Various Works

  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