Authors/Ockham/Summa Logicae/Book III-1/Chapter 28

Latin	English
Cap. 28. De uniformi ex propositionibus de contingenti in tertia figura	Chapter 28. On the uniform syllogism from propositions de contingenti in the third figure.
In tertia figura si ambae praemissae sumantur in sensu divisionis et subiectum utriusque supponat pro his quae sunt, sequitur conclusio de contingenti, sumpto subiecto conclusionis pro eo quod contingit non pro eo quod est. Nam sequitur ‘omnem hominem contingit esse album; omnem hominem contingit esse scientem; igitur quod contingit esse scientem, contingit esse album’. Sed non sequitur ista conclusio ‘quod est sciens, contingit esse album’, nam posito quod nullus homo aliquid sciat sed tantum angelus, praemissae sunt verae et conclusio falsa.	In the third figure if both premises are taken in the sense of division and the subject of both supposits for things that are, a conclusion de contingenti follows, taking the subject of the conclusion for that which is contingent not for that which is. For it follows ‘every man is contingent to be white; every man is contingent to be knowing; therefore a thing that is contingent to be knowing, is contingent to be white’. But this conclusion ‘a thing that is knowing, is contingent to be white’ does not follow, for if it is assumed that no man knows anything but only an angel, the premises are true and the conclusion false.
Similiter, posito quod tantum equus sit albus, tunc sunt istae praemissae verae ‘omne risibile contingit esse hominem; omne risibile contingit esse album’, et haec conclusio est falsa ‘quod est album, contingit esse hominem’, cum quaelibet singularis sit falsa.	Similarly, assuming that only a horse is white, then these premises are true: ‘every thing that can laugh happens to be a man; every thing that can laugh happens to be white’, and this conclusion is false: ‘a thing that is white happens to be a man’, since each singular is false.
Similiter, si subiectum. utriusque praemissae supponat pro his quae contingunt, sequitur conclusio de contingenti, sumpto subiecto pro his quae contingunt, non pro lus quae sunt. Quod patet per praecedens exemplum. Similiter, si subiectum in una supponat pro his quae sunt et in alia pro his quae contingunt, sequitur consimilis conclusio.	Similarly, if the subject of both premises supposits for things that are contingent, a conclusion de contingenti follows, taking the subject for things that are contingent, not for things that are. This is clear from the preceding example. Similarly, if the subject in one supposits for things that are and in the other for things that are contingent, a similar conclusion follows.
Sed si una praemissarum sumatur in sensu compositionis et alia in sensu divisionis, non sequitur conclusio. Non enim sequitur omnem hominem esse Deum est contingens; omnem hominem contingit esse humanitatem; igitur aliquam humanitatem contingit esse Deum’, et hoc si subiectum minoris sumatur pro his quae sunt; nam praemissae sunt verae et conclusio falsa.	But if one of the premises is taken in the sense of composition and the other in the sense of division, the conclusion does not follow. For it does not follow: that every man is God is contingent; it is contingent for every man to be human; therefore it is contingent for some human to be God,' and this if the subject of the minor is taken for those things which are; for the premises are true and the conclusion false.
Quod enim maior sit vera, patet: nam ista ‘omnis homo est Deus’ est modo falsa, et tamen potest esse vera, nam si nullus homo esset nisi Christus, tunc haec esset vera; igitur haec est contingens ‘omnis homo est Deus’; igitur maior est vera. Etiani posito quod natura assumpta a ƿ Verbo esset deposita, tunc esset minor vera, quia tunc omnis humanitas esset homo. Quia suppono ad praesens, quod alias est probatum, quod haec est vera de virtute sermonis ‘omnis homo est humanitas’, nisi ‘humanitas’ includat aliquod syncategorema vel aequivalenter aliquod complexum propter quod falsificetur. Sed hoc non impedit propositum, quia volo quod hoc nomen ‘humanitas’ semper supponat pro illa natura creata sine inclusione tali quacumque. Et tunc patet quod minor est vera. Et tunc tamen erit conclusio falsa, nam illa natura creata nullo modo potest esse Deus. Unde de facto, quamvis homo sit Deus, tamen illa natura creata non est Deus, sicut quamvis album sit homo, tamen illa albedo inhaerens homini non est homo.	For that the major is true is clear: for this ‘every man is God’ is only false, and yet it can be true, for if there were no man but Christ, then this would be true; therefore this is the contingent ‘every man is God’; therefore the major is true. Etianus, assuming that the nature assumed by the Word had been deposited, then the minor would be true, because then all humanity would be man. For I suppose for the present, which otherwise has been proven, that this is true literally ‘every man is humanity’, unless ‘humanity’ includes some syncategorematic term or equivalently some complex because of which it is falsified. But this does not hinder the proposition, because I want this name ‘humanity’ to always stand for that created nature without any such inclusion. And then it is clear that the minor is true. And then nevertheless the conclusion will be false, for that created nature can in no way be God. Hence, in fact, although man is God, yet that created nature is not God, just as although some white thing is a man, yet that whiteness inherent in a man is not a man.
Per idem patet quod si maior accipiatur in sensu divisionis et minor in sensu compositionis, syllogismus non valet. Similiter, si subiectum propositionis acceptae in sensu divisionis supponat pro his quae contingunt, non valet syllogismus. Non enim sequitur ‘omne quod contingit esse ens, contingit creari; haec est contingens: omne ens est Deus; igitur Deum contingit creari’. Utrum autem ista propositio ‘omne ens contingit creari’ possit de virtute sermonis habere talem sensum ‘'omne quod contingit esse ens, contingit creari’ non est modo curandum, quia illa foret magis difficultas vocalis quam realis, eo quod voces sunt ad placitum. Sic igitur patet quomodo contingit arguere ex illis de contingenti in tertia figura.	By the same token, it is clear that if the major is taken in the sense of division and the minor in the sense of composition, the syllogism is not valid. Similarly, if the subject of a proposition taken in the sense of division supposits for things that are contingent, the syllogism is not valid. For it does not follow that ‘everything that happens to be a being is contingently created; this is contingent: every being is God; therefore God is contingently created’. But whether this proposition ‘everything that happens to be a being is contingently created’ can literally have such a sense as ‘everything that happens to be a being is contingently created’ is not something we need to worry about at this time, because that would be more of a verbal difficulty than a real one, because the words are at will. Thus, it is clear how it is contingent to argue from them de contingenti in the third figure.
Probat Aristoteles talem syllogismum in libro Priorum per conversionem minoris propositionis, ut si arguatur sic ‘contingit omne b esse a; contingit omne b esse c; igitur contingit aliquod c esse a ; nam conversa minore, sic ‘contingit omne b esse et igitur contingit aliquod c esse b’ erit uniformis in prima figura, sic ‘contingit omne b esse a; contingit aliquod c esse b; igitur contingit aliquod c esse a’. Et ita talis uniformis in tertia figura de contingenti reducitur in primam figuram per conversionem,	Aristotle proves such a syllogism in the book Prior Analytics by the conversion of the minor proposition, as if it were argued thus ‘it happens that every b is a; it happens that every b is c; therefore it happens that some c is a; for conversely, thus ‘it happens that every b is and therefore it happens that some c is b’ will be uniform in the first figure, thus ‘it happens that every b is a; it happens that some c is b; therefore it happens that some c is a’. And thus such a uniform syllogism in the third figure is reduced de contingenti to the first figure by conversion,
Sed istud videtur repugnare prius dicto. Dictum est enim ƿ in praecedenti tractatu quod ista de contingenti, sumpto subiecto pro eo quod est, non convertitur in illam de contingenti; igitur talis syllogismus in tertia figura non potest praedicto modo probari.	But this seems to contradict what was said before. For it was said in the preceding treatise that this de contingenti, taking the subject for what it is, is not converted into that de contingenti; therefore such a syllogism in the third figure cannot be proved in the aforementioned way.
Dicendum quod Aristoteles per istam conversionem non probat nisi uniformem de de contingenti in tertia figura, subiecto utriusque praemissae accepto pro his quae contingent praecise. Et illa de contingenti, accepto subiecto praecise pro his quae contingunt, convertitur in illam de contingenti, subiecto consequentis sumpto eodem modo. Et ita probatio Aristotelis est sufficiens ad intentum suum, nec repugnat dicto meo priori.	It should be said that Aristotle, by this conversion, proves only a uniform de contingenti in the third figure, with the subject of both premises taken as precisely those things that are contingent. And that de contingenti, with the subject taken as precisely those things that are contingent, is converted into that de contingenti, with the subject of the consequent taken in the same way. And thus Aristotle's proof is sufficient for his intention, and does not contradict what I said before.
Alii autem uniformes, de quibus dictum est quod tenent, non probantur illo modo. Ex dictis tamen Philosophi in illo loco et in aliis partibus logicae potest elici probatio eorum.	But other uniform propositions, of which it was said that they hold , are not proved in that way. However, from what the Philosopher says in that place and in other parts of logic, their proof can be elicited.
Ad cuius evidentiam est sciendum quod propositio de contingenti potest habere triplicem sensum penes acceptionem subiecti. Potest enim subiectum accipi praecise pro his quae sunt; potest etiam accipi tam pro his quae sunt quam pro his quae contingunt; et tertio modo potest accipi praecise pro his quae contingunt. Utrum autem isti duo sensus ultimi sint de virtute sermonis vel alter tantum, et si alter tantum, quis eorum, non curo ad praesens. Tamen prius locutus sum, quando dixi uniformem valere, secundum duos primos sensus. Et tunc quando subiectum alterius, scilicet maioris, accipitur pro his quae sunt, probatur talis syllogismus per conversionem minoris in illam de inesse, sic arguendo ‘contingit omnem hominem esse album; contingit omnem hominem esse scientem; igitur contingit scientem esse album’, convertitur ista minor ‘contingit omnem hominem esse scientem’ - subiecto stante praecise pro his quae sunt - in istam ‘aliquid, quod contingit esse scientem, est homo’. Nunc autem sequitur evidenter in prima figura ‘omnem hominem contingit esse album; - subiecto supponente praecise pro his quae ƿ sunt -; aliquid, quod contingit esse scientem, est homo; igitur illiquid, quod contingit esse scientem, contingit esse album’, quae aequivalet conclusioni primi syllogismi. Et ex isto et ista proposition ‘illa de contingenti subiecto supponente praecise pro his quae sunt, convertitur in illam de inesse’, cum ista regula infallibili ‘quidquid sequitur ad consequens, sequitur ad antecedens’ patent evidenter omnes propositiones omnium aliorum.	To make this clear, it should be known that a proposition de contingenti can have a threefold sense depending on the subject. For the subject can be taken precisely for things that are; it can also be taken both for things that are and for things that are contingent; and in a third way it can be taken precisely for things that are contingent. But whether these last are literally two senses or only one, and if only one, which of them, I do not care for the present. However, I spoke earlier, when I said that a uniform one is valid, according to the two first senses. And then when the subject of the other, namely the major, is taken for things that are, such a syllogism is proven by converting the minor into that assertoric, thus arguing ‘it happens that every man is white; it happens that every man is knowing; therefore it happens that a knowing man is white’, this minor ‘it happens that every man is knowing’ - with the subject standing precisely for things that are - is converted into that ‘something that happens to be knowing is a man’. Now, however, it follows clearly in the first figure ‘it happens that every man is white; - with a subject suppositing precisely for those things which are -; something which happens to be knowing is a man; therefore a thing which happens to be knowing happens to be white’, which is equivalent to the conclusion of the first syllogism. And from this and that proposition ‘that de contingenti subject suppositing precisely for those things which are, is converted into the assertoric’, with that infallible rule ‘whatever follows from the consequent, follows from the antecedent’ all propositions of all the others are evidently clear.
Sed si subiectum maioris accipiatur praecise pro his quae contingent et subiectum minoris praecise pro his quae sunt, uniformis non valet. Sicut non sequitur ‘omne quod contingit esse ens, contingit creari; omne quod est ens, contingit esse creantem; igitur aliquid, quod contingit esse creantem, contingit creari’, quia si nihil esset nisi Deus, praemissae essent verae et conclusio falsa. Et si minor sumatur particulariter, praemissae de facto erunt verae et conclusio falsa. Istud tamen exemplum tantum exempli gratia adducitur. Similiter, si transponantur tales propositiones diversimode acceptae, non valet. Patet igitur quando contingit arguere ex omnibus de contingenti et quo modo.	But if the subject of the major is taken precisely for those things that are contingent and the subject of the minor precisely for those things that are, the uniform syllogism is not valid. Just as it does not follow that ‘everything that happens to be a being happens to be created; everything that is a being happens to be creating; therefore something that happens to be creating happens to be created’, because if there were nothing but God, the premises would be true and the conclusion false. And if the minor is taken particularly, the premises would in fact be true and the conclusion false. However, this example is only given for the sake of example. Similarly, if such propositions are transposed, taken in different ways, they are not valid. It is therefore clear when it is possible to argue from all de contingenti and in what way.
Est etiam intelligendum quod sicut in prima figura non refert arguere ex omnibus affirmativis de contingenti et negativis, nisi quod negativus syllogismus perficitur per conversionem propositionum negativarum per oppositas qualitates, ita in tertia figura contingit arguere eodem modo ex omnibus negativis vel indifferenter ex altera, et perficiuntur tales syllogismi per conversionem per oppositas qualitates.	It should also be understood that just as in the first figure, it does not matter to argue from all affirmatives de contingenti and negatives, except that a negative syllogism is completed by converting negative propositions through opposite qualities, so in the third figure it is possible to argue in the same way from all negatives or indifferently from the others, and such syllogisms are completed by converting through opposite qualities.