
range than the various species. Moreover, if any of the species be
predicated of it, the result will be that the differentia is a
species: if, for instance, 'man' be predicated, the differentia is
clearly the human race. Again, see if the differentia fails to be
prior to the species: for the differentia ought to be posterior to the
genus, but prior to the species.
Look and see also if the differentia mentioned belongs to a
different genus, neither contained in nor containing the genus in
question. For the general view is that the same differentia cannot
be used of two non-subaltern genera. Else the result will be that
the same species as well will be in two non-subaltern genera: for each
of the differentiae imports its own genus, e.g. 'walking' and
'biped' import with them the genus 'animal'. If, then, each of the
genera as well is true of that of which the differentia is true, it