by Aristotle
between the expression and the term, in order to establish that the
former is a definition, but a definition must have also all the
other characters already announced.
3
This then is the way, and these the arguments, whereby the attempt
to demolish a definition should always be made. If, on the other hand,
we desire to establish one, the first thing to observe is that few
if any who engage in discussion arrive at a definition by reasoning:
they always assume something of the kind as their starting points-both
in geometry and in arithmetic and the other studies of that kind. In
the second place, to say accurately what a definition is, and how it
should be given, belongs to another inquiry. At present it concerns us
only so far as is required for our present purpose, and accordingly we
need only make the bare statement that to reason to a thing's
definition and essence is quite possible. For if a definition is an
expression signifying the essence of the thing and the predicates
contained therein ought also to be the only ones which are
predicated of the thing in the category of essence; and genera and
differentiae are so predicated in that category: it is obvious that if
one were to get an admission that so and so are the only attributes
predicated in that category, the expression containing so and so would
of necessity be a definition; for it is impossible that anything
else should be a definition, seeing that there is not anything else
predicated of the thing in the category of essence.
That a definition may thus be reached by a process of reasoning is
obvious. The means whereby it should be established have been more
precisely defined elsewhere, but for the purposes of the inquiry now
before us the same commonplace rules serve. For we have to examine
into the contraries and other opposites of the thing, surveying the
expressions used both as wholes and in detail: for if the opposite
definition defines that opposite term, the definition given must of
necessity be that of the term before us. Seeing, however, that
contraries may be conjoined in more than one way, we have to select
from those contraries the one whose contrary definition seems most
obvious. The expressions, then, have to be examined each as a whole in
the way we have said, and also in detail as follows. First of all, see
that the genus rendered is correctly rendered; for if the contrary
thing be found in the contrary genus to that stated in the definition,
and the thing before you is not in that same genus, then it would
clearly be in the contrary genus: for contraries must of necessity
be either in the same genus or in contrary genera. The differentiae,
too, that are predicated of contraries we expect to be contrary,
e.g. those of white and black, for the one tends to pierce the vision,
while the other tends to compress it. So that if contrary differentiae
to those in the definition are predicated of the contrary term, then
those rendered in the definition would be predicated of the term
before us. Seeing, then, that both the genus and the differentiae have
been rightly rendered, clearly the expression given must be the
right definition. It might be replied that there is no necessity why
contrary differentiae should be predicated of contraries, unless the
contraries be found within the same genus: of things whose genera
are themselves contraries it may very well be that the same
differentia is used of both, e.g. of justice and injustice; for the
one is a virtue and the other a vice of the soul: 'of the soul',
therefore, is the differentia in both cases, seeing that the body as
well has its virtue and vice. But this much at least is true, that the
differentiae of contraries are either contrary or else the same. If,
then, the contrary differentia to that given be predicated of the
contrary term and not of the one in hand, clearly the differentia
stated must be predicated of the latter. Speaking generally, seeing
that the definition consists of genus and differentiae, if the
definition of the contrary term be apparent, the definition of the
term before you will be apparent also: for since its contrary is found
either in the same genus or in the contrary genus, and likewise also
the differentiae predicated of opposites are either contrary to, or
the same as, each other, clearly of the term before you there will
be predicated either the same genus as of its contrary, while, of
its differentiae, either all are contrary to those of its contrary, or
at least some of them are so while the rest remain the same; or,
vice versa, the differentiae will be the same and the genera contrary;
or both genera and differentiae will be contrary. And that is all; for
that both should be the same is not possible; else contraries will
have the same definition.
Moreover, look at it from the point of view of its inflexions and
coordinates. For genera and definitions are bound to correspond in
either case. Thus if forgetfulness be the loss of knowledge, to forget
is to lose knowledge, and to have forgotten is to have lost knowledge.
If, then, any one whatever of these is agreed to, the others must of
necessity be agreed to as well. Likewise, also, if destruction is
the decomposition of the thing's essence, then to be destroyed is to
have its essence decomposed, and 'destructively' means 'in such a
way as to decompose its essence'; if again 'destructive' means 'apt to
decompose something's essence', then also 'destruction' means 'the
decomposition of its essence'. Likewise also with the rest: an
admission of any one of them whatever, and all the rest are admitted
too.
Moreover, look at it from the point of view of things that stand
in relations that are like each other. For if 'healthy' means
'productive of health', 'vigorous' too will mean 'productive of
vigour', and 'useful' will mean 'productive of good.' For each of
these things is related in like manner to its own peculiar end, so
that if one of them is defined as 'productive of' that end, this
will also be the definition of each of the rest as well.
Moreover, look at it from the point of and like degrees, in all
the ways in which it is possible to establish a result by comparing
two and two together. Thus if A defines a better than B defines and
B is a definition of so too is A of a. Further, if A's claim to define
a is like B's to define B, and B defines B, then A too defines a. This
examination from the point of view of greater degrees is of no use
when a single definition is compared with two things, or two
definitions with one thing; for there cannot possibly be one
definition of two things or two of the same thing.
4
The most handy of all the commonplace arguments are those just
mentioned and those from co-ordinates and inflexions, and these
therefore are those which it is most important to master and to have
ready to hand: for they are the most useful on the greatest number
of occasions. Of the rest, too, the most impo
rtant are those of most
general application: for these are the most effective, e.g. that you
should examine the individual cases, and then look to see in the
case of their various species whether the definition applies. For
the species is synonymous with its individuals. This sort of inquiry
is of service against those who assume the existence of Ideas, as
has been said before.' Moreover see if a man has used a term
metaphorically, or predicated it of itself as though it were something
different. So too if any other of the commonplace rules is of
general application and effective, it should be employed.
5
That it is more difficult to establish than to overthrow a
definition, is obvious from considerations presently to be urged.
For to see for oneself, and to secure from those whom one is
questioning, an admission of premisses of this sort is no simple
matter, e.g. that of the elements of the definition rendered the one
is genus and the other differentia, and that only the genus and
differentiae are predicated in the category of essence. Yet without
these premisses it is impossible to reason to a definition; for if any
other things as well are predicated of the thing in the category of
essence, there is no telling whether the formula stated or some
other one is its definition, for a definition is an expression
indicating the essence of a thing. The point is clear also from the
following: It is easier to draw one conclusion than many. Now in
demolishing a definition it is sufficient to argue against one point
only (for if we have overthrown any single point whatsoever, we
shall have demolished the definition); whereas in establishing a
definition, one is bound to bring people to the view that everything
contained in the definition is attributable. Moreover, in establishing
a case, the reasoning brought forward must be universal: for the
definition put forward must be predicated of everything of which the
term is predicated, and must moreover be convertible, if the
definition rendered is to be peculiar to the subject. In
overthrowing a view, on the other hand, there is no longer any
necessity to show one's point universally: for it is enough to show
that the formula is untrue of any one of the things embraced under the
term.
Further, even supposing it should be necessary to overthrow
something by a universal proposition, not even so is there any need to
prove the converse of the proposition in the process of overthrowing
the definition. For merely to show that the definition fails to be
predicated of every one of the things of which the term is predicated,
is enough to overthrow it universally: and there is no need to prove
the converse of this in order to show that the term is predicated of
things of which the expression is not predicated. Moreover, even if it
applies to everything embraced under the term, but not to it alone,
the definition is thereby demolished.
The case stands likewise in regard to the property and genus of a
term also. For in both cases it is easier to overthrow than to
establish. As regards the property this is clear from what has been
said: for as a rule the property is rendered in a complex phrase, so
that to overthrow it, it is only necessary to demolish one of the
terms used, whereas to establish it is necessary to reason to them
all. Then, too, nearly all the other rules that apply to the
definition will apply also to the property of a thing. For in
establishing a property one has to show that it is true of
everything included under the term in question, whereas to overthrow
one it is enough to show in a single case only that it fails to
belong: further, even if it belongs to everything falling under the
term, but not to that only, it is overthrown in this case as well,
as was explained in the case of the definition. In regard to the
genus, it is clear that you are bound to establish it in one way only,
viz. by showing that it belongs in every case, while of overthrowing
it there are two ways: for if it has been shown that it belongs either
never or not in a certain case, the original statement has been
demolished. Moreover, in establishing a genus it is not enough to show
that it belongs, but also that it belongs as genus has to be shown;
whereas in overthrowing it, it is enough to show its failure to belong
either in some particular case or in every case. It appears, in
fact, as though, just as in other things to destroy is easier than
to create, so in these matters too to overthrow is easier than to
establish.
In the case of an accidental attribute the universal proposition
is easier to overthrow than to establish; for to establish it, one has
to show that it belongs in every case, whereas to overthrow it, it
is enough to show that it does not belong in one single case. The
particular proposition is, on the contrary, easier to establish than
to overthrow: for to establish it, it is enough to show that it
belongs in a particular instance, whereas to overthrow it, it has to
be shown that it never belongs at all.
It is clear also that the easiest thing of all is to overthrow a
definition. For on account of the number of statements involved we are
presented in the definition with the greatest number of points for
attack, and the more plentiful the material, the quicker an argument
comes: for there is more likelihood of a mistake occurring in a
large than in a small number of things. Moreover, the other rules
too may be used as means for attacking a definition: for if either the
formula be not peculiar, or the genus rendered be the wrong one, or
something included in the formula fail to belong, the definition is
thereby demolished. On the other hand, against the others we cannot
bring all of the arguments drawn from definitions, nor yet of the
rest: for only those relating to accidental attributes apply generally
to all the aforesaid kinds of attribute. For while each of the
aforesaid kinds of attribute must belong to the thing in question, yet
the genus may very well not belong as a property without as yet
being thereby demolished. Likewise also the property need not belong
as a genus, nor the accident as a genus or property, so long as they
do belong. So that it is impossible to use one set as a basis of
attack upon the other except in the case of definition. Clearly, then,
it is the easiest of all things to demolish a definition, while to
establish one is the hardest. For there one both has to establish
all those other points by reasoning (i.e. that the attributes stated
belong, and that the genus rendered is the true genus, and that the
formula is peculiar to the term), and moreover, besides this, that the
formula indicates the essence of the thing; and this has to be done
correctly.
Of the rest, the property is most nearly of this kind: for it is
easier to demolish, because as a rule it contains several terms; while
it is the hardest to establish, both because of the number of things
that people must be brought to accept, and, besides this, because it
belongs to its subject alone and is predicated convertibly with its
subject.
The easiest thing of all to establish is an accidental predicate:
for in other cases one has to show not only that the predicate
belongs, but also that it belongs in such and such a particular way:
whereas in the case of the accident it is enough to show merely that
it belongs. On the other hand, an accidental predicate is the
hardest thing to overthrow, because it affords the least material: for
in stating accident a man does not add how the predicate belongs;
and accordingly, while in other cases it is possible to demolish
what is said in two ways, by showing either that the predicate does
not belong, or that it does not belong in the particular way stated,
in the case of an accidental predicate the only way to demolish it
is to show that it does not belong at all.
The commonplace arguments through which we shall be well supplied
with lines of argument with regard to our several problems have now
been enumerated at about sufficient length.
Book VIII
1
NEXT there fall to be discussed the problems of arrangement and
method in pitting questions. Any one who intends to frame questions
must, first of all, select the ground from which he should make his
attack; secondly, he must frame them and arrange them one by one to
himself; thirdly and lastly, he must proceed actually to put them to
the other party. Now so far as the selection of his ground is
concerned the problem is one alike for the philosopher and the
dialectician; but how to go on to arrange his points and frame his
questions concerns the dialectician only: for in every problem of that
kind a reference to another party is involved. Not so with the
philosopher, and the man who is investigating by himself: the
premisses of his reasoning, although true and familiar, may be refused
by the answerer because they lie too near the original statement and
so he foresees what will follow if he grants them: but for this the