by Aristotle
these things to be the contrary of the term originally used, then
clearly neither of the definitions rendered later could be the
definition of the contrary of the term originally defined: and
therefore the definition originally rendered of the original term
has not been rightly rendered either. Seeing, moreover, that of
contraries, the one is sometimes a word forced to denote the privation
of the other, as (e.g.) inequality is generally held to be the
privation of equality (for 'unequal' merely describes things that
are not equal'), it is therefore clear that that contrary whose form
denotes the privation must of necessity be defined through the
other; whereas the other cannot then be defined through the one
whose form denotes the privation; for else we should find that each is
being interpreted by the other. We must in the case of contrary
terms keep an eye on this mistake, e.g. supposing any one were to
define equality as the contrary of inequality: for then he is defining
it through the term which denotes privation of it. Moreover, a man who
so defines is bound to use in his definition the very term he is
defining; and this becomes clear, if for the word we substitute its
definition. For to say 'inequality' is the same as to say 'privation
of equality'. Therefore equality so defined will be 'the contrary of
the privation of equality', so that he would have used the very word
to be defined. Suppose, however, that neither of the contraries be
so formed as to denote privation, but yet the definition of it be
rendered in a manner like the above, e.g. suppose 'good' to be defined
as 'the contrary of evil', then, since it is clear that 'evil' too
will be 'the contrary of good' (for the definition of things that
are contrary in this must be rendered in a like manner), the result
again is that he uses the very term being defined: for 'good' is
inherent in the definition of 'evil'. If, then, 'good' be the contrary
of evil, and evil be nothing other than the 'contrary of good', then
'good' will be the 'contrary of the contrary of good'. Clearly,
then, he has used the very word to be defined.
Moreover, see if in rendering a term formed to denote privation,
he has failed to render the term of which it is the privation, e.g.
the state, or contrary, or whatever it may be whose privation it is:
also if he has omitted to add either any term at all in which the
privation is naturally formed, or else that in which it is naturally
formed primarily, e.g. whether in defining 'ignorance' a privation
he has failed to say that it is the privation of 'knowledge'; or has
failed to add in what it is naturally formed, or, though he has
added this, has failed to render the thing in which it is primarily
formed, placing it (e.g.) in 'man' or in 'the soul', and not in the
'reasoning faculty': for if in any of these respects he fails, he
has made a mistake. Likewise, also, if he has failed to say that
'blindness' is the 'privation of sight in an eye': for a proper
rendering of its essence must state both of what it is the privation
and what it is that is deprived.
Examine further whether he has defined by the expression 'a
privation' a term that is not used to denote a privation: thus a
mistake of this sort also would be generally thought to be incurred in
the case of 'error' by any one who is not using it as a merely
negative term. For what is generally thought to be in error is not
that which has no knowledge, but rather that which has been
deceived, and for this reason we do not talk of inanimate things or of
children as 'erring'. 'Error', then, is not used to denote a mere
privation of knowledge.
10
Moreover, see whether the like inflexions in the definition apply to
the like inflexions of the term; e.g. if 'beneficial' means
'productive of health', does 'beneficially' mean productively of
health' and a 'benefactor' a 'producer of health'?
Look too and see whether the definition given will apply to the Idea
as well. For in some cases it will not do so; e.g. in the Platonic
definition where he adds the word 'mortal' in his definitions of
living creatures: for the Idea (e.g. the absolute Man) is not
mortal, so that the definition will not fit the Idea. So always
wherever the words 'capable of acting on' or 'capable of being acted
upon' are added, the definition and the Idea are absolutely bound to
be discrepant: for those who assert the existence of Ideas hold that
they are incapable of being acted upon, or of motion. In dealing
with these people even arguments of this kind are useful.
Further, see if he has rendered a single common definition of
terms that are used ambiguously. For terms whose definition
corresponding their common name is one and the same, are synonymous;
if, then, the definition applies in a like manner to the whole range
of the ambiguous term, it is not true of any one of the objects
described by the term. This is, moreover, what happens to Dionysius'
definition of 'life' when stated as 'a movement of a creature
sustained by nutriment, congenitally present with it': for this is
found in plants as much as in animals, whereas 'life' is generally
understood to mean not one kind of thing only, but to be one thing
in animals and another in plants. It is possible to hold the view that
life is a synonymous term and is always used to describe one thing
only, and therefore to render the definition in this way on purpose:
or it may quite well happen that a man may see the ambiguous character
of the word, and wish to render the definition of the one sense
only, and yet fail to see that he has rendered a definition common
to both senses instead of one peculiar to the sense he intends. In
either case, whichever course he pursues, he is equally at fault.
Since ambiguous terms sometimes pass unobserved, it is best in
questioning to treat such terms as though they were synonymous (for
the definition of the one sense will not apply to the other, so that
the answerer will be generally thought not to have defined it
correctly, for to a synonymous term the definition should apply in its
full range), whereas in answering you should yourself distinguish
between the senses. Further, as some answerers call 'ambiguous' what
is really synonymous, whenever the definition rendered fails to
apply universally, and, vice versa, call synonymous what is really
ambiguous supposing their definition applies to both senses of the
term, one should secure a preliminary admission on such points, or
else prove beforehand that so-and-so is ambiguous or synonymous, as
the case may be: for people are more ready to agree when they do not
foresee what the consequence will be. If, however, no admission has
been made, and the man asserts that what is really synonymous is
ambiguous because the definition he has rendered will not apply to the
second sense as well, see if the definition of this second meaning
applies also to the other meanings: for if so, this meaning must
clearly be synonymous with those others. Otherwise, there will be more
than one definition of those other meanings, for there are
applicable to them two distinct definitions in explanation of the
term, viz. the one previously rendered and also the later one.
Again, if any one were to define a term used in several senses, and,
finding that his definition does not apply to them all, were to
contend not that the term is ambiguous, but that even the term does
not properly apply to all those senses, just because his definition
will not do so either, then one may retort to such a man that though
in some things one must not use the language of the people, yet in a
question of terminology one is bound to employ the received and
traditional usage and not to upset matters of that sort.
11
Suppose now that a definition has been rendered of some complex
term, take away the definition of one of the elements in the
complex, and see if also the rest of the definition defines the rest
of it: if not, it is clear that neither does the whole definition
define the whole complex. Suppose, e.g. that some one has defined a
'finite straight line' as 'the limit of a finite plane, such that
its centre is in a line with its extremes'; if now the definition of a
finite line' be the 'limit of a finite plane', the rest (viz. 'such
that its centre is in a line with its extremes') ought to be a
definition of straight'. But an infinite straight line has neither
centre nor extremes and yet is straight so that this remainder does
not define the remainder of the term.
Moreover, if the term defined be a compound notion, see if the
definition rendered be equimembral with the term defined. A definition
is said to be equimembral with the term defined when the number of the
elements compounded in the latter is the same as the number of nouns
and verbs in the definition. For the exchange in such cases is bound
to be merely one of term for term, in the case of some if not of
all, seeing that there are no more terms used now than formerly;
whereas in a definition terms ought to be rendered by phrases, if
possible in every case, or if not, in the majority. For at that
rate, simple objects too could be defined by merely calling them by
a different name, e.g. 'cloak' instead of 'doublet'.
The mistake is even worse, if actually a less well known term be
substituted, e.g. 'pellucid mortal' for 'white man': for it is no
definition, and moreover is less intelligible when put in that form.
Look and see also whether, in the exchange of words, the sense fails
still to be the same. Take, for instance, the explanation of
'speculative knowledge' as 'speculative conception': for conception is
not the same as knowledge-as it certainly ought to be if the whole
is to be the same too: for though the word 'speculative' is common
to both expressions, yet the remainder is different.
Moreover, see if in replacing one of the terms by something else
he has exchanged the genus and not the differentia, as in the
example just given: for 'speculative' is a less familiar term than
knowledge; for the one is the genus and the other the differentia, and
the genus is always the most familiar term of all; so that it is not
this, but the differentia, that ought to have been changed, seeing
that it is the less familiar. It might be held that this criticism
is ridiculous: because there is no reason why the most familiar term
should not describe the differentia, and not the genus; in which case,
clearly, the term to be altered would also be that denoting the
genus and not the differentia. If, however, a man is substituting
for a term not merely another term but a phrase, clearly it is of
the differentia rather than of the genus that a definition should be
rendered, seeing that the object of rendering the definition is to
make the subject familiar; for the differentia is less familiar than
the genus.
If he has rendered the definition of the differentia, see whether
the definition rendered is common to it and something else as well:
e.g. whenever he says that an odd number is a 'number with a
middle', further definition is required of how it has a middle: for
the word 'number' is common to both expressions, and it is the word
'odd' for which the phrase has been substituted. Now both a line and a
body have a middle, yet they are not 'odd'; so that this could not
be a definition of 'odd'. If, on the other hand, the phrase 'with a
middle' be used in several senses, the sense here intended requires to
be defined. So that this will either discredit the definition or prove
that it is no definition at all.
12
Again, see if the term of which he renders the definition is a
reality, whereas what is contained in the definition is not, e.g.
Suppose 'white' to be defined as 'colour mingled with fire': for
what is bodiless cannot be mingled with body, so that 'colour'
'mingled with fire' could not exist, whereas 'white' does exist.
Moreover, those who in the case of relative terms do not distinguish
to what the object is related, but have described it only so as to
include it among too large a number of things, are wrong either wholly
or in part; e.g. suppose some one to have defined 'medicine' as a
science of Reality'. For if medicine be not a science of anything that
is real, the definition is clearly altogether false; while if it be
a science of some real thing, but not of another, it is partly
false; for it ought to hold of all reality, if it is said to be of
Reality essentially and not accidentally: as is the case with other
relative terms: for every object of knowledge is a term relative to
knowledge: likewise, also, with other relative terms, inasmuch as
all such are convertible. Moreover, if the right way to render account
of a thing be to render it as it is not in itself but accidentally,
then each and every relative term would be used in relation not to one
thing but to a number of things. For there is no reason why the same
thing should not be both real and white and good, so that it would
be a correct rendering to render the object in relation to any one
whatsoever of these, if to render what it is accidentally be a correct
way to render it. It is, moreover, impossible that a definition of
this sort should be peculiar to the term rendered: for not only but
the majority of the other sciences too, have for their object some
real thing, so that each will be a science of reality. Clearly,
then, such a definition does not define any science at all; for a
definition ought to be peculiar to its own term, not general.
Sometimes, again, people define not the thing but only the thing
in a good or perfect condition. Such is the definition of a
rhetorician as 'one who can always see what will persuade in the given
circumstances, and omit nothing'; or of a thief, as 'one who pilfers
in secret': for clearly, if they each do this, then the one will be
a good rhetorician, and the other a good thief: whereas it is not
; the actual pilfering in secret, but the wish to do it, that
constitutes the thief.
Again, see if he has rendered what is desirable for its own sake
as desirable for what it produces or does, or as in any way
desirable because of something else, e.g. by saying that justice is
'what preserves the laws' or that wisdom is 'what produces happiness';
for what produces or preserves something else is one of the things
desirable for something else. It might be said that it is possible for
what is desirable in itself to be desirable for something else as
well: but still to define what is desirable in itself in such a way is
none the less wrong: for the essence contains par excellence what is
best in anything, and it is better for a thing to be desirable in
itself than to be desirable for something else, so that this is rather
what the definition too ought to have indicated.
13
See also whether in defining anything a man has defined it as an
'A and B', or as a 'product of A and B' or as an 'A+B'. If he
defines it as and B', the definition will be true of both and yet of
neither of them; suppose, e.g. justice to be defined as 'temperance
and courage.' For if of two persons each has one of the two only, both
and yet neither will be just: for both together have justice, and
yet each singly fails to have it. Even if the situation here described
does not so far appear very absurd because of the occurrence of this
kind of thing in other cases also (for it is quite possible for two
men to have a mina between them, though neither of them has it by
himself), yet least that they should have contrary attributes surely
seems quite absurd; and yet this will follow if the one be temperate
and yet a coward, and the other, though brave, be a profligate; for
then both will exhibit both justice and injustice: for if justice be
temperance and bravery, then injustice will be cowardice and
profligacy. In general, too, all the ways of showing that the whole is
not the same as the sum of its parts are useful in meeting the type
just described; for a man who defines in this way seems to assert that