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be found in the genus stated, suppose the genus have no contrary: for if the contrary be found in it, clearly the species in question is found in it as well. Moreover, see if the intermediate species is found in the genus stated: for whatever genus contains the intermediate contains the extremes as well. Again, if the genus have a contrary, look and see whether also the contrary species is found in the contrary genus: for if so, clearly also the species in question is found in the genus in question.
Again, consider in the case of the inflexions and the co-ordinates of species and genus, and see whether they follow likewise, both in demolishing and in establishing a view. For whatever attribute belongs or does not belong to one belongs or does not belong at the same time to all; e.g. if justice be a particular form of knowledge, then also ‘justly’ is ‘knowingly’ and the just man is a man of knowledge: whereas if any of these things be not so, then neither is any of the rest of them.
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Again, consider the case of things that bear a like relation to one another. Thus (e.g.) the relation of the pleasant to pleasure is like that of the useful to the good: for in each case the one produces the other. If therefore pleasure be a kind of ‘good’, then also the pleasant will be a kind of ‘useful’: for clearly it may be taken to be productive of good, seeing that pleasure is good. In the same way also consider the case of processes of generation and destruction; if (e.g.) to build be to be active, then to have built is to have been active, and if to learn be to recollect, then also to have learnt is to have recollected, and if to be decomposed be to be destroyed, then to have been decomposed is to have been destroyed, and decomposition is a kind of destruction. Consider also in the same way the case of things that generate or destroy, and of the capacities and uses of things; and in general, both in demolishing and in establishing an argument, you should examine things in the light of any resemblance of whatever description, as we were saying in the case of generation and destruction. For if what tends to destroy tends to decompose, then also to be destroyed is to be decomposed: and if what tends to generate tends to produce, then to be generated is to be produced, and generation is production. Likewise, also, in the case of the capacities and uses of things: for if a capacity be a disposition, then also to be capable of something is to be disposed to it, and if the use of anything be an activity, then to use it is to be active, and to have used it is to have been active.
If the opposite of the species be a privation, there are two ways of demolishing an argument, first of all by looking to see if the opposite be found in the genus rendered: for either the privation is to be found absolutely nowhere in the same genus, or at least not in the same ultimate genus: e.g. if the ultimate genus containing sight be sensation, then blindness will not be a sensation. Secondly, if there be a sensation. Secondly, if there be a privation opposed to both genus and species, but the opposite of the species be not found in the opposite of the genus, then neither could the species rendered be in the genus rendered. If, then, you are demolishing a view, you should follow the rule as stated; but if establishing one there is but one way: for if the opposite species be found in the opposite genus, then also the species in question would be found in the genus in question: e.g. if ‘blindness’ be a form of ‘insensibility’, then ‘sight’ is a form of ‘sensation’.
Again, look at the negations of the genus and species and convert the order of terms, according to the method described in the case of Accident: e.g. if the pleasant be a kind of good, what is not good is not pleasant. For were this no something not good as well would then be pleasant. That, however, cannot be, for it is impossible, if ‘good’ be the genus of pleasant, that anything not good should be pleasant: for of things of which the genus is not predicated, none of the species is predicated either. Also, in establishing a view, you should adopt the same method of examination: for if what is not good be not pleasant, then what is pleasant is good, so that ‘good’ is the genus of ‘pleasant’.
If the species be a relative term, see whether the genus be a relative term as well: for if the species be a relative term, so too is the genus, as is the case with ‘double’ and ‘multiple’: for each is a relative term. If, on the other hand, the genus be a relative term, there is no necessity that the species should be so as well: for ‘knowledge’is a relative term, but not so ‘grammar’. Or possibly not even the first statement would be generally considered true: for virtue is a kind of ‘noble’ and a kind of ‘good’ thing, and yet, while ‘virtue’ is a relative term, ‘good’ and ‘noble’ are not relatives but qualities. Again, see whether the species fails to be used in the same relation when called by its own name, and when called by the name of its genus: e.g. if the term ‘double’ be used to mean the double of a ‘half’, then also the term ‘multiple’ ought to be used to mean multiple of a ‘half’. Otherwise ‘multiple’ could not be the genus of ‘double’.
Moreover, see whether the term fail to be used in the same relation both when called by the name of its genus, and also when called by those of all the genera of its genus. For if the double be a multiple of a half, then ‘in excess of ‘will also be used in relation to a ‘half’: and, in general, the double will be called by the names of all the higher genera in relation to a ‘half’. An objection may be raised that there is no necessity for a term to be used in the same relation when called by its own name and when called by that of its genus: for ‘knowledge’ is called knowledge ‘of an object’, whereas it is called a ‘state’ and ‘disposition’ not of an ‘object’ but of the ‘soul’.
Again, see whether the genus and the species be used in the same way in respect of the inflexions they take, e.g. datives and genitives and all the rest. For as the species is used, so should the genus be as well, as in the case of ‘double’ and its higher genera: for we say both ‘double of’ and ‘multiple of’ a thing. Likewise, also, in the case of ‘knowledge’: for both knowledge’ itself and its genera, e.g. ‘disposition’ and ‘state’, are said to be ‘of’ something. An objection may be raised that in some cases it is not so: for we say ‘superior to’ and ‘contrary to’ so and so, whereas ‘other’, which is the genus of these terms, demands not ‘to’ but ‘than’: for the expression is ‘other than’ so and so.
Again, see whether terms used in like case relationships fail to yield a like construction when converted, as do ‘double’ and ‘multiple’. For each of these terms takes a genitive both in itself and in its converted form: for we say both a half of’ and ‘a fraction of’ something. The case is the same also as regards both ‘knowledge’ and ‘conception’: for these take a genitive, and by conversion an ‘object of knowledge’ and an ‘object of conception’ are both alike used with a dative. If, then, in any cases the constructions after conversion be not alike, clearly the one term is not the genus of the other.
Again, see whether the species and the genus fail to be used in relation to an equal number of things: for the general view is that the uses of both are alike and equal in number, as is the case with ‘present’ and ‘grant’. For a present’ is of something or to some one, and also a ‘grant’ is of something and to some one: and ‘grant’ is the genus of ‘present’, for a ‘present’ is a ‘grant that need not be returned’. In some cases, however, the number of relations in which the terms are used happens not to be equal, for while ‘double’ is double of something, we speak of ‘in excess’ or ‘greater’ in something, as well as of or than something: for what is in excess or greater is always in excess in something, as well as in excess of something. Hence the terms in question are not the genera of ‘double’, inasmuch as they are not used in relation to an equal number of things with the species. Or possibly it is not universally true that species and genus are used in relation to an equal number of things.
See, also, if the opposite of the species have the opposite of the genus as its genus, e.g. whether, if ‘multiple’ be the genus of ‘double’, ‘fraction’ be also the genus of ‘half’. For the opposite of the genus should always be the genus of the opposite species. If, then, any one were to assert that knowledge is a kind of sensation, then also the object of knowledge will have to be a kind of object