The Complete Works of Aristotle One and Two

Next, look from the point of view of affirmations and negations; and first from [5] the point of view of the predicates taken by themselves. This commonplace rule is useful only for a destructive purpose. Thus (e.g.) see if the affirmation or the attribute predicated affirmatively is a property of the subject; for then neither the negation nor the attribute predicated negatively will be a property of the subject. Also if the negation or the attribute predicated negatively is a property of the [10] subject, then neither the affirmation nor the attribute predicated negatively will be a property of the subject: e.g. inasmuch as animate is a property of living creature, inanimate will not be a property of living creature.

Secondly look from the point of view of the predicates, positive or negative, and their respective subjects; and see, for destructive purposes, if the affirmation fails to [15] be a property of the affirmation; for then neither will the negation be a property of the negation. Also, if the negation fails to be a property of the negation, neither will the affirmation be a property of the affirmation. Thus (e.g.) inasmuch as animal is not a property of man, neither will not-animal be a property of not-man. Also if [20] not-animal seems not to be a property of not-man, neither will animal be a property of man. For constructive purposes, on the other hand, see if the affirmation is a property of the affirmation; for then the negation will be a property of the negation as well. Also if the negation is a property of the negation, the affirmation will be a property of the affirmation as well. Thus (e.g.) inasmuch as it is a property of [25] not-animal not to live, it will be a property of animal to live; also if it seems to be a property of animal to live, it will also seem to be a property of not-animal not to live.

Thirdly, look from the point of view of the subjects taken by themselves, and see, for destructive purposes, if the property rendered is a property of the [30] affirmation; for then the same term will not be a property of the negation as well. Also, if the term rendered is a property of the negation, it will not be a property of the affirmation. Thus (e.g.) inasmuch as animate is a property of living creature, animate will not be a property of not-living creature. For constructive purposes, on the other hand, see if the term rendered fails to be a property of the affirmation; for [35] if it is not a property of the affirmation,27 it will be a property of the negation. This commonplace rule is, however, false; for an affirmation is not a property of a [136b1] negation, or a negation of an affirmation. For an affirmation does not belong at all to a negation, while a negation, though it belongs to an affirmation, does not belong as a property.

Next, look from the point of view of the co-ordinate members of a division, and see, for destructive purposes, if none of the one set of co-ordinate members is a property of any of the remaining set of co-ordinate members; for then neither will [5] the term stated be a property of that of which it is stated to be a property. Thus (e.g.) inasmuch as perceptible living being is not a property of any of the other living beings, intelligible living being will not be a property of God. For constructive purposes, on the other hand, see if some one or other of the remaining co-ordinate members is a property of each of these co-ordinate members; for then the remaining [10] one too will be a property of that of which it has been stated not to be a property. Thus (e.g.) inasmuch as it is a property of prudence to be essentially the natural virtue of the rational faculty, and so too taking each of the other virtues in this way, it will be a property of temperance to be essentially the natural virtue of the faculty of desire.

[15] 7 · Next, look from the point of view of the inflexions, and see, for destructive purposes, if the inflexion fails to be a property of the inflexion; for then neither will the other inflexion be a property of the other inflexion. Thus (e.g.) inasmuch as beautifully is not a property of justly, neither will beautiful be a property of just. For constructive purposes, on the other hand, see if the inflexion is a property of the inflexion; for then also the other inflexion will be a property of the [20] other inflexion. Thus (e.g.) inasmuch as being terrestrial and two-footed is a property of man, it will be a property of ‘to a man’ to be described as ‘to a terrestrial and two-footed thing’. Not only in the case of the actual term mentioned should one look at the inflexions, but also in the case of its opposites, as we said in the case of the former commonplace rules as well.28 Thus, for destructive purposes, see if the [25] inflexion of the opposite fails to be the property of the inflexion of the opposite; for then neither will the inflexion of the other opposite be a property of the inflexion of the other opposite. Thus (e.g.) inasmuch as ‘well’ is not a property of ‘justly’, neither will ‘badly’ be a property of ‘unjustly’. For constructive purposes, on the other hand, see if the inflexion of the opposite is a property of the inflexion of the opposite; for [30] then also the inflexion of the other opposite will be a property of the inflexion of the other opposite. Thus (e.g.) inasmuch as best is a property of the good, worst also will be a property of the evil.

Next, look from the point of view of things that are in a like relation, and see, for destructive purposes, if what is in a like relation fails to be a property of what is in a like relation; for then neither will what is in a relation like that of the first be a property of what is in a relation like that of the second. Thus (e.g.) inasmuch as the [35] relation of the builder towards the production of a house is like that of the doctor towards the production of health, and it is not a property of a doctor to produce health, it will not be a property of a builder to produce a house. For constructive [137a1] purposes, on the other hand, see if what is in a like relation is a property of what is in a like relation; for then also what is in a relation like that of the first will be a property of what is in a relation like that of the second. Thus (e.g.) inasmuch as the relation of a doctor towards the possession of ability to produce health is like that of a trainer towards the possession of ability to produce vigour, and it is a property of a [5] trainer to possess the ability to produce vigour, it will be a property of a doctor to possess the ability to produce health.

Next, for destructive purposes, see if the predicate qualified by the verb ‘to be’ fails to be a property of the subject qualified by the verb ‘to be’; for then neither will the destruction of the one be a property of the other qualified by the verb ‘to be destroyed’, nor will the becoming of the one be a property of the other qualified by the verb ‘to become’. Thus (e.g.) inasmuch as it is not a property of man to be an animal, neither will it be a property of becoming a man to become an animal; nor [25] will the destruction of an animal be a property of the destruction of a man. You should argue from becoming to being and to being destroyed, and from being destroyed to being and to becoming, exactly as we have just argued from being to becoming and being destroyed. For constructive purposes, on the other hand, see if [30] the predicate qualified by the verb ‘to be’ is a property of the subject so qualified; for then also the subject qualified by the verb ‘to become’ will have the predicate qualified by ‘to become’ as its property, and the subject qualified by the verb ‘to be destroyed’ will have as its property the predicate rendered with this qualification. Thus, for example, inasmuch as it is a property of man to be a mortal, it will be a [35] property of becoming a man to become a mortal, and the destruction of a mortal will be a property of the destruction of a man. In the same way one should argue from becoming and being destroyed both to being and to the conclusions that follow [137b1] from them, exactly as was said in the case of destruction.

Next take a look at the Idea of the subject stated, and see, for destructive purposes, if it fails to belong to the Idea, or fails to belong to it in virtue of that character which causes it to bear the description of which the property was [5] rendered; for then what has been stated to be a property will not be a property. Thus (e.g.) inasmuch as being motionless does not belong to man-himself qua man, but qua Idea, it could not be a property of man to be motionless. For constructive purposes, on the other hand, see if the property in question belongs to the Idea, and belongs to it in that respect in virtue of which there is predicated of it that character of which the predicate in question has been stated not to be a property; for then [10] what has been stated not to be a property will be a property. Thus (e.g.) inasmuch as it belongs to living-creature-itself to be compounded of soul and body, and further this belongs to it qua living-creature, it will be a property of living-creature to be compounded of soul and body.

8 · Next look from the point of view of greater and less degrees, and first for [15] destructive purposes, see if what is so-and-so to a greater degree fails to be a property of what is such-and-such to a greater degree; for then neither will what is less be a property of what is less, nor least of least, nor most of most, nor will what is so-and-so without qualification be a property of what is such-and-such without qualification. Thus (e.g.) inasmuch as being more highly coloured is not a property of what is more a body, neither will being less highly coloured be a property of what [20] is less a body, nor being coloured be a property of body at all. For constructive purposes, on the other hand, see if what is more is a property of what is more; for then also what is less will be a property of what is less, and least of least, and most of most, and without qualification of without qualification. Thus (e.g.) inasmuch as a higher degree of perception is a property of a higher degree of life, a lower degree of [25] perception will be a property of a lower degree of life, and the highest of the highest and the lowest of the lowest degree, and perception without qualification of life without qualification.

Also you should look at the argument from unqualified predication to these qualified types, and see, for destructive purposes, if what is so-and-so without qualification fails to be a property of what is such-and-such without qualification; [30] for then neither will more be a property of more, nor less of less, nor most of most, nor least of least. Thus (e.g.) inasmuch as virtuous is not a property of man, neither will more virtuous be a property of what is more human. For constructive purposes, on the other hand, see if what is without qualification is a property of what is [35] without qualification; for then more will be a property of more, and less of less, and least of least, and most of most. Thus (e.g.) a tendency to move upwards by nature is [138a1] a property of fire, and so also a greater tendency to move upwards by nature will be a property of what is more fiery. In the same way too one should look at the arguments from the others to all these.

Secondly, for destructive purposes, see if the more fails to be a property of the [5] more; for then neither will the less be a property of the less. Thus (e.g.) inasmuch as perceiving is more a property of animal than knowing of man, and perceiving is not a property of animal, knowing will not be a property of man. For constructive purposes, on the other hand, see if the less is a property of the less; for then too the more will be a property of the more. Thus (e.g.) inasmuch as to be naturally [10] civilized is less a property of a man than to live of an animal, and it is a property of man to be naturally civilized, it will be a property of animal to live.

Thirdly, for destructive purposes, see if the predicate fails to be a property of that of which it is more a property; for then neither will it be a property of that of which it is less a property; while if it is a property of the former, it will not be a [15] property of the latter. Thus (e.g.) inasmuch as to be coloured is more a property of a surface than of a body, and it is not a property of a surface, to be coloured will not be a property of body; while if it is a property of a surface, it will not be a property of a body. For constructive purposes, on the other hand, this commonplace rule is not of any use; for it is impossible for the same thing to be a property of more than one [20] thing.

Fourthly, for destructive purposes, see if what is more a property of a given subject fails to be its property; for then neither will what is less a property of it be its property. Thus (e.g.) inasmuch as perceptible is more a property of animal than divisible, and perceptible is not a property of animal, divisible will not be a property of animal. For constructive purposes, on the other hand, see if what is less a property [25] of it is a property; for then what is more a property of it will be a property as well. Thus, for example, inasmuch as perception is less a property of animal than life, and perception is a property of animal, life will be a property of animal.

Next, look from the point of view of the attributes that belong in a like degree, [30] and first, for destructive purposes, see if what is as much a property fails to be a property of that of which it is as much a property; for then neither will that which is as much a property as it be a property of that of which it is as much a property. Thus (e.g.) inasmuch as desiring is as much a property of the faculty of desire as [35] reasoning is a property of the faculty of reason, and desiring is not a property of the faculty of desire, reasoning will not be a property of the faculty of reason. For constructive purposes, on the other hand, see if what is as much a property is a property of that of which it is as much a property; for then also what is as much a property as it will be a property of that of which it is as much a property. Thus (e.g.) [138b1] inasmuch as it is as much a property of the faculty of reason to be the primary seat of prudence as it is of the faculty of desire to be the primary seat of temperance, and it is a property of the faculty of reason to be the primary seat of prudence, it will be a property of the faculty of desire to be the primary seat of temperance. [5]

Secondly, for destructive purposes, see if what is as much a property of anything fails to be a property of it; for then neither will what is as much a property be a property of it. Thus (e.g.) inasmuch as seeing is as much a property of man as hearing, and seeing is not a property of man, hearing will not be a property of man. For constructive purposes, on the other hand, see if what is as much a property of it [10] is its property; for then what is as much a property of it will be its property as well. Thus (e.g.) it is as much a property of the soul for a part of it to be the primary seat of desire as for a part to be the primary seat of reason, and it is a property of the soul for a part of it to be the primary seat of desire, and so it will be a property of the soul [15] for a part of it to be the primary seat of reason.

Thirdly, for destructive purposes, see if it fails to be a property of that of which it is as much a property; for then neither will it be a property of that of which it is as much a property; while if it is a property of the former, it will not be a property of the other. Thus (e.g.) inasmuch as to burn is as much a property of flame as of live coals, and to burn is not a property of flame, to burn will not be a property of live [20] coals: while if it is a property of flame, it will not be a property of live coals. For constructive purposes, on the other hand, this commonplace rule is of no use.

The rule based on things that are in a like relation differs from the rule based on attributes that belong in a like degree, because the former point is secured by [25] analogy, not from reflection on the belonging of any attribute, while the latter is judged by a comparison based on the fact that an attribute belongs.

9 · Next, for destructive purposes, see if in rendering the property potentially, he has also through that potentiality rendered the property relatively to something that does not exist, when the potentiality cannot belong to what does not [30] exist; for then what is stated to be a property will not be a property. Thus (e.g.) he who has said that breathable is a property of air has rendered the property potentially (for that is breathable which is such as can be breathed), and he has also rendered the property relatively to what does not exist (for while air may exist, even though there exists no animal so constituted as to breathe the air, it is not possible to [35] breathe it if no animal exists; so that it will not be a property of air to be such as can be breathed at a time when there exists no animal such as to breathe it) and so it follows that breathable will not be a property of air.

[139a1] For constructive purposes, see if in rendering the property potentially he renders the property either relatively to something that exists, or to something that does not exist, when the potentiality can belong to what exists;30 for then what has been stated not to be a property will be a property. Thus (e.g.) he who renders it as a [5] property of existing to be capable of being acted upon or of acting, in rendering the property potentially, has rendered the property relatively to something that exists; for when it is existent, it will be capable of being acted upon or of acting in a certain way; so that to be capable of being acted upon or of acting will be a property of existing.

Next, for destructive purposes, see if he has stated the property in the [10] superlative; for then what has been stated to be a property will not be a property. For people who render the property in that way find that of the object of which the account is true, the name is not true as well; for though the object perishes the account will continue in being none the less; for it will belong in the greatest degree to something that is in being. An example would be supposing anyone were to [15] render the lightest body as a property of fire; for, though fire may perish, there will still be some form of body that is the lightest, so that the lightest body will not be a property of fire. For constructive purposes, on the other hand, see if he has avoided rendering the property in the superlative; for then the property will in this respect have been correctly stated. Thus (e.g.) inasmuch as he who states a naturally civilized animal as a property of man has not rendered the property in the superlative, the property will in this respect have been correctly stated. [20]

BOOK VI

1 · The discussion of definitions falls into five parts. For you have to show either that it is not true at all to apply the account to that to which the name is [25] applied (for the definition of man ought to be true of every man); or that though the object has a genus, he has failed to put the object defined into the genus, or to put it into the appropriate genus (for the framer of a definition should first place the object in its genus, and then append its differences; for of the elements of the definition the genus seems to be the principal mark of the substance of what is defined); or that the account is not proper to the object (for, as we said above as [30] well,31 a definition ought to be proper); or else see if, though he has observed all the aforesaid cautions, he has yet failed to define the object, that is, to express the essence of what is being defined. It remains, apart from the foregoing, to see if he has defined it, but defined it incorrectly. [35]

Whether, then, the account is not also true of that of which the name is true you should examine according to the commonplace rules that relate to accident. For there too the question is always ‘Is so and so true or untrue?’; for whenever we argue [139b1] that an accident belongs, we declare it to be true, while whenever we argue that it does not belong, we declare it to be untrue. Whether he has failed to place the object in the appropriate genus, or whether the given account is not proper, we must examine according to the commonplace rules that relate to genus and property. [5]

It remains, then, to say how to investigate whether the object has been either not defined at all, or else defined incorrectly. First, then, we must examine if it has been defined incorrectly; for with anything it is easier to do it than to do it correctly—clearly, then, more mistakes are made in the latter task on account of its greater difficulty, so that the attack becomes easier in the latter case than in the [10] former.

Incorrectness falls into two branches: first, the use of obscure language (for the language of a definition ought to be the very clearest possible, seeing that the purpose of rendering it is to make something known); secondly, if the account is [15] longer than is necessary (for all additional matter in a definition is superfluous). Again, each of the aforesaid branches is divided into a number of others.

2 · One commonplace rule, then, in regard to obscurity is to see if what is stated is homonymous with something, e.g. that becoming is a passage into being, or [20] that health is the balance of hot and cold elements. Here passage and balance are homonymous; it is accordingly not clear which of the several possible senses of the term he intends to convey. Likewise also, if the term defined is used in different [25] ways and he has spoken without distinguishing between them; for then it is not clear to which of them the definition rendered applies, and one can then bring a captious objection on the ground that the account does not apply to all the things whose definition he has rendered—this kind of thing is particularly easy in the case where the definer does not see the homonymy. Or, again, the questioner may himself [30] distinguish the various uses of the term rendered in the definition, and then produce a deduction; for if the expression used is not adequate to the subject in any of its senses, it is clear that he cannot have defined it aright.

Another rule is to see if he has used a metaphorical expression, as, for instance, if he has defined knowledge as unsupplantable, or the earth as a nurse, or temperance as a harmony. For a metaphorical expression is always obscure. It is [35] possible, also, to argue captiously against the user of a metaphorical expression as though he had used it in its literal sense; for the definition stated will not apply, e.g. in the case of temperance; for harmony is always found between notes. Moreover, if harmony is the genus of temperance, then the same object will occur in two genera [140a1] of which neither contains the other; for harmony does not contain virtue, nor virtue harmony.

Again, see if he uses terms that are not in current use, as when Plato describes the eye as brow-shaded, or a certain spider as poison-fanged, or the marrow as [5] bone-formed. For an unusual phrase is always obscure.

Sometimes a phrase is used neither homonymously, nor yet metaphorically, nor yet literally, as when the law is said to be the measure or image of the things that are by nature just. Such phrases are worse than metaphor; for metaphor does make [10] what it signifies to some extent familiar because of the likeness involved (for those who use metaphors do so always in view of some likeness), whereas this kind of thing makes nothing familiar, (for there is no likeness in virtue of which the law is a measure or image nor is the law ordinarily so called). So then, if a man says that the law is literally a measure or an image, he speaks falsely; for an image is something [15] produced by imitation, and this is not found in the case of the law. If, on the other hand, he does not mean the term literally, it is clear that he has used an obscure expression, and one that is worse than any sort of metaphorical expression.

Moreover, see if from the expression used the account of the contrary is not clear; for definitions that have been correctly rendered also indicate their contraries [20] as well. Or, again, see if, when it is merely stated by itself, it is not evident what it defines—just as in the works of the old painters, unless there were an inscription, the figures used to be unrecognizable.

3 · If, then, the definition is not clear, you should examine on lines such as these. If he has phrased the definition redundantly, first of all look and see whether [25] he has used any attribute that belongs universally, either to entities in general, or to all that fall under the same genus as the object defined; for the mention of this is sure to be redundant. For the genus ought to divide the object from other things, and the differentia from any of the things contained in the same genus. Now any term that belongs to everything separates off the given object from absolutely nothing, while any that belongs to all the things that fall under the same genus does [30] not separate it off from the things contained in the same genus. Any addition, then, of that kind will be pointless.

Or see if, though the additional matter is proper to the given term, yet when it is struck out the rest of the account too is proper and makes clear the substance of the term. Thus, in the account of man, the addition ‘capable of receiving knowledge’ [35] is superfluous; for strike it out, and still the account is proper and makes clear his substance. Speaking generally, everything is superfluous upon whose removal the [140b1] remainder still makes the term that is being defined clear. Such, for instance, would also be the definition of the soul, assuming it to be stated as a self-moving number; for the soul is just what is self-moving, as Plato defined it.32 Or perhaps the expression used, though proper, yet does not show the substance if number is [5] eliminated. Which of the two is the real state of the case it is difficult to determine clearly: the right way to treat the matter in all cases is to be guided by convenience. Thus (e.g.) it is said that the definition of phlegm is the undigested moisture that comes first off food. What is first is one, not many; so that the addition of the word ‘undigested’ is superfluous; so that even when this is left out the remaining account [10] will still be proper; for it is impossible that both phlegm and also something else should both be the first to arise from the food. Or perhaps the phlegm is not absolutely the first thing to come off the food, but only the first of the undigested matters, so that the addition ‘undigested’ is required; for stated the other way the definition would not be true unless the phlegm comes first of all. [15]

Moreover, see if anything contained in the account fails to apply to everything that falls under the same species; for this sort of account is worse than those which include an attribute belonging to all things universally. For in that case, if the remainder of the account is proper, the whole too will be proper; for absolutely always, if to something proper anything whatever that is true is added, the whole too [20] becomes proper. Whereas if any part of the account does not apply to everything that falls under the same species, it is impossible that the account as a whole should be proper; for it will not be predicated convertibly with the object; e.g. a terrestrial two-footed animal six feet high—for an account of that kind is not predicated convertibly with the object, because being six feet high does not belong to [25] everything that falls under the same species.

Again, see if he has said the same thing more than once, saying (e.g.) that desire is appetition for the pleasant. For desire is always for the pleasant, so that what is the same as desire will also be for the pleasant. Accordingly our definition of desire becomes appetition for the pleasant for the pleasant; for there is no difference [30] between desire and appetition for the pleasant, so that both alike will be for the pleasant. Or perhaps there is no absurdity in this; for man is a biped; therefore, what is the same as man is a biped; but a terrestrial biped animal is the same as man, and [35] therefore a terrestrial biped animal is a biped. But this involves no real absurdity. For biped is not predicated of terrestrial animal (if it were, then we should certainly have biped predicated twice of the same thing); but the subject said to be a biped is [141a1] a terrestrial biped animal, so that biped is only predicated once. Likewise in the case of desire as well; for being of the pleasant is not predicated of appetition, but rather of the whole, so that there too the predication is only made once. Absurdity results, [5] not when the same word is uttered twice, but when the same thing is more than once predicated of a subject—as Xenocrates says that prudence defines and contemplates reality; for definition is a certain type of contemplation, so that by adding ‘and contemplates’ he says the same thing twice over. Likewise those who say that [10] cooling is the privation of natural heat. For all privation is a privation of some natural attribute, so that the addition of ‘natural’ is superfluous: it would have been enough to say privation of heat, for privation itself makes it familiar that the heat meant is natural heat.

[15] Again, see if a universal has been mentioned and then a particular case of it added as well, e.g. Equity is a remission of what is expedient and just; for what is just is a branch of what is expedient and is therefore included in the latter: it is therefore redundant, an addition of the particular after the universal has been already stated. So also, if he defines medicine as knowledge of what makes for [20] health in animals and men, or the law as the image of what is by nature noble and just; for what is just is a branch of what is noble, so that he says the same thing more than once.

4 · Whether, then, a man defines a thing correctly or incorrectly you should examine on these and similar lines. But whether he has mentioned and defined its [25] essence or not, should be examined as follows.

First of all, see if he has failed to make the definition through terms that are prior and more familiar. For a definition is rendered in order to come to know the term stated, and we come to know things by taking not any random terms, but such [30] as are prior and more familiar, as is done in demonstrations (for so it is with all teaching and learning); accordingly, it is clear that a man who does not define through terms of this kind has not defined at all. Otherwise, there will be more than one definition of the same thing; for clearly he who defines through terms that are prior and more familiar has framed a better definition, so that both will then be definitions of the same object. This sort of thing, however, does not seem to be so; for [35] of each entity there is a single essence; if, then, there are to be a number of definitions of the same thing, the object defined will be the same as the essences represented in each of the definitions; but these are not the same, inasmuch as the [141b1] definitions are different. Clearly, then, any one who has not defined a thing through terms that are prior and more familiar has not defined it at all.

The statement that a definition has not been made through more familiar terms may be understood in two ways either supposing that its terms are without qualification less intelligible, or supposing that they are less intelligible to us; for [5] either way is possible. Thus the prior without qualification is more familiar than the posterior, a point, for instance, than a line, a line than a plane, and a plane than a solid; just as a unit is more intelligible than a number; for it is prior to and a principle of all number. Likewise, also, a letter is more familiar than a syllable. Whereas to us it sometimes happens that the converse is the case; for a solid falls under perception most of all, and a plane more than a line, and a line more than a [10] point; for most people learn such things earlier; for any ordinary intelligence can grasp them, whereas the others require a precise and exceptional understanding.

Absolutely, then, it is better to try to come to know what is posterior through [15] what is prior, inasmuch as such a way of procedure is more scientific. Of course, in dealing with persons who cannot recognize things through terms of that kind, it may perhaps be necessary to frame the account through terms that are familiar to them. Among definitions of this kind are those of a point, a line, and a plane, all of which [20] explain the prior by the posterior; for they say that a point is the limit of a line, a line of a plane, a plane of a solid. One must, however, not fail to observe that those who define in this way cannot show the essence of what they define, unless it so happens that the same thing is more familiar both to us and also without qualification, since [25] a correct definition must define a thing through its genus and its differentiae, and these belong to the order of things which are without qualification more familiar than, and prior to, the species. For annul the genus and differentia, and the species too is annulled, so that these are prior to the species. They are also more familiar; for if the species is known, the genus and differentia must of necessity be known as [30] well (for any one who knows what a man is knows also what animal and terrestrial are), whereas if the genus or the differentia is known it does not follow of necessity that the species is known as well; thus the species is less intelligible. Moreover, those who say that such definitions, viz. those which proceed from what is familiar to [35] some individual, accord with the truth, will have to say that there are several definitions of one and the same thing. For in fact different things are more familiar to different people, not the same things to all; and so a different definition would have to be rendered to each several person, if the definition is to be constructed from [142a1] what is more familiar to particular individuals. Moreover, to the same people different things are more familiar at different times: first of all the objects of sense; then, as they become more acute, the converse; so that those who hold that a definition ought to be rendered through what is more familiar to particular individuals will not have to render the same definition at all times even to the same [5] person. It is clear, then, that the right way to define is not through terms of that kind, but through what is without qualification more familiar; for only in this way could the definition come always to be one and the same. Perhaps, also, what is familiar without qualification is what is familiar, not to all, but to those who are in a [10] sound state of understanding, just as what is without qualification healthy is what is healthy to those in a sound state of body. All such points as this ought to be made very precise, and made use of in the course of discussion as occasion requires.

The demolition of a definition will most surely win a general approval if the definer happens to have framed his account neither from what is without qualification [15] more intelligible nor yet from what is so to us.

One form, then, of the failure to work through more familiar terms is the exhibition of the prior through the posterior, as we remarked before. Another form occurs if we find that the account has been rendered of what is at rest and definite [20] through what is indefinite and in motion; for what is still and definite is prior to what is indefinite and in motion.

Of the failure to use terms that are prior there are three forms. The first is when an opposite has been defined through its opposite, e.g. good through evil; for opposites are always simultaneous by nature. Some people think, also, that both are [25] objects of the same science, so that the one is not even more familiar than the other. One must, however, observe that it is perhaps not possible to define some things in any other way, e.g. the double without the half, and all terms that are essentially relative; for in all such cases to be them is the same as to be somehow related to [30] something, so that it is impossible to know the one without the other, and accordingly in the account of the one the other too must be embraced. One ought to recognize all such points as these, and use them as occasion may seem to require.

Another is—if he has used the term defined itself. This passes unobserved when the actual name of the object being defined is not used, e.g. supposing anyone [142b1] had defined the sun as a star that appears by day. For in bringing in day he brings in the sun. To detect errors of this sort, exchange the name for its account, e.g. the account of day as the passage of the sun over the earth. Clearly, whoever has [5] mentioned the passage of the sun over the earth has mentioned the sun, so that in bringing in the day he has brought in the sun.

Again, see if he has defined one co-ordinate member of a division by another, e.g. an odd number as that which is greater by one than an even number. For the co-ordinate members of a division that are derived from the same genus are [10] simultaneous by nature, and odd and even are such terms; for both are differentiae of number.

Likewise also, see if he has defined a superior through a subordinate term, e.g. an even number as a number divisible into halves, or the good as a state of virtue. For ‘into halves’ is derived from ‘two’, and two is an even number; and virtue is a [15] kind of good—so that the latter terms are subordinate to the former. Moreover, in using the subordinate term one is bound to use the other as well; for whoever introduces virtue introduces the good, seeing that virtue is a certain kind of good; likewise, also, whoever employs ‘into halves’ employs the even, for to be divided into halves means to be divided into two, and two is even.

[20]5 · Generally speaking, then, one commonplace rule relates to the failure to frame the account by means of terms that are prior and more familiar; and of this the subdivisions are those specified above. A second is to see whether, though the object is in a genus, it has not been placed in a genus. This sort of error is always found where what the object is does not stand first in the account, e.g. the definition [25] of body as that which has three dimensions, or the definition of man, supposing anyone to give it, as that which knows how to count; for it is not stated what it is that has three dimensions, or what it is that knows how to count; whereas the genus is meant to indicate what it is, and is submitted first of the terms in the definition.

Moreover, see if, while the term to be defined is used in relation to many [30] things, he has failed to render it in relation to all of them; as (e.g.) if he defines grammar as the knowledge how to write from dictation; for he ought also to say that it is a knowledge how to read as well. For one who renders it as knowledge of writing has no more defined it than one who renders it as knowledge of reading: neither in fact has succeeded, but only one who mentions both these things, since it is impossible that there should be more than one definition of the same thing. It is only, however, in some cases that what has been said corresponds to the actual state [143a1] of things: in some it does not, e.g. all those terms which are not used in their own right in relation to both things—as medicine is said to deal with the production of disease and health; for it is said in its own right to do the latter, but the former only by accident; for it is absolutely alien to medicine to produce disease. Here, then, the [5] man who renders medicine as relative to both of these things has not defined it any better than he who mentions the one only. In fact he has done it perhaps worse; for any one else besides the doctor is capable of producing disease.

Moreover, in a case where the term to be defined is used in relation to several things, see if he has rendered it as relative to the worse rather than to the better; for [10] every form of knowledge and potentiality is generally thought to be relative to the best.

Again, if the thing in question is not placed in its own proper genus, one must examine it according to the elementary rules in regard to genera, as has been said before.

Moreover, see if he passes over the genera, defining, e.g., justice as a state that [15] produces equality or distributes what is equal; for by defining it so he passes over virtue, and so by leaving out the genus of justice he fails to express its essence; for the substance of a thing in each case involves its genus. This is the same as not putting the object into its nearest genus; for the man who puts it into the nearest one [20] has stated all the higher genera, seeing that all the higher genera are predicated of the lower. Either, then, it ought to be put into its nearest genus, or else to the higher genus all the differentiae ought to be appended whereby the nearest genus is defined. For then he would not have left out anything, but would have mentioned the subordinate genus by an account instead of by a name. On the other hand, he [25] who mentions merely the higher genus by itself, does not state the subordinate genus as well: in mentioning a plant a man does not mention a tree.

6 · Again, in regard to the differentiae, we must examine in like manner whether the differentiae that he has stated are those of the genus. For if a man has [30] not defined the object by the differentiae to it, or has mentioned something such as is utterly incapable of being a differentia of anything, e.g. animal or substance, clearly he has not defined it at all; for the aforesaid terms are not differentiae of anything at all. Further, we must see whether the differentia stated possesses anything that is co-ordinate with it in a division; for, if not, clearly the one stated [35] will not be a differentia of the genus. For a genus is always divided by differentiae that are co-ordinate members of a division, as, for instance, animal by terrestrial, [143b1] and winged [and aquatic and biped].33 Or see if, though the contrasted differentia exists, it yet is not true of the genus; for then, clearly, neither of them could be a [5] differentia of the genus; for differentiae that are co-ordinates in a division are all true of the genus. Likewise, also, see if, though it is true, yet the addition of it to the genus fails to make a species. For then, clearly, this will not be a specific differentia of the genus; for a specific differentia, along with the genus, always makes a species. If, however, this is no differentia, no more is the one adduced, seeing that it is a [10] co-ordinate member of a division with this.

Moreover, see if he divides the genus by a negation, as those do who define a line as length without breadth; for this means simply that it has not any breadth. The genus will then be found to partake of its own species; for, since of everything [15] either the affirmation or the negation is true, length must always either lack breadth or possess it, so that length as well, i.e. the genus of line, will be either with or without breadth. But length without breadth is the account of a species, as also is length with breadth; for without breadth and with breadth are differentiae, and the [20] genus and differentia constitute the account of the species. Hence the genus will admit of the account of its species. Likewise, also, it will admit of the account of the differentia, seeing that one or the other of the aforesaid differentiae is of necessity predicated of the genus. This principle is useful against those who posit Ideas; for if [25] length itself exists, how will it be predicable of the genus that it has breadth or that it lacks it? For one assertion or the other will have to be true of length universally, if it is to be true of the genus; and this is contrary to the fact; for there exist both lengths which have, and lengths which have not, breadth. Hence the only people [30] against whom the rule can be employed are those who assert that every genus is numerically one; and this is what is done by those who posit the Ideas; for they allege that length itself and animal itself are the genus. It may be that in some cases the definer is obliged to employ a negation, e.g. in defining privations. For a thing is blind which cannot see when its nature is to see.

[35] There is no difference between dividing the genus by a negation, and dividing it by such an affirmation as is bound to have a negation as its co-ordinate in a division, e.g. supposing he had defined something as length possessed of breadth; for [144a1] co-ordinate in the division with that which is possessed of breadth is that which possesses no breadth and that only, so that again the genus is divided by a negation.

[5] Again, see if he rendered the species as a differentia, as do those who define contumely as insolence accompanied by jeering; for jeering is a kind of insolence, hence it is a species and not a differentia.

Moreover, see if he has stated the genus as the differentia, e.g. virtue as a good [10] or noble state; for good is the genus of virtue. Or possibly good here is not the genus but the differentia, on the principle that the same thing cannot be in two genera of which neither contains the other; for good does not include state, nor vice versa; for [15] not every state is good nor every good a state. Both, then, will not be genera, and consequently, if state is the genus of virtue, clearly good cannot be its genus: it must rather be a differentia. Moreover, a state indicates what virtue is, whereas good indicates not what it is but a quality, and to indicate a quality seems to be the function of the differentia.

See, further, whether the given differentia indicates a certain ‘this’ rather than [20] a quality; for it seems that the differentia always expresses a quality.

Look and see, further, whether the differentia belongs only by accident to the object defined. For the differentia is never an accidental attribute, any more than [25] the genus is; for the differentia of a thing cannot both belong and not belong to it.

Moreover, if either the differentia or the species, or any of the things which are under the species, is predicated of the genus, then he will not have defined the term. For none of the aforesaid can be predicated of the genus, seeing that the genus is the [30] term with the widest range of all. Again, see if the genus is predicated of the differentia; for it seems that the genus is predicated, not of the differentia, but of the objects of which the differentia is predicated. Animal (e.g.) is predicated of man and ox and other terrestrial animals, not of the differentia itself, which we predicate [35] of the species. For if animal is to be predicated of each of its differentiae, then many animals will be predicated of the species; for the differentiae are predicated of the species. Moreover, the differentiae will be all either species or individuals, if they [144b1] are animals; for every animal is either a species or an individual.

Likewise you must inquire also if the species or any of the objects that come under it is predicated of the differentia; for this is impossible, seeing that the [5] differentia is a term with a wider range than the species. Moreover, if any of the species is predicated of it, the result will be that the differentia is a species: if man is predicated, the differentia is clearly man. Again, see if the differentia fails to be prior to the species; for the differentia ought to be posterior to the genus, but prior to [10] the species.

Look and see also if the differentia mentioned belongs to a different genus, neither contained in nor containing the genus in question. For it seems that the same differentia cannot be used of two genera neither of which contains the other. Otherwise, the result will be that the same species as well will be in two genera [15] neither of which contains the other; for each of the differentiae imports its appropriate genus, e.g. terrestrial and biped import with them animal. Hence each of the genera as well is true of that of which the differentia is true; and it clearly follows that the species must be in two genera neither of which contains the other. Or perhaps it is not impossible for the same differentia to be used of two genera [20] neither of which contains the other, and we ought to add ‘if they do not both fall under the same genus’. Thus terrestrial animal and winged animal are genera neither of which contains the other, and biped is a differentia of both. So we ought to add ‘if they do not both fall under the same genus’; for both these are subordinate [25] to animal. From this possibility, that the same differentia may be used of two genera neither of which contains the other, it is clear also that there is no necessity for the differentia to carry with it every appropriate genus, but only the one or the other together with the genera that are higher than this, as biped carries with it either winged or terrestrial animal. [30]

See, too, if he has rendered being in something as the differentia of a thing’s substance; for it seems that locality cannot differentiate between one substance and another. Hence, too, people condemn those who divide animals by means of the terms terrestrial and aquatic, on the ground that terrestrial and aquatic indicate [35] locality. Or possibly in this case the censure is undeserved; for aquatic does not mean ‘in’ anything; nor does it denote a locality, but a certain quality; for even if the thing is on the dry land, still it is aquatic—and likewise a land animal, even though [145a1] it is in the water, will still be a land animal and not aquatic. But all the same, if ever the differentia does denote being in something, clearly he will have made a mistake.

Again, see if he has rendered an affection as the differentia; for every affection, if intensified, subverts the substance of the thing, while the differentia is [5] not of that kind; for the differentia seems rather to preserve that which it differentiates; and it is absolutely impossible for a thing to exist without its appropriate differentia—if there is nothing terrestrial, there will be no man. To speak generally, a thing cannot have as its differentia anything in respect of which it is subject to alteration; for all things of that kind, if intensified, subvert its [10] substance. If, then, a man has rendered any differentia of this kind, he has made a mistake; for we undergo absolutely no alteration in respect of our differentiae.

Again, see if he has failed to render the differentia of a relative term relatively to something else; for the differentiae of relative terms are themselves relative, as in [15] the case of knowledge. This is classed as speculative, practical, and productive; and each of these denotes a relation; for it speculates upon something, and produces something, and does something.

Look and see also if the definer renders each relative term relatively to its [20] natural correlative; for while some things can be used in relation to their natural correlative only and to nothing else, some can be used in relation to something else as well. Thus sight can only be used for seeing, but a strigil can also be used to draw off liquid. Still, if any one were to define a strigil as an instrument for drawing off [25] liquid, he would make a mistake; for that is not its natural correlative. The definition of a thing’s natural correlative is that for which it would be used by the prudent man, acting as such, and by the science appropriate to that thing.

Or see if, whenever a term happens to be used in a number of relations, he has failed to introduce it in its primary relation: e.g. by defining prudence as the virtue [30] of man or of the soul, rather than of the reasoning faculty; for prudence is the virtue primarily of the reasoning faculty; for it is in virtue of this that both the man and his soul are said to be prudent.

Moreover, if the thing of which the term defined has been stated to be an affection or disposition, or whatever it may be, is unable to admit it, the definer has [35] made a mistake. For every disposition and every affection is formed naturally in that of which it is an affection or disposition, as knowledge is formed in the soul, being a disposition of soul. Sometimes, however, people make mistakes in matters of [145b1] this sort, e.g. all those who say that sleep is an incapacity to perceive, or that perplexity is a state of equality between contrary reasonings, or that pain is a violent disruption of parts that are naturally conjoined. For sleep is not an attribute of perception, whereas it ought to be, if it is an incapacity to perceive. Likewise, perplexity is not an attribute of opposite reasonings, nor pain of parts naturally [5] conjoined; for then inanimate things will be in pain, since pain will be present in them. Similar in character, too, is the definition of health, if it is a balance of hot and cold elements; for then health will be necessarily exhibited by the hot and cold elements; for a balance of anything belongs to those things of which it is the [10] balance, so that health will be an attribute of them. Moreover, people who define in this way put effect for cause, or cause for effect. For the disruption of parts naturally conjoined is not pain, but a cause of pain; nor again is an incapacity to perceive sleep, but the one is the cause of the other—for either we go to sleep [15] because of the incapacity, or we are incapable because we go to sleep. Likewise also an equality between contrary reasonings would seem to be a cause of perplexity; for it is when we reflect on both sides of a question and find everything alike to be in keeping with either course that we are perplexed which of the two we are to do. [20]

Moreover, with regard to all periods of time look and see whether there is any discrepancy: e.g. supposing the immortal to be defined as a living thing immune at present from destruction. For a living thing that is immune at present from destruction will be immortal at present. Possibly, indeed, in this case this result does not follow, owing to the ambiguity of the words ‘immune at present from destruction’; for they may mean either that the thing has not been destroyed at [25] present, or that it cannot be destroyed at present, or that at present it is such that it never can be destroyed. Whenever, then, we say that a living thing is at present immune from destruction, we mean that it is at present a living thing of such a kind as never to be destroyed; and this is equivalent to saying that it is immortal, so that it is not meant that it is immortal only at present. Still, if ever it does happen that [30] the attribute given by the account belongs in the present or past, whereas that given by the name does not so belong, then the two will not be the same. So, then, this commonplace rule ought to be used as we have said.

7 · You should look and see also whether the term defined is applied in consideration of something other than the account given. Suppose (e.g.) a definition [35] of justice as the ability to distribute what is equal. Now it is the man who chooses, rather than the man who is able, to distribute what is equal who is just; so that justice will not be an ability to distribute what is equal; for then also the most just [146a1] man will be the man with the most ability to distribute what is equal.

Moreover, see if the object admits of degrees, whereas what is given by the account does not, or, vice versa, what is given by the account admits of degrees while [5] the object does not. For either both must admit them or else neither, if indeed what is given by the account is the same as the object. Moreover, see if, while both of them admit of degrees, they yet do not both become greater together: e.g. suppose love to be the desire for intercourse; now he who is more intensely in love has not a [10] more intense desire for intercourse, so that both do not become intensified at once: they certainly should, however, had they been the same thing.

Moreover, suppose two things to be before you, see if the object applies in greater degree to the one to which the content of the account is less applicable. [15] Take, for instance, the definition of fire as the body that consists of the most rarefied particles. For flame is fire in greater degree than light is, but flame is less the body that consists of the most rarefied particles than is light; but both ought to be applicable in greater degree to the same thing, if they had been the same. Again, see if the one applies in equal degree to both the objects before you, while the other [20] does not apply to both alike, but more particularly to one of them.

Moreover, see if he renders the definition relative to two things taken separately: thus, the beautiful is what is pleasant to the eyes or to the ears; or the existent is what is capable of being acted upon or of acting. For then the same thing will be both beautiful and not beautiful, and likewise will be both existent and [25] non-existent. For pleasant to the ears will be the same as beautiful, so that not pleasant to the ears will be the same as not beautiful; for of identical things the opposites, too, are identical, and the opposite of beautiful is not beautiful, while of pleasant to the ears the opposite is not pleasant to the ears—clearly, then, not pleasant to the ears is the same thing as not beautiful. If, therefore, something is [30] pleasant to the eyes but not to the ears, it will be both beautiful and not beautiful. In like manner we shall prove also that the same thing is both existent and non-existent.

Moreover, of both genera and differentiae and all the other terms rendered in definitions you should frame accounts in lieu of the names, and then see if there is [35] any discrepancy between them.

8 · If the term defined is relative, either in itself or in respect of its genus, see whether the definition fails to mention that to which the term, either in itself or in [146b1] respect of its genus, is relative, e.g. if he has defined knowledge as an incontrovertible belief or wishing as painless appetition. For of everything relative the substance is relative to something else, seeing that the being of every relative term is identical with being in a certain relation to something. He ought, therefore, to have [5] said that knowledge is belief about a knowable and that wishing is appetition for a good. Likewise, if he has defined grammar as knowledge of letters—for in the definition there ought to be rendered either the thing to which the term itself is relative, or that to which its genus is relative. Or see if a relative term has been [10] described not in relation to its end, the end in anything being whatever is best or gives its purpose to the rest. Certainly it is what is best or final that should be stated, e.g. that desire is not for the pleasant but for pleasure; for this is our purpose in choosing what is pleasant.

Look and see also if that in relation to which he has rendered the term is a process or an activity; for nothing of that kind is an end, for the completion of the [15] activity or process is the end rather than the process or activity itself. Or perhaps this rule is not true in all cases; for almost everybody would rather be enjoying themselves than have ceased enjoying themselves, so that they would count the activity as the end rather than its completion.

[20] Again see in some cases if he has failed to distinguish the quantity or quality or place or other differentiae of an object; e.g. the quality and quantity of the honour the striving for which makes a man ambitious—for all men strive for honour, so that it is not enough to define the ambitious man as him who strives for honour, but the aforesaid differentiae must be added. Likewise, also, in defining the covetous man the quantity of money he aims at, or in the case of the incontinent man the quality of [25] the pleasures, should be stated. For it is not the man who gives way to any sort of pleasure whatever who is called incontinent, but only he who gives way to a certain kind of pleasure. Or again, people sometimes define night as a shadow on the earth, or an earthquake as a movement of the earth, or a cloud as condensation of the air, or a wind as a movement of the air; whereas they ought to specify as well quantity, [30] quality, place, and cause. Likewise, also, in other cases of the kind; for by omitting any differentiae whatever he fails to state the essence. One should always attack deficiency. For a movement of the earth does not constitute an earthquake, nor a movement of the air a wind, irrespective of its manner and the amount involved. [35]

Moreover, in the case of appetitions, and in any other cases where it applies, see if the word ‘apparent’ is left out: e.g. wishing is an appetition after the good, or desire is an appetition after the pleasant—instead of the apparently good or [147a1] pleasant. For often those who exhibit the appetition do not perceive what is good or pleasant, so that their aim need not be really good or pleasant, but only apparently so. They ought, therefore, to have rendered the definition accordingly. On the other hand, any one who maintains the existence of Ideas ought to be brought face to face [5] with his Ideas, even though he does render the term in question; for there can be no Idea of anything apparent and it seems that an Idea is always spoken of in relation to an Idea—thus desire itself is for the pleasant itself, and wishing itself is for the good itself; they therefore cannot be for an apparently good or an apparently pleasant; for the existence of the apparently good (or pleasant) itself would be an [10] absurdity.

9 · Moreover, if the definition is of the state of anything, look at what is in the state, while if it is of what is in the state, look at the state; and likewise in other cases of the kind. Thus if the pleasant is essentially beneficial, then, too, the man who is pleased is benefited. Speaking generally, in definitions of this sort it happens [15] that what the definer in a sense defines is more than one thing; for in defining knowledge, a man in a sense defines ignorance as well, and likewise also what has knowledge and what lacks it, and what it is to know and to be ignorant. For if the first is made clear, the others become in a certain sense clear as well. We have, then, [20] to be on our guard in all such cases against discrepancy, using the elementary principles drawn from consideration of contraries and of co-ordinates.

Moreover, in the case of relative terms, see if the species is rendered as relative to a species of that to which the genus is rendered as relative, e.g. supposing belief to be relative to the object of belief, see whether a particular belief is made relative to [25] some particular object of belief; and, if a multiple is relative to a fraction, see whether a particular multiple is made relative to a particular fraction. For if it is not so rendered, clearly a mistake has been made.

See, also, if the opposite of the term has the opposite account, whether (e.g.) [30] the account of half is the opposite of that of double; for if double is that which exceeds another by an equal amount to that other, half is that which is exceeded by an amount equal to itself. In the same way, too, with contraries. For to the contrary term will apply the account that is contrary in some one of the ways in which contraries are conjoined. Thus (e.g.) if useful is productive of good, injurious is productive of evil or destructive of good—for one or the other of these is bound to be [147b1] contrary to the term originally used. Suppose then, neither of these things to be the contrary of the term originally used, then clearly neither of those rendered later will be an account of the contrary; and therefore the account originally rendered has not [5] been rightly rendered either. Seeing, moreover, that of contraries, the one is sometimes named by the privation of the other, as (e.g.) inequality seems to be the privation of equality (for things that are not equal are called unequal), it is therefore clear that the contrary named by the privation must of necessity be defined through the other; whereas the other cannot then be defined through the one named by the privation; for else we should find that each was being made known [10] by the other. We must in the case of contrary terms keep an eye on this mistake, e.g. supposing any one were to define equality as the contrary of inequality; for then he is defining it through the one named by the privation of it. Moreover, a man who so defines is bound to use in his definition the very term he is defining; and this becomes clear, if for the name we substitute its account. For to say ‘inequality’ is the [15] same as to say ‘privation of equality’. Therefore equality will be the contrary of the privation of equality, so that he will have used the very term to be defined. Suppose, however, that neither of the contraries is named by the privation, but yet the account of it is rendered in a manner like the above, e.g. suppose good to be defined as the contrary of evil, then it is clear that evil will be the contrary of good (for the accounts of things that are contrary in this way must be rendered in a like manner), [20] so that again he uses the very term being defined—for good is inherent in the account of evil. If, then, good is the contrary of evil, and evil is nothing other than the contrary of good, then good will be the contrary of the contrary of good. Clearly, [25] then, he has used the very term to be defined.

Moreover, see if in rendering a term named by the privation, he has failed to render the term of which it is the privation, e.g. the state, or contrary, or whatever it may be whose privation it is; also if he has omitted to add that in which the privation is naturally formed—either without qualification or else that in which it is naturally [30] formed primarily: e.g. whether in defining ignorance as a privation he has failed to say that it is the privation of knowledge; or has failed to add in what it is naturally formed, or, though he has added this, has failed to render the thing in which it is primarily formed, placing it (e.g.) in man or in the soul, and not in the reasoning faculty; for if in any of these respects he fails, he has made a mistake. Likewise, also, if he has failed to say that blindness is the privation of sight in an eye; for a proper [148a1] rendering of what it is must state both of what it is the privation and what it is that is deprived.

Examine further whether he has defined as a privation something not named by a privation—a mistake of this sort would seem to be incurred in the case of ignorance by any one who is not using it as a merely negative term. For what seems [5] to be ignorant is not that which has no knowledge, but rather that which has been deceived (for this reason we do not talk of inanimate things or of children as being ignorant). Ignorance, then, is not named by the privation of knowledge.

10 · Moreover, see whether the like inflexions in the account apply to the [10] like inflexions of the word; e.g. if beneficial is productive of health, is beneficially productively of health and a benefactor a producer of health?

Look too and see whether the definition given will apply to the Idea as well. For in some cases it will not do so; e.g. in the Platonic definition where he adds the word [15] ‘mortal’ in his definitions of living creatures; for the Idea (e.g. man itself) is not mortal, so that the account will not fit the Idea. In general, wherever the words ‘capable of acting on’ or ‘capable of being acted upon’ are added, the definition and the Idea are bound to be discrepant; for those who assert the existence of Ideas hold [20] that they are incapable of being acted upon, or of motion. In dealing with these people arguments of this kind are useful.

Further, see if he has rendered a single common account of terms that are used homonymously. For things whose account corresponding to their name is one and the same, are synonymous; if, then, the definition applies in a like manner to the [25] whole range of the homonym, it does not define any one of the objects described by the term. This is what happens to Dionysius’ definition of life when stated as a movement of a creature sustained by nutriment, congenitally present with it; for this is found in plants as much as in animals, whereas life seems to be not one kind of thing only, but one thing in animals and another in plants. It is possible to hold the [30] view that life is synonymous and of one kind only, and therefore to render the definition in this way on purpose; or it may quite well happen that a man may see the homonymy and wish to render the definition of the one sense only, and yet fail to see that he has rendered an account common to both instead of proper to one. In [35] either case, whichever course he pursues, he is equally at fault. Since homonymies sometimes pass unobserved, it is best in questioning to treat them as though they were synonymous (for the definition of the one will not apply to the other, so that [148b1] the answerer will seem not to have defined it correctly—for it should apply to the whole range of the synonym, whereas in answering you should yourself distinguish between them). Further, as some answerers call homonymous what is really synonymous, whenever the given account fails to apply to the whole range, and, vice versa, call synonymous what is really homonymous if it applies to both, one should [5] secure a preliminary agreement on such points, or else prove beforehand that so-and-so is homonymous or synonymous, as the case may be; for people are more ready to agree when they do not foresee what the consequence will be. If, however, no agreement has been made, and the man asserts that what is really synonymous is [10] homonymous because the account he has given will not apply to the second sense as well, see if the account of this second sense applies to the others; for if so, this must clearly be synonymous with those others. Otherwise, there will be more than one [15] definition of the others; for there are applicable to them two accounts corresponding to their names, viz. the one previously rendered and also the later one. Again, if anyone were to define a term used in several ways, and, finding that his account does not apply to them all, were to contend not that the term is homonymous, but that the name does not apply to all of them, just because his account will not do so [20] either, then one may retort to such a man that though in some things one must not speak with the vulgar, yet in a question of terminology one is bound to employ the received and traditional usage and not to upset matters of that sort.

11 · Suppose now that a definition has been rendered of some complex, take [25] away the account of one of the elements in the complex, and see if the rest of the account defines the rest of it: if not, it is clear that neither does the whole account define the whole complex. Suppose, e.g., that some one has defined a finite straight line as the limit of a finite plane, such that its centre is in a line with its extremes; if now the account of a finite line is the limit of a finite plane, the rest (viz. ‘such that [30] its centre is in a line with its extremes’) ought to be an account of straight. But an infinite straight line has neither centre nor extremes and yet is straight, so that the remainder is not an account of the remainder.

Moreover, if the term defined is a compound, see if the account given has as many members as the term defined. An account is said to have as many members as [35] the term defined when the number of the elements compounded is the same as the number of names and verbs in the account. For in such cases, there is bound to be an exchange of word for word, in the case of some if not of all, seeing that there are no [149a1] more words used now than formerly; whereas in a definition words ought to be rendered by accounts, if possible in every case, or if not, in the majority. For at that rate, simple objects too could be defined by merely calling them by a different name, e.g. cloak instead of doublet.

[5] The mistake is even worse, if in addition a less intelligible word is substituted, e.g. pellucid mortal for white man; for it is no definition, and is less clear when put in that form.

Look and see also whether, in the exchange of words, the sense fails still to be the same. Take, for instance, the explanation of speculative knowledge as speculative [10] belief; for belief is not the same as knowledge—as it certainly ought to be if the whole is to be the same too; for though the word ‘speculative’ is common to both accounts, yet the remainder is different.

Moreover, see if in replacing one of the names by something else he has [15] exchanged the genus and not the differentia, as in the example just given; for speculative is less intelligible than knowledge; for the one is the genus and the other the differentia, and the genus is always the most familiar of all; so that it is not this, but the differentia, that ought to have been changed, seeing that it is the less [20] intelligible. (It might be held that this criticism is ridiculous because there is no reason why the most familiar name should not describe the differentia, and not the genus; in which case, clearly, the word to be altered should be that denoting the genus and not the differentia.) If, however, a man is substituting for a word not a word but an account, clearly it is of the differentia rather than of the genus that a [25] definition should be rendered, seeing that the object of rendering the definition is to make the subject familiar; for the differentia is less familiar than the genus.

If he has rendered the definition of the differentia, see whether the definition rendered is common to it and something else as well: e.g. whenever he says that an [30] odd number is a number with a middle, further definition is required of how it has a middle; for number is common to both accounts, and it is the word ‘odd’ for which the account has been substituted. Now both a line and a body have a middle, yet they are not odd; so that this will not be a definition of odd. And if having a middle is [35] used in several ways, the way here intended requires to be defined. So that this will either discredit the definition or prove that it is no definition at all.

12 · Again, see if the account is given of an entity, whereas what falls under the account is a non-entity. E.g., suppose white to be defined as colour mingled with [149b1] fire; for what is bodiless cannot be mingled with body, so that colour cannot be mingled with fire, whereas white does exist.

Moreover, those who in the case of relative terms do not distinguish to what the object is related, but have described it only so as to include it among a number of [5] things, are wrong either wholly or in part; e.g. suppose some one to have defined medicine as a science of what exists. For if medicine is not a science of anything that exists, the definition is clearly altogether false; while if it is a science of some things, but not of others, it is partly false; for it ought to hold of everything, if it is said to be of what exists essentially and not accidentally—as is the case with other relative [10] terms; for every object of knowledge is relative to knowledge. Likewise, also, with other relative terms, inasmuch as all such are convertible. Moreover, if the right way to render account of a thing is to render it as it is not in itself but accidentally, then each relative term will be used in relation not to one thing but to a number of things. For there is no reason why the same thing should not be both existent and [15] white and good, so that it will be a correct rendering to render the object in relation to any one whatsoever of these, if to render what it is accidentally is a correct way to render it. It is, moreover, impossible that an account of this sort should be proper to the term rendered; for not only medicine, but the majority of the other sciences too, [20] have for their object some entity, so that each will be a science of what exists. Clearly, then, such a definition does not define any science at all; for a definition ought to be proper, not common.

Sometimes, again, people define not the object but only the object in a good or perfect condition. Such is the definition of an orator as one who can see what will [25] persuade in any circumstances, and omit nothing; or of a thief, as one who pilfers in secret; for clearly, if they each do this, then the one will be a good orator, and the other a good thief; whereas it is not the actual pilfering in secret, but the wish to do it, that constitutes the thief. [30]

Again, see if he has rendered what is desirable for its own sake as desirable for what it produces or does, or as in any way desirable because of something else, e.g. by saying that justice is what preserves the laws or that wisdom is what produces happiness; for what produces or preserves something else is one of the things [35] desirable because of something else. It might be said that it is possible for what is desirable in itself to be desirable because of something else as well; but still to define what is desirable in itself in such a way is none the less wrong; for what is best in anything is especially part of its substance, and it is better for a thing to be desirable in itself than to be desirable because of something else, so that the definition ought rather to have indicated this.

[150a1] 13 · See also whether in defining anything a man has defined it as these things, or as made from these things or as this together with that. If he defines it as these things, the definition will be true of both and yet of neither of them; suppose, e.g., justice to be defined as temperance and courage. For if of two persons each has [5] one of the two only, both and yet neither will be just; for both together have justice, and yet each singly fails to have it. Even if the situation here described does not so far appear very absurd because of the occurrence of this kind of thing in other cases also (for it is quite possible for two men to have a pound between them, though neither of them has it by himself), yet at least that they should have contrary [10] attributes surely seems quite absurd; and yet this will follow if the one is temperate and cowardly, and the other brave and profligate; for then both will exhibit both justice and injustice; for if justice is temperance and bravery, the injustice will be [15] cowardice and profligacy. In general, too, all the ways of showing that the whole is not the same as the sum of its parts are useful in meeting the type just described; for a man who defines in this way seems to assert that the parts are the same as the whole. The arguments are particularly appropriate in cases where the process of putting the parts together is obvious, as in a house and other things of that sort; for [20] there, clearly, you may have the parts and yet not have the whole, so that parts and whole cannot be the same.

If he has said that the term being defined is not these things but made from these things, look and see in the first place if they cannot in the nature of things have a single product; for some things are so related to one another that nothing can come [25] from them, e.g. a line and a number. Moreover, see if the term that has been defined is in the nature of things found primarily in some single subject, whereas the things from which he has said it is made are not found primarily in any single subject, but each in a separate one. If so, clearly that will not be made from these things; for the whole is bound to be in the same things wherein its parts are, so that the whole will [30] then be found primarily not in one thing, but in a number of them. If, on the other hand, both parts and whole are found primarily in some single subject, see if that is not the same, but one thing in the case of the whole and another in that of the parts. Again, see whether the parts perish together with the whole; for it ought to happen vice versa, that the whole perishes when the parts perish: when the whole perishes, [35] there is no necessity that the parts should perish too. Or again, see if the whole is good or evil, and the parts neither, or, vice versa, if the parts are good or evil and the whole neither. For it is impossible either for a neutral thing to produce something [150b1] good or bad, or for things good or bad to produce a neutral thing. Or again, see if the one thing is more good than the other is evil, and yet the product is no more good than evil, e.g. suppose shamelessness is the product of courage and false opinion: here courage is more good than false opinion is evil; accordingly the product of these ought to follow the greater, and be either good without qualification, or at least [5] more good than evil. Or it may be that this does not necessarily follow, unless each is in itself good or bad; for many things that are productive are not good in themselves, but only in combination; or, vice versa, they are good taken singly, and bad or neutral in combination. What has just been said is more clearly illustrated in the [10] case of things that make for health or sickness; for some drugs are such that each taken alone is good, but if they are both administered in a mixture, bad.

Again, see whether the whole, as produced from a better and worse, fails to be worse than the better and better than the worse element. This again, however, need [15] not necessarily be the case, unless the elements compounded are in themselves good; if they are not, the whole may very well not be good, as in the cases just instanced.

Moreover, see if the whole is synonymous with one of the elements; for it ought not to be, any more than in the case of syllables; for a syllable is not synonymous [20] with any of the letters of which it is made up.

Moreover, see if he has failed to state the manner of their composition; for saying that it is made from these things is not enough to make the thing intelligible. For the substance of any compound thing is not merely that it is made from these things, but that it is made from them in such and such a way, as in the case of a [25] house; for here the materials do not make a house irrespective of the way they are put together.

If a man has defined an object as this together with that, the first thing to be said is that this together with that is the same as these things, or as what is made from these things. For ‘honey together with water’ means either ‘honey and water’, or ‘what is made from honey and water’. If, then, he admits that this together with [30] that is the same as either of these two things, the same criticisms will apply as have already been given for meeting each of them. Moreover, distinguish between the different ways in which one thing may be said to be together with another, and see if there is none of them in which this is together with that. Thus e.g. supposing one thing to be together with another either in that some identical thing contains them (as e.g. justice and courage are found in the soul), or as being in the same place or in [35] the same time, and if this is in no way true of the things in question, clearly the definition rendered will not hold of anything, as this is not in any way together with that. If, however, among the various ways distinguished, each is found in the same [151a1] time as the other, look and see if possibly the two are not used in the same relation. Thus e.g. suppose courage to have been defined as daring with right reasoning: here it is possible that a person exhibits daring in robbery, and right reasoning in regard to the means of health—but he is not courageous just because he has this together [5] with that at the same time. Moreover, even though both are used in the same relation, e.g. in relation to medical treatment (for a man may exhibit both daring and right reasoning in respect of medical treatment), still a man who has this together with that is not yet courageous. For the two must not relate to any casual [10] object that is the same, any more than each to a different object; rather, they must relate to the function of courage, e.g. meeting the perils of war, or whatever is more properly speaking its function than this.

Some definitions rendered in this form fail to come under the aforesaid division [15] at all, e.g. a definition of anger as pain with a consciousness of being slighted. For what this means to say is that it is because of a consciousness of this sort that the pain occurs; but to occur because of a thing is not the same as to occur together with it in any of the aforesaid ways.

[20] 14 · Again, if he has described the whole as the composition of these things (e.g. a living creature as a composition of soul and body), first of all see whether he has omitted to state the kind of composition, as (e.g.) in a definition of flesh or bone as the composition of fire, earth, and air. For it is not enough to say it is a composition, but you should also go on to define the kind of composition; for these [25] things do not form flesh irrespective of the manner of their composition, but when compounded in one way they form flesh, when in another, bone. It appears, moreover, that neither of the aforesaid things is the same as a composition at all; for a composition always has a dissolution as its contrary, whereas neither of the aforesaid has any contrary. Moreover, if it is equally plausible that every compound [30] is a composition and that none is, and if every kind of living creature, though a compound, is not a composition, then no other compound will be a composition either.

Again, if two contraries are equally liable to occur naturally in a thing, and the thing has been defined through the one, clearly it has not been defined; otherwise there will be more than one definition of the same thing; for how is it any more a [35] definition to define it through this one than through the other, seeing that both are equally liable to occur naturally in it? Such is the definition of the soul, if defined as [151b1] a substance capable of receiving knowledge; for it has an equal capacity for receiving ignorance.

Also, even when one cannot attack the definition as a whole because the whole [5] is not familiar, one should attack some part of it, if it is familiar and is evidently incorrectly rendered; for if the part is demolished, so too is the whole definition. Where, again, a definition is obscure, one should first of all correct and reshape it in order to make some part of it clear and get a handle for attack, and then proceed to examine it. For the answerer is bound either to accept the sense as taken by the [10] questioner, or else himself to explain clearly whatever it is that his account means. Moreover, just as in the assemblies the ordinary practice is to introduce a law and, if the introduced law is better, to repeal the existing one, so one ought to do in the case of definitions as well: one ought oneself to propose a second definition; for if it is [15] seen to be better, and more indicative of the object defined, clearly the definition laid down will have been demolished, on the principle that there cannot be more than one definition of the same thing.

In combating definitions it is always one of the chief elementary principles to take by oneself a happy shot at a definition of the object before one, or to adopt some correctly expressed definition. For one is bound, with the model (as it were) before [20] one’s eyes, to discern both the lack of any features that the definition ought to have, and also any superfluous addition, so that one is better supplied with lines of attack.

As to definitions, then, let so much suffice.

BOOK VII

1 · Whether two things are the same or different, in the most strict of the meanings ascribed to ‘sameness’ (and we said 34 that the same applies in the most strict sense to what is numerically one), may be examined in the light of their inflexions and coordinates and opposites. For if justice is the same as courage, then [30] too the just man is the same as the courageous man, and justly is the same as courageously. Likewise, too, in the case of their opposites; for if two things are the same, their opposites also will be the same, in any of the recognized forms of opposition. For it is the same thing to take the opposite of the one or that of the other, seeing that they are the same. Again it may be examined in the light of those [152a1] things which tend to produce or to destroy the things in question, of their formation and destruction, and in general of anything that is related in like manner to each. For where things are the same without qualification, their formations and destructions also are the same, and so are the things that tend to produce or to destroy them.

Look and see also, in a case where one of two things is said to be something or [5] other in a superlative degree, if the other of these identical things can also be described by a superlative in the same respect. Thus Xenocrates argues that the happy life and the good life are the same, seeing that of all forms of life the good life is the most desirable and so also is the happy life; for only one thing is the most desirable and greatest. Likewise also in other cases of the kind. Each of the two [10] things termed greatest or most desirable must be numerically one: otherwise no proof will have been given that they are the same; for it does not follow because Peloponnesians and Spartans are the bravest of the Greeks, that Peloponnesians are the same as Spartans, seeing that Peloponnesian and Spartan are not numerically [15] one; it only follows that the one must be included under the other as Spartans are under Peloponnesians—for otherwise, if the one class is not included under the other, each will be better than the other. For then the Peloponnesians are bound to be better than the Spartans, seeing that the one class is not included under the [20] other; for they are better than anybody else. Likewise also the Spartans must perforce be better than the Peloponnesians; for they too are better than anybody else; each then is better than the other. Clearly therefore what is styled best and [25] greatest must be numerically one, if it is to be proved to be the same as another. This is why Xenocrates fails to prove his case; for the happy life is not numerically one, nor yet the good life, so that it does not follow that, because they are both the most [30] desirable, they are therefore the same, but only that the one falls under the other.

Again, look and see if, supposing the one to be the same as something, the other also is the same as it; for if they are not both the same as the same thing, clearly neither are they the same as one another.

Moreover, examine them in the light of their accidents or of the things of which they are accidents; for any accident belonging to the one must belong also to [35] the other, and if the one belongs to anything as an accident, so must the other also. If in any of these respects there is a discrepancy, clearly they are not the same.

See further whether, instead of both being found in one class of predicates, the one signifies a quality and the other a quantity or relation. Again, see if the genus of [152b1] each is not the same, the one being good and the other evil, or the one being virtue and the other knowledge; or see if, though the genus is the same, the differentiae predicated of either are not the same, the one being distinguished as a speculative [5] science, the other as a practical science. Likewise also in other cases.

Moreover, from the point of view of degrees, see if the one admits an increase of degree but not the other, or if though both admit it, they do not admit it at the same time; just as it is not the case that a man desires intercourse more intensely, the more intensely he is in love, so that love and the desire for intercourse are not the same.

[10] Moreover, examine them by means of addition, and see whether the addition of each to the same thing fails to make the same whole; or if the subtraction of the same thing from each leaves a different remainder. Suppose (e.g.) that he has declared double a half to be the same as a multiple of a half: then, subtracting a half [15] from each, the remainders ought to have signified the same thing; but they do not; for double and a multiple do not signify the same thing.

Inquire also not only if some impossible consequence results directly from the statement—but also whether it may result from a supposition as happens to those [20] who assert that empty is the same as full of air; for clearly if the air is exhausted, the vessel will not be less but more empty, though it will no longer be full of air. So that by a supposition, which may be true or may be false (it makes no difference which), the one character is annulled and not the other, showing that they are not the same.

[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: they 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.

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, because 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 is 40 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.

[25] 5 · Inasmuch as no rules are laid down for those who argue for the sake of training and of examination—for the aim of those engaged in teaching or learning is quite different from that of those engaged in a competition; as is the latter from that of those who discuss things together in the spirit of inquiry; for a learner should always state what he thinks (for no one tries to teach what is false); whereas in a [30] competition the business of the questioner is to appear by all means to produce an effect upon the other, while that of the answerer is to appear unaffected by him; on the other hand, in dialectical meetings held in the spirit not of a competition but of an examination and inquiry, there are as yet no articulated rules about what the [35] answerer should aim at, and what kind of things he should and should not grant for the correct or incorrect defence of his position—inasmuch, then, as we have no tradition bequeathed to us by others, let us try to say something upon the matter for ourselves.

The thesis laid down by the answerer before facing the questioner’s argument is bound of necessity to be either reputable or implausible or neither; and reputable [159b1] or implausible either without qualification or else with a restriction, e.g. to some given person, to the speaker, or to some one else. But the way in which it is reputable or implausible, whatever it be, makes no difference; for the right way to answer, i.e. to admit or to refuse to admit what has been asked, will be the same in either case. If, then, the thesis is implausible, the conclusion is bound to be reputable, whereas if [5] the former is reputable the latter will be implausible; for the conclusion which the questioner tries to draw is always the opposite of the thesis. If, on the other hand, what is laid down is neither implausible nor reputable, the conclusion will be of the same type as well. Now since a man who deduces correctly demonstrates his conclusion from premisses that are more reputable and more familiar, it is clear [10] that where the view laid down by him is implausible without qualification, the answerer ought not to grant either what does not seem to be the case without qualification, or what seems to be the case, but to a less degree than the conclusion. For if the thesis is implausible the conclusion will be reputable, so that the premisses secured by the questioner should all be reputable, and more reputable than this [15] proposed conclusion, if the less familiar is to be inferred through the more familiar. Consequently, if any of the questions put to him is not of this character, the answerer should not grant it. If, on the other hand, the thesis is reputable without qualification, clearly the conclusion will be implausible without qualification. Accordingly, the answerer should admit all views that seem to be the case and, of those that do not, all that are less implausible than the conclusion. For then he will be thought to have argued sufficiently well. Likewise, too, if the thesis is neither [20] implausible nor reputable; for then, too, anything that appears to be true should be granted, and, of the views that do not seem true, any that are more reputable than the conclusion; for in that case the result will be that the arguments will be more reputable. If, then, the view laid down by the answerer is reputable or implausible [25] without qualification, then the views that are accepted without qualification must be taken as the standard of comparison; whereas if the view laid down is not reputable or implausible without qualification, but only to the answerer, then he must judge with reference to himself what seems or does not seem, and must grant or refuse to grant the point asked accordingly. If, again, the answerer is defending some one else’s opinion, then clearly it will be the latter’s judgement to which he must have regard in granting or denying the various points. This is why those who introduce others’ opinions—e.g. that good and evil are the same thing, as Heraclitus [30] says—refuse to admit that contraries do not belong at the same time to the same thing; not because they do not themselves believe this, but because on Heraclitus’ principles one has to say so. The same thing is done also by those who take on the defence of one another’s theses; their aim being to speak as would the man who stated the thesis. [35]

6 · It is clear, then, what the aims of the answerer should be, whether the position he lays down is reputable either without qualification or to some definite person. Now every question asked is bound to be either reputable or implausible or neither, and is also bound to be either relevant to the argument or irrelevant; if then it seems to be true and is irrelevant, the answerer should grant it and remark that it [160a1] seems to be true; if it does not seem to be true and is irrelevant, he should grant it but add a comment that it does not seem to be true, in order to avoid the appearance of being a simpleton. If it is relevant and seems to be true, he should admit that it seems to be true but say that it lies too close to the original proposition, and that if it [5] is granted the problem proposed collapses. If the axiom is relevant but too implausible, the answerer, while admitting that if it is granted the conclusion sought follows, should yet protest that the proposition is too silly. If it is neither implausible nor reputable, then, if it is irrelevant to the argument, it may be granted without restriction; if, however, it is relevant, the answerer should add the comment [10] that, if it is granted, the original problem collapses. For then the answerer will not be held to be personally accountable for what happens to him, if he grants the several points with his eyes open, and the questioner will be able to draw his inference, seeing that all the premisses that are more reputable than the conclusion are granted him. Those who try to deduce from premisses more implausible than the conclusion clearly do not deduce correctly; hence, when men ask these things, they [15] ought not to be granted.

7 · The questioner should be met in a like manner also in the case of terms used obscurely and in several ways. For the answerer, if he does not understand, is [20] always permitted to say ‘I do not understand’, and he is not compelled to reply ‘Yes’ or ‘No’ to a question which may mean different things. Clearly, then, in the first place, if what is said is not clear, he ought not to hesitate to say that he does not understand it; for often people encounter some difficulty from assenting to questions that are not clearly put. If he understands the question and yet it covers [25] many senses, then supposing what it says to be universally true or false, he should give it an unqualified assent or denial; if, on the other hand, it is partly true and partly false, he should add a comment that it bears different senses, and that in one it is true, in the other false; for if he leaves this distinction till later, it becomes uncertain whether originally he perceived the ambiguity. If he does not foresee the ambiguity, but assents to the question having in view the one sense of the words, [30] then, if the questioner takes it in the other sense, he should say, ‘That was not what I had in view when I admitted it; I meant the other sense’—for if a name or account covers more than one thing, disputes easily arise. If, however, the question is both clear and simple, he should answer either ‘Yes’ or ‘No’.

[35] 8 · Every deductive proposition either is one of the constituent elements in the deduction, or else goes to establish one of these (and you can always tell when it is secured in order to establish something else by the fact of a number of similar questions being put; for people for the most part secure the universal by means either of induction or of likeness); accordingly the particular propositions should all [160b1] be admitted, if they are true and reputable; but against the universal one should try to bring some objection; for to bring the argument to a standstill without an objection, either real or apparent, shows ill-temper. If, then, a man refuses to grant the universal when supported by many instances, although he has no objection, he [5] obviously shows ill-temper. If, moreover, he cannot even attempt a counter-proof that it is not true, far more likely is he to be thought ill-tempered. (Although even that is not enough; for we often hear arguments that are contrary to common opinions, whose solution is yet difficult, e.g. the argument of Zeno that it is impossible to move or to traverse the stadium; but still, this is no reason for omitting [10] to assert the opposites of these views.) If, then, a man refuses to admit the proposition without having either an objection or some counter-argument to bring against it, clearly he is ill-tempered, for ill-temper in argument consists in answering in ways other than the above, so as to wreck the reasoning.

9 · Before maintaining either a thesis or a definition the answerer should try [15] his hand at attacking it by himself; for clearly his business is to oppose those positions from which questioners demolish what he has laid down.

He should beware of maintaining an implausible hypothesis: and this it may be in two ways; for it may be one which results in absurd statements (e.g. suppose anyone were to say that everything is in motion or that nothing is); and also there [20] are those which a bad character would choose, and which are opposed to men’s wishes (e.g. that pleasure is the good, and that to do injustice is better than to suffer it). For people then hate him, supposing him to maintain them not for the sake of argument but because he really thinks them.

10 · When arguments reason to a false conclusion the right solution is to demolish the point on which the falsity depends; for the demolition of any random point is no solution, even if the point demolished is false. For the argument may [25] contain many falsehoods, e.g. suppose someone assumes that he who sits, writes and that Socrates is sitting; for from these it follows that Socrates is writing. Now we may demolish the proposition that Socrates is sitting, and still be no nearer a solution of the argument. ‘Yet the axiom is false’. But it is not on that that the falsity of the argument depends; for supposing that anyone should happen to be [30] sitting and not writing, it would be impossible in such a case to apply the same solution. Accordingly, it is not this that needs to be demolished, but rather that he who sits, writes; for not everyone who sits writes. He, then, who has demolished the point on which the falsity depends, has given the solution of the argument [35] completely. Anyone who knows that it is on such and such a point that the argument depends, knows the solution of it, just as in the case of a figure falsely drawn. For it is not enough to object, even if the point demolished is a falsehood, but the reason of the falsity should also be demonstrated; for then it will be clear whether the man makes his objection with his eyes open or not.

There are four possible ways of preventing a man from working his argument [161a1] to a conclusion. It can be done either by demolishing the point on which the falsity that comes about depends, or by stating an objection directed against the questioner—for often when a solution has not as a matter of fact been brought, yet the questioner is rendered thereby unable to pursue the argument any farther. Thirdly, one may object to the questions asked; for it may happen that what the questioner [5] wants does not follow from the questions he has asked because he has asked them badly, whereas if something additional is granted the conclusion comes about. If, then, the questioner is unable to pursue his argument farther, the objection will be directed against the questioner; if he can do so, then it will be against his questions. The fourth and worst kind of objection is that which is directed to the time allowed for discussion; for some people bring objections of a kind which would take longer to [10] answer than the length of the discussion in hand.

There are then, as we said, four ways of making objections; but of them the first alone is a solution: the others are just hindrances and stumbling-blocks to prevent the conclusions. [15]

11 · Criticism of an argument when taken in itself and when presented in the form of questions, is not the same. For often the failure to carry through the argument correctly in discussion is due to the person questioned, because he will not grant the steps of which a correct argument might have been made against his thesis; for it is not in the power of the one side only to effect properly a result that [20] depends on both alike. Accordingly it sometimes becomes necessary to attack the speaker and not his thesis, when the answerer lies in wait for the points that are contrary to the questioner and becomes abusive as well: when people lose their tempers in this way, their argument becomes contentious, not dialectical. Moreover, [25] since arguments of this kind are held not for the sake of instruction but for purposes of practice and examination, clearly one has to deduce not only true conclusions, but also false ones, and not always through true premisses, but sometimes through false as well. For often, when a true proposition is put forward, the dialectician is compelled to demolish it; and then false propositions have to be put forward. Sometimes also when a false proposition is put forward, it has to be demolished by [30] means of false propositions; for it is possible for a man to believe what is not the case more firmly than the truth. Accordingly, if the argument is made to depend on something that he holds, he will be persuaded rather than helped. He, however, who would rightly convert anyone to a different opinion should do so in a dialectical and [35] not in a contentious manner, just as a geometrician should reason geometrically, whether his conclusion is false or true (what kind of deductions are dialectical has already been said).41 The principle that a man who hinders the common business is a bad partner, clearly applies to an argument as well; for in arguments as well there is a common aim in view—except with mere contestants, for these cannot both [161b1] reach the same goal; for more than one cannot win. It makes no difference whether he effects this as answerer or as questioner; for both he who asks contentious questions is a bad dialectician, and also he who in answering fails to grant the obvious answer or to accept whatever question the questioner wishes to put. What [5] has been said, then, makes it clear that criticism is not to be passed in a like manner upon the argument in itself and upon the questioner; for it may very well be that the argument is bad, but that the questioner has argued with the answerer in the best possible way—for when men lose their tempers, it may perhaps be impossible to [10] make one’s deductions just as one would wish: we have to do as we can.

Inasmuch as it is indeterminate when people are claiming the admission of contrary things, and when they are claiming what originally they set out to prove—for often when they are talking by themselves they say contrary things, and admit afterwards what they have previously denied; for which reason they often [15] assent, when questioned, to contrary things and to what originally had to be proved—the argument is sure to become vitiated. The responsibility, however, for this rests with the answerer, because he refuses to grant some things and grants others of that sort. It is, then, clear that criticism is not to be passed in a like manner upon questioners and upon their arguments.

In itself an argument is liable to five kinds of criticism. The first is when [20] neither the proposed conclusion nor indeed any conclusion at all is drawn from the questions asked, and when most, if not all, of the premisses on which the conclusion rests are false or implausible, when, moreover, neither withdrawals nor additions nor both together can bring the conclusion about. The second is if the deduction, [25] though constructed from the premisses, and in the manner, described above, is irrelevant to the thesis. The third is if certain additions would bring a deduction about but yet these additions would be weaker than those that were put as questions, and less reputable than the conclusion. Again, supposing certain withdrawals could effect the same; for sometimes people secure more premisses than are necessary, so that it is not through them that the deduction comes about. [30] Moreover, suppose the premisses are more implausible and less convincing than the conclusion, or if, though true, they require more labour to demonstrate than the problem.

One must not demand that for every problem the deductions should be equally reputable and convincing; for it is a direct result of the nature of things that some [35] subjects of inquiry shall be easier and some harder, so that if a man concludes from opinions that are as reputable as the case admits, he has argued correctly. Clearly, then, the argument is not open to the same criticism when taken in relation to the proposed conclusion and when taken by itself. For there is nothing to prevent the argument being open to reproach in itself, and yet commendable in relation to the problem, or again, vice versa, being commendable in itself, and yet open to reproach [162a1] in relation to the problem, whenever there are many propositions both reputable and true whereby it could easily be proved. It is possible also that an argument, even though brought to a conclusion, may sometimes be worse than one which is not so concluded, whenever the premisses of the former are silly, while the problem is not [5] so; whereas the latter requires some additional premisses which are reputable and true, and moreover does not rest as an argument on these additions. With those which bring about a true conclusion by means of false premisses, it is not fair to find fault; for a false conclusion must of necessity always be deduced from false premisses, but a true conclusion may sometimes be deduced from false premisses; [10] as is clear from the Analytics.42

Whenever by the argument stated something is demonstrated, but that something is other than what is wanted and has no bearing whatever on the conclusion, then there is no deduction as to the latter; and if there appears to be, it will be a sophism, not a demonstration. A philosopheme is a demonstrative [15] deduction; an epichireme is a dialectical deduction; a sophism is a contentious deduction; an aporeme is a deduction that reasons dialectically to a contradiction.

If something were to be proved from premisses both of which seem true, but not to the same degree, it may very well be that what is proved seems more true than [20] either. If, on the other hand, the one seems true and the other neither, or if the one seems true the other does not, then, if they are equally balanced the conclusion will be also; if, on the other hand, the one preponderates, the conclusion too will follow suit.

It is also a fault in deduction when a man proves something through a long chain of steps, when he might employ fewer steps and those already included in his [25] argument: suppose him to be showing (e.g.) that one opinion is more properly so called from another, and suppose him to postulate that a thing-itself is most properly called that thing and that there genuinely exists an object of opinion in itself, so that it is more properly called an object of opinion than the particular objects of opinion; now what is called such-and-such relative to what is more properly called so-and-so is more properly called such-and-such; and there exists a [30] genuine opinion-in-itself, which will be more precise than the particular opinions. Now it has been postulated both that a genuine opinion-in-itself exists, and that a thing-in-itself is most properly called that thing; therefore this opinion will be more precise. Wherein lies the viciousness of the reasoning? Simply in that it conceals the ground on which the argument depends.

[35] 12 · An argument is clear in one, and that the most ordinary, sense, if it is so brought to a conclusion as to make no further questions necessary; in another sense, and this is the type most usually advanced, when the propositions assumed necessitate the conclusion, and the argument is concluded through premisses that [162b1] are themselves conclusions; moreover, it is so also if it claims less than some very reputable views.43

An argument is called false in four senses: first, when it appears to be brought to a conclusion, and is not really so—what is called a contentious deduction. Again, [5] when it comes to a conclusion but not to the conclusion proposed—which happens principally in the case of reductio ad impossibile. Or when it comes to the proposed conclusion but not according to the mode of inquiry appropriate to the case, as happens when a non-medical argument is taken to be a medical one, or one which is [10] not geometrical for a geometrical argument, or one which is not dialectical for dialectical, whether the result reached is true or false. Again, if the conclusion is reached through false premisses: of this type the conclusion is sometimes false, sometimes true; for while a false conclusion is always the result of false premisses, a [15] true conclusion may be drawn from premisses that are not true, as was said above as well.

Falsity in argument is due to a mistake of the arguer rather than of the argument; yet it is not always the fault of the arguer either, but only when he is not aware of it; for we often accept in itself in preference to many true ones an argument which demolishes some true proposition, if it does so from premisses as far as [20] possible generally accepted. For an argument of that kind does demonstrate other truths; for one of the premisses laid down ought never to be there at all, and this will then be demonstrated. If, however, a true conclusion were to be reached through premisses that are false and utterly childish, the argument is worse than many arguments that lead to a false conclusion—though an argument which leads to a [25] false conclusion may also be of this type. Clearly then the first thing to ask in regard to the argument in itself is whether it reaches a conclusion; the second, whether the conclusion is true or false; the third, on what kind of premisses does it depend. For if it depends on false but reputable premisses, the argument is dialectical; if on true but implausible premisses, it is bad; if they are both false and also entirely implausible, clearly it is bad, either without qualification or else in relation to the [30] particular matter in hand.

13 · Of the ways in which a questioner may postulate the point at issue and postulate contraries the true account has been given in the Analytics44; but an account on the level of opinion must be given now.

People appear to postulate the point at issue in five ways: the first and most obvious being if any one postulates the actual point requiring to be proved; this is [35] easily detected when put in so many words; but it is more apt to escape detection in the case of synonyms, and where a name and an account mean the same thing. A second way occurs whenever anyone postulates universally something which he has [163a1] to demonstrate in a particular case: suppose (e.g.) he were trying to prove that the knowledge of contraries is one, and were to claim that the knowledge of opposites in general is one—for then he seems to be postulating, along with a number of other things, that which he ought to have proved by itself. A third way is if anyone were to [5] postulate in particular cases what he has undertaken to prove universally: e.g. if he undertook to show that the knowledge of contraries is always one, and postulated it of certain pairs of contraries; for he seems to be postulating independently and by itself what, together with a number of other things, he ought to have proved. Again, if he divides up the problem and postulates its parts (supposing e.g. that he had to prove that medicine is a science of what leads to health and to disease, and were to [10] claim first the one, then the other); or if he postulates the one or the other of a pair of statements that necessarily follow one other (e.g. if he had to prove that the diagonal is incommensurable with the side, and were to postulate that the side is incommensurable with the diagonal).

The ways in which people assume contraries are equal in number to those in which they postulate the point at issue. For it would happen, firstly, if any one were [15] to postulate opposites, affirmation and negation; secondly, if he were to postulate the contrary terms of an antithesis, e.g. that the same thing is good and evil; thirdly, suppose anyone were to claim something universally and then proceed to postulate its contradictory in some particular case, e.g. if having assumed that the knowledge of contraries is one, he were to claim that the knowledge of what makes for health or for disease is different; or suppose him, after postulating the latter view, to try to secure universally the contradictory statement. Again, suppose a man postulates the [20] contrary of what necessarily comes about through the premisses laid down—even without postulating the opposites themselves but postulating two premisses such that the opposite contradiction will follow from them. The securing of contraries differs from postulating the point at issue in this way: in the latter case the mistake [25] lies in regard to the conclusion (for it is looking at the conclusion that we say that the point at issue has been postulated); whereas contrary views lie in the propositions, viz. in a certain relation which they bear to one another.

14 · The best way to secure training and practice in arguments of this kind is in the first place to get into the habit of converting the arguments. For in this way [30] we shall be better equipped for dealing with the proposition stated, and from a few cases we shall know thoroughly several arguments. For conversion is taking the reverse of the conclusion together with the remaining propositions asked and so demolishing one of those that were conceded; for it follows necessarily that if the [35] conclusion is untrue, some one of the propositions is demolished, seeing that, given all of them, the conclusion was bound to follow. In dealing with any thesis, be on the look-out for a line of argument both pro and con; and on discovering it at once set [163b1] about looking for the solution of it; for in this way you will soon find that you have trained yourself at the same time in both asking questions and answering them. If we cannot find any one else to argue with, we should argue with ourselves. Select, moreover, arguments relating to the same thesis and range them side by side; for [5] this produces a plentiful supply of arguments for carrying a point by force, and in refutation also it is of great service, whenever one is well stocked with arguments pro and con—for then you find yourself on your guard against contrary statements. Moreover, as contributing to knowledge and to philosophic wisdom the power of [10] discerning and holding in one view the results of either of two hypotheses is no mean instrument; for it then only remains to make a right choice of one of them. For a task of this kind a certain natural ability is required: in fact real natural ability just is the power rightly to choose the true and shun the false. Men of natural ability can [15] do this; for by a right liking or disliking for whatever is proposed to them they rightly select what is best.

It is best to know thoroughly arguments upon those problems which are of most frequent occurrence, and particularly in regard to those theses which are primary; for in discussing these answerers frequently give up in despair. Moreover, [20] get a good stock of definitions; and have those of reputable and primary ideas at your fingertips; for it is through these that deductions are effected. You should try, moreover, to master the heads under which other 45 arguments mostly tend to fall. For just as in geometry it is useful to be practised in the elements, and in arithmetic [25] having the multiplication table up to ten at one’s fingers’ ends makes a great difference to one’s knowledge of the multiples of other numbers too, likewise also in arguments it is a great advantage to be well up in regard to first principles, and to have a thorough knowledge of propositions by heart. For just as in a person with a trained memory, a memory of things themselves is immediately caused by the mere mention of their ‘places’, so these habits too will make a man readier in [30] reasoning, because he has his premisses classified before his mind’s eye, each under its number. It is better to commit to memory a proposition of general application than an argument; for it is not very difficult to get a supply of first principles and hypotheses.

Moreover, you should get into the habit of turning one argument into several, [35] and conceal your procedure as darkly as you can: this kind of effect is best produced by keeping as far as possible away from topics akin to the subject of the argument. This can be done with arguments that are entirely universal, e.g. that there cannot [164a1] be one knowledge of more than one thing—for that is the case with both relative terms and contraries and co-ordinates.

Records of discussions should be made in a universal form, even though one has argued only some particular case; for this will enable one to turn a single argument into several. (A like rule applies in rhetoric as well to enthymemes.) For [5] yourself, however, you should as far as possible avoid universalizing your deductions. You should, moreover, always examine arguments to see whether they rest on principles of general application; for all particular arguments reason universally as well, and a particular demonstration always contains a universal demonstration, [10] because it is impossible to deduce at all without using universals.

You should display your training in inductive reasoning against a young man, in deductive against an expert. You should try, moreover, to secure from those skilled in deduction their premisses, from inductive reasoners their parallel cases; [15] for this is the thing in which they are respectively trained. In general, too, from your exercises in argumentation you should try to carry away either a deduction on some subject or a solution or a proposition or an objection, or whether some one put his question properly or improperly (whether it was yourself or some one else) and the point which made it the one or the other. For this is what gives one ability, and the object of training is to acquire ability, especially in regard to propositions and [164a1] objections. For it is the skilled propounder and objector who is, speaking generally, a dialectician. To formulate a proposition is to form a number of things into one (for the conclusion to which the argument leads must be taken generally, as a single thing), whereas to formulate an objection is to make one thing into many (for the [5] objector either distinguishes or demolishes, partly granting, partly denying the statements proposed).

Do not argue with every one, nor practise upon the man in the street; for there are some people with whom any argument is bound to degenerate. For against anyone who is ready to try all means in order to seem not to be beaten, it is indeed [10] fair to try all means of bringing about one’s conclusion; but it is not good form. Therefore the best rule is, not lightly to engage with the man in the street, or bad argument is sure to result. For you see how in practising together people cannot refrain from contentious argument. [15]

It is best also to have ready-made arguments relating to those problems in which a very small stock will furnish us with arguments serviceable on a very large number of occasions. These are those that are universal, and those in regard to which 46 it is rather difficult to produce material from everyday experience.