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Moreover, if the definition be of the state of anything, look at what is in the state, while if it be of what is in the state, look at the state: and likewise also in other cases of the kind. Thus if the pleasant be identical with the beneficial, then, too, the man who is pleased is benefited. Speaking generally, in definitions of this sort it happens that what the definer defines is in a sense more than one thing: for in defining knowledge, a man in a sense defines ignorance as well, and likewise also what has knowledge and what lacks it, and what it is to know and to be ignorant. For if the first be made clear, the others become in a certain sense clear as well. We have, then, to be on our guard in all such cases against discrepancy, using the elementary principles drawn from consideration of contraries and of coordinates.
Moreover, in the case of relative terms, see if the species is rendered as relative to a species of that to which the genus is rendered as relative, e.g. supposing belief to be relative to some object of belief, see whether a particular belief is made relative to some particular object of belief: and, if a multiple be relative to a fraction, see whether a particular multiple be made relative to a particular fraction. For if it be not so rendered, clearly a mistake has been made.
See, also, if the opposite of the term has the opposite definition, whether (e.g.) the definition of "half" is the opposite of that of "double": for if "double" is "that which exceeds another by an equal amount to that other", "half" is "that which is exceeded by an amount equal to itself". In the same way, too, with contraries. For to the contrary term will apply the definition that is contrary in some one of the ways in which contraries are conjoined. Thus (e.g.) if "useful"="productive of good", "injurious"=productive of evil" or "destructive of good", for one or the other of thee is bound to be contrary to the term originally used. Suppose, then, neither of these things to be the contrary of the term originally used, then clearly neither of the definitions rendered later could be the definition of the contrary of the term originally defined: and therefore the definition originally rendered of the original term has not been rightly rendered either. Seeing, moreover, that of contraries, the one is sometimes a word forced to denote the privation of the other, as (e.g.) inequality is generally held to be the privation of equality (for "unequal" merely describes things that are not equal’), it is therefore clear that that contrary whose form denotes the privation must of necessity be defined through the other; whereas the other cannot then be defined through the one whose form denotes the privation; for else we should find that each is being interpreted by the other. We must in the case of contrary terms keep an eye on this mistake, e.g. supposing any one were to define equality as the contrary of inequality: for then he is defining it through the term which denotes privation of it. Moreover, a man who so defines is bound to use in his definition the very term he is defining; and this becomes clear, if for the word we substitute its definition. For to say "inequality" is the same as to say "privation of equality". Therefore equality so defined will be "the contrary of the privation of equality", so that he would have used the very word to be defined. Suppose, however, that neither of the contraries be so formed as to denote privation, but yet the definition of it be rendered in a manner like the above, e.g. suppose "good" to be defined as "the contrary of evil", then, since it is clear that "evil" too will be "the contrary of good" (for the definition of things that are contrary in this must be rendered in a like manner), the result again is that he uses the very term being defined: for "good" is inherent in the definition of "evil". If, then, "good" be the contrary of evil, and evil be nothing other than the "contrary of good", then "good" will be the "contrary of the contrary of good". Clearly, then, he has used the very word to be defined.
Moreover, see if in rendering a term formed to denote privation, he has failed to render the term of which it is the privation, e.g. the state, or contrary, or whatever it may be whose privation it is: also if he has omitted to add either any term at all in which the privation is naturally formed, or else that in which it is naturally formed primarily, e.g. whether in defining "ignorance" a privation he has failed to say that it is the privation of "knowledge"; or has failed to add in what it is naturally formed, or, though he has added this, has failed to render the thing in which it is primarily formed, placing it (e.g.) in "man" or in "the soul", and not in the "reasoning faculty": for if in any of these respects he fails, he has made a mistake. Likewise, also, if he has failed to say that "blindness" is the "privation of sight in an eye": for a proper rendering of its essence must state both of what it is the privation and what it is that is deprived.
Examine further whether he has defined by the expression "a privation" a term that is not used to denote a privation: thus a mistake of this sort also would be generally thought to be incurred in the case of "error" by any one who is not using it as a merely negative term. For what is generally thought to be in error is not that which has no knowledge, but rather that which has been deceived, and for this reason we do not talk of inanimate things or of children as "erring". "Error", then, is not used to denote a mere privation of knowledge.