Authors/Ockham/Summa Logicae/Book III-1/Chapter 10

 

Latin	English
[Cap. 10. De syllogismis faciendis in secunda figura ex propositionibus de recto]	[Chapter 10.  On syllogisms that are to be made in the second figure, from direct propositions]
Post praedicta videndum est quomodo fit talis syllogismus in secunda figura ex propositionibus de recto.	After what was said before, we should see how such a syllogism is made in the second figure from direct [i.e. nominative] propositions.
Et est primo sciendum quod semper in secunda figura altera praemissarum debet esse negativa nisi in duobus casibus, de quibus dicetur inferius. Cuius ratio est, nam secunda figura est quando medius terminus praedicatur in utraque. Sed nunc est ita quod superius praedicatur universaliter de quolibet inferiori, ubi tamen unum inferius universaliter negatur a reliquo; igitur per tale medium, quod praedicatur de utroque, numquam potest concludi unum extremum affirmari de reliquo. Igitur per talem discursum praecise potest concludi unum extremum negari de reliquo, et per consequens oportet quod altera praeƿmissarum sit negativa, cum ex affirmativis numquam sequatur syllogistice conclusio negativa.	And first, it should be known that in the second figure always one of the premisses ought to be negative, except in two cases which will be discussed below.  The reason of this is that the second figure is when the middle term is predicated in both.  But now it is such that a superior is predicated universally of any inferior, yet where one inferior is universally denied of the other, then through such a middle, which is predicated of both, the conclusion can never be that one extreme is affirmed of the other.  Therefore, through such a discourse it can be concluded precisely that one extreme is denied of the other, and as a consequence it has to be that one of the premisses is negative, since from affirmatives a negative conclusion never follows syllogistically .
Secundo sciendum quod in secunda figura semper oportet quod maior sit universalis. Nam si maior esset particularis, sive affirmativa sive negativa, posset medium primo affirmari particulariter vel negari de superiori, et postea universaliter negari vel affirmari de inferiori ad illud superius; et tamen non sequeretur illud superius universaliter nec particulariter negari ab inferiori. Verbi gratia, cum hoc quod ‘animal’ particulariter affirmatur de ‘substantia’ et universaliter negatur a ‘lapide’, non sequitur quod ‘substantia’ universaliter vel particulariter negetur a ‘lapide’. Non enim sequitur ‘aliqua substantia est animal; nullus lapis est animal; igitur aliquis lapis non est substantia’.	Second, it should be known that in the second figure the major always has to be universal. For if the major were particular, whether affirmative or negative, the middle could first be particularly affirmed or denied of the superior, and then universally denied or affirmed of the inferior to that superior, and yet it would not follow that the superior would be universally or particularly denied of the inferior. For example, when 'animal' is particularly affirmed of 'substance', and universally denied of 'stone', it does not follow that 'substance' is universally or particularly denied of 'stone'.  For "some substance is an animal, no stone is an animal, therefore some stone is not a substance" does not follow.
Similiter, ex hoc quod ‘animal’ particulariter negatur a ‘substantia’ et universaliter affirmatur de ‘homine’ non sequitur quod ‘substantia’ particulariter negatur ab ‘homine’. Non enim sequitur ‘aliqua substantia non est animal; omnis homo est animal; igitur aliquis homo non est substantia’. Et ratio quare maior in secunda figura non potest esse particularis, est quia unum inferius, puta a, potest particulariter negari a suo superiori, puta a b, et illud praedicatum inferius, scilicet a, potest universaliter negari a c quod est inferius ad b, et universaliter affirmari de d, quod est etiam inferius ad b; et tamen illud superius, scilicet b, a nullo suo inferiori vere negatur, nec universaliter nec particulariter. Sicut ‘animal’ particulariter negatur a ‘substantia’ et universaliter negatur a ‘lapide’ et universaliter praedicatur de ‘homine’, et tamen ‘substantia’ praedicatur de omnibus istis universaliter.	Similarly, from 'animal' being particularly denied of 'substance', and universally affirmed of 'man', it does not follow that 'substance' is particularly denied of 'man'.  For "some substance is not an animal, every man is an animal, therefore some man is not a substance" does not follow.  And the reason why the major in the second figure cannot be particular, is that one inferior, e.g. a, can be particularly denied of its superior, e.g. of b, and that inferior predicate, namely a, can be universally denied of c that is inferior to b, and universally affirmed of d, that is also inferior to b, and yet that superior, namely b, is truly denied of nothing inferior to it, either universally or particularly.  For example, 'animal' is particularly denied of 'substance', and universally denied of 'stone', and is universally predicated of 'man', and yet 'substance' is universally predicated of all of these.
Ex istis duobus sequitur quod in secunda figura non sunt nisi quatuor modi coniugationum utilium, directe concludentium. Nam si utraque praemissa sit negativa, possunt fieri quatuor combinationes per universale et particulare, sed quaelibet erit inutilis, quia semper oportet alteram praemissarum esse affirmativam. Si etiam utraque sit affirmativa, possunt fieri quatuor combinationes per universale et particulare, sed quaelibet erit inutilis, quia dictum est quod in secunda figura ƿ oportet alteram praemissarum esse negativam. Et ita habemus quatuor coniugationes inutiles. Si autem una sit affirmativa et alia negativa, aut igitur maior est affirmativa et minor negativa, vel e converso. Si primo modo, possunt fieri quatuor combinationes per particulare et universale, quia aut utraque est universalis, et tunc habetur secundus modus utilis, scilicet Camestres, in quo maior est universalis affirmativa et minor universalis negativa.	And from these two things it follows that in the second figure, there are only four modes of useful combinations, concluding directly.  For if both premisses are negative, there can be four combinations of universal and particular, but each will be useless, because one of the premisses always has to be affirmative.  If both are also affirmative, there can be four combinations of universal and particular, but each will be useless, because it was said that in the second figure one of the premisses has to be negative.  And so we have four useless combinations. But if one is affirmative and the other negative, then either the major is affirmative and the minor negative, or conversely.  If the first, there can be four combinations of particular and universal, because either both are universal, and then we have the second useful mode, namely Camestres, in which the major is universal affirmative and the minor universal negative.
Aut utraque est particularis, et tunc est coniugatio inutilis, quia dictum est quod semper maior debet esse universalis. Aut maior est universalis affirmativa et minor particularis negativa, et tunc est quartus modus, scilicet Baroco. Aut maior est particularis et minor universalis, et tunc est coniugatio inutilis, quia dictum est quod maior debet esse universalis. Si autem sit e converso, scilicet quod maior est negativa et minor affirmativa, adhuc possunt fieri quatuor combinationes per particulare et universale, quia aut utraque est universalis, et sic habetur primus modus secundae figurae, in quo maior est universalis negativa et minor universalis affirmativa, scilicet Cesare. Aut utraque est particularis, et tunc est coniugatio inutilis, propter causam saepius dictam. Aut maior est universalis et minor particularis, et habetur tertius modus, scilicet Festino. Aut maior est particularis et minor universalis, et sic est coniugatio inutilis, propter causam superius dictam.	Either both are particular, and then the conjugation is useless, because it was said that the major must always be universal. Or the major is universal affirmative and the minor particular negative, and then there is a fourth mode, namely Baroco. Or the major is particular and the minor universal, and then the conjugation is useless, because it was said that the major must be universal. But if it is the other way around, namely that the major is negative and the minor affirmative, four combinations can still be made through the particular and the universal, because either both are universal, and thus we have the first mode of the second figure, in which the major is universal negative and the minor universal affirmative, namely Cesare. Or both are particular, and then the conjugation is useless, for the reason often stated. Or the major is universal and the minor particular, and then there is a third mode, namely Festino. Or the major is particular and the minor universal, and thus the conjugation is useless, for the reason stated above.
Sic igitur patet quod cum non possint fieri nisi sexdecim combinationes per istas quatuor differentias ‘universale-particulare’, ‘negativum-affirmativum’, duodecim sunt inutiles et quatuor tantum utiles. Quarum exempla sunt ista ‘nullus lapis est animal; omnis homo est animal; igitur nullus homo est lapis’; ‘omnis homo est rationalis; nullus asinus est rationalis; igitur nullus asinus est homo’; ‘nullus homo est lapis; quaedam substantia est lapis; igitur quaedam substantia non est homo'; ‘omnis homo est animal; quaedam substantia non est animal; igitur quaedam substantia non est homo’.	Thus it is clear that since only sixteen combinations can be made through these four differences ‘universal-particular’, ‘negative-affirmative’, twelve are useless and only four are useful. Examples of which are these: ‘no stone is an animal; every man is an animal; therefore no man is a stone’; ‘every man is rational; no donkey is rational; therefore no donkey is a man’; ‘no man is a stone; a certain substance is a stone; therefore a certain substance is not a man’; ‘every man is an animal; a certain substance is not an animal; therefore a certain substance is not a man’.
ƿ Exempla coniugationum inutilium sunt ista 'omnis homo est animal; omnis asinus est animal; igitur omnis asinus est homo'. Et est inutilis, quia cum praemissis stat quod nullus asinus est homo. Et hoc exemplum sufficit ad probandum quod ex omnibus affirmativis, qualitercumque combinentur per universale et particulare, non contingit arguere in secunda figura, ex quo cum ambabus universalibus stat universalis negativa de eisdem extremis. Pro omnibus ex omnibus negativis sit illud exemplum ‘nullum animal est albedo; nullus homo est albedo’ et stat quod ‘omnis homo est animal’. Et sic habemus octo coniugationes inutiles. Pro aliis quatuor sunt ista exempla ‘quaedam substantia non est animal; omnis homo est animal’ et stat quod ‘omnis homo est substantia’; ‘quaedam substantia est animal; nullus lapis est animal’ et stat quod ‘omnis lapis est substantia’. Et ista eadem exempla sufficiant ad probandum quod alii duo, quorum uterque est ex una particulari affirmativa et particulari negativa, non valent.	Examples of useless conjunctions are 'every man is an animal; every donkey is an animal; therefore every donkey is a man'. And it is useless, because with the premises it stands that no donkey is a man. And this example suffices to prove that from all affirmatives, however they are combined by universal and particular, it is not possible to argue in the second figure, from which with both universals a universal negative stands about the same extremes. For all of all negatives let the example be 'no animal is whiteness; no man is whiteness' and it stands that 'every man is an animal'. And thus we have eight useless conjunctions. For the other four there are these examples 'a certain substance is not an animal; every man is an animal' and it stands that 'every man is a substance'; 'a certain substance is an animal; no stone is an animal' and it stands that 'every stone is a substance'. And these same examples suffice to prove that the other two, each of which is from one particular affirmative and one particular negative, are not valid.
Et est sciendum quod praedicti quatuor modi ita tenent in terminis accidentalibus sicut in terminis substantialibus. Immo, nihil penitus refert ad bonitatem syllogismi an termini sint substantiales an accidentales, et ideo commutatio unius praedicamenti in aliud vel quale quid in hoc aliquid vel e converso non facit fallaciam figurae dictionis nec fallaciam accidentis in praedictis, dummodo aliae circumstantiae debite observentur.	And it should be known that the aforementioned four modes hold in accidental terms as well as in substantial terms . Indeed, it has absolutely no bearing on the goodness of the syllogism whether the terms are substantial or accidental, and therefore the change of one category into another or of what kind of something into this something or vice versa does not create a fallacy of the figure of speech nor a fallacy of accident in the aforementioned, provided that other circumstances are duly observed.
Et ideo in talibus nulla est fallacia ‘omnis essentia divina intelligitur a me; nulla sapientia divina intelligitur a me; igitur nulla sapientia divina est essentia divina’; ‘omnis intellectus divinus est principium producendi Filium; nulla voluntas divina est principium proƿ ducendi Filium; igitur nulla voluntas divina est intellectus divinus’; ‘omnis voluntas divina est principium producendi Spiritum Sanctum; nullum velle divinum est principium producendi Spiritum Sanctum; igitur nullum velle divinum est voluntas divina’; ‘nullum veniens cognosatur a me; Coriscus cognoscitur a me; igitur Coriscus non est veniens’; ‘nulla differentia individualis est realiter communicabilis; omnis natura specifica est realiter communicabilis; igitur nulla natura specifica est realiter differentia individualis’.	And therefore in such there is no fallacy ‘every divine essence is understood by me; no divine wisdom is understood by me; therefore no divine wisdom is divine essence’; ‘every divine intellect is the principle of producing the Son; no divine will is the principle of producing the Son; therefore no divine will is divine intellect’; ‘every divine will is the principle of producing the Holy Spirit; no divine willing is the principle of producing the Holy Spirit; therefore no divine willing is divine will’; ‘noone coming is known by me; Coriscus is known by me; therefore Coriscus is not coming’; ‘no individual difference is really communicable; every specific nature is really communicable; therefore no specific nature is really an individual difference’.
Verumtamen si aliquis terminorum positorum in praedictis syllogismis vel in aliquo eorum includat aequivalenter aliquod syncategorema, quo expresso syllogismus non teneret quia non convenienter ordinaretur in modo et in figura, tunc talis syllogismus non valet. Sed hoc posset ita contingere in terminis substantialibus sicut in accidentalibus. Unde sic arguendo ‘omnis homo est risibilis; nulla humanitas est risibilis; ergo nulla humanitas est homo’, non valet si li humanitas includat aequivalenter hoc syncategorema ‘per se primo modo’. Et talis defectus posset hic assignari ‘nullus homo est animal; omne risibile est animal; igitur nullum risibile est homo', scilicet per alicuius determinati syncategorematis inclusionem per aequivalentiam.	However, if any of the terms posited in the aforementioned syllogisms or in any of them includes equivalently some syncategorematic term, which if expressed the syllogism would not hold because it would not be suitably ordered in mode and figure, then such a syllogism is not valid. But this could happen in substantial terms as well as in accidental terms. Hence, thus arguing ‘every man is laughable; no humanity is laughable; therefore no humanity is man’, it is not valid if humanity includes equivalently this syncategorematic term ‘per se in the first way’. And such a defect could be assigned here ‘no man is an animal; every laughable thing is an animal; therefore no laughable thing is man’, namely by the inclusion of some determined syncategorematic term by equivalence.
Ideo dicendum est quod sicut in prima figura, quando praemissae sunt dispositae in modo et in figura, non potest aliquis defectus plus assignari si omnes termini sint in genere accidentis, vel unus in genere substantiae et alius in genere accidentis, quam si omnes essent in genere substantiae vel omnes in aliquo uno praedicamento, ita etiam in secunda figura non plus peccat discursus quando fit in terminis accidentalibus praecise, vel ex uno termino substantiali et aliis accidentalibus sive e converso, quam si fieret in omnibus terminis substantialibus.	Therefore, it must be said that just as in the first figure, when the premises are arranged in mode and figure, no more defect can be assigned if all the terms are in the genus of accident, or one in the genus of substance and another in the genus of accident, than if all were in the genus of substance or all in some one predicate, so also in the second figure the discourse is no more faulty when it is made precisely in accidental terms, or from one substantial term and other accidental ones, or vice versa, than if it were made in all substantial terms.
Et ideo ubicumque servatur talis modus arguendi, est bonus syllogismus, nisi impediatur per aequivocationem vel per amphiboliam vel per compositionem et divisionem vel per accentum vel per hoc quod aliquis terminus est importans aliquam rem quae est plures res, cuiusmodi est ƿ essentia divina, vel per aliquem talem defectum, cuiusmodi ita potest inveniri in terminis substantialibus sicut in accidentalibus et e converso.	And therefore wherever such a manner of argument is observed, it is a good syllogism, unless it is hindered by equivocation or by amphiboly or by composition and division or by accent or by the fact that some term is implying some thing which is several things, such as the divine essence, or by some such defect, such as can be found in substantial terms as in accidental terms and vice versa.
Et ideo Philosophus, in libro Priorum, ad probandum aliquos modos coniugationum esse inutiles non tantum instat per terminos substantiales sed etiam per terminos accidentales, sicut per huiusmodi ‘album’, ‘nigrum’, ‘corvus’, ‘currens’, ‘movens’, ‘animal’ et huiusmodi; et ideo omnes syllogismi aequivalent in terminis accidentalibus sicut essentialibus. Et ideo errant qui volunt semper assignare fallaciam accidentis quando aliquid primo attribuitur rei subiectae et postea accidenti. Sic enim esset dicere quod hic esset fallacia accidentis ‘omnis homo est animal; aliquod album est homo; igitur aliquod album est animal’; et hic ‘nullus homo est albus; omne calidum est album; igitur nullum calidum est homo’. Quod nullus diceret, nisi qui ignoraret omnem modum arguendi.	And therefore the Philosopher, in the book 'Priorum' , insists on proving that some modes of conjugation are useless not only by substantial terms but also by accidental terms, as by such terms as 'white', 'black', 'raven', 'running', 'moving', 'animal' and the like; and therefore all syllogisms are equivalent in accidental terms as in essential terms. And therefore they err who always want to assign the fallacy of accident when something is first attributed to the subject and then to the accident. For thus it would be to say that here it would be a fallacy of accident ‘every man is an animal; something white is a man; therefore something white is an animal’; and here ‘no man is white; everything hot is white; therefore nothing hot is a man’. Which no one would say, except one who was ignorant of every method of argument.
Sciendum est etiam quod illae regulae quae dictae sunt prius circa primam figuram, sunt etiam servandae circa secundam. Et ideo tot modis potest fallere discursus in secunda figura et propter eosdem defectus propter quos in prima.	It should also be noted that those rules which were stated previously concerning the first figure, are also to be observed concerning the second. And therefore discourse in the second figure can be misleading in as many ways and because of the same defects as in the first.
Intelligendum est quod sicut ex praemissis aliquando in prima figura sequuntur plures conclusiones, et propter hoc ponuntur aliqui modi concludentes indirecte, ita est etiam aliquando in secunda figura. Unde ex praemissis utriusque syllogismi universalis sequuntur quatuor conclusiones, scilicet duae directe, videlicet universalis negativa et sua subalterna, et duae indirecte, scilicet conversa primae conclusionis universalis et subalterna ipsius. Ex praemissis autem syllogismorum particularium sequitur una conclusio sola, scilicet particularis negativa, quia illa non est convertibilis nec simpliciter nec per accidens. Sed ex praemissis de terminis transpositis et propositionibus transpositis non ƿ sequitur aliqua conclusio in secunda figura, quia tunc praemissae erunt in tertia figura dispositae.	It is to be understood that just as several conclusions sometimes follow from the premises in the first figure, and for this reason some indirect concluding modes are posited, so it is also sometimes in the second figure. Hence from the premises of each universal syllogism four conclusions follow, namely two directly, namely the universal negative and its subaltern, and two indirectly, namely the converse of the first universal conclusion and its subaltern. But from the premises of the particular syllogisms only one conclusion follows, namely the particular negative, because that is not convertible either simply or accidentally. But from the premises of transposed terms and transposed propositions no conclusion in the second figure follows, because then the premises will be arranged in the third figure.