Volume 2 · pp. 479–482
Book VII of the Topics, Tractate I. On the determination of the same and the diverse.
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LIBER VII TOPICORUM.
TRACTATUS I. DE DETERMINATIONE EJUSDEM ET DIVERSI.
CAPUT I. De locis determinantibus idem in quantum est praedicatum adjunctum diffinitioni.
Utrum autem aliquid alteri sit idem vel diversum ab eo, non quidem genere idem vel specie, sed secundum principaliorem modum ejus quod est idem, quid est idem numero et idem diffinitione et nomine, sicut diffinitio et diffinitum sunt idem, nunc considerandum est: quia tale idem vel diversum praedicatum adjunctum diffinitioni est: interempto enim quod non est idem, interimitur diffinitio, quamvis non construatur illo constructo. Dicebatur in praehabitis in primo hujus scientiae libro principaliter idem, quod idem numero est. Hoc igitur quod diximus, quod utrum idem sit aliquid alteri vel diversum, primo considerabimus interimendo, et deinde redibimus ad construendam diffinitionem: per locos enim in quibus interimitur per se diffinitio, per consequens construitur: hoc autem in sequentibus erit manifestum. Ad interimendum autem idem primo locos communes inducemus, eo quod illi ad hoc efficaciores sunt quam proprii et intrinseci.
Incipiens igitur destruere, quod aliquid sit idem alteri, considerandum primo ex casibus et conjugatis: nam in casibus et conjugatis inspiciendo si justitia est idem fortitudini, sicut principale principali, et justum forti, sicut sumptum sumpto, et casus casui erit idem. Similiter autem considerandum est in oppositis: nam si duo sunt quorum utrumque habeat oppositum, et opposita sint eadem, et illa sunt eadem: et si non sunt eadem, nec ista sunt eadem secundum quemlibet modum oppositionis generaliter: nihil enim differt hunc modum vel illum oppositionis sumere ad probandum, quod eadem opposita: quia secundum omne genus sequitur oppositionis.
Rursum idem considerandum est ex effectivis et corruptivis, et generationibus et corruptionibus, et omnino sive universaliter ex omnibus his quae similiter secundum proportionem se habent ad alterutrum sive ad invicem comparata: nam quaecumque similiter sunt eadem nomine vel numero vel diffinitione, illorum etiam generationes sunt eaedem, et effectiva et corruptiva eorum etiam sunt eadem.
Considerandum etiam per magis et minus, et praecipue in superlativo gradu: quia quod per abundantiam dicitur, uni soli convenit 1. Considerandum ergo si duo sint, quorum alterum aliquid dicitur maxime in superlativo, si alterum secundum idem accidens dicitur maxime, sequitur quod illa non sunt eadem: sicut Xenocrates beatam et studiosam vitam assignavit sive probavit esse idem numero, cum omnium vitarum maxime utraque sit eligenda et maxima bonitate et dignitate. Similiter autem et in aliis hujus considerandum est. Indiget tamen ista consideratio correctione et determinatione, quia adhuc probetur quod maximum est maxime eligendum, constat quod sicut est idem, oportet quod sic sit unum numero quod dicitur hinc et inde maximum et maxime eligendum. Si autem non sic dicatur quod oportet esse idem numero, sequitur quod non erit ostensum quod est idem simpliciter: non necessarium enim si fortissimi Graecorum sunt Peloponenses et Lacedaemonii, ita quod Pelopis sicut provincia et Lacedaemonia sicut civitas in provincia illa: non erit tunc in quantum veritas, quod idem numero sint Peloponii et Lacedaemonii, eo quod non sunt unum et idem numero Peloponius et Lacedaemonius, sed contineri necesse unum sub altero, ut totum continet partem, sicut Lacedaemonii a Peloponiis continentur. Si autem non sic dicatur, sequitur sive accidit seipsis etiam invicem fortiores esse: quod sic patet: detur enim quod Lacedaemonii sint fortissimi: ergo fortiores sunt Peloponiis. Similiter detur quod Peloponii sint fortissimi: sunt ergo fortiores Lacedaemoniis: sed si sunt fortiores Peloponiis, erunt fortiores seipsis: et hoc sequitur si non continentur alteri sub alteris: et hoc sequitur ex hoc quod utrique omnibus reliquis a se sunt fortitudine meliores. Similiter autem e converso et Lacedaemoniis si non a se continentur, necesse est meliores esse Peloponenses: nam et omnibus caeteris sunt meliores: propter quod se invicem sunt meliores, quod est inconveniens.
BOOK VII OF THE TOPICS.
TRACTATE I. ON THE DETERMINATION OF THE SAME AND THE DIVERSE.
CHAPTER I. On the places determining the same insofar as it is a predicate joined to definition.
But whether something is the same as another or diverse from it, not indeed the same in genus or species, but according to the more principal mode of what is same, namely what is the same in number and the same in definition and name, as definition and defined thing are the same, must now be considered; because such same or diverse is a predicate joined to definition. For when it is destroyed that it is not the same, the definition is destroyed, although it is not constructed when that is constructed. It was said in what preceded, in the first book of this science, that principally same is what is the same in number. Therefore this which we have said, whether something is the same as another or diverse, we shall first consider by destroying, and then we shall return to constructing definition; for through the places in which definition is destroyed through itself, it is constructed consequently. This will be manifest in what follows. But for destroying the same, first we shall introduce common places, because those are more efficacious for this than proper and intrinsic places.
Therefore beginning to destroy that something is the same as another, one must first consider from cases and conjugates. For in cases and conjugates, by inspecting whether justice is the same as fortitude, as principal to principal, and just the same as brave, as derivative to derivative, case will be the same as case. Similarly one must consider in opposites; for if there are two things of which each has an opposite, and the opposites are the same, then those things are the same; and if they are not the same, neither are these the same according to any mode of opposition generally. For it makes no difference to take this mode or that mode of opposition for proving that the opposites are the same, because it follows according to every genus of opposition.
Again the same must be considered from effectives and corruptives, and generations and corruptions, and wholly or universally from all those things which similarly have themselves according to proportion compared to one another or mutually; for whatever things are similarly the same in name or number or definition, their generations also are the same, and their effective and corruptive things are also the same.
One must also consider through more and less, and especially in the superlative degree, because what is said by superabundance belongs to one alone 1. Therefore one must consider, if there are two things of which one is called something most of all in the superlative, whether the other is called most of all according to the same accident; it follows that those things are not the same. Thus Xenocrates assigned or proved blessed life and studious life to be the same in number, since each is most choiceworthy and greatest in goodness and dignity among all lives. Similarly one must consider in other things of this sort. Yet this consideration needs correction and determination, because, if it is further proved that the greatest is most choiceworthy, it is clear that just as it is the same, so it must be one in number which is called greatest and most choiceworthy from here and from there. But if it is not said in this way that it must be the same in number, it follows that it will not have been shown that it is the same simply. For it is not necessary, if the Peloponnesians and Lacedaemonians are the bravest of the Greeks, so that Pelops is as a province and Lacedaemonia as a city in that province, that it will then be true that the Peloponnesians and Lacedaemonians are the same in number, because Peloponnesian and Lacedaemonian are not one and the same in number; rather one must be contained under the other, as whole contains part, as Lacedaemonians are contained by Peloponnesians. But if it is not said in this way, it follows or happens that they are stronger even than themselves by turns. This is clear thus: let it be granted that the Lacedaemonians are the strongest; therefore they are stronger than the Peloponnesians. Similarly let it be granted that the Peloponnesians are the strongest; therefore they are stronger than the Lacedaemonians. But if they are stronger than the Peloponnesians, they will be stronger than themselves, and this follows if one is not contained under the other; and this follows from the fact that each is better in fortitude than all the rest apart from itself. Similarly, conversely, the Peloponnesians must be better than the Lacedaemonians if they are not contained apart from themselves; for they too are better than all the rest. Therefore they are better than each other, which is unsuitable.
Manifestum ergo, quoniam id quod in superlativo dicitur, debet esse unum numero, si debet idem ostendi esse simpliciter. Et non probatur per hanc considerationem, quod sit idem id quod optimum et maximum dicitur: quia oportet quod ostendatur, quod sit idem simpliciter quod est idem numero: propter quod etiam Xenocrates non idem esse assignavit sive probavit studiosam et bonam esse vitam, quia utraque maxime est eligenda: quia potest esse unum sub altero, ut contineatur ut bonum sub studioso. Et attendendum quod hoc tempore quando continens et contentum maxime dicitur rationis communis, inferius est ex superiore.
Rursum comparando duo quae idem volumus esse ostendere, comparando tertium potest unum alii idem ostendi: si enim est ad tertium cui alterum duorum est idem, et reliquum eidem tertio sit idem, sequitur quod ipsa invicem sunt idem: quaecumque enim eidem sunt eadem, et ipsa sunt eadem: et si eidem non sunt idem, neque ipsa inter se sunt idem.
Amplius considerandum est ex accidentibus: si enim aliqua duo sunt idem numero et simpliciter, oportet tunc quod quidem accidit uni, accidat et alteri: unde considerandum est in his quae illis accidunt, et etiam in subjectis quibus hoc accidit quae illis accidere dicuntur: nam, sicut diximus, si eadem numero sunt, tunc quaecumque uni eorum accidunt, accidunt et alteri: quia unum est utriusque subjectum: et si aliquo accidentium dissonant, ita quod uni eorum aliquid accidit, quod non alteri, palam est quia non sunt ejusdem subjecti, sed subjecto differunt.
Adhuc autem comparando ea quae videntur eadem ad genus, videndum est si sunt in uno genere vel non, si hoc sit quale, illud autem quantum, vel ad aliquid indicet pro genere: quae enim non sunt ejusdem generis, non erunt idem nomine et diffinitione.
Therefore it is manifest that what is said in the superlative ought to be one in number, if it must be shown to be the same simply. And by this consideration it is not proved that what is called best and greatest is the same, because it must be shown that what is the same in number is the same simply. On account of this Xenocrates also did not assign or prove studious and good life to be the same because each is most choiceworthy, since one can be under the other, as good is contained under studious. And it must be noted that at this time, when containing and contained are most of all said of a common account, the inferior is from the superior.
Again, comparing two things which we wish to show to be the same, by comparing a third, one can be shown to be the same as the other; for if it is to a third to which one of the two is the same, and the remaining one is the same as the same third, it follows that they are the same with each other. For whatever things are the same as the same thing are themselves the same; and if they are not the same as the same thing, neither are they the same among themselves.
Furthermore, one must consider from accidents: for if two things are the same in number and simply, then what happens to one must happen to the other. Hence one must consider in those things which happen to them, and also in the subjects to which this happens which are said to happen to them. For, as we said, if they are the same in number, whatever things happen to one happen also to the other, because one thing is the subject of each; and if they disagree in some accident, so that something happens to one which does not happen to the other, it is plain that they are not of the same subject but differ in subject.
Further, comparing those things which seem the same to genus, one must see whether they are in one genus or not, whether this indicates quality, that quantity, or toward something as genus; for things which are not of the same genus will not be the same in name and definition.
Rursum autem comparando ad genus in motibus, considerandum si utriusque non est idem, sed hoc quidem bonum sive in genere boni, illud autem aliud malum sive in genere mali, quae sunt genera opposita: aut hoc quidem est virtus moralis ad actum ordinata, illud autem scientia, quae sunt genera disparata: tunc enim palam quod non sunt idem quae idem esse dicebantur.
Considerandum etiam si genus quidem duorum sit idem, differentiae autem substantiales constituentes ea non sint idem: tunc enim palam quod non sunt idem quae idem numero et nomine et diffinitione esse dicebantur.
Adhuc autem quando idem genus de utroque praedicatur, sed diversimode acceptum: et si scientia sit illud genus, sed cum scientia duplex est contemplativa et activa quae est prudentia vel ars: de uno autem praedicatur scientia prout est contemplativa, de altero autem prout est activa: tunc enim palam est quoniam non sunt idem quae idem esse dicuntur. Similiter autem considerandum in aliis his similibus quae dicuntur idem secundum quod possunt comparari.
CAPUT II. De considerando magis et minus in terminando idem.
Amplius autem ex magis et minus plures habentur considerationes. Primo quidem, quod si unum duorum quae dicuntur idem, suscipit magis, et alterum non suscipit: aut si ambo ea quae idem dicuntur magis suscipiunt, sed non simul, ita quod quando unum suscipit, et reliquum magis non suscipit: si enim non sic suscipiunt, palam quoniam non idem nomine et diffinitione. Cujus exemplum est, quia non est necessarium quod qui magis amat amore amicitiae, quod etiam magis concupiscat coitum: propter quod etiam sequitur, quod non est idem amor amicitiae quod concupiscentiae coitus.
Amplius ex appositione considerandum, an aliqua sint eadem: si enim idem ad utrumque appositum totum non facit idem, ita quod post appositionem ejusdem totum sit idem sicut prius, palam est quod illa non sunt idem: aut si eodem utrobique ablato, quod relinquitur, non remanet idem, planum est quod illa non sunt idem. Cujus exemplum est, ut si comparentur ad idem utrique additum, ut si dicatur duplum dimidii duplum, et dicatur aliud multiplex esse dimidii, ablato ab utroque eo quod est dimidii, oportet quod duplex et multiplex erunt idem significantia: quia multiplex se habere non potuit ad dimidium nisi in specie multiplicis quae est duplum: nihilominus tamen non sunt idem, quia ablato utroque dicimus, non idem significant, sed unum est species et alterum est genus: quia non sunt idem nomine et diffinitione.
Considerandum iterum ex accidentibus vel praedicatis duobus quae dicuntur idem, si etiam ex uno accidit impossibile per consequentiam, quod non accidit ex reliquo: et non solum hoc considerandum, sed etiam si per hypothesim et positionem alicujus sequitur impossibile ex uno, quod non sequitur ex altero: tunc enim non sunt idem quae esse dicuntur. Hujus exemplum est in hypothesi eorum qui dicunt idem esse vacuum et plenum, sicut vulgus communiter dicere solet: palam enim est, quoniam si de pleno aere exeat aer qui eo erat, adhuc non minus erit vacuum quam prius: sed jam postquam exivit aer, non erit plenum aere: propter quod posito aliquo quod accidit ex uno et non ex reliquo, sive hoc verum sit secundum rem, sive falsum (hoc enim nihil differt quantum ad praesentem intentionem) si ex tali positione alterum eorum quae idem dicuntur interimitur, et alterum non interimitur, oportet quod illa non sunt idem numero vel nomine vel diffinitione.
Again, comparing to genus in motions, one must consider whether the genus of each is not the same, but this one is good or in the genus of good, while that other is evil or in the genus of evil, which are opposite genera; or whether this is moral virtue ordered to act, while that is science, which are disparate genera. For then it is plain that the things which were said to be the same are not the same.
One must also consider whether the genus of two things is indeed the same, but the substantial differences constituting them are not the same; for then it is plain that the things which were said to be the same in number and name and definition are not the same.
Further, when the same genus is predicated of both, but is received in diverse ways, and if science is that genus, but science is twofold, contemplative and active, which is prudence or art, and science is predicated of one as contemplative and of the other as active, then it is plain that the things which are said to be the same are not the same. Similarly one must consider in other similar things which are said to be the same according as they can be compared.
CHAPTER II. On considering more and less in terminating the same.
Furthermore, several considerations are had from more and less. First, that if one of two things which are called the same receives more, and the other does not receive it; or if both things which are said to be the same receive more, but not together, so that when one receives it the remaining one does not receive more, then, if they do not receive it in this way, it is plain that they are not the same in name and definition. The example is that it is not necessary that one who loves more with the love of friendship should also more desire intercourse; on account of which it also follows that the love of friendship is not the same as desire for intercourse.
Furthermore, from apposition one must consider whether some things are the same: for if the same thing appended to each does not make the whole the same, so that after apposition of the same thing the whole is the same as before, it is plain that those things are not the same; or if, when the same thing is removed from each, what is left does not remain the same, it is plain that those things are not the same. The example is if they are compared to the same thing added to each, as if double of half is said to be double, and another multiple is said to be of half; when that which is of half is removed from each, double and multiple would have to be the same in signification, because multiple could not have itself to half except in the species of multiple which is double. Nevertheless they are not the same, because when both are removed we say they do not signify the same thing, but one is species and the other is genus, because they are not the same in name and definition.
Again one must consider from accidents or two predicates which are said to be the same, whether from one there also happens an impossible thing by consequence which does not happen from the other; and not only must this be considered, but also whether through hypothesis and the positing of something an impossible thing follows from one which does not follow from the other. For then the things which are said to be are not the same. The example is in the hypothesis of those who say that void and full are the same, as the common crowd is wont to say. For it is plain that if from full air the air which was in it goes out, it will still be no less void than before; but after the air has now gone out, it will not be full of air. Therefore, when something is posited which happens from one and not from the other, whether this is true according to the thing or false, for this makes no difference as regards the present intention, if from such a position one of those things which are said to be the same is destroyed and the other is not destroyed, those things must not be the same in number or name or definition.
Universaliter autem in omnibus quae idem dicuntur, considerandum est in praedicatis quae quolibet modo substantiali vel accidentali de utroque eorum quae idem dicuntur, praedicantur. Et videndum si alicui dissonet, quod idem praedicetur de uno et de altero, quia tunc interemptum erit quod sint idem: nam si duo sint idem nomine vel diffinitione, quaecumque de uno praedicantur, et de altero: et etiam de quibus subjectis alterum duorum praedicatur, oportet praedicari et reliquum, etc.
CAPUT III. Qualiter interimitur idem numero respiciendo ad modos identitatis.
Amplius autem respiciendo ad modos identitatis interimitur idem numero, ita quod non necesse est esse idem: quoniam enim multipliciter dicuntur aliqua esse eadem (sicut in primo hujus scientiae libro dictum est) considerandum si ea quae dicuntur eadem, secundum aliquem modum alium quam numero eadem sunt: nam genere vel specie eadem non necesse est eadem numero esse: unde considerandum utrum sint eadem numero sic vel non, quae dicuntur esse eadem. Amplius adhuc ad modum identitatis inspiciendo considerandum si potest alterum sine altero esse: si enim sic, constat quod non erunt idem nomine, diffinitione et numero.
Epilogatur ergo dicendo, tanti loci considerationum dicuntur ad idem terminandum et affirmative et negative. Palam autem ex his quae dicta sunt, quod omnes destructivi loci qui sunt ad idem interimendum, utiles etiam per consequens sunt ad diffinitiones interimendas, sicut dictum est. Cujus ratio est, quia si non idem indicet et nomen diffiniti et ratio diffinitiva, palam quod non erit diffinitio quae assignata est pro diffinitione. Constructivorum autem locorum qui sunt ad idem ad construendum, nullus est ad diffinitiones construendas utilis: nam non sufficit ad diffinitionem construendam, quod ostendatur aliquid esse idem id quod est sub ratione diffinitiva et sub nomine diffiniti: ad construendum, inquam, quod haec sit diffinitio: sed ostendendum omnia quae in sexto hujus scientiae libro annumerata sunt, et necessaria sunt ad hoc, scilicet ad diffinitionem cum illo modo quo destructivi loci utiles sunt, sic reducitur problema. Interimere autem diffinitionem (ut in sexto dictum est, et etiam per haec quae hic dicta sunt) tentandum est sive conandum.
But universally in all things which are said to be the same, one must consider the predicates which in any way, substantial or accidental, are predicated of both of those things which are said to be the same. And one must see whether it disagrees with either that the same is predicated of one and of the other, because then it will be destroyed that they are the same. For if two things are the same in name or definition, whatever things are predicated of one are predicated also of the other; and also, of whatever subjects one of the two is predicated, the remaining one must also be predicated, etc.
CHAPTER III. How the same in number is destroyed by looking to the modes of identity.
Furthermore, by looking to the modes of identity, the same in number is destroyed, so that it is not necessary to be the same; for since some things are said to be the same in many ways, as was said in the first book of this science, one must consider whether those things which are said to be the same are the same according to some mode other than number. For things the same in genus or species need not be the same in number; hence one must consider whether those things which are said to be the same are the same in number in this way or not. Further, still by inspecting the mode of identity, one must consider whether one can exist without the other; for if so, it is clear that they will not be the same in name, definition, and number.
Therefore it is epilogued by saying that so many places of considerations are said for terminating the same both affirmatively and negatively. But from what has been said it is plain that all destructive places which are for destroying the same are also consequently useful for destroying definitions, as has been said. The reason is that if the name of the defined thing and the defining account do not indicate the same thing, it is plain that the thing assigned as definition will not be a definition. But of the constructive places which are for constructing the same, none is useful for constructing definitions; for it is not sufficient for constructing a definition that something be shown to be the same as what is under the defining account and under the name of the defined thing, for constructing, I say, that this is the definition. Rather all those things which were enumerated in the sixth book of this science, and are necessary for this, namely for definition, must be shown; with that mode by which the destructive places are useful, the problem is thus reduced. But one must try or endeavor to destroy definition, as was said in the sixth book and also through these things which have been said here.
Notes
- According to that statement, what is said by superabundance belongs to one alone. P. J. (Juxta illud, quod per superabundantiam dicitur, uni soli convenit. P. J.) ↩
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