Aristotle

by Various Works [lit]

  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