by Aristotle
If he has rendered the definition of the differentia, see whether the definition rendered is common to it and something else as well: e.g. whenever he says that an [30] odd number is a number with a middle, further definition is required of how it has a middle; for number is common to both accounts, and it is the word ‘odd’ for which the account has been substituted. Now both a line and a body have a middle, yet they are not odd; so that this will not be a definition of odd. And if having a middle is [35] used in several ways, the way here intended requires to be defined. So that this will either discredit the definition or prove that it is no definition at all.
12 · Again, see if the account is given of an entity, whereas what falls under the account is a non-entity. E.g., suppose white to be defined as colour mingled with [149b1] fire; for what is bodiless cannot be mingled with body, so that colour cannot be mingled with fire, whereas white does exist.
Moreover, those who in the case of relative terms do not distinguish to what the object is related, but have described it only so as to include it among a number of [5] things, are wrong either wholly or in part; e.g. suppose some one to have defined medicine as a science of what exists. For if medicine is not a science of anything that exists, the definition is clearly altogether false; while if it is a science of some things, but not of others, it is partly false; for it ought to hold of everything, if it is said to be of what exists essentially and not accidentally—as is the case with other relative [10] terms; for every object of knowledge is relative to knowledge. Likewise, also, with other relative terms, inasmuch as all such are convertible. Moreover, if the right way to render account of a thing is to render it as it is not in itself but accidentally, then each relative term will be used in relation not to one thing but to a number of things. For there is no reason why the same thing should not be both existent and [15] white and good, so that it will be a correct rendering to render the object in relation to any one whatsoever of these, if to render what it is accidentally is a correct way to render it. It is, moreover, impossible that an account of this sort should be proper to the term rendered; for not only medicine, but the majority of the other sciences too, [20] have for their object some entity, so that each will be a science of what exists. Clearly, then, such a definition does not define any science at all; for a definition ought to be proper, not common.
Sometimes, again, people define not the object but only the object in a good or perfect condition. Such is the definition of an orator as one who can see what will [25] persuade in any circumstances, and omit nothing; or of a thief, as one who pilfers in secret; for clearly, if they each do this, then the one will be a good orator, and the other a good thief; whereas it is not the actual pilfering in secret, but the wish to do it, that constitutes the thief. [30]
Again, see if he has rendered what is desirable for its own sake as desirable for what it produces or does, or as in any way desirable because of something else, e.g. by saying that justice is what preserves the laws or that wisdom is what produces happiness; for what produces or preserves something else is one of the things [35] desirable because of something else. It might be said that it is possible for what is desirable in itself to be desirable because of something else as well; but still to define what is desirable in itself in such a way is none the less wrong; for what is best in anything is especially part of its substance, and it is better for a thing to be desirable in itself than to be desirable because of something else, so that the definition ought rather to have indicated this.
[150a1] 13 · See also whether in defining anything a man has defined it as these things, or as made from these things or as this together with that. If he defines it as these things, the definition will be true of both and yet of neither of them; suppose, e.g., justice to be defined as temperance and courage. For if of two persons each has [5] one of the two only, both and yet neither will be just; for both together have justice, and yet each singly fails to have it. Even if the situation here described does not so far appear very absurd because of the occurrence of this kind of thing in other cases also (for it is quite possible for two men to have a pound between them, though neither of them has it by himself), yet at least that they should have contrary [10] attributes surely seems quite absurd; and yet this will follow if the one is temperate and cowardly, and the other brave and profligate; for then both will exhibit both justice and injustice; for if justice is temperance and bravery, the injustice will be [15] cowardice and profligacy. In general, too, all the ways of showing that the whole is not the same as the sum of its parts are useful in meeting the type just described; for a man who defines in this way seems to assert that the parts are the same as the whole. The arguments are particularly appropriate in cases where the process of putting the parts together is obvious, as in a house and other things of that sort; for [20] there, clearly, you may have the parts and yet not have the whole, so that parts and whole cannot be the same.
If he has said that the term being defined is not these things but made from these things, look and see in the first place if they cannot in the nature of things have a single product; for some things are so related to one another that nothing can come [25] from them, e.g. a line and a number. Moreover, see if the term that has been defined is in the nature of things found primarily in some single subject, whereas the things from which he has said it is made are not found primarily in any single subject, but each in a separate one. If so, clearly that will not be made from these things; for the whole is bound to be in the same things wherein its parts are, so that the whole will [30] then be found primarily not in one thing, but in a number of them. If, on the other hand, both parts and whole are found primarily in some single subject, see if that is not the same, but one thing in the case of the whole and another in that of the parts. Again, see whether the parts perish together with the whole; for it ought to happen vice versa, that the whole perishes when the parts perish: when the whole perishes, [35] there is no necessity that the parts should perish too. Or again, see if the whole is good or evil, and the parts neither, or, vice versa, if the parts are good or evil and the whole neither. For it is impossible either for a neutral thing to produce something [150b1] good or bad, or for things good or bad to produce a neutral thing. Or again, see if the one thing is more good than the other is evil, and yet the product is no more good than evil, e.g. suppose shamelessness is the product of courage and false opinion: here courage is more good than false opinion is evil; accordingly the product of these ought to follow the greater, and be either good without qualification, or at least [5] more good than evil. Or it may be that this does not necessarily follow, unless each is in itself good or bad; for many things that are productive are not good in themselves, but only in combination; or, vice versa, they are good taken singly, and bad or neutral in combination. What has just been said is more clearly illustrated in the [10] case of things that make for health or sickness; for some drugs are such that each taken alone is good, but if they are both administered in a mixture, bad.
Again, see whether the whole, as produced from a better and worse, fails to be worse than the better and better than the worse element. This again, however, need [15] not necessarily be the case, unless the elements compounded are in themselves good; if they are not, the whole may very well not be good, as in the cases just instanced.
Moreover, see if the whole is synonymous with one of the elements; for it ought not to be, any more than in the case of syllables; for a syllable is not synonymous [20] with any of the letters of which it is made up.
Moreover, see if he has failed to state the manner of their composition; for saying that it is made from these things is not enough to make the thing intelligible. For the substance of any compound thing is not merely that it is made from these things, but that it is made from them in such and such a way, as in the case of a [25] house; for here the materials do not make a house irrespective of the way they are put together.
If a man has defined an object as this together with that, the fir
st thing to be said is that this together with that is the same as these things, or as what is made from these things. For ‘honey together with water’ means either ‘honey and water’, or ‘what is made from honey and water’. If, then, he admits that this together with [30] that is the same as either of these two things, the same criticisms will apply as have already been given for meeting each of them. Moreover, distinguish between the different ways in which one thing may be said to be together with another, and see if there is none of them in which this is together with that. Thus e.g. supposing one thing to be together with another either in that some identical thing contains them (as e.g. justice and courage are found in the soul), or as being in the same place or in [35] the same time, and if this is in no way true of the things in question, clearly the definition rendered will not hold of anything, as this is not in any way together with that. If, however, among the various ways distinguished, each is found in the same [151a1] time as the other, look and see if possibly the two are not used in the same relation. Thus e.g. suppose courage to have been defined as daring with right reasoning: here it is possible that a person exhibits daring in robbery, and right reasoning in regard to the means of health—but he is not courageous just because he has this together [5] with that at the same time. Moreover, even though both are used in the same relation, e.g. in relation to medical treatment (for a man may exhibit both daring and right reasoning in respect of medical treatment), still a man who has this together with that is not yet courageous. For the two must not relate to any casual [10] object that is the same, any more than each to a different object; rather, they must relate to the function of courage, e.g. meeting the perils of war, or whatever is more properly speaking its function than this.
Some definitions rendered in this form fail to come under the aforesaid division [15] at all, e.g. a definition of anger as pain with a consciousness of being slighted. For what this means to say is that it is because of a consciousness of this sort that the pain occurs; but to occur because of a thing is not the same as to occur together with it in any of the aforesaid ways.
[20] 14 · Again, if he has described the whole as the composition of these things (e.g. a living creature as a composition of soul and body), first of all see whether he has omitted to state the kind of composition, as (e.g.) in a definition of flesh or bone as the composition of fire, earth, and air. For it is not enough to say it is a composition, but you should also go on to define the kind of composition; for these [25] things do not form flesh irrespective of the manner of their composition, but when compounded in one way they form flesh, when in another, bone. It appears, moreover, that neither of the aforesaid things is the same as a composition at all; for a composition always has a dissolution as its contrary, whereas neither of the aforesaid has any contrary. Moreover, if it is equally plausible that every compound [30] is a composition and that none is, and if every kind of living creature, though a compound, is not a composition, then no other compound will be a composition either.
Again, if two contraries are equally liable to occur naturally in a thing, and the thing has been defined through the one, clearly it has not been defined; otherwise there will be more than one definition of the same thing; for how is it any more a [35] definition to define it through this one than through the other, seeing that both are equally liable to occur naturally in it? Such is the definition of the soul, if defined as [151b1] a substance capable of receiving knowledge; for it has an equal capacity for receiving ignorance.
Also, even when one cannot attack the definition as a whole because the whole [5] is not familiar, one should attack some part of it, if it is familiar and is evidently incorrectly rendered; for if the part is demolished, so too is the whole definition. Where, again, a definition is obscure, one should first of all correct and reshape it in order to make some part of it clear and get a handle for attack, and then proceed to examine it. For the answerer is bound either to accept the sense as taken by the [10] questioner, or else himself to explain clearly whatever it is that his account means. Moreover, just as in the assemblies the ordinary practice is to introduce a law and, if the introduced law is better, to repeal the existing one, so one ought to do in the case of definitions as well: one ought oneself to propose a second definition; for if it is [15] seen to be better, and more indicative of the object defined, clearly the definition laid down will have been demolished, on the principle that there cannot be more than one definition of the same thing.
In combating definitions it is always one of the chief elementary principles to take by oneself a happy shot at a definition of the object before one, or to adopt some correctly expressed definition. For one is bound, with the model (as it were) before [20] one’s eyes, to discern both the lack of any features that the definition ought to have, and also any superfluous addition, so that one is better supplied with lines of attack.
As to definitions, then, let so much suffice.
BOOK VII
1 · Whether two things are the same or different, in the most strict of the meanings ascribed to ‘sameness’ (and we said34 that the same applies in the most strict sense to what is numerically one), may be examined in the light of their inflexions and coordinates and opposites. For if justice is the same as courage, then [30] too the just man is the same as the courageous man, and justly is the same as courageously. Likewise, too, in the case of their opposites; for if two things are the same, their opposites also will be the same, in any of the recognized forms of opposition. For it is the same thing to take the opposite of the one or that of the other, seeing that they are the same. Again it may be examined in the light of those [152a1] things which tend to produce or to destroy the things in question, of their formation and destruction, and in general of anything that is related in like manner to each. For where things are the same without qualification, their formations and destructions also are the same, and so are the things that tend to produce or to destroy them.
Look and see also, in a case where one of two things is said to be something or [5] other in a superlative degree, if the other of these identical things can also be described by a superlative in the same respect. Thus Xenocrates argues that the happy life and the good life are the same, seeing that of all forms of life the good life is the most desirable and so also is the happy life; for only one thing is the most desirable and greatest. Likewise also in other cases of the kind. Each of the two [10] things termed greatest or most desirable must be numerically one: otherwise no proof will have been given that they are the same; for it does not follow because Peloponnesians and Spartans are the bravest of the Greeks, that Peloponnesians are the same as Spartans, seeing that Peloponnesian and Spartan are not numerically [15] one; it only follows that the one must be included under the other as Spartans are under Peloponnesians—for otherwise, if the one class is not included under the other, each will be better than the other. For then the Peloponnesians are bound to be better than the Spartans, seeing that the one class is not included under the [20] other; for they are better than anybody else. Likewise also the Spartans must perforce be better than the Peloponnesians; for they too are better than anybody else; each then is better than the other. Clearly therefore what is styled best and [25] greatest must be numerically one, if it is to be proved to be the same as another. This is why Xenocrates fails to prove his case; for the happy life is not numerically one, nor yet the good life, so that it does not follow that, because they are both the most [30] desirable, they are therefore the same, but only that the one falls under the other.
Again, look and see if, supposing the one to be the same as something, the other also is the same as it; for if they are not both the same as the same thing, clearly neither are they the same as one another.
Moreover, examine them in the light of their accidents or of the things of which they are accidents; for any accident belonging to the one must belong also to [35] the other, and if the one belongs to anything as an accident, so must the other also. If in any of these respects there i
s a discrepancy, clearly they are not the same.
See further whether, instead of both being found in one class of predicates, the one signifies a quality and the other a quantity or relation. Again, see if the genus of [152b1] each is not the same, the one being good and the other evil, or the one being virtue and the other knowledge; or see if, though the genus is the same, the differentiae predicated of either are not the same, the one being distinguished as a speculative [5] science, the other as a practical science. Likewise also in other cases.
Moreover, from the point of view of degrees, see if the one admits an increase of degree but not the other, or if though both admit it, they do not admit it at the same time; just as it is not the case that a man desires intercourse more intensely, the more intensely he is in love, so that love and the desire for intercourse are not the same.
[10] Moreover, examine them by means of addition, and see whether the addition of each to the same thing fails to make the same whole; or if the subtraction of the same thing from each leaves a different remainder. Suppose (e.g.) that he has declared double a half to be the same as a multiple of a half: then, subtracting a half [15] from each, the remainders ought to have signified the same thing; but they do not; for double and a multiple do not signify the same thing.
Inquire also not only if some impossible consequence results directly from the statement—but also whether it may result from a supposition as happens to those [20] who assert that empty is the same as full of air; for clearly if the air is exhausted, the vessel will not be less but more empty, though it will no longer be full of air. So that by a supposition, which may be true or may be false (it makes no difference which), the one character is annulled and not the other, showing that they are not the same.