Aristotle

The definiend, being compound, will contain both a generic and a differential term. In general, the generic term will be the better known of the two; yet sometimes the other is the better known. Whichever of the two is the better known, the definer ought to choose that, if all that he aims at is a mere substitution of one name in place of another. But, if he aims at something more or at the substitution of an explanatory proposition in place of a name (without which there can be no true definition), he ought then to choose the differentia in preference to the genus; for the definition is produced for the purpose of imparting knowledge, and the differentia, being usually less known than the genus, stands most in need of extraneous help to cognition.322 When the definition of the differentia has thus been tendered, you will examine whether it will be equally suitable for any other definiend also. If it be, you have an argument against the goodness of the definition. For example, the definition of odd number tendered to you may be — number having a middle. Here, since number is common both to the definiend and to the definition, having-a-middle is evidently put forward as the equivalent of odd. But this cannot stand as equivalent to odd; since various other subjects which are not odd (such, for example, as a body or a line), nevertheless have a middle. Since, then, we see that having-a-middle would be suitable in defining definiends which are not odd, it cannot be admitted, without some qualifying adjunct, as a good definition of odd. The adjunct annexed must declare in what sense middle is intended, since it is an equivocal phrase.323

29. If the definiend be a something really existent, the definition given of it ought not to be a proposition declaring an incompatible combination, such as neither does nor can exist. Some, for example, define white — colour mingled with fire; which is incompatible, since that which is incorporeal (colour) cannot be mingled with a body (fire).324

30. Again, suppose the definiend to be a Relatum: the correlate thereof must of course be declared in the definition. Care, however, must be taken that it shall be declared, not in vague generality but, distinctly and with proper specialization; otherwise, the definition will be incorrect either entirely or partially. Thus, if the respondent defines medicine — the science of the really existent, he is incorrect either wholly or partially. The relatum ought to reciprocate or to be co-extensive with its correlate.325 When the correlate, however, is properly specialized in the definition, it may be declared under several different descriptions; for the same real thing may be at once ens, album, bonum. None of these descriptions will be incorrect. Yet, if the correlate is thus described in the definition of a relatum, the definition cannot be considered good or sufficient. For it applies to more things besides the definiend; and a good definition ought to reciprocate or to be co-extensive with its definiend.326

31. Another mistake in defining is committed, when a man defines, not the subject purely and simply but, the subject in a high measure of excellence. Sometimes the rhetor (e.g.) is defined — one who can perceive and produce without omission all that there is plausible in any cause; the thief is defined — one who takes away secretly what belongs to another. But these are the definitions, not of a rhetor and a thief generally but, of a skilful rhetor and skilful thief. The thief is one who is bent on taking away secretly, not one who does take away secretly.327

32. Again, another error consists in defining what is desirable in itself and on its own account, as if it were desirable as a means towards some other end — as productive or preservative thereof. For example, if a man defines justice — that which is preservative of the laws; or wisdom — that which is productive of happiness, he presents them as if they were desirable, not for themselves but, with reference to something different from themselves. This is a mistake; and it is not less a mistake, though very possibly the same subject may be desirable both for itself and for the sake of something else. For the definition ought to enunciate what is best in the definiend; and the best of everything resides most in its essence, not in what it is relatively to something else. It is better to be desirable per se, than alterius causâ.328

33. Perhaps the definition tendered may be a complex proposition, enunciating two terms either jointly or severally, in one or other of three combinations. Either the definiend is A and B; or it is that which springs out of A and B; or it is A with B.329 In each of these three cases you may find arguments for impugning the definition.

a. Thus, take the first of the three. Suppose the respondent to define justice by saying, It is temperance and courage. You may urge against him, that two men, one of whom is temperate without being courageous, while the other is courageous without being temperate, will be just together, though neither of them separately is just; nay, that each of them separately (the one being temperate and cowardly, the other courageous and intemperate), will be both just and unjust; since, if justice is temperance and courage, injustice will be intemperance and cowardice.330 The definer is open to the farther objection that he treats enumeration of parts as identical with the whole; as if he defined a house — bricks and mortar, forgetting the peculiar mode of putting them together. Bricks and mortar may exist, and yet there may be no house.331

b. Next, suppose the definition to declare, that the definiend is that which springs from A and B — is a result or compound of A and B. You will then examine whether A and B are such as to yield any result; for some couples (as a line and a number) yield no result. Or, perhaps, the definiend may by its own nature inhere in some first subject, while A and B do not inhere in any one first subject, but one in the other; in which case the definition is assailable.332 Or, even granting that it is the nature of A and B to inhere in the same first subject, you may find that that first subject is not the same as the one in which the definiend inheres. Now the whole cannot thus inhere in one, and the parts in another: you will here have a good objection. Or, perhaps, it may appear that, if the whole be destroyed, the parts will be destroyed also; which ought not to be, but the reverse; for, when the parts are destroyed, the whole must necessarily vanish. Or, perhaps, the definiend may be good or bad, while the parts of the definition (A and B) are neither one nor the other. (Yet this last is not a conclusive objection; for it will sometimes happen in compound medicines that each of the ingredients is good, while they are bad if given in conjunction.)333 Or, perhaps, the whole may bear the same name as one of its parts: this, also, will render the definition impeachable. Still more will it be impeachable, if it enunciates simply a result or compound of A and B, without specifying the manner of composition; it ought to declare not merely the parts of the compound, but also the way in which they are put together to form the compound.334

c. Lastly, suppose the definition to declare that the definiend is A along with B. You will note, first, that this third head must be identical either with the first or with the second (e.g., honey with water means either honey and water, or the compound of honey with water); it will therefore be open to impeachment on one or other of the above-named grounds of objection, according as the respondent may admit.335 You may also distinguish all the different senses in which one thing may be said to be with another (e.g., when the two are in the same recipient, justice and courage together in the soul; or in the same place; or in the same time), and you may be able to show that in none of these senses can the two parts of the definition be truly said to be one along with the other.336 Or, if it be true that these two parts are co-existent in time, you may enquire whether they are not affirmed with relation to different correlates. E.g., The definition of courage may be tendered thus: Courage is daring along with right intelligence; upon which you may remark that daring may have reference to an act of spoliation, and that right intelligence may have reference to the preservation of health. Now a man who has both daring and right intelligence in these senses, cannot be termed courageous, and thus you will have an argument against the definition. And, even if they be affirmed with reference to the same correlate (e.g., the duties of a physician), a man who has both daring and right intelligence in reference to these duties will hardly be styled courageous; the term courage must be so defined as to have reference to its appropriate end; e.g., the dangers of war, or any still more public-spirited end.337 Another mistake may, perhaps, be committed in this same sort of definition — A along with B; as when, for example, the definition tendered of anger is — pain along with the belief of being treated with contempt. What the definer really intends here is, that the pain arises from the belief of being treated with contempt. But this is not expressed by the terms of his definition, in any one of their admissible meanings.338

34. Perhaps the definition, while including two or more distinct parts, may be tendered in this form: The definiend is the composition of A and B; e.g., animal is the composition of soul and body. You will first note that the definer has not declared what sort of composition. There is a great difference between one mode of composition and another; the mode must be specialized. Both flesh and bone may be defined — a composition of fire, earth, and water; but one mode of composition makes flesh, another makes bone, out of these same elements. You may also take the farther objection that to define a compound as composition is erroneous; the two are essentially disparate, one of them being abstract, the other concrete.339

35. If the definiend be in its nature capable of receiving two contrary attributes, and if the respondent define it by one or other of them, you have an argument against him. If one of them is admissible, the other must be equally so; and upon this supposition there would be two distinct definitions of the same subject; which has been already declared impossible. Thus, it is wrong to define the soul as a substance which is recipient of knowledge; the soul is also recipient of ignorance.340

36. Perhaps the definiend is not sufficiently well known to enable you to attack the definition as a whole, but you may find arguments against one or other of its parts; this is sufficient to upset it. If it be obscure and unintelligible, you should help to correct and re-model it until it becomes clear; you will then see what are the really assailable points in it. When you indicate and expose the obscurity, the respondent must either substitute some clearer exposition of his own meaning, or else he must acquiesce in that which you propose as substitute.341 If the improved definition which you propose is obviously clearer and better, his previous definition is of course put out of court; since there cannot be several definitions of the same subject.342

To conclude, one suggestion may be given bearing upon all the arguments that you have to carry on against definitions tendered by respondents:— Reflect on the definiend, and frame a definition of it for yourself, as cleverly as you can at the moment; or call to mind any good definition of it which you may have heard before. This will serve you as a standard with which to compare the definition tendered, so that you will see at once what there is in it either defective or redundant, and where you can find arguments against it.343

VII.

In the Seventh Book of the Topica Aristotle continues his review of the manner of debating theses which profess to define, but enters also on a collateral question connected with that discussion: viz., By what arguments are we to determine whether two Subjects or Predicates are the same Numero (modo maxime proprio), as distinguished from being the same merely Specie or Genere? To measure the extent of identity between any two subjects, is important towards the attack and defence of a definition.344

Two subjects (A and B) being affirmed as the same numero, you may test this by examining the Derivatives, the Co-ordinates, and the Opposites, of each. Thus, if courage is identical with justice, the courageous man will be identical with the just man; courageously will be identical with justly. Likewise, the opposite of courage (in all the four modes of Opposition) will be identical with the opposite of justice. Then, again, the generators and destroyers, the generations and destructions, of courage, will be identical with those of justice.345 If there be any predicate applied to courage in the superlative degree, the same predicate will also be applied to justice in the superlative degree.346 If there be a third subject C with which A is identical, B also will be identical therewith. The same attributes predicable of A will also be predicable of B; and, if the two be attributes, each will be predicable of the same subjects of which the other is predicable. Both will be comprised in the same Category, and will have the same genus and differentia. Both will increase or diminish under the same circumstances. Each, when added to or subtracted from any third subject, will yield the same result.347

Farther, in examining the thesis (A is identical numero with B) you must look not merely whether it involves actually any impossible consequences, but also whether any cases can be imagined in which it would involve such;348 whether the identity is not merely specie or genere; finally, whether the one can exist without the other.349

Such are the various loci available for argument against the thesis affirming the equivocal predicate same. All of them may be useful when you are impugning a definition; for the characteristic of this is to declare that the defining proposition is equivalent or identical with the defined name; and, if you can disprove such identity, you upset the definition. But these loci will be of little avail, if your task is to defend or uphold a definition; for, even if you succeed in establishing the above-mentioned identity, the definition may still be open to attack for other weaknesses or defects.350

To uphold, or prove by way of syllogism, requires a different procedure. It is a task hard, but not impossible. Most disputants assume without proving their definition, in the same way as the teachers of Geometry and Arithmetic do in their respective sciences. Aristotle tells us that he does not here intend to give a didactic exposition of Definition, nor of the proper way of defining accurately or scientifically. To do this (he says) belongs to the province of Analytic; while in the present treatise he is dealing merely with Dialectic. For the purposes, then, of Dialectic, he declares that syllogistic proof of a definition is practicable, inasmuch as the definition is only a proposition declaring what is essential to the definiend; and nothing is essential except genus (or genera) and differentiæ.351

Towards the establishment of the definition which you have to defend, you may find arguments by examining the Contraries and Opposites of the component terms, and of the defining proposition. If the opposite of the definition is allowed as defining properly the opposite of the definiend, you may argue from hence that your own definition is a good one.352 If you can show that there is declared in your definition a partial correspondence of contraries either separately in the genus, or separately in the differentia, you have a certain force of argument in your favour; and, if you can make out both the two separately, this will suffice for your entire definition.353 You may also draw arguments from the Derivatives, or Co-ordinates of your own terms; from Analogous Terms, or from Comparates (More or Less). If the definition of any one of these is granted to you, an argument is furnished for the defence of an analogous definition in the case of your own term. If it is conceded as a good definition that forgetfulness is — the casting away of knowledge, then the definition must also hold good that to forget is — to cast away knowledge. If destruction is admitted to be well defined — dissolution of essence, then to be destroyed is well defined — to be dissolved as to essence. If the wholesome may be defined — that which is productive of health, then also the profitable may be defined — that which is productive of good; that is, if the declaration of the special end makes a good definition in one case, so it will also in the other.354

These loci, from Analoga, from Derivatives, from Conjugates, are of the most frequent avail in dialectical debates or definitions. The disputant must acquire promptitude in the employment of them. He must learn, moreover, to test a definition tendered to him by calling to mind particulars and sub-species, so as to determine whether the definition fits them all. Such a procedure will be found especially serviceable in debate with one who upholds the Platonic Ideas. Care must also be taken to see whether the definiend is distorted from its proper signification, or whether it is used in defining itself.355

These last observations are addressed to the questioner or assailant of the definition. We have already seen however that his task is comparatively easy; the grand difficulty is to defend a definition. The respondent cannot at once see what he ought to aim at; and, even when he does see it, he has farther difficulty in obtaining the requisite concessions from his opponent, who may decline to grant that the two parts of the definition tendered are really the genus and differentia of the definiend; while, if there be any thing besides these two parts contained in the essence of the definiend, there is an excuse for declining to grant it.356 The opponent succeeds, if he can establish one single contradictory instance; accordingly, a syllogism with particular conclusion will serve his purpose. The respondent on the other hand, must meet each one of these instances, must establish an universal conclusion, and must show that his definition reciprocates with the definiend, so that, wherever the latter is predicable, the former is predicable likewise, and not in any other case whatever.357

So much greater are the difficulties belonging to the defence of a Definition, as compared with the attack upon it; and the same may be said about attack and defence of a Proprium, and of a Genus. In both cases, the assailant will carry his point, if he can show that the predicate in question is not predicable, in this relation, of all, or that it is not predicable, in this relation, of any one. But the defendant is required to make good the universal against every separate objection advanced against any one of the particulars. It is a general rule, that the work of destruction is easier than that of construction; and the present cases come under that rule.358 The hardest of all theses to defend, and the easiest to overthrow, is where Definition is affirmed; for the respondent in this case is required to declare well the essence of his subject, and he stands in need of the greatest number of auxiliary data; while all the Loci for attack, even those properly belonging to the Proprium, the Genus, and the Accident, are available against him.359 Next in order, as regards difficulty of defence, comes the theses affirming Proprium; where the respondent has to make out, not merely that the predicate belongs to the subject, but that it belongs thereunto exclusively and reciprocally: here also all the Loci for attack, even those properly belonging to Accident, are available.360 Easiest of all theses to defend, while it is the hardest to impugn, is that in which Accident alone is affirmed — the naked fact, that the predicate A belongs to the Subject B, without investing it with the character either of Genus or Proprium. Here what is affirmed is a minimum, requiring the smallest array of data to be conceded; moreover, the Loci available for attack are the fewest, since many of those which may be employed against Genus, Proprium, and Definition, have no application against a thesis affirming merely Accident.361 Indeed, if the thesis affirmed be only a proposition particular (and not universal), affirming Accident (and nothing more), the task of refuting it will be more difficult than that of maintaining it.362