by Aristotle
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 usefu
l 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.