PRIORUM ANALYTICORUM ARISTOTELIS LIBRI DUO AN. MANL. SEV. BOETIO INTERPRETE.
LIBER PRIMUS.
CAPUT PRIMUM.
De propositione, termino et syltogismo.
Primum dicendum circa quid etde quo estintentio,quoniam circa demonstrationem et de disciplina demonstrativa est.Deindedeterminandum quid propositio, et quid terminus, quid syllogismus, quis perfectus, et quis imperfectus.Postea vero quid est in toto esse, vel non esse hoc in illo,et quid dicimus de omni, aut de nullo praedicari. Propositio ergo est oratio affirmativa, vel negativa alicujus de aliquo. Hæc autem aut universalis,aut particularis,aut indefinita. Dico autemuniversalem quidem, cum aliquid omni, aut nulli inesse; particularem vero, cum aIicui,aut non alicui, aut non omni inesse. Indefinitam autem, cum quid inesse, vel non inesse significat, sive universali, vel particulari, ut contrariorum eamdemessedisciplinam,autvoluptalemnon esse bonum.Differt autem demonstrativa propositio a dialecticajquoniam demonstrativa quidem sumptio alterius partis contradictionis est. Non enim interrogpt,sed sumit, qui demonstrat.Dialectica vero interrogatio, contradictionis est. Nihilautem refertut fiat ex utraque syllogismus; nam et qui demonstrat, et qui interrogat,syllogizat,sumensaliquid de aliquo esse, vel non esse.
THE TWO BOOKS OF ARISTOTLE'S PRIOR ANALYTICS, TRANSLATED BY AN. MANL. SEV. BOETHIUS.
BOOK ONE.
CHAPTER ONE.
On proposition, term, and syllogism.
First it must be said what the subject is and what our inquiry concerns, namely that it concerns demonstration and demonstrative science. Next it must be determined what a proposition is, what a term is, what a syllogism is, which is perfect and which imperfect. After that, what it is to be in the whole, or for this not to be in that, and what we mean by predicating of every or of none. A proposition, then, is a sentence affirming or denying something of something. This is either universal, or particular, or indefinite. I call it universal when something is said to be in every or in none; particular when it is said to be in some, or not in some, or not in every. Indefinite when it signifies that something is or is not, without [specifying] universal or particular, as "contraries are the subject of the same discipline," or "pleasure is not good." A demonstrative proposition differs from a dialectical one, because the demonstrative assumption is of one part of a contradiction. For he who demonstrates does not ask a question but assumes. Dialectical [assumption], however, is an interrogation of a contradiction. It makes no difference, however, that a syllogism be formed from either; for both he who demonstrates and he who interrogates syllogize, assuming something to be or not to be of something.
Quare erit syllogistica quidem propositio,simpliciter affirmatio vel negatio alicujus de aliquosecundum dictummodum.Demonstrativa vero si vera sit,et per primas propositiones sumpta. Dialectica autem percontanti quidem interrogatio contradictionis est, syllogizanti vero sumptio apparentis et probabilis,quemadmodum in Topicis dictum est. Quid est ergo propositio, et quid differt syllogistica a demonstrativa et dialectica, diligentiusquidem in sequentibus dicetur. Ad praesentem veroutilitatem, sufficienter nobis determinata sint, quae nunc dicta sunt. Terminum autem voco, in quem resolviturpropositio,utpraedicatum,et de quo praedicatur, vel apposito, vel separato esse, vel non esse.Syllogismus est oratio in qua, quibusdam positis,aliud quiddam ab his quae posita sunt ex necessitate accidit, eo quod haec sunt. Dico autem eo quod haec sunt, propter hæc accidere. Propter haec vero accidere,est nullius extrinsecus termini indigere,ut fiat necessarium.Perfectum vero voco syllogismum, qui nullius alius indiget, praeter ea quae sumpta sunt,ut appareat necessarium.Imperfectum vero, qui indiget aut unius aut plurinm, quae sunt quidem necessaria per subjectos terminos,non autem sumpta sunt per propositiones. In toto autem esse alterum in altero, et de omni praedicari alterum de altero idem est.
Therefore a syllogistic proposition will be, simply, an affirmation or a negation of something of something in the manner stated. A demonstrative proposition is one that is true and taken through primary propositions. A dialectical proposition, for one who asks, is an interrogation of a contradiction; for one who syllogizes, it is an assumption of what is apparent and probable, as has been said in the Topics. What a proposition is, then, and how the syllogistic differs from the demonstrative and the dialectical, will be said more carefully in what follows. But for present usefulness, let what has now been said be sufficiently determined for us. I call a term that into which a proposition is resolved, as the predicate and that of which it is predicated, with being or not being added or separated. A syllogism is a discourse in which, certain things having been posited, something other than the things posited comes about by necessity because these things are so. I say "because these things are so" means that it comes about on account of these. And "on account of these" means that no external term is needed for the necessity to come about. I call a perfect syllogism one that needs nothing other than the things that have been assumed for the necessity to appear. An imperfect one is that which needs either one or several things that are indeed necessary through the underlying terms, but have not been assumed through propositions. To be in a whole as one thing in another, and for one thing to be predicated of every one of another, is the same.
Dicimus autem de omni praedicari, quando nibil est sumere subjecti, de quo non dicatur alterum, et de nullo similiter.
CAPUT II.
De conversione absolutarum propositionum.
Quoniam autem omnis propositio est, aut de inesse, aut ex necessitate inesse, aut contingere inesse; harum autem,hæ quidem affirmativae, illae autem negativae secundum unamquamque appella. tionem; rursus autem affirmativarum et negativarum,aliae sunt universales,aliae particulares,aliæindefinitae:universalemquidemprivativam deeoquod est inesse, necesse est in terminis converti. Ut si nulla voluptasestbonum,nequebonum nullum, erit voluptas. Praedicativam autem converti quidem necessarium est,non tamen universaliter,sed in parte, ut, si omnis voluptas est bonum,et bonum aliquod voluptas.Particularem autem affirmativam quidem converti necesse est particulariter.Nam si voluptas a:iqua,bonum,et bonum aliquod erit voluptas. Privativam vero non est necessarium. Non enim si homo non inestalicuianimali,etanimal non inestalicui homini.iPrimum ergo sit privativa universalis a propositio, si ereo nulli inest a, neque a nulli inerit b.Nam si alicui inest ut c,non verum erit nullum esse a.Nam eorum quae sunt aliquod est. Si vero omni binest a,et alicui a inest,nam si nulli neque a nulli inerit,sed positum erat omni inesse.
We say that something is predicated of every when there is no subject to take of which the other is not said, and similarly of none.
CHAPTER II.
On the conversion of absolute propositions.
Since every proposition is either of inherence, or of necessary inherence, or of contingent inherence; and of these, some are affirmative and others negative according to each designation; and again, of affirmatives and negatives, some are universal, some particular, some indefinite: the universal privative proposition concerning inherence must be converted in its terms. For if no pleasure is good, neither will any good be pleasure. But the predicative proposition must be converted, not however universally, but in part, as, if every pleasure is good, some good is pleasure. The particular affirmative must be converted particularly. For if some pleasure is good, some good will be pleasure. But the privative one it is not necessary [to convert]. For if man is not in some animal, neither is animal in some man. First, therefore, let the universal privative proposition be, if a is in no b, neither will b be in any a. For if it is in some, as c, it will not be true that a is in none. For it is something of those which are. But if a is in every b, and [is] in some a, for if in none, neither will a be in any, but it was posited to be in every.
Similiter autem etsi particularis est propositio,nam si inest a alicui b,el alicui eorum quae sunt a necesse est inesse; si enim nulli,nec a nulli inerit b. Si autem a alicui eorum quae sunt non inest, non necesse est et alicui a non inesse, ut si quidem sit animal,a vero homo, homo enim non omni animali, animal vero omni homini inest.
CAPUT III.
De conversione propositionum de modo
Eodem autemmodose habebit in necessariis propositionibus, nam universalis quidem privativa universaliter convertitur.Affirmativarum autem utraque particulariter. Nam si necesse est a nulli inesse, necesse est et nulli a inesse; si enim alicui contingit,et a alicui continget. Si autem ex necessitate a omni vel alicui inest, et alicui a necesse est inessse,nam si non ex necessitate inest,neque a alicui ex necessitate fuerit.Particularia vero privativa non convertitur, proptereamdemcausam, propter quam et supra diximus. In contingentibus vero, quoniam multipliciter dicitur contingere,nam et necessarium, et non necessarium,et possibile contingere dicimus; in affirmativis quidem,similitersehabebitsecundua] conversionem in omnibus. Nam siaomniautalicui contingit, et alicui a contingit,si enim nulli, nec a nulli b, ostensum est enim hoc prius.
Similarly, even if the proposition is particular — for if A is present in some B, it is also necessary that it be present in some of the things that are A; for if it were in none, neither would A be present in any B. But if A is not present in some of the things that are B, it is not necessary that it also not be present in some A — as, for instance, if B is animal and A is man; for man is not present in every animal, but animal is present in every man.
CHAPTER III.
On the conversion of modal propositions
The same way of proceeding will hold in necessary propositions; for the universal negative is converted universally, but each of the affirmatives is converted particularly. For if it is necessary that A be present in no B, it is necessary that B be present in no A; for if it were possible for it to be present in some, it would also be possible for A to be present in some. But if A is present in every or in some B by necessity, it is also necessary that B be present in some A; for if it were not present by necessity, neither would A be present in any B by necessity. But the particular negative is not converted, for the same reason that we also stated above. In contingent propositions, however, since "to be contingent" is said in many ways — for we say that both the necessary and the non-necessary and the possible are contingent — in the case of affirmatives the same will hold with respect to conversion in all cases. For if A is contingent of every or of some B, it is also contingent of some A; for if it were of none, neither would A be of any B, for this was shown earlier.
In negativis vero non similiter,sed quaecunque quidem contingere dicuntur, ex eo quod ex necessitate non insunt, vel in eo quod non ex necessitate insunt similiter. Ut si quis dicat hominem contingere non esseequum, aut album nulli tunicæinesse,Horumenim hoc quidem ex necessitate inest, illud vero non ex necessitate inest,et similiter convertitur propositio.Nam si contingit nulli homini equum inesse, etjhominem contingit nulli equo inesse, et si album contingit nulli lunicæ,et tunica. contingit nulli albo, si enim alicuinecessario, etalbumtunicsealicuiinerilex necessitate, hoc enim ostensum est prius. Similiter autem et in particulari negativa.Qucecunque vero ut in pluribus,et in eo quod nata sunt dicuntur contingere secundum quemmodumdeterminamuscontingens, non similiter se habebit in privativis conversionibus.Sed et universalis quidem privativa propositio non convertitur,particularis vero convertitur. Hoc autem erit manifestum quando de contingenti dicemus.Nunc autemnobis tantum sit cur. iisquce dicta sunt, manifestum, quoniam coutingere nulli aut alicui non inesse atfirmativam habet figuram, nam et contingit ipsi est similiter ordinatur.Est autem,quibuscunque adjacens prædicatur,affirmationem semper facit,et omnino, ut:estnon bonum, vel est non album, vel simpliciter,est non hoc.
In negatives, however, it is not similarly so; but all those things that are said to be contingent from the fact that they are not present of necessity, or in that they are not present of necessity, [are related] similarly. For example, if someone says that a man contingently is not a horse, or that white is present in no cloak — for of these, the one is present of necessity, the other is not present of necessity — and the proposition converts similarly. For if it is contingent that no horse is present in a man, it is also contingent that a man is present in no horse; and if it is contingent that white is present in no cloak, it is also contingent that a cloak is present in nothing white. For if it were of necessity present in some white thing, white would also be present of necessity in some cloak; for this was shown earlier. And similarly also in the particular negative. But all those things that are said to be contingent as for the most part and in what they are naturally suited [to be], according to the mode by which we determine the contingent, will not be related similarly in privative conversions. But indeed the universal privative proposition does not convert, whereas the particular one does convert. This, however, will be manifest when we speak about the contingent. For now let it be sufficient for us that, from what has been said, it is manifest that to be contingent that it is present in none or in some not to be present has the figure of an affirmation; for "it is contingent" is also ordered similarly to it. But in all cases where an adjacent predicate is predicated, it always makes an affirmation, and generally, as: "is not good," or "is not white," or simply "is not this.
Ostendetur autem et hoc per sequentia, secundum conversiones autem similiter se habebunt in iis.
CAPUT IV.
De modis syllogisticis et asyllogistis absolutis primas figuræ.
His vero determinatis dicemus jam per quae et quando et quomodo fit omnis syllogismus, postea vero dicendum de demonstratione. Prius enim de syllogismo dicendum quam de demonstratione, eo quod universalior est syllogismus,nam demonstratio quidem syllogismus quidam est; syllogismus vero non omnis demonstratio.Quando igitur tres termini sic se habent ad invicem,ut et postremus sit in toto medio,etrnediusintoto primo vel sit, vel non sit, necesseestextremitatum perfectum esse syllogismum. Voco autem medium quod et ipsum in alio,et aliud in ipso est,quod et positione medium est; extrema vero quod et ipsum in alio, et in quo aliud est. Si enim a de omni b, et de omni c, necesse est a de omni praedicari. Prius enim dictum est quomodo de omni dicimus. Similiter autem est si a de nullo 6, autem de omni c, quoniam a nullic inerit.Si autem primum quidem omni medio consequens est, medium vero nulli postremo, non erit syllogismus extremitatum. Nihil enim necessarium accidit,eo quod haec sunt,nam et omni etnulli contingitprimum postremo inesse, quarenoqueparticulare,neque universale fit necessarium. Cum autem nihil est necessarium,per haec non erit syllogismus.
But this too will be shown through what follows; in conversions, however, they will be related similarly in these.
CHAPTER IV.
On the absolute syllogistic and asyllogistic modes of the first figure.
With these determined, we shall now say through what, when, and how every syllogism comes about; afterwards, however, we must speak of demonstration. For one must speak of syllogism before demonstration, because syllogism is more universal; for demonstration is indeed a kind of syllogism, but not every syllogism is a demonstration. When, therefore, three terms are related to one another in such a way that the last is in the whole middle, and the middle is in the whole first, or is not, it is necessary that there be a perfect syllogism of the extremes. I call the middle that which is itself in another and another in it, and which is also middle by position; the extremes, however, that which is itself in another and in which another is. For if a is predicated of every b, and of every c, it is necessary that a be predicated of every c. For it was said earlier how we say "of every." Similarly, if a is of no b, but of every c, then a will be in no c. If, however, the first follows every middle, but the middle [follows] no last, there will be no syllogism of the extremes. For nothing necessary results from the fact that these are so; for it is possible for the first to be in the last both universally and in no case, so that neither particular nor universal becomes necessary. But when nothing is necessary, there will be no syllogism through these.
Termini vero ejus quod est omni inesse, animal,homo,equus; ejus vero quod est nulli,animal, homo, lapis. Quando vero nec primum medio, nec medium postremo ulli inest,nec sic eritsyllogismus. Termini vero ut inesse, scientia, linea, medicina; ut non inesse, scientia, linea,unitas.Universalibus igitur existentibusterminis,manifestum est in hac figura quando erit,et quando non erit syllogismus, et quoniam cum est syllogismus, necessarium est terminos sic se habere, ut diximus, et sic se habens manifestum quoniam erilsyllogismus.Si autem hic quidem terminorum uni'lersaliter,alius vero particulariterad alium,quando universale quidem ponitur ad majorem extremitatem vel prædicativum,vel privativum,parHculare vero ad minorem praedicativum, necesse est syllogismum esse perfectum. Quando vero ad minorem vel quolibet modo alitersebabeant termini,impossibile est.Dico autem majorem extremitatem quidem in qua medium est, minorem vero, quae sub medio est. Insit enirn a quidem omni b, autem alicui c, ergo si est de omni praedicari, quod in principio dictum est,necesse est a alicui inesse. Et si a quidem nulli inest, vero alicui c, necesse est a alicui non inesse,determinatum est enim et de nullo, quomodo dicimus,quare erit syllogismus perfectus. Similiter autem et si indefinitum sit c. praedicativum,nam idem erit syllogismus in.
The terms for belonging to every are animal, man, horse; for belonging to none, animal, man, stone. But when neither the first term belongs to the middle nor the middle to the last, there will be no syllogism even so. The terms for belonging are knowledge, line, medicine; for not belonging, knowledge, line, unity. So when the terms are universal, it is clear in this figure when there will and when there will not be a syllogism, and that when there is a syllogism the terms must be related as we have said, and that when they are so related it is clear that there will be a syllogism. But if one of the terms is universal in relation to the other and the other particular, when the universal is posited in relation to the major extreme, whether predicative or privative, and the particular in relation to the minor as predicative, there must be a perfect syllogism. But when they are related to the minor in any other way, it is impossible. I call the major extreme that in which the middle is, and the minor that which is under the middle. For let A belong to every B, and to some C; then, if to be predicated of every is as was said at the beginning, it is necessary that A belong to some C. And if A belongs to no B, but to some C, it is necessary that A not belong to some C; for it has been determined also concerning belonging to none, as we say. Therefore there will be a perfect syllogism. Similarly also if C is indefinite as predicative, for the same syllogism will result in
definito et particulari sumpto.Si autem ad minorem extremitatem universaleponatur vel praedicativum, vel privativum, non erit syllogismus neque cum affirmativa, neque negativa, neque indefinita, neque particularis sit,ut si a quidem alicui inest,vel non inest, autem omni inest. Termini ut inesse, bonum, habitus, prudentia: ubi non inesse, bonum, habitus,indisciplina.Rursum si quidem nulli c, a vero alicui inest, vel non inest,vel non omni inest, nec sic eritsyllogismus.Terminiomniinesse,album, equus,cygnus; nulli inesse,album, equus, corvus. Idem autem et si ab indefinitum sit. Nec quando ad majorem extremitatem quidem univarsaIe ponatur vel prædicativum,vel privativum,ad minorem vero particulare privativum, non eritsyllogismus vel indefinito, vel particulari sumpto. Velut si a quidem omni inest, autem alicui non inest, vel non omni inest. Cui enim alicui non inest medium, hoc omne et nullum sequatur primum. Ponantur enim termini,animal, homo, album, deinde et de quibus albisnonpraedicaturhomo,sumantur cygnusetnix; ergo animal de uno quidem omni praedicatur, de alterovero nullo, quare non erit syllogismus.Rursum a quidem nulli insit, autem alicui non insit, et sint termini, inanimatum,homo,album, deinde sumantur alba, de quibus non praedicatur homo, cygnus et nix; nam inanimatum de hoc quidem,omni prædicatur, de illo vero nullo.
when the definition is taken with a particular term. But if a universal is placed at the minor extreme, whether affirmative or privative, there will be no syllogism, neither when it is affirmative nor when it is negative, nor when it is indefinite nor when it is particular—as, for instance, if A belongs to some one, or does not belong, while B belongs to every one. The terms for belonging are good, habit, prudence; for not belonging, good, habit, indiscipline. Again, if it belongs to no C, while A belongs to some one, or does not belong, or does not belong to every one, not even so will there be a syllogism. The terms for belonging to every one are white, horse, swan; for belonging to none, white, horse, crow. The same holds also if AB is indefinite. Nor when a universal is placed at the major extreme, whether affirmative or privative, but a particular privative at the minor, will there be a syllogism, whether the term is taken as indefinite or as particular—for example, if A belongs to every one, while B does not belong to some one, or does not belong to every one. For whatever the middle term does not belong to as some one, the first term follows both as belonging to every one and as belonging to none. For let the terms be animal, man, white; then let swan and snow be taken as the whites of which man is not predicated. Therefore animal is predicated of one of them as of every one, but of the other as of none; wherefore there will be no syllogism. Again, let A belong to none, while B does not belong to some one; and let the terms be inanimate, man, white; then let swan and snow be taken as the whites of which man is not predicated. For inanimate is predicated of the one as of every one, but of the other as of none.
Amplius: quoniam indefinitum est alicui eorum quae suntc non inesse b, verum est autem'et nulli inest,et si non omni,quoniam alicui non inest, sumptis autem his terminis velut nulli inesse, non fit syllogismus (hoc enim dictum est prius)manifestum;ergo estquoniam in eo quod sic se habent termini non erit syllogismus, esset enim et in his. Similiter autem ostendetur, et si universale ponatur privativum.Neque enim si ambo intervalla particularia prsedicative,vel privative dicantur,aut hoc quidem praedicativum,illud vero privativum,vel hoc quidemindefinitum,iHud verodefinitum, vel ambo indefinita, non erit syllogismus nullo modo.Termini vero communes omnium,animal,album,equus,animal,album,lapis.Manifestum est igitur ex iis quas dicta sunt quoniam si sit syllogismus in hac figura particularis,quoniam necesse est terminos sic se habere, ut diximus. Aliter enim sehabentibus,nullo[modo]fit.Palam autem quoniam omnes qui in hac sunt syllogismi perfecti sunt,omnes enim perficiuntur pcreaquæ ex principio sumuntur, et quoniam omnia problemataostenduntur perhanc figuram; etenim omni et nulli, alicui et non alicui inesse. Voco autem hujusmodi figuram,primam.
Further: since "not to be present to some of the things that are b" is indefinite, and it is true both that it is present to none and, if not to every one, that it is not present to some, yet when these terms are taken as though it were present to none, no syllogism results (for this was said earlier), it is clear; therefore it is evident that when the terms are disposed in this way there will be no syllogism, for otherwise there would be one in these cases too. In the same way it will be shown also if a universal is posited as privative. For neither if both intervals are stated as particular, whether predicatively or privatively, or this one predicative and that one privative, or this one indefinite and that one definite, or both indefinite, will there be a syllogism in any way. The terms common to all these are: animal, white, horse; animal, white, stone. It is evident, then, from what has been said that if there is a syllogism in this figure with a particular conclusion, the terms must be disposed as we have said. For when they are disposed otherwise, no syllogism results in any way. It is clear also that all the syllogisms in this figure are perfect, for they are all completed through the things assumed from the beginning, and that all problems are proved through this figure: namely, that something is present to all, to none, to some, and not to some. I call a figure of this kind the first.
CAPUT V.
De syllogismis absolutis in secunda figura.
Quando vero idem huic omni quidem, illi vero nulli inest,vel utique omni,vel nulli, figuram quidem hujusmodi voco secundam.Medium autem in hac dico quod de utraque praedicatur; extremitates vero de quibus dicitur hoc,majorem quidemextre- I mitatem, quae juxta medium posita est, minorem vero, quæ longius sita est a medio. Ponitur autem medium foras quidem extremitatum,primum vero positione.Perlectus igilur non erit syllogismus nullo modo in hac figura possibile vero erit et universalibus, et non universalibus existentibus terminis. Universalibus igitur terminis erit syllogismus quando medium huic quidem omni,illi vero nulli ir.erit, etsi ad utrumvis si privativum, aliter vero nullo modo. Prædicetur enim de quid em nullo,de vero omni, quoniam igitur convertitur privativa, nulli in inerit n,at omni supponebatur,quare nulli inerit: hoc enim ostensum est prius.Rursum si quidem omni inest,x vero nulli, neque nulli inerit. Nam si nulli x,nequex nulli inerit,at vero omni inerat,quare nulli inerit. Facta est enim rursum prima figura.Quoniam autem convertiturprivativum neque nulli inerit, quare erit idem syllogismus, est autem ostendere haec et ad impossibile ducentes.
CHAPTER V.
On absolute syllogisms in the second figure.
But when the same term is present to all of one and to none of the other, or to all of either, or to none, I call this kind of figure the second. In it I call the middle term that which is predicated of both; and the extremes are the things of which this is said — the major extreme being the one placed next to the middle, and the minor the one situated farther from the middle. The middle is placed outside the extremes, and is first in position. Therefore there will be no syllogism at all in this figure; but it will be possible when the terms are both universal and non-universal. With universal terms there will be a syllogism when the middle is present to all of one and to none of the other, and whether the privative term is taken toward either one; otherwise in no way. For let it be predicated of none of one and of all of the other: since the privative proposition converts, it will be present to none of that term of which it was supposed to be present to all; wherefore it will be present to none. For this was shown earlier. Again, if it is present to all of one and to none of the other, it will be present to none of that other. For if it is present to none of x, neither will x be present to any; but it was present to all; wherefore it will be present to none. For the first figure has again been produced. But since the privative proposition converts, it will be present to none; wherefore the syllogism will be the same. It is also possible to demonstrate these things by leading to the impossible.
Quoniam ergo fit syllogismus sic se habentibusterminis manifestum, sed non pertectus,non enimsolum ex iis quae ab initio sumpta sunt, sed ex aliis perficitur necessarium. Si autem de omni et praedicetur, non erit syllogismus. Termini inesse, substantia, animal, ratio; non inesse, substantia, animal, lapis, medium, substantia. Nee quando de nec de nullo praedicatur m.Termini inesse, linea, animal, homo"; non inesse, linea,animal,lapis. Manifestum ergo quoniam si fit syllogismus ex universalibus lerminis,necesse est terminos sic se habere, ut in principio diximus. Aliter enim sehabentibus terminis non fit conclusio necessaria. Si autem ad alterum sit universaliter medium,quando ad majus quidem fuerit universaliter vel praedicative, vel privative,ad minusautem est particulariter,et oppositae universali (dico autem oppositae,si universale quidem privativum particulare preedicativum, vel si universale prasdicativum, particulare privativurn), necesseestsyliogismumfieri privativum particulariter. Nam;si nulli quidem II, autem alicui irest, necesse estnaIicui non inesse.Quoniam enim convertitur privativum,nulli inerit, vero supponebatur alicui inesse, quare alicui eorum quae sunt non inerit.Fit enim syllogismus per primam figuram.
Therefore it is evident that a syllogism comes about when the terms are so related, but not a perfect one; for it is completed as necessary not only from the things assumed at the outset but also from other things. But if the middle term is predicated of all, there will not be a syllogism. Terms for belonging: substance, animal, reason; for not belonging: substance, animal, stone—the middle term being substance. Nor when it is predicated of neither, nor of none, is there a syllogism. Terms for belonging: line, animal, man; for not belonging: line, animal, stone. It is evident, therefore, that if a syllogism comes about from universal terms, the terms must be so related as we said at the beginning. For when the terms are otherwise related, no necessary conclusion comes about. But if the middle term is universal in relation to one of the extremes—when it is universal, either affirmatively or privatively, in relation to the greater, but particular in relation to the lesser, and opposite to the universal (I call it opposite to the universal if the universal is privative and the particular affirmative, or if the universal is affirmative and the particular privative)—then a privative syllogism in particular must come about. For if M belongs to no N, but to some O, it is necessary that N not belong to some O. For since the privative proposition converts, N will belong to no M; but M was supposed to belong to some O; therefore it will not belong to some of those which are O. For the syllogism comes about through the first figure.
Rursus si quidem omni m, vero alicui non inest,necesse est alicui non inesse.Nam si omni in est n, prædicatur autem et de omni necesse est omni inesse,supponebatur autem alicui non inesse. Et si omni quidem inest, autem non omni,erit syllogismus,quoniam non omni inest n. Demonstratio autem eadem. Si autem de quidem omni, de vero non omni praedicatur m, non erit syllogismus.Termini inesse,animal,substantia,corvus.Non inesse, animal,aIbum,corvus. Nec quando de quidem nullo, de vero aliquo.Termini inesse, animal, substantia, lapis. Non inesse, animal, substantia,scientia. Quando igitur oppositum est universate particulari, dictum est quando erit,et quando non erit syllogismus.Quando autem similis figurae fuerint propositiones,ut ambæ privativæ vel affirmativæ,nullo modo erit syllogismus.Sint enim primum privativae, et universale ponatur ad majorem extremitatem,ut quidem nulli,x autem alicui non insit;contingit ergo et omni,et nulli inesse n. Termini quidem nulli inesse,nigrum,nix,anima!. Omni vero inesse,non est sumere, si alicui quidem inest, alicui autem non.Nam si omni inest n, et nulli, etiam na nulli inerit; sed positum erat alicuiinesse, non igitur sic sumere contingit terminos. Ex indefinito autem ostendendum est.
Again, if it is present in all of m but not in some, it is necessary that it not be present in some. For if n is present in all, and it is predicated also of all, it is necessary that it be present in all; but it was supposed that it is not present in some. And if it is present in all but not in all, there will be a syllogism that n is not present in all. The demonstration is the same. But if m is predicated of all but not of all, there will not be a syllogism. Terms for being present: animal, substance, crow. For not being present: animal, white, crow. Nor when it is predicated of none but of some. Terms for being present: animal, substance, stone. For not being present: animal, substance, knowledge. Therefore, when the opposite is universal to a particular, it has been stated when there will be a syllogism and when there will not be. But when the propositions are of similar figure, as when both are privative or both affirmative, in no way will there be a syllogism. For let them first be privative, and let the universal be posited at the major extreme, so that it is present in none, but x is not present in some; it happens, then, that n is present in all and in none. Terms for being present in none: black, snow, animal. But for being present in all, it is not possible to take terms, if it is present in some but not in some. For if n is present in all and in none, then n will also be present in none of a; but it was posited that it is present in some; therefore it is not possible to take terms in this way. But it must be shown from the indefinite.
Quoniam enim verum est non inesse alicui x,et si nulli inest, nulli vero cum insit non erit syllogismus, manifestum quoniam neque nunc erit.Rursum sipraedicativae, et universale ponatur similiter,ut omni quidem n. autem alicui insit,contingit ergo et omni,et nulli inesse. Termini nulli inesse,album, cygnus, lapis. Omni vero non erit sumere terminos,propter eamdem causam qucem et prius, sed ex indefinito monstrandum est.Si autem universale ad minorem extremitatem est, et quidem nulli, vero alicui non inest, contingit n, et omni et nulii inesse. Termini inesse,album,animal, corvus; non inesse, album,lapis, corvus.Similiter aulem et si praedicativee fuerint propositiones. Termini non inesse, album, animal, nix; inesse, album, animal, cygnus. Manifestum est igitur quoniam si si milis figuræ sint propositiones, et haec quidem universalis, illa vero. particularis, quoniam nullo modo fit syllogismus. Sed nec si alicui, utrique inest, vel non inest, vel huic quidem inest, illi vero non, vel neutri omni, vel indefinitas.Termini autem communes omnium, album,animal, homo,album, animal, inanimatum.
For since it is true that it is not present in some x, and if it is present in none, but when it is present in none there will be no syllogism, it is clear that neither will there be one now. Again, if the propositions are affirmative, and the universal is posited similarly—for example, that n is present in all, but in some—it follows that it can be present in all and in none. The terms for being present in none: white, swan, stone. But for being present in all it is not possible to take terms, for the same reason as before, but it must be shown from an indefinite term. If, however, the universal is in relation to the lesser extreme, and it is present in none, but is not present in some, it follows that n can be present in all and in none. The terms for being present: white, animal, crow; for not being present: white, stone, crow. Similarly also if the propositions are affirmative. The terms for not being present: white, animal, snow; for being present: white, animal, swan. It is clear, therefore, that if the propositions are of such a figure, and one of them is universal while the other is particular, in no way does a syllogism come about. But neither if it is present in some, in both, or is not present, or is present in this one but not in that, or in neither universally, or indefinitely. The common terms for all these: white, animal, man; white, animal, inanimate thing.
Manifestum est igiturex prædictis quoniam si sic se habent termini ad invicem, ut dictum est, fit syllogismus ex necessitate, et si syllogismus, necesse est terminos sic se habere.Palam autem et quoniam omnea imperfecti sunt,qui in hac figura sunt syllogismi:omnes enim perficiuntur assumptis quibusdam,quae vel insunt terminis ex necessitate, vel ponunturvelut hypotheses, ut quando pec impossibile ostendimus. Et quoniam non fit affirmativus syllogismus per hanc figuram, sed omnes privativi, et universales, et particulares.
CAPUT VI.
De syllogismis absolutis tertiæ figuræ.
Si autem eidem hoc quidem omni,iJJud vero nulli inest,vel ambo omni vel nulli, figuram quidem bujusmodi voco tertiam. Medium autem in hac dico, quo ambo prædicamus;extremitates vero,quse praedicantur;majorem autem extremitatem,quæ longius est medio; minorem vero, quae propius. Ponitur autem medium foras quidem extremitat,um,ultimum vero positione est. Perfectus igitur non fit syllogismus, nec in hac figura, possibilis vero erit et universa liter, et non universaliter terminis existentibus ad medium. Universaliter quidem quando et et inerunt omni s, quoniam alicui inerit ex necessitate, nam quoniam convertitur praedicativa, inerit alicui r. Quare quoniam inest omni s, et alicui t', necesse est alicui inesse.Fit enim syllogismus per primam figuram.
From the foregoing, then, it is evident that if the terms are related to one another as has been said, a syllogism follows of necessity, and if there is a syllogism, the terms must be so related. It is also clear that all the syllogisms in this figure are imperfect; for they are all made perfect by assuming certain things which either belong to the terms of necessity or are posited as hypotheses, as when we prove by reductio ad impossibile. And it is clear that no affirmative syllogism is produced through this figure, but all are privative, both universal and particular.
CHAPTER VI
On the absolute syllogisms of the third figure.
But if one term belongs to the whole of the same subject and the other to none of it, or both to the whole or both to none, I call this kind of figure the third. In it I call the middle term that of which we predicate both; the extremes, those which are predicated; the major extreme, that which is further from the middle; the minor, that which is nearer. The middle is placed outside the extremes, and is last in position. An imperfect syllogism, then, is not produced in this figure either, but one will be possible both universally and non-universally when the terms are related to the middle. Universally, when both belong to the whole of s, because it will of necessity belong to some; for since the affirmative proposition is convertible, it will belong to some of r. Therefore, since it belongs to the whole of s and to some of t, it is necessary that it belong to some. For the syllogism is produced through the first figure.
Est autem et perimpossibile, et expositione facere demonstrationem: si enim ambo omni insunt,si sumatur aliquod eorum quae sunt s, ut huic et et inerunt ex necessitate, quare alicui ineritp. Et si omni quidem s, autem nulli inest, erit syllogismus, quoniam alicui non inerit ex necessitate. Nam idem modus erit demonstrationis, conversa propositione. Ostendetur autem et per impossibile,quemadmoduminprioribus.Si autem insit r,squidem nulli, vero omni s,non erit syllogismus.Termini inesse, animal, equus, homo; non inesse, animal, inanimatum, homo, neque quando ambo de nullo dicuntur, non erit syllogismus. Termini inesse, animal, equus, inanimatum; non inesse,homo, equus inanimatum, medium, insuimatum.Manifestum est igitur et in hac figura etquando erit,et quando non erit syllogismus ex universalibus terminis. Quando enim ambo termini sunt prædicativi,erit syllogismus, quoniam inest alicui extremitas extremitati;quando vero privativi,non erit syllogismus; quando autem hic quidem privativus,ille vero affirmativus;si major quidem fuerit privativus,alter vero affirmativus erit syllogismus,quoniam alicui non inest extremitas extremitati.
It is also possible to make a demonstration through the impossible and by exposition. For if both terms belong to every S, then if some one of the things that are S is taken, both will belong to it of necessity, and therefore P will belong to some. And if S belongs to every, but P to none, there will be a syllogism that P does not belong to some of necessity. For the same mode of demonstration will hold, with the proposition converted. It will also be shown through the impossible, as in the earlier cases. But if R belongs to no S, while P belongs to every S, there will be no syllogism. Terms for belonging: animal, horse, man; for not belonging: animal, inanimate, man. Nor, when both are said of nothing, will there be a syllogism. Terms for belonging: animal, horse, inanimate; for not belonging: man, horse, inanimate; middle term: inanimate. It is evident, therefore, in this figure too both when there will and when there will not be a syllogism from universal terms. For when both terms are predicative, there will be a syllogism, because one extreme belongs to some of the other; but when they are privative, there will be no syllogism. When, however, one is privative and the other affirmative, if the major is privative and the other affirmative, there will be a syllogism that one extreme does not belong to some of the other.
Si autem e converso, non erit.Si autem hic quidem situniversaliter ad medium, alter vero particulariter, si uterque sit praedicativus, necesse et fieri syllogism am, et si alteruter sit universalis terminorum; nam si omni insit,p vero alicui s, necesse est et alicui inesse, nam quoniam convertituraffirmativa, inerits alicui p,quare quoniam omni inest, autem alicui p; et alicui inerit, quare et alicui r. Rursum si alicui s, vero omni insit, necesse est et alicui inesse, nam idem modus demonstrationis.Est autem demonstrare et per impossibile, et expositione, quemadmodum in prioribus.Si autem unus quidem sit prædicativus,alius vero privativus,universaliter autem praedicativus, quando minor quidem fuerit praedicativus,erit syllogismus; nam si omni s, vero alicui non inest, necesse est alicui non inesse, si enim omni r, et omni s, et omni inerit, sed non inerat.Monstratur autem et sine deductione, si sumatur aliquid eorum quae sunt s, cui non inest. Quando vero major fuerit prasdicaticus, non erit syllogismus, ut si insit omni s, aulem alicuis non insit.Terminivero omniinesse,animatum; homo, animal.
But if the conversion is made, there will be no syllogism. If, however, one term is universal in relation to the middle and the other particular, and both are affirmative, a syllogism necessarily comes about even if either of the terms is universal; for if A belongs to every B and B to some C, then A necessarily belongs to some C. For since the affirmative converts, B will belong to some A; and therefore, since A belongs to every B and B to some A, A will belong to some A. Again, if B belongs to some C and A to every B, then A necessarily belongs to some C; for the same manner of demonstration applies. It is also possible to demonstrate through the impossible and by exposition, as in the earlier cases. But if one term is affirmative and the other privative, and the affirmative is universal, a syllogism will occur when the minor is affirmative; for if A belongs to every B and B does not belong to some C, A necessarily does not belong to some C. For if A belongs to every C and to every B, then B will belong to every C, but it did not. It is also proved without deduction if some one of the things that are C is taken, to which B does not belong. But when the major is affirmative, there will be no syllogism, as if A belongs to every B and A does not belong to some C. Terms of belonging to every: animal, man.
Nulli vero,non est sumere terminos si inest alicui quidem s,alicui autem non.Si enim omni inest p, autem alicui s,et inerit alicuir, sed positum eratnullir inesse.Sed quemadmodum in prioribus dicendum est; nam cum indefinitum est alicui non inesse, et quod nulli inest, verum est dicere alicui non inesse,nulli vero cum inesset,non erat syllogismus; manifestum ergo est.quoniam non erit syllogism us.Si autem privativus sit universalis terminus, quando major quidem privativus fuerit, minor autem prædicativus,erit syllogismus:Si enim nulli s, autem alicui inest s, et alicui non inerit. Rursum enim prima erit figura, propositione conversa.Quando autem minor fuerit privativus, non erit syllogismus. Termini inesse, animal, homo, ferum. Non inesse, animal, scientia, ferum,medium in utrisqueferum.Nec quando ambo privativi ponuntur,est autem unus quidem universalis, alter vero particularis. Termini inesse, quando minor est universalis ad medium,animal,homo,ferum, non inesse, animal, scientia, ferum. Quando autem major, non inesse quidem, corvus, nix, album; inesse vero non est sumere si alicui quidem inest s,alicui autem non inest.Si enim omnis rinsit, autem alicui s, et inerit alicui s. Positum est autem nulli, sed ex indefinito monstrandum est.
But for "no one," it is not possible to take terms if it is present in some and not in some. For if P is present in every S, and in some S, it will also be present in some, but it was posited to be present in none. But as must be said in the earlier cases; for when "not to be present in some" is indefinite, it is also true to say that what is present in none is not present in some; but when it was present in none, there was no syllogism; it is clear, therefore, that there will be no syllogism. But if the universal term is privative, when the major is privative and the minor affirmative, there will be a syllogism. For if it is present in no S, and is present in some S, it will also not be present in some. For again there will be the first figure, with the proposition converted. But when the minor is privative, there will be no syllogism. Terms for "to be present": animal, man, wild. For "not to be present": animal, knowledge, wild; the middle in both is wild. Nor when both are posited as privative, but one is universal and the other particular. Terms for "to be present," when the minor is universal in relation to the middle: animal, man, wild; for "not to be present": animal, knowledge, wild. But when the major is [universal], for "not to be present": crow, snow, white; but for "to be present" it is not possible to take terms if it is present in some and not present in some. For if R is present in every [S], and in some S, it will also be present in some S. But it was posited to be present in none, but this must be shown from the indefinite.
Neque si uterque alicui medio inest, vel non inest vel unus quidem inest, alter vero non inest, vel hic quidem alicui, ille vero non omni, vel indefinite, nullo modoeritsyllogismus.Termini autem communes omnium, animal, homo, album, animal, inanimatum, album. Manifestum est igitur, et in hac figura, quando erit, et quando non erit syllogismus, et quoniam habentibus se terminis, ut dictum est, fit syllogismus ex necessitate, et si sit syllogismus, necesse est terminos sic se habere. Manifestum est etiam,quia omnes imperfecti sunt in hacfigurasyllogisrni, omnes enim perficiuntur quibusdam assumptis.Et quoniam syllogizare universale per hanc figuram non erit, neque privativum,neque affirmativum.
CAPUT VII.
De tribus figuris et indirectis syllogismus ad invicem.
Palam autem et quoniam in omnibus figuris, aliquando nonfitsyllogismus.Cum prsedicativiquidem, vel privativi sunt utrique termini, et particulares, nihil omnino fit necessarium. Cum autem prædicativus,et privativus,et universalitersumptus privativus,semper fit syllogismus minoris extremitatis ad majorem,ut si a quidem omni vel alicui, autem nulli c; conversis enim propositionibus, necesse est alicui a non inesse.
Nor, if both are present in some middle term, or one is present and the other is not, or one is present in some and the other not in all, or indefinitely—in no way will there be a syllogism. The common terms for all these are: animal, man, white; animal, inanimate, white. It is clear, then, also in this figure, when there will and when there will not be a syllogism, and that when the terms are related as has been said, the syllogism follows of necessity, and if there is a syllogism, the terms must be so related. It is also clear that all the syllogisms in this figure are imperfect, for all are completed by certain assumptions. And that it is not possible to syllogize a universal through this figure, neither privative nor affirmative.
CHAPTER VII.
On the three figures and the indirect syllogisms in relation to one another.
It is also evident that in all the figures sometimes no syllogism results. When both terms are predicative or both privative, and particular, nothing at all follows of necessity. But when one is predicative and the other privative, and the privative is taken universally, there is always a syllogism from the minor extreme to the major, as if A belongs to every or some B, but to no C; for with the propositions converted, it is necessary that A not belong to some C.
Similiter autem et in aliis figuris, semper enim fit per conversionem syllogismus.Palam etiam quoniam indefinitum pro praedicativo particulari positum,eumdem2faciet syllogismum in omnibus figuris.Manifestum autemet quoniam omnes imperfecti syllogismi perficiuntur per primam figuram. Aut enim ostensive, aut per impossibile clauduntur omnes. Utrinque autem fit prima figura.Etostensive quidem perfectis,quoniam per conversionem claudebantur omnes, conversio autem primam faciebatfiguram,perimpossibilevero demonstratis, quoniam posito falso syllogismus fit. per primum figuram. Ut in postrema figura, si a et omni insunt, quoniam a alicui inest, nam si nulli et omni c, nulli inerit a, sed inerat omniSimiliter autem in aliis. Est etiam reducere omnes syllogismos ad universales syllogismos primae figuræ. Nam qui sunt in secunda figura, manifestum quoniam per illos perficiuntur,verum non similiteromnes, sed universales quidem privativa conversa; particulariumautem utraque per ad impossibile reductionem. Qui vero in prima sunt particulares, perficiuntur quidem per se.Est autem et per secundam figuram ostendere ad impossibile ducentes, ut si a omni 6, et alicui c, quoniam a alicui a inerit. Si enim nulli, autem omni, nulli inerit b.
Similarly also in the other figures, for the syllogism always comes about through conversion. It is also clear that an indefinite term, put in place of a particular affirmative, will produce the same syllogism in all the figures. It is also evident that all imperfect syllogisms are perfected through the first figure. For all are concluded either ostensively or through impossibility. And in either way the first figure comes about. For those perfected ostensively, because they were all concluded through conversion, and conversion produced the first figure; and for those demonstrated through impossibility, because when a falsehood is posited, the syllogism comes about through the first figure. As in the last figure, if A belongs to all and to some, that A belongs to some; for if it belongs to none and to all C, A will belong to none, but it did belong to all. Similarly also in the others. It is also possible to reduce all syllogisms to the universal syllogisms of the first figure. For those in the second figure, it is clear that they are perfected through those, though not all similarly, but the universals through the conversion of the privative premise; of the particulars, however, each through reduction to impossibility. But the particulars in the first figure are perfected through themselves. It is also possible to show through the second figure those that lead to impossibility, as if A belongs to all B and to some C, that A will belong to some B. For if it belongs to none, and to all B, B will belong to none.
Hoc enim scimus per secundum figuram.Similiter autem et in privativo erit demonstratio; si enim a nulli £, et alicui inest, a alicui non erit, nam si a omni c, autem nulli inest, nulli inerit b. Hæc autem fuit media figura;quarequoniam qui inmedia sunt syllogismi,ornnesreducunlur in primse figurae I universales syllogismos, qui vero particulares sunt in prima, ad eos qui sunt in media, manifestum est quoniam et particulares reducentur ad eos qui in prima figura sunt universales syllogismos; qui vero sunt in tertia,cum universales sint quidem termini, statim perficiuntur per illos syllogismos. Si autem particuIares,sumuntur perparticularessyllogismos primæ figurae, sed hi reducti sunt ad illos, quare et tertiae figuræ particulares.Manifestum ergo quoniamomnes reducentur in primae figurae universales syllogismos. Igitur syllogismi inesse vel non inesse ostendentes,dictum est quomodo se habent, et ad eos qui ex eadem sunt figura, et ad invicem, et ad eos qui ex aliis sunt figuris.
For we know this through the second figure. Similarly, the demonstration will also hold in the privative case; for if a belongs to no c, and to some [c], a will not belong to some [c]; for if a belongs to every c, but [b] belongs to none, b will belong to none. But this was the middle figure; wherefore, since the syllogisms that are in the middle [figure] are all reduced to the universal syllogisms of the first figure, while those that are particular in the first [figure] are reduced to those that are in the middle, it is clear that the particular [syllogisms] also will be reduced to the universal syllogisms that are in the first figure; and those that are in the third [figure], when the terms are universal, are immediately completed through those syllogisms. But if they are particular, they are taken up through the particular syllogisms of the first figure, but these have been reduced to those; wherefore also the particular [syllogisms] of the third figure. It is clear, therefore, that all are reduced to the universal syllogisms of the first figure. So, how the syllogisms showing belonging or not belonging stand, both in relation to those that are from the same figure, and to one another, and to those that are from other figures, has been stated.
CAPUT VIII.
De syllogismis ex necessario in tribus figuris.
Quoniam autem diversum est inesse,et ex necessitate inesse,et contingere inesse(nammultainsunt quidem, non tamen ex necessitate, alia vero neque ex necessitate, neque insunt omnino, contingit autem inesse),manifestum quoniam et syllogismus in unoquoque horum diversus est,el non similiterhabentibus se terminis,sed hic quidem ex necessariis, ille vero ex iis quae simpliciter insunt,ille autem ex contingentibus.Ergoin necessariisquidem fere similiter se habet, et in iis qui insunt. Similiter enim positis terminis, et in iii quae insunt, et in iis quae ex necessitate insunt vel non insunt, et erit, at non erit syllogismus. Verum distabit in eo quod adjacet terminis ex necessitate inesse, vel non inesse,nam et privativum similiter convertitur, et in toto esse, et de omni similiter assignabimus.F.rgo in aliis quidem eodem modo ostendetur per conversionem, quoniam conclusio necessaria, quomodo in eo quod est inesse.In media autem figura quandofuerit universalis affirmativa, particularis vero privativa, et rursum in tertia quando universalis q'udem praedicativa, particularis vero privativa,non similiter erit demonstratio, sed necesse est exponentes, cui alicui utrumquenon inest,dehoc facere syllogismum. Erit enim necessarius in hoc.
CHAPTER VIII.
On syllogisms from necessity in the three figures.
Since being present, being present of necessity, and being present contingently are different (for many things are present but not of necessity, while others are neither of necessity nor present at all, yet contingently present), it is clear that the syllogism in each of these cases is also different, and not the same when the terms are disposed alike, but one is from necessary [premises], another from those which are present simply, and another from contingent [premises]. Therefore in the case of necessary [premises] the situation is much the same as in those which are present. For with the terms posited similarly, both in those which are present and in those which are present or not present of necessity, there will and will not be a syllogism. But there will be a difference in that necessity of being present or not being present attaches to the terms; for the privative [premise] is converted similarly, and we shall assign being in the whole and predicated of every [term] similarly. Therefore in the other cases it will be shown in the same way through conversion that the conclusion is necessary, as in the case of being present. But in the middle figure, when the universal [premise] is affirmative and the particular is privative, and again in the third when the universal is predicative and the particular is privative, the demonstration will not be similar, but it is necessary, by setting out that to which each of the two does not belong, to make the syllogism concerning this. For it will be necessary in this case.
Si autem de exposito est necessarius, erit et de illo aliquo.Nam hoc quod est expositum, ipsum quidem illud aliquid est. Fit autem uterque syllogismus in propria figura.
CAPUT IX.
De mixtis ex una necessaria et altera absoluta in prima figura.
Accidit autem quandoque et altera propositione necessaria, necessarium fieri syllogismum, verum non utralibet, sed quae ad majorem extremitatem est, ut si a quidem, ex necessitate sumptum est inesse, vel non inesse, autem inesse tantum;sic enim sumptis propositionibus ex necessitate a ineritc vel non erit. Nam quoniam omni ex necessitate inest, vel non inesta, autem aliquid eorum quae sunt b, est manifestum quoniam et ex necessitate erit alterum horum. Si autem a quidem non necessaria,b autem necessaria;non erit conclusio necessaria. Nam si est, accidit a alicui inesse ex necessitate, per primam et tertiam figuram, hoc autem falsum, contingit enim tale esset cui possibile est a nulli inesse.
But if the syllogism concerning the exposed term is necessary, it will also be necessary concerning some one of that term. For what has been exposed is itself that very something. And each syllogism comes about in its proper figure.
CHAPTER IX.
On mixed syllogisms from one necessary and the other absolute proposition in the first figure.
It happens sometimes, when the other proposition is also necessary, that the syllogism becomes necessary—not, however, whichever of the two it may be, but the one that is toward the major extreme; for example, if A has been assumed to belong, or not to belong, of necessity, while B belongs only. For with the propositions so assumed, A will belong or not belong of necessity. For since it belongs of necessity to every, or does not belong to any, and something of the things that are B exists, it is evident that one of these will also be of necessity. But if A is not necessary while B is necessary, the conclusion will not be necessary. For if it were, it would happen that A belongs to something of necessity, by the first and third figures; but this is false, for it is possible that there be such a thing to which it is possible that A belong to none.
Amplius autem et ex terminis manifestum quoniam non eritconclusionecessaria; ut si a quidem sit motus,6 autem sitanimal,in quo autemchomo,namque homo animal est exnecessitate,moveturautemanimal non ex necessitate, quare nec homo.Similiter autem et si privativa sit a b;nam eadem demonstratio.In particularibus autemsyllogismis, si universalis quidem est necessaria,et conclusio erit necessaria; si autem particularis, non necessaria, sive privativa, sive praedicativa fuerit universalis propositio. Sit autem primo universalis ( necessaria, et a quidem omni insit ex necessitate, autem alicui insit solum, necesse est ergo a alicui inesse ex necessitate,nam sub est,b autem omni a inerat ex necessitate. Similiter autem et si privativus syllogismus s:t, nam eadem erit demonstratio. Si autem particularis est necessaria, non erit con. clusio necessaria nihil enim impossibile evenit, quemadmodum nec in universalibus syllogismis, similiter autem et in privativis. Termini, motus, animal, album.
Further, it is also clear from the terms that there will not be a necessary conclusion; for example, if A is motion, B is animal, and that in which C is, is man—for man is animal by necessity, but animal does not move by necessity, and therefore neither does man. The same holds similarly if A B is privative; for the demonstration is the same. But in particular syllogisms, if the universal proposition is necessary, the conclusion will also be necessary; but if the particular proposition is necessary, the conclusion will not be necessary, whether the universal proposition is privative or predicative. Let the universal proposition first be necessary, and let A belong to every B by necessity, but let A belong to some C only; then it is necessary that A belong to some C by necessity, for C is under B, and A belonged to every B by necessity. The same holds similarly if the syllogism is privative, for the demonstration will be the same. But if the particular proposition is necessary, the conclusion will not be necessary; for nothing impossible results, just as neither in universal syllogisms, and similarly also in privative ones. The terms are motion, animal, white.
CAPUT X.
De mixtis ex una necessaria et altera absoluta in se cunda figura.
In seeunda autem figura si privativa quidem propositio universalis sit et necessaria, conclusio erit necessaria. Si autem praedicativa, non necessaria. Sit enim primum privativa necessaria,et a quidem nulli contingat, autem insit tantum; quoniam ergo convertitur privativa; et nulli a contingit, a autem omni inest, quare nulli contingit b, nam sub a est. Similiter autem et si ad cponatur privativum, nam si a nulli contingit, et nulli a poterit inesse, a autem omni inest. Quare nulli eorum quæ sunt contingit c, fit enim prima figura. Rursum non ergo neque ipsi c, convertitur enim similiter. Si autem praedicativa propositio est necessaria, non erit conclusio necessaria, insit enim a omni ex necessitate, autem nulli insit tantum, conversa ergo privativa, fit prima figura.
CHAPTER X.
On mixtures of one necessary and one absolute premise in the second figure.
In the second figure, if the privative premise is universal and necessary, the conclusion will be necessary. But if it is predicative, the conclusion will not be necessary. For first let the privative premise be necessary, and let A belong to no B, but let it be assumed that A belongs to every C; since the privative premise converts, A belongs to no B, and A belongs to every C, so that B belongs to no C; for C falls under A. Similarly also if the privative premise is attached to C; for if A belongs to no B, and A can belong to no C, while A belongs to every B, then A belongs to none of the things that are C; for the first figure is produced. Again, therefore, neither will the conclusion be necessary in relation to C itself; for it converts in the same way. But if the predicative premise is necessary, the conclusion will not be necessary; for let A belong to every B by necessity, but let A be assumed to belong to no C; then, with the privative premise converted, the first figure is produced.
Ostensum est autem in prima quoniam cum non est necessaria quai ad majorem est privativa, nec conclusio erit necessaria, 'quare nec I in his erit ex necessitate, Amplius autem si concluSto est necessaria, accidit alicui a non inesse ex necessitate, si enim nulli inest ex necessitate, neque nulli inerit ex necessitate, baulem alicui a necesse est inesse, siquidem et a omni ex necessitate inerat, quare necesse est alicui anon inesse, sed nihil prohibet a hujusmodi accipere, cui omni contingat inesse.Amplius et si terminos ponentes sit ostendere, quoniam conclusio non est necessaria simpliciter. Et his existentibus, necessarium ut sit a animal, vero homo, autem album, et similiter propositiones sumptæ sint, contingit enim animal nulli albo inesse, non inerit ergo nec homo nulli albo, sed non ex necessitate. Contingit enim hominem fieri album, non tamen donec animal nulli albo ] insit, quare cum haec sint, necessaria erit conclusio, simpliciter autem non necessaria. Similiter autem se habebit et in particularibussyllogismis,quando privativa quidem propositio, et universalis fuerit, et necessaria, et conclusio erit necessaria. Quando autem praedicativa universalis fuerit necessaria,privativa vero particularis non necessaria, non erit conclusio necessaria.
It has been shown in the first figure that when the privative premise toward the major term is not necessary, neither will the conclusion be necessary; therefore neither in these cases will there be a conclusion from necessity. Moreover, if the conclusion is necessary, it happens that something does not belong to something from necessity. For if it belongs to no thing from necessity, neither will it belong to no thing from necessity; for it is necessary that it belong to some thing, if indeed it belonged to every thing from necessity. Therefore it is necessary that it not belong to some thing, but nothing prevents taking a case of this sort in which it happens to belong to every thing. Moreover, also by positing terms it can be shown that the conclusion is not simply necessary. And with these things being so, it is necessary that A be animal, B man, and C white, and let the propositions be assumed similarly; for it happens that animal belongs to no white thing, therefore man will not belong to any white thing either, but not from necessity. For it happens that man becomes white, but not while animal belongs to no white thing; therefore, when these things are so, the conclusion will be necessary, but not simply necessary. It will be similar also in particular syllogisms, when the privative proposition is both universal and necessary, the conclusion will also be necessary. But when the predicative universal proposition is necessary, while the privative particular proposition is not necessary, the conclusion will not be necessary.
Sit enim primum privativa,et universalis necessaria, et ab quidem nullicontingat inesse, autem alicui insit, quoniam ergo convertitur privativa, et nulli a continget inesse, a autem alicuicinest, quare ex necessitate alicui eorum quae sunt, non inerit b. Rursum sit prsedicativa, et universalis, et necessaria. etponatur ad quidem praedicativum, si ergo a omni ex necessitate inest, autem alicui non inest,quoniam non inerit alicui manifestum, sed non ex necessitats. Nam iidem termini;eruntad demonstrationem,qui in universalibus syllogismis: sed nec si privativa necessaria est particulariter sumpta, erit conclusio necessaria. Nam per eosdem terminos demonstratio.-
CAPUT XI.
De syllogismis mixtis ex altera necessaria et altera absoluta in tertia figura.
In postrema autem figura terminis quidem universalibus ad medium, et prEedicativis utrisque propositionibus, si utralibet sit necessaria, et conclusio erit necessaria. Si autem haec quidem sit privativa, illa vero prsedicativa,quandoprivativa quidem fuerit necessaria, et conclusio erit necessaria,quando autem prædicativa,non eritnecessaria. Sint enim primum utræque prædicativæ propositiones, et a et omni insint, necessaria autem sit a c, quoniam ergo omni inest, et alicui inerit, eo quod consertitur universalis particulariter. Quare si a inest omni ex necessitate, et alicui b, et a alicui necessarium inesse, nam sub est.
For let the first premise be privative, universal, and necessary, and let it be impossible for A to belong to any B, but let A belong to some C. Since then the privative premise converts, it will be impossible for A to belong to any B, but A belongs to some C; therefore of necessity A will not belong to some of the things that are B. Again, let the premise be predicative, universal, and necessary, and let A be posited as predicated of every B. If then A belongs to every B of necessity, but does not belong to some C, it is manifest that it will not belong to some C, but not of necessity. For the same terms will serve for the demonstration as in the universal syllogisms. But neither, if the privative premise is necessary when taken particularly, will the conclusion be necessary. For the demonstration is through the same terms.
CHAPTER XI.
On mixed syllogisms from one necessary and one absolute premise in the third figure.
In the last figure, with universal terms related to the middle, and with both premises predicative, if either one is necessary, the conclusion will also be necessary. But if one is privative and the other predicative, when the privative premise is necessary, the conclusion will also be necessary; but when the predicative premise is necessary, the conclusion will not be necessary. For first let both premises be predicative, and let A belong to every B and to every C, and let the premise A C be necessary. Since then A belongs to every C, it will also belong to some C, because the universal converts to the particular. Therefore if A belongs to every C of necessity, it will also belong to some B of necessity, for B is under C.
Fit igitur prima figura. Similiter autem ostendetur, et si est necessaria, convertitur enim calicui £quare si omni inest ex necessitate, et a alicui inerit ex necessitate. Rursum sit a quidem privativa, vero affirmativa, necessaria autem privativa, quoniam ergo convertituraffirmativa, eritcalicui b, aautem nullic ex necessitate, neque a alicui inerit ex necessitate, nam sub est. Si autem prædicativa sit necessaria, non erit conclusio necessaria.Sit enim prædicativa et necessaria, a. autem privativa et non necessario, quoniam ergo convertituraffirmativa,ineritetcalicui ex necessitate. Quare si a quidem nullieorum quae sunt inest,cautem alicui eorum quae sunt & eta alicui eorum quae sunt non inerit,sed non ex necessitate.Ostensum est enim in prima figura quoniam privativa propositione necessaria, nec conclusio erit necessaria. Amplius autem et per terminos sit manifestum, sit enim a quidem bonum in quo animal, autem equus, ergo bonum quidem contingit nulli equo inesse, animal vero necesse est omni equo inesse, sed non necesse est aliquod animal non esse bonum, siquidem contingit omne esse bonum. Aut si non hoc possibile, sed vigilare, vel dormire terminum ponendum. Omne enim animal susceptibile est horum.
The first figure is thus produced. The same will be shown likewise even if it is necessary; for the affirmative premise converts. Therefore if it belongs to every one by necessity, it will also belong to some one by necessity. Again, let A be privative, but the other affirmative, and let the privative be necessary. Since then the affirmative converts, it will belong to some B, but A to no C by necessity; neither will A belong to any C by necessity, for C is subordinate. But if the predicative premise is necessary, the conclusion will not be necessary. For let the predicative premise be both affirmative and necessary, but let A be privative and not necessary. Since then the affirmative converts, it will belong to some C by necessity. Wherefore if A belongs to none of the things that are in C, but C belongs to some of the things that are, then A will not belong to some of the things that are, but not by necessity. For it has been shown in the first figure that when the privative premise is necessary, the conclusion will not be necessary. Moreover, let this be made clear also through terms. For let A be good, of which animal is the middle term, and let B be horse. Then good can belong to no horse, but animal must belong to every horse; yet it is not necessary that some animal not be good, since it can happen that every animal is good. Or if this is not possible, one must take as the term to be awake or to sleep. For every animal is susceptible of these.
Si igitur termini universaliter ad medium sint, dictum est quando erit conclusio necessaria.Si autem hic quidem universalis, ille vero particularis praedicativus uterque, quando universalis fuerit necessarius, et conclusio erit necessaria. Demonstratio autem eadem quae prius,convertitur enim et particularis affirmativa. Si ergo necesse est omni inesse, a autem sub est, necesse est alicui a inesse.Si autem alicui a, et a alicui inesse necessarium, convertitur enim. Similiter autem et si a sit necessaria universalis, nam sub est. Si autem particularis est necessaria, non erit conclusio hecessaria. Sit enim particularis et necessaria,a autem insit omni c, non tamen ex necessitate, conversa ergo bc prima fit ligura,et universalis quidem propositio non necessaria,particularis autem necessaria, quando autem sic se habebant propositiones, non erat conclusio necessaria, quare nec in his. Amplius autem et ex terminis manifestum.Sit enim a quidem vigilatio, autem bipes, in quo autem animal, ergo alicui necesse est inesse, a autem omni contingit, et a non necessario b, non enim necesse est aliquem bipedem dormire vel vigilare. Similiter autem per eosdem terminos ostendetur etiam si a sit particularis et necessaria. Si autem hic quidem terminorum sit prasdicativus, ille privativusetnecessarius, quandouniversalis fueri!
If, then, the terms are related universally to the middle, it has been stated when the conclusion will be necessary. But if one is universal and the other particular, and both are affirmative, then when the universal is necessary, the conclusion will also be necessary. The demonstration is the same as before, for the particular affirmative also converts. Therefore if it is necessary that it belong to every one, and a is under the middle term, it is necessary that it belong to some one. But if it is necessary that it belong to some one, and a belongs to some one, it is necessary, for it converts. Likewise also if a is a necessary universal, for it is under the middle term. But if the particular is necessary, the conclusion will not be necessary. For let the particular be necessary, and let a belong to every c, but not by necessity; then with bc converted, the first figure results, and the universal premise is not necessary, but the particular is necessary. But when the premises were so disposed, the conclusion was not necessary; therefore neither in these cases. Moreover, this is also clear from the terms. For let a be waking, b two-footed, and that in which animal is; then it is necessary that it belong to some one, but a belongs to every one contingently, and a does not belong to b by necessity; for it is not necessary that some two-footed thing sleep or wake. Likewise, by the same terms, it will be shown even if a is particular and necessary. But if one of the terms is affirmative, the other privative and necessary, when the universal has been...
privativus et necessarius, et conclusio erit necessaria.Si enim a nulli ex necessitate contingit,6 autem alicui inest, necesse est a alicui non inesse, quando autem affirmativa necessariaponeturvel universalis vel particularis, vel privativa particularis, non erit conclusio necessaria.Nam alia quidem eadem quae et in prioribus dicemus. Termini autem cum universalis quidem affirmativa est necessaria, vigilatio, animal,homo,medium homo: cum autem particularis prædicativa necessaria, vigilatio,animal,album. Animal enim necesse est alicui albo inesse, vigilatio autem contingit nulli,et non necesse est alicui animali non inesse vigilationem.Quandoautem privativa particularis est necessaria, bipes, motus, animal, medium Ilnimal.Manifeslum igitur quoniam inesse quidem non est syllogismus, si utraeque propositiones non sunt in eo quod est inesse, necessaria vero est, et altera solum existente necessaria. In utriusque autem affirmativis et privativis existentibus syllogismis necesse est alteram propositionem similem esse conclusioni. Dico autem similem, si inesse quidem, inexistentem, si autem necessaria, necessariam.Quare et hoc palam,quoniam non erit conclusio neque necessari0 neque inesse,non sumpta vel necessaria, vel quæ £inesse significet propositione. Igitur de necessario quomodo fit, et quam differentiam habeat ad inesse,sufficientem pene dictum est.
If the privative premise is necessary, the conclusion will also be necessary. For if A belongs to no B by necessity, and B belongs to some C, then A necessarily does not belong to some C. But when either an affirmative necessary premise is posited, whether universal or particular, or a particular privative one, the conclusion will not be necessary. For we shall say the same things as in the previous cases. The terms, when the universal affirmative premise is necessary, are: waking, animal, man, with man as the middle term. When the particular affirmative premise is necessary: waking, animal, white. For animal necessarily belongs to some white thing, while waking belongs to no white thing by contingency, and it is not necessary that waking not belong to some animal. When the particular privative premise is necessary: two-footed, motion, animal, with animal as the middle term. It is clear, then, that there is no syllogism of belonging when both premises are not stated in respect of belonging, but there is one of necessity when only one premise is necessary. In syllogisms where both premises are affirmative or privative, one premise must be similar to the conclusion. I mean similar: if the conclusion is of belonging, a premise of belonging; if of necessity, a necessary one. Hence it is also clear that the conclusion will be neither necessary nor of belonging unless a premise is assumed that is either necessary or signifies belonging. So enough has been said about how the necessary comes about and what difference it has from belonging.
CAPUT XII.
De contingenti non necessario.
De contingente autem post haec dicemus,quando, et quomodo,et per quae erit syllogismus.Dico autem contingere, et contingens,quo non existente necessario, posito autem inesse, nihil erit propter hoc impossibile.Nam necessarium aequivoce contingere dicitur.Quoniam autem hoc est contingens,manifestam ex affirmationibus et negationibus oppositis. Nam non contingit esse, non possibile esse et impossibile esse, et necesse est non esse, vel eadem sunt, vel sequuntur se invicem, quare et opposita his contingit esse, et non impossibile esse, et non necesse non esse, eadem erunt,vel sequentia seinvicem. De omni enim affirmatio, vel negatio vera. Erit ergo contingens necessarium, et non necessarium contingens.Accidit autem omnes quæ secundum contingere sunt propositiones converti sibi invicem,dico autem non affirmativas negativis,sed quascunque affirmativam habentfiguram secundum oppositionem, ut ea quæ est contingit esse ei quae est contingit non esse,et ea quae est contingit omni ei quae est contingit nulli, vel non omni, et quæ alicui, et quae non alicui,eadem autem modo et in aliis. Quoniam enim quod est contingens non est necessarium,et quod non est. necessarium possibile est non esse, manifestum quoniam si contingit a inesse b,contingit et non inesse, et si omni contingit inesse, et omni contingit non inesse.
CHAPTER XII.
On the contingent that is not necessary.
Next we shall discuss the contingent: when, how, and through what terms a syllogism will arise. I call "to be contingent" and "the contingent" that which, when it is not necessary, and when it is posited to be present, nothing impossible results on account of this. For "necessary" is said to be contingent equivocally. Since this is the contingent, it is made clear from opposed affirmations and negations. For "it is not contingent to be," "it is not possible to be," "it is impossible to be," and "it is necessary not to be"—these are either the same or follow one another; therefore their opposites also are contingent to be: "it is not impossible to be" and "it is not necessary not to be" will be the same or will follow one another. For of every thing there is a true affirmation or negation. Therefore the necessary will be contingent, and the non-necessary contingent. It happens, moreover, that all propositions that are according to the contingent convert with one another—I mean not the affirmative with the negative, but those whatever that have an affirmative figure according to opposition: for example, "it is contingent to be" with "it is contingent not to be," and "it is contingent to belong to every" with "it is contingent to belong to none" or "not to every," and "to some" with "not to some," and in the same way also in the others. For since what is contingent is not necessary, and what is not necessary is possible not to be, it is clear that if it is contingent for A to belong to B, it is also contingent not to belong; and if it is contingent to belong to every, it is also contingent to belong to none.
Similiter autem et in particularibus affirmationibus,nam ea. dem demonstratio.Sunt autem hujusmodi propositiones prædicativæ,nam contingere ei quod est esse similiter ponitur, quemadmodum dictum est prius, Determinatis autem his, rursum dicimus quoniam contingere duobus modis dicitur; uno quidem,quod plerumque fit et deficit, necessarium, ut canescere hominem, vel augeri, vel minui, vel omnino quod natum est esse. Hoc enim non continuum habet necessarium,eo quod non semper est homo, cum tamen homo est, aut ex necessitate, aut ut in pluribus est.Alio autem modo infinitum,quod et sic, et non sic possibile, ut animal ambulare, vel ambulante fieri motum terræ,veI omnino quod casu fit, nihil enim magis sic natum est, vel contrario. Convertitur ergo et secundum oppositas propositiones utrumque contingens,non tamen eodem modo,sed quod natum quidem est esse ei quod non ex necessitate esse.Sic enim contingit non canescere hominem.
Similarly also in particular affirmations, for the demonstration is the same. Propositions of this sort are predicative, for "to be contingent" is posited of that which is to be in like manner, just as was said earlier. Having determined these things, we say again that "to be contingent" is spoken of in two ways: in one way, that which for the most part comes about and falls short, or is necessary, as for a man to grow gray, or to increase, or to diminish, or in general whatever is born to be. For this does not have necessity continuously, in that a man does not always exist; yet when he is a man, it is either of necessity or for the most part. In another way, the indefinite, which is possible both thus and not thus, as for an animal to walk, or for the earth to be moved while it walks, or in general whatever comes about by chance; for nothing is more born to be so, or the contrary. Therefore each kind of contingent is converted also according to opposed propositions, yet not in the same way, but that which is born to be is [converted] to that which is not of necessity. For thus it is contingent for a man not to grow gray.
Infinitum autem ei quod nihil magis sic, vel illo modo.Disciplina autem,et syllogismus demonstrativus,ex infinilisquidem non est,eo quod inordinatum et medium, ex iis vero qua nata sunt esse, pene orationes et considerationes fiunt de sic contiogentibus,ex illis autem possibile quidem est fieri syllogismum,non tamen solet quæri.Hæc ergo definientur magis in sequentibus,nuncautem dicemus quando et quomodo,et quis erit syllogismus ex contingentibuspropositionibus.Quoniamautem contingere hoc huic inesse dupliciter est accipere, aut enim cui inest hoc,aut cui contingit ipsum inesse, nam de quo b, a contingere horum alterum significat, aut de quo dicitur b, aut de quo contingit dici, de quo autem b,a contingere, aut omni possibile inesse a, nihil differt. Manifestum igitur quoniam dupliciter dicetur a omni inesse contingere.Primum ergo dicemus si de quo contingit 6, et de quo contingit a, quis erit,et qualis syllogismus, sic enim utræque propositiones sumuntursecundum contingere,quando autem de quo est contingit a, hæc quidem inesse,illa vero contingens,quare a similibus figuris incipiendum,quemadmodum est in aliis.
But the infinite is related to that to which nothing is more so in this way, or in that way. But discipline and demonstrative syllogism do not arise from things that are infinite, because they are unordered and lack a middle term; but from things that are naturally disposed to be so, discourses and considerations nearly come to be about things contingent in this way, while from those it is possible for a syllogism to come to be, yet it is not customary to seek it. These matters, then, will be defined more fully in what follows; but now we shall say when, and in what way, and what sort of syllogism there will be from contingent propositions. Since, however, to take "this to be contingent of that" is twofold—for either it is contingent of that to which this belongs, or it is contingent for this itself to belong to that; for "A to be contingent of that of which B is said" signifies one of these two, either of that of which B is said, or of that of which it is contingent to be said—but "A to be contingent of that of which B is said" differs in no way from "it is possible for A to belong to every [B]." It is clear, therefore, that "A to be contingent of every [B]" will be said in two ways. First, then, we shall say, if [we take] that of which B is contingent, and that of which A is contingent, what sort of syllogism there will be, and of what quality; for in this way both propositions are assumed according to the contingent; but when [we take] that of which A is contingent to be, one of these is [taken as] belonging, the other as contingent. Therefore one must begin from similar figures, just as is the case in other matters.
CAPUT XIII.
De syllogismis ex ambabus contingentibus in prima figura.
Quando ergo a contingit omni b,et omni c,syllogismus eri! perfectus, quoniam a contingit omni inesse.Hoc autem manifestum est ex definitione, nam contingere omni inesse sic dicebamus.Similiter autem et si a quidem contingit nulli b, autem omni c,quoniam a contingit nulli c. Nam de quo conlingit.a non contingere,hoc erat nullum dimittere sub contingentium.Quando autem a contingit omni b,b autem nulli c,per sumptas quidem propositiones nullus fit syllogismus,conversa autem secundum contingere, lit idem quemadmodum et prius,quoniam enim contingit nulli cinesse,contingit et omni inesse. Hoc autem dictum prius. Quare si quidem omni c,a autem omni 6,rursum idemfitsyllogismus.Similiterautem etsiad utrasque propositiones negatio ponatur cum contingere (dico autem ut si a contingit nulli b,et nulli c),igitur per sumptasquidempropositionesnullusfitsyllogismus conversis autem rursus idem erit qui et prius.Ma.nifestum est igitur quoniam negatione posita ad minorem extremitatem,vel ad utrasque propositiones, aut non fit syllogismus,aut fit quidem,sed non perfectus, ex conversione enim fit necessarium.
CHAPTER XIII.
On syllogisms from two contingent premises in the first figure.
When, therefore, A is contingent of every B, and of every C, there will be a perfect syllogism, since A is contingent of every C. This is evident from the definition, for we said that to be contingent of every is this. Similarly also if A is contingent of no B, but of every C, then A is contingent of no C. For that of which it is contingent that A not be, this was to leave nothing under the contingent. But when A is contingent of every B, and B of no C, no syllogism comes about through the premises as taken; but with the premise converted according to the contingent, there will be the same syllogism as before, since it is contingent of no C, it is also contingent of every C. This was said before. Wherefore if indeed of every C, and A of every B, again the same syllogism comes about. Similarly also if a negation is placed on both premises with the contingent (I mean, for instance, if A is contingent of no B, and of no C), then through the premises as taken no syllogism comes about; but with them converted, again there will be the same one as before. It is evident, therefore, that when a negation is placed on the lesser extreme, or on both premises, either no syllogism comes about, or one does come about, but not perfect; for it comes about by conversion.
Si autem hæc quidem propositionum universalis, illa vero particularis sumatur,ad majorem quidem extremitatem posita universali,syllogismus erit perfectus.Nam si a omni contingit,b autem alicui c,ft alicui contingit,hoc autem manifestum ex definitione contingentis.Rursum si a contingit nulli b, autem contingit alicui inesse, necesse est a contingere alicui non inesse. Demonstrntio autem eadem quae in his.Si autem privativa sumatur particularis propositio, universalis autem affirmativa, positione autem similiter se habeant (ut a quidem omni contingat, autem alicui contingat non inesse), per sumptas quidem propositiones non fit manifestus syllogismus,conversa autem particulari et posito alicui contingere inesse, eadem erit conclusio quæ et prius, quemadmodum in iis quae ex principio.Si autem quae ad majorem extremitatem particularis sumatur,quse ad minorem universalis,sive utraeque sumantur affirmativae, sive privativae,sive non similis figuræ,sive utræque indefinitae,vel particulares, nullo modo erit syllogismus.
But if one of the premises is taken as universal and the other as particular, with the universal placed at the major extreme, the syllogism will be perfect. For if A is contingent of every B, and B of some C, then A is contingent of some C; and this is evident from the definition of the contingent. Again, if A is contingent of no B, and B is contingent of some C, it is necessary that A be contingent of some C not to be. The demonstration is the same as in these cases. But if the privative premise is taken as particular and the universal as affirmative, and they are arranged similarly (for instance, A is contingent of every B, and B is contingent of some C not to be), no syllogism is made evident through the premises as taken; but when the particular premise is converted and it is posited that B is contingent of some C to be, the conclusion will be the same as before, just as in the cases from the beginning. But if the particular premise is taken at the major extreme and the universal at the minor, whether both are taken as affirmative or as privative, or not of similar figure, or both indefinite or particular, there will in no way be a syllogism.
Nihil enim prohibet transcendere a, et non praedicari de aequis,in quo enim transcendit a sumat c,huic neque omni,neque nulli,neque alicui,neque non alicui continġit a inesse,siquidem convertuntur secundum contingere propositiones, et pluribus contingit quam a inesse.Am plius autem ex terminis manifestum est,nam sic se habentibus propositionibus primum postremo et nulli contingit, et omni ex necessitate inesse. Termini autem communes omnium,inesse quidem ex necessitate, animal, album, homo, non contingere vero, animal, album, vestis.Manifestum igitur quoniam hoc modo habentibus se terminis,nullus fit syllogismus,nam omnis syllogismus vel ejus quod est inesse est, vel ex necessitate vel contingere,non est autem ejus quod est inesse,neque necessarii, manifestum quoniam non est,nam affirmativus interimitur privativo,et privativus affirmativo,relinquitur ergo ejus quod contingere esse: hoc autem impossibile. Ostensum est enim quoniam sic se habentibus terminis,et omni postremo primum necesseinesse,et nulli contingere inesse,quare non erit ejus quod est contingeresyllogismus, nam necessarium uno erat contingens. Manifestum autem et quoniam cum universalessunt termini in contingentibus propositionibus, semper fit syllogismas in prima figura, sive sunt praedicativi, sive privativi. Verum ex praedicativis quidem perfectus, ex privativis autem imperfectus.
For nothing prevents A from extending beyond and not being predicated of equals; for let C be that in which A extends beyond, and it is contingent that A belongs neither to every C nor to none nor to some nor to not some, since the propositions convert according to contingency, and it is contingent for A to belong to more things. Moreover, it is clear from the terms, for with the propositions thus related, it is contingent that the first belongs to the last neither to any nor to all, and it is necessary that it belongs to every. The common terms of all are: for necessary belonging—animal, white, man; for not being contingent—animal, white, garment. It is clear, therefore, that with the terms thus related, no syllogism comes about; for every syllogism is either of what is, or of necessity, or of contingency. But it is not of what is, nor of the necessary, it is clear that it is not; for the affirmative is destroyed by the privative, and the privative by the affirmative. It remains, therefore, that it is of what is contingent; but this is impossible. For it has been shown that with the terms thus related, it is necessary for the first to belong to every last, and it is contingent that it belongs to none; wherefore there will not be a syllogism of what is contingent, for the necessary was one thing, the contingent another. It is clear also that when the terms are universal in contingent propositions, a syllogism always comes about in the first figure, whether they are affirmative or privative. But from affirmatives it is perfect, while from privatives it is imperfect.
Oportet autem contingere sumere non in necessariis, sed secundum dictam definitionem, aliquoties autem latet hujusmodi.
CAPUT XIV.
De syllogismis ex una absoluta et altera contingente in prima figura.
Si autem haec quidem inesse,illa vero contingere sumatur propositionum, quando quae ad majorem quidem extremitatem contingere significaverit perfecti erunt omnes syIlogismi,et contingentis secundum dictam determinationem, quando autem quae ad minorem,et imperfecti omnes,et privativi syllogismi,nun contingentis secundum dictam determinationem, sed ejus quod est nulli,aut non omni ex necessitate inesse. Si enim nulli,aut non omni ex necessitate contingere dicimus,et nulli,et non omni inesse. Contingat enim a omni b, autem omni ponatur inesse;quoniam igitur sub best c,a autem contingit omni manifestum quoniam et omni contingit l!,fit ergo perfectus syllogismus.Similiter autem et cum privativa est a prupositio,b autem autem affirmativa, et haec quidem contingere, illa vero inesse sumetur,perfectus erit syllogismus,quoniarn a contingit nulli inesse.Quoniam ergo inesse posito ad minorem extremitatem, perfecti syllogismi fiunt,manifestum.Quod autem contrariae se habentes erunt syllogismi, per impossibile monstrandum est,simulautemeritmanifestum et quoniam imperfecti,nam ostensio non.ex sumptis propositionibus.
But one must take "contingent" not in the case of necessities, but according to the stated definition; sometimes, however, such a thing escapes notice.
CHAPTER XIV.
On syllogisms from one absolute and the other contingent proposition in the first figure.
If, however, one of the propositions is taken as belonging and the other as contingent, then when the proposition signifying contingency is attached to the major extreme, all the syllogisms will be perfect and of the contingent according to the stated determination; but when it is attached to the minor extreme, all will be imperfect, and the privative syllogisms will be not of the contingent according to the stated determination, but of that which is of necessity belonging to none or not to every. For if we say it is contingent to belong to none or not to every, we say it belongs to none and not to every. For let A be contingent of every B, and let it be posited as belonging to every C; since, therefore, B is under C, and A is contingent of every B, it is evident that it is also contingent of every C; a perfect syllogism results. Similarly also when the proposition A is privative and B is affirmative, and the one is taken as contingent and the other as belonging, the syllogism will be perfect, since A is contingent of belonging to none. That, therefore, when the belonging proposition is posited at the minor extreme, perfect syllogisms come about, is evident. But that the syllogisms will stand in contrary relations must be shown through impossibility, and at the same time it will be evident that they are imperfect; for the demonstration does not proceed from the assumed propositions.
Primum aulem dicendum quoniam si cum est a, necesse est esse b,et cum possibile est esse a possibile erit ex necessitate.Sit enim sic se habentibus rebus ut in quo qaidem a possibile, in quo autem impossibile,si ergo aliud possibile quidem est,cum possibile esse, ipsum fiet, boc vero impossibile, quoniam impossibile,non utique fiet, simul autem. si a possibile,et impossibile, continget fieri præster b,si autem fieri et esse. Nam quod fit, quando factum est, est.Oportet autem accipere non solum in generatione possibile et impossibile,sed et in verum esse, et in quod actu est,et quocunque modo simpliciter aliter dicitur possibile,in omnibus enim similiter se habebit.Amplius cum est a,b esse,non tanquam uno aliquo existente a,erit b,oportet opinari, nihil enim est ex necessitate uno aliquo existente,sed duobus ad minus,ut quando propositiones sic se habent (ut dictum est) secundum syllogismum, nam sic dicitur de d, autem de e, et de e ex necessitate,et si utrumque possibile,et conclusio erit possibilis. Quemadmodum ergo si quis ponat a quidem porpositioncs, autem conclusionem,accidet non solum a existente necessario,et simul esse necessario,sed etiam necessarium possibile.
First, however, it must be said that if, when A is, B must be, then when A is possible, B will also necessarily be possible. For let things be so disposed that in one case A is possible, in another impossible. If, then, one thing is possible, when it is possible to be, it will come to be; but the other is impossible, and since it is impossible, it will certainly not come to be—at the same time, however, if A is possible and impossible, it will follow that it comes to be apart from B, if it is both to come to be and to be. For what comes to be, when it has been made, is. But one must take "possible" and "impossible" not only in generation, but also in being true, and in what is in act, and in whatever way "possible" is said simply in other senses; for in all these cases it will be alike. Moreover, when A is, for B to be—not as though A were some one thing—one must hold that B will be; for nothing is by necessity from one thing existing, but from at least two, as when propositions are so disposed (as has been said) according to the syllogism. For thus it is said of D, and of E, and of E by necessity; and if both are possible, the conclusion will also be possible. Just as, therefore, if someone posits A as the propositions and the conclusion, it will happen that not only, when A exists, it is necessary and at the same time necessary to be, but also that the necessary is possible.
Hoc autem ostenso manifestum est quoniam falso posito, et non impossibili, et quod accidit propter positionem falsum erit,et non impossibile, ut si a falsum quidem est,non tamen impossibile, cum autem sit a et b, et erit falsum quidem,non tamen impossibile.Nam ostensum est quoniam cum est a, est b, et cum possibile est a,possibile est b. Positum autem est a possibile esse, et erit possibile,si enim impossibile est b,simul idem erit possibile et impossibile.Determinatis autem iis,insit a omni b,b autem contingit omni c,nece3se est a igitur contingere omni inesse. Non enim contingat, autem omni ponatur inesse, hoc autem falsum quidem, non tamen impossibile, si ergo a quidem non contingit omni c, autem omni insit, a non omni contingit.Fit enim syllogismus pertertiam figuram.Sed positum erat omni contingere inesse, necesse est ergo a omni contingere. Falso enim posito,et non impossibili,quod accidit estimpossibile.Possibile est autem et primam figuram facere impossibile ponentes inesse c, nam si omni a ip-est,a autem omni contingit,et omni continget a,sed positum erat non omni possibile inesse.Oportet autem accipere omni inesse non secundum tempus determinantes, ut nunc, aut in hoc tempore, sed simpliciter (per hujusmodi enim propositiones et syllogismos facimus), quoniam secundum nunc sumpta propositione, non erit syllogismus.
This having been shown, it is manifest that when a false but not impossible premise is posited, what follows because of the positing will be false but not impossible—for example, if A is false but not impossible, and when A is, B is, then B will be false but not impossible. For it has been shown that when A is, B is, and when A is possible, B is possible. But it has been posited that A is possible; therefore B will be possible. For if B is impossible, the same thing will at once be possible and impossible. With these things determined, let A belong to every B, and let B possibly belong to every C; then it is necessary that A possibly belong to every C. For let it not be possible, but let it be posited to belong to every C; this is false, but not impossible. If, then, A does not possibly belong to every C, while B belongs to every C, A does not possibly belong to every C. For the syllogism is produced through the third figure. But it was posited that A possibly belongs to every C; therefore it is necessary that A possibly belong to every C. For when a false but not impossible premise is posited, what follows is not impossible. It is also possible to make the first figure by positing that C belongs to every A impossibly; for if A belongs to every C, and A possibly belongs to every B, then A will possibly belong to every B. But it was posited that A does not possibly belong to every B. One must, however, understand “to belong to every” not by determining a time, as “now” or “in this time,” but simply (for it is through propositions of this sort that we make syllogisms), since when the proposition is taken with respect to “now,” there will not be a syllogism.
Nihil enim fortasse prohibet quandoque et omni moventi hominem inesse,ut si nihil aliud moveatur,movens autem contingit omni equo, sed homo nulli equo contingit. Amplius: sit primum quidem animal, medium vero movens,postremum vero homo, ergo propositiones quidem similiter se habebunt,conclusio vero erit necessaria, non contingens. Ex necessitate enim homo est animal, manifestum igitur quoniam universale sumendum simpliciter, et uon tempore determinantes.Rursum: sit privativa propositio universalis a b, et sumatur a quidem nulli inesse, autem contingat omni inesse.His igitur positis necesse est a contingere nulli inesse, non enim contingat,6 autem ponaturinessecsicutprius, necesse est igitur a alicui inesse, fit enim syllogismus per tertiam figuram.Hoc autem impossibile, quare contingit a,nuIli c.Posito enim falso,et non impossibili, impossibile est quod accidit. Hic ergo syllogismus non est contingentis secundum definitionem, sed nulli inesse ex necessitate. Haec est contradictio factas hypothesis. Positum est enim ex necessitate a alicui inesse,syllogismus autem per impossibile, oppositas est contradictionis.
For perhaps nothing prevents "moving a man" from sometimes belonging to every mover, as if nothing else is moved; but "moving" belongs to every horse, whereas "man" belongs to no horse. Further: let the first term be animal, the middle moving, and the last man; then the premises will stand similarly, but the conclusion will be necessary, not contingent. For man is necessarily an animal. It is manifest, therefore, that the universal must be taken without qualification, and not by determining it in time. Again: let the privative universal proposition be A B, and let A be taken to belong to none, while let it be contingent that it belong to every. With these posited, then, it is necessary that A contingently belong to none. For if it does not contingently belong, but is posited to belong to some, as before, then it is necessary that A belong to some; for a syllogism is produced through the third figure. But this is impossible; therefore A contingently belongs to no C. For when something false but not impossible is posited, what results is impossible. This syllogism, then, is not of the contingent according to the definition, but of belonging to none by necessity. This is the contradiction of the hypothesis made. For it was posited that A belongs to some by necessity, but the syllogism through the impossible is of the opposite contradiction.
Amplius autem et ex terminis manifestum quoniam non erit conclusio contingens, sit enim a quidem corvus,in quo autem intelligens, in quo autem homo,nulli ergo inest a, nam nullum intelligens, corvus, autem contingit omni c, omni enim homini inest intelligere, sed a ex necessitate nulli c, non igitur conclusio contingens.Sed nec necessaria semper: sit enim quidem rnovens,b autem scientia, in quo autem homo, ergo a quidem nulli inerit, autem omni contingit, et non erit conclusio necessaria,non enim necesse est nullum hominem moveri,sed necesse estaliquem.Manifestum igitur quoniam est conclusio ejus quod est nulli ex necessitate inesse. Sumendum autem melius terminos.
Si autem privativum ponatur ad majorem extremitatem contingere significans, ex ipsis quidem sumptis propositionibus, nullus erit syllogismus, con versa autem secundumcontingens propositione, erit quemadmodum in prioribus.Insit enim a omni btb autem contingat nulli c,sic ergo habentibus se terminis, nihil erit necessarium. Si autem convertatur c,et sumatur contingere omni c, fiet syllogismusquemadmodum prius,similiter enim habent se termini positione.
Further, it is also clear from the terms that there will not be a contingent conclusion. For let A be raven, that in which B is understanding, and that in which C is man; then A belongs to no B (for no understanding is a raven), but A belongs contingently to every C (for understanding belongs to every man); yet A belongs to no C by necessity, so the conclusion is not contingent. Nor is it always necessary: for let A be moving, B knowledge, and that in which C is man; then A will belong to no B, but belongs contingently to every C, and the conclusion will not be necessary, for it is not necessary that no man be moved, but it is necessary that some man be. It is evident, therefore, that the conclusion is that A belongs by necessity to no C. But the terms must be taken better.
If, however, the privative proposition is posited at the major extreme signifying contingency, from the propositions as taken there will be no syllogism; but with the contingent proposition converted, there will be one, as in the earlier cases. For let A belong to every B, and let B belong contingently to no C; with the terms thus related, nothing will be necessary. But if C is converted and it is taken that B belongs contingently to every C, a syllogism will come about as before, for the terms are similarly related in position.
Eodem autem modo et cum privativa sunt utraque intervalla,si a quidem non in esse, autem nulli, contingere significat, nam per ea quidem quae sumpta sunt nullo modo fit necessarium, conversa autem secundum contingens propositione erit syllogismus,sumatur enim a quidem,nulli inesse,6 autem contingere nulli c, per haec quidem nihil necessarium. Si autem sumatur omni contingere, quod verum est, a autem propositio similiter se habeal,rursus erit idem syllogismus. Si autem non inesse; ponatur omni c, et non contingere non inesse, non erit syllogismus nullo modo, sive privativa sit, sive affirmativa a propositio. Termini autem communes exnecessitate quidem inesse,album, animal, nix. Non contingere autem, album, animal, pix. Manifestum est igitur quoniam cum universales sunt termini,et hæc quidem propositionum inesse,illa vero sumitur contingens, quando quas ad minorem est extremitatem contingere sumitur propositio, semper fit syllogismus,verumtamen quandoquidem ex ipsis, quando autem propositione conversa, quando vero utrumque horum,et ob quam causam,diximus.
In the same way also when both intervals are privative, if A signifies not belonging and B belongs to none, it signifies contingency; for from the things assumed no necessity results in any way, but with the contingent proposition converted there will be a syllogism. For let A be taken to belong to none, and B to contingently belong to no C; from these nothing necessary follows. But if it is taken to contingently belong to every C, which is true, and the proposition A is similarly disposed, again there will be the same syllogism. But if it is taken as not belonging, let it be posited to belong to every C, and not to contingently not belong, there will be no syllogism in any way, whether the proposition A is privative or affirmative. The common terms for necessary belonging are white, animal, snow. For not contingently belonging: white, animal, pitch. It is clear, therefore, that when the terms are universal, and some of the propositions are of belonging while the other is taken as contingent, whenever the proposition concerning the minor extreme is taken as contingent, a syllogism always results, but sometimes from the propositions themselves, sometimes from the converted proposition, and sometimes from both of these; and for what reason, we have stated.
Si autem hocquidemuniversale,illud vero particularesumitur intervallorum,quando ad majorem quidem extremitatem universale ponitur, et contingens sive negativum,siveaffirmativum,particuIare autem affirmativum et inesse,erit syllogismus perfectus,quemadmodum et cum universales sunt termini, demonstratio autem eadem quæ et prius.Quando autem universale quidem fuerit,ad majorem extremitatem inesse, et non contingens,alterum vero particulare,et contingens,sive affirmative,sive negative ponantur utrasque, sive haec quidem negativa, illa vero affirmativa, omnino erit syllogismus imperfectus. Verum. hi quidem per impossibile ostenduntur,illi vero per conversionem contingentis,quemad modum in prioribus.Erit autem syllogismus per conversionem, et quando universalis quidem ad majorem extremitatem posita significaverit inesse,vel non inesse,particularis vero cum sit privativa,sumatur contingens, ut si a quidem omni inest,vel non inest,b autem alicui contingit non inesse, conversa enim c, secundum contingere fit syllogismus. Quandoautem non inesse sumetur particulariter posita propositio, non erit syllogismus.
But if one of the intervals is taken as universal and the other as particular, when the universal is placed at the major extreme and is contingent, whether negative or affirmative, while the particular is affirmative and signifies belonging, there will be a perfect syllogism, just as when the terms are universal, and the demonstration is the same as before. But when the universal at the major extreme signifies belonging and not contingency, while the other is particular and contingent, whether they are posited as affirmative or negative on both sides, or one negative and the other affirmative, there will in every case be an imperfect syllogism. Some of these are proved through impossibility, others through conversion of the contingent, just as in the earlier cases. There will also be a syllogism through conversion when the universal placed at the major extreme signifies belonging or not belonging, while the particular, being privative, is taken as contingent; for example, if A belongs or does not belong to every B, and B contingently does not belong to some C, then with C converted the syllogism comes about according to contingency. But when the proposition signifying not belonging is taken as particular, there will be no syllogism.
Termini inesne, album, animal, nix; non inesse autem, album, animal, pix, per indefinitum enim est sumenda demonstratio.Si autem universale quidem ponatur ad minorem extremitatem,particulare autem ad majorem sive privativum, sive affirmativum, sive contingens, sive inesse utrumvis, nullo modo erit syllogismus.Nec cum particulares, vel indefinitae ponentur propositiones, sive contingere sumptæ, sive inesse, seu permutatim,nec sic erit syllogismus,demonstratio autem eadem quæ in prioribus. Termini autem com munes inessequidem,ex necessitate,animal,album homo; non contingere vero, animal,album,tunica. Manifestum est igitur quoniam universali posito ad majorem extremitatem semper erit syIlogismus,ad minorem autem nunquam.
CAPUT XV.
Mixtio necessarii et contingentis in prima figura.
Quandoautemhaecquidem propositionum ex necessitate inesse,vel non inesse,illa vero contingere significat,syllogismus quidem erit hoc modo habentibus se terminis.
The terms for belonging are white, animal, snow; for not belonging, white, animal, pitch; for the demonstration must be taken through the indefinite. But if the universal is placed at the minor extreme, and the particular at the major, whether privative or affirmative, whether contingent or belonging in either way, there will be no syllogism in any way. Nor when particular or indefinite propositions are posited, whether taken as contingent or as belonging, or interchangeably, will there be a syllogism even so; and the demonstration is the same as in the earlier cases. The common terms for belonging, of necessity: animal, white, man; for not being contingent: animal, white, cloak. It is clear, therefore, that when the universal is placed at the major extreme there will always be a syllogism, but at the minor extreme never.
CHAPTER XV
The mixture of the necessary and the contingent in the first figure.
But when some of the propositions signify belonging or not belonging of necessity, while the other signifies being contingent, there will be a syllogism when the terms are disposed in this way.
Et perfectus,quando ad minorem extremitatem ponetur necessaria.Conclusio autem, si praedicativi sunt quidem termini,contingentis,et non inesse erit, universaliter, sive non universaliter ponantur,si autem sint hoc quidem affirmativum,illud veroprivativum,quanoafiirmativum qui dem,tuerit necessariumetcontingentiseritconclusio et non ejus quod est non inesse.Quando autem privativum necessarium,etcontingentis non esse,et non inesse, sive universales, sive non universales sint termini. Contigere autem in conclusione eodem modo accipiendum est quo in prioribus.Ejus autem quod est ex necessitate non inesse, non erit syliogismus,aliud enim est non ex necessitate inesse,et ex necessitate non inesse.Quoniam igitur universalibus affirmativis existentibus terminis non fit conclusio necessaria,manifestum: insit enim a omni ex necessitale,6 autem contingat omni c,erit igitur syllogismus imperfectus,quoniam a contingit omni inesse.Quoniamautemimperfectus,exdemonstratione palam, eodem enim modo ostendetur quo et in prioribus.
And it is perfect when the necessary term is placed at the minor extreme. But the conclusion, if the terms are affirmative, will be of the contingent and of not belonging, universally, whether they are posited universally or not universally; but if one is affirmative and the other privative, when the affirmative is necessary, the conclusion will be both necessary and contingent, and not of that which is not to belong. But when the privative is necessary, the conclusion will be both of the contingent not to be and of not belonging, whether the terms are universal or not universal. And "to be contingent" in the conclusion must be taken in the same way as in the earlier cases. But of that which belongs of necessity not to belong there will be no syllogism; for it is one thing to belong not of necessity, and another to belong of necessity not to belong. Therefore, since no necessary conclusion comes about when the terms are universal affirmatives, it is clear; for let A belong to every [B] of necessity, and let B be contingent of every C; there will therefore be an imperfect syllogism, since A is contingent of every [C]. But that it is imperfect is clear from the demonstration; for it will be shown in the same way as in the earlier cases.
Rursum a quidem contingat omni binesse, autem omni cinsitexnecessitate,erititaquesyllogismus,quoniam a contingat omni cinesse,sed non quoniam inest,et perfectus quidem,sed non imperfectus, statim enim perficitur ex principio propositionis.Si autem nonsimilisfigurae sint propositiones,sitprimumprivativanecessariaetaquidemnulli contingat ex necessitate, autem contingat omnic, necesse est igitur a nulli inesse. Ponatur enim a inesseautomni,aut alicui,positum autem estanulli contingere b,quoniam ergo convertitur privativa,et nulli a contingit,a autem positum est inesse aut ornni,aut alicui,quare nulli,aut non omni continget inesse, sed supponebatur omni ex principio. Manifestum autem quoniam et ejus quod estcontingere non inesse fit syllogismus,siquidem non in esse. Rursum sit affirmativa quidem propositio necessaria et a quidem contingat nulli inesse,b autem insit omni ex necessitate.Ergo fit syllogismus quidem perfectus,sed non ejus quod est non inesse,sedejus quod est contingere non inesse. Nam et propositio sic sumptaest,quae ad majorem est extremitatem,et ad impossibile non est ducere: nam si ponatur a inesse ulli c, positum est autem et a contingere nulli inesse, nihil accidit per haec impossibile. Si autem ad minorem extremitatem ponatur privativum quan do contingere quidem significaverit syllogismus erit per conversionem,quemadmodum in prioribus.
Again, let A be contingent of every B, but let B belong to every C by necessity; there will then be a syllogism that A is contingent of every C, but not that it belongs, and it is perfect, not imperfect, for it is brought to completion immediately from the premise. But if the propositions are not of the same figure, let first the privative necessary proposition be posited: let A be contingent of no B by necessity, but let B be contingent of every C; it is necessary, then, that A belong to no C. For let A be posited to belong to every C or to some C; but it has been posited that A is contingent of no B. Since, then, the privative proposition converts, and A is contingent of no B, but A has been posited to belong either to every C or to some C, therefore it will be contingent to belong to no C or not to every C; but it was assumed from the outset to be of every C. It is clear, moreover, that a syllogism of contingent not belonging also comes about, if it is of not belonging. Again, let the affirmative proposition be necessary, and let A be contingent of no B, but let B belong to every C by necessity. A perfect syllogism then comes about, but not of not belonging, but of contingent not belonging. For the proposition is also taken thus, which is toward the major extreme, and it cannot be led to an impossibility; for if A is posited to belong to some C, but it has also been posited that A is contingent of no B, nothing impossible results from these. But if the privative proposition is placed at the minor extreme, when it has signified "to be contingent," the syllogism will come about through conversion, as in the earlier cases.
Quando autem non contingere,noneritexnecessitate nec quando utraque quidem propositioprivativa,non est autem contingens quod ad minorem est.Termini autem inessequidem,album,animal,nix;non inesse quidem, album,animal,pix.Eodem autem modo se habebit et in particularibus syllogismis.Quando enim fueritprivativanecessaria,etconclusioeritejusquod est non inesse,utsi a quidemnulli contingit inesse ex neeessitate,b autem alicui ccontinvatinesse,necesse est a alicui eorum quae sunt non inesse.Si enim aomni cinest,nulli autem contingit b,et nulli a contingit inesse: quare si omni inest a,nulli contingit b,sed positum erat alicui contingere. Quando autem particularis affirmativa necessaria fuerit,quae in privativo est syllogismo,ut c,aut universalis in affirmativo, ut a b,non erit inesse syllogismus.Demonstratio autem eadem quae in prioribus.Si autem universalequiden ponatur ad minorem extremitatem vel affirmativum vel privativum contingens,particulate autem necessarium non erit syllogismus. Termini autem inesse quidem ex necessitate,animal,album, homo; non contingere autem, animal, album tunica. Quando similiter universale quidem est necessarium,particulare autem contingens,cumprivativum quidem est universale,ine8se quidem termini, animal, album, corvus; non inesse, animal,album, pix.Cum autem affirmativum,inesse quidem,animal album,cygnus;non contingereautem,animal,album, nix.
But when it is not contingent, there will not be a syllogism from necessity, nor when both propositions are privative, but the one toward the lesser term is not contingent. Terms for belonging: white, animal, snow; for not belonging: white, animal, pitch. It will be the same way also in particular syllogisms. For when the privative proposition is necessary, the conclusion will be of not belonging, as if A is necessarily contingent of no B, but B belongs to some C, it is necessary that A not belong to some of the things that are. For if A belongs to every C, but it is contingent of no B, and A is contingent of no B, then if A belongs to every C, it is contingent of no B—but it was posited that it is contingent of some. But when the particular affirmative is necessary, which is in the privative syllogism, as C, or the universal in the affirmative, as A B, there will not be a syllogism of belonging. The demonstration is the same as in the earlier cases. But if the universal is posited toward the lesser extreme, either affirmative or privative contingent, while the particular is necessary, there will not be a syllogism. Terms for belonging by necessity: animal, white, man; for not being contingent: animal, white, cloak. When similarly the universal is necessary, but the particular contingent, when the universal is privative, terms for belonging: animal, white, crow; for not belonging: animal, white, pitch. But when it is affirmative, for belonging: animal, white, swan; for not being contingent: animal, white, snow.
Nee quando indefinitae sumuntur propositiones, aut utraequeparticulares, non sic erit syllogismus. Termini autem communes,inesse quidem,animal,album,homo;non inesse autem,animal,album,inanimatum.Nam et animal alicui albo etetalbum inanimato alicui est. necessarium inesse,etnon contingitinesse et in contingenti similiter, quare ad omnia utiles sunt termini. Manifestum ergoexiisquaedictasunt, quoniam similiter habentibus se terminis,etin eo quod es inesse.et in necessariis,et fit,et non fit syllogismus, veruratamensecunduminessequidempositaprivativa propositione,ejus quod est contingere erat syllogismus,secundum necessarium autem privativa,et contingere,et non inesse.Palam autem et quoniam omnes imperfecti syllogismi, et quomodo perficiuntur per praedictas figuras.
CAPUT XVI.
De syllogismis ex ambabus contingentibus in secunda figura.
Nor will there be a syllogism when the propositions are taken as indefinite, or when both are particular. The common terms are: for belonging, animal, white, man; for not belonging, animal, white, inanimate. For animal belongs to some white thing, and white to some inanimate thing. For the necessary, [terms for] belonging and not contingent to belong, and similarly for the contingent; wherefore the terms are useful for all cases. It is clear, then, from what has been said, that when the terms are similarly disposed, both in the case of belonging and in the case of the necessary, a syllogism both comes about and does not come about, but in the case of belonging, when a privative proposition has been posited, there was a syllogism of the contingent; but in the case of the necessary, [there is a syllogism] both of the privative and of the contingent and of not belonging. It is clear also that all imperfect syllogisms are perfected through the figures mentioned above.
CHAPTER XVI.
On syllogisms from both propositions being contingent in the second figure.
secundaautera figura quando contingentes quidem sumuntur utræque propositiones, nullus erit syllogismus, sive sint affirmativæ, sive privativae, sive universaIes,sive particulares.Quando autem haee quidem inesse, illa vero contingere significat,affirmativaquideminessesignificantenunquam erit syllogismus,privativa universali existente,semper.Eodem modo et quando hæc quidem ex necessitate, ilIa vero contingere assurnatur,oportet autem et in his accipere quod in concIusionibus estcontingensquem admodum in prioribus.Primum igiturostendendum quoniam non convertitur in contingenti,privativa, ut si a contingit nulli b,non necesse est et contingere nulli a.Ponalur enim hoc et contingat nulli a inesse ergo quoniam convertuntur quæ sunt in eo quo est contingere affirmationesnegationibus,etcontrariae, et contrajacentes,b autem contingit nulli a inesse,manifestum est quoniam et omni a contingit6 inesse.Hoc autem falsum est.Non enim si hoc huic omni contingit,et hoc huic contingat necessarium, quare non convertiturprivativa.Amplius autem nihil prohibetaquidemcontingerenullib,bautemalicui a ex necessitate non inesse,utalbum quidem contingit omni homini non inesse,nam et inesse hominem autem non verumestdicerequonianicontingitnulli albo, pluribus enim ex necessitate non inest,necessarium autem non inerat contingens.Sed nec ex impossibili ostendet con vertens, ut si quis putet quoniam falsum
In the second figure, when both propositions are taken as contingent, there will be no syllogism, whether they are affirmative or privative, universal or particular. But when one signifies belonging and the other signifies being contingent, there will never be a syllogism when the affirmative signifies belonging, but always when the privative is universal. In the same way also when one is assumed as necessary and the other as contingent; but in these too one must take what is contingent in the conclusions, just as in the earlier cases. First, then, it must be shown that the privative does not convert in the contingent, as if it is contingent that A belongs to no B, it is not necessary that it also be contingent that it belong to no A. For let this be posited, and let it be contingent that it belong to no A; therefore, since the affirmations in the contingent are converted with the negations, both the contraries and the contradictories, and it is contingent that B belong to no A, it is evident that it is also contingent that it belong to every A. But this is false. For it is not the case that if this is contingent to every one of that, it is also necessary that this be contingent to this one; wherefore the privative does not convert. Moreover, nothing prevents it from being contingent that it belong to no B, while B does not belong of necessity to some A, as it is contingent that white belong to no man—for it is also possible for it to belong—but it is not true to say that man is contingent to no white; for it does not belong of necessity to many, and the necessary was not present in the contingent. But neither will one who converts show it from the impossible, as if someone should think that because it is false
est contingere nulli a inesse, verum non contingere nullia,affirmatio enim et negatio, siautem hoc verum,ex necessitate alicui a inesse £b,quare eta alicui inesse,hoc autem impossibile.Non enim si a non contingit nulli b,necesse est a alicui inesse.Nam non contingere nulli dicitur dupliciter,hoc quidem si ex necessitate alicui inest,illud vera si ex necessitate alicui non inest.Nam quod ex necessitate alicui eorum quae sunt a non inest, non est verum dicere quoniam omni contingit non inesse,quemadmodum nec alicui inest ex necessitate, quoniam omni contingit inesse. Si ergo aliquis putet quoniam contingit omni inesse,ex necessitate alicui non inesse ipsum falsum sumet,omnieniminest,si contingat,sed quoniam quibusdam ex necessitate inest, propter hoc dicimus non omni contingere.
Quare ei quod est contingere omni inesse, et ea quæ est ex necessitate alicui noninesse,similiter autem et ei quæ est contingere nulli.Palam ergo quoniam ad sic continges,et noncontingens,utin principio definivimus,non solum ex necessitate alicui inesse,sed et ex necessitate alicui non inesse sumendum.
It is possible that it belongs to no a, but not possible that it belongs to no a—for affirmation and negation—but if this is true, it necessarily belongs to some a b; therefore it also belongs to some, but this is impossible. For if it is not possible that a belongs to no b, it is not necessary that a belongs to some. For "not possible to belong to none" is said in two ways: in one way if it necessarily belongs to some, in the other if it necessarily does not belong to some. For of those things which are a, whatever necessarily does not belong to some, it is not true to say that it is possible that it belongs to none, just as neither [is it true to say] that it belongs to some necessarily, because it is possible that it belongs to all. If, therefore, someone supposes that because it is possible that it belongs to all, it necessarily does not belong to some, he will take a false premise; for it belongs to all, if it is possible, but because it necessarily belongs to certain ones, on this account we say that it is not possible that it belongs to all.
Wherefore, to "it is possible that it belongs to all" and to "it necessarily does not belong to some," and similarly also to "it is possible that it belongs to none." It is clear, therefore, that with respect to the possible and the non-possible, as we defined at the beginning, one must take not only "it necessarily belongs to some," but also "it necessarily does not belong to some.
Hoc autem sumpto,nihil accidit impossibile, quarenonfitsyllogismus.Manifestum ergoexiisquae dicta sunt quoniam non convertitur privativa.Hoc autem ostenso ponatur a,bquidem contingere nulli, vero omni,per conversionem ergo non erit syllogismus.Dictum est enim quoniam non convertitur hujusmodi propositlO.Sed nec per impossibile,nam posito 6omnic contingere inesse, nihil accidit falsum,continget enim a et omni et nuIli inesse.Omnino autem si est syllogismus,palam quoniam contingens erit,eo quod neutra propositionum sumpta est in eo quod est inesse,et hic vel affirmalivus,vel privativus: neutro autem modo possibile est,affirmativoenim posito ostendetur per terminos quoniam non contingit inesse; privativo a.utem,quon iam conclusio non est contingens, sed necessaria. Sit enim a quidem album, autem homo, in quo autem, equus,ergo album a clintingit huic quidem omni,illi vero nulli inesse, sed neque in esse contingit c,ne. que noninesse.Quoniam igiturinessenon possibile, est manifestum,nullusenim equusbomo,sed neque contingere non inesse necesse est enim nullum equum hominem esse,necessarium autemnon erat contingens,nonigiturfitsyllogismus.Similiterautemosteudetur,et si e converso ponatur privativa,etsiutr£eque affirmative ponantur, vel privative,nam per eosdem terminos erit demonstratio.
But with this assumed, nothing impossible follows; therefore there is no syllogism. It is clear, then, from what has been said that the privative proposition is not converted. But this having been shown, let it be posited that a belongs contingently to no b, but to every c; therefore, by conversion, there will be no syllogism. For it has been said that a proposition of this kind is not converted. Nor can it be shown through the impossible; for if it is posited that b belongs to every c, nothing false follows, since a will contingently belong both to every c and to no c. In general, if there is a syllogism, it is clear that it will be contingent, because neither of the propositions taken is of the kind that belongs simply, and this syllogism is either affirmative or privative; but in neither way is it possible. For if the affirmative is posited, it will be shown by terms that it does not contingently belong; but if the privative is posited, it will be shown that the conclusion is not contingent but necessary. For let a be white, b man, and that to which c applies, horse; then white a contingently belongs to every b and to no c; but neither does it contingently belong to c nor contingently not belong. That it therefore does not belong is manifest, for no horse is a man; but neither does it contingently not belong, for it is necessary that no horse be a man; but the necessary was not contingent. Therefore no syllogism results. In like manner it will be shown if the privative proposition is posited in reverse, and if both are posited as affirmative or as privative; for the demonstration will be through the same terms.
Et quando hæc quidem universalis, illa veroparticularis,vel utræque particulares, vel indefinitae, aut quolibet modo aliter contingit permutari propositiones, semper enim eritpereosdemterminosdemonstratio. Manifestum ergo quoniam utrisque propositionibus secundum contingere positis, nullus fit syllogismus.
CAPUT XVII.
Mixtio absoluti et contingentis in secunda figura.
Si autem altera quidem inesse,altera vero contingere significat, praedicativa quidem inesse posita, privativa vero contingere, nunquam erit syllogismus sive universaliter,sivE' particulariter sumantur termini,demonstratio autem eadem,etpereosdem terminos.Quando autem affirmativa quidem contingere privativa inesse, erit syllogismus. Sumatur enim a quidem nulli inesse,c vero omnia contingere,conversa ergo privativa,b inest nulli a,a autem omni contingebat, fit ergo syllogismus,quoniam ficontingi nulli c, per primam figuram. Similiter autern et si ad ponatur privativa. Si autem utræque sint privativæ,significet autem hæc quidem non inesse,illa vero contingere noninesse,per ea quidem quæ sumpta sunt nihil accidit necessarium,conversa autem secundum contingere propositione fit syllogismus, quoniam contingit nulli inesse, quemadmodum in prioribus,erit enim rursum prima figura.Si autem utræque ponantur prædicativæ, non eritsyllogismus. Termini quideminessesanitas,equus,homo.
And when one proposition is universal but the other particular, or both are particular, or indefinite, or however else the propositions happen to be interchanged, the demonstration will always be through the same terms. It is clear, therefore, that when both propositions are assumed according to contingency, no syllogism results.
CHAPTER XVII.
The mixture of the absolute and the contingent in the second figure.
But if one proposition signifies inherence and the other contingency, with the predicative proposition posited as inherence and the privative as contingency, there will never be a syllogism, whether the terms are taken universally or particularly; and the demonstration is the same and through the same terms. But when the affirmative is contingent and the privative is of inherence, there will be a syllogism. For let A be posited as belonging to no C, and let C be contingent of all B; then, with the privative converted, B belongs to no A, while A was contingent of every B; therefore a syllogism results that C is contingent of no B, through the first figure. Likewise, moreover, if the privative is posited at the other extreme. But if both are privative, and one signifies non-inherence while the other signifies contingent non-inherence, nothing necessary follows from what has been assumed; but with the proposition according to contingency converted, a syllogism results that it is contingent of none, as in the earlier cases, for the first figure will again result. But if both are posited as predicative, there will be no syllogism. The terms of inherence are health, horse, man.
Eodem autem modo sehabebitet in particularibus syllogis • mis. Quando autem erit affirmativa inesse, sive universaliter,sive particulariter sumpta,nullus erit syllogismus;boc aulem simiIiter,et per eosdem termioos demonstratur,quibus et prius.Quando autem et privativa,erit per conversionem, quemadmodum in prioribus.Rursum si ambo quidem intervalla privativa sumantur,universaliter autem quod non inesse,ex ipsis quidem propositionibus non erit necessarium,conversa autem contingenti sicut in prioribus, erit syllogismus. Si autem inesse quidem si privativa, particulariter quidem sumpta, non eri syllogismus,neque prædicativa,neque privativa existente altera propositione.Nec quando utraeque ponuntur indefinitiæ,veI affirmativæ,veI negativae,aut particulares;demonstratio autem eadem et per eosdem terminos.
CAPUT XVIII.
Mixtio necessari et contingentis in secunda figura.
In the same way it will also hold in particular syllogisms. But when the affirmative proposition is taken to belong, whether universally or particularly, there will be no syllogism; and this too is demonstrated similarly and through the same terms as before. But when the privative proposition is involved, the syllogism will come about through conversion, as in the earlier cases. Again, if both intervals are taken as privative, but the one stating that something does not belong is taken universally, no syllogism will be necessary from the propositions themselves; but with the proposition converted, a syllogism will be possible in relation to the contingent, as in the earlier cases. If, however, the one stating that something belongs is privative, and it is taken particularly, there will be no syllogism, whether the other proposition is predicative or privative. Nor will there be one when both propositions are posited as indefinite, whether affirmative or negative, or as particular; but the demonstration is the same and through the same terms.
CHAPTER XVIII.
The mixture of the necessary and the contingent in the second figure.
Si autem hæc quidem propositionum ex necesritate,illa vero contingere significat,privativa quidem necessaria, erit syllogismus,non solum quoniam contingit non inesse,sed et quoniam non inest,affirmativa autem non erit.Ponatur autem a quidem nulli inesse ex necessitate, autem omni contingere, conversa ergo privativa,et nulli a inerit,a autem omni e eontingebat.Fit igitur rursum per primam figuram syllogismus,quoniam contingit nulli inesse.Simul autem manifestum quoniam neque inest nulli c, ponatur enim inesse, ergo si a nulli contingit, b, autem inest alicui c, a alicui non contingit, sed omni ponebatur contingere. Eodem autem modo ostendetur,et si ad ponatur privativum. Rursum. Sit prædicativa quidem necessaria,altera autem privativa,et contingens,et a contingat nulli,c autem omni insit ex necessitate, sic ergo habentibus seter.minis,nuIlus erit syllogismus,accidit enim ex necessitate non inesse. Sit enim a quidem album, in quo autem b,homo, in quo vero c, cygnus, ergo album cygno quidem ex necessitate inest, homini autem contingit nuIli,et homo nulli cygno ex necessitate.Quoniam igitur ejus quod est contingere non est syllogismus,manifestum eat,nam ex necessitate non erat contingens.ced tamen non necessari,nam necessarium aut ex utrisque necessariis, aut ex pri,.
But if one of the propositions signifies necessity and the other contingency, then when the privative proposition is necessary there will be a syllogism, not only to show that it contingently does not belong, but also that it does not belong; the affirmative proposition, however, will not yield a syllogism. For let A be posited to belong to no B by necessity, and to belong to every C contingently. With the privative proposition converted, then, A will belong to no B, and A belonged to every C contingently. Thus again a syllogism is produced through the first figure, concluding that it contingently belongs to none. At the same time it is clear that it does not belong to any C either; for let it be posited to belong: then, since A contingently belongs to no B, and B belongs to some C, A contingently does not belong to some C; but it was posited to belong to every C contingently. In the same way it will be shown also if the privative proposition is attached to B. Again: let the predicative proposition be necessary, and the other privative and contingent; and let A contingently belong to no B, while C belongs to every B by necessity. With the terms so disposed, there will be no syllogism; for it happens that A does not belong by necessity. For let A be white, that in which B is, man, and that in which C is, swan. Then white belongs to swan by necessity, but contingently to no man, and man belongs to no swan by necessity. It is clear, therefore, that there is no syllogism of the contingent, for what was necessary was not contingent. Nor yet of the non-necessary; for the necessary conclusion comes either from both premises being necessary, or from the first...
vativa necessaria contingebat.Amplius et possibile est iis positis inesse c.Nihil enim prohibetc quidem sub esse, a autem quidem omni contingere, vero ex necessitate inesse,ut si quidem vigilia, autem animal,in quo autem a motus. Nam vigilanti quidem ex necessitate inest motus, animali autem nulli contingit,et omne vigilans animal.Manifestum ergo quoniam non ejus quod est non inesse,siquidem sic se habentibus terminis,necesse et inesse,neque autem oppositarum affirmationum,quare nullus erit syllogismus. Similiter autem ostendetur, et e converso posita affirmativa.Si autem similis figurae sint propositiones,cum privativæ sint,pemper fit syllogismus,conversasecundumcontingerepropositione quemadmodum in prioribus. Si sumatur enim a quidem ex necessitate non inesse,c autem contingere noninesseconversis autem propositionibus bquidem nulli inesse a, a autem omni contingit, fit igitur prima figura,et si ad ponatur privativum similiter. Si autem aedicativ£eponantur,noneritsyllogismus.
For when the privative proposition is necessary, the conclusion follows as contingent. Moreover, with these terms posited, it is possible for c to belong. For nothing prevents c from falling under b, while a belongs contingently to every b and belongs by necessity to c—for example, if b is waking and c is an animal in which a, namely motion, is present. For motion belongs by necessity to what is waking, but to no animal does it belong contingently, and every waking thing is an animal. It is evident, therefore, that there will be no syllogism of the proposition that a does not belong, since with the terms so disposed it is necessary that a belong, nor of the opposite affirmations; wherefore there will be no syllogism. In like manner it will be shown also when the affirmative proposition is posited in reverse. But if the propositions are of the same figure, when they are privative, a syllogism always comes about, with the contingent proposition converted, just as in the earlier cases. For if it is assumed that a belongs by necessity to no b, and that c contingently does not belong, and with the propositions converted, that b belongs to no a, while a belongs contingently to every c, the first figure results, and likewise if the privative proposition is added. But if the propositions are posited as affirmative, there will be no syllogism.
nam ejus quod est non inesse,aut ejus quod est ex necessita;enoninessemanifestumquoniamnonerit, eo quod non sumpta sit privativa propositio,neque in eo quod est inesse,neque in eo quod est ex necessitateinesse,sed nequeejusquod estcontingere non inesse,ex necessitate enim sic se habentibus,5 non inerit c, ut si a ponatur album, in quo autem cygnus,in quo autem homo,neque oppositarum affirmationum quoniam ostensum estb ex necessitate non inesse c,non ergo fit syllogismus omnino.Si militerautem se habebit et in particularibus syllogismis.
For in the case of what is not to belong, or of what belongs of necessity, it is evident that there will be no conclusion, because the privative proposition has not been assumed, neither in the sense of belonging nor in the sense of belonging of necessity, nor yet in the sense of contingently not belonging. For when things are so related of necessity, c will not belong—as, for instance, if a is posited as white, and that in which c is as swan, and that in which b is as man. Nor, again, in the case of the opposed affirmations, since it has been shown that c does not belong of necessity. Therefore no syllogism is produced at all. And the same will hold likewise in particular syllogisms.
Quando autem fuerit privativa,et universalis,et necess aria, semper erit syllogismus, et ejus quod est contingere non ineese,et ejus quod est non inesse, demonstratio autem per conversionern.Quando aur tem affirmativa nunquam,eodem autem modo ostendetur quo et in universalibus,et per eosdem terminos.Nec quando utræ que sumuntur affirmative,nam et hujus eadem demonstratio,quae et prius.Quando utraeque quidem privativae,universalis autem et necessaris, quas non inesse significat, per ea quidem quæ sumpta sunt, non erit necessarium, conversa autem secundum contingere propositione,erit syllogismus,quemad modum in prioribus.Si autem utraequae indefinitæ,vel particulares sumantur, non erit syllogismus,demonstratio autem eadem,et per eosdem terminos.Manifestum igitur ex praedictis quoniam privativaquidem universalis posita necessaria, semper fit syllogismus, non solum ejus, quod est contingere non inesse,sed et non inesse,affirmativa autem nunquam.Et quoniameodem modo se babentibus, et in necessariis, et in iis quæ insunt, fit et non fit syllogismus. Palam et quoniam imperfecti omnes sunt syllogismi,et quoniam omnes perficiuntur per prædictas figuras.
But when the proposition is privative, universal, and necessary, there will always be a syllogism, and a demonstration both of what is contingent not to belong and of what does not belong, and the demonstration is by conversion. But when it is affirmative, never; and it will be shown in the same way as in the universal cases, and through the same terms. Nor when both are assumed as affirmative, for the demonstration of this too is the same as the one given above. When both are privative, but the one is universal and necessary, signifying that the terms do not belong, there will not be a necessary conclusion from the premises as assumed; but with the contingent proposition converted, there will be a syllogism, as in the earlier cases. But if both are assumed as indefinite or particular, there will be no syllogism; the demonstration, however, is the same and through the same terms. It is clear, then, from what has been said that when the universal privative proposition is posited as necessary, a syllogism always results, not only of what is contingent not to belong but also of what does not belong; but when it is affirmative, never. And since matters stand in the same way in necessary propositions and in those that belong, a syllogism both comes about and does not come about. It is evident also that all syllogisms are imperfect, and that all are perfected through the figures mentioned above.
CAPUT XIX.
De syllogismis ex ambabus contingentibus in tertia figura.
In postremaautem figura,et utrisque contingentibus, et altera, erit syllogismus. Quando ergo contingere significant propositiones, et conclusio erit contingens.Et quando haec quidem contingere, illa vero inesse,similiter erit syllogismo.Quando autem altera ponitur necessaria,si affirmativa quidem non erit conclusio, neque necessaria, neque inesse. Si autem privativaejus quod est non inesseeritsyllogismus,quemadmodum in prioribus. Sumendum au. tem et in his similiter, quod est in conclusionibus contingens.Sint ergo primum contingentes,et a et contingant omnicinesse9quoniamergo convertitur affirmativa particulariter,6 autem omni ccontingit, et alicui contingit,quare si a quidem omni contingit, autem alicui b, et a alicui contingit, fit enim prima figura.Et si a quidem contingit nullic inesse, autem onjni contingat, necesse et a alicui contingere non inesse,erit enim rursum prima.
CHAPTER XIX.
On syllogisms from both premises contingent in the third figure.
In the last figure, however, there will be a syllogism both when both premises are contingent and when one of them is. Therefore, when the propositions signify contingent, the conclusion also will be contingent. And when one of them signifies contingent and the other belongs, there will likewise be a syllogism. But when one of them is posited as necessary, if it is affirmative, there will be no conclusion, neither necessary nor of belonging. But if the privative premise is of not belonging, there will be a syllogism, just as in the earlier cases. But one must also take the contingent in the conclusions in these cases in the same way. So let them first be contingent, and let A and B be contingent of all C; since the affirmative proposition converts partially, and B is contingent of all C, it is also contingent of some; therefore, if A is contingent of all C, and B of some C, then A is contingent of some B; for the first figure results. And if A is contingent of no C, but B is contingent of all C, it is necessary that A be contingent of some B not to belong; for again there will be the first figure.
figura per conversionem.Si autem utraeque privativæ ponantur,ex his quidem quæ sumpta sunt non erit necessarium, conversis autem propositionibus erit aylJogismus,quemadmodurn in prioribus.Si enim a et contingunt non inesse,si£transmutaturcontingere non inesse,rursum erit primajfigura per conversionem.Si autem hicquidemterminorumestuniversalis,ille vero particularis,eodem modo se habentibus terminis quo inesse,et erit,et non erit syllogismus.Contingat enim a quidem omni c,b autem alicui inesse,erit ergo rursum prima figura particulari propositione conversa,nam si a omni c,c autem aIicui,b et a alicui contingit.Et si ad ponatur universale, similiter. Similiter autem et si a quidem privativa sit,b autem affirmativa, erit unum rursum prima figura per conversionem, si autem utræque privativae ponantur,hæc quidem universaliter,illa vero particulariter,per ea quidem quas sumpla sunt non erit syllogismus,conversis autem propositionibus erit quemodmodum in prioribus.Quando autem utraeque indefinitæ vel particulares sumuntur,non erit syllogismus, etenim necesse est a omni b,et nulli inesse. Termini inesse,animal,homo album: non inesse, equus, homo, medium album.
figure by conversion. If, however, both premises are taken as privative, from the premises as assumed there will not be a syllogism, but with the propositions converted there will be a syllogism, as in the earlier cases. For if A and B contingently do not belong, if "contingently not to belong" is changed, again there will be the first figure by conversion. If, however, one of the terms is universal and the other particular, with the terms related in the same way as in belonging, there will and there will not be a syllogism. For let A contingently belong to all C, and B to some C; therefore there will again be the first figure with the particular proposition converted, for if A belongs to all C, and C to some B, then A contingently belongs to some B. And if the universal is added to B, similarly. Similarly, however, if A is privative and B affirmative, there will again be one first figure by conversion; but if both are taken as privative, one universally and the other particularly, from the premises as assumed there will not be a syllogism, but with the propositions converted there will be, as in the earlier cases. When, however, both are taken as indefinite or particular, there will not be a syllogism, for it is necessary that A belong to all B and to no B. Terms for belonging: animal, man, white; for not belonging: horse, man, white as the middle term.
CAPUT XX.
Mixtio contingent is et inesse in tertia figura.
Si autem haec quidem propositionum inesse, illa autem contingere significet, conclusio quidem erit quoniamcontingit,etnouquoniaminest,synogismus autem erit eodem modo se habentibus terminis,quo et in prioribus.Sint enim primum prædicativæ,et a quidem omni insit,b autem omni contingat, conversa ergo erit primafigura,et conclusio quoniam contingit a alicui inesse,cum enim altera propositionumin prima figura significabit contingere etconclusioeritcontingensSimiliter autem etsi cquidem inesse,a autem contingit inesse.Et si a quidem privativa,b autem prasdicativa, insit autem alterutrautrinque,contingenseritconclusio,fit enimrursum prima figura.Ostensum est autem quoniam si altera propositio significet contingere in prima figura et conclusio erit contingens. Si autem contingens privativa ponatur ad minorem extremitatem,vel si utraque ponatur privativa, per eaquidem quae posita suntnonerit syllogismus conversisautemeritquemadmodum et in prioribus. Si autem haec quidem propositionum sit universalis,illa vero particularis, utrisque quidemprxdicativis,autuniversali quidem privativa, particulari autem affirmativa, idem modus erit syllogismorum,omnes enim clauduntur per primam figuram.
CHAPTER XX.
The mixture of contingent and present-in [predications] in the third figure.
If one of the premises signifies present-in and the other signifies contingent, the conclusion will be that it is contingent, not that it is present-in, and the syllogism will come about with the terms related in the same way as in the earlier cases. For let the premises first be affirmative, and let A be present in every [B], but let B be contingent of every [C]; the first figure will then be produced by conversion, and the conclusion will be that A is contingent of some [C]. For when one of the premises in the first figure signifies contingency, the conclusion too will be contingent. The same holds if C is present in every [B] and A is contingent of every [B]. And if A is privative and B affirmative, with either one present in either [term], the conclusion will be contingent; for the first figure is produced again. It has been shown, moreover, that if one premise in the first figure signifies contingency, the conclusion too will be contingent. But if the contingent [premise] is taken as privative with respect to the lesser extreme, or if both are taken as privative, there will not be a syllogism from the premises as assumed, but with the propositions converted there will be, as in the earlier cases. If, however, one of the premises is universal and the other particular, with both affirmative, or with the universal privative and the particular affirmative, there will be the same mode of syllogisms; for all are concluded through the first figure.
Quare manifestum quoniam ejus quod est contingere, et non ejus quod est inesse, erit syllogismus.Si autem affirmativa quidem u niversalis,privativa autem particularis, per impossibile erit demonstratio.Insit enim quidem omni,c a autem contingat alicui non inesse,necesse est ergo a alicui contingere non inesse,nam si omni inest a ex necessitate,6 autem omni positum est inesse, a omni ex necessitate inerit.Hoc autem ostensum est prius, sed positum est alicui contingere non inesse. Quando autem indefinitae, vel particulares sumuntur utræque non erit syllogismus demonstratio autem eadem quæ et in universis et per eosdem terminos.
CAPUT XXI.
Mixlio necessarii et contingentis in tertia figura.
Therefore it is clear that the syllogism will be of what is contingent, and not of what is present-in. But if the affirmative premise is universal and the privative one particular, the demonstration will be through impossibility. For let it be present-in to all, and let C contingently not be present-in to some; then it is necessary that A contingently not be present-in to some. For if A is present-in to all of necessity, and it has been posited that B is present-in to all, then A will be present-in to all of necessity. But this was shown earlier; yet it has been posited that it contingently is not present-in to some. When, however, both premises are taken as indefinite or particular, there will be no syllogism; but the demonstration is the same as in the universal cases and through the same terms.
CHAPTER XXI.
The mixture of necessary and contingent in the third figure.
Si autem esthaecquidem propositionumnecessaria illa vero contingens,si praedicativi quidem sunt termini,semper ejus quod est contingere erit syllogismus.Quando autem fuerit hicquidem praedicativus, ille autem privativus,si sit affirmativus quidem necessarius,ejus erit quod est contingere noninesse,si autem privativus, et ejus quod est contingere non inesse,et ejus quod est non inesse; ejus autem quod est ex necessitate non inesse non erit syllogismus, quemadmodum etin aliis figuris.Sint ergo praedicativi termini primum,et a quidem omni insit ex necessitate,d autem omni contingat inesse,quoniam ergo a omni necessario inest,c autem alicui contingit,et a alicui contingens erit,et non inerit,sic enim accidit in primafigura.Similiter autem ostendetur,et si c'quidem ponatur necessaria, a autem, contingens.Rursum sit hoc quidem preedicativum, illud vero privativum,necessarium autem praedicativum,et a quidem contingat nulli inisse,b autem omni insit ex necessitate c,erit ergo rursum prima figura,et conclusio contingens,sed non inesse.Nam privativa propositio contingere significatManifeslum est igitur quoniam conclusio erit contingens; cum enim sic se habebant propositiones in prima figura, et conclusio erat contingens.Si autem privativa sit propositio necessaria, et conclusio erit, quoniam contingit alicui non inesse,et quoniam non inesse.
But if one of the premises is necessary and the other contingent, then if the terms are affirmative, the syllogism will always be of what is contingent. But when one is affirmative and the other privative, if the affirmative is necessary, the conclusion will be of what is contingent not to be present; but if the privative is necessary, the conclusion will be both of what is contingent not to be present and of what is not to be present; but there will not be a syllogism of what is of necessity not to be present, just as also in the other figures. So let the terms first be affirmative, and let a be present with every one of necessity, and let d be contingent to every one. Since, therefore, a is present with every one of necessity, and c is contingent to some, a will also be contingent to some, and will not be present; for thus it happens in the first figure. But it will be shown similarly also if c is posited as necessary and a as contingent. Again, let this one be affirmative and that one privative, but let the affirmative be necessary, and let a be contingent to be present with none, but let b be present with every one of necessity. Therefore there will again be the first figure, and the conclusion will be contingent, but not to be present. For the privative premise signifies to be contingent. It is manifest, therefore, that the conclusion will be contingent; for when the premises were thus disposed in the first figure, the conclusion was also contingent. But if the privative premise is necessary, the conclusion will also be that it is contingent for something not to be present, and that it is not present.
Ponatur enim a non inesse c,ex necessitate,b autem omni contingere,conversa ergo affirmativa,pri. ma erit figura, et necessaria privativa propositio. Cum autem sic se habebant propositiones accidebat a et contingere alicuic non inesse,etnoninesse,quare et a necesse est alicui non inesse.Quando autem privativum ponitur ad minorem extremitatem si contingens quidem,erit syllogismus transsumptapropositione,quemadmodum est in prioribus.Si autem necessarium,non erit.Etenim necesse est omni et nulli contingat inesse. Termini omni inesse, somnus, equus,dormiens homo.Nulli inesse,somnus,equus, vigilans homo.Similiter autem se habebit,et si hic quidem terminorum situniversalis ille autem particularisad medium,nam si utrique sint prædicativi, ejus quod est contingere,et non ejus quod est in esse erit syllogismus. Et quando hoc quidem privativum sumetur illud vero affirmativumnecessarium autem affirmativum,hujus quod est contingere.Quando autem privativum necessarium,et conclusio erit quod est non inesse,nam idem modus erit demonstrationis,et cum universales et non universales sunt termini.Necesse est enim per primam figuram perfici syllogismus,quare ut in illis, ut in his necessarium accidere.
For let it be posited that A does not belong to C by necessity, and that B belongs to every C contingently. Then, with the affirmative premise converted, there will be the first figure, and the privative premise will be necessary. But when the premises were related in this way, it followed that A contingently does not belong to some C, and also that it does not belong; therefore it is also necessary that A does not belong to some C. But when the privative premise is placed at the minor extreme, if it is contingent, there will be a syllogism with the premise transposed, as in the earlier cases. But if it is necessary, there will not be one. For it is necessary that it belong to every and to none contingently. Terms for belonging to every: sleep, horse, sleeping man. For belonging to none: sleep, horse, waking man. It will be similarly related also if one of the terms is universal and the other particular in relation to the middle; for if both are affirmative, the syllogism will be of what is contingent and not of what is in being. And when one is taken as privative and the other as affirmative, but the affirmative is necessary, the conclusion will be of what is contingent. But when the privative is necessary, the conclusion will be that of not belonging; for the mode of demonstration will be the same both when the terms are universal and when they are not universal. For the syllogism must be completed through the first figure; therefore, as in those cases, so in these, what is necessary will result.
Quando autem privativum universaliter sumptum poniturad minorem extremilalem,si contingens quidem, erit syllogismusperconversionem, si autem necessarium sit,nonerit,ostendeturautem eodem modo quo et in universalibus, et per eosdem terminos. Manifestum ergo et in hac figura quando et quomodo erit syllogismus, et quando ejus quod est contingere,et quando ejus quod est inesse.Palam autem et quoniam omnes imperfecti,etquoniam perficiuntur per primam figuram.
CAPUT XXII.
De syllogismo ostensivo.
Quoniamigiturquiin his figuris sunt syllogismi perficiunturpereosqui in prima figurasuntuniversales sylIogismos,et in hos reducuntur,palam ex dic- • tis.Quoniam autemsimpliciteromnissyllogismussicse habebit,nunc erit manifestum,cum ostensus fueritomnis qui fit, per aliquam harum figurarum fieri. Necesse est ergo omnem demonstrationem et omnem syllogismum aut inesse quid, aut non inesse monstrare.Ethoc aut universaliter, aut particulariter, amplius aut ostensive, aut hypothesi. Ejus autem quod est ex bypothesi,pars est perimpossibile.Primum ergo dicemus de ostensivis,his enim ostensis, manifestum erit et de iis qui ad impossibile,et omni.
But when the privative premise is taken universally and posited as applying to the minor extreme, if it is contingent, there will be a syllogism through conversion; but if it is necessary, there will not be one, and it will be shown in the same way as in the universal cases, and through the same terms. It is clear, then, also in this figure when and how there will be a syllogism, and when of what is contingent and when of what belongs. It is evident also that all are imperfect, and that they are perfected through the first figure.
CHAPTER XXII.
On ostensive syllogism.
That the syllogisms in these figures are perfected through the universal syllogisms in the first figure, and are reduced to them, is clear from what has been said. But that simply every syllogism is so disposed will now be evident, when it has been shown that every syllogism that comes about comes about through one of these figures. It is necessary, then, that every demonstration and every syllogism show either that something belongs or that it does not belong. And this either universally or particularly, and further either ostensively or by hypothesis. Of what is by hypothesis, a part is through the impossible. First, then, we shall speak of the ostensive ones; for when these have been shown, it will be clear also concerning those that lead to the impossible, and concerning every one.
no de iis qui ex hypothesi.Si ergo oporteat a de syllogizare,velinesse,vel nun inesse, necesse est sumere aliquid dealiquo.Siergo a aumalurb,quod ex principio erit sumptum, si autem a de c, autem de nullo alio,necillud deilloc, neqlledea alterum, neque de altero a, nullus erit syllogismus, nam in eo quod unum de uno sumitur, nihil accidit ex necessitate, quare assumenda est altera propositio. Si gitur sumaturade alio,aut aliud de a,aut de alterum, esse quidem syllogismum nihil prohibet,ad autem non eritpereaquae sumptasunt,necquandocinestatteri, et illud alii, et hoc alteri,non copuletur autem ad' necsic eritad syllogismus ipsiusa. Omnino enim dicimus quoniam nullus nunquam erit syllogismus alius de alio,non sumpto aliquo medio, quod ad utrumque se habet quoquo modo praedicationibus.
Concerning those which come from a hypothesis. If, then, one must syllogize that A belongs or does not belong to something, it is necessary to take something of something. If, then, A is taken of B, which will have been taken from the principle, but if A is taken of C, and C of nothing else, nor that of that, nor either of the other, nor the other of A, there will be no syllogism; for in that which is taken as one of one, nothing results of necessity, wherefore the other premise must be assumed. If, then, it is assumed that A is of another, or another of A, or of the other, nothing prevents there being a syllogism, but it will not be through the things assumed, nor when one thing is in another, and that in a third, and this in a fourth, unless they are coupled together; nor even so will there be a syllogism of A itself. For in general we say that there will never be any syllogism of one thing concerning another unless some middle term is taken which stands in some way in relation to both by predications.
Nam syllogismus quidem simpliciter ex propositionibus est, ad hoc autem syllogismus ex propositionibus,quae ad hoc,qui autem est hujus ad hoc, per propositiones hujus ad hoc,impossibileestautem ad sumere propositionem, nihil neque praedicantes de eo,neque negantes,aut rursum ejus quod est a ad b,nihiI communes sumentes,sed utriusque propria quædam prcedicantes,aut negantes, quare sumendum, utriusque quod copulet praedicationes, si erithujusad hocsyllogisrnus.Ergo si necesse est aliquod sumere ad utrumque commune, hoc autem contigit tripliciter, aut enim a de et de proedicantes,aut deutriusque,aut utraque de hae autem sunt tres dictae figuræ.Manifestum quoniam omnem syllogismum necesse est fieri per aliquam harum figurarum.Nam eadem ratio est,etsi per plura copuletur ad b,eadem enim erit figura et in pluribus. Quoniam igitur ostensivi terminantur per prædictas figuras, manifestum est.
For a syllogism simply is from propositions, but a syllogism for this end is from propositions that are for this end, and the syllogism that is of this in relation to this is through propositions of this in relation to this. But it is impossible to assume a proposition while predicating or denying nothing of it, or again, in the case of that which is A in relation to B, to assume no common terms, but rather to predicate or deny certain properties of each. Wherefore one must assume what joins the predications of each, if there is to be a syllogism of this in relation to this. Therefore, if it is necessary to assume something common to both, and this happens in three ways—for either one predicates A of both, or both of a third, or both of each—and these are the three figures that have been stated, it is manifest that every syllogism must come about through one of these figures. For the same account holds even if the connection to B is made through more terms; for the figure will be the same even with more terms. That demonstrative syllogisms are concluded through the aforesaid figures is therefore manifest.
CAPUT XXIII.
De syllogisma ex hypothesi.
Quoniam autem et qui ad impossibile, palam erit per haec, omnes enim qui per impossibile concludunt, falsum quidem syllogizant. Quod autem ex principio erat, ex hypothesi demonstrant, quando aliquid accidit impossibile posita contradictione,ut quoniamdiameterestasymeter, eoquod fiunt abundentia aequalia perfectis,posito symetro.Ergo æqualia quidem fieri abundantia perfectis syllogizant, asymetrum autem esse diametrum, ex hypothesi, monstrant,quoniam falsum accidit propter contradictionem.Hoc enim fuit per impossibile syllogizare ostendere aliquid impossibile propter priorem hypothesin.Quare quoniam falsus fit syllogismus ostensivus in his quae ad impossibile deducuntur,quod autem est ex principio, ex hypothesi monstratur, ostensivos autem diximus prius, quoniam per has terminantur nguras,mamfestum quoniam etper impossibile syllogismi per has erunt figuras. Similiter autem et alii omnes qui sunt ex hypothesi, in omnibus his enim syllogismus quidem fit ad transsumptum, quod autem estex principio, terminatur per confessionem aut per aliquam aliam hypothesin. Si autemhocverum,necesseest omnem demonstrationem et omnem syllogismum fieri per tres praedictas figuras.Hoc autem ostensos, palam quoniam omnis syllogismus perficitur per primam figuram, et reducitur in hujus universales syllogismos.
CHAPTER XXIII.
On the syllogism from a hypothesis.
Since this is so, it will also be clear from these things regarding the syllogism that leads to the impossible. For all who conclude through the impossible syllogize something false, but they demonstrate what was from the beginning from a hypothesis, when something impossible results once the contradiction is posited—for example, that the diagonal is incommensurable, because equal magnitudes come to be when the side is posited as commensurable. So they syllogize that equal magnitudes come to be, but they show from a hypothesis that the diagonal is incommensurable, because something false results on account of the contradiction. For this was to syllogize through the impossible: to show that something impossible follows on account of the prior hypothesis. Therefore, since the ostensive syllogism becomes false in those things that lead to the impossible, but what was from the beginning is shown from a hypothesis—and we said earlier that ostensive syllogisms are completed through these figures—it is evident that syllogisms through the impossible will also be through these figures. Likewise, all the others that are from a hypothesis are so too; for in all of these a syllogism comes about with respect to what is transsumed, but what was from the beginning is concluded through an admission or through some other hypothesis. If this is true, it is necessary that every demonstration and every syllogism come about through the three aforementioned figures. That this is so is clear from what has been shown, since every syllogism is perfected through the first figure and is reduced to its universal syllogisms.
CAPUT XXIV.
De qualitate et quantitate terminorum syllogismi.
Amplius autem in omnibus oportet aliquem terminorum praedicativum esse et universalem, sine universali enim non erit syllogismus,aut non ad hoc quod positum est, aut quod ex principio est petet. Ponatur enim musicam voluptatem esse studiosam, si ergo poposcerit voluptatem esse studiosam, non addens omnem, non erit syllogismus, si autem aliquam voluptatem esse studiosam,si aliam quidem, nihil ad hoc quod positum est, si autem eamdem, quod ex principio erat, sumit.
CHAPTER XXIV.
On the quality and quantity of the terms of the syllogism.
Moreover, in all cases one of the terms must be predicated and universal; for without a universal there will be no syllogism, or it will not be toward the proposed conclusion, or it will beg the question. For let it be posited that musical pleasure is desirable; if, then, he demands that pleasure is desirable, without adding "all," there will be no syllogism; but if he says that some pleasure is desirable, if indeed it is another pleasure, it is nothing to the proposed conclusion; but if it is the same one, he assumes what was from the beginning.
Magis autem fit manifestum in tJguris,ut quoniam aequicruris aequales sunt anguli, qui sunt ad basim: sint enim in centrum ductæ a b, si ergo aequalem sumpserit a angulum ei qui est d, non omnino petens aequales eos qui sunt semicirculorum,et rursum ei qui est d,non omnem assumens eum qui est incisionis.Amplius,ab aequalibus existentibus,totis angulis,æqualibus demptis, aquales esse reliquos, scilicet e /, quod ex principio est petet, nisi sumat ab omnibus aequalibus,aequis demptis,aequalia relinqui.Manifestumigitur quoniam in omni syllogismo oportet universale esse.Et quoniam universalequidem ex omnibusterminis universalibus monstratur,particulare autem et sic,et aliter.Quare si conclusio sit universalis,et terminos necesse est universales esse, si autem universales sint termini,contingit conclusionem non universalem esse.Palam etiam qnoniam in omni syllogismo aut ulramque,aut alteram propositionem similem necesse est fieri conclusioni, dico autem non solum in eo quod affirmativa sit, vel negativa, sed in eo quod necessaria aut inesse, aut contingens: considerare autem oportet et alia praedicamenta.Manifestum autem et simpliciter quando erit,et quando non erit syllogismus,et quando perfectus,et quoniam si est syllogismus, necessarium est habere terminos secundum aliquem dictorum modorum.
But it becomes more evident in the figures, as that the angles at the base of an isosceles triangle are equal; for let a and b be drawn to the center. If, then, one assumes the angle a to be equal to the angle d, without assuming in every case that the angles of the semicircles are equal, and again assumes the angle d to be not every angle of the segment—further, when the whole angles are equal and equal parts are taken away, the remaining angles are equal, namely e and f, one will be begging the principle, unless one assumes that from all equal wholes, when equal parts are taken away, equal parts remain. It is evident, therefore, that in every syllogism the universal must be present. And that the universal is indeed demonstrated from all universal terms, but the particular both in this way and otherwise. Wherefore, if the conclusion is universal, the terms must also be universal; but if the terms are universal, it happens that the conclusion is not universal. It is clear also that in every syllogism either both propositions or one of them must be similar to the conclusion—I mean not only in respect of being affirmative or negative, but in respect of being necessary, or present, or contingent; but one must also consider the other categories. It is evident also simply when there will be a syllogism and when there will not be, and when it is perfect, and that if there is a syllogism, it is necessary that it have its terms according to some one of the modes stated.
CAPUT XXV.
De numero terminorum syllogismi.
Palam autem et quoniam omnis demonstratio erit per tres terminos,et non per plures, nisi per alia et alia eadem conclusio fiat, ut e per a b, et per d, aut per a b, et a r., et c, plura enim media eorumdem nihil esse prohibet, haeo autem cum sint, nnn unus, scd plures sunt syllogismi.Aut rursum, quanto utrumque a sumitur per syllogismum, ut a per e, et rursum per a, aut hoc quidem inductione, illud autem syllogismo, sed et si plures erunt syllogismi,plures enim conclusiones sunt. ul a et c. Si igitur non plures, sed unus (sic autem contingit fieri per plura media eamdem conclusionem,ut e quidem per a e d), impossibile.Sit enim e conclusio ex a & d, ergo necesse est aliquid eorum, aliud ad aliud sumptum esse, hoc quidem ut totum, illud vero ut pars, hoo enim ostensum est prius, quoniam si est syllogismus, necesse est sic aliquos se habere terminornm. Uabeat se ergo a sic ad b, itaque aliqua ex eis conclusio, aut ergo e, aut alterum eorum quafi sunt d, aut altarum aliud quidem praeter hæc. Et si e quidem,ex a tantum, erit syllogismus, autem quidem se habeant sic, ut sit hoc quidem ut notum,illud vero ut pars, erit aliquid ex illis aut e,aut aliquid eorum quaesunt ab, aut alterum aliud quidem praeter haec.El sie quidem auteorum quæ sunta alterum, aut plures erunt syllogismi, aut (ut contingebat) idem per plures ter.
CHAPTER XXV.
On the number of terms in a syllogism.
It is also clear that every demonstration will be through three terms, and not through more, unless the same conclusion is produced through different terms, as e through a b, and through d, or through a b, and through a r, and c; for nothing prevents there being several middle terms of the same things, but when these exist, there are not one but several syllogisms. Or again, inasmuch as each of the two is assumed through a syllogism, as a through e, and again through a, or this one indeed by induction, that one by syllogism; but even if there are several syllogisms, there are several conclusions, as a and c. If, then, there are not several, but one (for thus it happens that the same conclusion is produced through several middle terms, as e through a e d), it is impossible. For let e be the conclusion from a and d; therefore it is necessary that something of them be taken as one in relation to another, this indeed as a whole, that as a part; for this was shown earlier, that if there is a syllogism, it is necessary that some of the terms be related in this way. Let a therefore be related thus to b, so that some conclusion comes from them, either e, or one of those which are d, or some other thing besides these. And if indeed e, the syllogism will be from a alone; but if they are related thus, that this is as known and that as a part, there will be something from them, either e, or something of those which are a b, or some other thing besides these. And if indeed it is one of those which are a, either there will be several syllogisms, or (as was happening) the same thing through several terms.
minos concludi accidit,si autem aliud quidem præter hæc,plures erunt et inconjuncti syIlQgismi ad invicem,si autem non sic se habeat ad ut faciat syllogismum vane erunt sumpta, nisi inductionis, aut celationis,aut alioujus alius talium gratia. Si autem ex a non e, sed alia quædam fit conclusio, ex autem aut horum alterum, aut aliud præter hsec,et plures fiunt syllogismi, et non ejus quod positum est. Ponebatur enim ejus quod est esse syllogismnm. Si autem non fiat ex nulla conclusio, et vane sumpta esse ea accidit,et non ejus quod est ex principio esse syilogismum.Quare manifestum quoniam omnis demonstratio et omnis syllogismus erit per tres terminos solos.
CAPUT XXVI.
De numero propositionum et prosyllogismis.
Hoc autem manifesto,paIam quoniam et ex duabus propositionibus,et non pluribus,nam tres termini,duæ sunt propositiones, nisi assumatur aliquid (quemadmodum in prioribus dictum est) ad perfectionem syllogismorum.
unless it happens that the conclusion is established through different terms; but if there is something else besides these, there will be more syllogisms and they will be unconnected with one another. But if it is not related in such a way as to produce a syllogism, the assumptions will be vain, unless for the sake of induction, or concealment, or some other such thing. But if from a there is not e, but some other conclusion is produced, and from these either one of the two, or something else besides these, then there also come to be more syllogisms, and not of the thing that was posited. For it was posited as being a syllogism of it. But if no conclusion follows from them, then it happens that they were assumed in vain, and that the syllogism is not of the principle. Wherefore it is clear that every demonstration and every syllogism will be through three terms only.
CHAPTER XXVI.
On the number of propositions and on prosyllogisms.
With this made clear, it is also plain that [a syllogism is composed] from two propositions and not more; for there are three terms, [and] two propositions, unless something is assumed (as was said in the earlier passages) for the perfection of syllogisms.
Manifestum igitur quando, ut in oratione: syllogisticafnon pares sunt propositiones per quas fit conclusio principalis (quasdam enim superiorem conclusionem necessarium est esse propositiones), haec oratio siut pon syllogistica est, aut plura necessariis interrogavitad positionem.Secundum igitur principales propositiones sumptis syllogismisjomnis syllogismus erit ex propositionibus quidem perfectis,ex terminis autem abundantibus,uno enim plures termini propositionibus,erunt autem et conclusiones dimidietas propositionum. Quando antem per pro syllogism os concluditur, aut per plura media non continua,ut a per c.d, multitudo quidem terminorum similiter uno superabit propositiones,aut enim extrinsecus,aut medium ponetur intercidens terminus, utrinque autem accidit uno minus esse intervallo quam terminos, propositiones autem aequales sunt intervallis. Non tamen hae quidem semper perfectae erunt, illi vero abundantes, sed permutatim, quia cum propositiones quidem sunt perfectae, abundantes erunt termini, cum vero termini perfecti,abundantes erunt propositiones simul enim termino addito,una additur propositio, undecunque addatur terminus.
It is clear, then, when—as in an argument—the propositions through which the principal conclusion is produced are not equal in number (for some of them must be propositions of a higher conclusion), this argument is either not syllogistic, or it has asked more questions than are necessary for the thesis. Therefore, when syllogisms are taken according to the principal propositions, every syllogism will consist of perfect propositions but of abundant terms; for one term is more numerous than the propositions, and the conclusions will also be half the propositions. But when the conclusion is reached through things that are not syllogistic, or through several non-continuous middle terms—as A through C and D—the multitude of terms will likewise exceed the propositions by one; for either an external term is assumed, or a middle term is inserted in between. In either case it happens that the intervals are one fewer than the terms, while the propositions are equal to the intervals. Yet these will not always be perfect and those abundant, but alternately; for when the propositions are perfect, the terms will be abundant, and when the terms are perfect, the propositions will be abundant. For at the same time, when a term is added, one proposition is added, wherever the term is added.
Quare quoniam hee propositiones quidem perfectae, illi vero abundantes erant, necesse est transmutare eadem, additione facta.Conclusiones autem non etiam eum habebunt ordinem neque ad terminos, neque ad propositiones, uno enim termino addito,conclusiones adjungentur uno,pauciores preeexistentibusterminis,ad solum enim ultimum non facit copclusionem,ad alios autem omnes. Ut si eis quae sunt a c, adjacet d, statim et conclusiones duae adjacent. quæ ad a, et ad b, similiter autem et in aliis.Si autem ad medium intercidat, eodem modo,ad unutq enim solum non faciet syllogismum, quare multo plures conclusiones erunt et terminis et propositionibus.
CAPUT XXVII.
De problematisthocest propositis in unaquaque figura facile et difficile construendis et destruendis.
Quoniam autem habemus ex quibus syllogismi,et quale in unaquaque figura, et quot modis monstratur,manifestum nobis est, et qqse propositio facile, et quæ difficile argumentabilis est.Nam quae in pluribus figuris et per plures casus concluditur,facilis; quae autem in paucis et per pauciores,difficilius argumentabilis. Ergo affirmativa quidem universalis per primam tantumfiguram monstratur,etper hanc simpliciter, Privativa vero et per primam, et per mediam. Per primam quidem simpliciter, per mediam autem dupliciter. Particularis autem affirmativa per primam et per postremam, simpliciter quidem per primam.
Therefore, since some of these propositions were perfect and others were abundant, it is necessary to transpose the same ones, with an addition made. But the conclusions will not also have the same order, neither with respect to the terms nor with respect to the propositions; for when one term is added, conclusions are joined by one, fewer than the pre-existing terms, for it does not produce a conclusion with respect to the last alone, but with respect to all the others. For example, if d is adjacent to those which are from c, immediately two conclusions are also adjacent, those to a and to b; and similarly in other cases. But if it falls in the middle, in the same way, for it will not make a syllogism with respect to one alone; wherefore there will be many more conclusions than both terms and propositions.
CHAPTER XXVII.
On problems, that is, on propositions, easily and with difficulty constructed and destroyed in each figure.
Since we have [the principles] from which syllogisms [are made], and what sort [of syllogism] is in each figure, and in how many ways it is demonstrated, it is clear to us also which proposition is easy and which is difficult to argue. For that which is concluded in more figures and through more cases is easy; but that which [is concluded] in few and through fewer [cases] is more difficult to argue. Therefore, the universal affirmative is demonstrated through the first figure only, and through this simply; but the privative [is demonstrated] both through the first and through the middle. Through the first indeed simply, but through the middle in two ways. But the particular affirmative [is demonstrated] through the first and through the last, indeed simply through the first.
tripliciter autem per postremam. Privativa vero particularis in omnibus figqris monstratur, verum in prima quidem semel,in media autem et postrema,in illa quidem dupliciter, in hac verQ tripliciter,Manifestum ergQ quoniam universalem affirmativam construere quidem difficillimum, destruere autem facillimum, omnino autem est interimenti quidem,universalia quam particularia facilius.Etenim si nulli,etsi alicui non insitinteremptum est, horum autem alicui quidem non in omnibus figuris monstratur, nulli autem in duabus. Eodem autem modo et in privativis, etenim si omni, et si alicui, interemptum est quod ex principio. Hoc autem fuit in duabus figuris. In particularibus autem simpliciter,aut omni,aut nulli ostendentem inesse. Construenti auten:,facilius est particularia,nam in pluribus figuris,et per plures modos.Omnino autem non oportet latere quoniam destruere quidem per se invicem est, et universalia per particularia, et hæc per universalia; construere autem non est per particularia universalia,per illa vero haec est, Nam si omni, et alicui Simul autem manifestum quoniam destruere quam construere facilius.Quomodo ergo fit omnis syllogismus,et per quot terminos et propositiones, et quomodo habentes se ad invicem, amplius autem quae propositio in unaquaque figura, et quae in pluribus,et quæ in paucioribus monstratur, palam ex his quae dicta sunt.
But in three ways through the last figure. A particular privative proposition is proved in all the figures, but in the first figure in one way, in the middle and the last, in the former in two ways, in the latter in three. It is evident, therefore, that to establish a universal affirmative is most difficult, but to destroy it is most easy; and in general, to destroy universals is easier than particulars. For if it is predicated of none, even if it is not present in some, it has been destroyed; but of these, that it is not present in some is not proved in all the figures, while that it is present in none is proved in two. In the same way also in privative propositions; for if it is predicated of all, and if of some, what was from the beginning has been destroyed. But this was in two figures. In particulars, however, simply, either by showing that it is present in all or in none. But for one who establishes, particulars are easier; for it is in more figures and through more modes. But in general it must not escape notice that to destroy is by turns, both universals through particulars and these through universals; but to establish universals is not through particulars, but through those these are. For if it is predicated of all, also of some. At the same time it is evident that to destroy is easier than to establish. In what way, therefore, every syllogism comes about, and through how many terms and propositions, and how they are disposed toward one another, and further, which proposition is proved in one figure and which in more, and which in fewer, is clear from what has been said.
CAPUT XXVIII.
De abundantia propnsitionum.
Quomodo autem idonei erimus semper syllogizare ad propositum, et per quam viam sumemus circa unumquodque principia,nunc dicendum.Non enim solum fortasse oportet generationem considerare syllogisrnorum, sed et potestatem habere faciendi. Omnium igitur quæ sunt, hæc qnidem sunt tali a, ut de nullo alio praedicentur vere universaliter, ut Oleon, et Callias,et quod singulare, et sensibile, de his autem alia,nam et homo, et animal uterque horum est. Illa vero et ipsa quidem de aliis prædicantur, de illis autem alia prius non prædicantur, alia autem et ipsa de aliis,et de his alia,ut homo de Callia,et de homine animal.Quoniam ergo quaedam eorum quae sunt de nullo nata sunt dici, palam: namsensibilium pene unumquodque est hujusmodi, ut de nullo prædicelur,nisi,ut secundum accidens, dicimus enim quandoque album illud Socratem esse, et hoc veniens Galliam. Quoniam autem in sursum pergentibus statur quandoque, rursum dicemus.
CHAPTER XXVIII.
On the abundance of propositions.
We must now say how we shall always be ready to syllogize toward the proposed conclusion, and by what path we shall take the principles concerning each thing. For perhaps it is not only necessary to consider the generation of syllogisms, but also to have the power of making them. Of all the things that are, some are of such a kind that they are not truly predicated universally of anything else, as Oleon, and Callias, and what is singular and perceptible; but others are predicated of these, for both man and animal are each of these. And some things are themselves predicated of others, while others are not predicated of them prior; but others are themselves predicated of others, and others of these, as man of Callias, and animal of man. Since, therefore, it is plain that some of the things that are are naturally predicated of nothing—for almost each of the perceptible things is of this sort, so that it is predicated of nothing, except as we speak in virtue of an accident; for we sometimes say that that white thing is Socrates, and this one coming from Gaul. But since in going upward one comes to a stop at some point, we shall speak of this again.
Nunc autem sit hoepositum,de iis ergo pradicatum aliquod non est demonstrare nisi secundum opinionem,sed hæc de aliis,neque singularia de aliis, sed alia de ipsis.Qus autem in medio sunt,manifestum quoniam utrumque contingit,nam et hæc de aliis, et alia de his dicuntur, et pene rationes et considerationes sunt maxime de his.Oportet ergo propositiones circa unumquoque horum sic snmere supponentem,ipsum primum et definitiones,et quæcunque propria eunt rei,deinde post hoc quascunque sequuntur, rem. Et rursum quæ res sequitur,et quaecunque non contingit ipsi inesse,quibus autem ipsa non contingit,non surnendum,eo quod convertitur privativa, Dividendum autem est, et eorum quae sequuntur, quaecunque in eo quod quid est,et quæcunque ut propria, et quaecunque ut accidentia praedicantur, et horum quæ secundum opinionem,et quae secundum veritatem. Quanto enim plurium talium abundaverit quis,citius inveniet conclusionem,quanto autem veriorum,magis demonstrabit. Oportet autem eligere non quse sequuntur aliquam, sed quæcunque totam rem sequuntur, ut non quod aliquem hominem, sed quod omnem hominem sequitur, per universales enim propositiones fit syllogismus. Cum autem est indefinitum,incertum si universalis est propositio, cum vero definitum, manifestum. Similiter autem eligendum et quae ipsum sequitur tota, propter dictam causam.
But now let this be laid down: it is not possible to demonstrate anything predicated of these things except according to opinion, but these things are said of other things, and singulars are not said of other things, but other things of them. But those which are in the middle, it is manifest that both are possible, for both these are said of other things and other things are said of these, and reasonings and considerations are for the most part about these. One must therefore take propositions about each of these in this way, supposing first the thing itself and its definitions, and whatever things are proper to the thing, and then after this whatever things follow the thing. And again, what the thing follows, and whatever things cannot be present in it; but those things which cannot be present in it, one must not take, because of the conversion of the privative. One must divide also, of the things that follow, whatever things are predicated in the what-it-is, and whatever things as proper, and whatever things as accidents, and of these, those according to opinion and those according to truth. For the more abundant one is in such things, the more quickly will he find the conclusion; but the more true things he has, the more will he demonstrate. One must choose not the things that follow some particular, but whatever things follow the whole thing, as not what follows some man, but what follows every man; for it is through universal propositions that the syllogism comes about. But when it is indefinite, it is uncertain whether the proposition is universal; but when it is definite, it is manifest. In like manner one must choose also the things that follow the thing itself as a whole, for the reason stated.
Jpsum autem quod sequitur, non est sumendum totum sequi,dico ut hominem omneanimal, aut musicam, omnem disciplinam, sed simpliciter solum sequi quemadmodum et praetendimus, etenim inutile alterum et impossible,ut omnem hominem esse omne animal, vel justitiam omne bonum, sed cui consequens est, in illo omni esse dicitur. Quando autem ab aliquocontinetur subjectum, cujus consequentia oportet sumere, quae universale quidem sequuntur, vel non sequuntur, non eligendum in his, sumpta enim sunt in illis quaecunque animal et hominem sequqntur, et quaecunque non animali insunt,similiter. Quæ autem in unoquoque sunt propria,sumendum: sunt enim quædam speciei propria praeter genus,necesse est enim diversis speciebus propria quasdam inesse.Neque autem universale eligendum iis quae sequitur quod continetur, ut animal iis quæ sequitur homo, necesse est enim si hominem sequitur animal,et haec omnia sequi,convenientioraautem haechominiselectioni.Sumendum autem et quæ plerumque sequuntur eaquae consequuntur, nam et problematibus quae plerumque, et syllogismus ex propositionibus,quae pIerumquc aut in omnibus, aut aliquibus, similis enim est uniuscujusqueconcl usio principiis.Amplius quæ omnibus sequentia sunt,non eligendum,non enim erit syllogismus exipsis,ob quam autem causam,in sequentibus erit manifestum.
But what follows next must not be taken as "everything follows," I mean as "every animal follows man" or "every discipline follows music," but only simply as we have also set out before; for the other is both useless and impossible, as that every man is every animal, or that justice is every good, but that to which something is consequent is said to be in that whole. But when the subject is contained by something, whose consequents one must take, those which follow the universal, or do not follow, are not to be chosen in these cases; for whatever follows animal and man has been taken in those, and similarly whatever is present in non-animal. But the properties in each individual thing must be taken; for there are certain properties of a species beyond the genus, for it is necessary that certain properties be present in different species. Nor again is the universal to be chosen for those things which the contained thing follows, as animal for those things which man follows; for it is necessary that if animal follows man, all these also follow, but these are more suitable for the selection of man. One must also take the things which for the most part follow those things which are consequent; for both in problems that hold for the most part, and in the syllogism from propositions that hold for the most part or in all or in some cases, the conclusion of each is similar to the principles. Moreover, things that follow all are not to be chosen, for there will not be a syllogism from them; and for what reason, will be made clear in what follows.
CAPUT XXIX.
Medii syllogismorum inveniendi regulas.
Construere ergo volentibus aliquid de aliquo toto, ejus quidem quod construitur, inspiciendum ad subjecta de quibus ipsum dicitur, de quoautem oportet praedicari quascunque hoc sequuntur. Si enim aliquod horum sit idem, alterum alteri necesse est inesse. Si autem non quoniam omni, sed quoniam alicui, quae sequiturutrumque, si enim aliquod horum idem fuerit, necesse est alicui inesse. Quando autem nulli oporteat inesse,cui quidem oportet non inesse, ad sequentia subjecti, quod autem oportet non inesse,inspiciendum ad ea quae non contingunt illi adesse. Aut conversim cui quidem oportet non inesse, ad ea quae non contingunt eidem adesse, quod vero non inesse, inspiciendum ad sequentia Nam si haec sint eadem utrorumque,nulli contingit alteri alterum inesse,fitenim quandoque quidem in prima figurasyllogismus, quandoque autem in media.Si autem alicui non inesse,cui quidem oportet non inesse,quae consequitur: quod vero non inesse, quae non possibile est illi inesse. Si enim aliquid horum sit idem, necesse est alicui non inesse. Magis autem fortasse erit sic, unumquodque eorum quae dieta sunt manifestum.
CHAPTER XXIX.
Rules for finding the middle terms of syllogisms.
Therefore, for those who wish to construct something about a whole, of that which is being constructed one must examine the subjects of which it is said, and of that about which it ought to be predicated, whatever follows it. For if any of these be the same, the one must necessarily belong to the other. But if not as belonging to every, but as belonging to some, one must examine what follows both; for if any of these be the same, it is necessary that it belong to some. But when it ought to belong to none, of that to which it ought not to belong one must examine the things that follow the subject, and of that which ought not to belong, one must examine those things which cannot be present to it. Or conversely, of that to which it ought not to belong, one must examine those things which cannot be present to the same, and of that which ought not to belong, one must examine the things that follow. For if these be the same on both sides, it cannot belong to any, the one to the other; for sometimes a syllogism comes about in the first figure, sometimes in the middle. But if it ought not to belong to some, of that to which it ought not to belong, one must examine what follows; and of that which ought not to belong, those things which it is not possible for it to belong to. For if any of these be the same, it is necessary that it not belong to some. But perhaps it will be clearer in this way, each of the things that have been stated.
Sint enim sequentia quidem a, in quibus b, quae autem ipsum sequitur, in quibns, c,quæ autem non contingunt ei inesse,in quibus, rursum autem ipsi e quae quidem insunl, in quibus /, quae autem ipsum sequitur, in quibus y, quæ autem non contingunt eidem inesse, in quibus h. Si ergo eidem aliquid eorum quae sunt c, alicui eorum quas sunt f, necesse est aomni e inesse, nam quidem omni a, c, autem omni a, quare omni e inest. Si autem et idem, necesse est alicui e inesse a, nam id quod est e a, vero quod est et omne ei sequitur. Si autem et sint idem, nulli e inerit ex proprio syllogismo, quoniam enim con. vertitur privativa, et ei quod est idem, nulli inerit a, / autem omni e. Rursus si et idem, nulli e inerit a, nam a quidem omni, ei autem in quo e nulli inerit. Idem enim erat ei quod est A,; A autem nulli e inerat. Si autem et idem, a, alicui e non inerit, nam ei-quod est non inerit a, quoniam neque d, autem sub e est, quare alicui e non inerit. Si autem et idem, conversus erit syllogismus, nam inerit omni a, nam ei quod est a, e autem ei quod eat b, idem enim erat ei quod est g, a autem ei quod est e, omni quidem non necessarium est inesse, alicui autem necessarium, eo quod convertatur universale prædicativum in particu lare. Manifestum ergo quoniam ad praedicta perspiciendum utrinque in unaquaque quæstione,per haec enim omnes syllogismi.
For let the things that follow be a, those in which b is present, and those that follow b be the things in which c is present; and let the things that cannot be present to it be those in which r is present; and again, let the things that are present to e be those in which f is present, the things that follow e be those in which y is present, and the things that cannot be present to the same be those in which h is present. If, therefore, something among the things that are c is the same as some one of the things that are f, it is necessary that a be present to every e; for a is present to every c, and c is present to every a, and therefore it is present to every e. But if the same thing is also [present to some e], it is necessary that a be present to some e; for that which is e is the same as a, and that which is a follows every e. But if [c and f] are also the same, a will be present to no e by the proper syllogism; for since the privative proposition converts, a will be present to no e, and f will be present to every e. Again, if [c and y] are the same, a will be present to no e; for a is present to every c, but will be present to nothing in which e is; for it was the same as that which is a, and a was present to no e. But if [f and d] are also the same, a will not be present to some e; for it will not be present to that which is d, since neither is d under e, and therefore a will not be present to some e. But if [b and h] are also the same, the syllogism will be converted; for a will be present to every e; for e is the same as that which is a, and a is the same as that which is b; for it was the same as that which is g, and a is the same as that which is e. It is not necessary that it be present to every one, but it is necessary that it be present to some, because the universal affirmative converts into a particular. It is clear, therefore, that one must look to the things previously stated on both sides in each inquiry; for through these come all syllogisms.
Oportet autem et sequentium,et quibus sequitur singulum,ad prima et universalia maxime inspicere, ut e quidem magis ad fquam ad / solum, a autem ad magis quam ad solum. Si enim ei quod est finest a, et ei quod est finest et ipsi e, si vero hoc non sequitur a, possibile est id quod est sequi. Similiter autem et in quibus idem sequitur, considerandum, namsi primis, et iis quae sub ipsis sunt, sequitur; si autem non his, et iis quae sub ipsis sunt, possibile. Palam autem quoniam per tres terminos et duas propositiones consideratio, et per praedictas figuras syllogismi omnes,monstratur enim omniquidemeinesse. a, quando eorum quae sunt / idem, quiddam SIl-. mitur, hoc autem erit medium, extremitates autem;., et fit enim prima figura. Alicui autem quando et sumitur idem, hoc autem postrema figura, medium enim fit g. Nulli vero quando et / idem; sic autem et prima figura,et media: prima quidem, quoniam nulli finest a, siquidem convertitur privativa, autem omni e. Media autem quoniam a quidem nulli, e autem omni inest. Alicui autem non inesse, quando et idem fuerit, haec autem postrema figura, nam a quidem nulli inerit, e vero omni; manifestum igitur est quoniam perpraedictas figuras omnes syllogismi.
But one must also look especially at the things that follow and at the things to which each single thing follows, in relation to the primary and universal terms—for instance, e rather to f than to this alone, and a rather to that than to this alone. For if it follows what is f, and also follows what is f and e itself; but if this does not follow a, it is possible for what is to follow. Similarly also in the case of things to which the same thing follows, one must consider; for if it follows the primary things, it also follows the things under them; but if it does not follow these, it is possible for it to follow the things under them. It is clear, moreover, that the consideration is through three terms and two propositions, and that all syllogisms are through the aforementioned figures. For it is shown that it is present to every one, a, when something of the things that are the same is taken; and this will be the middle term, while the extremes are a and the rest; and the first figure results. But it is present to some one when the same thing is also taken; and this is the last figure, for g becomes the middle term. But it is present to none when the same thing is also taken; and in this way both the first and the middle figure result: the first, because it is present to no f, since the privative proposition converts, but it is present to every e; the middle, because a is present to none, but e is present to every one. But that it is not present to some one, when the same thing has also been taken, this is the last figure; for a will be present to none, but e to every one. It is evident, therefore, that all syllogisms are through the aforementioned figures.
Et quoniam non eligendum quaecunque omnibus sequuntur, eo quod nullus fiat syllogismus ex ipsis,nam construere quidem non omnino erat ex sequentibus,privare autem non contingit per ea quae omnibus sequuntur, oportet huic quidem inesse, illi vero non inesse. Manifestum autem quoniam et aliae considerationes quae secundum electiones, inutiles ad faciendum syllogismum. Ut si sequentia utrumque eadem sint, aut quæ sequitur a, et quæ non contingit e inesse, aut rursum quæcunque non possibile est utrique inesse, non enim fit syllogismus per haec. Nam si sequentia sunt eadem, ut et f, media fit figura prædicativas habens utrasque propositiones. Si autem ea quae sequitur, a, el quæ non contingit e, ut c, et h, prima erit figura privativam habens propositionem ad minorem extremitatem. Si autem quaecunque non contingunt utrique, ut et h, privativae utraeque propositiones erunt vel in prima figura, vel in media, sic autem nullo modoerit syllogismus.Palam autem et quae eadem, sumendum secundum considerationem, et non quae diversa vel contraria, primum quidem quoniam medii gratia, inspectio, medium autem non diversum, sed idem oportet sumere. Deinde et in quibus accidit fieri syllogismum quod sumentur contraria, aut non contingentia eidem inesse, in praedictos omnia reducuntur modos.
And since one must not choose whatever follows all things, because no syllogism comes about from them—for to construct [a syllogism] from things that follow was not at all [possible], and to privatively establish [something] does not come about through the things that follow all—it is necessary for [the term] to be present in one and not present in the other. But it is clear that the other considerations as well, which are made according to selections, are useless for producing a syllogism. For instance, if the things that follow each of the two are the same, or [if the same are] the things that follow a and the things that cannot be present in e, or again whatever things cannot be present in both—for no syllogism comes about through these. For if the things that follow are the same, as also f, the middle term produces a predicative figure having both propositions [affirmative]. But if [the same are] the things that follow a and the things that cannot be present in e, as c and h, the first figure will have a privative proposition toward the lesser extreme. But if [the same are] whatever things cannot be present in both, as also h, both propositions will be privative, either in the first figure or in the middle; but in this way there will in no way be a syllogism. It is clear also that one must take the things that are the same according to the consideration, and not the things that are diverse or contrary—first, indeed, because the inspection is for the sake of the middle term, and one must take the middle term not as diverse but as the same. Then also, in the cases in which it happens that a syllogism is produced when contraries are taken, or things that cannot be present in the same thing, all these are reduced to the modes stated above.
Ut si et sint contraria, aut non contingant eidem inesse, erit enim his sumptis syllogismus, quoniam nulli e inest, a, sed non ex ipsis, sed ex praedicto modo, nam a quidem omni, e autem nulli inerit, quare necesse est idem esse alicui eorum quae sunt A. Rursum si et non possint eidem adesse, erit quoniam alicui e non inerit a, nam et sic media erit figura, nam a quidem omni, g, vero nulli inerit, quare necesse est idem esse alicui eorum quae sunt, nam non contingere et eidem inesse nihil differt, aut alicui idem esse, omnia enim sumpta sunt in d, quae non contingunt a inesse. Manifestum ergo quoniam ex istis quidem inspectionibus nullus fit syllogismus, et si et sint contraria,idem esse alicui h,et syllogismum semper fieri per haec. Accidit ergo sic inspicientibus considerare viam aliam necessariam,eo quod quandoque lalet identitas horum quae sunt beth.
So if they are also contraries, or do not admit of belonging to the same thing, there will be a syllogism when these are assumed, that A belongs to no E, but not from these [premises] themselves, but from the previously stated manner; for A will belong to every [thing], but E to none, so that it is necessary that the same thing be one of those which are A. Again, if they also cannot be present to the same thing, there will be [a syllogism] that A does not belong to some E; for in this way too the middle figure will be [formed]; for A will belong to every [thing], but G to none, so that it is necessary that the same thing be one of those which are [E]; for not being able to be present to the same thing differs in no way from being the same as some one [of them], for all those things have been assumed in D which cannot belong to A. It is evident, therefore, that from these considerations no syllogism comes about, and if they are also contraries, that the same thing is some one of these, and that a syllogism always comes about through these. It happens, therefore, that those who examine in this way consider another necessary path, because sometimes the identity of those things which are B escapes notice.
CAPUT XXX.
De syllogismis asserloriis ad impossibile, et reliquis qui ex hypothesi.
Eodem autem modo se babent et qui ad impossibile deducunt syllogismi, ostensivis, nam et ipsi fiunt per ea quae sequuntur, et quibus sequitur utrumque. Et eadem consideratio in utrisque, nam qnod monstratur ostensive, et per impossibile est syllogizare, et per eosdem terminos, et quod per impossibile et ostensive. Ut quoniam a nulli e inest, ponatur enim alicui inesse, ergo quoniam omni a, a autem alicui e, et aIicui e inest a, si enim nulli e inest a, e autem omni g, nulli inerit a sed omni inerat. Similiter autem est in allis propositis, semper enim erit in omnibus per impossibile ostensio, ex sequentibus,et quibus sequitur utrumque.Et in uno quoque proposito,eadem consideratio et ostensive volenti syllogizare, et ad impossibile ducere, nam ex eisdem terminis utræque demonstrationes. Ut si ostensum est nulli e inesse a, quoniam accidit et alicui e inesse, quod est impossibile. Si sumptum sit e quidem nulli b, a autem omni inesse, manifestum est enim quoniam nulli e inerit a.
CHAPTER XXX.
On assertoric syllogisms leading to the impossible, and the rest which proceed from a hypothesis.
The syllogisms that lead to the impossible stand in the same relation to the ostensive ones, for they too are produced through the things that follow and through those which both follow from. And the same consideration applies in both cases, for what is demonstrated ostensively can also be syllogized through the impossible, and by the same terms, and what is [demonstrated] through the impossible can also be [demonstrated] ostensively. For example, that A belongs to no E: let it be supposed that it belongs to some; then, since A belongs to every [thing] and A belongs to some E, A belongs to some E. For if A belongs to no E, but E belongs to every G, A will belong to no [G]; but it belonged to every [G]. The same holds in the other propositions, for in all cases the demonstration through the impossible will always proceed from the things that follow and from those which both follow from. And in each proposition the same consideration applies both to one who wishes to syllogize ostensively and to one who leads to the impossible, for both demonstrations come from the same terms. For example, if it has been shown that A belongs to no E, because it also happened that it belongs to some E, which is impossible. If it is assumed that E belongs to no B, but that A belongs to every [B], it is evident that A will belong to no E.
Rursum si ostensive syllogizatum sit a inesse nulli e, suppositis inesse per impossibile monstrabitur nulli inesse,similiter autem et in aliis.In omnibus enim necesse est iis qui per impossibile communemaliquemsumereterminumaliumasubjectis, ad quem erit mendacii syllogismus, quare conversa ea propo3itione, altera autem similiter se habente, ostensivus erit syllogismus per eosdem terminos. Differt autem ostensivus ab eo qui ad impossibile, quoniam in ostensivo secundum veritatem ambæ propositiones ponuntur,in eo autem qui ad impossibile, falsa una. Haec vero erunt magis manifesta per sequentia quando de impossibili dicemus; nunc autem tantum nobis sit manifestus,quoniam ad hæc perspiciendum, et ostensive volentibus syllogizare, et ad impossibile deducere.
In aliis autem syllogismis quicunque sunt ex hypotbesi,ut:quicunque secundum transsumptionem, aut secundum qualitatem in subjectis,non in priori. bus, sed in transsumptis erit consideratio, modus autem inspectionis idem: considerare autem oportet, et dividere quot modis sunt ex hypothesi, monstratur ergo unumquodque propositorum sic. Est autem et alio modo quaedam syllogizare horum,ut univcrsalia per particularem inspectionem et bypolhesi.Si enim et eadem sint. solum autem sumatur e inesse, omnia inerit a, et rursum si et eadem, solum autem de praedicetur e, quoniam nulli e inerit a,manireslum ergo quoniam sic inspiciendum.
Again, if it has been syllogized ostensively that A belongs to no E, then, with it supposed that A belongs to E, it will be shown through the impossible that A belongs to no E; and similarly also in other cases. For in all of them it is necessary for those who argue through the impossible to take some common term besides the subjects, to which the syllogism of the falsehood will be directed; therefore, when that proposition is converted and the other remains similarly disposed, the ostensive syllogism will proceed through the same terms. But the ostensive syllogism differs from the one leading to the impossible in that in the ostensive both propositions are posited according to truth, whereas in the one leading to the impossible one is false. These things will be more manifest from what follows when we speak about the impossible; for now let this much be clear to us, that it is for the sake of examining these things, both for those wishing to syllogize ostensively and for those wishing to reduce to the impossible.
But in the other syllogisms, whatever ones are from a hypothesis—such as those according to transumption, or according to quality in subjects—the consideration will not be in the prior terms but in the transumed ones, yet the mode of inspection is the same. But one must consider and divide in how many ways they are from a hypothesis. Each of the proposed points is therefore shown thus. But there is also another way of syllogizing certain of these, as universals through particular inspection and hypothesis. For if they are also the same, but only it is assumed that E belongs, A will belong to all; and again, if they are also the same, but only E is predicated, then A will belong to no E. It remains, therefore, that one must inspect in this way.
Eodem autem modo et in necessariis, et in contingentibus, nam eadem consideratio, et per eosdem terminos erit, eodemque ordine et contingentis, et inesse syllogismus.Sumendum autem et in contingentibus st quæ non insunt,possibilia autem inesse. Ostensum est enim quoniam et per hæc fit contingentis syllogismus,similiter autem se habebit et in aliis praedicationibus.
CAPUT XXXI.
Quod omnium scientiarum syllogismi superioribus præceptis efficiantur.
Manifestum ergo ex praedictis quoniam non solum possibile est per hanc viam fieri omnes syllogismos, sed etiam quoniam per aliam impossibile. Omnis enimsyllogismusostensusest quoniam peraliquam praedictarumfigurarumfit, has autem non contingit peraliaconstituiquampersequentiaetquaesequitur unumquodque, ex his enim propositiones,et medii sumptio,quare nec syllongismum possibile est fieri per alia.Ergo methodus quidem de omnibus eadem est, et circa philosophiam, et circa autem quamlibet disciplinam.
In the same way also in the case of necessary and contingent propositions; for the same consideration will apply, and the syllogism of the contingent will be through the same terms and in the same order, and also the syllogism of belonging. But in the case of contingent propositions one must also assume things that do not belong but are possible to belong. For it has been shown that through these too the syllogism of the contingent comes about; and it will be similarly in other predications.
CHAPTER XXXI.
That the syllogisms of all sciences are effected by the foregoing precepts.
It is evident, then, from what has been said that not only is it possible for all syllogisms to come about through this method, but also that through another it is impossible. For every ostensive syllogism has been shown to come about through one of the figures mentioned above; and these figures cannot be constituted through anything other than the things that follow and are followed by each one; for from these come the propositions and the assumption of the middle term, so that it is not possible for a syllogism to come about through other things. Therefore the method is indeed the same concerning all things, both concerning philosophy and concerning any discipline whatsoever.
Oportet enim quæ insunt,et quibus insunt circa unumquodque colligere,et his quamplurimis ahundare,et boc per tres terminos considerare, destruentem quidem sic,construentem vero sic, et secundum veritatem quidem,ex iis quae secundum veritatem scripta sunt inesse, ad dialecticos autem syIloigsmos,ex propositionibus quæsuntsecundum opinionem.Principia autem syliogismorum universaliter quidem dicta sunt,et quomodo se habeant, et quomodo oportet inquirere ea,quatenus non aspiciamus ad omnia quæ dicuntur,neque eadem construentes et destruentes,neque construentes de omni aut de aliquo,destruentesab omnibus aut ab:aliquibus,sed ad paucioraetdeterminata.Secundum singulum autem eorum quae sunt eligere, ut de bono aut disciplina.Propria autem in unaquaque sunt plurima,quare principia quidem quae sunt circa unumquodque, experimento est crescere, dico autem ut astrologicam quidem experientiam astrologica disciplinae,sumptis enim sufficienter apparentibus,sic inventæ sunt astrologicce demonstrationes.Similiter autem circa quamlibet aliam se habet et artem et disciplinam. Quare si sumantur quae insunt circa unumquodque, nostrum erit.
For one must collect the attributes that belong and the subjects to which they belong in each case, and abound in these as much as possible, and consider this through three terms—refuting in this way, establishing in that way—and according to truth, from the things that are written according to truth to belong, but for dialectical syllogisms, from propositions that are according to opinion. The principles of syllogisms have been stated universally, both how they are disposed and how one ought to inquire into them, insofar as we do not look to all things that are said, nor both establishing and refuting the same things, nor establishing concerning every or some, refuting from all or from some, but to fewer and determinate ones. And according to each single one of the things that are, to choose, as concerning the good or discipline. But proper principles in each case are very many; wherefore the principles that are about each thing it is for experience to increase—I mean, for example, astrological experience for the astrological discipline; for when the appearances have been sufficiently assumed, thus the astrological demonstrations were discovered. Similarly also in the case of any other art and discipline it is disposed. Wherefore if the attributes that belong about each thing are assumed, it will be ours.
jam demonstrationes prompte declarare: si enim nihil secundum historiam omittalur eorum quae subtiliter et vere insunt rebus, habebimus de omni (cujus quidem non est demonstratio) hanc invenire et demonstrare,cujus autem non nata est demonstratio,hoc facere manifestum.UmversaIiter ergo quo oportet modo propositiones eligere pene dictum est, pene diligentiam autem pertransivimus in eo negotio quod circa dialecticam est.
CAPUT XXXII.
De divisione et ejus syllogismo.
Quoniam autem divisio per genera parva quaedam particula est dicta? methodi facile videre: est enim divisio velut infirmus syIlogismus,narn quod oporteat quidem ostendere petitur,sylJogizatur vero semper aliquid superiorum. Primum autem idem hoc latuit omnes utentes ea,el suadere conati sunt quoniam esset possibile de substantia demonstrationem fieri,et de eoquod estquid;quarenequequoniam contingebatsyllogizare eos qui dividunt,intellexerunt,nequequoniamcontingebat sic quemadmodum diximus. Ergo in demonstrationibus quidem cum oporteat quid syllogizare, oportet medium per quod fit syllogismus minus semper esse, et non universaliter de prima extremitate.Divisio autem contra.
To set out demonstrations readily: for if nothing is omitted, according to the inquiry, of the things that belong to things subtly and truly, we shall have the means to discover and demonstrate this concerning every subject of which there is no demonstration; but for that of which demonstration is not naturally possible, to make this manifest. In general, then, the way in which one ought to select propositions has been almost stated; but we have almost passed over diligence in that business which concerns dialectic.
CHAPTER XXXII.
On division and its syllogism.
But that division through genera is said to be a small part of the method, it is easy to see: for division is like a weak syllogism; for what ought to be shown is indeed assumed as a premise, but something of the higher terms is always syllogized. First, this very point escaped all those who use it, and they attempted to persuade that it was possible for a demonstration to be made concerning substance and concerning what a thing is; wherefore neither did they understand that those who divide were syllogizing, nor that it was possible in the way we have said. In demonstrations, then, when one must syllogize something, the middle term through which the syllogism is made must always be less, and not universally predicated of the first extreme. Division, however, is the opposite.
rium vult,nam universalius sumit medium.Sitenim animal quidem in quo a, mortale autem in quo Ii, et immortalein qua c,homo vero cujus terminumoportet sumere in quo d,omne ergo animal accipit aut mortale, aut immortale: hoc autem est quidquid erat,omne esse aut b,aut c.
He wants the middle term taken more universally; for let animal be that in which A is, mortal that in which B is, and immortal that in which C is, but man, whose term must be taken, that in which D is. Every animal, then, is taken either as mortal or as immortal—this is whatever it was—so that every animal is either B or C.
Rursum hominem semper qui dividit, ponit animal esse,quare de sumit a esse,ergo syllogismus quidem est,quoniam d, aut b, aut omne erit, quare hominem aut mortalem, aut immortalem oportet sumere,nam mortale quidem, aut immortale esse necessarium est animal, mortale autem non necessarium est,sed petitur.Hoc autem eratquod oportebat syllogizare.Et rursus qui ponita quidem animal mortale in quo autem pedes habens,in quo autem c,non habens pedes,hominem vero d, similiter sumit a quidem, aut in b,aut in esse.Omnes enim animal mortale aut pedes habens, aut pedes non habens est, de autem a, nam hominem animal mortale sumpsit esse, quare habens pedes, vel non habens pedes esse animal, necesse est hominem, pedes autem habens non necesse est, sed sumit,hoc autem erat quod oportebat rursum ostendere.Et ad hunc modum semper dividentibus, universale quidem accidit eis medium sumere, de quo oporteat ostendere et differentias et extremitates.In fine autem quoniam hoc est bomo,aut quidquid erat quod quæritur,nihiI dicunt manitestum, quare necessarium est esse,etenim aliamviam faciunt omnem,non quidem contingentes idoneitates, opinantes esse. Manifestum est autem quoniam neque destruere hac via est, neque de accidente aliquid, aut de proprio sylIogizare,neque de genere, neque de quibus ignoretur utrum hoc modo aut illo se bahet,ut putasne diameter est symeter,vel asymeter?
Again, one who divides always posits that man is animal; therefore he assumes A of D. Hence there is indeed a syllogism, since D will be either B or every [animal], and therefore one must assume man to be either mortal or immortal; for it is necessary that animal be either mortal or immortal, but it is not necessary that it be mortal—rather, this is assumed. But this was what needed to be syllogized. And again, one who posits A to be mortal animal, B to be footed, C to be footless, and D to be man, similarly assumes A to be either in B or in C. For every mortal animal is either footed or footless; but he has assumed A of D, for he has assumed man to be a mortal animal; therefore it is necessary that man be a footed or footless animal. But it is not necessary that he be footed—rather, this is assumed. And this again was what needed to be shown. And in this way, for those who always divide, it happens that they take the universal as the middle term, of which one ought to demonstrate both the differentiae and the extremes. But at the end, that this is man, or whatever it was that was being sought, they say nothing clear; therefore it is necessary that it be. For they make every other path as well, not indeed supplying suitable means, but thinking they do. It is clear, however, that by this method one can neither refute nor syllogize anything about an accident, or about a property, nor about a genus, nor about those things in which it is unknown whether they are disposed this way or that—for example, do you think the diameter is commensurate or incommensurate?
si enim sumat quoniam omnis longitudo est symetros vel asymetros,diameter autem longitudo, syllogizatum est quoniam symetervel asymeterest diameter.Si autem sumetur incommensurabile, quod oportebat syllogizare sumetur, non ergo est ostendere, nam via quidem haec,per hanc autem non est ostendere symetrum vel asymetrum, in quo a longitudo,b autem symeter aut assymeter,diameterc. Manifestum est igitur quoniam neque ad omnem considerationem congruit inquisitionis modus,neque in quibus maxime videtur convenire,in his est utilis. Ex quibus ergo demonstrationes fiunt, et quomodo, et ad quae perspiciendum secundum unumquodque propositum manifestum ex dictis.
CAPUT XXXIII.
De resolutione syllogismorum in propositiones.
Quomodo autem reducemus syllogismos in praedietas figuras, dicendum erit post haec, restat enim consideratio hæc, si enim et generationem syllogismorum inspiciamus,et inveniendi habeamus potestatem,amplius autem factos reducamus prædictas figuras,finem habebit quod ex principio propositum. est, accidet etiam simul quas prædicla sunt confirmari et manifestiora esse, quoniam sic se habent per ea quae nunc dicenda sunt. Oportet enim omne quod verum est, ipsum sibi ipsi manifestum esse omnino.Primum ergo oportet tentare duas propositiones accipere syllogismi, facilius enim in majora dividere quam in minora: majora autem compositiora sunt quam ea ex quibus componuntur.
For if one assumes that every length is commensurable or incommensurable, and the diameter is a length, it has been syllogistically concluded that the diameter is commensurable or incommensurable. But if one assumes the incommensurable, what was to be syllogistically concluded is assumed; therefore it is not possible to demonstrate. For this is indeed the way, but through it it is not possible to show that the diameter is commensurable or incommensurable, in which A is length, B is commensurable or incommensurable, and C is the diameter. It is clear, therefore, that the mode of inquiry is not suited to every consideration, nor is it useful in those matters in which it especially seems to fit. From what things, then, demonstrations are made, and how, and to what one must look in accordance with each proposed question, is clear from what has been said.
CHAPTER XXXIII.
On the resolution of syllogisms into propositions.
In what way, however, we shall reduce syllogisms to the aforementioned figures must be said after this; for this consideration remains. For if we inspect both the generation of syllogisms and have the power of discovering them, and further reduce those already made to the aforementioned figures, what was proposed from the beginning will have its end. It will also happen at the same time that the things previously stated are confirmed and made clearer, since they are so by the things that must now be said. For everything that is true must be entirely manifest to itself. First, therefore, one must attempt to take the two propositions of the syllogism; for it is easier to divide into larger parts than into smaller ones, but larger parts are more composite than the things from which they are composed.
Deinde considerare utra in toto,e, utra in parte. Et si non ambæ sumptæ sint,eum qui ponit alteram.Aliquoties enim universalem protendentes,eam quae inhac est non sumunt,neque scribentes,neque interrogantes,aut has quidem protendunt,per quas autem hae concluduntur,omittunt,alia vero vane interrogant. Considerandum autem si quid superfluum sumptum sit,et si quid necessariorum omissum, et hoc quidem ponendum, illud vero auferendum, donec veniat quis ad duas propositiones,sine his enim non est reducere sic interrogatas orationes.ln aliquibus ergo facile est videre quod minus est, aliqui vero latent,et videntur quidem syllogizare, eo quod necessarium quid accidit ex iis quæ posita sunt. Ut si sumatur, non substantia interempta substantiam non interimi, ex quibus autem est,interemptis, et quod ex eis est corrumpi. His enim positis, necessarium est substantiae partem esse substantiam, non tamen syllogizatum est quod ea quae sumpta sunt,sed desunl,propositiones, Rursum si cum est homo,necesse est esse animal, et cum est animal, substantiam,et cum est homo, necesse est esse substantiam,sed nondum syllogizatum est,non enim se habent propositiones ut duximus. Fallimur autem in talibus eo quod necessarium quiddam accidat ex his quæ posita sunt,quam est syllogismus, necessarium est.
Next, one must consider which term is taken in the whole and which in the part, and whether both have not been assumed by the one who posits only one of them. For sometimes, when they extend the universal, they do not assume the one that is contained in it, neither writing it down nor asking about it; or they extend those terms through which the conclusion is drawn but omit the others, while interrogating other things to no purpose. One must consider whether something superfluous has been assumed and whether something necessary has been omitted, and the one is to be posited while the other is to be removed, until one arrives at two propositions; for without these it is not possible to reduce arguments that have been interrogated in this way. In some cases, then, it is easy to see what is lacking, but in others it escapes notice, and they seem to syllogize because something necessary follows from what has been posited—for example, if one assumes that when substance is destroyed substance is not destroyed, and that when the things from which it is composed are destroyed, that which is from them is corrupted. For with these posited, it is necessary that a part of substance be substance; yet it has not been syllogistically concluded, because the propositions that were assumed have not been taken, but are lacking. Again, if when man exists it is necessary that animal exist, and when animal exists it is necessary that substance exist, and when man exists it is necessary that substance exist—still it has not yet been syllogistically concluded; for the propositions do not stand as we have stated. But we are deceived in such cases because something necessary follows from what has been posited, though it is not a syllogism, which is what is necessary.
in plus autem est necessarium quam syllogismus,nam omnis syllogismus,necessarium, necessarium autem non omne syllogismus. Quare non (si quid accidat positis quibusdam) statim tentandum est reducere, sed primum secundum est duas propositiones.
CAPUT XXXIV.
De resolutione in terminos.
Deindesicdividendum interminos.Medium autem ponendum terminorum, qui utrisque propositionibus dicitur,necesseestenim mediuminutrisqueesse in omnibus figuris.Si ergo subjiciatur et prædicetur medium, aut ipsum quidem praedicetur, aliud vero illo abnegetur, prima erit figura, Si autem et praedicetur, et negetur ab aliquo, media erit figura: si vero alia de illo praedicentur,aut hoc quidem praedicetur,illud vero ab illo negetur, postrema,sic enim se habuit in postrema figura medium,similiter autem etsi non universales sint propositiones, nam est eadem determinatio medii. Manifestum igitur quoniam in qua oratione non dicilur idem frequenter,non fit syllogismus,non enim sumptum est medium.Quoniam autem habemus quod propositorum in unaquaque figura clauditur,et in qua universale, et in qua particulare, mauifestum est quoniam non ad omnes figuras perspiciendum,sed in unoquoque proposito ad propriam.Quaecunque vero,in pluribus concluduntur,rnedii positione cognoscimus figuram.
But it is necessary that it extend to more than the syllogism; for every syllogism is necessary, but not every necessary thing is a syllogism. Wherefore, if something follows from certain posited premises, one must not immediately attempt to reduce it, but first consider the second of the two propositions.
CHAPTER XXXIV.
On resolution into terms.
Next, one must divide the terms in this way. The middle term must be posited as the term that is predicated in both propositions; for it is necessary that the middle be in both in all figures. If, then, the middle is both subject and predicate, or is itself predicated while something else is denied of it, it will be the first figure. If it is both predicated and denied of something, it will be the middle figure. But if other things are predicated of it, or one thing is predicated and another denied of it, it will be the last figure; for thus the middle was situated in the last figure. The same determination of the middle holds similarly even if the propositions are not universal. It is clear, therefore, that in whatever discourse the same term is not stated frequently, no syllogism arises, for the middle has not been assumed. Since we have what is concluded from the premises in each figure, and in which figure the universal and in which the particular, it is clear that one must not look to all the figures, but in each premise to its proper figure. But whatever things are concluded in several figures, we recognize the figure by the position of the middle term.
CAPUT XXXV.
De necessario et thesi terminorum.
Frequenter ergo falli accidit circa syllogismos propter necessarium, quemadmodum dictum est prius: aliquoties autem propter similitudinem positionis terminorum,quod non oportet latere uos. Ut si a de dicitur,et de c,videbiturenim sic se habentibus terminis esse syllogismus, non fit autem neque necessarium quidquam, aeque syllogismus. Sit enim in quo a semper esse, in quo autem intelligibilis Aristomenes, in quo autem Aristomenes, verum est autem a inesse b, semper enim est intelligibilis Aristomenes, sed et de nam Aristo menes est intelligibilis Aristomenes, a autem non inestc, corruptibilis estenim Aristomenes; non igitur fiebat syllogismus sic se habentibus terminis, sed oportebat universaliter a frsumipropositionem: hoc vero falsum quod putabat omnem intelligibilem Arisfomenem semper esse, cum Aristomenessit corruptibilis. Rursum sit in quo quidem Micalus, in quo autem musicus Micalus,inquoautema corrumpicras. Verum est ergo de prædicari, nam Micalus est musicus Micalus, sed et a de b, corrumpeturenim eras musicusMicalus, aautem de ct'alsum hoc autem idem est priori, non enim verum est universaliter, Micalus musicus quoniam corrumpetur cras. Hoc autem non sumpto non erat syllogismus. Hæc ergo fallacia fit in eo quod pene, ut enim nihil differens dicere hoc huic inesse, aut hoc huic omni inesse, concedimus.
CHAPTER XXXV.
On the necessary and the position of terms.
It often happens, then, that error occurs concerning syllogisms on account of the necessary, as was said earlier; but sometimes on account of the similarity of the position of the terms, which ought not to escape you. For example, if A is said of D, and D of C, it will seem that a syllogism results when the terms are so related, but it does not come about, nor is anything necessary, nor is it equally a syllogism. For let there be that in which A is always, that in which intelligible Aristomenes is, and that in which Aristomenes is; and it is true that A is in B—for Aristomenes is always intelligible—but also D is in C, for Aristomenes is intelligible Aristomenes; but A is not in C, for Aristomenes is corruptible. Therefore no syllogism came about with the terms so related, but it was necessary to take the proposition A universally; but this is false, that one thought every intelligible Aristomenes to be always, since Aristomenes is corruptible. Again, let there be that in which Micalus is, that in which musical Micalus is, and that in which A is corrupt tomorrow. It is true, then, that D is predicated of C, for Micalus is musical Micalus; but also A of B, for musical Micalus will be corrupted tomorrow; but A of C is false. And this is the same as the former; for it is not true universally that Micalus is musical because he will be corrupted tomorrow. But with this not assumed, there was no syllogism. This fallacy, then, occurs in what is nearly so; for as though there were no difference, we concede that this is in that, or that this is in every that.
CAPUT XXXVI.
De ecthesi terminorum.
Frequenter autem mentiri evenit, eo quod non bene exponnntur secundum propositionem termini, ut si a quidem sit sanitas, autem ægritudo, vero homo, verum est enim dicere quoniam a nulli contingit inesse, nulli enim Eegritudinisanitas inest; et rursum quoniam inest omni c, omnis enim homo susceptibilisest segriludinis, videbitur ergo accidere nulli homini contingere sanitatem inesse. Hujus autem causa est quod non bene exponuntur termini secundum locutionem, quoniam transsumptis quae iis suntsecundum habitudines,non eritsyllogismus: Ut si pro sanitate quidem ponatur sanum, pro aegritudine autem aegrum. non enim verum est dicere quoniam non contingit segrotanti inesse sanum esse, hocautem non sumpto, non fit syllogismus, nisi contingentis. Hoc autem nonimpossibile,contingitenim nulli homini inesse sanitatem. Hursusin media figurasimilitereritfalsum.Nam sanitatem ægritudini quidem nulli, homini vero omni contingit inesse, quare nulli homini ægritudo. In tertia autem figura secundum contingere accidit falsdm, etenim sanitatem, etasgritudinem, etdiscipiinam, et ignorantiam et omnino contraria omnii eidem contingit inesse, sibi vero invicem impossibile, hoc autem confessum in praedictis. Cum enim eidem plnra contingere inesse, contingebant et sibi invicem.
CHAPTER XXXVI.
On the exposition of terms.
It often happens that error arises because terms are not correctly set out with respect to the proposition: for example, if A is health, B is sickness, and C is man. For it is true to say that A belongs to no B—for health belongs to no sickness—and again that it belongs to every C, for every man is susceptible of sickness. It will therefore appear to follow that health belongs to no man. The cause of this is that the terms are not correctly set out according to the wording, since when the things that stand in relations are transposed, there will not be a syllogism—as, for instance, if for health one puts "healthy" and for sickness "sick." For it is not true to say that being healthy cannot belong to one who is sick; but if this is not assumed, no syllogism results, except of the contingent. This, however, is not impossible, for it is contingent that health belong to no man. Again, in the middle figure the same thing will turn out false in like manner. For health belongs to no sickness, but to every man it is contingent to belong; therefore sickness belongs to no man. In the third figure, however, what is false occurs with respect to the contingent. For health and sickness, and knowledge and ignorance, and in general all contraries, are contingent to belong to the same thing, but to one another they are impossible—and this has been admitted in what was said before. For when several things are contingent to belong to the same thing, they were also contingent to one another.
Manifestum igitur quoniam in omnibus bis fallacia fit propter terminorum expositionem, transsumptis enim his quae sunt secundum habitudines, nibil fit falsum. Palam ergo quoniam secundum hujusmodi propositiones semper quod est secundum habitum, pro habitu sumendum et ponendum terminum.
CAPUT XXXVII.
De ecthesi terminorum compositorum et obliquorum syllogismi.
Non oportet autem terminos semper quaerere nomine exponi, saepe enim erunt orationes quibus non ponunturnomina, quareet difficileeritreducerehujusmodi syllogismos, aliquoties autem et talli accidet propter hujusmodi inquisitionem, ut quoniam immediatorum erit syllogismus; sit enim a duo recti, autem triangulus, vero æquicrurus; ergo ei quod est inest a propter; ei vero quod est b, non iterum propter aliud, per se enim triangulus habet duos rectos, quare non erit medium ejus quod est a b, cum sit demonstrativum. Manifestum enim quoniam medium non sic semper est sumendum ut hoc aliquid, sed aliquando orationem, quod accidit et in praedicto. Inesse autem primum medio, et hoc postremo non oportet sumere, ut prædicentur semper ad se invicem similiter, et primum de medio, et hoc de postremo, et in non inesse similiter, sed quoties dicitur esse et verum dicere, boc toties arbitrari oportet significare et inesse.
It is clear, therefore, that in all these cases the fallacy occurs because of the exposition of terms; for when those things which are according to relations are taken up, nothing false results. It is evident, then, that in propositions of this kind one must always take and posit as the term that which is according to habit, in place of the habit.
CHAPTER XXXVII.
On the ecthesis of composite and oblique terms in syllogisms.
One ought not always to seek to expound terms by a name, for often there will be phrases for which no names are posited, which is why it is difficult to reduce syllogisms of this kind; and sometimes this also happens because of such an inquiry, as that there will be a syllogism of immediate premises. For let A be two right angles, B a triangle, and C an isosceles triangle; then A belongs to C through B, but to B no longer through another term, for a triangle has two right angles in itself; therefore there will be no middle term of A and B, since it is demonstrative. For it is clear that the middle term must not always be taken as this particular thing, but sometimes as a phrase, which also happens in the case just stated. But one must not take it that the first belongs to the middle and this to the last, as though they were always predicated of one another in the same way, both the first of the middle and this of the last, and similarly in the case of non-being; but whenever it is said to be and to speak truly, one must judge that this signifies and belongs in just as many cases.
Ut quoniam contrariorum una est disciplina: sit enim a unam esse disciplinam, autem contraria sibi invicem, a ergoinest b, non quoniam contraria unum esse eorum disciplinam, sed quoniam verum est dicere de ipsis unam esse eorum disciplinam. Accidit autem quandoque primum de medio dici, medium autem de tertio non dici, ut si sophia est disciplina, boni autem est sophia: conclusio, quoniam boni est disciplina, et non bonum quidem est disciplina, sophia autem est disciplina. Quandoque autem medium quidem de tertio dicitur, primum autem de medio non dicitur, ut siqualisomnisestdisciplina,autcontrarii.Bonura autem est, et contrarium, et quale: conclusio quidem, quoniam boni est disciplina. Non est autem bonum disciplina, neque quale, neque contrarium, sed omnium disciplina.Non estautembonum disciplina, neque conclusio secundum rectum, neque quale, neque contrarium, sed bonum hæc. Est autem quandoque neque primum de medio, neque hoc de tertio, primo de tertio quandoque quidem dicto, quandoque autem non dicto.Ut si cujus est disciplina, hujusestgenus, boniautemestdisciplina: conclusio quoniam boni est genus. Praedicatur autem nullum de nullo, si autem cujus est disciplina, genus est hoc, boni autem est disciplina; conclusio, quoniam bonum est genus: ergo de extremo quidem[praBdicatur primum, de se autem invicem non dicuntur.
For example, since there is one discipline of contraries: let A be "one discipline," and let B be "contraries to each other"; then A is in B—not because contraries are one discipline of them, but because it is true to say of them that there is one discipline of them. But sometimes it happens that the first term is predicated of the middle, while the middle is not predicated of the third: for instance, if wisdom is a discipline, and wisdom is of the good; the conclusion is that there is a discipline of the good—and not that the good is a discipline, but that wisdom is a discipline. Sometimes, however, the middle is predicated of the third, while the first is not predicated of the middle: for instance, if every quality is a discipline, and the contrary is a quality. But the good is both a quality and a contrary; the conclusion is that there is a discipline of the good. But the good is not a discipline, nor is a quality, nor a contrary, but there is a discipline of all. But the good is not a discipline, nor is the conclusion in accordance with what is correct, nor is a quality, nor a contrary, but the good is these. Sometimes, however, neither is the first predicated of the middle, nor this of the third, though the first is sometimes stated of the third and sometimes not. For instance, if of whatever there is a discipline, this is a genus, and there is a discipline of the good; the conclusion is that the good is a genus. But nothing is predicated of nothing; if, however, of whatever there is a discipline, this is a genus, and there is a discipline of the good; the conclusion is that the good is a genus. Therefore, the first term is indeed predicated of the extreme, but they are not said of each other.
Eodem autem modo et nun inesse sumendum non enim semper significat non inesse hoc huic, non esse hoc, hoc; sed aliquando non esse hoc hujus, aut hoc huic: ut quoniam non est motionis motus, autgenerationisgeneratio, voluptatis autem est, non ergo voluptas generatio. Aut rursus quoniam risus est signum, signi autem non est signum, quare non est signum risus; similiter autem et in aliis, in quibus intermitur propositum, eo quod dicitur aliquo modo ad id genus. Rursus quoniam occasio non est tempus opportunum, Deo enim occasio quidem est, tempus autem opportunum non est, eo quod nihil sit Deo conferens. Terminos enim ponendum est occasionem, et tempus opportunum, etDeum. Propositio autem sumenda secundum nominiscausam, simpliciter enim hoc dicimus de omnibus, quoniamterminos quidem semper ponendum secundum declinationes nominum, ut homo, aut bonum, aut contraria, authominis,autboni, autcontrariorum.Propositiones autem sumendum secundum cujusque casus, aut enim quoniam huic ut sequale,autquoniamhujusut duplum, aut quoniam hoc ut feriens, vel videns, aut quoniam hic ut homo, animal,aut si quolibet modo aliter cadit nomen secundum propositionem, inesse autem hoc huic, et verum esse hoc de hoc, toties sumendum, quoties praedicamenta divisa sunt, et hæc aut aliquo modo, aut simpliciter, amplius aut simplicia, aut complexa. Similiter autem et non inesse.
But in the same way we must also take "not to be present," for it does not always signify that this is not in this, or that this is not this, but sometimes that this is not of this, or this is not for this: for example, since there is no motion of motion, nor generation of generation, but there is of pleasure, therefore pleasure is not generation. Or again, since laughter is a sign, but there is no sign of a sign, therefore it is not a sign of laughter. And similarly in other cases in which the proposition is refuted because it is said in some way in relation to that genus. Again, since opportunity is not opportune time—for opportunity is with God, but opportune time is not, because nothing is advantageous to God. For we must set down as terms opportunity, opportune time, and God. But the proposition must be taken according to the cause of the name; for we say this simply of all things, that terms must always be set down according to the inflections of names, as man, or good, or contraries, or of man, or of good, or of contraries. But propositions must be taken according to each case; for either "because it is to this," as equal, or "because it is of this," as double, or "because it is this," as striking or seeing, or "because this is," as man, animal, or in whatever other way the name falls according to the proposition. But "to be present in this" and "to be true of this" must be taken as many times as the categories are divided, and these either in some way or simply, and further either simple or complex. And similarly also "not to be present.
Considerandum haec autem, et determinandum optimum.
CAPUT XXXVIII.
De anadiplosi et thesi syllogismorum, hoc est de gemi natione et positione.
Reduplicatum autem in propositionibus ad primam extremitatem ponendum, non ad medium, dico autem ut si fiat syllogismus, quoniam justitiae est disciplina quoniam bonum, ad primam extremitatem ponendum. Si enim a disciplina quoniam bonum, in quo autem bonum, in quo autem cjustitia, ergo verum est a de praedicari. Nam boni est disciplinaquoniam bonum. Sed et bdec, namjustitia quiddam bonum est; sic ergo fit resolutio. Si autem ad ponatur, quoniam bonum, non erit, nam a quidem de verum erit, autem de non erit verum, nam bonum quoniam bonum praedicaride justitiafalsum est, et non intelligibile. Similiter autem et si salubre ostendatur, quoniam disciplinatum est in eo quod bonum, aut hircocervus, opinabilis in eo quod existens, aut homo corruptibilis in eo quod sensibile, in omnibusenim prædicatis ad extremum reduplicationem ponendum. Non est autem eadem positio terminorum, quando simpliciter quidem syllogizatum fuerit, et quando hoc aliquid, aut quo, aut quomodo. Dico autem ut quando bonum disciplinatum ostensum erit, et quando disciplinatum quoniam bonum. Sed simpliciter quidem disciplinatum ostensumestmediumponendum ens, si autem quoniam bonum, quid ens.
But these things must be considered and determined as best.
CHAPTER XXXVIII.
On anadiplosis and the position of syllogisms, that is, on doubling and position.
The reduplicated term in propositions must be placed with the first extreme, not with the middle. I mean, for example, that if a syllogism is made to the effect that the knowledge of justice is of the good, the reduplication must be placed with the first extreme. For if A is knowledge of the good, and that in which the good is, is B, and that in which justice is, is C, then it is true that A is predicated of C. For the knowledge of the good is of the good. But B is also predicated of C, for justice is a certain good; and thus the resolution is made. But if the reduplication "insofar as good" is placed with B, it will not hold; for A will indeed be truly predicated of B, but B will not be truly predicated of C, for to predicate the good of justice insofar as it is good is false and unintelligible. The same applies if one shows that the healthy is knowable insofar as it is good, or the goat-stag is opinable insofar as it exists, or man is corruptible insofar as he is sensible; for in all cases the reduplication must be placed with the extreme predicate. But the position of the terms is not the same when the syllogism has been made simply and when it has been made with respect to something, or in what respect, or in what way. I mean, for example, when the good has been shown to be knowable, and when the knowable has been shown to be knowable insofar as it is good. But when it has been shown simply that the knowable is knowable, the middle term must be placed as being; but when it has been shown that it is knowable insofar as it is good, the middle term must be placed as a certain being.
Sit enim a disciplina quoniam quid ens, inquo autem ens, quid, in quo autem bonum, verum est:ergo a. de prædicari, erat enimdisciplinaalicujusentis, quoniam quid ens, est et de c4 nam in quo ens quid, quare et a de c, erit ergo disciplina boniquoniambonum, erat enim quid ens, proprie substantiæ signum. Si autem ens medium positum sit, et ad extremum ens simpliciter, et non quid ens dictum sit, non erit syllogismus, quoniam est disciplina boni quoniam honum, sed quoniam ens, ut si sit in quo a disciplina quoniam ens, in quo ens, in quo bonum. Manifes. tum igitur quoniam in particularibus syllogismis sic sumendum terminos.
CAPUT XXXIX.
Pro debita resolutione praecepta.
Oportet autem accipere qua; idem possunt nomina pro nominibus, et oraliones pro orationibus, et nomen et orationem et semper pro orationem nomen suscipere, facilior est enim terminorum expositio, utsinil differt dicere suspicabileopinabilis non esse genus,autnon esse idem quiddam suspicabile, quod opinabile, nam si idem est quod significatur, pro oratione dicta, suspicabile et opinabile terminos ponendum. Quoniam vero non est idem voluptatem esse bonum, et esse voluptatem quod bonum, non similiter ponendum terminos; sed siest syllogismus quoniam voluptas quod bonum, terminum ponendum quod bonum; si autem quoniam bonum, bonum, similiter autem et in aliis.
For let a be "from discipline" in the sense of "what being," and let the middle term be "in which" being, "what," and "in which" good, it is true; therefore a is predicated of... for it was "discipline of some being," in the sense of "what being," and it is also of c; for "in which" being is "what," wherefore also a is of c; therefore there will be "discipline of the good" because it is good, for it was "what being," a sign of proper substance. But if "being" is posited as the middle term, and "being" simply is predicated of the extreme, and not "what being," there will not be a syllogism that it is "discipline of the good" because it is good, but because it is being—as if a is "discipline" in the sense of "being," the middle is "in which" being, and the extreme is "in which" good. It is manifest, therefore, that in particular syllogisms the terms must be taken in this way.
CHAPTER XXXIX.
Precepts for the proper resolution.
But one must accept that names can stand for names, and phrases for phrases, and always take a name for a phrase and a phrase for a name; for the exposition of terms is easier, as it makes no difference to say that "the opinable is not a genus of the suspicable" or that "the suspicable is not the same as the opinable"; for if what is signified is the same, when a phrase is spoken, "suspicable" and "opinable" must be posited as terms. But since "pleasure is good" and "pleasure is that which is good" are not the same, the terms must not be posited in the same way; but if the syllogism is that "pleasure is that which is good," the term must be posited as "that which is good"; but if it is that "pleasure is good," then "good"; and similarly in other cases.
Non estau [em idem neque esse, neque dicere quoniam cui inest, huic quoque omni a inest, et dicere, cui omni idest, et a inest omni, nihil enim prohibet inesse c, non autem omni. Ut sit pulchrum quid, autem album, si igitur alicui albo inest pulchrum quid, verum est dicere quoniam albo inest pulchrum, sed non omni fortasse. Si ergo a inest 6, non omni autem de quo (neque si omni c, inest 6, neque si solum alicui), non necesse est ei quod est inesse a, non quia non omni, sed nec inesse ei quod est c. Si autem de quocunque dicaturvere, huic omniinest a, accidet a de quo omni dicitur, de eo omni dici. Si autem a dicitur de omni de quo dicatur, nihil prohibet ei quod est inesse b, non omni autem a, aut noninesse omnino. In tribus igitur terminis manifestum est quoniam de quo quidem omni, et a dicitur, hoc est de quibuscunque dicitur de omnibus dicitur et a, et si quidem de omni, et a similiter si autem non de omni, non necesse est a inesse omni. Non oportet autem arbitrari propter expositionem accidere aliquod inconveniens, non enim laboramus in eoquod aliquid sit hoc, sed quemadmodum geometer pedalem, et rectam hanc esse et sine latitudine dicit quas non est, sed non sic utitur, ut eis syllogizans.
For it is not the same thing either to be, or to say that a is present with every one of those things with which it is present, and to say that a is present with every one of those things with which it is present—for nothing prevents c from being present with something, but not with every. For example, let it be a certain beautiful thing, but white; if, then, a certain beautiful thing is present with some white thing, it is true to say that a beautiful thing is present with the white thing, but perhaps not with every. If, therefore, a is present with b, but not with every thing of which it is said (neither if c is present with every thing, is b present, nor if it is present with some only), it is not necessary that a be present with that which is; not because it is not present with every, but because it is not present with that which is c. But if it is said of whatever thing truly, a is present with every one of these, it will happen that a is said of every thing of which it is said. But if a is said of every thing of which it is said, nothing prevents b from being present with that which is, but not with every a, or not being present at all. In three terms, therefore, it is clear that of whatever thing a is said of every, that is, of whatever things it is said of all, a is also said; and if indeed of every, a likewise; but if not of every, it is not necessary that a be present with every. But one ought not to think that any inconvenience arises on account of the exposition; for we do not labor over the fact that something is this, but just as the geometer says that this foot-length and this straight line are without breadth, which they are not, but he does not use them in such a way as to syllogize from them.
Omnino enim quod non est ut totum ad partem, et aliud ad hoc ut pars ad totum, ex nullo talium ostendit demonstrator, neque enim fit syllogismus, expositione autem sic utimur, ut et sentiat qui discit dicentes, non enim sic ut sine bis non possibile sit demonstrare, quemadmodum ex quibus est syllogismus. Non lateat autem nos, quoniam in eodem syllogismo, non omnes conclusion.es perunam eamdem figuram sunt, sed hæc quidem per hanc, illa vero per aliam. Palam ergo quoniam et resolutiones sic faciendum. Quoniamautem nonomne propositum in omni figura, sed in unaquaque ciisposita sunt,manifestum est exconclusione in qua figura sit quaerendum. Et ad definitiones orationum quaecunque ad unum' quiddam suntargumentat:p in eorum quae insunt termino, ad quod argumentatum est ponendum terminum, et non totam orationem, minus enim contingitperturbari propterlongitudinem, ut si quis aquam ostendit quoniam est humidus potus, potum et aquam terminos ponendum.
For in general, the demonstrator shows nothing from any of those [terms] that are not related as whole to part, and as one thing to another as part to whole—for neither does a syllogism come about—but we use exposition in such a way that the one who is learning also understands those who speak; for it is not [used] in such a way that without these it would be impossible to demonstrate, as [it is] from those things of which the syllogism consists. But let it not escape us that in the same syllogism not all conclusions [come about] through one and the same figure, but some through this one, others through another. It is clear, therefore, that resolutions must also be made in this way. But since not every proposition [is placed] in every figure, but they are set out in each one, it is evident that from the conclusion one must seek in which figure it is. And for definitions of speeches, whatever arguments are directed toward one single thing, the term must be posited among those things that are contained in the term toward which the argument was directed, and not the whole speech—for one is less likely to be disturbed on account of length—as if someone, showing that water is a moist drink, should posit "drink" and "water" as terms.