Topics (Aristotle)/Book 7
Whether a thing be the same or different, according to the most proper of the before-mentioned modes about the same thing, (and that was said to be most properly the same, which is one in number,) we must consider from cases, co-ordinates and opposites. For if justice be the same with fortitude, a just man is also the same with a brave man, and justly with courageously. So also with opposites, for if these be the same, the opposites to these also are the same, according to any of the modes of opposition stated, since it makes no difference whether we take an opposite to this or that, as they are the same. Again, from efficients and corruptives, also from generations, corruptions, and in short, from things which subsist similarly with reference to either, for whatever are simply the same, the generations and corruptions also of these are the same, and besides, the efficients and corruptives.
Examine also, whether of those things of which one is especially said to be a certain thing, another also is especially predicated according to the same; as Xenocrates shows that a happy and a worthy life are the same, because a worthy and a happy, are the most eligible of all lives, for the most eligible, and the greatest, are one thing. Likewise, in other things of the same kind; yet it is necessary that each of those which are said to be the greatest, or the most eligible, should be one in number, otherwise it will not be demonstrated that it is the same, since it is not necessary, if the Peloponnesians and the Lacedæmonians are the bravest of the Greeks, that the Peloponnesians should be the same with the Lacedæmonians, as a Peloponnesian and a Lacedaemonian are not one in number. Still it is requisite that one should be contained under the other, as Lacedæmonians under Peloponnesians, otherwise it will happen that they are better than each other, if the one be not comprehended under the other, for it is necessary that the Peloponnesians should be better than the Lacedæmonians, if the one be not contained under the other, for they are better than all the rest (of the Greeks). So also it is necessary that the Lacedæmonians should be better than the Peloponnesians, for these also are better than all the rest, so that they are better than each other. It is clear then, that what is said to be best, and greatest, ought to be one in number, if we would show that it is the same, for which reason also Xenocrates does not demonstrate, for a happy, and a worthy life, are not one in number, so that it is not necessary they should be the same, because both are most eligible, but that one should be under the other.
Again consider, whether one (of the things proposed) is the same (as a third thing), also whether another (is the same with it), for if both are not the same with it, it is clear that (they are not the same) with each other.
Moreover, observe from the accidents of these, and from those things to which these are accidents, since whatever are accidents to the one, must of necessity be also accidental to the other, and to what one of them happens, the other must also happen; now if any discrepancy subsists amongst these, they are evidently not the same.
Notice also, whether both are not in one genus of category, but the one denotes quality, the other quantity or relation; again, whether the genus of each is not the same, but the one is good, and the other evil, or the one virtue, and the other science: or whether the genus is indeed the same, yet there are not the same differences predicated of each, but of the one, that it is contemplative science, of the other, that it is practical, and so of other things.
Further, from the more, if one indeed receives the more, but the other not, or if both indeed receive it, yet not at the same time; thus he who loves more, does not more desire intercourse, so that love, and the desire of intercourse, are not the same.
Besides, from addition, if each being added to the same, does not make the whole the same, or if the same being taken away from each, the remainder is different; as if some one said, that the double of the half, and the multiple of the half, were the same. For the half being taken away from each, the remainder ought to signify the same, yet it does not, for the double, and the multiple, do not denote the same.
Observe however, not only whether any impossibility now happens on account of the thesis, but also whether it is possible to be from the pothesis; as (happens) to those who say that a vacuum, and a plenum of air, are the same, since it is clear that if the air should depart, there will not be a less, but a greater vacuum, yet there will no longer be a plenum of air. Hence, a certain thing being supposed, whether false or true, (it makes no difference,) one of them is subverted, but the other not, hence they are not the same.
In a word, from those things which are in any way predicated of each, and of which these are predicated, we must consider if there be any discrepancy; for whatever are predicated of the one, ought likewise to be predicated of the other, and of which the one, is predicated, it is necessary that the other also, should be.
Besides, since the same thing is predicated multifariously, examine whether after some other mode they are the same, since it either is not necessary, or not possible that those which are the same in species or genus, should be the same in number, but we will investigate whether they are the same in this way, or not in this way.
Again, whether the one can possibly be without the other, for they would not be the same.
The places then pertaining to the same thing, are said to be so many, but it is clear from what has been stated, that all places belonging to the same thing, which are subversive, are useful also to definition, as was observed before; for if both the name, and the definition, do not denote the same, it is evident that the proposed sentence will not be a definition. On the other hand, none of the confirmative places is useful to definition, since it is not sufficient to show that what is under definition, and name, is the same thing, in order to confirm definition; but definition must necessarily possess all those other things which have been mentioned.
To subvert definition then, we must make our attempt always in this manner, and through these things; but if we desire to confirm, it is first necessary to know, that no one, or few, of those who discuss, syllogistically infer definition, but all assume such sort of thing, as a principle; for instance, both those who are conversant with geometry and numbers, and other such instructions: next, that it is the business of another treatise accurately to assign both what definition is, and how it is necessary to define, but now only so much must be observed, as is sufficient for our present purpose, viz. that it is possible there may be a syllogism of definition, and of the very nature of a thing. For if definition be a sentence denoting the very nature of a thing, and it is necessary that things predicated in the definition should alone be predicated in (reply to) what a thing is, but genera and differences are predicated in reply to this question, it is evident that if any one assumes those things only to be predicated in reference to what a thing is, that the sentence which contains these, will evidently be a definition, since there cannot be possibly another definition, as nothing else is predicated of the thing, in reference to what it is.
Evidently then, there may be a syllogism of definition, but from what we ought to construct it, has been more accurately determined in other places; these same places, however, are useful for the proposed method. For in contraries, and other opposites, we must observe whole sentences, observing them also, according to parts; as if the opposite (be the definition) of the opposite, it is necessary that what is stated, should be of the thing proposed. Since however, there are many connexions of contraries, we must select from them, that definition which especially appears contrary; whole sentences then, must be considered in the manner stated, but according to parts, thus. In the first place, (it must be shown) that the assigned genus is rightly assigned, for if the contrary be in the contrary genus, but the thing proposed is not in the same, it will clearly be in the contrary (genus), since contraries must of necessity either be in the same, or in contrary genera. We also think that contrary differences are predicated of contraries, as of white and black, for the one is dissipative, the other is collective of vision. Wherefore, if contraries are predicated of a contrary, the assigned (differences) would be predicated of the thing proposed, so that since both genus and differences are rightly assigned, it is evident that what is assigned, will be a definition. Or it is not necessary that contrary differences should be predicated of contraries, unless they should be contraries in the same genus, yet of those of which the genera are contrary, there is nothing to prevent the same difference being predicated of both; e. g. of justice and injustice, for the one is a virtue, but the other a vice of the soul, so that the word "of the soul," being a difference, is predicated of both, since there is of the body also, a virtue and a vice. Nevertheless, this at least is true, that the differences of contraries are either contrary or the same; if then a contrary be predicated of a contrary, but not of this, it is evident that the difference adduced, will be predicated of this. In short, since definition consists of genus and differences, if the definition of the contrary be manifest, the definition also of the thing proposed, will be manifest. For as what is contrary, is either in the same, or in a contrary genus, and likewise either contrary or the same differences, are predicated of contraries, it is evident, that the same genus will be predicated of the thing proposed, which was also of the contrary; but the differences are contrary, either all or some, yet the remainder are the same, or on the contrary, the differences are the same, but the genera are contrary, or both genera and differences are contrary, for both cannot possibly be the same, or else there will be the same definition of contraries.
Besides, (we must argue) from cases, and conjugates, since genera must of necessity follow genera, and definitions be consequent to definitions: thus, it oblivion be the loss of science, to become oblivious, will be to lose science, and to have forgotten, to have lost science; any one then of the before-mentioned particulars being admitted, the rest must necessarily be admitted. Likewise, also, if destruction be a dissolution of substance, to be destroyed will be for substance to be dissolved, and destructively will be dissolvingly, and if what is destructive is dissolvent of substance, destruction is a dissolution of substance; similarly also, of other things, wherefore any one being assumed, all the rest will be conceded.
Also, (we must argue) from things which subsist similarly as to each other; for if the salubrious is productive of health, the productive of a good habit will be effective of a good habit, and the beneficial will be productive of good. For each of the above named, subsists similarly with regard to its proper end, so that if the definition of one of them, is to be effective of the end, this will also be the definition of each of the rest.
Moreover, from the more and the similar, in as many ways as it is possible to confirm, comparing two with two, thus; if this is more the definition of that, than something else of another thing, but the less is a definition, the more also (will be a definition); also if this is similarly the definition of that, and another thing of something else, if the one is a definition of the other, the remainder will also be of the remainder. When however, one definition is compared with two things, or two definitions with one, the consideration from the more is of no use, as neither can there possibly be one definition of two things, nor two of the same.
Those which have already been stated, and also the others from cases and conjugates, are the most appropriate places; wherefore we ought especially to retain these, and to have them at hand, since they are most useful to the greatest number (of problems). Of the rest also, those which are especially common, for these are the most efficacious of the remaining ones; as, for instance, to regard singulars, and to consider in species, whether the definition is suitable, as species is synonymous. Such however is useful against those who lay down that there are ideas, as was before observed; moreover, whether a name is introduced metaphorically, or whether the same thing is predicated of itself as different, and if there be any other place common and efficacious, we must employ it.
That it is more difficult to confirm, than to subvert definition, is evident from what will next be said, since it is not easy for him (who interrogates) to perceive and take from those who are interrogated, propositions of this kind; as that of the things in the assigned definition, one is genus, but another difference, and that genus and differences are predicated (in reply) to what a thing is. Still without these there cannot possibly be a syllogism of definition, as if certain other things also are predicated of a thing, in respect of what it is, it is dubious whether what is stated, or something else, is its definition, since definition is a sentence signifying what is the very nature of a thing. Now it is evident from what follows, for it is more easy to conclude one, than many things. To the subverter indeed, it is sufficient to dispute against one (part of the definition), (for having subverted any one part, we shall have subverted the definition,) but it is necessary for the confirmer, to prove that all those things are inherent, which are in the definition. Moreover, the confirmer must adduce an universal syllogism, since it is requisite that of every thing of which a name is predicated, the definition should be predicated, and besides this, vice versâ, if the assigned definition is to be proper. On the other hand, it is not requisite for the subverter to demonstrate the universal, since it suffices to show that the definition is not verified of any one of the things under the name, if also it should be necessary to subvert universally, neither thus, is reciprocation necessary in subversion, for it is enough that the subverter show universally, that the definition is not predicated of some one of those things, of which the name is predicated. On the contrary, it is not necessary to show that the name is predicated, of what the definition is not predicated. Further, if also it is present with every thing under the name, yet not with it alone, the definition will be subverted.
In like manner, it is with regard to property and genus, since in both, it is easier to subvert, than to confirm. About property then, it is evident from what we have stated, as for the most part property is assigned in conjunction, so that it is possible to subvert by taking away one (word); but he who confirms, must of necessity conclude every thing by syllogism. Now almost every thing else, which may be said of definition, will also be suitable to say of property, since the confirmer ought to show that it is inherent in every thing under the name, but it suffices for the subverter to show it non-inherent in one thing; if also it is inherent in every thing, but not in it alone, thus too, it becomes subverted, as was observed about definition. Concerning genus indeed, (it is evident,) because it is necessarily confirmed only in one way, if a person shows it present with every individual; nevertheless, it is subverted in two ways, for both if it has been shown not present with any, and not with a certain one, what was assumed in the beginning is subverted. Moreover, it is not enough, for the confirmer to show that it is inherent, but also it must be shown that it is inherent, as genus; but to the subverter it is enough to show it non-inherent, either in a certain or in every individual: still it seems, as in other things, to destroy, is easier than to produce, so in these, subversion, is easier than confirmation.
In the case of accident, we can more easily subvert, than construct the universal, for the confirmer must show that it is present with every, but the subverter need only show it non-inherent in one. On the contrary, it is easier to confirm, than to subvert the particular, as it suffices for the confirmer to show it present with a certain one, but the subverter must show that it is present with none.
It appears also clear why it is the easiest thing of all, to subvert definition, for many things being asserted in it, very many are given; but from the greater number, a syllogism is more quickly made, since it is likely that error should arise in many, more than in few, things. Moreover, it is possible to argue against definition through other things also, since whether the sentence be not appropriate, or whether what is assigned be not genus, or something of those in the definition be non-inherent, the definition will be subverted; but against other things, neither can we assume those arguments which are derived from definitions, nor all others, since those only which belong to accident, are common to all the particulars mentioned. For it is necessary that each of the things stated should be inherent, if however genus is not inherent as property, the genus will not yet be subverted; likewise, also property need not be inherent as genus, nor accident as genus or property, but merely inherent. Wherefore it is impossible to argue from some things to others, except in definition; hence, it is evident that to subvert definition is the easiest thing of all, but to confirm it the hardest, since we must syllogistically infer all those particulars, (viz. that all the above-named are inherent, and that what is assigned is genus, and that the sentence is appropriate,) and besides these, that the sentence denotes the very nature of a thing, and it is necessary to do this well.
Among other things, property is especially a thing of this sort, for it is easier to subvert it, from its consisting, for the most part, of many things, and it is most difficult of confirmation, because we must combine many things, and besides, show that it is inherent in this alone, and reciprocates with a thing.
Of all however, the easiest is to confirm accident, for in others, not only inherency, but inherency thus, must be shown; but as to accident it suffices to show its inherency only. On the other hand, accident is the hardest to subvert, because the fewest things are given in it, for it is not signified in accident, over and above other things, how it is inherent, so that subversion is possible in two ways; as to the rest, either by showing non-inherency, or non-inherency in this way; but in accident, it is impossible to subvert, except by showing that it is not inherent.
The places then, through which we shall be well provided with arguments against the several problems, have almost sufficiently been enumerated.