Aristotle · a new plain-English translation from the original language
1| — so that being capable of being affected or of acting would be a proprium of what exists. Next, for demolishing, see whether he has stated the proprium by means of an extreme superlative; for then the thing posited to be a proprium will not be a proprium. For it turns out, for those who assign the proprium in this way, that the name is not truly said of that of which the formula is true; for even once the thing has perished, the formula will hold no less, since it belongs, in the highest degree, to some one among the things that exist. For example, if someone were to assign 'the lightest body' as a proprium of fire: for even once fire has perished, there will still be some body that is the lightest, so that 'the lightest body' would not be a proprium of fire. For establishing, see whether he has stated the proprium without a superlative; for on this point the proprium will have been well laid down. For example, since the one who posits 'an animal tame by nature' as a proprium of man has assigned the proprium without a superlative, on this point the proprium would have been well laid down. Book Six.
2| There are five parts to the study of definitions. For the attack is either that it is simply not true to predicate the formula also of that of which the name is predicated (for the definition of man must be true of every man); or that, a genus existing, he has not placed the thing in the genus, or has not placed it in its proper genus (for the person defining must place the thing in its genus and then attach the differentiae, since of the elements in a definition it is above all the genus that seems to signify the substance of the thing defined); or that the formula is not proper to the thing (for a definition must be proper, as has been said before); or that, although he has done everything just mentioned, he has still not defined the thing, and has not stated its essence. What remains, beyond what has been said, is the case where the thing has indeed been defined, but not well defined. If, then, the formula is not true of that of which the name is true, the examination must proceed by means of the commonplaces concerning accident. For there too the whole inquiry turns on whether it is true or not true: whenever we argue that the accident belongs, we say that it is true, and whenever we argue that it does not belong, we say that it is not true. But if he has not placed the thing in its proper genus, or if the formula given is not proper to it, the examination must proceed by means of the commonplaces stated concerning genus and proprium. What remains is to state how one is to proceed if the thing has not been defined, or has not been well defined. First, then, one must examine whether it has not been well defined; for it is easier to do anything at all than to do it well. It is clear, then, that error is more frequent on this point, since it is more laborious, so that the attempt against it is easier than the attempt against the other.
3| There are two parts to 'not well': one is using an unclear expression (for the person defining must use as clear an expression as possible, since a definition is given for the sake of making something known); the second is whether he has stated the formula at greater length than necessary, for everything added on beyond what is needed in a definition is superfluous. And again, each of these two is divided into several further parts.
4| One commonplace, then, for detecting unclearness is whether what has been said is homonymous with something else — for example, that coming-to-be is 'a passage into substance,' or that health is 'a proportion of hot and cold things.' For 'passage' and 'proportion' are both said in more than one way; so it is unclear which of the things signified by the term he means. Likewise too if, the thing being defined itself being said in several senses, he has spoken without distinguishing them; for it is unclear of which sense he has given the definition, and it becomes possible to raise a captious objection on the ground that the formula does not fit all the things of which he has given the definition as applying. This is most possible to do when the homonymy passes unnoticed. It is also possible, by distinguishing for oneself in how many ways the term given in the definition is said, to construct a deduction against it; for if it has not been adequately stated in any of the ways, it is clear that the thing would not have been properly defined. Another commonplace: whether he has spoken by way of metaphor — for example, calling knowledge 'unshifting,' or the earth 'a nurse,' or temperance 'a harmony.' For everything said by way of metaphor is unclear. It is also possible, when someone has spoken metaphorically, to raise a captious objection against him as though he had spoken in the strict sense; for the definition as stated will not fit — for example in the case of temperance, since every harmony is among sounds. Further, if 'harmony' is the genus of temperance, the same thing will fall under two genera that do not contain one another; for harmony does not contain virtue, nor does virtue contain harmony.
5| Further, whether he uses words that are not established usage — as Plato calls the eye 'brow-shaded,' or the venomous spider 'flesh-rotting-biter,' or marrow 'bone-engendering'; for everything not customary is unclear. Some expressions are said neither by way of homonymy, nor by way of metaphor, nor in the strict sense — for example, that law is 'a measure' or 'an image' of the things that are just by nature. Expressions of this kind are worse than metaphor; for a metaphor makes what is signified known, in a way, through the resemblance — since everyone who uses a metaphor transfers the term on the basis of some resemblance — whereas an expression of this other kind makes nothing known, since neither does the resemblance exist in virtue of which law is a measure or an image, nor is it customary for it to be said in the strict sense either. So that if he says, in the strict sense, that law is a measure or an image, he speaks falsely; for an image is a thing whose coming-to-be is through imitation, and this does not belong to law. And if not in the strict sense, it is clear that he has spoken unclearly, and worse than any of the things said by way of metaphor. Further, whether the formula of the contrary is not made clear from what has been said; for definitions well given also indicate their contraries besides. Or whether, said just by itself, it is not plain what it is a definition of, but is like the works of the ancient painters — where, unless someone had written a caption, it would not have been recognized what each thing was.
6| If, then, the definition has been stated unclearly, the examination must proceed from considerations of this kind. But if he has stated the definition at greater length than needed, one must first examine whether he has used something that belongs to everything — either to things that exist in general, or to the things falling under the same genus as the thing defined; for this is necessarily stated at greater length than is required. For the genus must mark the thing off from the other things, while the differentia must mark it off from some of the things within the same genus. Now what belongs to everything without qualification marks the thing off from nothing, while what belongs to all the things falling under the same genus does not mark it off from the things in that same genus, so that adding a term of this kind is pointless.
7| Or: is the addition proprium, but once it is removed does the remaining account also state something proprium and reveal the substance? For example, in the account of man, adding "capable of receiving knowledge" is superfluous; for even with this removed the remaining account is proprium and reveals the substance. To put it generally, anything is superfluous whose removal leaves the remainder still making clear what is being defined. Such, too, is the definition of soul, if it is "a number moving itself"; for what moves itself is soul, as Plato has defined it. Or perhaps: what is stated is proprium, but does not reveal the substance once "number" is removed. Which way the matter stands is hard to make clear; one must, in all such cases, argue whichever way is advantageous. For example: the definition of phlegm is "the first fluid from nourishment that is unconcocted." For if it is the first, it is not many things, so that adding "unconcocted" is superfluous; for even with this removed the remainder will be a proprium account, since it is not possible for both this and something else to be first from nourishment. Or else: phlegm is not the first thing from nourishment without qualification, but the first of the unconcocted things, so that "unconcocted" must be added; for stated the other way, the account is not true, if indeed it is not first of all things.
8| Again, see whether some element in the account fails to belong to all the things that fall under the same species; for such a person has defined worse than those who use something that belongs to all beings. For in that other case, if the remaining account is proprium, then the whole account too will be proprium; for in general, once something true is added to a proprium, the whole becomes proprium. But if some element in the account fails to belong to all things under the same species, it is impossible for the whole account to be proprium; for it will not be predicated convertibly of the thing. For example: "animal, footed, two-footed, four cubits tall"; such an account is not predicated convertibly of the thing, because "four cubits tall" does not belong to all things under the same species. Again, see whether he has said the same thing more than once, as when someone says appetite is "desire for the pleasant"; for every appetite is of the pleasant, so that "the same as appetite" will also be "of the pleasant." The definition of appetite then becomes "desire for the pleasant pleasant"; for it makes no difference to say "appetite" or "desire for the pleasant," so that each of them will be "of the pleasant." Or perhaps there is nothing strange in this; for man too is two-footed, so that what is the same as man will also be two-footed. And "animal, footed, two-footed" is the same as man, so that "animal, footed, two-footed" is two-footed.
9| But nothing strange results from this; for "two-footed" is not predicated of "animal, footed" (for in that case "two-footed" would be predicated twice of the same thing), but "two-footed" is said of "animal, footed, two-footed," so that "two-footed" is predicated only once. Likewise too with appetite; for "being of the pleasant" is not predicated of "desire," but of the whole together, so that here too the predication occurs only once. And uttering the same name twice is not among the strange cases, but predicating the same thing more than once of something is — as when Xenocrates says practical wisdom is "determinative and theoretical of the things that are." For the determinative is a kind of theoretical, so that he says the same thing twice by adding "and theoretical" as well. Likewise too with all those who say that chilling is "privation of the natural heat"; for every privation is of what belongs by nature, so that adding "natural" is superfluous, and it would have sufficed to say "privation of heat," since the privation itself makes it known that what is meant is the natural heat. Again, see whether, having stated the universal, he adds also the particular, as when someone defines decency as "a diminishing of what is advantageous and just"; for the just is a kind of advantageous, so that it is contained within the advantageous. "Just" is therefore redundant, so that having spoken universally he has added the particular too. So also if someone defines the medical craft as "of the things healthy for an animal and for man," or the law as "an image of the things fine and just by nature"; for the just is a kind of fine, so that he says the same thing more than once.
10| Whether it has been stated well or not well, then, is to be examined by these and similar means; but whether one has stated and defined the essence or not is to be examined from what follows. First, see whether the definition has not been constructed through things prior and more knowable. For since a definition is rendered for the sake of making known the thing spoken of, and we come to know not from just anything but from things prior and more knowable, as in demonstrations (for all teaching and learning work this way), it is clear that one who defines not through such things has not defined at all. If not, there will be several definitions of the same thing. For it is clear that the one defined through things prior and more knowable is better defined, so that both would be definitions of the same thing. But this is not held to be so; for each of the things that are has one thing that it is to be just what it is; so that if there will be several definitions of the same thing, then being just what the thing is, as made clear according to each of the definitions, will be the same. But these are not the same, since the definitions are different. It is clear, then, that one who has defined not through things prior and more knowable has not defined. Now the phrase "the definition has not been stated through more knowable things" can be taken in two ways:
11| for either it means through things more unknown without qualification, or through things more unknown to us; for it is possible in either sense. Now what is more knowable without qualification is what is prior to what is posterior — for example, a point is more knowable than a line, a line than a plane, and a plane than a solid, just as a unit is more knowable than number; for it is prior to and the starting point of every number. Likewise too an element is more knowable than a syllable. But for us the opposite sometimes happens; for the solid falls under perception most of all, the plane more than the line, and the line more than the point. For most people come to know things of that sort first; for these belong to any ordinary intelligence, while those others require an exact and exceptional intelligence to grasp. Without qualification, then, it is better to try to make the posterior known through the prior, for this is more scientific. Still, for those unable to gain knowledge through such means, it is presumably necessary to construct the account through things known to them. Among definitions of this sort are that of the point, that of the line, and that of the plane; for all of them make the prior known through the posterior, saying that a point is the limit of a line, a line of a plane, and a plane of a solid. But one must not fail to notice that those who define in this way cannot make clear to the thing defined what it is to be that thing, unless it happens that the same thing is both more knowable to us and more knowable without qualification — given that one who defines well must define through the genus and the differentiae, and these belong among the things more knowable without qualification and prior to the species.
12| For the genus and the differentia together do away with the species when they are removed, so that these are prior to the species. And they are also more knowable; for when the species is known, the genus and the differentia are necessarily known as well (for one who knows man also knows animal and footed), but when the genus or the differentia is known, it is not necessary for the species also to be known, so that the species is less knowable. Further, for those who say that such definitions — the ones made from things known to each individual — are the true kind, it will follow that they are speaking of many definitions of the same thing; for different things happen to be more knowable to different people, and not the same things to all, so that a different definition would have to be rendered for each person, if indeed the definition must be constructed from what is more knowable to each. Further, for the same people different things are more knowable at different times: at first the perceptible things, but for those who become more exact, the reverse — so that not even for the same person must the same definition always be rendered by those who claim the definition must be rendered through what is more knowable to each individual. It is clear, then, that one should not define through such things, but through what is more knowable without qualification; for only in this way could one and the same definition always result. And perhaps, too, what is knowable without qualification is not what is knowable to everyone, but what is knowable to those whose intellect is well disposed, just as what is healthy without qualification is what is healthy for those whose bodies are in good condition.
13| So one must work out the precise details of each such point, but in arguing use them as suits the occasion. A definition can most conclusively be demolished if its account has been built neither from things more knowable without qualification nor from things more knowable to us. Now one way of failing to proceed through more knowable things is explaining the earlier by means of the later, as we said before; another is if the account of what is at rest and determinate has been given by means of the indeterminate and of what is in motion; for what is stable and determinate is prior to what is indeterminate and in motion. Of the ways of not proceeding from what is prior there are three. The first is if the opposite has been defined by means of the opposite, for instance the good by means of the bad; for opposites are simultaneous in nature. To some it also seems that the same knowledge covers both, so that neither is more knowable than the other. But one must not fail to notice that some things perhaps cannot be defined otherwise, for instance the double without the half, and all things that are said to be relative in their own right; for in all such cases their being is the same as standing in some relation, so that it is impossible to know the one without the other, and hence the one must necessarily be included in the account of the other as well.
14| Now one must know all such points, but use them as seems to serve one's purpose. Another way is if he has used the very term being defined. This escapes notice when he does not use the actual name of the thing defined, for instance if someone defined the sun as the star that shines by day; for whoever uses 'day' uses 'sun'. To catch such cases one must substitute the account for the name, for instance that day is the passage of the sun above the earth; for it is clear that whoever has spoken of the passage of the sun above the earth has spoken of the sun, so that whoever has used 'day' has used 'sun'. Again, if the correlatively divided term has been defined by means of its correlative, for instance the odd as what is greater than the even by a unit. For things divided off from the same genus by correlation are simultaneous in nature, and odd and even are so divided off; for both are differentiae of number. Likewise too if the higher term has been defined by means of what is lower, for instance an even number as one divisible into two halves, or the good as a state of virtue; for 'in half' is derived from 'two', which is even, and virtue is a kind of good, so that these are lower than those. Further, whoever uses the lower term is necessarily using the higher one too; for whoever uses virtue uses the good, since virtue is a kind of good;
15| and likewise whoever uses 'in half' uses 'even', since 'in half' signifies being divided into two, and two is even.
16| To speak generally, then, there is one common topic — not constructing the account from things prior and more knowable — and the points mentioned are parts of it. A second topic is: if, though the thing belongs in a genus, it is not placed in a genus. This is a mistake in all cases where the account is not meant to state what the thing is, for instance the definition of body as that which has three dimensions, or if someone were to define man as that which knows how to count. For it has not been said what, being such-and-such, has three dimensions, or what, being such-and-such, knows how to count; and the genus is meant to signify the what-it-is, and is posited first among the things stated in the definition. Further, if the thing defined is spoken of in relation to several things and the account has not been fitted to all of them, for instance if grammatical knowledge is defined as knowledge of writing what is dictated; for it also needs to add 'and of reading', since it is no more by virtue of writing than of reading that it has been defined, so that neither one alone but the one who states both is the one who has defined it, since more than one definition of the same thing cannot exist. Now in some cases this holds as a matter of truth, as has been said, but in others it does not, namely in cases where the thing is not said in its own right in relation to both, as medicine is said to produce disease and health; for it is said of health in its own right, but of disease accidentally, since producing disease is absolutely alien to medicine. So one who has given the definition in relation to both is no more accurate than one who gave it in relation to the one alone, but perhaps even worse, since any of the rest is also capable of producing disease. Further, if he has fitted the account not to the better but to the worse, when there are several things in relation to which the thing defined is spoken of; for every science and power is thought to be of the best. Again, if what is stated is not placed in its proper genus, one must examine it by means of the elements concerning genera, as was said before.
17| Further, if he says something that oversteps the genera, for instance one who defines justice as a state productive of equality or distributive of the equal. For in defining it this way he oversteps virtue. So by leaving out the genus of justice he does not state the essence; for the substance of each thing comes together with its genus. And this is the same as not placing the thing in its nearest genus; for whoever places it in its nearest genus has stated all the genera above it as well, since all the higher genera are predicated of the lower ones. So one must either place it in its nearest genus, or else attach to the higher genus all the differentiae by which the nearest genus is defined. For in this way he would have left out nothing, but would have stated the lower genus in an account instead of by a name. But whoever states only the higher genus by itself does not thereby also state the lower genus; for whoever says 'plant' does not say 'tree'.
18| Again, in the case of the differentiae one must likewise examine whether he has also stated the differentiae of the genus. For if the thing has not been defined by the differentiae proper to it, or if he has stated something of such a kind that it cannot possibly be the differentia of anything, for instance animal or substance, it is clear that it has not been defined; for what has been stated is a differentia of nothing. One must also look and see whether there is something set off correlatively against the stated differentia. For if there is not, it is clear that what was stated could not be the differentia of the genus; for every genus is divided by correlatively opposed differentiae, as animal is divided by footed and winged and aquatic and two-footed. Or if the correlative differentia does exist but is not truly predicated of the genus. For it is clear that neither could then be the differentia of the genus; for all correlatively opposed differentiae are truly predicated of their proper genus. Likewise too if it is truly predicated but, when added to the genus, does not produce a species. For it is clear that this could not then be a species-making differentia of the genus; for every species-making differentia, together with the genus, produces a species. And if this is not a differentia, neither is the one stated, since it is set off correlatively against this one.
19| Further, if he divides the genus by negation, as those do who define the line as length without breadth. For this signifies nothing other than that it does not have breadth. It will then follow that the genus partakes of the species; for every length either lacks breadth or has breadth, since of everything either the affirmation or the negation is true, so that the genus of the line, being length, will be either without breadth or having breadth. But length without breadth is the account of a species, and likewise length having breadth; for 'without breadth' and 'having breadth' are differentiae, and the account of the species comes from the differentia together with the genus, so that the genus would admit the account of the species. And likewise the account of the differentia, since one of the differentiae mentioned is necessarily predicated of the genus. Now the topic just stated is useful against those who posit that Forms exist. For if length itself exists, how will it be predicated of the genus that it has breadth or is without breadth? For one or the other of these must be true of every length, if it is indeed going to be true of the genus. But this does not turn out to be so; for there are lengths without breadth and lengths having breadth.
20| So this topic is useful only against those who say that the genus is one in number. This is what those do who posit the Forms: they say that length itself and animal itself are a genus. But perhaps in some cases the person giving the definition must also use negation, as in the case of privations: for the blind is what does not have sight, when it is natural to have it. It makes no difference whether one divides the genus by negation, or by an affirmation of a kind against which a negation must be counter-divided, as if length were defined as having breadth: for what does not have breadth is counter-divided against what has breadth, and nothing else, so that the genus is again divided by negation. Again, one must see if he has rendered the species as a differentia, as those do who define insult as hubris accompanied by mockery: for mockery is a kind of hubris, so that mockery is not a differentia but a species. Further, if he has stated the genus as a differentia, as when virtue is defined as a good or excellent state: for the good is a genus of virtue. Or rather the good is not a genus but a differentia, if it is true that the same thing cannot be in two genera that do not contain one another. For neither does the good contain the state, nor does the state contain the good: for not every state is good, nor is everything good a state, so that both could not be genera.
21| If then the state is the genus of virtue, clearly the good is not a genus but rather a differentia. Further, the state signifies what virtue is, but the good does not signify what a thing is but of what quality it is; and the differentia seems to signify a quality of some kind. One must also see whether the differentia rendered signifies not a quality but a 'this': for every differentia seems to indicate some quality. One must also examine whether the differentia belongs to the thing defined accidentally. For no differentia is among the things that belong accidentally, any more than the genus is: for it is not possible for the differentia to belong to a thing and not belong to it. Further, if the differentia, or the species, or something below the species, is predicated of the genus, the definition cannot be correct: for none of the things mentioned can be predicated of the genus, since the genus is said of the greatest number of things of all. Again, if the genus is predicated of the differentia: for the genus seems to be predicated not of the differentia but of the things of which the differentia is said, as animal is predicated of man and of ox and of the other footed animals, not of the differentia itself that is said of the species.
22| For if animal were to be predicated of each of the differentiae, many animals would be predicated of the species; for the differentiae are predicated of the species. Further, differentiae will all turn out to be species or individuals, if indeed they are animals: for each of the animals is either a species or an individual. One must likewise examine whether the species, or something below the species, is predicated of the differentia: this is impossible, since the differentia is said of a wider range than the species. Further, it will follow that the differentia is a species, if one of the species is predicated of it: for if man is predicated of it, clearly the differentia is a man. Again, if the differentia is not prior to the species: for the differentia must be posterior to the genus but prior to the species. One must also examine whether the differentia stated belongs to another genus that neither contains nor is contained by the genus in question. For the same differentia does not seem to belong to two genera that do not contain one another. If it does, it will follow that the same species also is in two genera that do not contain one another: for each of the differentiae brings along with it its own proper genus, just as footed and two-footed together bring along animal. So that whatever the differentia is predicated of, each of the two genera will be predicated of as well.
23| It is clear, then, that the species is not in two genera that do not contain one another. Or rather, it is not impossible for the same differentia to belong to two genera that do not contain one another, but one must add the qualification that the two genera are also not both under the same genus. For footed animal and winged animal are genera that do not contain one another, and two-footed is a differentia of both of them. So one must add that the two are also not both under the same thing: for both of these are under animal. It is also clear that the differentia need not bring along with it every one of its proper genera, since it is possible for the same differentia to belong to two genera that do not contain one another; rather it need only bring along the one, together with the things above that one, just as two-footed brings along with it winged or footed, and animal. One must also see whether he has rendered as the differentia of a substance something's being in something: for one substance does not seem to differ from another substance by where it is. This is why people also censure those who divide animal into footed and aquatic, on the ground that footed and aquatic signify where a thing is. But in these cases the censure is not correct: for aquatic signifies not being in something, nor where a thing is, but a quality of some kind; for even if a thing is in what is dry, it is aquatic just the same;
24| and likewise the land-dweller, even if it is in what is wet, will be a land-dweller and not aquatic. But all the same, if the differentia ever does signify being in something, it is clear that it will be mistaken. Again, one must see if he has rendered an affection as a differentia. For every affection, when it increases, removes the thing from its substance, but the differentia is not of this kind: rather the differentia seems more to preserve the thing of which it is the differentia, and it is in general impossible for anything to exist without its proper differentia; for if footed did not exist, there would be no man. To put it simply, whatever respects a thing is altered in, none of these is a differentia of it: for all such things, when they increase, remove the thing from its substance. So that if anyone has rendered such a thing as a differentia, he has erred; for in general we are not altered in respect of our differentiae. And also, if he has rendered the differentia of something relative without reference to something else: for the differentiae of relatives are also relative, as with knowledge; for knowledge is called theoretical and practical and productive, and each of these signifies something relative to something: theoretical of something, and productive of something, and practical of something. One must also examine whether the person defining renders each of the relatives with reference to that toward which it is naturally directed. For with some relatives it is possible to use each of them only with reference to that toward which it is naturally directed, and for nothing else, while with others it is possible to use them for something else too, as sight only for seeing, but a strigil one might also use to bail water with;
25| but all the same, if one were to define the strigil as an instrument for bailing water, one would be mistaken: for it is not naturally directed to this. The definition of that toward which a thing is naturally directed is that toward which the practically wise person, qua practically wise, would use it, together with the proper science concerned with each thing. Or, if he has not rendered the primary object, when the thing happens to be said with reference to several things, as when practical wisdom is defined as the virtue of man or of the soul, and not of the rational part: for practical wisdom is the virtue of the rational part primarily; for it is in virtue of this that both the soul and the man are said to be practically wise. Further, if the thing said to possess the given affection or disposition or anything else whatever is not receptive of it, he has erred. For every disposition and every affection naturally comes to be in that of which it is the disposition or affection, just as knowledge too, being a disposition of the soul, comes to be in the soul. But sometimes people err in such cases, as those who say that sleep is an incapacity of perception, and that perplexity is an equality of opposing calculations, and that pain is a violent separation of connate parts: for sleep does not belong to perception—yet it ought to, if indeed it is an incapacity of perception. Likewise, neither does perplexity belong to the opposing calculations, nor pain to the connate parts;
26| For inanimate things will feel pain, if pain is present in them. Such also is the definition of health, if it is a balance of hot and cold; for it will be necessary that hot and cold things be healthy - for the balance of each thing exists in those things of which it is a balance, so that health would belong to them. Again, those who define in this way happen to be putting what is produced in place of what is productive, or the reverse. For pain is not the separation of connate parts, but is productive of pain; nor is sleep the incapacity of perception, but each is productive of the other - for either we sleep because of the incapacity, or we are incapacitated because of sleep. Similarly the equality of opposing calculations would seem to be productive of puzzlement; for when, reckoning on both sides, everything appears to us to come out alike on either side, we are at a loss which of the two to do. Again, one should look across all the times, to see if it conflicts anywhere - for instance if someone defined the immortal as an animal now indestructible; for what is now an indestructible animal will now be immortal. Or does this not follow in this case? For 'now indestructible' is ambiguous: it may mean either that it has not now perished, or that it is not now capable of perishing, or that it is now such as never to perish.
27| So when we say that an animal is now indestructible, we mean by this that it is now such an animal as never to perish. But this is the same thing as the immortal, so that it does not follow that it is now immortal in the sense objected to. But all the same, if it turns out that what is given according to the account holds now or earlier, while what is given according to the name does not hold, they would not be the same. One must use the topic, then, as has been said.
28| One must also examine whether the thing defined is said rather in accordance with something else than in accordance with the account given - for instance, if justice is defined as the power of distributing what is equal. For a man is more just for choosing to distribute what is equal than for being able to; so that justice would not be the power of distributing what is equal - for indeed the man most able to distribute what is equal would be most just on that definition. Again, look whether the thing admits the more while what is given according to the account does not admit it, or conversely whether what is given according to the account admits the more while the thing does not. For both must admit it or neither must, if indeed what is given according to the account is the same as the thing. Again, look whether, though both admit the more, they do not receive the increase at the same time - for instance if love is defined as desire for intercourse; for the man who loves more does not desire intercourse more, so that the more is not admitted by both together; yet it ought to be, if they were the same. Again, look whether, when two things are proposed, that in respect of which the thing is said more is that of which the account is said less - for instance if fire is defined as the body of finest parts;
29| for flame is fire more than light is, but as body of finest parts flame is less than light; but both ought to belong more to the same thing, if they were the same. Again, look whether one thing belongs alike to both of the things proposed, while the other does not belong alike to both but more to one. Again, if he gives the definition with reference to two things according to each - as when the fine is defined as what is pleasant through sight or through hearing, and being as what is capable of being affected or of acting - then the same thing will be at once fine and not fine, and likewise both being and not being. For pleasant through hearing will be the same as fine, so that not pleasant through hearing will be the same as not fine - for opposites belong to the same things, and opposed to fine is not fine, while opposed to pleasant through hearing is not pleasant through hearing. It is clear, then, that not pleasant through hearing is the same as not fine. If, then, something is pleasant through sight but not through hearing, it will be both fine and not fine. We shall show similarly that the same thing is also both being and not being.
30| Again, one should take the accounts in place of the names for the genera and the differentiae and everything else given in the definitions, and see whether anything conflicts. If the thing defined is relative, either in its own right or in respect of its genus, one should examine whether what it is said in relation to has not been stated in the definition, either the thing itself or its genus - for instance if he defined knowledge as a supposition not to be changed by persuasion, or wish as desire free from pain. For the substance of everything relative is relative to something else, since for each relative, being is the same as being related to something in a certain way. He ought, then, to have said that knowledge is supposition of a knowable object, and wish desire for a good. Similarly too if he defined grammar as knowledge of letters - for one ought to give, in the definition, either that to which the thing itself is said to relate, or that to which its genus at some point relates. Or look whether, though it has been stated as relative, it has not been given with reference to the end. For in each case the end is the best thing, or the thing for the sake of which everything else exists. One should therefore state either the best thing or the furthest thing - for instance, appetite should be defined not as desire for the pleasant thing but as desire for pleasure; for it is for the sake of pleasure that we choose the pleasant thing too. One should also examine whether what he has given is a coming-to-be or an activity in each case; for none of such things is an end - for having-been-active and having-come-to-be are ends more than coming-to-be and being-active are.
31| Or is this not true in every case? For most people, pretty much, wish to be enjoying pleasure rather than to have stopped enjoying it, so that they would make being-active more the end than having-been-active. Again, in some cases one should examine whether he has not marked off the quantity or quality or place or the other differentiae - for instance, in defining the lover of honor, of what kind and how much honor he desires; for everyone desires honor, so it is not enough to say that the lover of honor is the one who desires honor, but the aforementioned differentiae must be added. Similarly too the lover of money is the one who desires how much money; or the incontinent person, in regard to what kind of pleasures - for it is not the person overcome by just any pleasure whatever who is called incontinent, but the person overcome by a certain kind. Or again, as people define night as the shadow of the earth, or earthquake as a motion of the earth, or cloud as a condensation of air, or wind as a motion of air - one must add how much and of what kind and by what. Similarly too in the other such cases; for by leaving out any differentia whatever, one fails to state the essence. And one must always attack the point that is lacking; for it is not the case that, however the earth is moved and to whatever extent, there will be an earthquake, nor likewise that, however the air is moved and to whatever extent, there will be wind.
32| Again, in the case of desires, one should examine whether 'apparent' has not been added, and in as many other cases as this is fitting - for instance, that wish is desire for the good, and appetite desire for the pleasant, rather than for the apparent good or the apparent pleasant. For often those who desire are unaware what the good or pleasant thing is, so that it need not be good or pleasant, but only apparent. One ought, then, to have made the definition in this way too. But if he does give it as stated, one must lead the person who posits that there are Forms toward the Forms; for there is no Form of anything apparent, while a form is held to be said in relation to a form - for instance, appetite itself is for pleasant itself, and wish itself is for good itself. It is not, then, for apparent good nor for apparent pleasant; for it would be absurd for the very thing itself to be apparent good or apparent pleasant.
33| Again, if the definition given is of the state, look to see whether it applies to the thing that has the state; if it is of the thing that has the state, look to the state; and likewise for other such pairs. For example, if what is pleasant is what is beneficial, then the person feeling pleasure is being benefited. In general, in definitions of this sort it turns out that, in a way, the person giving the definition defines more than one thing at once. For the person who defines knowledge in a way also defines ignorance, and likewise the knowing subject and the unknowing subject, and knowing and being ignorant; for once the first is made clear, in a way the rest become clear too. One must therefore examine all such cases to see whether there is any discrepancy, using as tools the terms drawn from the opposites and the coordinate terms. Again, in the case of relatives, examine whether, corresponding to what the genus is said in relation to, the species is also said in relation to some corresponding thing — for example, if supposing is in relation to something supposable, then a particular supposing is in relation to some particular supposable thing; and if the multiple is in relation to the fraction, then a particular multiple is in relation to a particular fraction. For if it is not rendered in this way, clearly a mistake has been made. One should also see whether the account of the opposite is the opposite of the account given — for example, whether the account of the half is opposite to that of the double;
34| for if the double is what exceeds by an equal amount, the half is what is exceeded by an equal amount. And likewise with contraries: for the account of the contrary must be the contrary of the account of the other, by some pairing of contraries — for example, if the beneficial is what produces good, the harmful is what produces evil, or what destroys good; for one or the other of these must necessarily be contrary to what was originally said. If, then, neither is contrary to what was originally said, clearly neither of the accounts subsequently given would be the account of the contrary, so that the one originally given has not been correctly given either. But since some contraries are spoken of as the privation of the other — for example, inequality seems to be the privation of equality (for things not equal are called unequal) — clearly the term spoken of by way of privation must necessarily be defined by means of the other, whereas the other must not in turn be defined by means of the term spoken of by way of privation; for otherwise it would turn out that each is known by means of the other. One must therefore examine, in the case of contraries, for this kind of mistake — for example, if someone were to define equality as the contrary of inequality; for this defines it by means of the term spoken of by way of privation. Moreover, the person who defines in this way must necessarily be using the very term being defined. This becomes clear if the account is substituted for the name;
35| for to say 'inequality' differs not at all from saying 'privation of equality.' Equality will accordingly be the contrary of the privation of equality, so that he would be using the very term itself. But if neither of the contraries is spoken of by way of privation, and yet the account is rendered in the same way — for example, the good is the contrary of the evil — clearly the evil will be the contrary of the good; for of contraries so related the account must be rendered in the same way in each direction. So again it turns out that he uses the very term being defined; for the good is present within the account of the evil. So that if the good is what is contrary to the evil, and the evil differs not at all from what is contrary to the good, then the good will turn out to be the contrary of what is contrary to the good. It is clear, then, that he has used the term itself. Again, see whether, in rendering the term spoken of by way of privation, he has failed to state that of which it is the privation — for example, of the state, or of the contrary, or of whatever it is the privation; and whether he has failed to add that in which it naturally occurs, either without qualification or in that in which it primarily and naturally occurs — for example, if in saying that ignorance is a privation he did not say it was privation of knowledge, or did not add that in which it naturally occurs, or, having added it, did not give that in which it primarily occurs, saying for instance not that it occurs in the rational faculty but in man or in soul;
36| for if he fails to do any of these things, he has made a mistake. Likewise too if he said that blindness is privation of sight without adding 'in the eye'; for the person correctly rendering what a thing is must also render both of what it is the privation and what it is that has been deprived. One should also see whether he has defined by privation something that is not spoken of by way of privation — for example, in the case of ignorance, such a mistake would seem to belong to those who do not describe ignorance in terms of negation. For what has no knowledge does not seem to be ignorant, but rather what has been deceived; hence we say that neither inanimate things nor children are ignorant, so that ignorance is not spoken of as the privation of knowledge.
37| Again, see whether, of similar inflections of the name, similar inflections of the account apply as well — for example, if the beneficial is what is productive of health, then 'beneficially' should mean 'in a way productive of health,' and 'has benefited' should mean 'has produced health.' One should also examine whether the stated definition will apply to the Form. For in some cases it does not — for example, as Plato defines things, attaching 'mortal' in his definitions of living creatures; for the Form will not be mortal, for example the Man-itself, so that the account will not apply to the Form. And in general, wherever 'productive' or 'affected by' is added, the definition must necessarily be at odds with the Form; for those who say there are Forms hold that Forms are unaffected and unchanging. Against such people arguments of this sort are also useful. Again, see whether, for things spoken of homonymously, he has rendered one account common to them all. For things are synonymous when there is one account corresponding to the name, so that the definition given applies to none of the things falling under the name, if indeed it applies equally to everything the homonymous term covers. This is what has happened to Dionysius's definition of life too, if it is 'a self-caused motion of a nourishing kind, sustained continuously'; for this belongs no more to animals than to plants, whereas life does not seem to be spoken of according to a single form, but is thought to belong to animals in one way and to plants in another.
38| It is indeed possible to render the definition deliberately in this way, as though 'life' were synonymous and spoken of according to a single form covering all of it; but nothing prevents someone who is aware of the homonymy, and who wishes to give the definition of one of the two things, from unwittingly rendering an account that is not proper to it but common to both. But no less, if he has done either of these, he has made a mistake. And since some cases of homonymy go unnoticed, when questioning one must treat them as synonymous (for the definition of one will not apply to the other, so it will seem that the definition has not been correctly given; for it must apply to everything synonymous), but when answering oneself, one must draw the distinction. And since some of those who answer say that what is synonymous is homonymous, whenever the account given does not apply to everything, and that what is homonymous is synonymous, if it applies to both, one must reach prior agreement about such cases, or argue in advance by syllogism that it is homonymous or synonymous, whichever it is; for people concede more readily when they do not foresee what will follow. And if, without any such agreement having been reached, someone says that what is synonymous is homonymous because the account given does not apply to this case too, one should examine whether the account of this case applies to the remaining ones as well; for clearly it would then be synonymous with the rest.
39| But if not, there will be more definitions than one of the remaining cases; for two accounts corresponding to the name will apply to them, the one given earlier and the one given later. Again, if someone, having defined something that is spoken of in several ways, finds that the account does not apply to all of them, and yet says it is not homonymous, while denying that the name applies to all the cases just as the account does not — one should say to such a person that one must use the name in its traditional and customary sense and not disturb such usage, though some things must not be said in the same way as the many say them.
40| If a definition has been given of one of two things joined together, one should look, by stripping away the account of one of the two joined items, at whether the remaining part of the account also fits the remaining item; for if it does not, it is clear that the whole does not fit the whole either. For example, if someone defined a finite straight line as "the boundary of a plane figure that has boundaries, whose middle screens the boundaries": if the account of "finite line" is "boundary of a plane figure that has boundaries," then the remainder, "whose middle screens the boundaries," ought to belong to "straight." But an infinite line has neither a middle nor boundaries, and yet it is straight; so the remainder does not fit the remainder. Again, when the thing being defined is composite, check whether the account given is matched clause for clause with it. An account is called matched clause for clause when, however many components make up the thing, that many nouns and verbs occur in the account. For in cases like this, some or all of the words are bound to be exchanged, since no more words are now used than before; and the definer must give his account in place of the words, all of them if possible, or if not, most of them. That is how, even in simple cases, someone who substitutes a word for a word would count as having given a definition — for example "cloak" instead of "garment." It is a still greater fault, moreover, if he has substituted less familiar words, for example "pale mortal" for "white man": the thing is no better defined that way, and it is spoken less clearly.
41| One should also check, in the exchange of words, whether the meaning has actually stayed the same — for example, someone who calls theoretical knowledge "theoretical supposition." For supposition is not the same as knowledge, yet it must be, if the whole is to remain the same; for "theoretical" is common to both accounts, while the remaining part differs. Again, check whether, in substituting one of the words, he has replaced not the differentia but the genus, as in the case just mentioned. For "theoretical" is less familiar than "knowledge": the one is the genus, the other the differentia, and the genus is always the more familiar of the two; so it was the differentia, not the genus, that should have been replaced, since it is the less familiar. Or perhaps this objection is silly: nothing prevents the differentia from being expressed in the more familiar word while the genus is not; and if that is how things stand, clearly it is the genus, not the differentia, that must be substituted for by name. But if he substitutes not a word for a word but an account for a word, clearly it is a definition of the differentia rather than of the genus that must be given, since a definition is given for the sake of making something known, and the differentia is less familiar than the genus.
42| If he has given the definition of the differentia, check whether the definition given also fits something else, for example when he says an odd number is "a number having a middle term": one must further specify what having a middle term means. For "number" belongs in common to both accounts, while the account of "odd" is the part substituted; but a line and a body also have a middle, without being odd. So this could not be a definition of "odd." And if "having a middle" is said in several ways, one must specify in what way it has a middle. The result will be either an objection or a proof by syllogism that it has not been defined.
43| Again, check whether the thing whose account he gives belongs among the things that are, while what falls under the account does not, for example if he defined white as "a color mixed with fire": for it is impossible for something bodiless to be mixed with a body, so that there could be no such thing as "a color mixed with fire" — yet white exists. Again, all those who, in dealing with relatives, fail to specify that in relation to which the thing is said, but instead speak of it as embracing several things, are lying either wholly or in part — for example, if someone said that the science of medicine is a science of what is. For if medicine is not a science of anything that is, clearly he is wholly mistaken, while if it is a science of some things but not of others, he is mistaken in part; for it must hold of every case, given that a thing is said to be what it is in its own right and not accidentally, just as with the other relatives — for everything knowable is spoken of in relation to knowledge. The same holds for the other relatives too, since all relatives are convertible. Again, if the person who makes his statement not in its own right but accidentally is giving it correctly, then each relative would be said in relation not to one thing but to several. For nothing prevents the same thing from being both a being and white and good, so that giving the account in relation to any one of these whatever would be giving it correctly, if indeed the person who gives it accidentally gives it correctly.
44| Again, it is impossible for such an account to be peculiar to the thing defined; for not only medicine but most of the other sciences too are spoken of in relation to what is, so that each science would be a science of what is. It is clear, then, that such an account is a definition of no science; for a definition must be peculiar, not common. Sometimes people define not the thing itself but the thing in its good or completed state. Such is the definition of the orator and of the thief, if indeed the orator is one able to see what is persuasive in each case and to leave nothing out, and the thief is one who takes secretly; for it is clear that, on this account, the one will be a good orator and the other a good thief — since it is not the one who takes secretly but the one who wishes to take secretly who is a thief. Again, check whether he has given what is choiceworthy for its own sake as choiceworthy for the sake of something else, as productive or practical, or in whatever way choiceworthy on account of something else — for example, calling justice "preservative of the laws," or wisdom "productive of happiness"; for being productive or preservative belongs among things choiceworthy on account of something else. Or perhaps nothing prevents what is choiceworthy for its own sake from also being choiceworthy on account of something else; nonetheless, whoever defines what is choiceworthy for its own sake in this way has erred none the less,
45| for in each thing the best element lies especially in its substance, and being choiceworthy for its own sake is better than being choiceworthy on account of something else, so that the definition ought rather to have signified this. One should also check, in giving the definition of something, whether he has defined it as these things, or as what comes from these things, or as this together with this. For if as these things, it will follow that it belongs to both and to neither — for example, if he defined justice as temperance and courage; for since these are two, if each person has one of them, both will be just and neither will be, since both together have justice while each separately does not. And if what has been said is not yet altogether absurd, because the same thing happens in other cases too (for nothing prevents both together having a mina while neither has it), still, at any rate, that contrary attributes should belong to them would seem altogether absurd. And this will follow if one of them has temperance and cowardice, and the other courage and self-indulgence; for both will then have justice and injustice. For if justice is temperance and courage, injustice will be cowardice and self-indulgence. And in general, all the lines of argument available for showing that the parts are not the same as the whole are useful for the point now made; for one who defines in this way seems to be saying that the parts are the same as the whole. Such accounts are most apt when the composition of the parts is evident, as with a house and other things of that kind.
46| For it is clear that, given the parts, nothing prevents the whole from not existing, so that the parts are not the same as the whole. But if he said that the thing defined is not these parts but what is made out of them, first one must consider whether it is not natural for a single thing to come to be out of the things named; for some things stand to one another in such a way that nothing comes to be out of them, for instance a line and a number. Again, if what is defined is naturally found in some single primary thing, while the things he said it is made of are not found in any single primary thing but each in a different thing, then clearly that thing could not be made out of these; for wherever the parts are, the whole must also be present, so that the whole is not in one primary thing but in several. But if both the parts and the whole are in some single primary thing, one must consider whether the whole is not in the same thing as the parts but in a different one. Again, one must ask whether the parts perish along with the whole; for the reverse ought to hold — when the parts perish, the whole perishes, but when the whole perishes, it is not necessary that the parts have also perished. Or whether the whole is good or bad while the parts are neither, or conversely the parts are good or bad while the whole is neither;
47| for it is not possible for something good or bad to come from two things neither of which is good or bad, nor for something neither good nor bad to come from things that are bad or good. Or whether one of the two is more good than the other is bad, while what is made out of them is not more good than bad — for instance, if shamelessness is said to be made out of courage and false belief. For courage is more good than false belief is bad; so what is made out of them ought to follow the greater, and be either good without qualification, or more good than bad. Or this is not necessary, unless each of the two is good or bad in its own right; for many productive things are not good in their own right but become so when mixed, or conversely each is good by itself but becomes bad, or neither, when mixed. What has just been said is most evident in the case of healthy and disease-causing things; for some drugs are such that each by itself is good, but if both are given mixed together, the result is bad. Again, one must ask whether, being made out of a better and a worse thing, the whole is not worse than the better and better than the worse. Or this too is not necessary, unless the things it is composed of are good in their own right; nothing prevents the whole from failing to be good, just as in the cases just mentioned.
48| Again, one must ask whether the whole is synonymous with either of the two; for it should not be, just as in the case of syllables — for the whole syllable is synonymous with none of the letters it is composed of. Again, one must ask whether he has stated the manner of the combination. For it is not sufficient for making the thing known to say it is made out of these; for the substance of each compound thing is not simply being made out of these, but being made out of these in this particular way — as with a house, for it is not a house however these materials happen to be put together. But if he has rendered it as 'this together with that,' first it must be said that 'this together with that' is the same either as 'these' or as 'what is made out of these'; for one who says 'honey with water' means either honey and water, or what is made out of honey and water, so that whichever of the stated alternatives he agrees 'this together with that' is the same as, the same objections will fit that were raised earlier against each of the two. Again, having distinguished the ways in which one thing is said to be 'with' another, one must consider whether 'this together with that' holds in none of them. For instance, if one thing is said to be with another either as being in some one and the same receptacle, as justice and courage are in the soul, or as being in the same place at the same time — and the statement in question turns out to be true in neither of these ways — clearly the definition given would apply to nothing, since 'this together with that' does not hold in any way.
49| But if it is true, on the division made, that each of the two is present at the same time, one must consider whether it is possible that the two are not said in relation to the same thing. For instance, if he defined courage as boldness together with correct thinking; for it is possible to have boldness for the purpose of committing theft, and correct thinking about matters of health — but a person who has, at the same time, this together with that in this sense is not yet courageous. Again, one must consider whether even if both are said in relation to the same thing, for instance to matters of medicine — for nothing prevents someone from having both boldness and correct thinking with respect to medical matters — even so this person, who has this together with that, is not courageous either. For neither should each of the two be said in relation to something different from the other, nor in relation to any random thing that happens to be the same for both, but in relation to the end proper to courage, for instance in relation to the dangers of war, or whatever end is more properly its own than this. Some definitions rendered in this fashion do not fall under the stated division at all — for instance, if anger is defined as pain accompanied by a supposition of being slighted. For what this wants to show is that the pain comes about because of this sort of supposition; and for something to come about because of this is not, in any of the ways stated, the same as for this to exist together with that.
50| Again, one must ask whether he has called the whole a combination of these, for instance calling an animal a combination of soul and body; first one must consider whether he has failed to state what kind of combination it is — just as if, in defining flesh or bone, one said it was a combination of fire, earth, and air. For it is not enough to say 'combination'; one must also further specify of what kind — for it is not by these being combined in just any way that flesh comes to be, but by their being combined in this particular way flesh results, and in that particular way bone results. And it seems that neither of the things named is, in general, the same as combination at all; for to every combination dissolution is contrary, but to neither of the things named is anything contrary. Again, one must consider whether it is equally plausible that every composite thing is a combination, or that none is; and since each animal, though composite, is not a combination, none of the other composite things would be a combination either. Again, one must ask whether contrary things are equally natural to be present in something, yet the thing has been defined by way of one of the two only — clearly in that case it has not been defined. For otherwise, several definitions of the same thing will result; for why should the person who defined by way of this one have spoken more truly than the one who defined by way of the other, given that both are equally natural to come about in it? Such is the definition of the soul, if it is said to be a substance receptive of knowledge;
51| for it is equally receptive of ignorance. And even if one's argument is not addressed to the whole of the definition, because the whole is not well known, one must still try to attack some part of it, if that part is well known and appears to have been badly rendered; for once the part is destroyed, the whole definition is destroyed along with it. As for definitions that are unclear, having first jointly corrected and reshaped them so as to make something clear and to have a point of attack, one should examine them in that form; for the answerer must either accept the sense grasped by the questioner, or himself make clear what exactly is meant by the formula. Again, just as in assemblies people are accustomed to bring in a new law, and if the one brought in is better they repeal the earlier one, so too one must do with definitions and bring forward a different definition oneself; for if it appears better and makes what is being defined clearer, clearly the one already laid down will have been overturned, since there cannot be several definitions of the same thing. And for dealing with all definitions, not the least important element is defining the subject at issue skillfully for oneself, or adopting a well-stated definition already given; for then, as if looking at a model, one is bound to see clearly both what is lacking that the definition ought to have, and what is superfluously added, so that one is better supplied with points of attack.