Authors/Ockham/Summa Logicae/Book III-3/Chapter 9

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CAP. 9. DE REGULIS DESERVIENTIBUS CONSEQUENTIIS INFERENTIBUS NEGATIVAM EX AFFIRMATIVA VEL E CONVERSO.	Chapter 9. On the rules governing consequences inferring a negative from a positive or the converse.
Post haec videndum est de regulis deservientibus consequentiis inferentibus negativam ex affirmativa vel e converso. Et est una regula talis: ab affirmatione contrarii sequitur negatio alterius contrarii; sicut sequitur `Sortes est albus, igitur Sortes non est niger'.	After this, it must be seen about the rules governing the consequences inferring the negative from the positive or vice versa. And there is one such rule: from the affirmation of an opposite follows the negation of another opposite; as it follows, `Socrates is white, therefore Socrates is not black.'
Ex isto patet quod in motu idem subiectum primum non est simul sub contrariis. Nam, sicut dictum est prius, ab inesse ad esse respectu subiecti primi est bona consequentia, et per consequens sequitur `isti subiecto primo inest albedo, ergo istud subiectum est album'; et ultra sequitur `illud subiectum est album, igitur non est nigrum'; et ultra `igitur isti non inest nigredo tamquam subiecto primo', et per consequens idem non est simul sub albedine et nigredine.	From this it is clear that in motion the same subject is not at the same time under opposites. For, as was said before, there is a good consequence from being to being with respect to the first subject, and as a consequence it follows that `whiteness is present in this subject first, therefore this subject is white'; and further it follows, `that subject is white, therefore it is not black'; and further, `therefore these things are not in black as the first subject,' and consequently the same thing is not at the same time under whiteness and blackness.
Alia regula est: a negatione unius contrarii ad positionem alterius est bona consequentia; sicut sequitur `Sortes non est sanus, igitur Sortes est aeger'. Sciendum est quod quaedam sunt contraria mediata, quaedam immediata. De contrariis mediatis non intelligitur regula, sed de contrariis immediatis tenet; sed numquam est consequentia simplex, nisi esse praedicetur necessario de subiecto. Si autem praedicetur contingenter, tunc est consequentia ut nunc solum, quia quando talis propositio est vera, tunc est consequentia bona; sicut quando haec est vera `Sortes est', ƿ ista est bona consequentia `Sortes non est sanus, igitur Sortes est aeger'; quando autem non est vera, tunc non valet consequentia. Intelligendum est etiam quod quandoque non oportet alterum contrariorum immediatorum verificari de subiecto; sicut si virtus et vitium sint contraria immediata, non oportet aliquod istorum de subiecto verificari, quia homo ante usum rationis nec est virtuosus nec vitiosus. Quandoque autem necesse est alterum contrariorum inesse suo subiecto; et tunc est consequentia bona, sed ut nunc solum, sicut dictum est.	Another rule is: from the negation of one opposite to the position of the other, there is a good consequence; as it follows, `Socrates is not healthy, therefore Socratess is sick.' It must be known that some opposites are mediated, some immediate. The rule is not understood of mediate opposites, but of immediate opposites; but a consequence is never simple, unless it is necessarily predicated of its subject. But if it is predicated contingently, then the consequence is as now only, because when such a proposition is true, then the consequence is good; just as when this is true `Socrates is', this is a good consequence `Socrates is not healthy, therefore Socrates is sick'; but when it is not true, then the conclusion is not valid. It must also be understood that sometimes it is not necessary to verify one of the immediate opposites of the subject; just as if virtue and vice are immediate opposites, it is not necessary for any of these to be verified from the subject, because man is neither virtuous nor vicious before the use of reason. And sometimes it is necessary to have one of the opposites in its subject; and then the consequence is good, but as now only, as has been said.
Verumtamen hic est sciendum quod nulla sunt contraria, nec mediata nec immediata, quin possint amoveri a subiecto per potentiam divinam, ipso manente.	Nevertheless, here it must be known that there are no opposites, neither mediate nor immediate, that cannot be removed from the subject by the divine power, which is itself abiding.
Unde etiam ignem posset Deus facere sine omni calore et aquam sine omni frigiditate. Alia regula est: a positione habitus sequitur negatio privationis et e converso; sicut sequitur `Sortes est videns, igitur Sortes non est caecus'; et sequitur `materia non est privata forma, igitur est informata forma'.	Wherefore also God could make fire without all heat, and water without all coldness. Another rule is: from the position of attitude follows the negation of privation and vice versa; as it follows, `Socrates is seeing, therefore Socrates is not blind'; and it follows that 'matter is not a private form, therefore it is an informed form'.
Sciendum quod nomina privativa sunt in multiplici differentia.	It should be known that proper names are differences in miltiple ways.
Aliquod enim est nomen privativum quod praecise dicit privationem et carentiam formae in aliquo cui additur, et tale nomen privativum aequivalet nomini infinito. Alia sunt nomina privativa quae important formam in aliquo non esse, connotando determinatum subiectum. Alia sunt privativa quae important in aliquo non esse formam talem nec esse posse, connotando determinatum subiectum, et tale privativum est hoc nomen `caecus'; nam quando dicitur `Sortes est caecus', importatur Sortem non videre nec videre posse per naturam, et tamen quod individuo eiusdem rationis cum Sorte non repugnat videre, sive quod non repugnat homini videre. Quantum ad prima privativa est dicendum quod semper a negatione formae ad nomen privativum est bona consequentia si esse exsistere ƿ verificetur de subiecto.	For something is a privative noun which precisely expresses privation and lack of form in something to which it is added, and such a privative noun is equivalent to an infinite noun. There are other privative nouns which mean that the form is not in something, connoting a definite subject. There are other privatives which imply that in something there is no such form nor that it cannot exist, connoting a determined subject, and such a privative is the word `blind'; for when it is said that 'Socrates is blind', it is implied that Socrates cannot see or see by nature, and yet that it is not contrary to an individual of the same reasoning as Socrates to see, or that it is not contrary to man to see. As for the first privative, it must be said that there is always a good consequence from the negation of the form to the privative noun, if the existence of the subject is verified.
De secundis privativis debet dici quod non valet talis consequentia a negatione formae ad positionem nominis privativi, nisi contineatur sub tali subiecto vel sit tale de quo universaliter nomen talis formae possit verificari.	Of second privatives it must be said that such a consequence from the negation of the form to the position of the privative noun is not valid, unless it is contained under such a subject or is such that the name of such a form can be universally verified.
Et ideo non sequitur `lapis non est iustus, ergo lapis est iniustus', quia haec est impossibilis	And therefore it does not follow that `a stone is not just, therefore a stone is unjust,' because this is impossible
'omnis lapis est iustus' et semper fuit. Sed loquendo de tertiis, oportet addere quod tale nomen formae nec verificetur nec verificari possit de tali subiecto, et simul cum hoc quod aliquando talis propositio non fuit impossibilis.	'every stone is just' and always has been. But speaking of third parties, it is necessary to add that such a name of form is neither verified nor can be verified of such a subject, and at the same time that at one time such a proposition was not impossible.
Unde ista est vera modo `Sortes est caecus', quia Sortes non videt nec videre potest, et tamen aliquando non fuit haec impossibilis `Sortes videt'. Unde si haec semper fuisset impossibilis `Sortes videt', ista non esset modo vera `Sortes est caecus'.	Hence this is only true, `Socrates is blind,' because Lotes does not see and cannot see, and yet at one time this was not impossible, `Socrates sees.' Hence, if this had always been impossible, `Socrates sees,' then this would not be true, `Socrates is blind.'
Sed e converso semper est bona consequentia, nam semper ab affirmatione privationis ad negationem habitus sibi oppositi est bona consequentia.	But on the contrary, there is always a good consequence, for there is always a good consequence from the affirmation of privation to the negation of the condition opposite to it.
Unde de quocumque ista consequentia est bona `a est caecus, igitur a non est videns'. Alia regula est ista: ab affirmativa de praedicato infinito ad negativam de praedicato finito est bona consequentia; sicut sequitur `Sortes est non albus, igitur Sortes non est albus'.	Whence this conclusion is good of whomsoever, `a is blind, therefore a is not sighted.' Another rule is this: from the affirmative of an infinite predicate to the negative of a finite predicate, there is a good consequence; as it follows, `Socrates is non-white, therefore Socrates is not white.
Sciendum est quod ista regula habet instantiam quando alterum extremorum accipitur in obliquo. Sicut si quilibet homo habeat asinum et bovem, haec est vera `hominis est non asinus', quia cuiuslibet hominis est aliquis bos; et tamen haec est falsa `hominis non est asinus', quia cuiuslibet hominis est aliquis asinus.	It must be known that this rule has an instance when one of the extremes is taken obliquely. Just as if every man has an ass and an ox, this is true, `man's is a non-ass,' because every man has some ox; and yet this is false, `an ass is not a man's,' because every man has an ass.
Similiter non sequitur `quilibet homo videt non hominem, ergo quilibet homo non videt hominem', nam si quilibet homo videret hominem et asinum, antecedens esset verum et consequens falsum.	Similarly, it does not follow that `every man sees not a man, therefore every man does not see a man', for if every man saw a man and an ass, the antecedent would be true and the consequent falsity.
Similiter ista regula habet instantiam quando propositio est de praeterito vel de futuro; quia non sequitur `Sortes fuit non albus, igitur Sortes non fuit albus', nam posito quod Sortes uno tempore fuisset albus et alio tempore niger, antecedens esset verum et consequens falsum.	Similarly, this rule has an instance when the proposition is about the past or the future; because it does not follow that 'Socrates was non-white, therefore Socrates was not white'; for supposing that Socrates had been white at one time and black at another, the antecedent would be true and the consequent false.
ƿ Similiter non sequitur `Sortes erit non vivens, igitur Sortes non erit vivens'. Alia regula est: ad affirmativam de praedicato finito sequitur negativa de praedicato infinito; sicut sequitur `Sortes est albus, ergo Sortes non est non albus'.	In the same way it does not follow that `Socrates will be non-living, therefore Socrates will not be living.' Another rule is: the affirmative of a finite predicate is followed by a negative of an infinite predicate; as it follows, `Socrates is white, therefore Socrates is not non-white.'
Ista regula, sicut prior, debet intelligi in terminis rectis et propositionibus de praesenti et non de praeterito nec de futuro. Alia regula est: ad negativam de praedicato finito sequitur affirmativa de praedicato infinito; sicut sequitur `Sortes non est albus, igitur Sortes est non albus.	This rule, like the previous one, must be understood in correct terms and propositions about the present and not about the past or the future. Another rule is: the negative of a finite predicate is followed by an affirmative of an infinite predicate; as it follows, `Socrates is not white, therefore Socrates is non-white.
Sciendum quod ista regula habet instantiam quando negatio additur solum uni parti extremi. Et ideo non sequitur `Sortes non est lignum album, ergo Sortes est non-lignum album', quia si Sortes sit niger, antecedens est verum et consequens falsum, et hoc quia negatio additur solum isti termino `lignum', et non toti praedicato.	It should be known that this rule has an instance when the negation is added only to one extreme part. And therefore it does not follow that `Socrates is not white wood, therefore Sores is white non-wood', because if Sores is black, the antecedent is true and the consequent is false, and this is because the negation is added only to this term 'wood', and not to the whole predicate.
Et ideo proprie loquendo non arguitur a negativa de praedicato finito ad affirmativam de praedicato infinito, sed ad affirmativam habentem unam partem praedicati quae est terminus infinitus, quia totum praedicatum est hoc totum `non lignum album', cuius una pars est `non lignum'.	And therefore, properly speaking, it is not argued from the negative of a finite predicate to the affirmative of an infinite predicate, but to the affirmative having one part of the predicate which is the infinite term, because the whole of the predicate is this whole `white non-wood', one part of which is `not wood'.
Similiter ista regula habet instantiam quando de subiecto non verificatur esse exsistere. Hoc saltem est verum quando per subiectum implicatur aliqua uniri a parte rei. Quod dico propter terminos importantes simpliciter simplicia, cuiusmodi sunt `Deus', 'angelus', et huiusmodi.	Similarly, this rule has an instance when the subject is not verified to exist. At least this is true when by the subject it is implied that some part of the object is united. What I say is because of the important terms that are simply simple, such as 'God', 'angel', and the like.
Et ideo talis consequentia non valet Sorte exsistente mortuo `Sortes non est albus, ergo Sortes est non albus'. Similiter non sequitur `homo albus non est homo, ergo homo albus est non homo', nam posito quod nullus homo sit albus, antecedens est verum et consequens falsum.	And therefore such a conclusion does not apply to Socrates existing dead: `Socrates is not white, therefore Socrates is non-white. Similarly, it does not follow that `a white man is not a man, therefore a white man is a non-man, for if it is assumed that no man is white, the antecedent is the truth and the consequent is the falsity.
Veritas antecedentis patet, nam sequitur `nullus homo est homo albus, ergo homo albus non est homo'; et antecedens est verum, isto casu posito, ergo consequens est falsum. Falsitas consequentis patet, nam haec est falsa `aliquis non homo est homo albus'; consequens est falsum, quia quaelibet singularis eius est falsa, ut patet inductive.	The truth of the preceding is clear, for it follows that 'no man is a white man, therefore a white man is not a man'; and the antecedent is true, given this case, therefore the consequent is false. The falsity of the conclusion is clear, for this is a falsity: `someone who is not a man is a white man'; the consequence is false, because every particular of it is false, as is clear inductively.
Siƿmiliter sequitur `homo albus est non homo, igitur homo est albus'; consequens est falsum, isto casu posito, igitur antecedens. Similiter regula habet instantiam in illis de obliquo et in propositionibus de praeterito et de futuro, sicut priores; et ita regula tenet in terminis simplicibus cum constantia subiecti et de recto et de praesenti. Alia regula est: ad negativam de praedicato infinito sequitur affirmativa de praedicato finito; sicut sequitur `Sortes non est non albus, igitur Sortes est albus'.	Similarly, it follows that `a white man is a non-man, therefore a man is white'; the consequent is false, given this case, therefore the antecedent. Similarly, the rule has an instance in those about the oblique and in propositions about the past and the future, like the previous ones; and thus the rule holds in simple terms with the consistency of the subject both of the right and of the present. Another rule is: the negative of an infinite predicate is followed by an affirmative of a finite predicate; as it follows, `Socrates is not non-white, therefore Socrates is white.
Et debet intelligi ista regula sicut prior, scilicet in propositionibus de recto et de praesenti et cum constantia subiecti. Per constantiam autem subiecti intelligitur quod esse exsistere praedicetur de subiecto significative sumpto; et ideo talis consequentia non valet `homo albus non est non homo, ergo homo albus est homo', si haec sit falsa `homo albus est'.	And this rule must be understood like the previous one, that is, in propositions about the right and the present and with the consistency of the subject. Now by the constancy of the subject is meant that the existence is predicated of the subject taken as significant; and therefore such a conclusion does not hold, `a white man is not a non-man, therefore a white man is a man', if this is false, `a white man is a man.'
Et si dicatur quod alterum contradictoriorum dicitur de quolibet, igitur altera istarum erit vera `homo albus est homo', `homo albus est non homo', quamvis nullus homo sit albus: Similiter sequitur `homo albus est homo albus, igitur homo albus est homo', per regulam prius datam `ab inferiori ad superius est consequentia simplex', sed antecedens est necessarium, cum propositio in qua praedicatur idem de se sit necessaria; igitur consequens est necessarium, et per consequens haec disiunctiva est necessaria `homo albus est homo vel homo albus est non homo': Ad primum istorum dicendum quod non semper alterum contradictoriorum incomplexorum dicitur de quolibet, sed oportet ad hoc addere quod de illo subiecto verificetur esse exsistere.	And if it be said that one of the two contradictory things is said of any one, then the other of these will be true, `a white man is a man,' 'a white man is a non-man,' although no man is white. Similarly, it follows that `a white man is a white man, therefore a white man is a man,' by the rule previously given, `from the lower to the higher is a simple consequence,' but the antecedent is necessary, since the proposition in which the same is predicated is necessary of itself; therefore the consequent is necessary, and as a consequence this disjunctive is necessary: ​​`a white man is a man or a white man is a non-man': To the first of these we must say that the second of the complex contradictions is not always said of anyone, but we must add to this that it is verified to exist of that subject.
Unde si nullus homo sit, neutra istarum est vera `homo est animal', `homo est non animal', et hoc quia in utraque istarum implicatur falsum. Propter hoc enim quod utraque istarum `homo est animal', `homo est non animal' est simpliciter affirmativa, implicatur quod aliquod compositum ƿ ex corpore et anima sit homo, quod est simpliciter falsum, et ideo utraque istarum est falsa.	Therefore, if there is no man, neither of these is true: `man is an animal', `man is a non-animal', and this because in both of these falsities are implied. Because both of these statements ``man is an animal and ``man is a non-animal are simply affirmative, it is implied that a man is something composed of body and soul, which is simply false, and therefore both of these are false.
Ad secundum dicendum quod haec consequentia est bona `homo albus est homo albus, igitur homo albus est homo', sed antecedens non est necessarium, immo est contingens; nec omnis propositio in qua praedicatur idem de se est necessaria, immo aliquando est impossibilis.	To the second it must be said that this conclusion is good: `a white man is a white man, therefore a white man is a man', but the antecedent is not necessary, rather it is contingent; nor is every proposition in which the same thing is predicated of itself necessary, indeed sometimes it is impossible.
Haec enim est impossibilis `omne verum de necessitate est verum' et similiter ista `omne verum contingenter est verum', et tamen praedicatur idem de se. Et quod dicit Boethius quod `nulla propositio est verior illa in qua idem praedicatur de se', debet sic intelligi: quod nulla propositio in qua praedicatur aliquid aliud de subiecto sine omni determinatione compositionis vel totius propositionis est verior illa in qua praedicatur idem de eodem sine omni tali determinatione.	For this is impossible, `all truth is necessarily true,' and likewise that `all truth is contingently true,' and yet the same thing is predicated of itself. And what Boethius says that 'no proposition is truer than that in which the same thing is predicated of itself' must be understood thus: that no proposition in which something else is predicated of the subject without any determination of the composition or of the proposition as a whole is truer than that in which the same thing is predicated of the same without any such determination.
Ita quod nulla propositio in qua `homo' subicitur est verior illa in qua tam subicitur quam praedicatur `homo' sine omni determinatione compositionis vel propositionis. Unde nulla talis `homo albus est homo', `homo albus est animal', `homo albus currit', et sic de huiusmodi, est verior ista `homo albus est homo albus', et tamen ista `homo albus potest esse homo' est verior ista `homo albus est homo albus'.	So that no proposition in which 'man' is submitted is truer than that in which 'man' is both submitted and predicated without any determination of composition or proposition. Hence there is no such thing as `a white man is a man', `a white man is an animal', 'a white man runs', and so on. It is truer that `a white man is a white man', and yet that `a white man can be a man' is truer than that `a white man is a white man'.
Sic igitur Boethius comparat propositiones de praesenti, sine omni determinatione compositionis, in qua subicitur idem et non praedicatur idem, ad unam propositionem de praesenti, sine omni determinatione compositionis, in qua idem tam subicitur quam praedicatur.	So then Boethius compares propositions about the present, without any determination of composition, in which the same is submitted and the same is not predicated, to one proposition about the present, without any determination of composition, in which the same is both submitted and predicated.
Et tunc nulla talis est verior illa in qua praedicatur idem de se, et tamen quaelibet istarum aliquando est contingens. Alia regula est: ab affirmativa de una specie specialissima ad negativam de alia specie specialissima condividente est bona consequentia; sicut sequitur `Sortes est homo, igitur Sortes non est asinus'.	And then there is no such thing more true than that in which the same is predicated of itself, and yet each of these is sometimes contingent. Another rule is: from the affirmative of one very special species to the negative of another very special species, there is a good consequence; as it follows, `Socrates is a man, therefore Socrates is not an ass.
Sed e converso non sequitur: non enim sequitur `angelus non est asinus, igitur angelus est homo'.	But it does not follow the other way around: for it does not follow that 'an angel is not an ass, therefore an angel is a man'.
ƿ Sciendum quod ista regula est vera de speciebus specialissimis condividentibus et est vera de speciebus specialissimis mere absolutis, sed de speciebus quarum una est mere absoluta et alia relativa vel connotativa, vel de pluribus relativis vel connotativis non valet. Non enim sequitur `Sortes est homo, igitur Sortes non est pater', et tamen `pater' est species specialissima. Et si dicatur quod `pater' non est species specialissima sed `paternitas', et bene sequitur `Sortes est homo, igitur Sortes non est paternitas', dicendum est quod `pater' est species specialissima.	It should be known that this rule is true of very special species that share, and it is true of very special species that are merely absolute, but it does not apply to species of which one is merely absolute and the other relative or connotative, or of several relative or connotative species. For it does not follow that `Socrates is a man, therefore Socrates is not a father,' and yet `father' is a very special species. And if it is said that `father' is not the most special species, but `paternity,' and it follows that `Socrates is a man, therefore Socrates is not paternity,' it must be said that `father' is the most special species.
Cuius ratio est, nam `ad aliquid' vel relatio est unum praedicamentum importans veras res et pro eis supponens, igitur similiter species suae supponunt pro rebus et res important; igitur si `paternitas' sit species, oportet quod supponat pro re.	The reason for this is, for `to something' or relation is one predicate importing true things and suppositing them for them; therefore, in the same way, they supposit their species for things and carry things; therefore, if 'paternity' is a species, it must stand for a thing.
Et quaero: pro qua re? Nonnisi pro illo qui est pater, nec aliud significabit nisi consignificando.	And I ask: for what purpose? Only for him who is the father, and will not signify anything else except by consignation.
Et hoc facit `pater'; igitur si `paternitas' sit species, `pater' erit species. Ideo dicendum est quod apud Aristotelem `pater' et `paternitas' vel erant nomina synonyma, et tunc manifestum est quod si `paternitas' sit species specialissima, `pater' erit species specialissima; vel `paternitas' significabit suum concretum, ita quod hoc nomen `pater' erit `paternitas', sicut hoc nomen `pater' est relativum et ad aliquid.	And this is what the father does; therefore, if 'paternity' is a species, 'father' will be a species. Therefore it must be said that for Aristotle `father' and `paternity' were synonymous nouns, and then it is clear that if `paternity' is the most special kind, then `father' will be the most special kind; or `paternity' will signify its concreteness, so that this name `father' will be `paternity', just as this name `father' is relative and to something.
Manifestum est enim quod hoc nomen `pater', cum dicatur ad convertentiam, est relativum et ad aliquid; et tunc sicut ad aliquid non est praedicamentum sic nec `paternitas' est species specialissima.	For it is manifest that this name 'father', when it is said of conversion, is relative and to something; and then, just as there is no predicate for something, so neither is `paternity' a very special species.
Et ideo forte non est aliquod nomen impositum illi praedicamento, nisi aequivocum, quod significat aequivoce tam res quae significantur per nomina inferiora relativa quam ipsa nomina relativa.	And therefore perhaps there is no name imposed upon it by the predicate, except equivocal, which equivocally signifies both the things signified by lower relative nouns and the relative nouns themselves.
Unde relatio significat et haec et illa, et ideo in uno sensu est haec vera `pater est relatio' et similiter ista `Sortes est relatio', sicut haec est vera `Sortes est pater', et in alio sensu haec est falsa ` Sortes est relatio'.	Wherefore relation signifies both this and that, and therefore in one sense this is true, `father is a relation,' and likewise that `Socrates is a relation,' just as this is true, `Socrates is a father,' and in another sense this is false, `Socrates is a relation.'
ƿ Habet etiam ista regula instantiam de speciebus tam connotativis quam relativis, quia non sequitur `Sortes est pater, igitur Sortes non est filius', nec sequitur `Sortes est linea, igitur Sortes non est superficies', secundum principia Aristotelis loquendo.	This rule also has an instance of both connotative and relative species, because it does not follow that `Socrates is a father, therefore Socrates is not a son, nor does it follow that `Socrates is a line, therefore Socrates is not a surface, speaking according to Aristotle's principles.
Alia regula est: ab affirmativa de uno genere ad negativam de alio genere non subalterno est bona consequentia; sicut sequitur ` Sortes est corpus animatum, igitur Sortes non est corpus inanimatum'.	Another rule is: from the affirmative of one kind to the negative of another kind, there is no subordinate good consequence; as it follows, `Socrates is an animate body, therefore Socrates is not an inanimate body.'
Sciendum est quod ista regula non est generaliter vera, sed tantum est vera quando unum genus universaliter removetur ab alio. Quando autem unum genus praedicatur de alio, quamvis particulariter solum, non valet consequentia, quia non est inconveniens idem contineri sub diversis generibus.	It must be known that this rule is not generally true, but is only true when one type is universally removed from another. But when one genus is predicated of another, even if only in particular, the consequence is not valid, because it is not inconvenient that the same thing should be contained under different genera.
Et ideo non sequitur `Sortes est substantia, igitur Sortes non est quantitas', secundum principia Aristotelis.	And therefore it does not follow that `Socrates is substance, therefore Socrates is not quantity', according to Aristotle's principles.
Et si dicatur quod secundum Philosophum, I Posteriorum, haec est immediata `nulla substantia est quantitas', et universaliter quaelibet negativa in qua removetur unum praedicamentum ab alio est immediata, dicendum quod Aristoteles falso allegatur in illo passu, quia non facit ibidem mentionem nec de substantia nec de quantitate nec de aliquibus praedicamentis, sed tantum docet quae negativa est immediata.	And if it is said that according to the Philosopher, 1 of the Posteriors, this is immediate, `no substance is quantity', and universally any negative in which one predicate is removed from another is immediate, it must be said that Aristotle falsely stated in that step, because he makes no mention there either of substance, or of quantity, or of any predicates, but only teaches that which is negative is immediate.
Pro tota parte praecedente est notandum primo quod omnes praedictae regulae intelligendae sunt quando omnes termini supponunt personaliter et significative, quia si termini supponerent materialiter vel simpliciter, non tenerent.	For the whole of the preceding part, it must first be noted that all the aforesaid rules are to be understood when they assume all the terms personally and meaningfully, because if the terms were assumed materially or simply, they would not hold.
Secundo notandum quod multae regulae quae ponuntur deservire consequentiis ex omnibus affirmativis, deserviunt etiam consequentiis ex affirmativa et negativa et e converso.	Secondly, it should be noted that many rules which are supposed to serve all positive consequences also serve positive and negative consequences and vice versa.
Sciendum etiam quod multae regulae de praedictis non tenent in propositionibus de praeterito et de futuro; sicut non sequitur `Sortes fuit albus, igitur Sortes non fuit niger', nec sequitur `Sortes fuit sanus, ergo Sortes non fuit aeger'.	It must also be known that many of the aforementioned rules do not hold in propositions about the past and the future; just as it does not follow that `Socrates was white, therefore Socrates was not black,' nor does it follow that `Socrates was healthy, therefore Socrates was not sick.'
Et ita de multis aliis, quas longum esset pertractare.	And so about many others, which it would be a long time to go through.