{"slug":"tmp1026.tmp1026.opp-lat1","id":"latin:ogl-pl:tmp1026.tmp1026.opp-lat1","title":"Priorum Analyticorum Aristotelis Libri Duo","title_source":"Priorum Analyticorum Aristotelis Libri Duo","author":"Boethius. Severinus","genre":"treatise","date":"","tradition":"latin","coverage":"not-located","coverage_claim":{"status":"not-located","text":"No English translation could be identified: a language model asked twice could not name one, though it could not rule one out either. That is not proof that none exists — translations in dissertations, recent books and other modern languages are easily missed."},"publication":{"status":"machine-draft","reviewed_by":null,"model":"deepseek/deepseek-v4.1-flash:floor","provider":"Baidu","generated":"2026-11-15T20:43:11Z","cost_usd":0.01664},"source":{"registry_id":"latin:ogl-pl:tmp1026.tmp1026.opp-lat1","work_id":"tmp1026.tmp1026.opp-lat1","edition":"ogl-pl","language":"","license":"Available under a Creative Commons Attribution-ShareAlike 4.0 International License","url":"https://github.com/OpenGreekAndLatin/patrologia_latina-dev/blob/master/data/tmp1026/tmp1026/tmp1026.tmp1026.opp-lat1.xml"},"stats":{"passages":176,"english_words":47858,"coptic_letters":0,"source_letters":170056,"commentary_units":0,"commentary_kinds":0,"derived_notes":3,"ambiguities":0,"work_notes":0,"external_links":0,"timeline":0},"summary":{},"links":[{"kind":"source","label":"Open Greek and Latin Patrologia Latina","url":"https://github.com/OpenGreekAndLatin/patrologia_latina-dev/blob/master/data/tmp1026/tmp1026/tmp1026.tmp1026.opp-lat1.xml"}],"checks":{"work":"tmp1026.tmp1026.opp-lat1","status":"pass","blocking":[],"warnings":[],"stats":{"passages":176,"translated":176,"commentary_passages":0,"commentary_units":0,"english_words":47858,"source_letters":169741,"commentary_kinds":0},"model":"deepseek/deepseek-v4.1-flash:floor"},"work_notes":[],"derived_work_notes":[{"kind":"coverage","severity":"info","text":"No English translation could be identified: a language model asked twice could not name one, though it could not rule one out either. That is not proof that none exists — translations in dissertations, recent books and other modern languages are easily missed."},{"kind":"limit","severity":"caution","text":"The English is a machine draft produced passage by passage from the transcribed Latin; no human has verified it. The commentary is model-written and cites only keys the pipeline could resolve."},{"kind":"register","severity":"info","text":"Register: treatise in Latin; the English keeps the liturgical formulae and the vocatives rather than normalising them."},{"kind":"structure","severity":"info","text":"Passages: 176 narrative."},{"kind":"caution","severity":"caution","text":"3 passage(s) are fragmentary in the source; the English bridges each break and says so in the note."},{"kind":"source","severity":"info","text":"Source edition: ogl-pl."},{"kind":"source","severity":"info","text":"Licence: Available under a Creative Commons Attribution-ShareAlike 4.0 International License"}],"derived_structure":{"narrative":176},"term_index":[],"citations":{},"segments":[{"i":1,"ref":"p1","source":"PRIORUM ANALYTICORUM ARISTOTELIS LIBRI DUO AN. MANL. SEV. BOETIO INTERPRETE.\n\nLIBER PRIMUS.\n\nCAPUT PRIMUM.\n\nDe propositione, termino et syltogismo.\n\nPrimum 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.","english":"THE TWO BOOKS OF ARISTOTLE'S PRIOR ANALYTICS, TRANSLATED BY AN. MANL. SEV. BOETHIUS.\n\nBOOK ONE.\n\nCHAPTER ONE.\n\nOn proposition, term, and syllogism.\n\nFirst 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":2,"ref":"p2","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":3,"ref":"p3","source":"Dicimus autem de omni praedicari, quando nibil est sumere subjecti, de quo non dicatur alterum, et de nullo similiter.\n\nCAPUT II.\n\nDe conversione absolutarum propositionum.\n\nQuoniam 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.","english":"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.\n\nCHAPTER II.\n\nOn the conversion of absolute propositions.\n\nSince 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":4,"ref":"p4","source":"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.\n\nCAPUT III.\n\nDe conversione propositionum de modo\n\nEodem 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.","english":"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.\n\nCHAPTER III.\n\nOn the conversion of modal propositions\n\nThe 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":5,"ref":"p5","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":6,"ref":"p6","source":"Ostendetur autem et hoc per sequentia, secundum conversiones autem similiter se habebunt in iis.\n\nCAPUT IV.\n\nDe modis syllogisticis et asyllogistis absolutis primas figuræ.\n\nHis 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.","english":"But this too will be shown through what follows; in conversions, however, they will be related similarly in these.\n\nCHAPTER IV.\n\nOn the absolute syllogistic and asyllogistic modes of the first figure.\n\nWith 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":7,"ref":"p7","source":"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.","english":"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","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":8,"ref":"p8","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":9,"ref":"p9","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[{"kind":"lacuna","severity":"caution","text":"The source is fragmentary here: the edition marks a break or an editorial bracket, and the English carries across it. Treat the bridge as supplied, not translated."}]},{"i":10,"ref":"p10","source":"CAPUT V.\n\nDe syllogismis absolutis in secunda figura.\n\nQuando 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.","english":"CHAPTER V.\n\nOn absolute syllogisms in the second figure.\n\nBut 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":11,"ref":"p11","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":12,"ref":"p12","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":13,"ref":"p13","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":14,"ref":"p14","source":"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.\n\nCAPUT VI.\n\nDe syllogismis absolutis tertiæ figuræ.\n\nSi 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.","english":"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.\n\nCHAPTER VI\n\nOn the absolute syllogisms of the third figure.\n\nBut 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":15,"ref":"p15","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":16,"ref":"p16","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":17,"ref":"p17","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":18,"ref":"p18","source":"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.\n\nCAPUT VII.\n\nDe tribus figuris et indirectis syllogismus ad invicem.\n\nPalam 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.","english":"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.\n\nCHAPTER VII.\n\nOn the three figures and the indirect syllogisms in relation to one another.\n\nIt 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":19,"ref":"p19","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":20,"ref":"p20","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":21,"ref":"p21","source":"CAPUT VIII.\n\nDe syllogismis ex necessario in tribus figuris.\n\nQuoniam 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.","english":"CHAPTER VIII.\n\nOn syllogisms from necessity in the three figures.\n\nSince 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":22,"ref":"p22","source":"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.\n\nCAPUT IX.\n\nDe mixtis ex una necessaria et altera absoluta in prima figura.\n\nAccidit 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.","english":"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.\n\nCHAPTER IX.\n\nOn mixed syllogisms from one necessary and the other absolute proposition in the first figure.\n\nIt 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":23,"ref":"p23","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":24,"ref":"p24","source":"CAPUT X.\n\nDe mixtis ex una necessaria et altera absoluta in se cunda figura.\n\nIn 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.","english":"CHAPTER X.\n\nOn mixtures of one necessary and one absolute premise in the second figure.\n\nIn 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":25,"ref":"p25","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":26,"ref":"p26","source":"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.-\n\nCAPUT XI.\n\nDe syllogismis mixtis ex altera necessaria et altera absoluta in tertia figura.\n\nIn 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.","english":"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.\n\nCHAPTER XI.\n\nOn mixed syllogisms from one necessary and one absolute premise in the third figure.\n\nIn 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":27,"ref":"p27","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":28,"ref":"p28","source":"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!","english":"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...","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":29,"ref":"p29","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":30,"ref":"p30","source":"CAPUT XII.\n\nDe contingenti non necessario.\n\nDe 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.","english":"CHAPTER XII.\n\nOn the contingent that is not necessary.\n\nNext 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":31,"ref":"p31","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":32,"ref":"p32","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":33,"ref":"p33","source":"CAPUT XIII.\n\nDe syllogismis ex ambabus contingentibus in prima figura.\n\nQuando 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.","english":"CHAPTER XIII.\n\nOn syllogisms from two contingent premises in the first figure.\n\nWhen, 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":34,"ref":"p34","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":35,"ref":"p35","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":36,"ref":"p36","source":"Oportet autem contingere sumere non in necessariis, sed secundum dictam definitionem, aliquoties autem latet hujusmodi.\n\nCAPUT XIV.\n\nDe syllogismis ex una absoluta et altera contingente in prima figura.\n\nSi 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.","english":"But one must take \"contingent\" not in the case of necessities, but according to the stated definition; sometimes, however, such a thing escapes notice.\n\nCHAPTER XIV.\n\nOn syllogisms from one absolute and the other contingent proposition in the first figure.\n\nIf, 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":37,"ref":"p37","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":38,"ref":"p38","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":39,"ref":"p39","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":40,"ref":"p40","source":"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.\n\nSi 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.","english":"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.\n\nIf, 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":41,"ref":"p41","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":42,"ref":"p42","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":43,"ref":"p43","source":"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.\n\nCAPUT XV.\n\nMixtio necessarii et contingentis in prima figura.\n\nQuandoautemhaecquidem propositionum ex necessitate inesse,vel non inesse,illa vero contingere significat,syllogismus quidem erit hoc modo habentibus se terminis.","english":"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.\n\nCHAPTER XV\n\nThe mixture of the necessary and the contingent in the first figure.\n\nBut 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":44,"ref":"p44","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":45,"ref":"p45","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":46,"ref":"p46","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":47,"ref":"p47","source":"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.\n\nCAPUT XVI.\n\nDe syllogismis ex ambabus contingentibus in secunda figura.","english":"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.\n\nCHAPTER XVI.\n\nOn syllogisms from both propositions being contingent in the second figure.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":48,"ref":"p48","source":"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","english":"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","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":49,"ref":"p49","source":"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.\n\nQuare 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.","english":"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.\n\nWherefore, 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":50,"ref":"p50","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":51,"ref":"p51","source":"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.\n\nCAPUT XVII.\n\nMixtio absoluti et contingentis in secunda figura.\n\nSi 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.","english":"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.\n\nCHAPTER XVII.\n\nThe mixture of the absolute and the contingent in the second figure.\n\nBut 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":52,"ref":"p52","source":"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.\n\nCAPUT XVIII.\n\nMixtio necessari et contingentis in secunda figura.","english":"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.\n\nCHAPTER XVIII.\n\nThe mixture of the necessary and the contingent in the second figure.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":53,"ref":"p53","source":"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,.","english":"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...","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":54,"ref":"p54","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":55,"ref":"p55","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":56,"ref":"p56","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":57,"ref":"p57","source":"CAPUT XIX.\n\nDe syllogismis ex ambabus contingentibus in tertia figura.\n\nIn 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.","english":"CHAPTER XIX.\n\nOn syllogisms from both premises contingent in the third figure.\n\nIn 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":58,"ref":"p58","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":59,"ref":"p59","source":"CAPUT XX.\n\nMixtio contingent is et inesse in tertia figura.\n\nSi 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.","english":"CHAPTER XX.\n\nThe mixture of contingent and present-in [predications] in the third figure.\n\nIf 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":60,"ref":"p60","source":"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.\n\nCAPUT XXI.\n\nMixlio necessarii et contingentis in tertia figura.","english":"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.\n\nCHAPTER XXI.\n\nThe mixture of necessary and contingent in the third figure.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":61,"ref":"p61","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":62,"ref":"p62","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":63,"ref":"p63","source":"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.\n\nCAPUT XXII.\n\nDe syllogismo ostensivo.\n\nQuoniamigiturquiin 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.","english":"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.\n\nCHAPTER XXII.\n\nOn ostensive syllogism.\n\nThat 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":64,"ref":"p64","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":65,"ref":"p65","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":66,"ref":"p66","source":"CAPUT XXIII.\n\nDe syllogisma ex hypothesi.\n\nQuoniam 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.","english":"CHAPTER XXIII.\n\nOn the syllogism from a hypothesis.\n\nSince 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":67,"ref":"p67","source":"CAPUT XXIV.\n\nDe qualitate et quantitate terminorum syllogismi.\n\nAmplius 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.","english":"CHAPTER XXIV.\n\nOn the quality and quantity of the terms of the syllogism.\n\nMoreover, 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":68,"ref":"p68","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":69,"ref":"p69","source":"CAPUT XXV.\n\nDe numero terminorum syllogismi.\n\nPalam 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.","english":"CHAPTER XXV.\n\nOn the number of terms in a syllogism.\n\nIt 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":70,"ref":"p70","source":"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.\n\nCAPUT XXVI.\n\nDe numero propositionum et prosyllogismis.\n\nHoc 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.","english":"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.\n\nCHAPTER XXVI.\n\nOn the number of propositions and on prosyllogisms.\n\nWith 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":71,"ref":"p71","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":72,"ref":"p72","source":"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.\n\nCAPUT XXVII.\n\nDe problematisthocest propositis in unaquaque figura facile et difficile construendis et destruendis.\n\nQuoniam 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.","english":"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.\n\nCHAPTER XXVII.\n\nOn problems, that is, on propositions, easily and with difficulty constructed and destroyed in each figure.\n\nSince 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":73,"ref":"p73","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":74,"ref":"p74","source":"CAPUT XXVIII.\n\nDe abundantia propnsitionum.\n\nQuomodo 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.","english":"CHAPTER XXVIII.\n\nOn the abundance of propositions.\n\nWe 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":75,"ref":"p75","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":76,"ref":"p76","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":77,"ref":"p77","source":"CAPUT XXIX.\n\nMedii syllogismorum inveniendi regulas.\n\nConstruere 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.","english":"CHAPTER XXIX.\n\nRules for finding the middle terms of syllogisms.\n\nTherefore, 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":78,"ref":"p78","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":79,"ref":"p79","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":80,"ref":"p80","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":81,"ref":"p81","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":82,"ref":"p82","source":"CAPUT XXX.\n\nDe syllogismis asserloriis ad impossibile, et reliquis qui ex hypothesi.\n\nEodem 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.","english":"CHAPTER XXX.\n\nOn assertoric syllogisms leading to the impossible, and the rest which proceed from a hypothesis.\n\nThe 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":83,"ref":"p83","source":"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.\n\nIn 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.","english":"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.\n\nBut 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":84,"ref":"p84","source":"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.\n\nCAPUT XXXI.\n\nQuod omnium scientiarum syllogismi superioribus præceptis efficiantur.\n\nManifestum 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.","english":"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.\n\nCHAPTER XXXI.\n\nThat the syllogisms of all sciences are effected by the foregoing precepts.\n\nIt 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":85,"ref":"p85","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":86,"ref":"p86","source":"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.\n\nCAPUT XXXII.\n\nDe divisione et ejus syllogismo.\n\nQuoniam 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.","english":"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.\n\nCHAPTER XXXII.\n\nOn division and its syllogism.\n\nBut 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":87,"ref":"p87","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":88,"ref":"p88","source":"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?","english":"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?","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":89,"ref":"p89","source":"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.\n\nCAPUT XXXIII.\n\nDe resolutione syllogismorum in propositiones.\n\nQuomodo 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.","english":"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.\n\nCHAPTER XXXIII.\n\nOn the resolution of syllogisms into propositions.\n\nIn 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":90,"ref":"p90","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":91,"ref":"p91","source":"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.\n\nCAPUT XXXIV.\n\nDe resolutione in terminos.\n\nDeindesicdividendum 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.","english":"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.\n\nCHAPTER XXXIV.\n\nOn resolution into terms.\n\nNext, 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":92,"ref":"p92","source":"CAPUT XXXV.\n\nDe necessario et thesi terminorum.\n\nFrequenter 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.","english":"CHAPTER XXXV.\n\nOn the necessary and the position of terms.\n\nIt 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":93,"ref":"p93","source":"CAPUT XXXVI.\n\nDe ecthesi terminorum.\n\nFrequenter 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.","english":"CHAPTER XXXVI.\n\nOn the exposition of terms.\n\nIt 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":94,"ref":"p94","source":"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.\n\nCAPUT XXXVII.\n\nDe ecthesi terminorum compositorum et obliquorum syllogismi.\n\nNon 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.","english":"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.\n\nCHAPTER XXXVII.\n\nOn the ecthesis of composite and oblique terms in syllogisms.\n\nOne 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":95,"ref":"p95","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[{"kind":"lacuna","severity":"caution","text":"The source is fragmentary here: the edition marks a break or an editorial bracket, and the English carries across it. Treat the bridge as supplied, not translated."}]},{"i":96,"ref":"p96","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":97,"ref":"p97","source":"Considerandum haec autem, et determinandum optimum.\n\nCAPUT XXXVIII.\n\nDe anadiplosi et thesi syllogismorum, hoc est de gemi natione et positione.\n\nReduplicatum 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.","english":"But these things must be considered and determined as best. \n\nCHAPTER XXXVIII.\n\nOn anadiplosis and the position of syllogisms, that is, on doubling and position.\n\nThe 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":98,"ref":"p98","source":"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.\n\nCAPUT XXXIX.\n\nPro debita resolutione praecepta.\n\nOportet 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.","english":"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.\n\nCHAPTER XXXIX.\n\nPrecepts for the proper resolution.\n\nBut 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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":99,"ref":"p99","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[{"kind":"lacuna","severity":"caution","text":"The source is fragmentary here: the edition marks a break or an editorial bracket, and the English carries across it. Treat the bridge as supplied, not translated."}]},{"i":100,"ref":"p100","source":"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.","english":"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.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":101,"ref":"p101","source":"CAPUT XL.\n\nDe resolutione syllogismorum ad impossibile et ex hypothesi.\n\nAmplius autem ex hypothesi syllogismos non est tentandum reducere, nam non est ex iis quae posita snnt reducere; non enim por syllogismum ostensi sunt, sed ad placitum concessi sunt omnes. Ut si quis ponat, si una quasdam potestas non sit contrariorum, neque disciplinam esse unam; deinde disputet quoniam non est una potestas contrariorum, utsanativi et ægrotativi, simulenim idem erit sanativum et fegrotativum. Quoniam autem non est omaium contrariorum una potestas,ostensum est, scd quoniam disciplina non una, non est ostensum; quamvis confiteri sit necesse,at non ex syllogismo, vcrum ex hypothesi; hoc igitur non est reducere, quoniam non una potestas est: hic enim fortasse erat syllogismus, illud autem hypothesis. Similiter autem in his qui per impossibile concluduntur,nam neque hoc est resolvere,sed ad impossibile quidem reductio est; syllogismo enim monstratur; alterum autem non est, nam ex hypothesi concluditur. Differunt, aucem a prædictis quoniam in illis quidem oportet prius confiteri, si debet concedere, ut si ostendatur una potestas contrariorum,etdisciplinam esse eamdem; hic autem et non prius confessi concedunt, eo quod manifestum sit falsum, ut posita diametro symetro, eo quod imparia esse æqualia partibus.","english":"CHAPTER XL.\n\nOn the resolution of syllogisms to the impossible and from hypothesis.\n\nFurthermore, one must not attempt to reduce syllogisms from hypothesis, for it is not from the things that have been posited that one can reduce them; for they have not been shown by syllogism, but all have been conceded at will. For example, if someone posits that if there is not one certain power of contraries, neither is there one discipline; then let him argue that there is not one power of contraries, as of the healthy and the sick—for at the same time the same thing will be healthy and sick. But that there is not one power of all contraries has been shown, yet that the discipline is not one has not been shown; although it must be confessed, not from syllogism but from hypothesis. This, therefore, is not to reduce, since there is not one power—for here perhaps was the syllogism, but that was the hypothesis. Similarly also in those which are concluded through the impossible, for neither is this to resolve, but it is a reduction to the impossible; for it is shown by syllogism, but the other is not, for it is concluded from hypothesis. They differ, however, from the aforementioned, because in those it is necessary first to confess, if one is to concede, as if it be shown that there is one power of contraries, and that the discipline is the same; but here they concede even without having first confessed, because the false is manifest, as when the diameter is posited as commensurable, because the odd are equal to the even parts.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":102,"ref":"p102","source":"Plures autem et diversi terminantur ex conditione, quos prospicere oportet, et notare apte. QucC ergo horum differentiæ, et quoties fiunt, qui sunt ex hypothesi, postea dicemus. Nunc autem tantum sit nobis manifestum quoniam non est resolvere in figuras hujusmodi syllogismos, et ob quam causam diximus.\n\nCAPUT XLI.\n\nDe reciproqua reductione syllogismorum unius figuræ in aliam.\n\nQuæcunque autem in pluribus figuris monstrantur proposita, si in altera syllogizetur, est reducere syllogismum in alteram, ut eum qui in prima est privativum in secundam figuram, et eum qui in media est in primam. Non omnes autem,3ed quosdam,eritautem in sequentibus manifestum.Si enim a nulli b, autem omni c, a nulli c, sic ergo prima figura; si autem convertatur privativa, media erit. Nam a quidem nulli, autem omni inerit.Similiter autem et si non universalis, sed particularis fit syllogismus,ut si a quidem nulli b,b autem alicui c, conversaenimprivativamediaeritfigura.Eorum au.. temsyllogismorum,qui suntin secunda figura, universales quidem reducentur in primam figuram, particularium autem alter solum.","english":"But many and diverse terms are delimited by condition, which one must foresee and note aptly. What, then, are the differences of these, and how many times they occur, and which are from hypothesis, we will say afterwards. For now, let it only be clear to us that it is not possible to resolve syllogisms of this kind into the figures, and for what cause we have said.\n\nCHAPTER XLI.\n\nOn the reciprocal reduction of syllogisms of one figure into another.\n\nWhatever propositions are demonstrated in several figures, if a syllogism is made in one of them, it is possible to reduce the syllogism into the other, as the privative one that is in the first figure into the second figure, and the one that is in the middle into the first. Not all, however, but some; and this will be made clear in what follows. For if a belongs to no b, but to every c, then a belongs to no c; thus, therefore, the first figure; but if the privative proposition is converted, it will be the middle figure. For a will belong to no b, but to every c. Similarly also if the syllogism is not universal but particular, as if a belongs to no b, but b to some c; for when the privative proposition is converted, it will be the middle figure. But of those syllogisms that are in the second figure, the universal ones are reduced into the first figure, but of the particular ones only one.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":103,"ref":"p103","source":"Insit enim a quidem nulli, vero omni,conversa privativa prima erit figura, nam quidem nulli a, a autem omni inerit.Si autem prsedicativum quidemsitad b,privativumautem ad c, primus terminus ponendus est c, hoc enim nulli a, a -autem.omni b, quare nulli inerit c, ergo et nullic, convertitur enim privativa. Si autem particularis sit syllogismus,quando privativum quidem erit ad majorem extremitatem,resolvetur in primam figuram, ut si a nulli b, autem alicui c, conversa enim privativa prima erit figura, nam quidem nulli a, a autem alicuic. Quando vero prcedicativum, non resolvetur, ut si a quidem omni b, vero non omni, non enim suscipit conversionem a b, neque cum fit, erit syllogismns. Rursus qui in tertia quidem sunt figura, non resolvuntur omnes in primam,qui autem sunt in prima,omnes in tertiam. Insit enim a quidem omni b, autem alicui c, ergo quia convertitur particularis praedicativa, inerit et alicui b,a vero omni inerat, quare fit tertia figura, Et si privativus sit syllogismus,similiter: convertitur enim particularis affirmativa, quare a quidem nulli 6,cautem alicui inerit. Eorum autem syllogismorum quisunt in postrema figura unus tantum non resolvitur in primam, quando non universalis ponitur privativa,alii autem omnes resolvuntur.","english":"For let a belong to none, but to every, the converted privative will be the first figure; for a belongs to none, but a will belong to every. But if the predicative term is to b, and the privative to c, the first term must be posited as c; for this belongs to no a, but a to every b, wherefore it will belong to no c, therefore also to no c, for the privative converts. But if the syllogism is particular, when the privative is to the major extreme, it will be resolved into the first figure, as if a belongs to no b, but to some c; for the converted privative will be the first figure, for a belongs to none, but a to some c. But when it is predicative, it will not be resolved, as if a belongs to every b, but not to every c; for a b does not admit of conversion, nor when it is made will there be a syllogism. Again, those in the third figure are not all resolved into the first, but those in the first are all resolved into the third. For let a belong to every b, but to some c; therefore, because the particular predicative converts, it will also belong to some b, but a belonged to every; wherefore the third figure is made. And if the syllogism is privative, similarly; for the particular affirmative converts, wherefore a will belong to no b, but c to some. But of the syllogisms that are in the last figure, one alone is not resolved into the first, when the privative is not posited as universal, but all the others are resolved.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":104,"ref":"p104","source":"Praedicentur enim de omni c., et a et 6, ergo convertetur ad utrumque particulariter; inerit ergo a alicui b,quare erit prima figura, siquidem a omni c, vero alicui 6; et si a quidem omni c, autem alicui c,eadem ratio, convenitur enim ad bc.Si autem 6quidem omni c, a autem alicui c. primus ponendus b, nam omni c, autem alicui a,quare alicui a, quoniam autem convertilur particularis,et a alicui inerit.Et si privativus sit syllogism us universalibus terminis,similiter sumendum. Insit enim omni c, a autem nulli c, ergo alicui inerit c, a autem nulli c,quare erit medium c. Similiter autem et si privativa quidem si universalis, prædicativa autem particularis, nam a quidem nulli c, c, autem alicui inerit. Si autem particularis sumatur privaliva,non erit resolutio,ut si quidem omni c, a autem alicui non inest, conversa enim c,utræque propositiones eruntparticulares.","english":"For let both a and b be predicated of every c; therefore it will be converted to each particularly; therefore a will belong to some b, so that it will be the first figure, since a belongs to every c, but to some b. And if a belongs to every c, but to some c, the same reasoning holds, for it is brought to bc. But if b belongs to every c, and a to some c, b must be placed first; for it belongs to every c, but to some a, therefore to some a; and since the particular is converted, a will also belong to some. And if the syllogism is privative with universal terms, it must be taken similarly. For let it belong to every c, but a to no c; therefore it will belong to some c, but a to no c, so that c will be the middle term. Similarly also if the privative is universal, but the predicative particular; for a belongs to no c, but c will belong to some. But if the privative is taken as particular, there will be no resolution, as if it belongs to every c, but a does not belong to some; for when c is converted, both propositions will be particular.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":105,"ref":"p105","source":"Manifestum autem quoniam ad resolvendum ad se invicem figuras, quæ ad minorem extremitatem est propositio, convertenda in utrisque figuris, hac conversa,transitio fit; eorum autem qui in media sunt figura, alter quidem resolvitur, alter vero non resolvitur in tertiam, nam cum sit universalis privativa, resolvitur.Sienim a nulli quidem b,alicui autem c, utraque similiter convertitur ad a,quare quidem nulli a, vero alicui,medium ergo a.Quando autem a omni b, autem alicui non insit, non fit resolutio, neutra enim propositionum ex conversione universalis. Qui autem ex tertia sunt figura, resolventur in mediam, quando fuerit universalis privativa, ut si a nulli c, autem alicui, aut omni nam c, a quidem nulli. autem alicui inerit.Si autem particularis sit privativa, non resolvetur, non enim suscipit conversionem particularis negativa. Manifestum ergo quoniam iidem syllogismi non resolvuntur in his figuris, qui nec in primam resolvebantur, et quoniam in primam figuram reductis syllogismis, isti soli syllogismi per impossibile clauduntur.Quomodo ergo oportet syllogismos reducere,et quoniam resolvuntur figuræ in se invicem, manifestum ex, dictis.","english":"It is evident that for resolving figures into one another, the proposition that pertains to the lesser extreme must be converted in both figures, and when it has been converted, the transition is made. Of those in the middle figure, one is resolved and the other is not resolved into the third; for when the universal privative proposition is present, it is resolved. For if a belongs to no b, but to some c, both are converted in like manner to a; therefore a belongs to no a, but to some a; therefore the middle term is a. But when a belongs to every b, but does not belong to some c, no resolution occurs, for neither proposition is universal by conversion. Those in the third figure are resolved into the middle when the universal privative proposition is present, as if a belongs to no c, but to some or to every c; for c belongs to no a, but to some a. But if the privative proposition is particular, it will not be resolved, for a particular negative does not admit conversion. It is evident, therefore, that the same syllogisms are not resolved in these figures which were not resolved into the first figure, and that when syllogisms have been reduced to the first figure, these alone are concluded through impossibility. In what way, then, one ought to reduce syllogisms, and that the figures are resolved into one another, is evident from what has been said.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":106,"ref":"p106","source":"CAPUT XLII.\n\nDe syllogismis infinitis, et regulis consequentiarum.\n\nDifFert autem in construendo vel destruendo opinari, aut idem, aut diversum significare, non esse hoc, et esse non hoc, ut non esse album, ei quod est esse non album; non enim idem significant,nec est negatio ejus puse est esse album ea quae est esse non album,sed non esse album. Ratio autem hujus hæc est; similiter enim se habet possibile est ambulare ad possibile non ambulare, id quae est esse album ad esse non album, et scit bonum ad scit non bonum: nam scit bonum velsciens bonum nihil differt, neque potest ambulare vel est potens acubulare; quare est opposita, non potest ambulare et non est potens ambulare. Si igitur non est potens ambulare idem significat et est potens non ambulare, ipsa simul inerunteidem,nam idem potestambulareetnonambulare, et idem sciens bonum et non bonum est. Affirmatio autem et negatio non sunt oppositas simul in eodem.","english":"CHAPTER XLII.\n\nOn infinite syllogisms, and the rules of consequences.\n\nBut in constructing or destroying an argument, it makes a difference whether one holds that \"not to be this\" and \"to be not this\" signify the same or different things—for example, \"not to be white\" and \"to be not white.\" For they do not signify the same thing, nor is \"not to be white\" the negation of \"to be white\"; rather, \"to be not white\" is. The reason for this is as follows: for \"it is possible to walk\" stands in the same relation to \"it is possible not to walk\" as \"to be white\" does to \"to be not white,\" and \"he knows the good\" to \"he knows the not-good.\" For \"he knows the good\" differs in no way from \"he is knowing the good,\" nor \"he is able to walk\" from \"he is capable of walking\"; wherefore the opposites are \"he is not able to walk\" and \"he is not capable of walking.\" If, then, \"he is not able to walk\" signifies the same as \"he is able not to walk,\" both will be present in the same subject at once; for the same person can walk and not walk, and the same person knows the good and the not-good. But affirmation and negation are not opposites present at the same time in the same subject.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":107,"ref":"p107","source":"Quemadmodum ergo non idem est, non scire bonum et scire non bonum, nec esse non bonum et non esse bonum, idem, nam proportionalium, si alterum sit, et alterum,nec esse noncequale et non esse aequale idem, huic enim quod est non æquale subjacet aliquid,et hoc estinsequale,illi vero nibil, eo quod æquale quidemvelinsequale non omne est, aequale autem vel non æquale omne: amplius, est non album lignum et non est album lignum non simul sunt, si enim est lignum non album, erit Iignum,quod autem non est album lignum, non necesse est esse lignum: quare manifestum est quoniam non est ejus quod est bonum, est non bonum, negatio; si ergo de omni uno vel affirmatio, vel negatio vera, si non est negatio, palam quoniam affirmatio aliquo modo erit; affirmationis autem omnis, negatio est, et hujus ergo, ea quae est non est, non bonum.Habent autem ordinem hunc ad invicem, sit esse quidem bonum in quo a, non esse autem bonum in quo b, esse autem non bonum in quo sub b, non esse autem non bonum in quo sub a, omni ergo inerit aut a, aut b, et nulli eidem, et omni aut c, aut d, et nulli eidem, et cui inest, necesse est omni inesse.","english":"Therefore, just as \"not to know the good\" and \"to know the not-good\" are not the same, neither are \"to be not-good\" and \"not to be good\" the same; for in proportional pairs, if one holds, the other does too, nor are \"to be not-equal\" and \"not to be equal\" the same. For under \"not equal\" something is subordinated, and this is \"unequal,\" whereas under the other there is nothing, because not everything is either equal or unequal, but everything is either equal or not equal. Moreover, \"the wood is not white\" and \"the wood is not-white\" are not simultaneous; for if the wood is not-white, there will be wood, but what is \"not white wood\" need not be wood. Hence it is clear that the negation of \"good\" is not \"not-good.\" Therefore, if of every single thing either the affirmation or the negation is true, and it is not the negation, it is plain that the affirmation will in some way hold; but of every affirmation there is a negation, and therefore of this one too, namely the one that is \"is not good.\" Now these have this order among themselves: let \"to be good\" be that in which a, \"not to be good\" that in which b, \"to be not-good\" that which is under b, \"not to be not-good\" that which is under a. Therefore a or b will belong to everything, and neither to the same thing, and c or d to everything, and neither to the same thing, and whatever c belongs to, it is necessary that it belong to everything.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":108,"ref":"p108","source":"Si enim verum est dicere quoniam est non album, et quoniam non est album, verum; impossibile est enim simul esse album et esse non album,aut esse lignum album et esse lignum non album: quare si non affirmatio,etnegatio inerit.Ei autem quod est b, non semper c, quod enim omnino non est lignum, neque lignum erit album, nec non album. E converso autem cui inest a, et omni inest, aut enim c, aut: quoniam autem non possunt simu: esse non album et ese album, inerit, nam de eo quod est album verum est dicere quoniam non est non album. De autem non omnino a erit, nam de eo quod omnino non est lignum, non verum est dicere a quoniam est lignum album; quare verum est, et a non verum, quoniam est lignum album.\n\nPalam autem quoniamet a et nulli eidem insunt, sed et contingit eidem alicuiinesse.Similiter autem sehabent et privationes ad prædicationes eadem positione: sit enim a quale in quo a, non aequale in quod b, inæquale in quo c, non ineequale in quo d. In pluribus autem quorum his quidem inest, illis vero non inest idem, negatio quidem similiter vera fit,ut quoniam non sunt alba omnia., aut quoniam non est album unumquodque, aut quoniam est non album unumquodque, aut quoniam omnia sunt non alba, falsum est. Similiter autem et ejus quæ est omne animal album, non hæc (est non album omne animal) negatio, ambae enim falsæ, sed es,non omne animal album.","english":"For if it is true to say that it is not-white, and that it is not white, [it is] true; for it is impossible for the same thing to be white and to be not-white at the same time, or for there to be white wood and not-white wood; wherefore if there is no affirmation, the negation will be present. But for that which is b, c does not always [follow]; for that which is altogether not wood will be neither white wood nor not-white. Conversely, however, for that to which a belongs, [c] also belongs to every [instance]; for either c, or—since it is impossible for not-white and white to be present at the same time—[the negation] will be present; for concerning that which is white it is true to say that it is not not-white. But concerning that which is not altogether [wood], a will not hold; for concerning that which is altogether not wood, it is not true to say a, that it is white wood; wherefore it is true, and a is not true, that it is white wood.\n\nIt is clear, moreover, that both a and [its negation] are not present in the same thing, but it also happens that they are present in some same thing. In like manner, privations are related to predications in the same arrangement; for let a be \"equal,\" in which [is] a; let \"not equal\" be that in which [is] b; let \"unequal\" be that in which [is] c; let \"not unequal\" be that in which [is] d. But in many things of which some have [a property] and others do not have the same, the negation likewise becomes true, as that all are not white, or that each one is not white, or that each one is not-white, or that all are not-white; [but] it is false. In like manner also, of the [proposition] \"every animal is white,\" this is not the negation: \"every animal is not-white\" (for both are false), but rather: \"not every animal is white.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":109,"ref":"p109","source":"Quoniam autem palam quod aliud significat est non album, et non est album, et illa. quidem affirmatio, haec vero negatio, manifestum quoniam non est idem modus monstrandi utrumque, ut quoniam quidquid est animal, non est album,aut contingit non esse album, et quoniam verum dicere non album,hoc enim est esse non album. Sed verum quidem dicere, est album, sive non album, idem modus.Constructive enimambae per primam ostenduntur figuram, nam verum ei quod est similiter ordinatur, ejus enim quae est, verum dicere album, non hæc, verum dicere non album, negatio,sedhæc, non est verum dicere album. Si enim verum dicere quidquid est homo musicum esse,autnonmusicum esse,quidquid est animal sumendum musicum esse, aut non musicum esse, et ostensum est. Non esse autem musicum quidquid esthomo,destructive monstratursecundum dictostresmodos.Simpliciter autem quando sicse habent a et b, ut simul quidem eidem non contingant, omni autem de necessitilte alterum, et rursum et similiter. Sequitur autem id quod est c, a, et non convertitur, et id quod est sequetur d, et non convertitur, et a quidem et contingunt eidem, autem et non contingunt.Primum ergo quoniam id quod est sequitur d, hinc manifestum quoniam eorum quse suntc alterum ex necessitate omniinest, cui autem non contingitc, eo quod simul infert a, a autem et non contingunt eidem, manifestum quoniam sequetur b.","english":"But since it is clear that \"is not-white\" signifies something different from \"is not white\"—the former being an affirmation, the latter a negation—it is manifest that the manner of demonstrating each is not the same: for instance, \"whatever is an animal is not white,\" or \"it is possible not to be white,\" and \"it is true to say not-white\" (for this is to be not-white). But \"it is true to say [it is] white\" and \"not-white\" [are demonstrated] in the same manner. For both are shown constructively through the first figure; for \"true\" is ordered similarly to the thing, since the negation of \"it is true to say white\" is not \"it is true to say not-white,\" but \"it is not true to say white.\" For if it is true to say that whatever is a man is musical or not musical, one must take that whatever is an animal is musical or not musical, and it has been demonstrated. But that whatever is a man is not musical is demonstrated destructively according to the three modes stated. Simply, however, when a and b are so related that they cannot at the same time belong to the same thing, but by necessity one of them belongs to every thing, and again similarly. And it follows that c [belongs to] a, and it does not convert, and that which is d will follow, and it does not convert, and a and [c] do belong to the same thing, but [b and d] do not belong. First, then, that which is [c] follows d—from this it is manifest that one of the things that are c belongs by necessity to every thing to which c cannot belong; and since a is inferred together with it, and a and [b] cannot belong to the same thing, it is manifest that b will follow.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":110,"ref":"p110","source":"Rursum quoniam ei quod est a non convertitur c, omni autem vel c, vel d, contingit a, et eidem inesse; autem et £ non contingit, eo quod consequitur a id quod est c, accidit enim quiddam impossibile.Manifestum est ergo quoniam nec ei quod est convertiur, eo quod contingit simul a, inesse. Accidit autem aliquoties in hujusmodi terminorum ordine falli,eo quod opposita non sumantur recte, quorum necesse est omni alterum inesse: ut se a et non contingunt simul eidem,necesse est auteminessecui non alterum, alterum, et rursus et rl similiter, cui autem omni sequitur a,accidet enim cui d,b inesse ex necessitate, quod falsum est; si sumatur enim negatio eorum quae sunta b, ea quae est in quibus f, et rursus eorum quae sunt d, ea quæ est in quibus g. Necesse est igitur omni inesse vel a, vel f, aut enim af'firmationem,aut negationem,et rursum, aut c, aut; affirmatio enim et negatio, et cui omni a subjacet, quare cui omni boc quod est g. Rursum quoniam eorum quæ sunt omni alterum, eteorum quae sunt similiter. Sequitur autem id quod est f, et id quod est sequitur 6, hoc enim seimus.","english":"Again, since c is not convertible with a, but it is possible for a to belong to every c or d and to the same thing; and it is not possible for both to belong, because c follows from a, something impossible results. It is clear, therefore, that neither is it convertible with that which is, because it happens that a belongs at the same time. But sometimes error occurs in an ordering of terms of this kind, because opposites are not correctly assumed, of which it is necessary that one belong to every thing: for example, if a and not-a cannot belong at the same time to the same thing, it is necessary that one belong to whatever the other does not, and again similarly for the rest. But whatever a follows in every case, it will happen that b belongs by necessity to that to which d belongs, which is false. For if one takes the negation of the things that are a and b, namely that which is in the things in which f is, and again of the things that are d, that which is in the things in which g is. It is necessary, therefore, that either a or f belong to every thing; for it is either an affirmation or a negation, and again either c or not-c; for it is an affirmation and a negation, and whatever a is subject to in every case, wherefore whatever g is. Again, since of the things that are, one of two opposites belongs to every thing, and similarly of the things that are not. But f follows, and that which is follows b; for this we know.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":111,"ref":"p111","source":"Si ergo a id quod est c, et id quod est sequetur b, boc autem falsum; e contrario enim erat in his (quæ sic se babent) consequentia, Non enim fortasse necessariumomni inesse, auta aut /, nee (aut:nonenimest negatio ejus quodestnhocquodestf,nam boni non bonumnegatio;nonautem est idem hoc quod estnonbonum ei quod est nequebonum neque non bonum; similiter autem et in d, nam negationes qllæ sumptæ sunt, duæ sunt.\n\nLIBER SECUNDUS.\n\nCAPUT PRIMUM.\n\nIn quot ergo figuris, et per quales, et quot propositiones, et quando, et quomodo fit syllogismus, ampliusautem ad quæ perspiciendum construenti et destruenti, et quomodo oporteat quærere de proposito secundum unamque artem, amplius autem per quam viam sumemus, quæ in singulis sunl principia jam pertransivimus. Quoniam autem alii quidem syllogismorum sunt universales, alii vero particulares: universales quidem omnes semper plura syllogizant,particularium autem praedicativi quidem plura, negativi vero conclusionem solam. Nam alix quidem propositiones convertuntur, privativa vero non convertitur. Conclusio vero aliquid de aliquo est, quare alii quidem syllogismi plurasyllogizant: ut si a ostensum sit omni aut alicui ineEse, et alicui a necessarium est inesse,et si nulli hinesse a, etb nulli n, bocautem aliud est a priore. Si autem a alicui non insit, non necesse est et alicuia non inesse; contingit enim omni a inesse.","english":"If, then, a is the same as c, and what is the same as c will also follow b, but this is false; for the converse was the consequence in things disposed in this way. For perhaps it is not necessary that it belong to every one, or a or f, nor is it the negation of that which is this which is f; for the negation of good is not good; but this which is not good is not the same as that which is neither good nor not good; and similarly also in d, for the negations that have been assumed are two.\n\nBOOK TWO\n\nCHAPTER ONE\n\nIn how many figures, then, and through what kinds, and how many propositions, and when, and in what way a syllogism comes about, and further what things one must look to in constructing and destroying, and in what way one ought to inquire about a proposed question according to each art, and further by what path we shall take the principles that are in each case—these things we have already gone through. Since, however, some syllogisms are universal and others particular: all universal syllogisms always conclude more things, while of particular syllogisms the affirmative conclude more, but the negative only the conclusion. For some propositions are convertible, but the privative one is not convertible. The conclusion, however, is something about something; wherefore some syllogisms conclude more things: for instance, if a has been shown to belong to every one or to some one, and it is necessary that a belong to some one, and if a belongs to no one of these, then b belongs to no one of these, but this is something other than the previous one. If, however, a does not belong to some one, it is not necessary that a also not belong to some one; for it is possible for it to belong to every one.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":112,"ref":"p112","source":"Haec ergo communis omnium causa universalium et part.icularium. Est autem de llniversalibus, et aliter dicere, quæcumqueenim aut sub medio autsubconclusione sunt, omnium erit idem syllogismus, si illa quidem in medio, baec vero in conclusione ponantur, ut si a conclusio per n, quaecunque sub baut sub sunt, necesse est de omnibus dicia, namd sim toto b, et in a, et erit in a. Rursum si e in toto c, et in toto a, et e in loto a erit. Similiter autem et si privativus sit syllogismus. In secunda aut figura quod sub conclusione erit, solum erit syllogizare, ut si a insit nulli b, et omni c, conclusio quoniam nulli inest; si autem sub est, manifestum quoniam non inestei 6, iisautem quoe sunt sub a,quoniam non inest, non palam est persyllogisrnum, et si non inest quod est e, si est e sub a, sed inesse.quidem nulli per syllogismum ostensum est, non inesse veroa hoc quod estb, indemonstratum sumpt.um est, quare nec per syllogismum accidit non inessec.In particularibus autem,eorum quidem quæ sub conclusione sunt, non erit necessarium, Non enim fit syllogismus, quando ea sumpta fuerit particularis; eorum autem quae sunt sub medio, erit ornnium,verumtamen non per syIlogismun, utsiaomni h, et alicui c: nam ejus quod sub est positum, non erit syllogismus, ejus vero quod sub erit, sed non proper eum qui prius factus est syllogismum.","english":"This, then, is the common cause of all universals and particulars. But concerning universals, it can also be stated otherwise: for whatever things are either under the middle term or under the conclusion, the same syllogism will apply to all of them, if those are placed in the middle term and these in the conclusion—for example, if a is the conclusion through n, whatever things are under b or under c, it is necessary that they be said of all; for if d is in the whole of b, and b in a, then d will also be in a. Again, if e is in the whole of c, and c in the whole of a, then e will also be in the whole of a. The same holds similarly if the syllogism is privative. In the second figure, however, only what is under the conclusion will be syllogized—for example, if a belongs to no b and to every c, the conclusion is that it belongs to no c; but if something is under c, it is evident that it does not belong to it, yet for those things that are under a, that it does not belong to them is not made clear through the syllogism—and if that which is e does not belong, if e is under a, but it was assumed to belong. That it belongs to none has been shown through the syllogism, but that it does not belong to this thing which is b was assumed undemonstrated; therefore it does not result through the syllogism that it does not belong. In particular cases, however, of those things that are under the conclusion, it will not be necessary; for no syllogism arises when a particular has been assumed. But of those things that are under the middle term, there will be a syllogism for all—yet not through the syllogism, for example, if a belongs to every b and to some c; for of that which is placed under c there will be no syllogism, but of that which is under b there will be, though not on account of the syllogism that was made previously.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":113,"ref":"p113","source":"Similiter autem et in aliisfiguris, nam ejus quidem quod sub conclusione est non erit, alterius vero erit, verum non per syllogismum, eo quod et in universalibus ex indemonstrata propositione quæ sunt sub medio ostendebantur; quare neque hic erit, vel et in illis.\n\nCAPUT II.\n\nQuoll ex falsis in prima figura uerum colligatur.\n\nEst ergo sic se babere, ut veræsint propositiones per quasft syllogismus; est autem ut falsae, estvero ut hæc quidem vera, illa autem falsa, concl usio autem aut vera, aut falsaex necessitate. Ex veris ergo non est falsum syIlogizare, ex falsis autem verum, tamen non propter quid,sed quia, nam ejus qui est propterquid non est ex falsis syllogism us, ob quam autem causam insequentibusdicetur,Primumergo quoniam ex veris non possibiIe falsum syllogizare hinc manifestum. Si enim cum est a, necesse est esse b, si non est b, necesse est a non esse; si ergo verum est a,necesse est et verum esse,aut accidet idem simul et esse etnonesse, hoc autemimpossi. bile. Non autemquoniamponitura unusterminus, accipiatur, contingere uno aliquo existente, ex nece\"Jsitate aliquid accidere, non enim potest. Nam quod accidit ex necessit:tte conclusio est, per quæ autem fit ad minimum tres sunt termini, duo autem intervalla et propositiones.","english":"Similarly also in the other figures; for it will not be of the one that is under the conclusion, but it will be of the other, yet not through a syllogism, because even in universals the things that are under the middle term were shown from an indemonstrable proposition; wherefore neither will it be here, or even in those.\n\nCHAPTER II.\n\nThat a true conclusion is inferred from false premises in the first figure.\n\nIt is, then, possible for the premises through which the syllogism is formed to be true; it is also possible for them to be false; and it is possible for one of them to be true and the other false, while the conclusion is either true or false by necessity. From true premises, then, it is not possible to syllogize a false conclusion; but from false premises a true conclusion is possible, yet not as to the reason why, but as to the fact; for the syllogism that gives the reason why does not come from false premises. The cause of this, however, will be stated in what follows. First, then, that it is not possible to syllogize a false conclusion from true premises is manifest from this: for if, when a is, it is necessary that b be, then if b is not, it is necessary that a not be. If, therefore, a is true, it is necessary that b also be true, or else it will happen that the same thing at once is and is not, which is impossible. Nor is it because one term is posited that it should be accepted that it is possible, when some one thing exists, for something to come about by necessity; for this cannot be. For what comes about by necessity is the conclusion, and the terms through which it comes about are at least three, with two intervals and premises.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":114,"ref":"p114","source":"Si ergo verum est cui omni inest et a, cui autem et b, cui c, necesse est a inesse, et non potest hoc falsum esse, simul enim erit idemet non inerit; ergo a ut unum, positum est duas propositiones colIigere. Similiterautem se habet et in privativis, non enim est ex veris ostendere falsum. Ex falsis autem est verum syllogizare, utrisque propositionibus faIsis,et una; hac autem non utralibet contingit, sed secunda, si quidem totam sumamus falsam, non tota autem sumpta est utralibet. Insit enim a onni c, ei autem quod est nulli, nec insit Cj conlingit autem boc,ut nulli lapidi unimal, et lapis nulli homini; si igitur sumatur a omni b,etb omni C, a omnic inerit, quare exutrisque falsis vera est conclusio, omnis enim homo animal.SirniIiter autem et privativum:in?itenim nulli, nec a, nee b, a autem omni, ut si eisdem terminis sumptis medium ponatur homo, lapidi enim nec animal, nea homo nulli inest, homini autem omni animal; quare si cuiquidem omni inest, sumamus nulli inesse, cui vero non inest, omni inesse, ex falsis utrisque vera eritconclusio. Similiter autem oslendeturet si in aliquo utraque falsa sumatur. Si autem altera ponaturfalsa, prima quidem tota falsa existente, ut a b, non erit conclusio vera, autem erit. Dico autem totam falsam quod contrariam veræ, ut si quod nulli in est,omni sumptum est; aut si quod omni nulli inesse.","english":"If therefore it is true that a belongs to everything to which b belongs, and b to everything to which c belongs, then a must belong to c, and this cannot be false; for at the same time it will and will not belong to the same thing. Therefore a, as one term, has been posited to combine two propositions. The same holds also in privative syllogisms, for it is not possible to prove a falsehood from true premises. But from false premises it is possible to syllogize a truth, when both propositions are false, and when one is false; and this does not happen with either one indifferently, but with the second, if indeed we take the whole proposition as false, whereas when it is not taken as a whole, either one may be false. For let a belong to every c, and to that which is b let it belong to none, nor let c belong to b; this can happen, as animal belongs to no stone, and stone to no man. If therefore it is assumed that a belongs to every b, and b to every c, then a will belong to every c; hence from both false premises the conclusion is true, for every man is an animal. Similarly also in the privative case: let b belong to no c, and neither a nor b belong to any c, but let a belong to every b; as, if with the same terms assumed, man is posited as the middle term, for animal belongs to no stone, nor does man belong to any stone, but animal belongs to every man. Therefore if we assume that what belongs to every one belongs to none, and that what does not belong belongs to every one, from both false premises the conclusion will be true. Similarly it will also be shown if both are assumed false in a particular proposition. But if one is posited as false, when the first is wholly false, as a belongs to b, the conclusion will not be true, but it will be true when the other is false. I call a proposition wholly false when it is the contrary of the true one, as if what belongs to none is assumed to belong to every one, or what belongs to every one to belong to none.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":115,"ref":"p115","source":"Insit enim a nulli, autem omni; si ergo quidem propositionem su mamus veram, a autem falsam totam, et omni inesse a, impossible est a conclusionem veram esse, nulli enim inerat a eorum quæ sunt c,si quidem cui nulli, autem omni c. Similiter autem nec si a omni inest, et omni c, sumpta sit autem quidem vera propositio, a autem falsa tota, et nulli cui inest a, conclusio falsa erit, omni enim inest a, siquidem cui omni et a,b autem omni c. Manifestum ergo quoniam prima tota sumpta fal sa, sive affirmativa, sive privativa altera autem vera, non fit vera conclusio. Non tota autem sumpta falsa erit: nam si a quidem omni inest, autem alicui, autem omni c, ut animal, cygno quidem omni, albo autem alicui, album autem omni cygno, si sumatur a omni b, et omni c, a omni inerit vere, omnis enim cygnus animal. Similiter autem et si privativa ani-sit a; possibile est enim ab quidem alicui inesse, vero nulli, autem omni c, ut mal alicui albo, nivi vero nulli, album vero omni nivi; si ergo sumatur a quidem nulli b, autem omni c, a nulli inerit.","english":"For let a belong to none, but b to all; if therefore we take the proposition b as true, but a as wholly false, and [say] that a belongs to all, it is impossible for the conclusion to be true; for a belonged to none of the things that are c, if indeed [it belongs] to none of those to which b belongs, but b to all c. Similarly, neither if a belongs to all, and to all c, but the proposition b is taken as true, while a is wholly false, and [we say] that a belongs to none of those to which it belongs, the conclusion will be false; for a belongs to all, if indeed [it belongs] to all to which b belongs, and b to all c. It is clear, therefore, that when the first [premise] is taken as wholly false, whether it is the affirmative or the privative one, while the other is true, the conclusion does not come out true. But when it is not taken as wholly false, it will be [true]: for if a belongs to all b, and to some c, but b to all c, as animal to all swan, but to some white, and white to all swan, if a is taken to belong to all b, and to all c, a will truly belong to all; for every swan is an animal. Similarly also if a is privative; for it is possible for a to belong to some b, but to none of those to which b belongs, and b to all c, as malice to some white, but to no snow, and white to all snow; if therefore a is taken to belong to none of b, but to all c, a will belong to none.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":116,"ref":"p116","source":"Si autem a quidem propositio tota sumatur veru, autem tota falsa, erit syllogismus verus, nihil enim prohibet a, et b,et omni inesse,b autem nulli c, ut quæcunque ejusdem generis sunt species non subalternæ, nam animal et homini et equo inest, equus autem nulli homini inest.; si ergo sumatur a omnib, et omni c, con ciusio vera eri, tota falsa propositione. Similiter autem cum universalis privativa est a propositio, contingit enim a neque b, neque nulli inesse, et nulli c, ut ex alio genere speciebus diversum genus, nam animal nec musicas, nec medicinæ inest, neque musica medicinæ. Sumpta ergo a quidem nulli b, autem omni c, vera erit conclusio. Et si non tota laIsa sit c, sed in aliquo, etiam sic erit conclusio vera. Nihil enim prohibet a, et betc toti inesse, 6autem alicui c, utgenus speci ei et differentiæ, nam animal homini omni et omni gressibili, homo autem alicui gressibili, et non omni; si ergo a omni b, et omni sumatur, a omni inerit, quod quidem erat verurn.SimiIiter autem cum pri-, vativa est a, propositio, conlingit enim a nec 6, nec nulli inesse, vero alicui c, at genus ex alio genere speciei et differentiæ,nam animal nec sapientiae nulli inest, nec contemplationi, sapientia vero alicui contemplationi; si ergo sumatur a nulli b, autem omni c, nulli inerit a, hoc autem erat verum.","english":"But if the proposition a is taken as wholly true, while b is wholly false, the syllogism will be true; for nothing prevents a from belonging both to b and to every c, while b belongs to no c—as, for instance, whatever species of the same genus are not subordinate to one another; for animal belongs both to man and to horse, but horse belongs to no man. If, therefore, a is taken as belonging to all b and to all c, the conclusion will be true, though the proposition b is wholly false. Similarly also when the universal privative proposition is a; for it is possible for a to belong neither to b nor to any c, as a genus different from another genus is related to the species of that other genus; for animal belongs neither to music nor to medicine, nor does music belong to medicine. If, therefore, a is taken as belonging to no b, but to all c, the conclusion will be true. And if c is not taken as wholly false, but as false in some part, even so the conclusion will be true. For nothing prevents a from belonging to all b and all c, while b belongs to some c—as a genus to a species and a differentia; for animal belongs to every man and to every walking thing, but man belongs to some walking things, and not to all. If, therefore, a is taken as belonging to all b and to all c, a will belong to all c, which was indeed true. Similarly also when a is a privative proposition; for it is possible for a to belong neither to b nor to any c, but to some c—as a genus from another genus is related to a species and a differentia; for animal belongs neither to wisdom nor to contemplation, but wisdom belongs to some contemplation. If, therefore, a is taken as belonging to no b, but to all c, a will belong to no c, and this was true.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":117,"ref":"p117","source":"In particularibus autem syllogismis contingit, prima propositione tota falsa existente, altera autem vera, veram esse conclusionem, et a in aliquo Falsa existente, autem vera, et a quidem vera, particulari autem falsa, et utrisque existentibus falsis.Nibil enim prohibet a quidem nulli inesse, autem alicui, et alicmc inesse, ut animal nulli nivi, albo autem alicui inest, et nix albo alicui. Si ergo ponatur medium nix primurn antem animal, et sumatur a quidem toti inesse, autem alicui c, a tota falsa, autem vera, et conclusio vera. Similiter autem et cum privativa est a propositio, possibile est enim a quidem toti inesse, autem alicui non inesse, vero alicui inesse, ut animal homini quidem omniinest,album autem aliquod non sequitur, homovero alicui alboinest; quare si medio posito homine sumatur a nulliinesse, et a'icui c, vera fit conclusio, cum sit tota falsaa proposito. Et si in aliquo sit falsa a propositio, vera existente,eritconcIusio vera. Nihil enim probibet a, et b, et c, alicui inesse, autem alicui c, ut animaIalicui puIchro,et alicui magno, et pulchrum alicui magno inest; si ergo sumatur a omni b,etb' alicui c, et a quidempropositioin aIiquo falsaerit, autem vera, et conclusio vera. Similiter autem et cum privativa est a propositio, nam iidem erunt termini, et:simiIiterpositi ad demonstrationem. Rursum si a quidem vera, autem falsa, vera erit, conclusio.","english":"But in particular syllogisms it happens that when the first proposition is wholly false and the other true, the conclusion is true; and when a belongs to some and is false, while the other is true; and when a is true but the particular proposition false; and when both are false. For nothing prevents a from belonging to none, while b belongs to some, and b belongs to some c—as, for instance, animal belongs to no snow, but white belongs to some, and snow belongs to some white. If, then, snow is posited as the middle term and animal as the first, and a is taken to belong to the whole of b, and b to some of c, then a is wholly false, b is true, and the conclusion is true. Likewise also when the proposition a is privative; for it is possible that a belongs to the whole, while b belongs to some and does not belong, and b belongs to some—as animal belongs to every man, but white does not follow some [man], and man belongs to some white. Hence if man is posited as the middle term and a is taken to belong to no b, and b to some c, the conclusion comes out true, although the proposition a is wholly false. And if the proposition a is false in some respect, while b is true, the conclusion will be true. For nothing prevents a, b, and c from belonging to some, and b from belonging to some c—as animal belongs to some beautiful thing, and to some great thing, and the beautiful belongs to some great thing. If, then, a is taken to belong to every b, and b to some c, then the proposition a will be false in some respect, b will be true, and the conclusion will be true. Likewise also when the proposition a is privative; for the same terms will be, and similarly posited, for the demonstration. Again, if a is true and b false, the conclusion will be true.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":118,"ref":"p118","source":"Nihil enim prohibet a quidem toti inesse 6, autem alicui, et nulli inesse: ut animal'. cygnus quidem omni,nigro autem alicui,cygnus vero nulli nigro; quare sisumatur a omni b, et alicui c, vera erit conclusio, cum sit falsa c. Similiter autem et privativasumpta a propositione, possibile enima quidem nulIi, autem alicui non inesse, et nulli r,, ut genus ex alio genere speciei et accidenti ejus speciebus,nam animal quem numero nulli inest, alio vero non alicui, numerus autem nulli albo; si ergo medium ponatur numerus,et sumatur a quidem nulli b,b autem alicui c, a alicui non inerit, quod fuit verum, cum a quidem si propositiovera, autem falsa.Etsi in aliquo sitfalsa a 6, falsa autem et c, erit conclusio vera. Nihil enim prohibet a alicui bet alicui inesse utrique,b autem nulli c, ut si sit contrarium ipis c,etamto accidentia eidem generi, nam animal alicui albo et alicui nigro inest, album autem nulli nigro inest; si ergo sumatur a omni b, et alicui c, vera erit conclusio. Et privativaquidem sumpta a b, similiter. Nam idem termini, etsimililer ponenturad demonstrationem. Et ex utrisque falsis eritconclusio vera. Possibile est enim a quidem nulli, caulem alicui inesse, vero nulli c. Ut genus ex alio genere speciei, et accidenti speciebus ejus, animal enim numero quidem nulli, albo vero aIicuiinest, et numerusnuIliaIbo.","english":"For nothing prevents a from belonging to the whole of b, or to some, and to none: as animal; for swan belongs to every [animal], but to some black thing, while swan belongs to no black thing; therefore if a is taken as belonging to every b, and to some c, the conclusion will be true, though it is false of c. And similarly when the proposition a is taken as privative; for it is possible for a to belong to none, or to some, and to none of r, as a genus from another genus of a species and an accident of its species; for animal belongs to no number, but to some other thing, while number belongs to no white thing; therefore if number is posited as the middle term, and a is taken as belonging to no b, but b to some c, a will not belong to some c, which was true, though the proposition a was true and the other false. And if a is false of some b, and c is also false, the conclusion will be true. For nothing prevents a from belonging to some b and to some of both, while b belongs to no c, as if it were the contrary of c itself, and also accidents of the same genus; for animal belongs to some white thing and to some black thing, but white belongs to no black thing; therefore if a is taken as belonging to every b, and to some c, the conclusion will be true. And similarly when a b is taken as privative. For the same terms, and similarly posited, will serve for the demonstration. And from both false premises the conclusion will be true. For it is possible for a to belong to no c, but to some other thing, and for b to belong to no c. As a genus from another genus of a species, and an accident of its species; for animal belongs to no number, but to some white thing, and number to no white thing.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":119,"ref":"p119","source":"Si ergo sumaturaomni b, et balicui j, conclusio quidem vera, propositiones vero ambae falsæ. Similiter autem etcum privativa esta b. Nihil enim prohibet a quidem toti inesse,c autem alicui non inesse, etneque nulIi c, ut animal cygno quidem omni, nigro autem alicui non inest, cygnus vero nulli nigro:quare si sumatur a nulli b,b autem alicui ca alicuic non inerit; ergo conclusio quidem vera, propositiones autem falsae.\n\nCAPUT III.\n\nQuod colligatur verum ex falsis ita secunda figura,\n\nIn media autem figura omnino contingit per falsa verum syIlogizare,et utrisque propositionibus totis falsis sumptis, et bac quidem vera, illa tota falsa, utralibet falsa posita,et si utraque in aliquo falsa?, et si haec quidem simpliciter vera, illa autem in aliquo falsa, et in universalibus, et in particularibus syllogismis. nulli,Si enim a quidem nulli inest, autem omni, ut lapidi animal quidem homini autem omni, si contrariae ponantur propositiones, et si sumatur a quidem omni, vero nulli,ex falsis totis propositionibus erit vera conciusio. Similiter autem et si a inest quidem omni, vero nulli, nam idem erit syllogismus. Rursum si altera quidem tota falsa, altera autem tota vera. Nihil enim prohibet a et et omni inesse,b autem nulli c, ut genus non subalternis speciebus.","english":"If then a is taken as belonging to every b, and b to some c, the conclusion is indeed true, but both premises are false. It is the same also when the privative proposition is about b. For nothing prevents a from belonging to the whole of c, but not to some c, and to no c: as animal belongs to every swan, but not to some black thing, while swan belongs to no black thing. Therefore if a is taken as belonging to no b, and b to some c, a will not belong to some c; therefore the conclusion is indeed true, but the premises are false.\n\nCHAPTER III.\n\nThat a true conclusion is inferred from false premises in this way in the second figure.\n\nIn the middle figure it is altogether possible to syllogize a true conclusion through false premises, both when both premises are taken wholly false, and when one is true and the other wholly false, whichever of the two is posited as false, and if both are false in some respect, and if one is simply true and the other false in some respect, both in universal and in particular syllogisms. For if a belongs to no c, but to every b, as animal to no stone but to every man, if the contrary propositions are posited, and if a is taken as belonging to every c but to no b, the conclusion will be true from wholly false premises. It is the same also if a belongs to every c but to no b; for the syllogism will be the same. Again, if one premise is wholly false and the other wholly true. For nothing prevents a from belonging both to every c and to no b, as a genus to species that are not subordinate.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":120,"ref":"p120","source":"Nam animal equo omni, et homini inest, et nullus homo equus;si ergo sunaaturanimal buicquidem omni,ilIi vero nulli inesse,bæc quidem erit falsa,iIla vero tota vero, et conclusio vera,ad quodlibet posito privativo. Et si altera in aliquo f'alsa, altera autem tota vera, possibile est enim a quidem alicui in esse, autem omni, et nulli c, animal albo quidem alieui, corvo autem omni, album vero nulli corvo. Si ergo sumatur a quidem nulli, autem toti inesse, a quidem propositio in aliquo falsa est, a autem tota vera, et conclusio vera, et transposita quidem privativa,sirniIiter.Nam per eosdem termi. nos demonstratio.Et si affirmativa quidcm propoaitio in aliquo faIsa,privativa autem tota vera,. nihil enim prohibet a quidem alicui inesse, autem toti non inesse, et nulli c, ut animal albo quidem aIicui,pici autem nulli,album vero nulli pici: quare si sumatur,a toti inesse,c autem nulli,a quidem in aliquo falsa, a r: autem tota vera, et conclusio vera. Et si utrasque propositiones in aliquo falsae, erit conclusio vera, possibile est enim a, et b, et alicui inesse, autem nulli c, ut animal, et albo alicui, et nigro alicui, album vero nulli nigro. Si ergo sumatur a quidem omni,c autem nulli,ambae quidem propositiones in aliquo falsæ,conclusio autem vera; similiter autem transposita privativa per terminos.","english":"For animal belongs to every horse and to every man, and no man is a horse. If then it is taken that animal belongs to every one of these and to none of those, the former premise will be false, the latter wholly true, and the conclusion true, with the privative proposition posited in relation to anything. And if one of the premises is false in some respect, while the other is wholly true—for it is possible for a to belong to some and to belong to every, and to no c, as animal belongs to some white thing and to every raven, while white belongs to no raven. If then it is taken that a belongs to none and to every, the premise about a is false in some respect, while the other is wholly true, and the conclusion is true; and when the privative proposition is transposed, similarly. For the demonstration is through the same terms. And if the affirmative premise is false in some respect, while the privative premise is wholly true—for nothing prevents a from belonging to some and not belonging to every, and to no c, as animal belongs to some white thing and to no woodpecker, while white belongs to no woodpecker; wherefore if it is taken that a belongs to every and c to none, the premise about a is false in some respect, while the other is wholly true, and the conclusion is true. And if both premises are false in some respect, the conclusion will be true; for it is possible for a and b to belong to some and to no c, as animal belongs to some white thing and to some black thing, while white belongs to no black thing. If then it is taken that a belongs to every and c to none, both premises are false in some respect, but the conclusion is true; and similarly when the privative proposition is transposed, through the terms.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":121,"ref":"p121","source":"Manifestum autem et in particularibus syllogism is, nibil enim prohibet a quidem omni,c autem alicui inesse,et alicui non inesse,ut animal omni homini, albo autem alicui, homo vero alicui albo non inerit. Si ergo ponatur a quidem nulli inesse,c autem alicui inesse, universalis quidem propositio tota falsa, particularis autem vera, et conclusio vera. Similiter autem et affirmativa sumpta a b, possibile est enim a quidem nulli, autem alicui non inesse,et alicui non inesse,ut animal nulli inanimato,aIbo autem alicui,et inanimatum non inerit alicui albo. Si ergo ponatur a quidem omni, vero alicui non inesse,a quidem propositio universalis tota faIsa,a autem vera, et conclusio vera. Et universali quidem vera posita, minori autem particulari falsa,nihil enim prohibet a nec nec nullum sequi, et alicui non inesse, ut animal nulli numero nec inanimato,et numerus aliquod inanimatum non sequitur. Si ergo ponatur a quidem nulli,c autem alicui,et conclusio vera, et universalis proposito vera, particularisautem falsa.Affirmativa autem universali similiter posita, possibile est enim a et et toti inesse, autem aliquod non sequi, ut genus speciem et differentiam.","english":"It is also evident in particular syllogisms; for nothing prevents A from belonging to every C and to some C and not to some C, as animal belongs to every man, but to some white thing, while man will not belong to some white thing. If then it is assumed that A belongs to no C, but to some C, the universal proposition is wholly false, the particular is true, and the conclusion is true. Similarly also if the affirmative premise AB is assumed; for it is possible that A belongs to no C and not to some C and not to some C, as animal belongs to no inanimate thing, but to some white thing, and the inanimate thing will not belong to some white thing. If then it is assumed that A belongs to every C, but not to some C, the universal proposition A is wholly false, but the other is true, and the conclusion is true. And when the universal is assumed true, but the particular minor premise false; for nothing prevents A from following neither no C nor some C, and from not belonging to some C, as animal follows no number nor inanimate thing, and number does not follow some inanimate thing. If then it is assumed that A belongs to no C, but to some C, the conclusion is true, and the universal proposition is true, but the particular is false. Similarly also when the universal affirmative is assumed; for it is possible that A belongs to the whole and does not follow some, as genus to species and difference.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":122,"ref":"p122","source":"Nam animal omnem hominem et totum gressibile sequitur, homo vero non omne gressibile: qua re si sumatur a quidem toti inesse, autem alicui non inesse,universaIis quidem propositio vera,particularis faIsa,concIusio autem vera.Manifesturn autem quoniam et utrisque falsis erit conclusio vera, siquidem contingit a et et huic quidem omni,illi vero nulli inesse, vero aliquod non sequi,nam sumpto a quidem nulli,:a autem alicui inesse, propositiones quidem ambæ falsæ, conclusio autem vera. Similiter autem et cum prædicativa fuerit uni versalis propositio, particularis autem privativa, possibile est enim a quidem nullum, autem omne sequi,et alicui non inesse, ut animal disciplinam quidem nullam, hominem autem omnem sequitur, disciplina vero non omnem hominem. Si ergo su matur a quidem toti inesse, autem aliquod non sequi,propositiones quidem falsæ,conclusio autem vera.","english":"For animal follows every man and every whole thing that walks, but man does not follow every thing that walks. Therefore, if it is assumed that A belongs to every C but not to some C, the universal proposition is true, the particular false, and the conclusion true. It is also clear that the conclusion will be true even when both propositions are false, since it is possible for A to belong to every C and to no C, and for B not to follow some C. For if A is taken to belong to no C, but to some C, both propositions are false, yet the conclusion is true. Likewise also when the proposition is universal affirmative but the particular is privative; for it is possible for A to follow no B but every C, and not to belong to some C, as animal follows no discipline but every man, while discipline does not follow every man. If, then, it is assumed that A belongs to every C but does not follow some C, the propositions are false, but the conclusion is true.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":123,"ref":"p123","source":"CAPUT IV.\n\nQuod ex falsis verum identidem colligatur in tertiafigura.\n\nErit autem et in postrema figura per falsas totas, et in aliquo utraque, et altera quidem vera, altera autem falsa, et hæc quidem in aliquo falsa, illa autem tota vera,et e converso, et quotquot modis aliter possibile est transumere propositiones. Nihil enim prohibet nec a nec nulli inesse, a autem alicui inesse, ut nec homo, nec gressibile, nullum inanimatum sequitur,homo autem alicui gressibili inest; si ergo sumatur a et omni messe,propositiones quidem totæ falsæ conclusio autem vera. Similiter autem ei cum hæc quidem est privativa, illa vero affirmativa, possibile est enim quidem nulli inesse,a autem omni, et a alicui non inesse, ut nigrum nulli cygno, animal autem omni, et ani mal non omni nigro; quare si sumatur quidem omni c, a vero nulli, alicui a non inerit, et conclusio quidem vera, propositiones autem falsæ. Et, si in aliquo fuerit utraque falsa, erit conclusio vera, nihil enim prohibet et a et alicui inesse, et a alicui b, ut album et pulchrum alicui animali inest, et album alicui pulchro; si ergo ponatur a et omni inesse, propositiones quidem in aliquo falsæ, conclusio autem vera. Et privativa a posita, inesse,b vero alicui inesse, et a non omni inesse, ut album alicui animali non inesse.","english":"CHAPTER IV.\n\nThat a true conclusion is sometimes inferred from false premises in the third figure.\n\nIt will also happen in the last figure through wholly false premises, and in the case of particular premises both false, and one true and the other false, and the one false in a particular, the other wholly true, and conversely, and in as many other ways as it is possible to transpose the propositions. For nothing prevents neither A nor B from belonging to any C, while A belongs to some B: for example, neither man nor walking belongs to any inanimate thing, but man belongs to some walking thing. If, then, it is assumed that A belongs to every B, the premises are wholly false but the conclusion true. Likewise when one of them is privative and the other affirmative: for it is possible for B to belong to no C and A to every C, and for A not to belong to some B: for example, black belongs to no swan, but animal to every swan, and animal not to every black thing. Therefore, if it is assumed that B belongs to every C and A to no C, A will not belong to some B, and the conclusion is true while the premises are false. And if both are false in a particular, the conclusion will be true: for nothing prevents both A and B from belonging to some C, and A from belonging to some B: for example, white and beautiful belong to some animal, and white to some beautiful thing. If, then, it is posited that A belongs to every B, the premises are false in a particular but the conclusion is true. And with A posited as privative, that it belongs, and B as belonging to some C, and A as not belonging to every B: for example, white does not belong to some animal.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":124,"ref":"p124","source":"Pulchrum autem alicui:nest,et album non omni pulchro: quare si sumatur a quidem nulli, autem omni, utraque propositiones quidem in aliquo faIsæ, concIusio au. tem vera. Similiter autem et hæc quidem tota falsa, illa vero tota vera sumpta.PossibiIe est enim a et omne sequi,et a alicui non inesse,ut animal et album omne cygnum sequitur,et animal non omni inest albo; positis igitur bis terminis,si sumatur quidem toti inesse,a vero toti non inesse,h quidem tota erit vera, a autem tota faIsa,et conclusio vera. Similiter autem et. si quidem falsa, a autem vera,nam hi quidem termini ad demonstrationem, nigrum, animatum, cygnus. Sed et si utraeque assumantur affirmare, nihil enim prohibet quidem omne sequi,a autem toti non inesse, et a alicui inesse,ut omni cygno animal,nigrum vero nulli cygno,et nigrum inest alicui animali: quare si sumatur a et omni inesse,b quidem tota vera, a autem tota falsa, et conclusio vera. Similiter autem et a sumpta vera,nam per eosdem terminos demonstratio. Rursum hac quidem Lota vera esistente,illa vero in aliquo l'aIsa,possibile est enim quidem omni inesse,a autem alicui et alicui b,ut bipes quidem omni hommi,pulchrum non omni,et pulchrum alicui bipedi inest.Si ergo sumatur a et toti inesse,b quidem tota vera, a autem in aliquo faIsa,concIusio autem vera.","english":"But it is possible for something to be beautiful and for white not to belong to every beautiful thing; therefore if one premise is taken as belonging to none and the other as belonging to all, both propositions are in some respect false, but the conclusion is true. And similarly, one premise may be taken as wholly false and the other as wholly true. For it is possible for something to follow every instance of a thing, and yet for that thing not to belong to some instance of another, as animal follows every swan, and animal does not belong to every white thing. So when the terms are set out in this way, if one premise is taken as belonging to all and the other as belonging to none, the one will be wholly true, the other wholly false, and the conclusion true. And similarly if one is false and the other true; for the terms for this demonstration are black, animate, swan. But also if both premises are assumed affirmative—for nothing prevents one term from following every instance of another, while the second does not belong to every instance of the first and yet belongs to some instance of it, as animal belongs to every swan, black to no swan, and black belongs to some animal. Therefore if one premise is taken as belonging to all and the other as belonging to none, the one will be wholly true, the other wholly false, and the conclusion true. And similarly if the one is taken as true; for the demonstration is through the same terms. Again, when one premise is wholly true and the other false in some respect—for it is possible for one term to belong to every instance of another, while the second belongs to some instances of the first and to some instances of the second, as two-footed belongs to every man, beautiful not to every man, and beautiful belongs to some two-footed thing. If, then, one premise is taken as belonging to all and the other as belonging to none, the one will be wholly true, the other false in some respect, but the conclusion true.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":125,"ref":"p125","source":"Similiter autem et a quidem vera,b autem falsa in aliquo sumpta, transpositis enim eisdem terminis erit demonstratio. Et cum haec quidem est privativa,illa vero affirmativa,quoniam possibile est quidem toti inesse, a autem alicui c,et quando sic se habeant,non omni inesse a.Si ergo assumatur quidem toti inesse, a autem nulli, privativa quidem aliquo falsa, altera autem tota vera,et conclusio erit vera,Rursum quoniam ostensum est quod cum a quidem nulli inest,et alicui, evenit a alicui non inesse, rnanifestum igitur quoniam et cum a tota est vera, autem in aliquo falsa, contingit conclusionem esse veram: si enim sumatur a quidem nulli c, autem omni, a e quidem tota vera, autem in aliquo falsa.Manifestum autem et in particularibus syllogismis quoniam omnino per falsaerit verum, non iidem termini sumendi,et quando universales fuerint propositiones, in prædicativis quidem prædicativi,in privativis autem privativi; nihil enim iffert,cu nulli inerat, universaIiter sumere inesse, et si alicui inerat,universaIiter sumere ad terminorum positionem; similiter autem et in privati vis. Manifestum igitur quod quando sit conclusio falsa, necesse est ea exquibus est oratio faIsaeese,automnia,aut aliqua; quando autem vera,non necesse est verum esse nec aliquod quidem, nec omne.","english":"Likewise also when one premise is true and the other false in some respect; for with the same terms transposed, the demonstration will hold. And when one is privative and the other affirmative, since it is possible for it to belong to the whole and for A to belong to some C, and when they are so related, for A not to belong to every. If then it is assumed that it belongs to the whole, but A to none, the privative premise is false in some respect, while the other is wholly true, and the conclusion will be true. Again, since it has been shown that when A belongs to none and to some, it results that A does not belong to some, it is therefore evident that when A is wholly true but the other false in some respect, it happens that the conclusion is true; for if it is assumed that A belongs to no C, but the other to every, A is wholly true, but the other false in some respect. It is evident also in particular syllogisms that a true conclusion may come about entirely through false premises, but the same terms are not to be assumed, and when the propositions are universal, in affirmative syllogisms the terms must be affirmative, in privative ones privative; for it makes no difference, when it belonged to none, to assume universally that it belongs, and if it belonged to some, to assume universally with respect to the positing of the terms; similarly also in privative syllogisms. It is evident therefore that when the conclusion is false, it is necessary that the premises from which the argument is formed be false, either all or some; but when it is true, it is not necessary that any of them be true, nor all.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":126,"ref":"p126","source":"Sed est cum nullum sit verum eorum quae sunt in syllogismis, et conclusionem similiter esse veram, non tamen ex necessitate. Causa autem quoniam cum duo sic se habent ad invicern,ut cum alterum sit, ex necessitate esse alterum, hoc cum non sit quidem, nec alterum erit; cum autem sit, non necesse est esse alterum idem autem cum sit, et non sit,impossibile ex necessitate esse idem.Dico autem, cum sit a album, esse magnum ex necessitate, ecum non sit a aIbum,b esse magnum exnecessitate; quando enim cum hoc sit (ut a) album, illud necesse est (ut b) esse magnum, cum autem sit rnagnum,c non esse album, necesse est,si a sit album,c non esse aIbum.Et quando duobus existentibus, cum alterum sit, necesse est alterum esse, hoc autem cum non sit,necesse est a non esse,cum ergo non sit magnum, a non potest album esse, cum vero a non sit album, necesse est magnum esse,accidit ex necessitate cum magnum non sit; idem esse magnum: hoc autem im possibiIe, nam si non est magnum,a non eritalbum ex necessitate; si ergo cum non sita aIbum,b erit magnurn,accidit, si non est magnum,b esse magnurn,ut ertria.","english":"But it happens that when none of the things that are in the syllogisms is true, the conclusion is likewise true, yet not of necessity. The reason is that when two things are so related to each other that, when the one is, the other is of necessity, then if this one is not, neither will the other be; but when it is, there is no necessity for the other to be. And the same thing, when it is and is not, cannot of necessity be the same. I mean: when a is white, it is of necessity large; and when a is not white, b is of necessity large. For when, with this being (say a) white, that (say b) is of necessity large, and when it is large, c is not white, then if a is white, c is of necessity not white. And when, two things existing, with the one being, the other is of necessity, but this one when it is not, a is of necessity not, then when it is not large, a cannot be white; but when a is not white, it is of necessity large. It happens of necessity, when it is not large, that the same thing is large; but this is impossible. For if it is not large, a will of necessity not be white; if therefore, when a is not white, b will be large, it happens that, if it is not large, b is large, as has been said.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":127,"ref":"p127","source":"CAPUT V.\n\nDe circulari ostensione in prima figura.\n\nCirculo autem, et ex se invicem ostendere est per concIusionem,et e converso praedicationem atteram sumentem propositionem concludere rcliquam, quam sumpserat in altero syllogismo, ut si oportuit ostendere quoniam a inest omni c, ostendat autem per c,rursus si monstret quoniam a inest b, sumens a quidem inesse c,c autem,et a inerit b,prius autem econverso sumpsitb in esse c,aut si quoniam inest c,oportert ostendere si sumat a de c, quæ fuit concIusio,b autem dea esse,prius autem sumptum est e converso a de b. AIiLer vero non est ex se invicem ostendere,sive enim aliud medium surmetur, non circuIo,nil enim sumitur eorumdem,sivehorum quiddam,necesee est alterum soIum,nam si ambo, eadem erit conclusio, at oportet diversam esse. In iis igitur quae non convertuntur ex indemonstrata altera propositione fit syllogisrnus,non enim est demonstrare per hos terminos,quoniam medio inest tertiurn,aut primo medium.","english":"CHAPTER V.\n\nOn circular demonstration in the first figure.\n\nTo demonstrate circularly and from each other is to conclude, by means of the conclusion and conversely, the remaining proposition by taking the other predication, which had been assumed in the other syllogism; for example, if it was required to show that A belongs to every C, and one shows it through C, then again if one shows that A belongs to B, assuming that A belongs to C and C to B, A will also belong to B; but previously the converse was assumed, that B belongs to C. Or if it is required to show that A belongs to C, one assumes A of C, which was the conclusion, and B of A; but previously the converse was assumed, A of B. In another way it is not possible to demonstrate from each other; for whether another middle term is assumed, there is no circle, since nothing of the same terms is assumed; or if something of these is assumed, it is necessary that only one be assumed, for if both, the conclusion will be the same, but it ought to be different. In those things, therefore, which are not convertible, the syllogism comes about from one indemonstrable proposition; for it is not possible to demonstrate through these terms that the third belongs to the middle, or the middle to the first.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":128,"ref":"p128","source":"In iis autem quae convertuntur,erit omnia monstrare per se invicem, ut si a, et b, etcconvertuntur sibi invicem: ostendatur enim a per medium b, et rursum a per conclusionem,et per propositionem conversam; similiter autem et c, et per conclusionern, et per a propositionem conversam; oportet autem et b, et a propositionem demonstrare, nam his demonstratis asi sumus soIis.Si ergo sumatur omni inesse,etc omnia a, syllogismus erit ejus quod est ad a.Rursus si sumatur,' omni a inesse,et a omni necesse est inesse omni b. In utrisque ergo syltogismis a propositiosumpta estindemonstrata, am aliae probatæ erant: quare si hanc ostenderimus, omnes erunt approbatæ per se invicem; si ergo sumatur comni b,et omni a inesse, utraeque propositiones Jemonstralæ sumuntur. et necesse est inesse a. Manifestum est ergo quoniam in solis iis quae convertuntur,circulo et per se invicem contingit fieri demonstrationes, in aliis vero quemadmodum prius diximus. Accidit autem et in iis eodem quod monstratur uti ad demonstrationem, nam de 6, et de a monstratur sumpto de a dici, autem de aper hasostenditur propositiones; quare conclusione utimur ad de,nonstrationem.","english":"In those things, however, which are convertible, it will be possible to demonstrate all things through one another, as if a and b and c are converted with one another; for let a be demonstrated through the middle term b, and again a through the conclusion and through the converted proposition; and similarly also c, both through the conclusion and through the converted proposition of a. But it is necessary also to demonstrate b and the proposition of a, for when these have been demonstrated we are in possession of all of them. If, therefore, it is assumed that [b] belongs to every [c], and [c] to every a, the syllogism will be of that which is to a. Again, if it is assumed that [b] belongs to every a, and a necessarily belongs to every b. In both syllogisms, therefore, the proposition of a has been assumed undemonstrated, while the others had been proved; wherefore if we have demonstrated this one, all will have been approved through one another. If, therefore, it is assumed that [b] belongs to every c and to every a, both propositions are assumed as demonstrated, and it is necessary that a belongs. It is manifest, therefore, that only in those things which are convertible do demonstrations come about circularly and through one another, but in others in the way we said before. It happens, however, also in these that the same thing which is being demonstrated is used for the demonstration; for it is demonstrated of b and of a when it is assumed that [b] is said of a; but it is shown that [b] is said of a through these propositions; wherefore we use the conclusion for the demonstration.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":129,"ref":"p129","source":"In privativis autem syllogismis hoc modo monstratur ex se invicem: sit quidem omni ineGse,a autem nulli b, conclusio autem quoniam a nulli c,Si ergo rursum oporteat concludere quoniam a nulli b, quod prius sumptum erat,erit a quidem nulli c, autem omni b, sic enim e converso propositio. Si autem quoniam inesl c,oporteat concludere,non jam similiter convertendum a b, nam eadem propositio est nulli a,et a nulli inesse,eed sumendum,cui a nulli inest, huic omni inesse. Sit enim a nulli inesse, quod quidem fuit conclusio,cui autem a nulli b. si sumatur omni inesse,necesse est ergo omni e inesse: quare cum sint tria,unurnquodque conclusio est facta, et circulo demonstrare, hoc est concIusionern sumentem et e converso alleram propositionem,reliquam syllogizare. In particuiaribus autem syllogismis universalem quidem propositionem non est demonstrare per alias,particularern autem est; quoniam autem non est demonstrare universalem, manifestum, nam universale monstratur per universalia,conclusio autem non est universalis,oportet autem ostendere ex conclusione et altera propositione. Amplius, omnino non fit syllogismus conversa propositione,narn particulares fiunt utræque propositiones.","english":"In privative syllogisms, however, this is shown from one another in this way: let a belong to every c, but a to no b, and the conclusion be that a belongs to no c. If, then, it should again be concluded that a belongs to no b, which was previously assumed, there will be a belonging to no c, but c to every b; for thus the proposition is converted. But if it should be concluded that c belongs, then a to b must no longer be converted in the same way; for the same proposition is \"a belongs to no b\" and \"b belongs to no a,\" and one must assume that to which a belongs to no b, to this belongs to every b. For let a belong to no c, which indeed was the conclusion, and let a belong to no b. If it is assumed that c belongs to every b, it is necessary, therefore, that c belongs to every b; wherefore, since there are three terms, each one has been made a conclusion, and to demonstrate in a circle is this: taking the conclusion and converting the other proposition, to syllogize the remaining one. In particular syllogisms, however, it is not possible to demonstrate the universal proposition through the others, but the particular one it is possible; that the universal one cannot be demonstrated is clear, for the universal is shown through universals, but the conclusion is not universal, and one must show it from the conclusion and the other proposition. Moreover, a syllogism does not come about at all when the proposition is converted, for both propositions become particular.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":130,"ref":"p130","source":"Particulare autem est ostendaturenim a de aliquo per b, si ergo sumatur omni a, et conclusio maneat, alicui inerit, fit enim prima figura,et est a rnedium.Si autem fit privativus syHogismus,universalem quidem propositionem non est ostendere,propter boc quod prius dictum est, particularem(si simpliciter convertatur a quemadmodum etin universaltbus) non est, per assumptionem autem est,ut cui a alicui nun insit, alicui inesse; nam aliter se habentibus non fitsyllogismus,eo quod negativa est particularis propositio.\n\nCAPUT VI.\n\nDe eadem cyclica ostensione in secunda figura,\n\nIn secunda autem figura affirmativam quidem non est ostendere per hunc modum, privativam autem est; ergo praedicativa quidem non ostenditur, eo quod non sunt utræque propositiones affirmativae, nam conclusio privativa,prædicativa autem ex utrisque ostendebatur affirmativis. Privativa autem sic ostenditur: insit enim a omni b,c autem nulIi,conclusia quoniam nulli c,si ergosumaturbomniain- ] esse,et nulli c,necesse est nulli inesse,tlt enim secunda figura, medium 6. Si autem a privativa sumpta sit, altera vero praedicativa, prima erit iigura,narn quidem omni a,b autem nulli c,quare nulli a,ergo nec a b,medium c; ergo per conelusionem quidem et unam propositionem non fitsyIlogismus,assumpta autem altera erit.","english":"But the particular is shown thus: let a belong to some thing through b. If, then, a is taken as belonging to every [b], and the conclusion remains, it will belong to some; for the first figure comes about, and a is the middle term. But if a privative syllogism is made, the universal proposition indeed cannot be shown, on account of what was said before; the particular cannot be shown (if a is converted simply, just as also in universal propositions), but it can be shown by assumption, as that to which a does not belong to some, belongs to some; for with things otherwise disposed no syllogism comes about, because the particular proposition is negative.\n\nCHAPTER VI.\n\nOn the same circular demonstration in the second figure.\n\nIn the second figure, however, the affirmative cannot be shown in this way, but the privative can. Therefore the predicative is not shown, because both propositions are not affirmative; for the conclusion is privative, whereas the predicative was shown from both affirmatives. But the privative is shown thus: let a belong to every b, but c to no b, and the conclusion be that a belongs to no c. If, then, b is taken as belonging to every a and to no c, it is necessary that it belong to no [c]; for thus the second figure comes about, and b is the middle term. But if a is taken as privative and the other as predicative, there will be the first figure; for a belongs to every b, and b to no c, wherefore a to no c; therefore neither does a belong to b; the middle term is c. Therefore through the conclusion and one proposition no syllogism comes about, but when the other is assumed, it will.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":131,"ref":"p131","source":"Si autem non universalis sit syllogismus,quæ in toto quidem est propositio non ostenditur,propter eamdem causam quam quidem diximus et prius,quæ autem in parte, ostenditur quando universalis sit prædicativa.Insit einm a omni to, autem non omni, conclusio c; si ergo sumatur omni a, autem non omni,conclusio a alicui non inerit medium b. Si autem est universalis privativa, non ostenditur a propositio, conversa a b, accidit enim utrasque aut alteram propositionem fieri negativam: quare non eritsylIogismus;sed similiter ostendetur quemadmodum et universalibus, si sumatur, cui alicui non inest a alicui inespe.\n\nCAPUT VII.\n\nDe cyclica ratiocinatione in tertia MUl'a.\n\nIn tertia autem figura, quando utræque propositiones universaliter sumentur, non contingit ostendere per se invicem propositionem. Nam universalis quidem ostenditur per universalia, in hac autem conc:usio semper est particularis: quaremanifestum quonam omnino non contingit ostendere per hanc figuram universalem propositionem. Si autem haec quidem universalis sit, illa vero particularis, quandoque quidem erit, quandoque vero non inerit; quando ergo utraeque prædicativæ sumantur, et universalis sit ad minorem extremitatem, erit; quando vero ad alteram, non erit. Insit enim a omni c, autem alicui c, conclusio a b.","english":"But if the syllogism is not universal, the proposition that is in the whole is not shown, for the same reason that we have also stated before; but the proposition that is in part is shown when the universal proposition is affirmative. For let a belong to every t, but not to every u, and let the conclusion be c; if, then, a is taken as belonging to every [t], but not to every [u], the conclusion will be that a does not belong to some b. But if the universal proposition is privative, the proposition a is not shown by converting a b; for it happens that both propositions, or one of them, become negative; therefore there will not be a syllogism; but it will be shown in the same way as in the case of universal propositions, if it is taken that to which a does not belong to some, [a belongs] to some.\n\nCHAPTER VII.\n\nOn circular reasoning in the third figure.\n\nIn the third figure, when both propositions are taken universally, it is not possible to show one proposition through the other. For a universal proposition is shown through universals, but in this figure the conclusion is always particular; therefore it is clear that it is altogether impossible to show a universal proposition through this figure. But if one proposition is universal and the other particular, sometimes it will be possible and sometimes not; for when both are taken as affirmative and the universal is attached to the lesser extreme, it will be possible; but when it is attached to the other, it will not. For let a belong to every c, but to some c, and let the conclusion be a b.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":132,"ref":"p132","source":"Si ergo sumatur omni a inesse conversa universali, et a inesse b, quod erat conclusio, quidem ostensum est alicui inesse, autem alicui tJ, non est ostensum, quamvis necesse est si alicui b, et alicui inesse; sed non idem est hoc iili, et illud huic inesse, sed assumendum est, si hoc alicui illi, etalt-erum alicui huic,hoc autem sumptojam non sit ex conclusione et altera propositione syllogismus. Si autem quidem omni c, a autem alicui c, erit ostendere a c, quando sumatur quidem omni binesse, a autem alicui; nam sic omni binest,a autem alicui b, necesse est a alicui inesse, medium 6. Et cum fuerit haec prædicativa quidem, illa vero privativa,universalis autem prædicativa, ostendetur altera. Insit enimbomnic, aautem aIicuinoninsit, conclusio quoniam a alicui non inest. Si ergo assumatur omni inesse, inerat auteII1 et a non omni b, necesse est a alicui non inesse medium b. Cum autem privativa universalis sit, non ostenditur altera nisi sicut in prioribus, si sumatur cui hoc alicui non inest, alterum alicuHnesse, ut si a nulli c, autem alicui, conclusio quoniam a alicui non inest. Si ergo sumatur cui ft alicui non inest,eidem alicui inesse, necesse est alicui L inesse; aliter autem non est convertentem universalem propositionem ostendere alteram, nullo enim modo erit syllogismus.","english":"If, then, it is assumed that A belongs to every C by converting the universal proposition, and that A belongs to B, which was the conclusion, it has indeed been shown that A belongs to some C; but that it belongs to some B has not been shown, although it is necessary that if A belongs to some B, it also belongs to some C. But it is not the same thing for this to belong to that and for that to belong to this; rather, it must be assumed that if this belongs to some of that, the other also belongs to some of this. But once this is assumed, there is no longer a syllogism from the conclusion and the other proposition. But if B belongs to every C and A to some C, it will be possible to show that A belongs to C when it is assumed that B belongs to every C and A to some C; for in this way, if B belongs to every C and A to some B, it is necessary that A belong to some C, with B as the middle term. And when one of the propositions is affirmative and the other privative, and the universal one is affirmative, the other will be shown. For let B belong to every C and let A not belong to some C; the conclusion is that A does not belong to some C. If, then, it is assumed that B belongs to every C, and A belongs to some B, it is necessary that A not belong to some C, with B as the middle term. But when the universal proposition is privative, the other is not shown except as in the earlier cases, if it is assumed that what this does not belong to some of, the other belongs to some of, as if A belongs to no C and B to some C; the conclusion is that A does not belong to some C. If, then, it is assumed that what B does not belong to some of, A belongs to the same some of, it is necessary that A belong to some C; but otherwise, by converting the universal proposition, it is not possible to show the other, for in no way will there be a syllogism.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":133,"ref":"p133","source":"Manifestum igitur quoniam in prima quidem figura per se invicem est ostensio, et per primam,et per tertiam figuram fit: nam cum prædicativa quidem estconcIusio, perprimam,cum autem privativa, per postremam, sumitur enim cui hoc nulli, aHerum ornni,inesse. In media autem, cum universalis est quidem syllogismus et per ipsarn,et perprimam figuram, etper postremam; cum autem particularis, et per ipsam, et per postremam. In tertia vero per ipsam,;:omnes. Manifestum etiam quoniam in media et in tertia qui non per ipsas fiunt sylIogisrnus,aut non sunt secundum eam qure circulo est ostensionem, aut imperfecti sunt.\n\nCAPUT VIII.\n\nDe syllogismo conversiO.\n\nConvertere autem est transponentem conclusionem facere syllogismum, quoniam vel extremum medio non inerit, vel hoc postremo;necesse est enim conc 'usione conversa,et altera remanente propositione, interimi reliquam; nam si erit, et conclusio erit: ditfert autem opposite aut contrarie convertere conclusionem, non enim fit idem syllogismus utrolibet conversa; paIam autem bocerit persequentia.Dico autem opponi quidem omni inesse non omni, et alicui nulli,contrarie autem omni nuIli,et alicui non alicui inesse.Sit enim ostensum a de per me dium; si igitur sumatur a nulli inesse,omni autem b,nuIli inerit b,et si a quidem nulli e, autem omni c,a non omni b,et non omnino nulIi,non enim ostendebatur universale per tertiam figuram.","english":"It is clear, then, that in the first figure the proof proceeds through the propositions themselves, and it comes about both through the first and through the third figure; for when the conclusion is affirmative, it is through the first, but when it is privative, through the last—for one takes that which belongs to no one of this, and the other that it belongs to every one. In the middle figure, however, when the syllogism is universal, it comes about both through itself and through the first figure and through the last; but when it is particular, both through itself and through the last. In the third figure, however, all come about through itself. It is also clear that in the middle and in the third figure the syllogisms that are not produced through the figures themselves are either not according to that demonstration which is by circular proof, or are imperfect.\n\nCHAPTER VIII\n\nOn the conversion of the syllogism.\n\nTo convert is to make a syllogism by transposing the conclusion, showing that either the extreme does not belong to the middle, or this does not belong to the last; for with the conclusion converted and one of the premises remaining, the other must be destroyed; for if it remains, the conclusion will also remain. But it makes a difference whether one converts the conclusion oppositely or contrarily, for the same syllogism does not result whichever way it is converted; that this will be clear from what follows. I say that \"to belong to every\" is opposed to \"not to belong to every,\" and \"to belong to some\" to \"to belong to none\"; but contrarily, \"to belong to every\" to \"to belong to none,\" and \"to belong to some\" to \"not to belong to some.\" For let it have been shown that A belongs to no B through the middle; if, then, it is assumed that A belongs to no B, and that it belongs to every C, then B will belong to no C; and if A belongs to no C, but to every B, then A will not belong to every C, and not entirely to none; for the universal was not shown through the third figure.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":134,"ref":"p134","source":"Omnino autem eam quæ est ad majorem extremitatem propositionem non est detruere universaliter per conversionem,semper enim interimitur per tertiam figuram,necesse enim ad postremam extremitatem utrasque sumere propositiones.Et si privativus sit syllogismus similiter: ostendatur enim a nulli inesse per b,ergo si sumatur a omni inesse, nulli autem b,nuIli inerit b. Et si a et omni c,a alicui b,sed nulli inerat.Si autem opposite convertatur conclusio, et alii syllogismi oppositi, et non universales erunt,fit enim altera propositio particularis, quare conclusio erit particularis. Sit enim praedicativus syllogismus, et convertatur sic, ergo si a non omni c,b autem cmni b,non omni c. Et si a quidem non omni c,b autem omni a,non omni b. Similiter autem et si privativus sitsyllogismus,nam si a alicui inest,b autem nulIi,b alicui non inerit, et non simpliciter nulIi, et si a quidem alicui c, autem omni,quemadmodurn in principio sumptum est,a alicui inerit.ln particularibus autem syJlogismis quando opposite convert itur concJusio,interimuntur utræque propositiones,quando vero contrariæ,neutra; non enim jam accidit quemadmodum in universalibus interimere deficiente conclusione secundum conversionem,sed nec omnino interimere. Ostendatur enim a de aliquo per; ergo si suma.","english":"But in general the proposition that relates to the major extreme cannot be destroyed universally by conversion; for it is always refuted through the third figure, since it is necessary to take both propositions in relation to the last extreme. And similarly if the syllogism is privative; for let it be shown that A belongs to no B; therefore if it is assumed that A belongs to every B, and to no B, then B will belong to no B. And if A belongs to every C, and A to some B, but belonged to no B. But if the conclusion is converted to the opposite, the other opposite syllogisms also result, and they will not be universal; for one of the propositions becomes particular, and therefore the conclusion will be particular. For let the syllogism be affirmative, and let it be converted thus: therefore if A does not belong to every C, but B belongs to every C, then A does not belong to every C. And if A does not belong to every C, but B belongs to every A, then A does not belong to every B. Similarly also if the syllogism is privative; for if A belongs to some B, but to no B, then B will not belong to some B, and not simply to none. And if A belongs to some C, but to every B, as was assumed at the beginning, A will belong to some B. But in particular syllogisms, when the conclusion is converted to the opposite, both propositions are destroyed; but when to the contrary, neither; for it no longer happens, as in universal syllogisms, to destroy by conversion when the conclusion is lacking, but not to destroy at all. For let it be shown that A belongs to some B; therefore if it is assumed...","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":135,"ref":"p135","source":"tur a nulli inesse,b autem alicui c,a alicui non inerit,et si a nulli c,b autem omni, nulli inerit b; quareinterimentur utræque.Si autem contrarie convertantur,neutra; nam si a alicui non inest,b autem omni,b alicui non inerit, sed nondum interimitur quod ex principio, contingit enim alicui inesse,et alicui non inesse: universali autem sublato a b,omnino non fit syllogismus. Si enim a quidem alicui non inest,b autem alicui inest, neutra propositionum universalis est. Similiter autem et si privativus sit syllogismus,si enim sumatur a omni inesse,interimuntur utræque; si autem alicui,neutra; demonstratio autem eadem.\n\nCAPUT IX.\n\nDe syllogismo conversivo ill secunda figura,\n\nIn secunda autem figura,earn quidem quae est ad majorem extremitatem propositionem, non est interim ere contrarie,quolibet modo conversione facta, semper erit conclusio in tertia figura, universalis autem non fuit in hac syllogismus, alteram autem in hac interimemus,similiter conversione.Dico autem similiter: si contrarie quidem convertitur, contrarie; si opposite,opposile. Insit enim a omni b, autem nulli,conclusio c.Si erga sumatur omni inesse et a maneat,a omni inerit,fitenim prima figura.","english":"But if it is converted with respect to neither, and B belongs to some C, then A will not belong to some C; and if A belongs to no C, but B to all, then B will belong to none; hence both propositions will be destroyed. But if they are converted contrarily, neither will be destroyed; for if A does not belong to some, but B to all, then B will not belong to some, but the original conclusion is not yet destroyed, for it is possible for it to belong to some and not to some; but when the universal proposition is removed, no syllogism at all comes about. For if A does not belong to some and B belongs to some, neither proposition is universal. Similarly also if the syllogism is privative: for if A is taken to belong to all, both propositions are destroyed; but if to some, neither; and the demonstration is the same.\n\nCHAPTER IX.\n\nOn the convertible syllogism in the second figure.\n\nIn the second figure, the proposition that relates to the major extreme cannot be destroyed by a contrary conversion in any way, since the conclusion will always be in the third figure, but there was no universal syllogism in this figure; but we shall destroy the other proposition in this figure, similarly by conversion. I mean similarly: if it is converted contrarily, contrarily; if oppositely, oppositely. For let A belong to all B, or to none, and let the conclusion be C. If then it is taken to belong to all and A remains, A will belong to all, for the first figure comes about.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":136,"ref":"p136","source":"Si autem omni c, a autem nulli c, a non omni b, figura postrema.Si autem opposite convertatur c,a quidem similiter ostendetur,a autem opposite: nam si alicui c,a autem nulli c,a alicui non inerit; rursum si alicui c,a autem omni b,a alicui c, quare oppositus fit syllogismus. Similiter autem ostendetur et si e converso se habeant propositiones.Si autem particularis est syllogismus, contrarie quidem conversa conclusione neutrapropositionurn interimitur,quemadmodum nec in prima flgura,opposite autem, utræque. Ponatur enim a quidem nulli inesse, autem alicui, conclusio c. Si igitur ponatur alicui inesse, et a maneat conclusio erit quoniam a alicui non inesl,sed non interimitur quod ex principio, contingit enim alicui inesse et non inesse.Rursum si alicui c,et a alicui c,non erit syllogismus, neutrum enim universale eorum quae sumpta sunt,quare non interimitur a b.Si autem opposite convertatur,interimuntur utræque, non si omni c,a autem nulli b,nulli c,a erit autem alicui. Rursum si omni c,aautemalicuic,alicui b,a*.Eadem autem demonstratio et si universalis sit prædictiva.","english":"But if A belongs to all C and to no C, then A does not belong to all B: the last figure. But if the opposite is converted, C, A will indeed be shown similarly, but the opposite: for if A belongs to some C and to no C, then A will not belong to some; again, if A belongs to some C and to all B, then A belongs to some C, so the syllogism becomes opposite. It will be shown similarly also if the propositions are related conversely. But if the syllogism is particular, when the conclusion is converted contrarily, neither proposition is destroyed, just as neither was in the first figure; but when converted oppositely, both are destroyed. For let it be posited that A belongs to none, but to some, and the conclusion is C. If, then, it is posited that it belongs to some, and A remains, the conclusion will be that A does not belong to some, but the original assumption is not destroyed; for it is possible for it to belong to some and not to belong. Again, if A belongs to some C and to some C, there will be no syllogism; for neither of the things assumed is universal, so A B is not destroyed. But if the opposite is converted, both are destroyed: if A belongs to all C and to no B, it will belong to no C, but it will belong to some. Again, if A belongs to all C and to some C, then A belongs to some B. The same demonstration holds also if the predicative proposition is universal.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":137,"ref":"p137","source":"CAPUT X.\n\nDe syllogismo conversivo in tertia figura,\n\nIn tertia vero figura quandocontrariequidem convertitur conclusio,neutra propositionem interimitur secundum nullum syllogismorum; quando autem op. posite,utræque in omnibus.Si enim ostensum a alicui inesse,medium autem sumptum c, et sint llniversales propositi ones, si ergo sumatur a alicuib non inesse,b autem omni c,non fit syllogismus ejus quod est a de c.Neque si a alicui non inest,c autem omni,non erit ejus quod est syIlogismus.SimiIiter autem ostendetur et si non universales sint ropositiones,aut enim utrasque necesse est particulares esse per conversionem,aut universalem ad minorem extremitatem fieri, sic autem non fiet syIIogismus,nec in prima figura,nec in media.Si autem opposite convertantur propositiones, interimuntur utræque, nam si a nulli b, autem omni c, a nulli c.Rursum si a quidem nulli,c autem omni,b nulli c.Et si altera non sit universalis, similiter; si enim a nulli b,b autem alicui c,a alicui non inerit.Si autem a quidem nulli, autam omni, nulli c, b. Similiter etsi privativus sit syllogismus; ostendatur enim ctalicui non inesse;si autem praedicativa quidem c, cac autem negativa, sic enim fiebat syIlogismus. Quando igiturcontrarium sumitur conclusioni non eritsyllogismus, nam si a alicui b, autem omni c, non fit syllogismus ejus quod est a et c.","english":"CHAPTER X.\n\nOn the convertible syllogism in the third figure.\n\nIn the third figure, when the conclusion is converted into its contrary, neither premise is destroyed by any of the syllogisms; but when it is converted into its contradictory, both premises are destroyed in all cases. For if A has been shown to belong to some B, and the middle term taken is C, and the premises are universal, then if it is assumed that A does not belong to some B, but B belongs to all C, no syllogism arises concerning A and C. Nor, if A does not belong to some C, but C belongs to all, will there be a syllogism concerning them. The same will be shown even if the premises are not universal; for either both must be particular by conversion, or the universal must be made the minor extreme, and in this way no syllogism will arise, neither in the first figure nor in the middle. But if the premises are converted into their opposites, both are destroyed: for if A belongs to no B, but B to all C, then A belongs to no C. Again, if A belongs to no C, but C to all, then B belongs to no C. And if one premise is not universal, it is likewise; for if A belongs to no B, but B to some C, then A will not belong to some C. But if A belongs to no B, but B to all C, then A belongs to no C. So too if the syllogism is privative; for it is shown that C does not belong to some. But if the premise concerning C is affirmative and that concerning A negative, for thus the syllogism came about. When, therefore, the contrary of the conclusion is assumed, there will be no syllogism; for if A belongs to some B, but B to all C, no syllogism arises concerning A and C.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":138,"ref":"p138","source":"Neque si a alicui b, nulli autem c, non fuit ejus quod nst a etcsyllogismus, quare non interimuntur propositiones. Quando vero oppositum, interimuntur; nam si a omni, 6, etomni c, a omni c, sed nulli inerat. Rursum si a cmni b, nulli autem c, nulli c, sed omni inerat. Similiter aulem monstratur, et si non universales sint propositiones: sit enim a universalis et privativa, altera autem parti;,ulariset in prædicutiva ergo si a quidem omni b, autem alicui c, a alicui accidit, sed nulli inerat. Rursum si a omni nulli autem et nulli c. Si autem a alicui b, et alicui c, non fit syllogismus. Neque si a alicuib. et nulli c, nec sic. Quare illo quidem modo interimuntur, sic autem non interimunturpropositiones. Manifestum est ergo ex iis quae dicta sunt quomodo conversa eonclusione in unaquaque figura fit syllogismus, et quando contrarie propositioni, et quando opposite: et quoniam in prima quidem figura per mediam et postremam fiunt syllogismi, etquæ quidem ad minorem extremitatem semper per mediam interimitur, quae veru ad majorem per postremam; in secunda autem, per primam et postremam, quae quidem ad minorem extremitatem semper per prirnam figuram quæ vero ad majorem, per postremam; in tertia vero, per primam et per mediam, et quæ quidem ad majorem per primam semper, quæ vero ad minorem per mediam semper.","english":"Nor, if a belongs to some b but to no c, was there a syllogism of the proposition that a belongs to no c; therefore the premises are not destroyed. But when the opposite is assumed, they are destroyed; for if a belongs to all b and to all c, then a belongs to all c, but it belonged to none. Again, if a belongs to all b but to no c, then it belongs to no c, but it belonged to all. The same is shown also if the premises are not universal: for let a be universal and privative, and the other particular and predicative; then if a belongs to all b but to some c, a will belong to some c, but it belonged to none. Again, if a belongs to all b and to no c, then it belongs to no c. But if a belongs to some b and to some c, no syllogism results. Nor if a belongs to some b and to no c, neither thus. Therefore in that way the premises are destroyed, but in this way they are not destroyed. It is clear, then, from what has been said, how, when the conclusion is converted, a syllogism is produced in each figure, and when it is produced against the contrary proposition and when against the contradictory; and that in the first figure syllogisms are produced through the middle and the last figure, and those directed at the minor extreme are always destroyed through the middle figure, while those directed at the major extreme are destroyed through the last; in the second figure, through the first and the last, those directed at the minor extreme always through the first figure, but those at the major through the last; in the third figure, through the first and the middle, those directed at the major extreme always through the first, but those at the minor always through the middle.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":139,"ref":"p139","source":"Quid ergo est convertere, et quomodo in unaquaque figura, et quis fit syllogismus manifestum.\n\nCAPUT XI.\n\nDe syllogismo per impossibile.\n\nPerimpossibile autem syllogismus ostendil ur qui. dem, quando contradictio ponitur conclusionis, et assumitur altera propositio. Fit autem in omnibus figuris, simile enim est conversioni. Verumtamen differt in tantum quoniam convertitur quidem facto syllogismo,et sumptis utriusque propositionibus. Deducitur autem ad impossibile non confesso opposito prius, sed manifesto quoniam est verum. Termini vero similiter se habent in utriusque, eteademsumptio utrorumque, ut si a inest omni b, medium autem c, si supponitur a non omni vel nulli inesse, vero, omni, quod fuit verum, necese est aut nulli aut nonomniinesse, hoc autem impossibile, quare falsum estquodsuppositurnest. Verumergo oppositum; si. militer autem in aliis figuris, quaecunque enim conversionem suscipiunt, et per impossibile syIlogismum. Ergo aliaquidempropositaomnia ostenduntur per impossibilein omnibus Hguris, universale autem praedicativum in media et in tertia monstratur, in prima autem non monstratur: supponatur enim a non omni baut nulliinesse,et assumatur alia propositio, utrolibetmodo, sive a omni inest c, sive omni (SIC enim erat prima figura); si ergo supponatur a non omni inesse, non fiet syllogismus quomodolibet sumpta propositiones.","english":"What conversion is, then, and how it works in each figure, and what syllogism results, is clear.\n\nCHAPTER XI.\n\nOn syllogism through the impossible.\n\nA syllogism through the impossible proves its point when the contradictory of the conclusion is posited and the other premise is assumed. It occurs in all the figures, for it is similar to conversion. Yet it differs to this extent, that conversion is effected after the syllogism has been made and both premises have been taken; but the reduction to the impossible is not made when the opposite has first been conceded, but when it is evident that it is true. The terms stand in the same relation in both, and the assumption of both is the same; for example, if a belongs to every b, and c is the middle term, if it is supposed that a belongs not to every b or to no b—which was true, namely that it belongs to every b—it is necessary that a belong to no c or not to every c; but this is impossible, wherefore what was supposed is false. The opposite, then, is true; and similarly in the other figures, for whatever admit of conversion also admit of syllogism through the impossible. Therefore all the other propositions are proved through the impossible in all the figures, but the universal affirmative is proved in the middle and in the third figure, while in the first it is not proved; for let it be supposed that a belongs not to every b or to no b, and let the other premise be assumed in either way, whether that a belongs to every c or to no c (for such was the first figure); if, then, it is supposed that a belongs not to every b, there will be no syllogism, however the premises are taken.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":140,"ref":"p140","source":"Si autem nulli bd, quidem assumatur, syllogismus quidem erit falsi, non ostenditur autem propositum; nam si a nulli b, autem omni d, a nulli d, buc autem sit impossibile, falsum igitur est nulli inesse a, sed non si nulli falsum, omni verum. Si autem ca assumatur, non fit syltogismus, nec quando supponiturnon omni inesse n; quare manifestum quoniam omni inesse non ostendttu!\" in prima figura per impossibiIe.AIicui autem, et nulli, et nun omni osienditur. Supponatur enim a nulli inesse, autem sumptum si omni aut alicui ergo necesse est a nulli aut non omni inesse, hoc autem impossibile. Sit enim verum et manifestum quoniam omni inest a, quaresi hoc falsum, necesse est a alicui inesse. Si autem ad a sumatur altera propositio, non erit syllogismus, neque quando sub contrarium conclusioni supponitur ut alicui non ines se; manifestum ergo quoniam oppositum sumendum est. Rursum supponatur a alicui inesse, sumptum autem eit omni a, necesse est igitur alicui inesse, boc autem sit impossibile, quare falsum quidem suppositum est;si autem sic, verum est nulli inesse Similiter autem et si privativa sumpta sit ca.Si autem ad sumptasit propositio,non erit syllogismus.","english":"But if it is assumed that A belongs to no B, and to all D, then there will indeed be a syllogism of a falsehood, but the proposed conclusion is not proved; for if A belongs to no B and to all D, then A belongs to no D. But let it be impossible that B belongs to no D; therefore it is false that A belongs to no B. Yet it is not the case that if this is false, then it is true that it belongs to all; but if the assumption concerning C is made, no syllogism results, nor when it is supposed that it does not belong to every N. Hence it is clear that belonging to every one is not proved in the first figure through the impossible. But belonging to some and to none and not to every one is proved. For let it be supposed that A belongs to no B, and let the other premise be assumed as belonging to every one or to some one; then it is necessary that A belong to no one or not to every one, but this is impossible. For let it be true and evident that A belongs to every one; therefore, if this is false, it is necessary that A belong to some one. But if the other premise is taken in relation to A, there will be no syllogism, nor when the contrary of the conclusion is supposed, namely that it belongs to some one not. It is clear, therefore, that the opposite must be assumed. Again, let it be supposed that A belongs to some one, and let the premise assumed be that it belongs to every one; then it is necessary that it belong to some one, but let this be impossible; therefore the supposition is indeed false; but if so, it is true that it belongs to no one. Similarly also if the privative premise is assumed. But if the premise is taken in relation to the assumption, there will be no syllogism.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":141,"ref":"p141","source":"Si autem contrarium supponatur, syIlogismus eritet impossibile, non tamen ostenditur quod est propositum: supponatur enim o omni 6, et sumptum sit omni a, ergo necesse estc omDi inesse: hoc autem impossibile, quare falsum est omni inesse a, sed nondum erit necessarium, si non omni, nuUnnesse. Similiter autem et si a sumaturaltera proposito: nam syllogismus quidem eritet irnpossibile,non interimitur autem hypothesis, quare oppositum supponendurn. Ad ostendendum autem non omni binesse a; supponendum omni inesse, nam si a omni b, etc omni a, omni inerit: si ergo hoc impossibile, falsum quod suppositurn est;; similiter autem etsi ad sumpta sit altera propositio. Et si privativa sit a, similiter, nam et sic fit syllogismus. Si autem ad sumpta sit privativa, nihil ostenrlitur, Si autem non omni, sed alicui inesse supponatur, non ostenditur quoniam non omni, sed quoniam nulli: si enim a alicui b, autem omni a, alicui inerit c; si ergo hoc impossibile, falsum est alicui inesse a, quare verum nulIi; hoc autem ostenso, interirniturverurn, nam a alicui quidem inerat,alicui vero non inerat, Amplius autem non tam propter hypothesin accidit impossibile, falsaenim erit, siquidem ex veris non est falsum syllogizare: nunc autemest vera,inestenim a alicui b, quare non supponendum alicui inesse, sed omni.","english":"But if the contrary is supposed, there will be a syllogism of an impossibility, yet what was proposed is not proved. For let it be supposed that A belongs to all B, and let it be assumed that A belongs to all C; then it is necessary that B belong to all C. But this is impossible; therefore it is false that A belongs to all B. But it will not yet be necessary that, if A does not belong to all B, it belongs to none. Similarly also if the other proposition is assumed. For there will indeed be a syllogism of an impossibility, but the hypothesis is not refuted; therefore the opposite must be supposed. But to show that A does not belong to all B, one must suppose that it belongs to all B; for if A belongs to all B and to all C, then B will belong to all C. If therefore this is impossible, what was supposed is false. Similarly also if the other proposition is assumed. And if A is privative, similarly; for in this way too a syllogism is produced. But if the assumed proposition is privative, nothing is shown. But if it is supposed that A does not belong to all B but to some, it is not shown that it does not belong to all, but that it belongs to none. For if A belongs to some B, and to all C, then B will belong to some C. If therefore this is impossible, it is false that A belongs to some B; therefore it is true that it belongs to none. But when this has been shown, the truth is refuted; for A belonged to some and did not belong to some. Moreover, the impossibility does not arise so much on account of the hypothesis; for it will be false, since it is not possible to syllogize a falsehood from true premises. But now it is true; for A belongs to some B. Therefore one must not suppose that it belongs to some, but to all.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":142,"ref":"p142","source":"Similiter autem et si alicui non inest a, ostenderemus: si enim idem est alicui non in esse, et non omni inesse, eadem in utrisque demonstratio. Manifestum ergo quoniam non contrarium, sed oppositum supponendum in omnibus syllogismis, sic enim necessarium erit et axioma probabile; nam si de omni vel affirmatio vel negatio, ostenso quoniam non negatio, necesse est affirmationem veram esse; rursum si non ponant veram esse affirmationarn, constat veram esse negationem; contrariam vero neutro modo contingit ratum facere. Neque enim Į necessarium, si nulli falsum, omni verum, neque probabile ut sit alterum falsum, quoniam alterum varum. Manifestum ergo quoniam in prima figura alia quidem proposita omnia ostenduntur per i1.1possibile, universale autem affirmativum non ostenditur.\n\nCAPUT XII.\n\nDe syllogismo per impossibile in secunda figura,","english":"Similarly, also if we show that A does not belong to some one, since to belong to some one not and not to belong to every one are the same, the same demonstration will apply in both cases. It is clear, therefore, that in all syllogisms one must suppose not the contrary but the opposite; for thus it will be both necessary and a probable axiom. For if of every thing there is either affirmation or negation, then when it has been shown that the negation does not hold, the affirmation must be true; again, if they do not grant that the affirmation is true, it is evident that the negation is true. But it is in no way possible to establish the contrary. For it is not necessary that, if it is false of none, it is true of all; nor is it probable that one is false because the other is true. It is clear, therefore, that in the first figure all other propositions are proved through the impossible, but the universal affirmative is not proved.\n\nCHAPTER XII.\n\nOn the syllogism through the impossible in the second figure,","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":143,"ref":"p143","source":"In media autem figura et postrema et hoc ostenditur. Ponaturenim a non oami inesse, sumptum sit autem omni inesse a; ergo si quidem non omni inest a, autem omni, non omni inest c, hoc autem impossibile. Sit enim manifestum quoniam omnib inest c, quare falsum quod suppositum est, verum est ergo omni inesse. Si autem contrarium supponatur, syllogismus quidem erit ad impossibile, non tamen ostenditur quod propositum est. Si enim a nulli b, omni autem c, nulli 6, c, hoc autem impossibile, quare falsum est, nulli inesse, sed non si hoc falsum, verum omni. Quando autem alicui inest a, supponatur a nulli inesse, autem omni insit; necesse est ergoc nulli inesse, quare si hoc impossibile, necesse est a alicui inesse. Si autem supponatur alicui non esse, eadem erunt quae in prima figura, Rursum supponatur a alicui inesse, autem nulliinsit necesse est igiturc alicui non inesse v sed omniinerat, quare falsum quod suppositum est, nulli ergo inerat a. Quando autem non omni inest a, supponatur omni inesse: autem nulli, necesse est ergo nulli inesse, hoc autem impossibile, quare verum est non omni inesse. Manifestum ergo quoniam omnes syllogismi fiunt per mediam figuram.","english":"But in the middle and last figure this also is shown. For let it be supposed that A does not belong to every B, and let it be assumed that A belongs to every C; therefore, if A does not belong to every B, but belongs to every C, then C does not belong to every B; but this is impossible. For let it be manifest that C belongs to every B; therefore the supposition was false, and so it is true that A belongs to every B. But if the contrary is supposed, there will indeed be a syllogism to an impossibility, yet what was proposed is not shown. For if A belongs to no B, but to every C, then C belongs to no B; but this is impossible; therefore it is false that A belongs to no B. But it does not follow that, if this is false, it is true that A belongs to every B. But when A belongs to some B, let it be supposed that A belongs to no B, and let it be assumed that A belongs to every C; then it is necessary that C belongs to no B; therefore, if this is impossible, it is necessary that A belongs to some B. But if it is supposed that A does not belong to some B, the same results will follow as in the first figure. Again, let it be supposed that A belongs to some B, and let it be assumed that A belongs to no C; it is necessary, therefore, that C does not belong to some B; but it belonged to every B; therefore the supposition was false; therefore A belonged to no B. But when A does not belong to every B, let it be supposed that A belongs to every B, and let it be assumed that A belongs to no C; it is necessary, therefore, that C belongs to no B; but this is impossible; therefore it is true that A does not belong to every B. It is manifest, therefore, that all syllogisms are produced through the middle figure.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":144,"ref":"p144","source":"CAPUT XIiI.\n\nDe ostensione per impossibile in tertia figura,\n\nSimiliter autem et per ultimam. Ponatur enim a alicui non inesse, autem omni b, ergo a alicui non iaerit; si ergo boc impossibile, falsum aliLmi non nesse, quare verum est omni. Si vero supponatur nulli inesse, syllogismus quidern edt, etimpossibiIe, non ostendit autem quod propositum est; si enim contrarium supponatur, eadem eruntquæ in prioribus. Sed ad ostendendum alicui inesse, eadem sumenda est hypothesis, nam si a nulli b, autem alicui b, a non omni c: si ergo hoc falsum, verum esta alicui inesse. Quando autem nulli inest a, supponatur alicui inesse, sumptum sit autem et omni inesse ergo, necesse est a alicui inesse; sed nulli inerat, quare falsum est alicui inesse a. Si autem supponatur omni inesse a, non ostenditur propoaitum: sed ad ostenden dum non omni inesse, eadem sumenda hypothesis, nam si a omni 5, et alicui b, a inest alicui; hoc autem non fuit, quare faI. sum est omni in esse, si autem sic, verum non omni. Si autem supponatur alicui inesse, eadem erunt quæ et in iis quæ prius dicta sunt. Manifestum ergo quoniam in omnibus per impossibile syllogismis oppositum supponendum. Palam,autern et quoniam in media figura ostenditur quodammodo affirmativurn, et in postrema universale.","english":"CHAPTER XIII.\n\nOn proof through impossibility in the third figure.\n\nLikewise also through the last figure. For let it be supposed that A does not belong to some [B], but [that A belongs] to every B; therefore A will not belong to some [B]. If, then, this is impossible, it is false that it does not belong to some; hence it is true that it belongs to every. But if it is supposed that it belongs to none, there is indeed a syllogism and an impossibility, but it does not show what was proposed; for if the contrary is supposed, the same things will result as in the earlier cases. But to show that it belongs to some, the same hypothesis must be assumed; for if A belongs to no B, but [A belongs] to some B, [then] A does not belong to every C. If, then, this is false, it is true that it belongs to some. But when A belongs to none, let it be supposed that it belongs to some; and let it also have been assumed that it belongs to every; therefore it is necessary that A belong to some; but it belonged to none, so it is false that A belongs to some. But if it is supposed that A belongs to every, what was proposed is not shown; but to show that it does not belong to every, the same hypothesis must be assumed; for if A [belongs] to every [B], and [A belongs] to some B, A belongs to some [C]; but this was not so, so it is false that it belongs to every; but if so, it is true that it does not belong to every. But if it is supposed that it belongs to some, the same things will result as in those which were said before. It is clear, therefore, that in all syllogisms through impossibility the opposite must be supposed. It is evident, moreover, also that in the middle figure the affirmative is in a certain way shown, and in the last figure the universal.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":145,"ref":"p145","source":"CAPUT XIV.\n\nQuo justa, et quæ ad impossibile ducit demonstratio, differant.\n\nDiffert autem quae ad impossibile demonstratio ab ea quae est oSlensiva,eo quod ponat quod vult intenmere, deducens ad confessum falsum, ostensiva autem incipit aconfessis positionibus veris. Sumunt ergo utræque duas propositiones confessas,sed haec quidem ex quibus est syllogismu5, illa vero unam quidem baru m, alteram vero contradictionem concIusionis. Et hinc quidem non necesse est notam esse conclusionem,neque prius op inari quoniam est, aut non est; illinc vero necesse est, quoniam non est. Differt autem nihil affirmativam, vel negativam esse concIusionem. sed similiter se habet in utrisque. Omnis enim quæ ostensive concluditur, et per impossibile monstrabitur, et quae per impossibile ostensive, et per eosdem terminos, non autem in eisdem figuris. Nam quando per impossibile syllogismus fit in prima figura, quod verum est in media erit, aut in postrerna, privativum quidem in media, prædicativum autem in postrema. Quando autem syIlogismus in media fit, quod verum est erit in prima figurain omnibus propositionibus, quando autem in postrerna syllogism us, quod verum est erit in prima et in media, affirmativa quidem in prima, privativa autem in media.","english":"CHAPTER XIV.\n\nHow the direct demonstration and the one leading to impossibility differ.\n\nThe demonstration leading to impossibility differs from the ostensive one in that it posits what it wishes to establish, deducing to an admitted falsehood, whereas the ostensive begins from admitted true positions. Both, then, take two admitted propositions, but the latter takes those from which the syllogism is formed, while the former takes one of these and the other the contradictory of the conclusion. And in the latter case it is not necessary that the conclusion be known beforehand, nor that it be previously opined that it is or is not; but in the former it is necessary, since it is not. It makes no difference whether the conclusion is affirmative or negative, but matters stand alike in both. For every conclusion reached ostensively will also be shown through impossibility, and every one shown through impossibility ostensively, and by the same terms, though not in the same figures. For when the syllogism through impossibility is formed in the first figure, what is true will be in the middle or in the last figure—privative in the middle, but predicative in the last. But when the syllogism is formed in the middle figure, what is true will be in the first figure in all the propositions; but when the syllogism is in the last figure, what is true will be in the first and in the middle—affirmative in the first, but privative in the middle.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":146,"ref":"p146","source":"Sit enim ostensum a nulli aut non omni per primam figuram, ergo hypothesis quidem erat alicui inesse a, autem sumebatur a quidem omni inesse, autem nulli sic enim fiebat syUog!smus ad impossibile. Hoc autem media figura, si a quidemomni,b!lutem nulli, inest, etmanifestumex his quoniam nulli inest a. Similiter autem et si non omni ostensum sit inesse, nam bypothesis quidem est omni a messe, autam sumebatur a quidem omni, autem non omni, et si privativa sit sumpta a, similiteretenimsic fitin media figura. Rursum sit ostensum alicui inesse a, ergo hypothesis quidem est nulli inesse, autem sumebatur omni in esse, et a vel omni vel alicui c, sic enim erit impossibiIc. Hoc autem postrema figura, si a et omni c, et manifestum ex his quia necesse est a alicui binesse, similiter autemet si alicui csumatur inesse vel a. Rursum in media figura ostensum sit a omni inesse, ergo hypothesis quidem fuit, non omni inesse a, sumptum est autem a omni C, et omni b, sic enim erit impossibile; boc autem prima figura, si a omni c, et omni b. Similiter autem et si ostensum sit alicui inesse, nam hapotbesis quidem fuit, nulli inesse a, sumptum est autem a omni c, et alicui b.","english":"For let it have been shown by the first figure that A belongs to none or not to all; therefore the hypothesis was that A belongs to some, but it was assumed that A belongs to all, and [that it belongs] to none—for thus the syllogism to the impossible came about. But this [happens] in the middle figure, if A belongs to all and B to none, and it is evident from these that A belongs to none. Similarly also if it has been shown that it does not belong to all; for the hypothesis was that A belongs to all, but it was assumed that A belongs to all and [that it belongs] not to all; and if the privative premise is assumed, it is similarly so in the middle figure. Again, let it have been shown that A belongs to some; therefore the hypothesis was that it belongs to none, but it was assumed that it belongs to all, and A [belongs] either to all or to some C—for thus it will be impossible. But this [happens] in the last figure, if A [belongs] to all C, and it is evident from these that A must belong to some B; similarly also if it is assumed that it belongs to some C or to A. Again, in the middle figure let it have been shown that A belongs to all; therefore the hypothesis was that A does not belong to all, but it was assumed that A belongs to all C and to all B—for thus it will be impossible; but this [happens] in the first figure, if A [belongs] to all C and to all B. Similarly also if it has been shown that it belongs to some; for the hypothesis was that A belongs to none, but it was assumed that A belongs to all C and to some B.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":147,"ref":"p147","source":"Si autem privativus fit syllogismus, hypothesis quidem a alicui inesse, sumptum est autem a nulli c, et omni b, quare fit prima figura, Et si non universalis sit syllogismus, sed a alicui ostensum sit nrn inesse, similiter:nam hypothesis quidem omnib inesse a, sumptum estautem a nulli c, et alicui b, sic enim prima figura, Rursum in tertia figura ostensum sit a inesse omni b, ergo hypotbesis quidem fuitnon omni inesse a, sumptum est autem omni,b, et a omni c, sic enim erit impossibila,boc autem prima figura. Similiter autem et si in aliquo sit demonstratio,non hypothesis qui. dem erit nulli,b inesse a,sumptumest autem alicui et a omni c,Si autem privativus sit syllogismus, hypothesis quidem a alicui inesse, sumptum est autem ftquidem nulli, autem omni, boc autem media figura. Similiter autem etsi non universalis sit demonstratio, nam hypothesisquidem eritomni inesse a, sumptum est autem a quidem nulli, autem alicui, hoc autem media figura. Manif'estum ergo quoniam per eosdem terminos et ostensive est demonstrare unumquodque propositum, et per impossibile. Similiter autem erit, et cum sint ostensivi s;yllogismi,ad impossibile deducere in terminis sumptis, quando opposita propositio conclusioni sumpta fuerit, nam fiunt iidem syllogismi.","english":"But if the syllogism becomes privative, the hypothesis was that A belongs to some, but it was assumed that A belongs to no C and to all B; for thus the first figure is produced. And if the syllogism is not universal, but it has been shown that A belongs to some, similarly: for the hypothesis was that A belongs to all B, but it was assumed that A belongs to no C and to some B; for thus the first figure. Again, in the third figure let it have been shown that A belongs to all B; therefore the hypothesis was that A does not belong to all, but it was assumed that [B belongs] to all and A to all C; for thus it will be impossible, and this is the first figure. Similarly, moreover, if the demonstration is that it belongs to some, the hypothesis will be that A belongs to none B, but it was assumed that [B belongs] to some and A to all C. But if the syllogism is privative, the hypothesis was that A belongs to some, but it was assumed that [B] belongs to none, or [A] to all; and this is the middle figure. Similarly, moreover, even if the demonstration is not universal: for the hypothesis will be that A belongs to all, but it was assumed that A belongs to none, or [B] to some; and this is the middle figure. It is evident, therefore, that through the same terms it is possible to demonstrate each proposed conclusion both ostensively and through impossibility. Similarly, moreover, it will also be the case, when the syllogisms are ostensive, to reduce to impossibility with the terms assumed, when the proposition opposite to the conclusion has been assumed; for the same syllogisms are produced.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":148,"ref":"p148","source":"iis qui sunt per convesionem, quare statim habemus et figuras per quas unumquodque erit.Palarn ergo quoniam omne propositum ostenditur per utrosque modos et per impossiblle et ostensive, et non contingit separari alterum ab altero.\n\nCAPUT XV.\n\nDe ratiocinatione ex oppositis.\n\nIn qua autem figura est ex oppositis propositionihus syllogizare, et in qua non est,sic erit manifeslum.Dico autem oppositas esse propositiones, secundum locut.ionem quidem quatuor, ut omni et,n ulli et omni et non omni, et aliqui et nulli, et alicui et non alicui inesse; secundum veritatem autem Ires, nam alicui et non alicui secundum locutionem opponuntur solum; harum autem contrarias quidem universales, omni nulli inesse, ut omnem disciplinam esse studiosam, nullam esse studiosam, alias vero oppositas.ln prima igitur figura non est ex oppositis propositionibus syllogismus, neque affirmativus, neque negativus; affirmativus quidem,quoniam oporlel utrasque affirmativas esse propositiones,oppositæ autem affirmatio et negatio; privativus autem,quoniarn oppositas quidem idem de eodem praedicant et negant,in trimaautem medium non dicitur de utrisque, sed de illo quidem aliud negatur,idem autem de alio prædicatur, hae vero non opponuntur.","english":"For those that come about through conversion, so that we immediately have also the figures through which each thing will be. It is clear, then, that every proposition is proved through both modes, both through the impossible and ostensively, and it is not possible for the one to be separated from the other.\n\nCHAPTER XV.\n\nOn reasoning from opposites.\n\nIn which figure it is possible to syllogize from opposite propositions, and in which it is not, will be made clear as follows. I say that opposite propositions are, according to wording, four: as \"to all\" and \"to none,\" \"to all\" and \"not to all,\" \"to some\" and \"to none,\" and \"to some\" and \"not to some\"; but according to truth, three, for \"to some\" and \"not to some\" are opposed only according to wording; of these, the contraries are the universals, \"to all\" and \"to none,\" as \"every discipline is studious,\" \"no discipline is studious,\" and the others are opposites. In the first figure, then, there is no syllogism from opposite propositions, neither affirmative nor negative; affirmative indeed, because it is necessary that both propositions be affirmative, but affirmation and negation are opposites; negative indeed, because opposites predicate and deny the same thing of the same thing, but in the third figure the middle is not said of both, but something else is denied of the one, and the same is predicated of the other, and these are not opposed.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":149,"ref":"p149","source":"CAPUT XVI.\n\nDe ratiocinatione ex oppositis in secunda figura,\n\nIn media autem figura.et ex oppositis, et ex contrariis contingit fieri sylJogismum.Sit enim bonum quidem in quo a, disciplina autem in quo et c; si ergo omnem disciplinam studiosam sumpsit,et nulIam,a inest omni b,et nulli c,quare nulli c, nulla ergo disciplina disciplina est. Similiter autem et si omnem sumens studiosam disciplinam,medicinam vero non studiosam sumpsit,nam a bquidem omni, autem nulli,quare aliqua disciplina non erit discipIina.Et si a quidem omni,b autem nulli, est autem quidem disciplina, autem medicina,a vero opinio,nulIam enim disciplinam opinionem sumens sumpsit aliquam disciplinam esseopinionem.Differt autem a priore in terminis converti,nam prius quidem ad b, nunc autem rd affirmativum. EL si sit non universalis altera propositio,similiter,semper enim medium est, quod ab altero quidem negative dicitur, de altero vero affirmative. Quare contingit opposita quidem perfici, non autem semper,neque omnino,sed sic se habeant, quae sunt sub medio, ut vel eadem sint, vel totum ad partem; aliter autem impossibile, non enimerunt propositiones ullo modo, neque contrariæ, neque oppositæ.","english":"CHAPTER XVI.\n\nOn reasoning from opposites in the second figure.\n\nIn the middle figure, syllogisms can arise both from opposites and from contraries. For let good be that in which A is, and let knowledge be that in which B and C are. If, then, he assumed that every branch of knowledge is good, and that no branch of knowledge is good, then A belongs to every B and to no C; wherefore to no C. Hence no branch of knowledge is a branch of knowledge. Likewise also if, assuming every branch of knowledge to be good, he assumed medicine not to be good; for A belongs to every B, but to no C; wherefore some branch of knowledge will not be a branch of knowledge. And if A belongs to every B and to no C, and B is knowledge while C is medicine, and A is opinion—for assuming no branch of knowledge to be opinion, he assumed some branch of knowledge to be opinion. But it differs from the previous case in the conversion of terms; for previously it was in relation to B, but now in relation to C, the affirmative proposition. And if one of the propositions is not universal, it works the same way; for the middle term is always that which is predicated negatively of one and affirmatively of the other. Wherefore it is possible for opposites to be brought to conclusion, but not always, nor in every case, but only when the things under the middle term are so related as to be either the same or related as whole to part; otherwise it is impossible, for the propositions will in no way be either contraries or opposites.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":150,"ref":"p150","source":"CAPUT XVII.\n\nDe syllogismo ex oppositis ira tertia figura.\n\nIntertiaverofiguraaffirmativusquidem sytlogismus nunquam eritex oppositis propositionibus propter causam dictam et in prima figura.Negativus autem erit sylJogismus,et universalibus,et non universafibus terminis. Sit enim disciplina in quo et c, medicina autem in quo a; si ergo sumat omnem mecHcinam, disciplinam, et nuHem medicinam discipIibam,b omni a sumpsit,et nulli a,quare erit aliqua disciplina non disciplina. Similiter autem eL si non universaliter sumpta sit a propositio,nam si est aliqua medicina disciplina,et rursum nulla mcdicina discipIina,accidit disciplinam aliquam non esse disciplinam.Suntautemuniversaliter quidem sumptis terminis contrariae propositiones,si auLem particularis altera sit, oppositae, Oportet autem scire quoniarn contingit oppositasic sumere quemadmodum dixim us,omnem disciplinam studiosam esse,et rursum nullam aut aliquam non esse studiosam, quod non solet latere;erit autem per alias interrogationes syllogizare alteram, Rt quemadmodum in Topicis dictum est, sumere.Quoniarn autem affimationum popositiones sunt tres, sexies accidit opposita sumere, aut omni et nulli, aut omni et non omni, aut alicui et nulli, et hoc converti in terminis, ut a omni et nulli c, aut omni et nulli b.","english":"CHAPTER XVII.\n\nOn the syllogism from opposites in the third figure.\n\nIn the third figure there will never be an affirmative syllogism from opposite propositions, for the reason stated also in the first figure. But a negative syllogism will arise, both with universal and with non-universal terms. For let discipline be that in which C is, and medicine that in which A is; if then one assumes that every medicine is a discipline, and that no medicine is a discipline, one has assumed B of every A and of no A, so that there will be some discipline that is not a discipline. Likewise also if the proposition is not taken universally; for if some medicine is a discipline, and again no medicine is a discipline, it follows that some discipline is not a discipline. Now when the terms are taken universally, the propositions are contraries; but if one of them is particular, they are opposites. It must be known, however, that it is possible to take opposites in the way we have said—that every discipline is studious, and again that no discipline, or some discipline, is not studious—which is not wont to escape notice; but one will syllogize the other through other interrogations, and take it as has been said in the Topics. Since, moreover, there are three affirmative propositions, it happens six times that opposites are taken: either every and none, or every and not every, or some and none, and this by conversion in the terms, as A of every and of no C, or of every and of no B.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":151,"ref":"p151","source":"aut huic quidem omni, illi vero non omni, et rursum boc converti secundum terminos: similiter autem et in tertia figura.Quare manifestum est de qnoties et in quibus figuris contingit per oppositas propositiones fieri syllogismum.Manifestum est quoniam ex falsis est verum syllogizare, quemadmodum dictum est prius; ex oppositis autem non est, semper enim contrarius syllogismus fit rei (ut si est bonum non esse bonus, aut si animal non animal) eo quod ex contradictione est syllogismus, et subjecti termini aut iidem sunt, aut hic quidem totum, ille autem pars. Palam autem quoniam in paralogismis nihil prohibet fieri hypotbeseos contradictionem,ut si est impar non esse impar, nam ex oppositis propositionibus contrarius erit syllogismus; si ergo sumpserit hoc rnodo,hypotbeseos erit contradictio.","english":"Or if [the predicate belongs] to every one of this [subject], but not to every one of that, and again this [term] is converted according to the terms; and similarly also in the third figure. Hence it is clear in how many cases and in which figures a syllogism can come about through opposite propositions. It is clear that it is possible to syllogize what is true from false premises, as was said earlier; but from opposites it is not possible, for the contrary syllogism is always produced of the thing (for example, if the good is not good, or if the animal is not an animal), because the syllogism arises from a contradiction, and the terms of the subject are either the same, or one is the whole and the other a part. But it is evident that in fallacies nothing prevents a contradiction of the hypothesis from occurring, for example, if the odd is not odd; for from opposite propositions the syllogism will be contrary. If, then, one has assumed it in this way, there will be a contradiction of the hypothesis.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":152,"ref":"p152","source":"Oportet autem considerare quoniam sic quidem non est contraria concludere ex uno syllogismo (ut sit condusio, quoniam non est bonum, bonum aut aliud quiddam tale),nisi statim hujusmodipropositio surnatur, ut omne animal esse album et non album, hominem autem animal, sed vel assumere oportet contradictionern,ut quoniam omnis disciplina opinio et non opinio, deinde sumere quoniam medicina discipJina.quidcm est, nulla autem opinio, quemadmodum redargutiones fiunt, vel ex duobus syllogismis.Quare esse quidem contraria secundum veritatem quae sumpta sunt,non est alio modo quam hoc quemadmodum dictum est prius.\n\nCAPUT XVIII.\n\nDe petitione principii..\n\nIn principio autem petere et accipere et quidem, ul in genere,sumere in eo quod non est demonstrare propositum.Hoc autem acciditmultipliciter, nam et si omnino non syllogizatur,et si per ignotiora aut similiter ignota, et si per posteriora quod prius est, demonstratio enim ex prioribus et notioribus est. Horum ergo nullum est petere quod ex principio est, sed quia haec quidem nata sunt per se cognosci, illa vero per alia (nam principia quidem per se, quae autem sub principiis, per alia), quando non per se notum est, per se aliquis conaturoslendere, tunc petit quod ex principio est.","english":"One must consider that it is not possible to conclude contraries from a single syllogism in this way (so that the conclusion is, for instance, that it is not good, or good, or some other such thing), unless one immediately takes a proposition of this sort, such as that every animal is white and not white, and that man is an animal; but one must either assume the contradiction, as that every discipline is opinion and not opinion, and then assume that medicine is a discipline, but no opinion, in the way refutations are produced, or [one must do it] from two syllogisms. Wherefore for the things assumed to be contraries in truth, this is not possible in any other way than as was said before.\n\nCHAPTER XVIII\n\nOn begging the principle.\n\nTo beg the principle and to take it, and indeed, generally speaking, to assume [what is needed] for what is not being demonstrated, is the proposed [fallacy]. This happens in many ways, for [it happens] both if no syllogism is produced at all, and if [the conclusion is reached] through things less known or equally unknown, and if through things posterior [what is] prior; for demonstration is from things prior and better known. None of these, then, is begging what is from the principle, but since some things are naturally known through themselves, while others through other things (for principles are through themselves, but the things under the principles are through other things), when something not known through itself is attempted to be shown through itself, then one begs what is from the principle.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":153,"ref":"p153","source":"Hoc autem est sic facere quidem at statam postulet id quod propositum est: contingit autem et transgredientes et ad alia eorum quæ nata sunt per illa ostendi per hæc monstrare quod ex principio est,ul si a ostendatur per b, et perr., autem natum sit ostendi per a, accidit enim idem It per se demonstrare eos qui sic syllogizant, quod faciunt qui parallelas arbitrantur scribere,latent enim ipsi seipsos talia sumentes quae non valent demonstrare,curn non sint paralleIæ.","english":"To do this in this way is just as the proposed goal demands; but it also happens that those who go beyond and demonstrate other things among those which are naturally shown through those [premises] show the principle through these, as if a is shown through b, and b is naturally shown through a; for it happens that those who syllogize in this way demonstrate the same thing through itself, which is what those do who think they are drawing parallel lines; for they themselves escape their own notice by assuming such things as cannot be demonstrated, since they are not parallel lines.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":154,"ref":"p154","source":"Quare accidit sic syllogizantibus unumquodque esse dicere si est unumquodque, sic autem omne erit perse notum, quod est impossibile.Si ergo aliquis dubitat assuropto dubio quoniam ainest c,similiter et quoniam b, petat autem inesse b,nondurn manifestum si quod in principio est petat,sed quoniam non demonstravit maHHestum,non enim est principum demonstrationis,quod similiter est incertum.Si autem ad sic se habet ut idem sit,aut manifestum quod convertuntur, autinestalterum alteri, quodinprincipio est petit,nam et quoniam a inest b,per illa monstrabit si convertantur, nunc autem hoc prohibet,sed non modus.Si autem hoc faciat,quod dictum est faciet, et convertet per tria, similiter autem et si sumat inesse c, quod similiter incertum sit, ut et si a inest c,nondum quod ex principio petit, sed neque demonstrat.Si autem idem sit a et b, aut eo quod convertuntur,aut eo quod a sequitur ei quod est b, quod ex principio est petit propter eamdem causam, nam fx principio quod valet, prius dictum est a nobis, quoniam per se monstrabitur quod non est per se manifestu:n.Si ergo est in principio petere per se monstrare quod non per se est manifestum, hoc autem et non ostendere quando similiter dubitantur quod monstratur et per quod monstratur, vel eo quod eadem idem,vel eo quod idem eisdem inesse sumitur,in media quidem figura et tertia utrorumque continget similiter quod est in principio","english":"Therefore it happens that those who syllogize in this way say that each thing is, if each thing is; but in this way everything will be known per se, which is impossible. If, then, someone doubts, when something doubtful has been assumed, that c is present, and similarly that b is present, and he asks that b be present, it is not yet clear whether he is begging the principle; but it is clear that he has not demonstrated it, for it is not a principle of demonstration that which is similarly uncertain. If, however, matters stand such that it is the same thing, either it is manifest that they are convertible, or one is present in the other, he begs the principle; for he will show that a is present in b through those things, if they are convertible; but now this prevents it, yet not the manner. If, however, he does this, he will do what has been said, and he will convert through three terms; and similarly also if he assumes that c is present, which would be similarly uncertain, as also if a is present in c, he does not yet beg the principle, but neither does he demonstrate. If, however, a and b are the same, either by the fact that they are convertible, or by the fact that a follows b, he begs the principle for the same reason; for we have said earlier that what is from a principle is such that it will be shown per se that which is not manifest per se. If, therefore, to beg the principle is to show per se that which is not manifest per se, this is also not to show when both what is demonstrated and that through which it is demonstrated are similarly doubted, either because the same things are the same, or because it is assumed that the same things are present in the same things; in the middle and third figures it will happen similarly for both, which is [to beg] the principle.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":155,"ref":"p155","source":"petere, in praedicativo quidem syllogismo et in tertia figura, et in prima, negative autem quando eadem ab eodem, et non similiter utraeque propositiones,similiterautem et in media, eo quod non convertuntur termini secundum negativos sylJogismus.Est autem in principio petere in demonstrationibus quidem quæ secundumveritatem sic se habent,in dialecticis autem, quae secundum opi nionem.\n\nCAPUT XIX.\n\nDe non propter hoc accidere falsum.\n\nXon propter hoe autem accidere Falsum (quod saepe in disputationibus solemus dicere) primum quidem est in iis qui ad impossibile syllogismis, quando ad contradictionem esthujus quod monstratum est ea quae ad impossibile. Nam neque qui non contradicit dicit non propter boc,sed quoniam falsum est aliquid poaitum priorum, neque in osten siva, non enim ponit quod contradicit.Amplius autem quando interimitur aliquid ostensive per a c,non est dicere quoniam non propter quod positum est factus est syllogismus,nam non propter hoc fieri tunc dicimus, quandointerempto hocnihilominus perficitur syIlogismus,quod non est in ostensivis, interempta enim propositione, nec qui ad hanc est erit syllogismus. Manifestum igitur quoniam'in iis qui ad impossibile sunt dicitur non propter hoc,et quando sic se habet ad impossibile quæ ex principio est hypothesis.","english":"To beg the question occurs in the predicative syllogism both in the third figure and in the first; in the negative case, however, when the same thing is predicated of the same thing, and not both propositions alike; and likewise in the middle figure, because the terms are not converted according to negative syllogisms. Now to beg the principle occurs in demonstrations that stand thus according to truth, but in dialectical arguments according to opinion.\n\nCHAPTER XIX.\n\nOn the false coming about not on account of this.\n\nThe false coming about not on account of this (which we are accustomed often to say in disputations) occurs first of all in those syllogisms that lead to the impossible, when the things that lead to the impossible stand in contradiction to that which has been demonstrated. For neither does he who does not contradict say \"not on account of this,\" but [says] that something of the prior premises has been falsely assumed; nor [does this apply] in the ostensive [syllogism], for it does not assume what contradicts. Moreover, when something is refuted ostensively through A C, it cannot be said that the syllogism was made not on account of what was assumed; for we say that it comes about not on account of this when, this being refuted, the syllogism is nonetheless completed—which is not the case in ostensive syllogisms; for when the proposition is refuted, neither will the syllogism that depends on it exist. It is clear, therefore, that \"not on account of this\" is said in those [arguments] that lead to the impossible, and when the hypothesis from the principle stands thus in relation to the impossible.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":156,"ref":"p156","source":"ut cum sit,veI cum non sit haec, nihilominus accidit impossibile Ergo manifestissimusquidem modus est non propter suppositionem esse faIsum,quando ab hypothesi inconjunctus est a mediis syllogismus ad irnpossibile,quod dictum estin Topicis, quod enim non est causa, ut causam ponere hoc est; ut si volens ostendere quoniam asymeter est diameter,conetur Zenonis ratione quoniam non est moveri, et ad boc inducat impossibile, nullo enim modo coatinuum est falsum, locutioni quae est ex principio.","english":"as when this is or is not, the impossible nevertheless follows. So the most manifest mode of the false conclusion not arising from a supposition is when the syllogism leading to the impossible is disconnected from the middle terms of the hypothesis, as was said in the Topics; for to posit as a cause what is not a cause is this: for example, if someone wishing to show that the diagonal is incommensurate should attempt by Zeno's argument to show that it does not move, and bring in the impossible for this purpose; for in no way is the false connected with the statement from the beginning.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":157,"ref":"p157","source":"Alius autem modus,si continuum quidem sit impossibile hypothesi, non tamen propter illam accidat, hoc autem possibile est fieri, et in hoc quod superius,et in hoc quod inferius sumenti, continuum, ut si a ponatur inesse b, autem c, vero d, hoc autem sit falsum inesse d, nam (si ablato a,nihilominus inest c, et d) non erit falsum propter eam quae ex principio est hypothesin.Aut rursum si quis in superiori sumat continuum, ut si a quidem b, autema, /' vero e, falsum autem sit finessea, nam et sic nihilominus erit impossibiIe,interempta quae est ex principio hypothesi.Sed oportet ad eos qui ex principio terminos copulare impossibile, sic enim erit propter hypothesin, ut in inferiori quidem sumenti continuum ad praedicatum terminum; nam si impossibile est a inesse d,interempto a, non amplius erit faIsum.In superiori autem de quo praedicatur; nam si non possibile est inesse b, interempto non amplius erit impossibile; similiter autem et cum privativi sint syllogismi. Manifestum ergo quoniam cum impossibile non ad priores terrninos,non propter positionem accidit falsum; an nec si semper propter hypothes?s erit falsum?","english":"But there is another mode: if the impossible is indeed continuous with the hypothesis, yet does not occur on account of it—this can happen both when one takes the continuous term in what is above and in what is below, as if A is posited to be in B, and C in A, and D in C, and let it be false that D is in A; for if A is removed, C is nonetheless in D, and it will not be false on account of the hypothesis made at the beginning. Or again, if someone takes the continuous term in the higher position, as if A is in B, and B in C, and let it be false that A is in C; for in this way too it will nonetheless be impossible once the hypothesis made at the beginning is destroyed. But one must join the impossible to the terms from the beginning; for thus it will be on account of the hypothesis, as when one takes the continuous term in the lower position up to the predicate term; for if it is impossible for A to be in D, once A is removed it will no longer be false. In the higher position, however, [one must join it] to that of which it is predicated; for if it is not possible for A to be in B, once it is removed it will no longer be impossible; and similarly also when the syllogisms are privative. It is evident, therefore, that when the impossible is not [joined] to the prior terms, the false conclusion does not occur on account of the positing; or will it not even so always be false on account of the hypothesis?","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":158,"ref":"p158","source":"nam si non ei quod est b, sed ei quod esl positum est inesse a, Ic autem c, et hoc d, etsic rnanetimpossibile; similiter autem etin sursum sumenti terminos, quare (quoniam cum est, et cum non est, hoc accidit impossibile) non erit propter positionem,aut cum non est hoc, nihilominus fieri falsum. Nee sic sumendum ut alio posito accidat impossibile, sed quando ablato hoc idem per reliquas propositiones concluditur impossibile, eo quod idem falsum accidere per plures hypotheses nihil fortass inconveniens est, ut parallelas, contingere, et si major est qui interius est, eo qui exteri us, et si triangulus habet plures rectos duobus.\n\nCAPUT XX.\n\nDe falsa ratiocinatione, catasyllogismo, hoc est corra-\n\ntiocinatione, et elencho.\n\nFalsa autem oratio fit propterprimum falsum: aut enim ex duabus propositionibus aut ex pluribus omnis est Byllogismus; ergo si ex duabus quidem, harum necesse est alteram, aut etiam utrasqucesse falsas, nam ex veris non erat falsus syIlogismus;si vero ex pluribus (ut sic quidem per a b, boc autem perd y g), horum erit aliquid superiorum faIsum,et propter boc oratio, nam a et per illa concluduntur quare propter illorum aliquid, accidit conclusio et falsum.","english":"For if it is not to B but to the term posited as A that A is taken to belong, and C to B, and this to D, and so the impossible remains; and similarly also for one taking the terms upward, so that (since both when it is and when it is not, this impossible results) it will not be on account of the hypothesis, or when this is not, the false will nonetheless come about. Nor must one take it thus, that when something else is posited the impossible results, but when this is removed the same impossible is concluded through the remaining propositions, because for the same falsehood to result through several hypotheses is perhaps nothing strange, as for parallel lines to meet, and for the term that is within to be greater than the one outside, and for a triangle to have more than two right angles.\n\nCHAPTER XX.\n\nOn false reasoning, catasyllogism, that is, counter-reasoning, and elenchus.\n\nFalse reasoning comes about on account of the first falsehood; for every syllogism is from two propositions or from more. Therefore if from two, one of these must be false, or even both; for from true premises there would not be a false syllogism. But if from more (as, for instance, in this way through A B, and this through D E F), something of these higher premises will be false, and on account of this the reasoning is false; for A and the rest are concluded through those, so on account of something of those, the conclusion and the falsehood result.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":159,"ref":"p159","source":"Ut autem non catasyllogizelur,observandum quando sine conclusionibus interrogat orationem, ut non detur his idem in propositionibus,eo quod scimus quoniam sine medio syllogismus nun fit, medium autem est quod plerumque dicitur. Quomodo autem oportet ad unanquanque conclusionem observare medium manifestum est, eo quod sciturquatein unaquaque figura ostenditur,hoc autem nos non latebit,eo quod videmus quomodo subrnittimusoratio. nero. Oportet autem quod custodire praecipimus respondentes, ipsos argumentantes tentare latere,boc autem erit primum quidem si conclusiones non prius syllogizent, sed sumptis necessariis non manifestae sint. Amplius autem si non propinqualinterrogant,sed quam maxime longe media,ut sisitopportunum conc:uderea e {, media e de, oportetergo inquirere si a b, et rur:.um non si e sed si e, deinde si c, et sicreliqua, et si per unum medium sit syllogismus, a medio incipere, maxime enim sic latebit respondentem.","english":"But in order that he may not be syllogizing falsely, it must be observed when he questions the argument without conclusions, that the same thing is not granted to him in the premises, since we know that a syllogism does not come about without a middle term, and the middle term is what is generally stated. How one ought to guard against each conclusion is clear from the fact that it is known how it is shown in each figure; and this will not escape us, since we see how we set down the argument. But what we have instructed the respondents to guard against, those who are arguing ought to try to conceal; and this will happen first, indeed, if they do not syllogize the conclusions beforehand, but, with the necessary premises taken, they are not evident. Furthermore, if they do not ask the questions closely connected, but as far as possible at a distance from the middle terms—so that, if it is expedient to conclude that A is in E, the middle terms are D, E—one ought therefore to inquire whether A is in B, and again not whether it is in E, but whether it is in D, then whether it is in C, and so on for the rest; and if the syllogism is through one middle term, to begin from the middle term; for in this way especially will it escape the respondent.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":160,"ref":"p160","source":"Quoniam ergo habemus quando et quomodo se habentibus terminis fit syilogismus, manifestum at quando erit, et quando non eritelenchus, nam omnibus affirmativis, vel permutatim positis responsionibus (ut bac quidem affirma,tiva,illa vero negativa), contingit fieri elenchum: erit enim syllogismus, et sic in illo modo se habentibus terminis; quare si id quod positum est contrarium sit conclusioni, necesse est fieri elenchum, nam elenchus syllogismus contradictionis est. Si vero nihil affirmetur, impossibile est fieri elenchum, nonenim erat syllogismus,cucQomnestermini erant privativi, quare nec elenchus: namsi eIenchus,necesse est syllogismum esse;cum autem estsy!Iogismus, non necesse estelenchum esse. Similiterautem si nihil positum sit secundum responsionem universa liter; nam eadem erit definitio syllogismi et elenchi.\n\nCAPUT XXI.","english":"Since, therefore, we have [established] when and how a syllogism comes about in the case of terms so disposed, it is manifest also when an elenchus will be and when it will not be. For when all the responses are affirmative, or are set down alternately (as when one is affirmative and the other negative), an elenchus can come about; for there will be a syllogism also when the terms are disposed in that way. Wherefore if what has been granted is contrary to the conclusion, an elenchus must come about, for an elenchus is a syllogism of contradiction. But if nothing is affirmed, it is impossible for an elenchus to come about, for there was no syllogism when all the terms were privative; wherefore neither [will there be] an elenchus. For if there is an elenchus, there must be a syllogism; but when there is a syllogism, it is not necessary that there be an elenchus. Likewise, moreover, if nothing has been granted in response universally; for the definition of syllogism and elenchus will be the same.\n\nChapter XXI","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":161,"ref":"p161","source":"De fallacia secundum opinionem.\n\nAcciditautem quandoque (quemad modum in positione terminorumfallebamur) et secundum opinionem fieri fallaciam, ut si contingal idem pluribus principaliter inesse,et hoc quidem latere aliquern,et putare nulli inesse,iJlud autem scire, ut insit a et per se, et haec omni similiter. Si igitur quidem putet omni a inesse, et hoc d, autem nulli a, et Loc omni d,ejusdem secundum idem habet disciplinam et ignorantiarn.Rursum si quis fallatur circa ea quæ suntex eadem conjugatione,ut si a inest b,hocautem c, et d, opinetur autem a inesse omni b,et rursum nulli o. Simul enim sciet,et non opinabitur inesse; ergo nibil aliud existimat ex iis quam scit,hoc non opinari, scit enim aliquo modo quoniam a inest per b, velut in universal; hoc quod est particulare; quare quod aliquo modo scil, hoc omnino existimat non opinari,quod est impossibile.","english":"On Fallacy According to Opinion.\n\nIt happens sometimes (just as we were deceived in the positing of terms) that a fallacy also arises according to opinion: for instance, if it happens that the same thing belongs primarily to several things, and one person is unaware of this and thinks it belongs to none, while another knows that it belongs—say, that A belongs per se, and similarly to every one. If, then, someone thinks that A belongs to every B, and that D belongs to no A, and that A belongs to every D, he has both knowledge and ignorance of the same thing in the same respect. Again, if someone is deceived about things that are from the same conjugation—for instance, if A belongs to B, and B to C and D, but he opines that A belongs to every B and again to no C. For at the same time he will know and will not opine that it belongs; therefore he thinks nothing other than what he knows from these things—namely, that he does not opine this; for he knows in some way that A belongs through B, as the particular in the universal. Wherefore what he knows in some way, he altogether thinks he does not opine, which is impossible.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":162,"ref":"p162","source":"In eo autem quod prius dictum est, si non ex eadem conjugatione sit medium, secundum utrumque quidem mediorum ambas propositioned non possibile est opinari ut a quidem omni,c autem nulli,bæc autem utraque omni d; accidit autem aut simpliciter aut in aliquo contrariam sumere primam propositionem.Si enim cui inest omnia opiuatur inesse, autem novit, et quoniam a novit, quare si rursum cui nulli.: putat a inesse, cai alicui inest, huic non putat a inesse, quod autem omni putat cui b, rursum alicui non putare cui b, aut simpliciter, aut in aliquo contrarium et; sic ergo non contingit opinari. Secundum utrumque autem unam,aut secundum al: terum utrasque,nihil prohibet a omni b, et d, et rursumcc nulli c.Nam similis hujusmodi I'allacia,veluti fallimur circa particularia, ut si a omni inest, autem omni c,a omni ineritvsi ergo aliquis novit quoniam a cui inestomni,novit etquoniam ei quod estc;sed nihil prohibet ignorare quoniam est,ut si a quidem duo recti,in quo autem triangulus,in quo vero sensibilis trianguIus; opinabitur enim aliquis non esse c,siens quoniam omnis triangulus habet duos rectos: quare simul sciet et ignorabit idem, nam scire omnem triangulum quoniam duobus rectis non simpIexest,sed hoc quidem universalemhabetdisciplinax,illud vero singularem. Sic ergo in universali novit c,quoniam duobus rectis in singulari autem non novit, quare non habebit contrarias.","english":"In what was said before, if the middle term is not from the same combination, it is not possible to hold both propositions according to each of the middle terms—for instance, that A belongs to every, C to none, and both of these to every D. But it happens that one takes the first proposition as contrary either simply or in some respect. For if someone opines that A belongs to everything to which it belongs, and knows that it belongs, and knows that it belongs to C, then if again he thinks that A belongs to nothing to which C belongs, he does not think that A belongs to that to which it does belong; but what he thinks belongs to everything to which B belongs, again he does not think belongs to something to which B belongs—either simply or in some respect it is contrary. Thus, then, it is not possible to opine. But according to both one proposition, or according to one both propositions, nothing prevents A belonging to every B and D, and again C to no C. For the fallacy of this sort is similar, as we are deceived about particulars—for instance, if A belongs to every B, and B to every C, A will belong to every C. If, therefore, someone knows that A belongs to everything to which it belongs, he also knows that it belongs to C; but nothing prevents him from being ignorant that C exists—for instance, if A is two right angles, and that in which it is is a triangle, and that in which it is is a perceptible triangle. For someone will opine that C does not exist, knowing that every triangle has two right angles; therefore he will at the same time know and be ignorant of the same thing. For to know that every triangle has two right angles is not simple, but the one has universal knowledge, the other singular. Thus, then, in the universal he knows C, that it has two right angles, but in the singular he does not know it; therefore he will not have contrary opinions.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":163,"ref":"p163","source":"Similiter autem est quae in Menone est oratio,quoniam disciplina est reminiscentio; nunquam enim accidit praescire quod singulare est, sed simul inductione sumere particularium disciplinam, velut recognoscentes. Nam quaedam scientes,statim scimus, ut quoniam duobus rectis, si scimus quoniam triangulus, similtterautemet in aliis. Ergo universali quidem speculamur particularia, propria autem non scimus; quare contingit et falli circa ea, verum non contrarie, sed habere quidem universale, decipi autem particulari. Similiter autem in praedictis non enim contraria quæ est secundum medium ei quae est secundum syllogismumdisciplinæ,nec quae est se. cundum utrumque mediorum opinatio,nihilenim pro. hibet scientem, et quoniam atoti inest, et rursum hoc totic,putare non inesse, ut quoniam omnis mula sterilis, et hæc mula, putare hanc habere in utero; non enim scit quoniam a, qui non conspicit,quod est secundum utrumque.Quare manifestum quoniam et si boc quidem novit, illud vero non novit,falletur, qdod habent universales ad particulares disciplinas; nullum enim sensibilium extra sensum fit scimus, nee si sentientes fuerimus sciæus,nisi etinuniversali,el in eo quod habet propriam disci pIinam,sed non in eo quod estin actum.Nam scire tripliciter dici. tur,aut ut universali.","english":"Similarly, the argument in the Meno—that learning is recollection—is of this sort; for it never happens that one foreknows the particular, but one grasps the knowledge of particulars together with the induction, as it were recognizing them. For there are things which, knowing, we know at once—for instance, that something is equal to two right angles, if we know that it is a triangle; and similarly in other cases. So by the universal we contemplate particulars, but we do not know the proper characteristics; hence it happens that we are also deceived about them—not, however, in a contrary way, but we have the universal and are deceived in the particular. Similarly in the cases mentioned before; for the opinion according to the middle term is not contrary to the knowledge according to the syllogism, nor is the opinion according to both middle terms. For nothing prevents one who knows both that A belongs to the whole and again that this whole belongs to something, from thinking that it does not belong—for instance, that every mule is sterile, and that this is a mule, yet thinking that this one has a fetus in the womb; for he does not know the A which he does not observe, namely that which is according to both. Wherefore it is clear that even if he knows one thing but does not know the other, he will be deceived—which is what universals have in relation to the knowledge of particulars. For we know none of sensible things apart from sense, nor, if we have perceived, do we know, unless in the universal and in that which has the proper knowledge, but not in that which is in act. For to know is said in three ways: either as in the universal...","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":164,"ref":"p164","source":"aut ut propria, aut ut in actu quare et decipi totidem modis, nihil ergo prohibete scire,et deceptum esse circa idem, verumtamen non contrarie.Quod accidit et ei qui secundum utramque scit propositionuu',et non pertractavit prius,nam opinans in utero habere mulam, non habet secundum actum disciplinam,neque propter opinionem fallaciam contrariam disciplinæ,syllogismus enim est contraria fallacia in universali.Qui autem opinatur quod bonum esse est malum esse,idem opinabitur bonum esse et malum. Sit enim bonum esse in quo a,malum autem essein quo b,rursurn bonum esse in quo; quoniam igitur idem opinatur et etcet esse opinabitur,et rursum esse asimiliter,q uare et e a, nam quemad' modum si erat verum de quo b, et de quo a. et de quo a verum erat,gic et in opinatione Similiter autem et in eo quod est esse.Nam cum idem sit et b, et rursum et a, a idem erit, quare et opinatione similiter; ergo hoc quidem necessarium si quis det primum. Sed fortasse illud falsum opinari aliquem quod malum esse est bonum esse, nisi secundum accidens; multipliciter enim possibile est hoc opinari, perspiciendum autem hoc melius.","english":"Or as proper, or as in act; hence also deception occurs in just as many ways. Nothing therefore prevents one from knowing and being deceived about the same thing, though not in a contrary manner. This happens also to one who knows both propositions and has not examined them beforehand; for one who opines that he has a mule in the womb does not have knowledge in act, nor does he have a falsehood contrary to knowledge on account of the opinion, for the syllogism of the contrary falsehood is in the universal. But one who opines that to be good is to be evil will opine the same thing to be both good and evil. For let \"to be good\" be in respect of A, and \"to be evil\" in respect of B; again, \"to be good\" in respect of A. Since therefore he opines the same thing and also that it is, he will opine it, and again that it is similarly, wherefore also A; for just as if it was true of that of which B, also of that of which A, and of that of which A it was true, so also in opining. And similarly also in respect of being. For since the same is both B and again A, A will be the same, wherefore also in opining similarly; therefore this is indeed necessary if one grants the first. But perhaps that is false—that someone opines that to be evil is to be good—except according to accident; for it is possible to opine this in many ways, but this must be examined better.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":165,"ref":"p165","source":"CAP'JT XXII.\n\nDe conversionibus terminorum.\n\nQuando vero convertuntur extremitates, necesse est et medium converti ad utramque; si enim a de per est, si convertitur et inest cui a omni, et a convertitur, et inestcui a omni,b per medium c, etc convertitur per medium a. Et in non esse itidem, ut si inest c, a vero non inest b, neque a inerit c. Si ergo convertatur ad a, et ad a convertetur: sit enim nulli a inexistens, ergo neque c, omni enim inerat 6, et si convertitur ad c, et a convertetur ad c; nam de quocunqueomnino 6, et c.Et. sic ad a convertitur, et convertetur ad a: cui enim inest,etc; cui autem c, a. non inest; et solum hoc a conclusione incipit,alia autem non similiter, utin prædicativo sy 1iogismo. Rursum si a et convertuntur, et et similiter, omni autem necesse est a aut inesse,et etdsic sehabebunt, utomni alterurn insit; quoniam enim cui a b, et cui d, omni autem a aut c, et non simul, manifestum quoniam et aut omni,et non simuI, utsi ingenitum, incorruptibile,et incorruptibile ingenitum, necesse est quod factum est corruptibile corruptibile factum esse, duo enim:syllogisml constituti sunt. Rursum si omni quidem,a vel b,et cvel d, simul autem non insunt,si convertitur net c, et etd convertetur. Nam si alicui non inest b, cuid,palam quoniama inest; si autem a,et c,convertuntur enim; quare simul et d, hoc autem impossibile.","english":"CHAPTER XXII.\n\nOn the Conversions of Terms.\n\nBut when the extremes are converted, the middle term must also be converted to both; for if a is present in every b through c, and if it is converted and is present in that to which a belongs universally, then a is converted, and it is present in every thing to which a belongs, b through the middle c, and c is converted through the middle a. And in the case of non-being likewise: as if c is present, but a is not present in b, then neither will a be present in c. If, therefore, it is converted to a, it will also be converted to a; for let it be present in none to which a is present; therefore neither will c be present, for it was present in every b, and if it is converted to c, a will also be converted to c; for of whatever thing b is universally predicated, of that thing c also is. And thus it is converted to a, and it will be converted to a: for that in which it is present, etc.; but that in which c is present, a is not present; and this alone begins from the conclusion, but the others do not similarly, as in the predicative syllogism. Again, if a and b are converted, and c and d similarly, but it is necessary that a or c be present in every thing, and they are so disposed that either is present in every thing; for since that in which a is present, b is present, and that in which c is present, d is present, but a or c is present in every thing, and not simultaneously, it is manifest that b or d is present in every thing, and not simultaneously; as, if the ungenerated is incorruptible, and the incorruptible is ungenerated, it is necessary that what has been made is corruptible and the corruptible has been made; for two syllogisms have been constituted. Again, if a or b is present in every thing, and c or d, but they are not present simultaneously, if b is converted with c, then d will also be converted. For if b is not present in some thing, it is clear that a is present in that thing; but if a is present, then c is present, for they are converted; wherefore d is also present simultaneously, but this is impossible.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":166,"ref":"p166","source":"Quando autem u toti bet inest, et de nullo alio prædicatur, inest autem et omni c, necesse esta etbconverti, quoniamenim desoJis bcdicitura, prædicaturautem bbet idem dese et de c,manifestum quoniam de qui bus a, et dicetur omnibus, verum et de a. Rursum quando a et b, toti insunt convertitur autem b, necesse est a omni inesse, quoniam enim omni ca, autem b,eo quod convert.untur, et a omni inerit. Quando autem duo fuerint opposita,ut a magis eligendum sit quam b,cum sint opposita, et quam csimiIiter,si magiseligenda sunta cquam d,a magis eligendum quamd. Similiterenim sequendum a,etfugiendum b,opposita enim, et ei quod est d,narn et haec opponuntur; si ergo a ei quod est simililereIigend um,etb ei quod est fugiendum,utrumque enim utrique similiter fugiendum eligendo; quare et hæc ambo a iis quae suntb d,quoniarn autem magis, non possibile similiter,nam et similiter erunt.Si autem dmagis eligendum quam a,et quam cminus fugiendum; nam quod minus est minori opponitur; magis autem eligendum est majus bonum et minus malum quam minus bonum et majus malum.","english":"But when a is present in the whole of b and is predicated of no other, and is also present in every c, it is necessary that b also be converted; for since it is said of every b, and b is predicated of the same things as c, it is manifest that it will be said of all the things of which a is said, and also of a. Again, when a and b are present in the whole, and b is converted, it is necessary that a be present in every c; for since a is in every c, and b is converted, a will also be present in every b. But when two things are opposed, as that a is more to be chosen than b, when they are opposed, and likewise than c, if a and c are more to be chosen than d, then a is more to be chosen than d. For similarly one must pursue a and avoid b, for they are opposites, and likewise in relation to d; for these too are opposed. If, therefore, a is similarly to be chosen and b similarly to be avoided, each of the two is similarly to be avoided and chosen; wherefore both these things are so in relation to the things that are b and d. But since it is more, it is not possible that they be similarly; for they will also be similarly. But if d is more to be chosen than a, and less to be avoided than c; for what is less is opposed to what is less; but more to be chosen is the greater good and the lesser evil than the lesser good and the greater evil.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":167,"ref":"p167","source":"Universum igitur magis eligendum quam a c, nunc autem non est, ergo magis a eligendum quam d,et ergo minus fugiendum quam b.Si ergo eligat omnis amans secundum amorem a sic sebabere,ut concedere, et non concedere in quo c, aut concedere in quo d, et non tale esse ut concederein quo b,manifestum quoniam a hujusmodi esse, magis eIigendum est quam concedere;ergo diligi quam conventio magis eligendum secundum amorem;magis ergo amorest in amicitia quam convenire. Si antem maxime hujus, et finis bæc, ergo convenire aut non est omnino, aut diligendi gratia,narn et alix concupiscentiæ etartes sic fiunt.Quomodo ergo se habent termini secundum conversiones, et in eo quod magis fugiendum vel magis eligendum -sit, manifestum est.\n\nCAPUT XlIII.\n\nDe epagoge, id est inductione.\n\nQuoniam autem non solum dialectici et demonstra. tivi syllogismi per prædialectici fiunt figuras, sed et rhetorici, sed et simplicitea quaecunque fides est,et secundum unamquamque artem,n unc eritdicend um Omnia enim credimus per syllogismum aut ex inductione; ergo si inductio quidem est, ex inductione syllogismus peralterum extremitatem medio syUogizare.Ut si eorum quae sunt a medium sit b,per ostendere a inesse b, sic enim facimus inductiones.","english":"Therefore the whole is more to be chosen than a c, but now it is not so; therefore a is more to be chosen than d, and therefore less to be shunned than b. If, then, every lover chooses according to love—a thus, for example, to concede, and not to concede in the case of c, or to concede in the case of d, and not to be such as to concede in the case of b—it is manifest that a being of this sort is more to be chosen than to concede; therefore to be loved is more to be chosen, according to love, than agreement; therefore love is more in friendship than to agree. But if this is most of all, and these are the end, then to agree is either not at all, or for the sake of being loved; for other desires and arts also come about in this way. In what way, then, terms stand in respect of conversions, and in respect of what is more to be shunned or more to be chosen, is manifest.\n\nCHAPTER XLIII.\n\nOn epagoge, that is, induction.\n\nSince, however, not only dialectical and demonstrative syllogisms are produced through the figures by pre-dialectical [arguments], but also rhetorical ones, and indeed simply whatever is a matter of belief, and according to each art, it must now be said. For we believe all things either through syllogism or from induction; therefore if induction indeed is [this], the syllogism from induction [proceeds] by syllogizing through the other extreme with the middle. As, for example, if b is the middle of the things that are a, by showing that a is present in b; for thus we make inductions.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":168,"ref":"p168","source":"Ut si a longævum, in quo autem choleram non habere, in quo vero singulare longævum,ut homo equus, et muIus.Ergo toti inest a, omne enim quod sibi cholera est,longævum,sed et non habere cho.leram, omni inest c; si ergo convertatur ei quod est b,et non transcendat medium,necesse este inesse, 6. Ostensum enim est prius quoniam,si duo aliqua eidem insunt,et ad alteram eorum convertatur extremum, converso et alterum inerit praedicatorum. Oportet autem intelligere ex singularibus omnibus compositum, nam inductio per omnia. SyIlogismus autem hujusmodi est primae et immediatae propositionis v quarum enim est medium, per medium est syllogismus; quorum vero non est, per inductionem. Et quodam modo opponitur inductio syllogisrno,nam hic quidem per medium extremum de tertio ostendit,illa autem per tertium extremum de medio. Ergo natura quidem prior et notior per medium syllogismus, nobis autem manifestior qui est per inductionem.","english":"For example, if a is long-lived, and that in which there is no bile, and that in which there is the individual long-lived thing, such as man, horse, and mule. Therefore a belongs to the whole; for everything that is free of bile is long-lived, but also not to have bile—c belongs to every such thing. If, then, b is converted to it and does not transcend the middle term, it is necessary that it be present. For it was shown earlier that, if two things are present in the same subject and the extreme is converted to one of them, the other of the predicates will also be present in the converted term. But one must understand the composite from all the singulars; for induction is through all. The syllogism of this kind is of the first and immediate proposition; for those things of which there is a middle term, the syllogism is through the middle term; but those of which there is no middle term, it is through induction. And in a certain way induction is opposed to syllogism; for the latter shows the extreme concerning the third through the middle term, while the former shows the middle through the third extreme. Therefore by nature the syllogism through the middle term is prior and more known, but to us the one that is through induction is more manifest.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":169,"ref":"p169","source":"CAPUT XXIV.\n\nDe paradigmate, hoc est exemplo.\n\nExemplum autem est, quando medio extremum inesse ostenditur per id quod est simile tertio.Oportet autem et medium tertio,et primum simili notius esse, inesse. Ut sit a malum, autem contra confines inlerre bellum,in quo autem A thenienses contra Thebanos,in quo autem Tbebanos contra Phocenses. Siergovolumus osterderequoniamThebanis pugnare malum est, sumendum quoniam contra confines pugnare est malum,hujus autem fides ex similibus,ut quoniam Thebanis contra Phocenses.Quoniam ergo contra confines malum,contra Thebanos autem contra confines est, manifestum quoniam contra Thebanos pugnare malum.Quonjam ergo beet inest,manifestum,utrumque enim est contra confines inferre bellum,et quoniam a d,Thebanis non enim fuit utile contra Phocenses bellum.Quoniam autem a inest b, per d. osteadetur,eodem autem modo et si per plura similia fides fiat medii ad extremum. Manifestum ergo quoniam exemplum est neque ut totum ad partern,neque ut pars ad totum, sed ut pars ad partem, quandoamboquideminsuntsubeodemnotumautem alterum. Etdiffertabinductione, quoniam hæcquidem ex omnibus indivjduisostendebat inesse estremum rnedio,et ad extremus non copulabat syllogigrnum,hoc autemet copulat,et non ex omnibus ostendit.","english":"CHAPTER XXIV.\n\nOn paradigm, that is, example.\n\nAn example is when it is shown that the extreme is present in the middle through that which is similar to a third term. It is necessary that both the middle be present in the third and the first be more known than the similar term, and that it be present. For let a be evil, and waging war against neighbors, and that in which the Athenians against the Thebans, and that in which the Thebans against the Phocians. If then we wish to show that for the Thebans to fight is evil, one must assume that to fight against neighbors is evil; the proof of this is from similar cases, as that for the Thebans against the Phocians. Since therefore to fight against neighbors is evil, and against the Thebans is against neighbors, it is clear that for the Thebans to fight is evil. Since therefore b is present in c, it is clear; for both are to wage war against neighbors, and that a is present in d, for the war against the Phocians was not useful for the Thebans. But that a is present in b will be shown through d. In the same way also, if proof of the middle in relation to the extreme is made through several similar cases. It is clear therefore that an example is neither as whole to part, nor as part to whole, but as part to part, when both are present under the same term and one of them is known. And it differs from induction, because induction showed from all individual cases that the extreme is present in the middle and did not join the syllogism to the extreme, whereas this does join it and does not show it from all cases.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":170,"ref":"p170","source":"CAPUT XXV.\n\nDe apagoge deductioneque.\n\nDeductio autem quando medio quidem primum palam est inesse, postremo autem medium dubium quidem similiter autem credibile aut magis conclusione. AmpIius,si pauciora sunt mediapostremoetmedio, omnino enim propinquius esse accidit scientiæ.Ut sit a docibile, in quo disciplina, justitia, ergo disciplina quoniam docibiIis,manifestum; justitia autem si disciplina,dubium.Si if!itur similiter aut magis credibile sit quam a c,deductio est, propinquius enim scientiæ,per quod assumpserint a c, disciplinam prius non babentes.Aut rursum si pauciora media sint c, nam et sic propinquius est scientiæ. Ut si sit quadrangulare,in quo autem e rectilineum,in quo j circulus,si ergo ejus quod est et unum solum sit medium,per lunares figuras æqualem fieri rectilineo circulum propinquius erit scientis. Quando autem neque credibilius est quam a c, neque pauca media, non dico deductionem, neque quando immediata est c, disciplina enim quod hujusmodi est.","english":"CHAPTER XXV.\n\nOn reduction and deduction.\n\nReduction, however, is when it is clear that the first term is present in the middle, but it is doubtful, though similarly or more credible than the conclusion, that the middle is present in the last term. Further, if the middle terms between the last term and the middle are fewer, for it happens to be altogether closer to knowledge. For example, let A be teachable, in which is discipline; let C be justice. That discipline is teachable is manifest; but whether justice is discipline is doubtful. If, then, it is similarly or more credible than the conclusion A C, there is a reduction; for that through which they have assumed A C is closer to knowledge, since they did not previously have discipline. Or again, if the middle terms of C are fewer, for in this way too it is closer to knowledge. For example, if it be a quadrilateral figure, in which is E, a rectilinear figure, in which is F, a circle: if, then, there is only one middle term of that which is E, that the circle is made equal to a rectilinear figure through lunular figures will be closer to knowledge. But when it is neither more credible than the conclusion A C, nor are the middle terms few, I do not call it a reduction, nor when C is immediate; for knowledge is of what is of this sort.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":171,"ref":"p171","source":"CAPUT XXVI.\n\nDe instantia,quam enstasin dicunt.\n\nInstantia autem est propositio propositioni contraria.Dilfert autem a propositione,quoniam contingit quidem instantiam esse in parte, propositionem vero aut omnino non contingit,aut non in universalibus syllogismus. Fertur autem instantia duobus modis et per duas figuras: duobus modis quidem, quoniam aut universalis aut particularis omnis instantia; per duas autem figuras, quoniam oppositae feruntur propositioni, opposita autem in prima et tertia figura perficiuntur soIis.Nam quando postutatur omni inesse, instamus quoniam nulli, aut quoniam alicui non inest. Horum autem nulli quidem ex prima figura, alicui autem non ex postremat Ut sit a unam esse disciplinam, in quo contraria; proponit ergo unam esse contrariorum discipIinam, aut quoniam omnino non est eadem oppositorum instant. Contraria al1lem opposita,quare fit prima llgura; aut quoniam noti et ignoti non una, haec autem tertia.","english":"CHAPTER XXVI.\n\nOn objection, which they call enstasis.\n\nAn objection is a proposition contrary to a proposition. It differs from a proposition because an objection may be partial, whereas a proposition either cannot be so at all, or the syllogism does not proceed in universals. An objection is brought in two ways and through two figures: in two ways, because every objection is either universal or particular; through two figures, because objections are brought against a proposition, and opposites are established only in the first and third figures. For when it is claimed that something belongs to every, we object that it belongs to none, or that it does not belong to some. Of these, the one that it belongs to none is from the first figure, but that it does not belong to some is from the last. For example, let A be that there is one science, in which case there are contraries; he therefore proposes that there is one science of contraries, or objects that it is not at all the same [science] of opposites. But contraries are opposites, and so the first figure results; or [he objects] that there is not one [science] of the known and the unknown, and this is the third.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":172,"ref":"p172","source":"Nam secundum tertiam notum et ignotum contraria quidem esse verum, unam autem esse eorum disciplinam, falsum.Rursum in privativa propositione similiter: cum postulat enim non esse contrariorum unam disciplinam, aut quoniam omnium oppositorum, aut quoniam contrariorum aliquorum est eadem discipHna,dicimus, ut sani et ægri, ergo omnium quideru ex prima, aliquorum vero ex tertia figura, Simpliciter autem in umnibus universaliter quidem instantibus, necesse est ad id quod nniversaie est proposito contradictionem dicere (ut. si non unam existimet contrariorum omnium, dicere oppositorum unam; sic autem necessse est primam esse figuram, medium enim fit universale ad hoc quod ex principio); quod autem ad hoc in parte est universale, dicitur propositio, ut noti et ignoti non eadem, nam contraria universale ad bæc, et fit tertia figura, medium enim in parte sumptum, ut notum et ignotum. Nam ex quibus est syllogizare contrarium, ex iis et iastantias conamus dicere, quare et ex his solis figuris ferimus,nam in his solis oppositi syllogismi,per mediam enim figuram non fuit arfirmare.Amplius autem et si sit,oratione indiget pIurima, quæ est per mediam figuram, ut si non concedant a inesseb,eo quod non sequitur hoc c, hoc enim per alias propositiones manifestum; non oportet autem instantiam converti ad alia, sed statim manifestam habere alteram propositionem.","english":"For according to the third figure, it is false that contraries are both known and unknown, and that there is one discipline of them. Again, similarly in a privative proposition: for when he demands that there is not one discipline of contraries, either because it is the same discipline of all opposites, or because it is the same discipline of some contraries, we say, as of the healthy and the sick, that it is of all indeed from the first figure, but of some from the third figure. But simply in all cases, when someone objects universally, it is necessary to state a contradiction to the proposition that is universal (for example, if he thinks there is not one discipline of all contraries, to say that there is one of opposites; and thus it is necessary that the first figure result, for the middle term becomes universal in relation to that which is from the principle); but what is universal in relation to this in part is called a proposition, as that the known and the unknown do not have the same discipline, for the contrary is universal in relation to these, and the third figure results, for the middle term is taken in part, as known and unknown. For from the same premises from which it is possible to syllogize the contrary, we also attempt to state objections; wherefore we also bear them from these figures alone, for in these alone are there opposite syllogisms, for through the middle figure it was not possible to affirm. Moreover, even if it were, it requires a very great deal of argument, which is through the middle figure, as if they do not concede that a is in b, because this c does not follow, for this is made clear through other propositions; but an objection ought not to be converted to other things, but immediately to have the other proposition manifest.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":173,"ref":"p173","source":"Quapropter et signum ex sola hac figura non est. Perspiciendum autem et de aliis instantiis, ut de iis qua? sunt ex contrario, et simili, et secundum opinionem, et si particularem ex prima, vel privativam ex media possibile est sumere.\n\nCAPUT XXVII.\n\nDe eicote, enthymemate. hoc est consentaneo signo, indicio, et\n\nEicos autem et signum non idem est, sed eicos quidem est propositio probabilis. Quod enim ut in pluribus sciunt sit factum;vel non factum, aut esse vel non esse, hoc est eicos, ut odire invidentes, vel diligere amantes.Signum autem vultesse;propositio demonstrativa, vel necessaria,vel probabilis; nam quo ex;stente est, vel quo facto prius vel posterius res,signum est vel fuissevel esse.Enthymema ergo est syllogismus imperfectus ex eicotibus et signis. Accipitur autem signum tripliciter,quoties et medium in figuris,aut enim ut in prima, aut ut in me. dia,aut ut in tertia: ut ostendere quidem parientem esse, eo quod lac babeat, ex prima figura, medium enim lac habere,in quo a parere b, lac habere mulicr in quo c.Quoniam autem sapientes,studiosi,narn Pittacus est studiosus, per postremam, in quo a studiosum, in quo sapientes, in quo Pittacus. Verum igitur etbde praedicari; sed hocquidem non dicunt quia notum sit,illud vero sumunt.","english":"Wherefore the sign is not from this figure alone. But one must also examine the other objections, as concerning those which are from contraries, and from similitude, and according to opinion, and whether it is possible to take a particular from the first figure, or a privative from the middle.\n\nCHAPTER XXVII.\n\nOn the eikos and the enthymeme, that is, the consentaneous sign, the indication, and\n\nThe eikos and the sign are not the same, but the eikos is a probable proposition. For that which they know happens as in the majority of cases—either done or not done, or being or not being—this is the eikos, as that the envious hate, or that lovers love. But the sign wishes to be a demonstrative proposition, either necessary or probable; for when that of which it is the sign exists, or when it has been done, the thing is either prior or posterior, and it is a sign either of having been or of being. The enthymeme, therefore, is an imperfect syllogism from eikota and signs. But the sign is taken in three ways, as often as the middle term is in the figures: for either as in the first, or as in the middle, or as in the third. For example, to show that she who has given birth is so, from the fact that she has milk, is from the first figure; for the middle term is having milk, in which a is having given birth, b is having milk, and the woman in which is c. But that the wise are studious—for Pittacus is studious—is through the last figure, in which a is the studious, in which the wise, in which Pittacus. Therefore it is true that b is predicated of c; but this they do not say because it is known, while that they assume.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":174,"ref":"p174","source":"Peperisse autem quoniam pallida,per mediam figuram vult esse; quoniam enim sequitur parientespallor, sequilur autem et hanc, ostensum esse arbitrantur quoniam peperit. Pallor in quo a, parere in quo b. mulier in quo c, Ergo si una quidem dicatur propositio,signurn fit solum, si autem et altera sumitur, syllogismus.Ut Pittacus liberalis, nam ambitiosi Iiberales,Pittacus autem ambiti05uS.Aut rursus,quoniam sapientes b01Ji, Pittacus autem bonus, sed et sapiens, sic ergo fiunt syllogismi. Verum quidem per primam figuram insolubilis, si verus sit, universalis enim est. Qui autem per postremam, est soIubilis,et si vera sit conclusio,eo quod non universaIis, est in tertia, nee ad rem syllogismus, non enim si Pittacus est studiosus, propter hoc et alios necesse est esse sapienles.Qui vera per mediarnfiguram est,semper et omnino solubilis nunquam enim sylIogismusfit,sic se habentibusterminis.Non enim si quæ peperit paIlida,pa lida autem et hæc,necesse est parere hanc; ergo verum est quidem in omnibus figUflS, differentias autem habent jam dictas. An igitur sic dividendum sign um?horumautem medium indicium surnendum,nam indicium dicunt esse quod scire facit, tale autem maxime medium, an vero quae quidem ab extremitatibus signa dicenda,quæ autem ex medio indicium? probabilissimum enim et maxime veram est quod est perprimam figuram.","english":"That she has given birth, because she is pale, he wants to establish through the middle figure; for since pallor follows upon those who have given birth, and this woman is also pale, they think it has been shown that she has given birth. Let pallor be A, having given birth be B, the woman be C. Therefore, if only one proposition is stated, a sign results; but if the other is also assumed, a syllogism results. As, for example, Pittacus is generous, for the ambitious are generous, and Pittacus is ambitious. Or again, that the wise are good, and Pittacus is good, but also wise; in this way, then, syllogisms are formed. The one through the first figure is indeed irrefutable, if it is true, for it is universal. But the one through the last figure is refutable, even if the conclusion is true, because it is not universal; it is in the third figure, and the syllogism does not bear on the matter, for it is not because Pittacus is studious that others must also be wise. The one through the middle figure is always and altogether refutable, for no syllogism results when the terms are so disposed. For it is not the case that if she who has given birth is pale, and this woman is also pale, this woman must have given birth. Therefore, it is true in all the figures, but they have the differences already stated. Should the sign, then, be divided in this way? But of these, the middle must be taken as the indication, for they call an indication that which makes one know, and such is especially the middle term; or should those from the extremes be called signs, and those from the middle an indication? For what is through the first figure is most probable and most true.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":175,"ref":"p175","source":"CAPUT XXVIII.\n\nDe syllogismo physiognomico.\n\nNaturas autem cognoscere possibile est, si quis concedat simul transmutare corpus etanimam,quæcunque sunt naturales passiones; discens enim aliquis fortasse musicam, transmutavit secundum quid animam,sed non earum quae naturanobisinsunt,bæc est passio, sed ut irae et concupiscentiæ, et naturalium motionurn.Si igitur et hoc det,et unum unius signum esse,et possumus sumere proprium uniuscujusque generis passionem et signum, poterimus naturas cognoscere.Si enim est proprie alicum generi individuo existens passio, ut si leonibus fortitudo, necesse est et signum esse aliquod, compati enirn sibi invicem positum est,et sit hoc magnas summitates habere, quod et aliis generibus,non totis contingit.Nam signum sic propriurn est,quoniam totius generis propria passio est, et non solius proprium, sicut solemus dicere.Erit ergo et in alio genere hoc, eterit fortis homo, et aliquod aliud animal; habebit ergo signum, unum enim unius erat. Si ergo bæc sunt,poterimus talia signa colligere in iis animatibus quae solum unam passionem habent aliquam propriam,unaquæque autem hahet signum,et quoniam unum habere necesse est,poterimus naturas cognoscere.Si vero duo habet propria totum genus, ut leo, forte et communicativum, quomodo cognoscemus utrum utrius sit signum,eorum signorum quae proprie sequuntur?","english":"CHAPTER XXVIII.\n\nOn physiognomic syllogism.\n\nIt is possible to know natures if one grants that body and soul change together in whatever natural affections there are; for someone learning music has perhaps changed his soul in some respect, but this is not one of the affections that are natural to us, but rather such things as anger and desire, and natural motions. If, then, one grants this too, and that one thing is the sign of one thing, and we can grasp the proper affection of each kind and its sign, we shall be able to know natures. For if there is an affection that belongs properly to some one kind, as strength to lions, there must also be some sign of it; for it is laid down that they are affected in sympathy with one another, and let this be having great extremities, which also happens to other kinds, though not to all. For a sign is proper in this way, because the affection is proper to the whole kind, and not proper to it alone, as we are accustomed to say. Therefore this will also be in another kind, and there will be a strong man, and some other animal; it will therefore have the sign, for one thing was the sign of one thing. If, then, these things are so, we shall be able to collect such signs in those animals that have only one proper affection, and each has a sign, and since it is necessary to have one, we shall be able to know natures. But if the whole kind has two proper affections, as a lion perhaps has both strength and a capacity for sharing, how shall we know which of the signs that properly follow is the sign of which?","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]},{"i":176,"ref":"p176","source":"An si et alii alicui non toti ambo,et in quibus non lotis utrumque,quando hoc quidem habet,illud autem non?nam sifortis quidem, liberalis autem non,habet autem duorum hoc,palam quoniam et in leone hoc signum fortitudinis.Est vero naluras cognoscere in prima quidem flgura,eo quod medium priori extremitati convertitur, tertiam autem transcendit,et non convertitur,ut sit fortitudo a, summitates magnas habere in quo b, autem leo; ergo cui c, omni, sed et aliis,cui autem b, a omni, et non pluribus, sed; convertitur si autem non, non erit unum unius signum.","english":"Or if both are not present in some other whole, and in those in which both are not present, when one has this, the other does not? For if he is brave but not generous, and he has one of the two, it is clear that this is also a sign of bravery in the lion. But it is possible to know natures in the first figure, because the middle term is converted with the first extreme, and it transcends the third and is not converted, so that bravery is a, having great extremities is in what b is, and the lion is c; therefore it belongs to every c, but also to others; and a belongs to every b, and not to more, but; if however it is not converted, there will not be one sign of one thing.","structure":"narrative","commentary":[],"ambiguities":[],"confidence":"","notes":[]}]}