by Aristotle
It is a useful rule, too, not to secure the axioms on which the deductions are based in their proper order, but alternately those that conduce to one conclusion and [25] those that conduce to another; for, if the appropriate ones are set side by side, the conclusion that will result from them is more obvious in advance.
One should also, wherever possible, secure the universal proposition by a definition relating not to the terms themselves but to their co-ordinates; for people are deceived whenever the definition is taken in regard to a co-ordinate, into [30] thinking that they are not making the admission universally. E.g. supposing one had to secure the admission that the angry man desires vengeance on account of an apparent slight, and were to secure that anger is a desire for vengeance on account of an apparent slight, for clearly, if this were secured, we should have universally what we intend. If, on the other hand, people formulate propositions relating to the actual terms themselves, they often find that the answerer refuses to grant them [35] because on the actual term itself he is readier with his objection, e.g. that the angry man does not desire vengeance, because we become angry with our parents, but we do not desire vengeance on them. Very likely the objection is not valid; for upon some people it is vengeance enough to cause them pain and make them sorry; but still it gives a certain plausibility and air of reasonableness to the denial of the [156b1] proposition. In the case, however, of the definition of anger it is not so easy to find an objection.
Moreover, formulate your proposition as though you did so not for its own sake, but in order to get at something else; for people guard against granting what an opponent’s case requires. Speaking generally, a questioner should leave it as far [5] as possible doubtful whether he wishes to secure an admission of the proposition or of its opposite; for if it is uncertain what the argument requires, people are more ready to say what they themselves think.
Moreover, try to secure admissions by means of likeness; for such admissions [10] are plausible, and the universal involved is less patent; e.g. that as knowledge and ignorance of contraries is the same, so too perception of contraries is the same; or vice versa, that since the perception is the same, so is the knowledge also. This argument resembles induction, but is not the same thing; for in induction it is the universal whose admission is secured from the particulars, whereas in arguments [15] from likeness, what is secured is not the universal under which all the like cases fall.
It is a good rule also, occasionally to bring an objection against oneself; for answerers are put off their guard against those who appear to be arguing impartially. It is useful too, to add that so and so is generally held or commonly said; [20] for people are shy of upsetting the received opinion unless they have some objection to urge; and at the same time they are cautious about upsetting such things because they themselves too find them useful. Moreover, do not be insistent, even though you really require the point; for insistence always arouses the more opposition. Further, formulate your premiss as though it were an illustration; for people admit [25] the more readily a proposition made to serve some other purpose, and not required on its own account. Moreover, do not formulate the very proposition you need to secure, but rather something from which that necessarily follows; for people are more willing to admit the latter, because it is not so clear from this what the result will be, and if the one has been secured, the other has been secured also. Again, one should put last the point which one most wishes to have conceded; for people are [30] specially inclined to deny the first questions put to them, because most people in asking questions put first the points which they are most eager to secure. But in dealing with some people propositions of this sort should be put forward first; for ill-tempered men admit most readily what comes first, unless the conclusion that will result actually stares them in the face, while at the close of an argument they [35] show their ill-temper. Likewise also with those who consider themselves smart at answering; for when they have admitted what comes first they finally quibble to the effect that the conclusion does not follow from their admissions; yet they make admissions readily, confident in their own character, and imagining that they [157a1] cannot suffer any reverse. Moreover, it is well to expand the argument and insert things that it does not require at all, as do those who draw false geometrical figures; for in the mass of material the whereabouts of the falsity is obscured. For this reason also a questioner sometimes evades observation as he adds in a corner what, [5] if he formulated it by itself, would not be granted.
For concealment, then, the rules which should be followed are the above. Ornament is attained by induction and distinction of things closely akin. What sort of process induction is is obvious; as for distinction, an instance of the kind of thing meant is the distinction of one form of knowledge as better than another by being either more precise, or concerned with better objects; or the distinction of sciences [10] into speculative, practical, and productive. For everything of this kind lends additional ornament to the argument, though there is no necessity to say them, so far as the conclusion goes.
For clearness, examples and illustrations should be adduced—and let the [15] illustrations be appropriate and drawn from things that we know, as in Homer and not as in Choerilus; for them the proposition is likely to become clearer.
2 · In dialectical argument, deduction should be employed in reasoning against dialecticians rather than against the crowd; induction, on the other hand, is [20] most useful against the crowd. This point has been mentioned previously as well.39 In induction, it is possible in some cases to ask the question in its universal form, but in others this is not easy, because there is no established general name that covers all the resemblances: in this case, when people need to secure the universal, they use [25] the phrase ‘in all cases of this sort’. But it is one of the very hardest things to distinguish which of the things adduced are of this sort, and which are not; and in this connexion people often mislead one another in their discussion, the one party asserting the likeness of things that are not alike, and the other disputing the likeness of things that are. One ought, therefore, to try oneself to coin a word to [30] cover all things of the given sort, so as to leave no opportunity either to the answerer to dispute, and say that the thing advanced does not answer to a like description, or to the questioner to suggest falsely that it does answer to a like description, for many things appear to answer to like descriptions that do not really do so.
If one has made an induction on the strength of several cases and yet the [35] answerer refuses to grant the universal proposition, then it is fair to demand his objection. But until one has oneself stated in what cases it is so, it is not fair to demand that he shall say in what cases it is not so; for one should make the induction [157b1] first, and then demand the objection. One ought, moreover, to claim that the objections should not be brought in reference to the actual subject of the proposition, unless that subject happens to be the one and only thing of the kind, as for instance two is the one prime number among the even numbers; for, unless he can say that this subject is unique of its kind, the objector ought to make his objection in regard to some other. People sometimes object to a universal proposition, and bring their objection not in regard to the thing itself, but in regard to some homonym of it; thus they argue that a man can very well have a colour or a foot or a [5] hand other than his own, for a painter may have a colour that is not his own, and a cook may have a foot that is not his own. To meet them, therefore, you should draw the distinction before putting your question in such cases; for so long as the ambiguity remains undetected, the objection to the proposition will seem valid. If, however, he checks the series of questions by an objection in regard not to some homonym, but to the actual thing asserted, the questioner should withdraw the [10] point objected to, and form the remainder into a universal proposition, until he secures what he requires; e.g. in the case of forgetfulness and having forgotten; for people refuse to admit that the man who has lost his knowledge of a thing has forgotten it, becaus
e if the thing alters, he has lost knowledge of it, but he has not forgotten it. Accordingly the thing to do is to withdraw the part objected to, and [15] assert the remainder, e.g. that if a person has lost knowledge of a thing while it still remains, he then has forgotten it. One should similarly treat those who object to the statement that the greater the good, the greater the evil that is its opposite, for they allege that health, which is a less good thing than vigour, has a greater evil as its opposite; for disease is a greater evil than debility. In this case too, therefore, we [20] have to withdraw the point objected to; for when it has been withdrawn, the man is more likely to admit the proposition, e.g. that the greater good has the greater evil as its opposite, unless the one good involves the other as well, as vigour involves health. This should be done not only when he formulates an objection, but also if, without so doing, he refuses to admit the point because he foresees something of the [25] kind; for if the point objected to is withdrawn, he will be forced to admit the proposition because he cannot foresee in the rest of it any case where it does not hold true: if he refuses to admit it, then when asked for an objection he certainly will be unable to render one. Propositions that are partly false and partly true are of this type; for in the case of these it is possible by withdrawing a part to leave the rest [30] true. If, however, you formulate the proposition on the strength of many cases and he has no objection to bring, you may claim that he should admit it; for a dialectical proposition is one which thus holds in several instances and to which no objection is forthcoming.
Whenever it is possible to deduce the same conclusion either through or without a reductio per impossibile, if one is demonstrating and not arguing [35] dialectically it makes no difference which method of deduction is adopted, but in argument with another deduction per impossibile should be avoided. For where one has deduced without the reductio per impossibile, no dispute can arise; if, on the other hand, one deduces an impossible conclusion, unless its falsehood is too plainly [158a1] manifest, people deny that it is impossible, so that the questioners do not get what they want.
One should put forward propositions that hold true of several cases, and to which either no objection whatever appears or at least not any on the surface; for [5] when people cannot see any case in which it is not so, they admit it for true.
The conclusion should not be put in the form of a question; otherwise if he rejects it, it looks as if the deduction has failed. For often, even if it is not put as a question but advanced as a consequence, people deny it, and then those who do not [10] see what follows from the previous admissions do not realize that those who deny it have been refuted; when, then, the one man merely asks it as a question without even saying that it follows, and the other denies it, it looks altogether as if the deduction has failed.
[15] Not every universal seems to be a dialectical proposition, e.g. ‘What is man?’ or ‘In how many ways is the good used?’ For a dialectical proposition must be of a form to which it is possible to reply ‘Yes’ or ‘No’, whereas to the aforesaid it is not possible. For this reason questions of this kind are not dialectical unless the questioner himself draws distinctions or divisions before expressing them, e.g. ‘Is [20] the good used in this way, or in this?’ For questions of this sort are easily answered by a Yes or a No. Hence one should endeavour to formulate propositions of this kind in this form. It is at the same time also perhaps fair to ask the other man how many uses of the good there are, whenever you have yourself distinguished and formulated them, and he will not admit them at all.
[25] Any one who keeps on asking one thing for a long time is a bad inquirer. For if he does so though the person questioned keeps on answering the questions, clearly he asks a large number of questions, or else asks the same question a large number of times: in the one case he merely babbles, in the other he fails to deduce; for every deduction rests on a small number of premisses. If, on the other hand, he does it because the person questioned does not answer the questions, he is at fault in not [30] taking him to task or breaking off the discussion.
3 · The same hypotheses may be both difficult to attack and easy to defend. Such are those things which stand first and those which stand last in the order of nature. For the former require definition, while the latter have to be arrived at through many steps if one wishes to secure a continuous proof from first principles, [35] or else the arguments wear the air of sophistry; for to demonstrate anything is impossible unless one begins with the appropriate principles, and connects inference with inference till the last are reached. Now to define first principles is just what answerers do not care to do, nor do they pay any attention if the questioner makes a definition; and yet until it is clear what it is that is proposed, it is not easy to tackle [158b1] it. This sort of thing happens particularly in the case of the first principles; for while the other propositions are proved through these, these cannot be proved through anything else: we are obliged to get to know every item of that sort by a definition.
[5] Things that lie close to the first principle are also hard to tackle; for it is not possible to bring many arguments in regard to them, because of the small number of those steps, between the conclusion and the principle, whereby the succeeding propositions have to be proved. The hardest, however, of all definitions to treat in argument are those that employ names about which, in the first place, it is uncertain whether they are used in one way or several, and, further, it is not known whether [10] they are used literally or metaphorically by the definer. For because of their obscurity, it is impossible to argue; and because of the impossibility of saying whether this obscurity is due to their being used metaphorically, it is impossible to criticize them. [15]
In general, it is safe to suppose that, whenever any problem proves intractable, it either needs definition, or has either several uses or a metaphorical use, or it is not far removed from the first principles; or else the reason is40 that we have yet to discover in the first place just this—in which of the aforesaid directions the source [20] of our difficulty lies: when we have made this clear, then obviously our business must be either to define or to distinguish, or to supply the intermediate premisses; for it is through these that the final conclusions are proved.
Many theses are not easy to argue about or tackle because the definition has not been correctly rendered: e.g. whether one thing has one contrary or many—here [25] when contraries have been properly defined, it is easy to argue whether it is possible for the same thing to have several contraries or not. Similarly also with other terms requiring definition. It appears also in mathematics that the difficulty in constructing a figure is sometimes due to a defect in definition; e.g. in proving that the line [30] which cuts the plane parallel to one side divides similarly both the line and the area. If the definition is given, the fact asserted becomes immediately clear; for the areas have the same fraction subtracted from them as have the sides and this is the definition of the same ratio. In general, the primary elements are very easy to prove, [35] if the definitions involved, e.g., the nature of a line or of a circle, are laid down (only the arguments that can be brought in regard to each of them are not many, because there are not many intermediate steps); if, on the other hand, the definitions of the principles are not laid down, it is difficult and may even prove quite impossible. It is [159a1] the same in the case of dialectical arguments.
One must be aware then, whenever a thesis is hard to tackle, that one or other of the aforesaid things has happened to it. Whenever, on the other hand, it is a harder task to argue about the axiom or the proposition than about the thesis, a [5] doubt may arise whether such claims should be admitted or not; for if a man is going to refuse to admit it and claim that it should be argued for, he will be prescribing a harder undertaking than was originally proposed; if, on the other hand, he grants it, he will be convinced on the strength of what is less convincing. If, then, it is essential not to enhance the difficulty of the problem, he had better grant it; if, on the other hand, it is essential to
deduce through premisses that are more familiar, he had [10] better refuse. In other words, one who is trying to learn ought not to grant it, unless it is more familiar; but one who is training should grant it, if he is merely satisfied of its truth. Clearly, then, the circumstances under which such admissions should be claimed are different for a questioner and for a teacher.
[15] 4 · As to the formulation, then, and arrangement of one’s questions, about enough has been said.
With regard to the giving of answers, we must first define what is the business of a good answerer, as of a good questioner. The business of the questioner is so to develop the argument as to make the answerer utter the most implausible of the [20] necessary consequences of his thesis; while that of the answerer is to make it appear that it is not he who is responsible for the impossibility or paradox, but only his thesis; for one may, no doubt, distinguish between the mistake of taking up a wrong thesis to start with, and that of not maintaining it properly, when once taken up.