Aristotle

Such are the four distinct helps, towards facility of syllogizing, enumerated by Aristotle. It will be observed that the third and fourth (study of Resemblances and Differences) bear more upon matters of fact and less upon words; while the second (τὸ ποσαχῶς), though doubtless also bearing on matters of fact and deriving from thence its main real worth, yet takes its departure from terms and propositions, and proceeds by comparing multiplied varieties of these in regard to diversity of meaning. Upon this ground it is, apparently, that Aristotle has given so much fuller development to the second head than to the third and fourth; for, in the Topica, he is dealing with propositions and counter-propositions — with opinions and counter-opinions, not with science and truth.

He proceeds to indicate the different ways in which these three helps (the second, third, and fourth) further the purpose of the dialectician — respondent as well as assailant. Unless the different meanings of the term be discriminated, the respondent cannot know clearly what he admits or what he denies; he may be thinking of something different from what the assailant intends, and the syllogisms constructed may turn upon a term only, not upon any reality.66 The respondent will be able to protect himself better against being driven into contradiction, if he can distinguish the various meanings of the same term; for he will thus know whether the syllogisms brought against him touch the real matter which he has admitted.67 On the other hand, the assailant will have much facility in driving his opponent into contradiction, if he (the assailant) can distinguish the different meanings of the term, while the respondent cannot do so; in those cases at least where the proposition is true in one sense of the term and false in another.68 This manner of proceeding, however, is hardly consistent with genuine Dialectic. No dialectician ought ever to found his interrogations and his arguments upon a mere unanalysed term, unless he can find absolutely nothing else to say in the debate.69

The third help (an acquaintance with Differences) will be of much avail on all occasions where we have to syllogize upon Same and Different, and where we wish to ascertain the essence or definition of any thing; for we ascertain this by exclusion of what is foreign thereunto, founded on the appropriate differences in each case.70

Lastly, the fourth help (the intelligent survey of Resemblances) serves us in different ways:— (1) Towards the construction of inductive arguments; (2) Towards syllogizing founded upon assumption; (3) Towards the declaration of definitions. As to the inductive argument, it is founded altogether on a repetition of similar particulars, whereby the universal is obtained.71 As to the syllogizing from an assumption, the knowledge of resemblances is valuable, because we are entitled to assume, as an Endoxon or a doctrine conformable to common opinion, that what happens in any one of a string of similar cases will happen also in all the rest. We lay down this as the major proposition of a syllogism; and thus, if we can lay hold of any one similar case, we can draw inference from it to the matter actually in debate.72 Again, as to the declaration of definitions, when we have once discovered what is the same in all particular cases, we shall have ascertained to what genus the subject before us belongs;73 for that one of the common predicates which is most of the essence, will be the genus. Even where the two matters compared are more disparate than we can rank in the same genus, the knowledge of resemblances will enable us to discover useful analogies, and thus to obtain a definition at least approximative. Thus, as the point is in a line, so is the unit in numbers; each of them is a principium; this, therefore, is a common genus, which will serve as a tolerable definition. Indeed this is the definition of them commonly given by philosophers; who call the unit principium of number, and the point principium of a line, thus putting one and the other into a genus common to both.74

II.

The First Book of the Topica, which we have thus gone through, was entitled by some ancient commentators τὰ πρὸ τῶν Τόπων — matters preliminary to the Loci. This is quite true, as a description of its contents; for Aristotle in the last words of the book, distinctly announces that he is about to enumerate the Loci towards which the four above-mentioned Organa will be useful.75

Locus (τόπος) is a place in which many arguments pertinent to one and the same dialectical purpose, may be found — sedes argumentorum. In each locus, the arguments contained therein look at the thesis from the same point of view; and the locus implies nothing distinct from the arguments, except this manner of view common to them all. In fact, the metaphor is a convenient one for designating the relation of every Universal generally to its particulars: the Universal is not a new particular, nor any adjunct superimposed upon all its particulars, but simply a place in which all known similar particulars may be found grouped together, and in which there is room for an indefinite number of new ones. If we wish to arm the student with a large command of dialectical artifices, we cannot do better than discriminate the various groups of arguments, indicating the point of view common to each group, and the circumstances in which it becomes applicable. By this means, whenever he is called upon to deal with a new debate, he will consider the thesis in reference to each one of these different loci, and will be able to apply arguments out of each of them, according as the case may admit.

The four Helps (ὄργανα) explained in the last book differ from the Loci in being of wider and more undefined bearing: they are directions for preparatory study, rather than for dealing with any particular situation of a given problem; though it must be confessed that, when Aristotle proceeds to specify the manner in which the three last-mentioned helps are useful, he makes considerable approach towards the greater detail and particularization of the Loci. In entering now upon these, he reverts to that quadruple classification of propositions and problems (according to the four Predicables), noted at the beginning of the treatise, in which the predicate is either Definition, Proprium, Genus, or Accident, of the subject. He makes a fourfold distribution of Loci, according as they bear upon one or other of these four. In the Second and Third Books, we find those which bear upon propositions predicating Accident; in the Fourth Book, we pass to Genus; in the Fifth, to Proprium; in the Sixth and Seventh, to Definition.

The problem or thesis propounded for debate may have two faults on which it may be impugned: either it may be untrue; or it may be expressed in a way departing from the received phraseology.76 It will be universal, or particular, or indefinite; and either affirmative or negative; but, in most cases, the respondent propounds for debate an affirmative universal, and not a negative or a particular.77 Aristotle therefore begins with those loci that are useful for refuting an Affirmative Universal; though, in general, the same arguments are available for attack and defence both of the universal and of the particular; for if you can overthrow the particular, you will have overthrown the universal along with it, while if you can defend the universal, this will include the defence of the particular. As the thesis propounded is usually affirmative, the assailant undertakes the negative side or the work of refutation. And this indeed (as Eudemus, the pupil of Aristotle, remarked, after his master78) is the principal function and result of dialectic exercise; which refutes much and proves very little, according to the analogy of the Platonic Dialogues of Search.

Aristotle takes the four heads — Accident, Genus, Proprium, and Definition, in the order here enumerated. The thesis of which the predicate is enunciated as Accident, affirms the least, is easiest to defend, and hardest to upset.79 When we enunciate Genus or Proprium, we affirm, not merely that the predicate belongs to the subject (which is all that is affirmed in the case of Accident), but, also something more — that it belongs to the subject in a certain manner and relation. And when we enunciate Definition, we affirm all this and something reaching yet farther — that it declares the whole essence of the definitum, and is convertible therewith. Accordingly, the thesis of Definition, affirming as it does so very much, presents the most points of attack and is by far the hardest to defend.80 Next in point of difficulty, for the respondent, comes the Proprium.

Beginning thus with the thesis enunciating Accident, Aristotle enumerates no less than thirty-seven distinct loci or argumentative points of view bearing upon it. Most of them suggest modes of assailing the thesis; but there are also occasionally intimations to the respondent how he may best defend himself. In this numerous list there are indeed some items repetitions of each other, or at least not easily distinguishable.81 As it would be tedious to enumerate them all, I shall select some of the most marked and illustrative.

1. The respondent has enunciated a certain predicate as belonging in the way of accident, to a given subject. Perhaps it may belong to the subject; yet not as accident, but under some one of the other three Predicables. Perhaps he may have enunciated (either by explicit discrimination, or at least by implication contained in his phraseology) the genus as if it were an accident, — an error not unfrequently committed.82 Thus, if he has said, To be a colour is an accident of white, he has affirmed explicitly the genus as if it were an accident. And he has affirmed the same by implication, if he has said, White (or whiteness) is coloured. For this is a form of words not proper for the affirmation of a genus respecting its species, in which case the genus itself ought to stand as a literal predicate (White is a colour), and not to be replaced by one of its derivatives (White is coloured). Nor can the proposition be intended to be taken as affirming either proprium or definition; for in both these the predicate would reciprocate and be co-extensive with the subject, whereas in the present case there are obviously many other subjects of which it may be predicated that they are coloured.83 In saying, White is coloured, the respondent cannot mean to affirm either genus, proprium, or definition; therefore he must mean to affirm accident. The assailant will show that this is erroneous.

2. Suppose the thesis set up by the respondent to be an universal affirmative, or an universal negative. You (the interrogator or assailant) should review the particulars contained under these universals. Review them not at once as separate individuals, but as comprised in subordinate genera and species; beginning from the highest, and descending down to the lowest species which is not farther divisible except into individuals. Thus, if the thesis propounded be, The cognition of opposites is one and the same cognition; you will investigate whether this can be truly predicated respecting all the primary species of Opposita: respecting Relata and Correlata, respecting Contraries, respecting Contradictories, respecting Habitus and Privatio. If, by going thus far, you obtain no result favourable to your purpose,84 you must proceed farther, and subdivide until you come to the lowest species:— Is the cognition of just and unjust one and the same? that of double and half? of sight and blindness? of existence and non-existence? If in all, or in any one, of these cases you can show that the universal thesis does not hold, you will have gained your point of refuting it. On the other hand, if, when you have enumerated many particulars, the thesis is found to hold in all, the respondent is entitled to require you to grant it as an universal proposition, unless you can produce a satisfactory counter-example. If you decline this challenge, you will be considered an unreasonable debater.85

3. You will find it useful to define both the accident predicated in the thesis, and the subject respecting which it is predicated, or at least one of them: you will see then whether these definitions reveal anything false in the affirmation of the thesis. Thus, if the thesis affirms that it is possible to do injustice to a god, you will define what is meant by doing injustice. The definition is — hurting intentionally: you can thus refute the thesis by showing that no injustice to a god can possibly be done; for a god cannot be hurt.86 Or let the thesis maintained be, The virtuous man is envious. You define envy, and you find that it is — vexation felt by reason of the manifest success of some meritorious man. Upon this definition it is plain that the virtuous man cannot feel envy: he would be worthless, if he did feel it. Perhaps some of the terms employed in your definition may themselves require definition; if so, you will repeat the process of defining until you come to something plain and clear.87 Such an analysis will often bring out some error at first unperceived in the thesis.

4. It will be advisable, both for assailant and respondent, to discriminate those cases in which the authority of the multitude is conclusive from those in which it is not. Thus, in regard to the meaning of terms and in naming objects, we must speak like the multitude; but, when the question is as to what objects deserve to be denominated so and so, we must not feel bound by the multitude, if there be any special dissentient authority.88 That which produces good health we must call wholesome, as the multitude do; but, in calling this or that substance wholesome, the physician must be our guide.

5. Aristotle gives more than one suggestion as to those cases in which the terms of the thesis have a double or triple sense, yet in which the thesis is propounded either as an universal affirmative or as an universal negative. If the respondent is himself not aware of the double sense of his thesis, while you (the questioner) are aware of it, you will prove the point which you are seeking to establish against him in one or other of the two senses, if you cannot prove it in both. If he is aware of it in the double sense, he will insist that you have chosen the sense which he did not intend.89 This mode of procedure will be available to the respondent as well as to you; but it will be harder to him, since his thesis is universal. For, in order to make good an universal thesis, he must obtain your assent to a preliminary assumption or convention, that, if he can prove it in one sense of the terms, it shall be held proved in both; and, unless the proposition be so plausible that you are disposed to grant him this, he will not succeed in the procedure.90 But you on your side, as refuting, do not require any such preliminary convention or acquiescence; for, if you prove the negative in any single case, you succeed in overthrowing the universal affirmative, while, if you prove the affirmative in any single case, you succeed in overthrowing the universal negative.91 Such procedure, however, is to be adopted only when you can find no argument applicable to the equivocal thesis in all its separate meanings; this last sort of argument, wherever it can be found, being always better.92

In cases where the double meaning is manifest, the two meanings must be distinguished by both parties, and the argument conducted accordingly. Where the term has two or more meanings (not equivocal but) related to each other by analogy, we must deal with each of these meanings distinctly and separately.93 If our purpose is to refute, we select any one of them in which the proposition is inadmissible, neglecting the others: if our purpose is to prove, we choose any one in which the proposition is true, neglecting the others.94

6. Observe that a predicate which belongs to the genus does not necessarily belong to any one of its species, but that any predicate which belongs to one of the species does belong also to the genus; on the other hand, that any predicate which can be denied of the genus may be denied also of all its contained species, but that any predicate which can be denied of some one or some portion of the contained species cannot for that reason be denied of the genus. You may thus prove from one species to the genus, and disprove from the genus to each one species; but not vice versâ. Thus, if the respondent grants that there exist cognitions both estimable and worthless, you are warranted in inferring that there exist habits of mind estimable and worthless; for cognition is a species under the genus habit of mind. But if the negative were granted, that there exist no cognitions both estimable and worthless, you could not for that reason infer that there are no habits of mind estimable and worthless. So, if it were granted to you that there are judgments correct and erroneous, you could not for that reason infer that there were perceptions of sense correct and erroneous; perceiving by sense being a species under the genus judging. But, if it were granted that there were no judgments correct and erroneous, you might thence infer the like negative about perceptions of sense.95

7. Keep in mind also that if there be any subject of which you can affirm the genus, of that same subject you must be able to affirm one or other of the species contained under the genus. Thus, if science be a predicate applicable, grammar, music, or some other of the special sciences must also be applicable: if any man can be called truly a scientific man, he must be a grammarian, a musician, or some other specialist. Accordingly, if the thesis set up by your respondent be, The soul is moved, you must examine whether any one of the known varieties of motion can be truly predicated of the soul, e.g., increase, destruction, generation, &c. If none of these special predicates is applicable to the soul, neither is the generic predicate applicable to it; and you will thus have refuted the thesis. This locus may serve as a precept for proof as well as for refutation; for, equally, if the soul be moved in any one species of motion, it is moved, and, if the soul be not moved in any species of motion, it is not moved.96

8. Where the thesis itself presents no obvious hold for interrogation, turn over the various definitions that have been proposed of its constituent terms; one or other of these definitions will often afford matter for attack.97 Look also to the antecedents and consequents of the thesis — what must be assumed and what will follow, if the thesis be granted. If you can disprove the consequent of the proposition, you will have disproved the proposition itself. On the other hand, if the antecedent of the proposition be proved, the proposition itself will be proved also.98 Examine also whether the proposition be not true at some times, and false at other times. The thesis, What takes nourishment grows necessarily, is true not always, but only for a certain time: animals take nourishment during all their lives, but grow only during a part of their lives. Or, if a man should say that knowing is remembering, this is incorrect; for we remember nothing but events past, whereas we know not only these, but present and future also.99

9. It is a sophistical procedure (so Aristotle terms it) to transfer the debate to some point on which we happen to be well provided with arguments, lying apart from the thesis defended. Such transfer, however, may be sometimes necessary. In other cases it is not really but only apparently necessary; in still other cases it is purely gratuitous, neither really nor apparently necessary. It is really necessary, when the respondent, having denied some proposition perfectly relevant to his thesis, stands to his denial and accepts the debate upon it, the proposition being one on which a good stock of arguments may be found against him; also, when you are endeavouring to disprove the thesis by an induction of negative analogies.100 It is only apparently, and not really, necessary, when the proposition in debate is not perfectly relevant to the thesis, but merely has the semblance of being so. It is neither really nor apparently necessary, when there does not exist even this semblance of relevance, and when some other way is open of bringing bye-confutation to bear on the respondent. You ought to avoid entirely such a procedure in this last class of cases; for it is an abuse of the genuine purpose of Dialectic. If you do resort to it, the respondent should grant your interrogations, but at the same time notify that they are irrelevant to the thesis. Such notification will render his concessions rather troublesome than advantageous for your purpose.101