Authors/Ockham/Summa Logicae/Book III-1/Chapter 42

Latin	English
Cap. 42. De mixtione talium modalium et de inesse in secunda figura	Chapter 42. On the mixture of such modes and assertoric in the second figure.
In secunda figura, si talis de modo accipiatur in sensu compositionis, raro vel numquam valet syllogismus quando modus addit aliquid ultra istum modum 'verum', cuiusmodi sunt tales modi 'scitum , 'demonstratum', 'per se notum', 'per se', 'primo verum' et huiusmodi. Quod autem mixtio talis non valeat, patet per instantiam in terminis. Noti enim sequitur, secundum opinionem Aristotelis, 'omnem hominem esse animal est per se; nullum album est animal; igitur nullum album esse hominem est per se'. Nec sequitur 'omnem personam divinam esse to Deum est per se; nullus homo est Deus; igitur nullum hominem esse personam divinam est per se'. Similiter non sequitur 'nullum hominem esse asinum est per se; omne album est asinus; igitur nullum album esse hominem est per se'. Nec sequitur 'nullam humanitatem esse Deum est per se; aliquis homo est Deus; igitur aliquem hominem non esse humanitatem est per se'. Et sicut est de isto modo 'per se', ita est de multis aliis.	In the second figure, if such a mode is taken in the sense of composition, the syllogism is rarely or never valid when the mode adds something beyond the mode 'true', of which kind are such modes as 'known,' 'demonstrated,' 'known in itself' 'per se,' 'primarily true' and the like. But that such a mixture is not valid is clear from the instance in the terms. For it follows from the known, according to Aristotle's opinion, 'that every man is an animal is per se; no white man is an animal; therefore no white man is a man is per se'. Nor does it follow 'that every divine person is a God is per se; no man is God; therefore no man is a divine person is per se'. Similarly it does not follow 'that no man is a donkey is per se; every white thing is a donkey; therefore no white man is a man is per se'. Nor does it follow 'that no human is God is per se; some man is God; therefore some man is not a human is per se'. And as is the case with this mode 'per se', so is the case with many others.
Si autem illa de modo accipiatur in sensu divisionis, vel aliqua aequivalens ei, sic etiam raro vel numquam valet mixtio, sive negativa sive affirmativa fuerit de modo, respectu conclusionis de consimili modo affirmato. Sicut non sequitur 'omne album scitur a Sorte esse homo; nullus asinus est homo; igitur omnis asinus scitur a Sorte non esse albus', nam posito quod nihil sit album nisi Plato, et quod Sortes hoc nesciat, nec etiam sciat an aliquis asinus sit albus vel non, et tamen quod sciat quod Plato est homo, tunc praemissae sunt verae et conclusio falsa. Haec enim est vera 'omne album scitur a Sorte esse homo', quia nihil est album nisi Plato et Plato scitur a Sorte esse homo, igitur omne album scitur a Sorte esse homo; et certum est quod haec est vera 'nullus asinus est homo', et tamen haec est falsa - per positum - 'omnis asinus scitur a Sorte non esse albus'.	But if that modal proposition is taken in the sense of division, or something equivalent to it, then also the mixture is rarely or never valid, whether it is negative or affirmative in mode, with respect to the conclusion affirmed in a similar manner. Just as it does not follow that 'every white thing is known by Socrates to be a man; no donkey is a man; therefore every donkey is known by Socrates not to be white', for assuming that nothing is white except Plato, and that Socrates does not know this, nor does he even know whether any donkey is white or not, and yet that he knows that Plato is a man, then the premises are true and the conclusion false. For this is true 'every white thing is known by Socrates to be a man', because nothing is white except Plato and Plato is known by Socrates to be a man, therefore every white thing is known by Socrates to be a man; and it is certain that this is true 'no donkey is a man', and yet this is false - by the posited - 'every donkey is known by Socrates not to be white'.
Et si dicatur quod haec non est vera, illo casu posito, 'omne album scitur a Sorte esse homo', quia Sortes nescit an aliquod album sit ƿ homo, hoc non valet, quia quamvis Sortes nesciat istam 'omne album est homo', tamen haec est vera 'omne album scitur a Sorte esse homo, quia per istam non plus denotatur nisi quod praedicatum competit omni illi pro quo subiectum supponit. Et hoc est veruin, quia subiectum non supponit nisi pro Platone, et manifestum est quod Platoni competit praedicatum. Haec enim est vera 'Plato scitur a Sorte esse homo, cum hoc tamen stat quod nesciat istam 'aliquod album est homo'. Sic igitur patet quod talis mixtio non valet. Similiter non sequitur 'omne album per se non est homo; omne risibile est homo; igitur omne risibile per se non est album', nam si nihil sit album nisi asinus, praemissae sunt verae et conclusio falsa. Haec enim est vera 'omne album per se non est homo , quia quaelibet singularis est vera; et minor est vera, certum est,	And if it is said that this is not true, in that case, 'every white thing is known by Socrates to be a man', because Socrates does not know whether any white thing is a man, this is not valid, because although Socrates does not know that 'every white thing is a man', nevertheless this is true 'every white thing is known by Socrates to be a man,' because by this nothing more is denoted except that the predicate belongs to everything for which the subject supposits. And this is true, because the subject does not supposit except for Plato, and it is clear that the predicate belongs to Plato. For this is true 'Plato is known by Socrates to be a man,' while this nevertheless stands, that he does not know that 'something white is a man.' Thus it is clear that such a mixture is not valid. Similarly, it does not follow that 'every white thing is not a man per se; everything that is able to laugh is a man; therefore everything that is able to laugh is not white per se', for if nothing is white except a donkey, the premises are true and the conclusion false. For this is true, 'every white thing is not a man in itself', because every singular thing is true; and the inferior is true, it is certain,
et conclusio est falsa, quia omne risibile per accidens non est album. Similiter non sequitur 'nullus homo est Deus; quaelibet persona divina per se est Deus; igitur quaelibet persona divina per se non est homo', nam ante incarnationem fuerunt praemissae verae et conclusio falsa. Et sicut est de istis modis, ita est de multis aliis.	and the conclusion is false, because everything that is able to laugh by accident is not white. Similarly, it does not follow that 'no man is God; every divine person is God per se; therefore every divine person per se is not man', for before the incarnation the premises were true and the conclusion false. And as is the case with these modes, so is it with many others.
Et si dicatur quod tales conclusiones 'omnis homo scitur non esse albus', 'omnis homo creditur non esse asinus' et huiusmodi, sunt affirmativae, ideo non debent sequi, dicendum quod quamvis tales sint affirmativae quantum ad compositionem modalem, hoc est quamvis verbum modale affirmetur in eis, tamen verbum aliud negatur. Et hoc sufficit ad intentum meum. Unde ista ponitur negativa 'omnis homo potest non esse albus', quamvis verbum modale affirmetur.	And if it is said that such conclusions as 'every man is known not to be white', 'every man is believed not to be a donkey' and the like, are affirmative, therefore they should not follow, it must be said that although such are affirmative as regards modal composition, that is, although a modal verb is affirmed in them, yet another verb is denied. And this suffices for my purpose. Hence this is put in the negative 'every man is able to not be white', although the modal verb is affirmed.
Patet igitur, quod dictum est prius, quod non sequitur conclusio de modo affirmato in tali mixtione, sive modus ille fuerit verbum, cuiusmodi sunt talia verba 'scitur', 'creditur', 'demonstratur' et huiusmodi, sive ille modus sit adverbium vel aequivalens adverbio, cuiusmodi sunt tales 'per se', 'primo verum', 'per accidens' et huiusmodi.	It is clear, therefore, as was said before, that no conclusion follows from the affirmed mode in such a mixture, whether that mode is a verb, such as the words 'scitur' (it is known), 'credur' (it is believed), 'demonstratur' (it is demonstrated) and the like, or whether that mode is an adverb or equivalent to an adverb, such as the words 'per se' (in itself), 'primo verum' (primarily truth), 'per accidens' (by accident) and the like.
Si autem in conclusione fuerit modus negatus, frequenter sequitur conclusio talis. Iste enim discursus est bonus 'omne album scitur esse homo; nullus asinus est homo; igitur nullus asinus scitur esse albus'. Similiter sequitur 'omne album per se non est homo; omne risibile est homo; igitur nullum risibile est per se album. Forte tamen cum qiu-busdam aliis modis non valet. ƿ	But if the mode is negated in the conclusion, such a conclusion frequently follows. For this is a good argument: 'every white thing is known to be a man; no donkey is a man; therefore no donkey is known to be white'. Similarly, it follows: 'every white thing is not per se a man; every that is able to laugh thing is a man; therefore nothing that is able to laugh is per se white.' Perhaps, however, it does not hold with some other modes.
Ex praedictis patet quod quamvis ex talibus propositionibus de modo, sumptis in sensu divisionis vel eis aequivalentibus, sit omnino idem modus arguendi in prima figura sicut si omnes propositiones essent de inesse, non tamen sic arguendum est ex eis in secunda figura. Et ratio est quia tales propositiones non eodem modo convertutitur sicut illae de inesse. Unde iste syllogismus 'omnis homo non est asinus; omne rudibile est asinus; igitur omne rudibile non est homo' potest probari per hoc quod ista 'omnis homo non est asinus' convertitur in istam 'omnis asinus non est homo', ex qua et minore sequitur praedicta conclusio in prima figura per syllogismum regulatum per dici de nullo, sic arguendo 'omnis asinus non est homo; omne rudibile est asinus; igitur omne rudibile non est homo'. Non sic est de isto syllogismo 'omne album per se non est asinus; omne rudibile est asinus; igitur omne rudibile per se so non est album', quamvis iste syllogismus in prima figura 'omnis asinus per se non est albus; omne rudibile est asinus; igitur omne rudibile per se non est album' sit bonus et regulatus per dici de nullo; et hoc, quia ista 'omne album per se non est asinus non convertitur in istam 'omnis asinus per se non est albus', quia posito quod nullus asinus sit albus, antecedens est verum, eo quod quaelibet singularis est vera, et tamen consequens falsum. Sed ista 'omne album per se non est asinus' convertitur in istam 'aliquid, quod per se non est asinus, est album'. Nunc autem manifestum est quod iste syllogismus non valet in prima figura 'aliquid, quod per se non est asinus, est album; omne rudibile est asinus; igitur omne rudibile per se non est album', eo quod maior est particularis in prima figura et similiter affirmativa et conclusio negativa, quae repugnant primae figurae.	From the above it is clear that although from such propositions of mode, taken in the sense of division or equivalent to them, there is exactly the same way of arguing in the first figure as if all propositions were assertoric, nevertheless it is not necessary to argue from them in the second figure. And the reason is that such propositions are not converted in the same way as those assertoric. Hence this syllogism 'every man is not a donkey; every tamable thing is a donkey; therefore every tamable thing is not a man' can be proved by the fact that this 'every man is not a donkey' is converted into this 'every donkey is not a man', from which and the minor the aforementioned conclusion in the first figure follows by a syllogism governed by 'dici de nullo', thus arguing 'every donkey is not a man; every tamable thing is a donkey; therefore every tamable thing is not a man'. This is not the case with this syllogism 'every white thing per se is not a donkey; every tamable thing is a donkey; Therefore, everything that can be tamed is not white per se,' although this syllogism in the first figure is 'every donkey is not white per se; everything that can be tamed is a donkey;' therefore every tamable thing per se is not white', although this syllogism in the first figure 'every donkey per se is not white; every tamable thing is a donkey; therefore every tamable thing per se is not white' is good and governed by 'dici de nullo'; and this, because this 'every white thing per se is not a donkey' is not converted into this 'every donkey per se is not white', because assuming that no donkey is white, the antecedent is true, because each singular is true, and yet the consequent is false. But this 'every white thing per se is not a donkey' is converted into this 'something that is not a donkey per se is white'. Now, however, it is clear that this syllogism is not valid in the first figure 'something that is not a donkey per se is white; every tamable thing is a donkey; therefore every tamable thing per se is not white', because the major is the particular in the first figure and likewise the affirmative and the negative conclusion, which are incompatible with the first figure.
Per idem patet quod si universalis negativa sit de inesse et affirmativa de modo, quod non valet talis mixtio, quia tunc in prima figura ex maiore de inesse et minore de tali modo sequitur conclusio de tali modo, quod falsum est. ƿ	By the same token it is clear that if the universal negative is assertoric and the modal is affirmative, that such a mixture is not valid, because then in the first figure from the major assertoric and the minor of such mode a conclusion of such mode follows, which is false.