Topics (Aristotle)/Book 6
There are live parts of the discussion of definition, for (the latter is reprehended), because it is not altogether true to assert that the sentence (is predicated) of what the name is; (since it is necessary that the definition of man, should be verified of every man;) or because when there is a genus, it does not place the thing defined in the genus, or not in its appropriate genus; (for it is necessary that the person defining, placing the thing defined in genus, should add the differences, since of things in the definition, genus especially seems to signify the substance of the thing defined;) or because the sentence is not proper; (since it is necessary that definition should be proper, as was before observed;) or if, though it has effected all the things stated, it does not define, nor state, what the nature is, of the thing defined. The remainder is, besides what we have mentioned, if it is defined indeed, but not defined well.
Whether, then, the sentence also is not verified of what the name is, must be observed from places belonging to accident, since there also the whole consideration is, whether it is true or not true, for when we show by discussion that accident is inherent, we say that it is true, but when that it is not inherent, (we call it) untrue. Whether, again, the assigned definition is not placed in its proper genus, or is not proper, must be observed from places spoken about genus and property.
It remains, then, to declare how we must institute an inquiry, whether a thing is not defined, or whether it is not rightly defined; first, indeed, then we must see whether it is not rightly defined, since it is easier to do any thing (merely), than to do it well. Now it is clear that an error is more frequent about this, because it is more difficult, so that reasoning about this is easier than about that.
Of the (question of defining) not rightly, there are two parts, one whether obscurity is employed in the interpretation, (since it is necessary that the person defining should make use of the clearest possible interpretation, as definition is assigned, for the sake of knowledge,) and the other, whether he has stated the definition more extensively than is requisite, as every thing added in the definition is superfluous. Again, each of the above-named is divided into many parts.
One place, then, belonging to the obscure is, if what is stated is equivocal with any thing, as that generation is a leading to substance, and that health is the harmony of hot and cold, for (the words) leading and harmony are equivocal, therefore it is doubtful which of the things signified, by what is multifariously predicated, a person wishes to assert. In like manner also, if when the thing defined is multifariously predicated, a person expresses himself without distinction, as it will be dubious of what he has given the definition, and it is possible to cavil, as if the definition were not adapted to every thing of which he has given the definition. Now, such a thing it is especially possible to do, when there is latent equivocation, and also it is possible, when a person has distinguished in how many ways what is assigned in the definition is predicated, to form a syllogism: for if it is not sufficiently stated in any mode, it is clear that it has not been defined according to that mode.
Another (place is), if it is spoken metaphorically, for instance, that science is that which cannot fall, or that the earth is a nurse, or that temperance is symphony, as everything enunciated metaphorically is obscure. It is also possible for him who uses a metaphor to cavil that he has spoken rightly, for the given definition will not suit, e. g. in the case of temperance, since all symphony is in sounds. Besides, if symphony be the genus of temperance, the same thing will be in two genera not containing each other, since neither does symphony contain virtue, nor virtue symphony.
Moreover, (the definition is obscure,) if established names are not used, as Plato calls the eye, that which is shaded by the eyebrows, or a spider, a feeder on putrescence, or the marrow, bone-begetter, since whatever is unusual, is obscure.
Some things, however, are asserted neither equivocally, nor metaphorically, nor properly, for instance, law (defined as) a measure, or an image of things naturally just. Such things, indeed, are worse than metaphor, for metaphor in some way makes known what is signified on account of similitude, as all who use metaphors do so according to a certain similitude, but this kind of thing does not make known, as neither is there any similitude, according to which law is a measure or an image, nor is it accustomed to be predicated properly. Wherefore, if a person says that law is properly a measure or an image, he speaks falsely, for an image is that, the generation of which is by imitation, but this does not exist in law: but if it is improperly, it is clear that he speaks obscurely, and worse than any thing spoken metaphorically.
Again, (it is reprehended,) if from what is stated, the definition of the contrary is not evident, since they who well define, signify also the contraries besides: or if it is not of itself evident of what the definition is spoken; but such cases, like ancient pictures, cannot be known, what each is, without a superscription.
If then definition be obscure, we must examine from such places as these, but if it has been stated excessively, we must first see whether any thing is employed which is present with all things, or simply with beings or with those which are under the same genus with the thing defined; since it must inevitably happen that this will be asserted in excess. For it is requisite to separate genus from other things, but difference from something of those in the same genus, wherefore what is present with all things is simply separated from nothing, but what is present with all under the same genus is not separated from those in the same genus, so that an addition of this kind is vain.
Or (we must observe), whether what is added be proper, but this being taken away the rcmaining definition is proper, and demonstrates substance, e. g. in the definition of man, receptive of science is superfluously added, since this being taken away, the remaining definition is appropriate, and manifests the substance. In a word, every thing is superfluous, which when taken away the remainder causes the thing defined to be manifest, such indeed is the definition of the soul, if it be number moving itself, for that which itself moves itself is soul, as Plato has defined it. Or is what has been mentioned property indeed, yet does not manifest essence when number is taken away? In what way then the thing is, is hard to explain, but we must use (this place) in all such things as may be expedient. For instance, that the definition of phlegm is, the first unconcocted moisture from food, for there is one first, not many, so that the addition of unconcocted is superfluous, since when this is taken away, what remains will be the proper definition, since it is impossible that this and something else, should be the first (moisture) arising from food. Or shall we say that phlegm is not simply the first thing from food, but the first of things unconcocted, so that unconcocted must be added, for if it is stated in that way the definition will not be true, since it is not the first of all things.
Moreover, (we must examine) whether some one of the things in the definition, is not present with all those under the same species, since such is defined worse than they do, who use that which is present with all substances. For in that way the remainder would be the proper definition, and the whole would be proper; since, in short, if any thing true is added to property, the whole (definition) becomes proper. If however something of those in the definition is not present with all those under the same species, it is impossible that the whole definition should be proper, since it will not be reciprocally predicated of the thing, e. g. an animal pedestrian biped of four cubits, for such a definition is not reciprocally predicated of the thing, from four cubits not being present with all those, which are under the same species.
Again, whether the same thing is frequently stated, as he who says, that desire is the appetite of the pleasant, for all desire is of the pleasant; wherefore what is the same with desire will also be of the pleasant, the definition then of desire is the appetite of the pleasant, for there is no difference between saying desire or the appetite of the pleasant, so that each of these will belong to the pleasant. Or is it that this is not at all absurd? for man also is a biped, so that what is the same with man will also be biped, but an animal pedestrian biped is the same as man, so that animal pedestrian biped is biped. Nevertheless, no absurdity happens on this account, for biped is not predicated of pedestrian animal, (for thus indeed biped would be twice predicated of the same thing,) but biped is predicated about animal pedestrian biped, wherefore biped is predicated once only. In the same manner, in the case of desire, for to be of the pleasant is not predicated of appetite, but of the whole (sentence), so that here also the predication is once. Still, that the same name should be twice pronounced does not belong to absurdity, but frequently to predicate the same about a certain thing, as when Xenocrates says that prudence is definitive and contemplative of beings, for the definitive is something contemplative, so that he twice says the same thing, again adding contemplative. They also do the same, who say that refrigeration is a privation of natural heat, for all privation is of what exists naturally, so that to add naturally, is superfluous, but it would have been sufficient to say privation of heat, since privation itself makes it known that it is spoken of what is naturally.
Again, whether what is universally asserted adds also something particular, as if (we defined) equity the diminution of things profitable and just, for the just is something profitable, wherefore it is contained in the profitable, so that just is superfluous, and speaking of the universal, the partial is added. Also, if (some one should define) medicine to be the science of things healthful for animal and man, or law to be the image of things naturally beautiful and just, for the just is something beautiful, so that he would say the same thing frequently.
Whether therefore (a thing be defined) well or ill, must be examined through these and similar (places), but whether (a person) has asserted and defined what a thing is or not, from the following.
First, if he has not made the definition through things prior and more known. For since definition is assigned for the sake of knowing what is said, but we know not from things casual, but from what are prior and more known, as in demonstrations, (for thus all doctrine and discipline subsists,) it is clear that he who does not define through such things as these, does not define (rightly). But if not, there will be many definitions of the same thing, since it is evident that whoever defines through things prior and more known, defines in a better manner, so that both definitions would be of the same thing; this however does not seem so, as to each being, to be what it is, is one thing, so that if there should be many definitions of the same thing, there will be the same essence of the thing defined, as is manifested by each of the definitions. These (essences) however are not the same, since the definitions are different, wherefore he has evidently not defined, who does not define through things prior and more known.
To assume then that a definition is not framed through things more known, is possible in two ways, either if (it is) simply from things more unknown, or from those which are more unknown to us, for in both ways it is possible. Simply then the prior is more known than the posterior, as a point than a line, and a line than a superficies, and a superficies than a solid, as also unity than number, for it is prior to, and the principle of, all number; likewise a letter than a syllable. Nevertheless, to us, the reverse sometimes happens, since a solid falls under sense rather than a superficies, but a superficies more than a line, and a line more than a point, for the multitude know these things in a greater degree, since some things it is possible for any casual intellect to discern, but others belong to an intellect accurate and transcendent.
Simply then, it is better to aim at the knowledge of things posterior through such as are prior, for a thing of this kind is more scientific; still by those who are incapable of knowing through things of this kind, it is perhaps necessary to frame the definition through things known to them. Now of such definitions, are those of a point, and of a line, and of a superficies, for all manifest things prior, through such as are posterior, for they say that one is the boundary of a line, the other of a superficies, and the other of a solid. Still we must not be unmindful that those who define thus, cannot denote what the nature is of the thing defined, unless the same thing should happen both to be more known to us, and simply to be more known, since he who well defines must necessarily do so, through the genus and the differences, but these are of the number of things more known simply than, and prior to, species. For genus and difference co-subvert species, so that these are prior to species. They are also more known, for if species is known, it is necessary that genus also and difference should be known, (as he who knows man, knows both animal and pedestrian,) but when genus or difference is known, it is not necessary that species also should be known, wherefore species is more unknown. Besides, to those who really call things of this kind, definitions, which consist of what are known to every one, it will happen to say that there are many definitions of the same thing, since some things are more known to some persons, and not the same to all, so that there would be a different definition to be given to each person, if it were necessary that definition should he framed from things more known to each severally. Further, to the same persons at a certain time, certain things are more known, at first indeed sensibles, but the reverse when they become more accurate, so that neither would the same definition have to be given to the same person, by those who say that a definition must be given through things more known to each. Clearly, then, we must not define through such things, but through those that are simply more known, since thus only would one and the same definition be always produced. Perhaps indeed what is simply known is not that which is known to all, but that (which is known) to those who have their intellect well disposed, just as what is simply wholesome is that which is so, to those whose bodies are in a good state. Hence it is necessary accurately to explain each of these, and to use them in discussion as may be expedient, but most confessedly is it possible to subvert definition, if it be neither framed from things simply more known, nor from those (which are so) to us.
One mode then (of proving) that it is not through things more known, is when the prior is manifested through the posterior, as we observed before; another, if the definition of what is at rest and definite, is a sign to us through the indefinite and through what is in motion, since the permanent and definite are prior to the indefinite, and to what is in motion.
The modes indeed (of showing a definition to be) not from things prior, are three, first, if the opposite is defined through the opposite, as good through evil, for opposites are naturally simultaneous. Still to some there seems to be the same science of both, so that the one is not more known than the other; nevertheless, we must bear in mind that some things perhaps it is impossible to define otherwise, as the double without the half, and whatever things are enunciated relatively per se, for in all these there is the same essence from their having relation in a certain spect, so that it is impossible to know the one without the other, wherefore in the definition of the one, the other must of necessity be comprehended. All such things, then, it is necessary to know, and to employ them as may appear useful.
Another (place) is, if in the definition the thing defined is used, but this is latent when a person does not employ the very name of the thing defined, as if he should define the sun to be a star apparent by day, for using day, he uses sun. In order to detect such, we must take the definition instead of the name, as the day is the motion of the sun above the earth; for it is clear that he who speaks of the motion of the sun above the earth, mentions the sun, so that he who uses day, uses sun.
Again, if what is in an opposite division is defined by what is in an opposite one, as the odd to be what is greater than the even, by unity: for things oppositely divided from the same genus are naturally simultaneous, but the odd and even, are divided oppositely, since both are differences of number.
Similarly also if the superior is defined through the inferior, as that the even number is what may be divided into two parts, or that good is the habit of virtue; for the expression, "into two parts," is assumed from two, which is an even number; virtue also is a certain good, so that these are under those. Besides, it is necessary that whoever uses the inferior should use also (the thing defined) itself; for both he who uses virtue uses good, since virtue is a certain good, and likewise also he who uses "in two parts" uses the even, because a division into two parts, signifies to be divided into two, but two is an even number.
Universally then, one place is, that a definition is not framed through things prior and more known, but the particulars of it are such as have been mentioned. The second place is, if when a thing is in genus it is not placed in genus, but in all such, an error occurs in the definition of which, what a thing is, is not previously declared; for instance, the finition of body as having three dimensions, or if any one should define man to be that which is cognizant of number. For it has not been stated what that is which has three dimensions, or what it is which is cognizant of number; but genus would signify what a thing is, and is the first thing supposed, of those predicated in the definition.
Besides, if when the thing defined belongs to many things, it is not adapted to all, as it some one should define grammar to be the science of writing what is dictated; for (the words) and of reading also, are wanting, since he has no more defined grammar, who defines it to be the art of writing, than he who states it to be the art of reading, so that neither defines, but he who states both of these, since there cannot be many definitions of the same thing. In some instances then, the case is really as we have stated, but in others it is not, as in those which do not essentially belong to both; thus, medicine (is the science) of producing disease and health, for of the one it is said (to be the science) essentially, but of the other accidentally, as to produce disease is simply foreign from medicine. Wherefore he does not more define, who refers to both, than he does who refers to one, of these, but perhaps even in a worse manner, since any other person is able to produce disease.
Besides, (he errs,) who does not refer to the better, but to the worse, when there are many things, to which that defined, belongs, since every science and faculty seems to belong to what is best.
Again, whether what is asserted is not placed in its proper genus, must be observed from the elements belonging to genera, as we stated before.
Moreover, if stepping over, he speaks of genera, as he who (defines) justice to be a habit productive of equality, or distributive of the equal, for when he thus defines, he passes over virtue. Omitting then the genus of justice, he does not state what its nature is, for the essence of every thing is connected with the genus. This however is the same thing with not placing it in the nearest genus, for he who places it in the nearest, has mentioned all the superior, since all the superior genera are predicated of the inferior. Hence, it must either be placed in the nearest genus, or he must add all the differences, through which the nearest genus is defined, to the superior genus; for thus he will have omitted nothing, but instead of a name, will have mentioned the inferior genus, in the definition. Whoever, on the other hand, speaks of the superior genus alone, does not mention also the inferior genus, for the one who calls a thing a plant, does not state it to be a tree.
Again, we must in like manner consider with regard to differences, whether those of genus are introduced, for unless a person defines by the proper differences of a thing, or altogether asserts what can be the differences of nothing, as animal or substance, he evidently does not define, since the things stated are not the differences of any thing. Observe also, whether any thing is divided oppositely to the difference stated, for if there is not, what is stated will evidently not be the difference of genus, since every genus is divided by differences oppositely divided, as animal by the pedestrian and winged, by the aquatic and biped. Or if indeed there is an oppositely divided difference, which however is not verified of the genus, since evidently neither would be the difference of genus, as all oppositely divided differences are verified of their proper genus. Likewise, if it is indeed verified, but (the difference) when added to genus does not produce species, since it is evident that this would not be the specific difference of genus, as every specific difference united with genus produces species; but if this be not the difference, neither will that which was mentioned, since it is divided oppositely to this.
Moreover (he errs), if he divides genus by negation, as those who define a line to be length without breadth, since this signifies nothing else than that it has no breadth; the genus then will happen to partake of the species, for every length is either with, or without breadth, since of every thing either affirmation or negation is verified, so that the genus of a line which is length, will either be without breadth, or will have breadth. But length without breadth is the definition of the species; likewise, length with breadth, for without breadth and with breadth are differences; but the definition of species is from the difference and the genus; so that genus would receive the definition of species; in like manner also, the definition of difference, since one of the above-named differences is necessarily predicated of genus. The place mentioned however is useful against those who assert that there are ideas, for if there is length itself, how will it be predicated of the genus that it has breadth or has it not, for it is necessary that one of these should be verified of every length, if it is to be verified of the genus. This however does not occur, since there are lengths without breadth, and those which have breadth, so that this place is useful against those only, who say that genus is one in number, and this they do who admit ideas, for they say that length itself and animal itself are genera.
Perhaps, indeed, in some cases it is necessary for a person when defining, to use negation, as in privations, for that thing is blind which has not sight when it is naturally adapted to have it. Still it makes no difference whether we divide genus by negation, or by such an affirmation, as to which it is necessary that negation should be oppositely divided; for instance, if length were defined to be that which has breadth, for to what has breadth that which has not breadth, is oppositely divided, but nothing else, so that the genus is again divided by negation.
Again (observe), whether species is assigned as difference, as they do who define contumely to be insolence with derision, for derision is a certain insolence, so that derision is not difference, but species.
Moreover, whether genus is assigned as difference as that virtue is a good or worthy habit, for good is the genus of virtue; or is good not a genus, but a difference, since it is true that the same thing cannot possibly be in two genera which do not comprehend each other? For neither does good contain habit, nor habit good, since not every habit is good, nor every thing good, a habit; hence they would not both be genera. If, then, habit be the genus of virtue, it is evident that good is not the genus, but rather the difference; besides, habit signifies what the virtue is, but good does not signify what, but what kind of thing it is; indeed difference, seems to signify quality.
Observe, also, whether the assigned difference does not signify quality, but this particular thing; since every difference appears to signify a certain quality.
Consider, also, whether difference is accidentally present with the thing defined, for no difference is of the number of things accidentally present, as neither is genus, since it is not possible that difference should be present with a certain thing, and not be present.
Moreover, if difference or species be predicated of genus, or something which is the subject of species, there will not be a definition, for nothing of what we have mentioned can possibly be predicated of genus, since genus is the most extensively spoken of all. Again, if the genus is predicated of the difference, for genus seems to be predicated not of difference, but of those of which difference (is predicated); thus, animal of man, and ox, and other pedestrian animals, and not of difference itself, which is spoken of species. For if animal were predicated of each of the differences, many animals would be predicated of the species, for differences are predicated of species. Again, all differences will either be species or individuals if they are animals, since each animal is either species or individual.
Likewise, we must observe, whether species or some one of those under species, is predicated of difference, for this is impossible, since difference is more widely predicated than species; further, difference will happen to be species, if a certain species is predicated of it, for if man is predicated (of difference), man is evidently a difference. Again, (see) whether difference be not prior to species, since difference must necessarily be posterior to genus, but prior to species.
Observe, too, whether the assigned difference is of another genus, neither contained by, nor containing it, as the same difference does not appear to be of two genera not comprehending each other. Otherwise, the same species would happen to be in two genera not comprehending each other, since each difference introduces its own appropriate genus, as pedestrian and biped co-introduce animal; wherefore, if each of the genera be predicated of what the difference is, it is evident that the species is in two genera not comprehending each other. Or is it not impossible that there should be the same difference of two genera not comprehending each other, but it must be added, neither are both under the same? For pedestrian animal, and winged animal, are genera not comprehending each other, and biped is a difference of both these, wherefore, it must be added, that neither are both under the same, for both of these are under animal. It is evident, also, that difference need not always introduce its appropriate genus, since there may be possibly the same (difference) of two genera not comprehending each other, but it is necessary that it should co-introduce one alone, and those which are above it, as biped, winged, pedestrian, co-introduce animal.
Observe, also, whether to be in a certain thing is assigned as the difference of substance, for substance does not seem to differ from substance in being some where, wherefore also, those are to be blamed, who divide animal by pedestrian and aquatic, as if pedestrian and aquatic signified being some where. Or are they not rightly blamed in these things? for the aquatic does not signify the being in something or some where, but a certain quality, since it would be similarly aquatic, if it should even be in a dry place; likewise, also, the terrestrial, even in a moist place, will be terrestrial and not aquatic; at the same time, if ever difference signifies the being in a certain thing, it is evident that (he who defines) will err.
Again, (notice) whether passion is assigned as difference; for every passion, when increased, alters the essence, but difference is not a thing of this kind, but difference appears rather to preserve that of which it is the difference, and it is simply impossible for any thing to be without its proper difference, since pedestrian not existing, there will not be man. In a word, nothing of those, according to which the thing possessing it, is changed in quality, is the difference of it, for all such, when increased, alter the essence, so that if any one assigns a certain difference of this kind, he errs, as, in short, we are not changed in quality, according to differences.
He also (mistakes), who assigns the difference of a certain relative, not with reference to something else; for of relatives, the difference is also a relative, as in the case of science, for it is said to be contemplative, practical, and effective; but each of these signifies relation, since it is contemplative of something, and effective, and practical of something.
Examine, also, whether he who defines, assigns that to which each relative is naturally adapted, for some things can only be employed for that to which each relative is naturally adapted, but for nothing else, some, on the other hand, for something else also; thus, the sight is (employed) for seeing only, but some one may draw up a weight, even with a strigil; notwithstanding, whoever should define a strigil an instrument for drawing would err, for it is not naturally adapted to this; the definition however of what a thing is naturally adapted to, is that for which a prudent man, so far as he is prudent, would use it, also the science which properly belongs to each.
Further, (examine) whether or not, the (definition) is assigned of what is first, when it happens to belong to many things, e.g. that prudence is the virtue of man, or of the soul, and not of the reasoning part, for prudence is the virtue of the reasoning part primarily, since according to this, both the soul and man are said to be prudent.
Again, he errs, unless that is receptive of which the thing defined is stated to be the passion, or disposition, or something else; for every disposition and every passion is naturally generated in that of which it is the disposition or passion, as science in the soul, being a disposition of the soul. Sometimes indeed men mistake in these things, as they do who say that sleep is the impotency of sense, and that doubt is the equality of contrary arguments, and that pain is a separation accompanied with violence, of connascent parts; for neither is sleep present with sense, which it ought to be if it is the impotency of sense, likewise neither is doubt present with contrary arguments, nor pain with eonnascent parts, for things inanimate would suffer pain, since pain would be present with them. Such also is the definition of health if it is the harmony of hot and cold, for it is necessary that things hot and cold should be in health, since the harmony of each, is in those of which it is the harmony, so that health would be in them; besides, by those who thus define, it happens that the thing made is reduced to the maker, or contrariwise, for neither is the separation of connascent parts, pain, but is productive of pain, nor is the impotency of sense, sleep, but one is effective of the other, for either we sleep in consequence of becoming powerless, or we become powerless in consequence of sleep. Likewise, also, the equality of contrary arguments would appear productive of doubt, for when in reasoning on both sides of a question, every thing appears to us to have equal weight on either side, then we doubt which we shall adopt.
Moreover, we must consider according to all times, whether there is any discrepancy, e. g. if one defined the immortal, to be what is now an incorruptible animal, for the animal now incorruptible will be now immortal. Or does this not happen in this case, for to be now incorruptible is ambiguous, for it either signifies that it is not now corrupted, or that it cannot now be corrupted, or that it is now a thing of that kind which can never be corrupted. When therefore we say that the animal is now incorruptible, we say this, that it is now such an animal, as never to be corrupted, and this would be the same with immortal, so that it does not happen that it is now immortal. Nevertheless, if it should happen that what is assigned according to the definition is now, or was before, inherent, but what is according to the name is not inherent, it will not be the same: wherefore this place must be used as we have stated.
It must also be considered whether the thing defined is enunciated by some others, rather than by that definition which was assigned, as if justice (should be defined) a power distributive of the equal. For he is rather a just man who deliberately chooses to distribute the equal, than he who is able, so that justice would not be a power distributive of the equal, since he would be especially just, who is most able to distribute the equal.
Moreover, whether the thing receives increase, but what is assigned according to the definition does not receive it, or on the contrary, what is assigned according to the definition receives, but the thing, not. For it is necessary that both should receive it or neither, if indeed what is assigned according to the definition is the same with the thing. Again, whether both indeed receive increase, yet both do not simultaneously receive accession, as if love is the desire of congress; for he who loves in a greater degree is not more desirous of congress, so that both do not simultaneously receive increase, which they should if they were the same.
Again, (examine) whether when two things are proposed, of what the thing (defined) is more predicated, that which is according to definition is less predicated, as if fire is the most subtle body; for flame is more fire than light, yet flame is less the most subtle body than light; it would be necessary however that both should in a greater degree be present with the same thing, if they were the same. Again, (notice) whether the one is similarly present with both things proposed, but the other not similarly with both, but in a greater degree with one of them.
Besides, whether a person accommodates the definition to two things, according to each, as if the beautiful (should be defined) what is pleasant through sight or through hearing, and being, that which is able to suffer or to act; for the same thing at one and the same time will be beautiful and not beautiful; likewise also will be being and not being. For what is pleasant through hearing will be the same with the beautiful, so that what is not pleasant through hearing will be the same with what is not beautiful, since opposites to the same are the same; but what is not beautiful is opposed to what is beautiful, and what is not pleasant through hearing to what is pleasant through hearing. It is clear then, that what is not pleasant through hearing is the same with what is not beautiful; if then any thing is pleasant through the sight, but not through the hearing, it will both be beautiful and not beautiful, and similarly we may show that the same thing is both being and non-being.
Again, when framing definitions of genera and differences, and of all other things assigned in definitions instead of names, consider whether there is any discrepancy.
If indeed what is defined should either be per se, or generically, a relative, consider whether that to which it is referred, either per se, or generically, has not been mentioned in the definition, as if some one had defined science to be immutable opinion, or the will, appetite unattended with pain. For the essence of every relative consists in a relation to something else, since the being of every thing which subsists with reference to another thing, is the same with that of being in a certain respect referred to something; wherefore it is necessary to say that science, is the opinion of the object of science, and the will, the appetency of good. Likewise, also, if a person defined grammar to be the science of letters, since it will be necessary in the definition to assign that to which the thing defined, or to which the genus, is referred. Also (consider), whether the definition of a certain thing referred to something, is not assigned with reference to the end; now the end in each thing is that which is best, or on account of which other things subsist, wherefore, either what is best, or what is last, must be stated; e. g. that desire is not of the pleasant, but of pleasure, for we even choose the pleasant for the sake of this.
Examine, moreover, whether that to which a thing is referred, be generation or energy, since nothing of this kind is an end; for to have energized, or to have been generated, are rather the end, than to generate or to energize, or is it not that such a thing as this is true in all, for almost all men rather desire to be delighted than to cease being delighted, so that they rather make the end to energize than to have energized?
In some cases again, (we must notice) whether there is not a definition of the quantity or quality, or the where, or according to the other differences; for instance, what the quality or quantity is of the honour, which the ambitious man desires; for all desire honour, so that it is not sufficient to say that he is ambitious who desires honour, but we must add the above-mentioned differences. Likewise, also, the quantity of riches which the avaricious man desires (must be mentioned), or what quality of pleasure the incontinent man seeks after, for he is not said to be incontinent who is vanquished by any pleasure whatever, but he who is so, by a certain one. Or again, as men define night, the shadow of the earth, or an earthquake, the motion of the earth, or a cloud, the condensation of the air, or wind, the motion of the air, for the quantity, quality, the where, and by what, must be added. In like manner, as to other such things, since he who omits any difference whatever, does not state what is the very nature of the thing; indeed we must always argue against what is wanting, for neither will an earthquake be the motion of earth in any manner, nor in any quantity, as neither will wind be the motion of air in any manner, nor in any quantity.
Moreover, in (defining) appetites, (there will be an error), if what appears is not added, and in as many other things as this is adapted to; for instance, that the will is the appetency of good, but desire the appetency of the pleasant, yet not of what appears good or pleasant. For oftentimes it escapes those who aspire after a thing that it is good or pleasant, so that it is not necessary that it should be good or pleasant, but only that it should appear to be so, wherefore it is necessary that the explanation should be made in this manner. If, on the other hand, what has been mentioned should be assigned, whoever asserts that there are ideas, must be led to ideas, since idea is not of any thing apparent, but form seems to be referred to form, thus desire itself is of the pleasant itself, and the will itself of the good itself. Now it will not be of the apparent good, nor of the apparent pleasant, since that a thing should be self-apparent good or pleasant is absurd.
Moreover, if there be the definition of a habit, take notice of what possesses it, but if the definition be of what possesses, consider the habit, and in like manner with regard to other things of this kind; e. g. if the pleasant is what is beneficial, he also who is pleased is benefited. In a word, it happens after a certain manner in such definitions, that the definer defines more things than one, since he who defines science, after a certain way defines ignorance also, likewise the scientific and the unscientific, also to know and to be ignorant, for the first being evident, the rest also in some way become evident. We must examine then, in all such cases, lest any thing should be discordant, employing the elements which are from contraries, and conjugates.
Examine too, in relatives, whether to what genus is referred, to that a certain species is referred, for instance, if apprehension to the object of apprehension, a certain apprehension also (is referred) to a certain object of apprehension, and if the multiple is to the sub-multiple, whether a certain multiple is to a certain sub-multiple, since if there is not such reference, there has been evidently an error.
Again, observe whether there is an opposite definition of the opposite, as whether the definition of the half is opposite to that of the double, since if the double be that which surpasses in the equal, the half will be what is surpassed in the equal. Likewise, also, in the case of contraries, for the definition of the contrary will be contrary according to one certain connexion of contraries, thus, if that is beneficial which is productive of good, what is productive of evil or is corruptive of good is injurious, since one of these must necessarily be contrary to that mentioned at first. If then neither be contrary to that mentioned at first, it is clear that neither of the definitions afterwards given, can be the definition of the contrary, so that neither has the definition given at first been rightly given. Nevertheless, since some contraries are said to be so, from the privation of another, as inequality seems the privation of equality, (for things are called unequal which are not equal,) it is clear that what is stated to be contrary as to privation, is necessarily defined through the other, but that it is no longer (necessary) that what remains (should be defined) through what is predicated as to privation, for each would happen to become known through each. We must pay attention, therefore, to such an error as this in contraries, as if some one should define equality to be the contrary to inequality, since it is defined through what is predicated according to privation. Further it is necessary that he who thus defines should use the thing defined, which indeed will be evident if the definition be assumed instead of the name, for there is no difference between saying inequality or the privation of equality, wherefore, equality will be the contrary to the privation of equality, so that the thing itself (defined) will be employed. Still if neither contrary should be predicated according to privation, but the definition similarly assigned, as that good is what is contrary to evil, it is evident that evil will be what is contrary to good, since of things thus contrary, the definition must be similarly assigned. Wherefore, again, the thing defined happens to be employed, as good is inherent in the definition of evil, so that if good is what is contrary to evil, but there is no difference between evil and the contrary to good, good will be that which is contrary to the contrary of good, so that the person has evidently used the thing itself.
Further, (remark) whether he who assigns what is predicated according to privation, has not assigned that of which it is the privation; for instance of habit, or of contrary, or of whatever it is the privation; or whether he has not added that in which it is naturally adapted to be generated, either simply, or in which first, it is adapted to be generated. Thus if stating ignorance to be privation, a person has not said that it is a privation of science, or has not added in what it is naturally adapted to be produced, or having added it, has not assigned in what first, as that it is not in the reasoning faculty, but in man or soul, for if he has not done some one of these, he commits an error. So also if he should not have said that blindness is privation of sight in the eye, for it is requisite that he who well assigns what (privation) is, should also assign of what it is the privation, and again, what that is, which is deprived.
Observe, also, whether a person has defined by privation, that which is not predicated according to privation, which fault they will appear to commit in the definition of ignorance, who do not speak of ignorance according to negation. For that which has not science does not seem to be ignorant, but rather that which is deceived, hence we neither say, that inanimate things nor children are ignorant, so that ignorance is not predicated according to the privation of science.
Again, (examine) whether similar cases of the definition agree with similar cases of the noun, for instance, if the beneficial is what produces health, whether beneficially be productively, and that was beneficial, which was productive of health.
Besides observe, whether the definition stated accords to the idea, since in some things this does not happen, as when Plato in his definition of animals, adds "mortals," for idea will not be mortal; for instance, man-self, wherefore the definition will not suit the idea. In short, it is necessary that the definition of those things to which the effective or the passive is added, should be discrepant with the idea, since ideas appear to those who say that there are ideas, to be impassive and immoveable, and against these such arguments are useful.
Yet further, in things predicated equivocally, (observe) whether a person has assigned one common definition of them all. For those are synonymous, of which there is one definition according to the name, wherefore the assigned definition is of no one of those (contained) under the name, since, indeed, the equivocal similarly suits every thing. The definition given by Dionysius, of life, has this fault, if it be the motion innate and consequent of a nourished genus, for this is not more inherent in animals, than in plants, but life does not seem predicated as to one species, but one kind of life to be inherent in animals, and another in plants. Therefore it is possible on purpose to assign a definition thus, as if all life were synonymous and predicated of one species, yet nothing prevents a man while he sees the equivocation, and wishes to assign the definition of the other, from being ignorant, that he does not assign a proper definition, but one common to both: notwithstanding, he will no less err if he has framed it in either way. Since, indeed, some equivocations escape us, the interrogator ought to use them as synonyms, (as the definition of the one will not be adapted to the other, so that it will appear in a way not to have been defined, as the synonymous ought to suit every thing,) on the other hand, the respondent must distinguish by division. Still since some respondents say, that the synonymous is equivocal, when the assigned definition does not suit every thing, but that the equivocal is synonymous if it suit both; it must be previously acknowledged, or previously inferred of these, that they are equivocal or synonymous, whichever they may be, since they more readily concur who do not foresee the result. Nevertheless, if they cannot agree, but some one should say that the synonymous is equivocal, because the assigned definition does not suit this, observe whether the definition of this, accords also to the rest, as it is evident it will be synonymous with the rest. If not, however, there will be many definitions of the remainder, since two definitions according to the name, accord to them, viz. both the prior and the posterior assigned. Again, if a person having defined any of those multifariously predicated, the definition also not suiting all, should not indeed say that it is equivocal, but should deny that the name suits all, because the definition does not, against such a one we may say that it is necessary to use that appellation which has been delivered and received, and not to disturb such things; nevertheless, some must not be enunciated in a way similar to the multitude.
If the definition of some connected thing should be given, consider, taking away the definition of one of the things connected, whether the remaining (definition) be that of what remains, for if not, neither it is evident will the whole be of the whole. Thus, if some one defined a finite straight line to be the boundary of a superficies having boundaries, of which the middle covers the extremities, if the definition of a finite line is the boundary of a superficies having boundaries, it is necessary that the remainder should be that of a straight line, of which the middle covers the extremities. Yet an infinite has neither middle nor extremities, but is nevertheless straight, so that the remainder is not the definition of the remainder.
Moreover (observe), if when what is defined is a composite, the definition is assigned consisting of as many members as the thing defined; now a definition is said to be of an equal number of members, when there are as many nouns and verbs in the definition as there are composites. For it is necessary in such cases, that there should be a change of the names, either of all, or of some of them, since there are no more names stated now than before; still it is requisite that he who defines should give a sentence instead of names, of all, if possible, but if not, of most things. For thus also in simple things, he who changes the name will have defined, as, for instance, (if he should say) vestment instead of garment.
Besides there is a greater error, if a person has made a change for names more unknown for instance, a white mortal instead of a white man, for neither is there a definition, and what is stated thus, is less clear.
Examine also in the change of names, whether he does not signify still the same thing, as when a person states that contemplative science is contemplative opinion, for opinion is not the same with science, at least indeed it must be, if the whole is to be the same, for contemplative is common in both definitions, but what remains is different.
Further, when a person changes one of the names, observe whether a change is made, not of the difference, but of the genus, as in the instance just now stated, since contemplative is more unknown than science, as the one is genus, and the other difference, and genus is most known of all, so that he ought to have made the change not of the genus, but of the difference, since this is the more unknown. Or is this reproof ridiculous, as there is nothing to prevent difference from being signified by a name most known, but genus not? but if this is the case, it is clear that we must make a change, as to the name of genus, and not of difference. Nevertheless, if (a person) does not assume a name for a name, but a sentence instead of a name, it is clear that he must give the definition of difference rather than of genus, since definition is given in order to make a thing known, for difference is less known than genus.
If however the definition of difference is assigned, examine whether the assigned difference is common to any thing else, as when it is said that an odd number is a number which has a middle, it must be defined in addition, how it has a middle. For number is common in both definitions, but instead of odd, a sentence is assumed; yet both a line and a body have a middle, though they are not odd numbers, so that this would not be the definition of the odd. Still, if that which has a middle be multifariously predicated, we must explain besides, how it possesses a middle, so that there will be either a reproof or a syllogism, that (the thing) has not been defined.
Again (observe), if that of which the definition is the sign, belongs to the number of beings, but what is under the definition does not; e. g. if white is defined colour mixed with fire, for it is impossible that the incorporeal should be mixed with body, so that it could not be colour mixed with fire, yet it is white.
Moreover, those who in (the definition of) relatives do not distinguish to what reference is made, but speak, comprehending many things, either wholly or in part enunciate falsely, as if some one should say that medicine is the science of being. For if medicine is the science of nothing which exists, it is evident that (the definition) is wholly false, but if it is of one, but not of another, it is partly false; for it is necessary (to be the science) of every thing, if it is said to be the science of being per se, and not accidentally, as is the case with other relatives, since every object of science is referred to science. Likewise, also in other things, since all relatives reciprocate. Besides, if he who explains a thing not per se, but accidentally, rightly explains it, each relative would not be referred to one, but to many things, as there is nothing to prevent the same thing, being both white, and good, so that he who explains by reference to one of these, would rightly explain, if he who explains from accident, does so rightly. Moreover, it is impossible that such a definition as this, should be peculiar to the thing assigned, for not only medicine, but many other sciences are referred to what exists, so that each will be the science of being; wherefore it is clear that such is the definition of no science, for it is necessary that definition should be peculiar, and not common.
Sometimes indeed, they define not the thing (only), but a thing in a good condition, or perfect; such is the definition of a rhetorician, and of a thief, since a rhetorician is one who is able to perceive what is persuasive in each thing, and to omit nothing; but a thief is one who takes on the sly, for it is evident that each being such, will be good, the one a good rhetorician, but the other a good thief, for not he who pilfers secretly is a thief, but he who wishes to pilfer secretly.
Again, (he errs,) who assigns what is of itself eligible, as practical or efficient, or in any way eligible on account of something else; as if he said that justice, is the preserver of the laws, or that wisdom, is effective of felicity, for what is effective, or preservative, is of the number of things eligible on account of something else. Or does nothing prevent what is eligible for itself, being eligible for something else also? nevertheless, he errs, who thus defines what is eligible per se, since in every thing, the best especially subsists in the essence, but it is better to be eligible per se, than on account of something else, so that definition ought of necessity rather to signify this.
Consider besides, whether he who assigns the definition of a certain thing, defines that it is these things, or that which consists of these, or this together with that; for if (it should he) those things, it would happen to be present with both, and with neither, as if he defined justice to be temperance and fortitude; for if when there are two, each has one of these, both will be just, and neither; since both indeed will possess justice, but each of them, not possess it. If however what has been said, be not very absurd from a thing of this kind happening in others also, (since nothing prevents two persons having a mina, though neither of them has,) yet that contraries should be present with the same, would appear to be altogether absurd. Nevertheless, this would occur if one of them has temperance and timidity, but the other, fortitude and intemperance, for both will have justice and injustice; for if justice be temperance and fortitude, injustice will be timidity and intemperance. Briefly, whatever arguments may be brought to prove that the parts and the whole are not the same, are all useful for what has now been stated, since he who thus defines, seems to say that the parts are the same as the whole. Still the arguments are especially appropriate in whatever the composition of the parts is evident, as in a house and other such things; for it is evident that when the parts exist, there is nothing to prevent the whole from not existing, so that the parts are not the same with the whole.
If, on the other hand, he should say that the thing defined is not these, but something consisting of these, we must first examine whether one certain thing, is not naturally adapted to be produced from these, for some things are so subsistent in relation to each other, as that nothing is produced from them, for instance, a line and number. Besides, whether the thing defined is naturally adapted to be in some one first, but those of which a person says that it (the thing defined) consists, are not in some one first, but each in the other, since it is clear that the thing would not consist of these, as in what the parts are inherent, it is necessary that the whole also should be inherent, so that the whole would not be in one first, but in many. Still if the parts and the whole are in one first, consider whether they are not in the same, but the whole in one, and the parts in another. Again, whether the parts are destroyed together with the whole, since it is necessary that it should happen vice versâ, the parts being destroyed that the whole should perish, but the whole being destroyed it is not necessary that the parts also should be destroyed. Or whether the whole be good or evil, but the parts neither, or vice versâ the parts indeed good or evil, but the whole neither, for neither is it possible that any good or evil should be produced from neither, nor that neither should be produced from evil or good. Or whether the one be more good than the other is evil, but what consists of these be not more good than evil; for instance, if impudence (should be said to consist) of fortitude and false opinion. For fortitude is more a good, than false opinion is an evil, wherefore it is necessary that what results from these, should be consequent to the more, and should either be simply good, or more good than evil. Or indeed is this unnecessary, unless each be good or evil, per se, for many effective things are not per se, good, but when mingled; or on the contrary each of them is good, but when mingled is evil, or neither (good nor evil). What has been now stated is especially apparent in the case of things wholesome and hurtful, since some drugs are of such a nature as that each is good, but if both be given mixed together, (the compound is) bad.
Again, (consider whether a thing be stated to consist) from the better and the worse, of which the whole is not worse than the better, but is better than the worse; or is neither this necessary, unless those of which the thing consists, be of themselves good? for there is nothing to prevent the whole not being good, as in the instances just now adduced.
Besides, whether the whole be synonymous with the other part, which it ought not to be, as neither is it in syllables, for a syllable is synonymous with no one of the elements of which it consists.
Moreover, (observe) whether a person has explained the mode of composition. For it is not sufficient to a knowledge of a thing, to say that it consists of these, because not merely to consist of these, but to consist of them in this manner, is the essence of composites; as in the case of a house, for the composition of these in any way whatever, is not a house.
If again this thing is assigned together with that, we must first state that this is with that, or is the same with these, or because this is from those; for he who says, honey with water, either says honey and water, or what consists of honey and water, so that whichever of these he allows to be the same as this with that, the same things it will be suitable to say, as were before urged against each of these. Further, distinguishing in how many ways one thing is said to be with another, consider whether this be in no way with that; e. g. if it is said that one is with another, either as in one same recipient, as justice and fortitude in the soul; or in the same place or time, but what is asserted as to these, should be by no means true, the assigned definition would, it is evident, not be the definition of any thing, as this is by no means with that. If, however, when the things are distinguished, it is true that each is in the same time, examine whether it is possible that each may not be referred to the same thing; as if (some one) should define fortitude to be daring joined with right conception, for it is possible for a man to have the daring to defraud, yet a right conception about things wholesome; still he is not yet a brave man, who has this, together with that, in the same time. Again, if both are referred to the same thing, as to things medical, since nothing prevents a man's having boldness and right conception about medical concerns, yet nevertheless he is not a brave man who possesses this with that; for neither ought each of them to be referred to different things, nor to any thing casually the same, but to the end of fortitude, as to warlike dangers, or if there be any thing more the end, than this.
Some indeed, of those thus explained, by no means fall under the above-mentioned division, as if anger is pain, joined with a notion of being despised: for this would show that pain arises from a notion of this kind, but that any thing should exist on account of this, is not the same as for this to be with that, according to any of the modes stated.
Moreover, if (a person) has stated the whole to be a composition of these, as that animal is a compound of soul and body, first observe, whether he has not stated the quality of the composition; as it defining flesh or bone, he should say that it is a compound of fire, earth, and air. For it is not enough to say it is a compound, but it must also be defined of what quality it (the compound) is, since flesh is not produced from the composition of these in any way whatever, but flesh, from things composed in this way, and bone, from those in that. It seems likely, indeed, that neither of those mentioned is altogether the same with composition, as to all composition, dissolution is contrary, but nothing to any of those stated; besides, if it is similarly probable, that every or no compound, is composition, but each animal being a compound is not composition, neither will any other compound be composition.
Again, if in like manner contraries are naturally adapted to be in something, and it has been defined through one of them (alone), there has evidently not been a definition. Otherwise, indeed, there will happen to be many definitions of the same thing, for what more does he state who has defined through this, than he who has done so through the other, since both are in a similar manner naturally adapted to be in it? such, indeed, is the definition of the soul, if it is an essence capable of science, for it is equally capable of ignorance.
Notwithstanding, if a person has it not in his power to argue against the whole definition from the whole not being known, he must attack some part, if it should be known, and apparently not be well assigned, since the part being subverted, the whole definition also, is subverted. (It is also requisite) correcting and reforming such definitions as are obscure, in order to render something evident, and to obtain an argument, to consider in this way: since it is necessary for the respondent, either to admit what is taken up by the interrogator, or himself to unfold what that is which is signified by the definition. Yet more, as men are accustomed in assemblies to introduce a law, and if what is introduced be better, they abrogate the former law, so we must act in definitions, and another definition must be introduced, since if (this) appear better, and more to develope the thing defined, it is evident that the definition laid down (previously) will be subverted, since there are not many definitions of the same thing.
Nevertheless, it is not the least element as to all definitions, to define with oneself sagaciously the thing proposed, or to take up a definition which has been well framed; since it is necessary, running as it were to an example, to survey what is deficient in the definition, and what is superfluously added, so as to be better provided with arguments.
Let, then, so much suffice for those points which pertain to definitions.