[25] Speaking generally, one ought to be on the look-out for any discrepancy anywhere in any sort of predicate of each term, and in the things of which they are predicated. For all that is predicated of the one should be predicated also of the other, and of whatever the one is a predicate, the other should be a predicate as well.
[30] Moreover, as sameness is a term used in many ways, see whether things that are the same in one way are the same also in a different way. For there is either no necessity or even no possibility that things that are the same specifically or generically should be numerically the same—and we face the question whether they are or are not the same in that sense.
Moreover, see whether the one can exist without the other; for, if so, they will [35] not be the same.
2 · Such is the number of commonplace rules that relate to sameness. It is clear from what has been said that all the destructive commonplaces relating to sameness are useful also in questions of definition, as was said before;35 for if what is signified by the name and by the account are not the same, clearly the account given will not be a definition. None of the constructive commonplaces, on the other hand, [153a1] helps in the matter of definition; for proving that what falls under the account and the name are the same does not suffice to establish that the former is a definition, but a definition must have also all the other characters already announced. [5]
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 deduction: they always assume something of the kind as their starting point—both in geometry and in arithmetic and the other studies of [10] 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 it is possible for there to be a deduction of a thing’s definition and essence. For if a definition is an account signifying the essence of the thing and the [15] predicates contained therein ought also to be the only ones which are predicated of the thing in what it is, and genera and differentiae are predicated in what it is it is obvious that if one were to get an admission that these are the only attributes predicated in what it is, the account containing them will of necessity be a [20] definition; for it is impossible that anything else should be a definition, seeing that there is not anything else predicated of the object in what it is.
That a definition may thus be reached by a process of deduction is obvious. The means whereby it should be established have been more precisely defined elsewhere,36 but for the purposes of the inquiry now before us the same common-place [25] rules serve. For we have to examine into the contraries and other opposites of the thing, surveying the accounts used both as wholes and in part; for if the opposite account defines the opposite term, the account given must define the term before us. Seeing, however, that contraries may be conjoined in more than one way, we have to [30] select from those contraries the one to whose definition the definition in question seems most contrary.37 The accounts, then, have to be examined each as a whole in the way we have said, and also in part as follows. First of all, see that the genus rendered is correctly rendered; for if the contrary is found in the contrary genus, and the thing before you is not in that same genus, then it will clearly be in the contrary genus; for contraries must of necessity be either in the same genus or in [35] contrary genera. And we claim that contrary differentiae are predicated of contraries, e.g. of white and black, for the one disperses the vision, while the other compresses it. So that if contrary differentiae are predicated of the contrary term, [153b1] then those rendered in the definition will be predicated of the term before us. Seeing, then, that both the genus and the differentiae have been rightly rendered, clearly the account given must be a definition. It might be replied that there is no [5] necessity why contrary differentiae should be predicated of contraries, unless the contraries are 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’, [10] 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 is 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 [15] genus and differentiae, if the definition of the contrary term is 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 [20] predicated of opposites are either contrary or the same, 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. For that both should be the same is not possible; else contraries will have the same definition.
[25] 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 is loss of knowledge, to forget is to lose knowledge, and to have forgotten is to have lost knowledge. If, then, anyone whatever of these is agreed to, [30] the others must of necessity be agreed to as well. Likewise, also, if destruction is dissolution of substance, then to be destroyed is for a substance to be dissolved, and destructively is in such a way as to dissolve; if again destructive is apt to dissolve the substance, then also destruction is dissolution of substance. Likewise also with the rest: get an admission of any one of them whatever, and all the rest are admitted [35] too.
Moreover, look at it from the point of view of things that stand in the same relation to each other. For if healthy is productive of health, vigorous will be [154a1] productive of vigour, and useful will be productive of good. For each of these things is related in like manner to its appropriate end, so that if one of them is defined as productive of that end, this will be the definition of each of the rest as well.
Moreover, look at it from the point of view of greater and equal degrees, in all [5] the ways in which it is possible to establish a result by comparing two and two together. Thus if this defines that better than something else defines something else, and the latter is a definition, so too is the former. Further, if this defines that to the same degree as something else defines something else, and the latter is a definition, then so too is the former. This examination from the point of view of greater degrees is of no use when a single definition is compared with two, or two definitions with [10] one; for there cannot possibly be one definition of two things or two of the same thing.
4 · The most handy of the commonplace arguments are those just mentioned and those from coordinates 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 important are those of [15] most general application; for these are the most effective, e.g. that you should examine the individual cases, and that you should look to see in the case of their various species whether the account 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.38 Moreover see if a man has used a name [20] 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 propositions of this sort [25] is no simple matter, e.g. that of the elements of the given account the one is genus and the other differentia, and that the genus and differentiae are predicated in what it is. Yet without these it is impossible to deduce a definition; for if any other things as well are predicated of the object in what it is, there is no telling whether the [30] account stated or some other one is its definition; for a definition is an account 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 [35] definition, one must argue that everything contained in the definition is attributable. Moreover, in establishing a case, the deduction brought forward must be universal; for the definition must be predicated of everything of which the name is, [154b1] and must moreover be convertible, if the definition rendered is to be proper to the subject. In overthrowing a view, on the other hand, there is no longer any necessity to prove one’s point universally; for it is enough to prove that the account is untrue of any one of the things embraced under the name. Further, even supposing it should be necessary to overthrow something by a universal proposition, not even so [5] is there any need for it to be convertible in case of overthrowing. For proving that the definition is predicated of none of the things of which the name is predicated, is enough to overthrow it universally; and there is no need to prove in addition the converse of this, that the name is predicated of things of which the [10] account is not predicated. Moreover, even if it applies to everything embraced under the term, but not to it alone, the definition is 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 the property is for the most part rendered in a [15] complex phrase, so that to overthrow it, it is only necessary to demolish one of the terms used, whereas to establish it it is necessary to deduce them all. Then, too, nearly all the other rules that apply to the definition will apply also to the property [20] of a thing. For in establishing a property one has to show that it is true of everything included under the name, 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 [25] overthrowing it there are two ways; for if it has been proved that it belongs either to none or not to some, the original statement has been demolished. Moreover, in establishing a genus it is not enough to prove that it belongs, but you must prove also that it belongs as a genus; whereas in overthrowing it, it is enough to prove that it [30] does not belong either to some or to all. It appears 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 prove that it belongs in [35] every case, whereas to overthrow it, it is enough to prove 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 prove that it belongs in a [155a1] particular instance, whereas to overthrow it, it has to be proved that it belongs to none.
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, [5] the quicker a deduction 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 account is not proper, or what is rendered is not the genus, or something included in the account does not belong, the [10] 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 each of the aforesaid kinds must belong; yet the genus may very well not belong as a property without as yet being thereby demolished; likewise also the [15] 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 deduction (i.e. that the attributes stated belong, [20] and that what is rendered is the genus, and that the account is proper), and moreover, besides this, that the account 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 for the most part it contains several terms; while it is the hardest to establish, both because of the number of things that you must argue for, and, [25] 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 prove not only that the predicate belongs, but also that it belongs in such and such a way; whereas in the case of the accident it is enough to prove merely that it belongs. On the other hand, an accidental predicate is the hardest thing to [30] overthrow, because it affords the least material; for in stating an 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 proving 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 prove that it does not belong [35] 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 putting 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 [155b5] 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 [10] 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 philosopher does not care. Indeed, he may possibly be even anxious to secure axioms as familiar and as near to the question in hand as possible; for these are the bases on which scientific deductions are built up. [15]
The sources from which one’s commonplace rules should be drawn have already been described: we have now to discuss the arrangement and formation of questions and first to distinguish the propositions, other than the necessary ones, which have to be adopted. By necessary propositions are meant those through which the deduction is constructed. Those which are secured other than these are of four [20] kinds: t
hey serve either inductively to secure the universal premiss being granted, or to lend weight to the argument, or to conceal the conclusion, or to render the argument more clear. Beside these there is no other proposition which need be secured: these are the ones whereby you should try to multiply and formulate your [25] questions. Those which are used to conceal the conclusion serve a contentious purpose; but inasmuch as an undertaking of this sort is always conducted against another person, we are obliged to employ them as well.
The necessary propositions through which the deduction is effected, ought not to be propounded directly in so many words. Rather one should keep as far away [30] from them as possible. Thus if one desires to secure an admission that the knowledge of contraries is one, one should claim it not of contraries, but of opposites; for, if he grants this, one will then deduce that the knowledge of contraries is also the same, seeing that contraries are opposites; if he does not, one should secure the admission by induction, by formulating propositions to that effect [35] in the case of particular contraries. For one must secure the necessary propositions either by deduction or by induction, or else partly by one and partly by the other, although any propositions which are too obvious may be formulated in so many words. This is because the coming conclusion is less easily discerned at the greater [156a1] distance and in the process of induction, while at the same time, even if one cannot reach the required premisses in this way, it is still open to one to formulate them in so many words. The propositions, other than these, that were mentioned above, must be secured with a view to the latter. The way to employ them is as follows: [5] induction should proceed from individual cases to the universal and from the familiar to the unknown; and the objects of perception are more familiar, either without qualification or to most people. Concealment is obtained by securing through preliminary deductions the premisses through which the deduction of the original proposition is going to be constructed—and as many of them as possible. This is likely to be effected by deducing not only the necessary propositions but also [10] some of those which are required to establish them. Moreover, do not state the conclusions but deduce them later all together; for this is likely to keep the answerer at the greatest possible distance from the original proposition. Speaking generally, a man who desires to get information by a concealed method should so put his questions that when he has put his whole argument and has stated the conclusion, [15] people still ask ‘Well, but why is that?’ This result will be secured best of all by the method above described; for if one states only the final conclusion, it is unclear how it comes about; for the answerer does not foresee on what grounds it is based, because the previous deductions have not been fully articulated; while the deduction [20] of the conclusion is likely to be least articulated if we lay down not the assumptions on which it is based, but only those by which the deduction proceeds.
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