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{| border=1 cellpadding=10" !valign = top width=45%|Latin !valign = top width=55%|English              ||                           ||                           ||            Now an affirmation is an affirmative proposition such as 'every man is an animal', 'a certain man is an animal'; but negation is a negative proposition, as 'some man is not an animal', 'no man is an animal'.  And every affirmation has only one proper negation according to the opposition of contradiction.  Now one opposition is of contradiction, the other is of contrariety.  For those among them which are contrary propositions, are especially opposed to each other by the opposition of contrariety, such as 'every man is just', no man is just', but those which are contradictory, with truth and falsity always dividing  among them, are repugnant to each other by the opposition of contradiction, such as 'every man is just', 'not every man is just', and also 'no man is just', 'some man is just', so also the singulars 'Socrates is just', 'it is not the case that Socrates is just'. ||           Now, in the introductions which we have written for the instruction of inexperienced logicians, we have more carefully made clear which among these are contrary or contradictory propositions, also, which are said to be to be subalternates or subcontraries, what inferences or differences they have among one another and what kinds of conversions they have. ||           It is not for us to dwell upon these things again, but rather let us postpone [that] treatise for deeper things, and furthermore distinguish more subtly the properties of affirmations and negations. For when a singular subject is posited, one acceptance of the subject causes only one negation or affirmation. But when the subject is a universal, variation of the subject according to signs holds many affirmations or negations. For of the affirmation of 'every man is just', since it seems to be the negation of 'no man is just', there is both that which states 'a certain man is not just' and 'not every man is just'. Also of the negation 'no man is just', there seem to be two affirmations: either 'every man is just' or 'some man is just' ||           And since to the same affirmation or negation there are two opposed, which clearly could not be true with it at the same time, one of them stands back very far from it by the opposition of contrariety, whereas the other [stands back] by the opposition of contradiction, so that what the affirmation was stating, it removes to the same extent, and absolutely contradicts it [*]. ||           For while 'no man is just' is opposed to the proposition 'every man is just' in a contrary way, the proposition 'not every man is just' is, on the other hand, opposed in a contradictory way. Furthermore, both extinguish the sense of that proposition, yet 'not every man is just' absolutely contradicts the first, whereas 'no man is just' contradicts it more, which shows not simply that 'being just' does not belong to every man, but also that it is removed from every man. ||           Whether contraries are more opposed than contradictories ||           Deservedly therefore this ['no man is just'], insofar as it is contrary, is opposed to the first ['every man is just'], to which it is especially adverse. For they define opposed contraries as what, on the face of it, are opposed to each other, i.e. those which are especially repugnant, such as white and black, which in no way can be contained in the same thing at the same time. But 'every man is just' is more adverse to the opposed 'no man is just', than to 'not every man is just', for it agrees more with 'not every man is just' than 'no man is just'. For the former is true on account of one [man], if he lacks justice [*], but the latter is not true unless all lack it. And by one man not being just, it could more easily affect what the universal affirmation says than by no just men existing. Wherefore it is clear that universal negation is more opposed to universal affirmation than particular negation. For indeed it takes away everything [*] that the latter gives. ||           But when we say that a particular cannot bear a universal with itself in falsity, but rather, if the one is false, the other is necessarily true, this does not pertain to the opposition of contrariety, but rather to the dividing of contradiction. For the fact that what they say cannot be be false together (i.e. that they cannot be absent at the same time), relates to the lack of an intermediary, rather than contrariety. But the fact that what they say cannot be true together, i.e. that they cannot be true together, pertains only to opposition or contrariety. For, from the nature of contraries, no contraries posit themselves as mutually destroyed, but rather when all are posited they mutually remove themselves. It is permissible to examine this in complex propositions as much as in simple ones. ||           That accordingly they cannot be absent at the same time, does not rule out opposition, but rather dividing, or the lack of an intermediary, whereas lack of an intermediary does not rule out opposition. For there are many things lacking intermediaries that are not opposed, for example the infinite name of a species (e.g. 'not man'), and the finite name of a genus (e.g. 'animal'). Nor also in the cases where lack of an intermediary leans towards composition, does the lack make the opposition greater, which from 'in white' and 'not in white' and 'in black' is carefully considered. For 'white' and 'not white' are not so opposed, although they are not absent at the same time, as are white and black, which cannot be absent at the same time. For it is not necessary to call things that are not white the contrary of white (i.e. black), but rather they can be yellow things or of another colour. ||           Accordingly, it pertains to opposition that things cannot exist at the same time, but to the lack of an intermediary that they cannot be absent at the same time. Wherefore, even if subcontraries cannot be absent at the same time, they do not seem to be opposed, in that certainly they can be present at the same time, namely in the contingent matter of propositions, just as the dividing ones can be absent at the same time, namely universal affirmatives and negatives, which it is appropriate to call contraries from their very great opposition, as was shown, though the rest are contradictories. ||           Accordingly it is manifest that 'no man is just' is more repugnant to 'every man is just' than 'not every man is just'. Wherefore deservedly from the universal affirmative, its contrary is supposed to be the universal negative, whereas the contradictory is called the particular. For while 'not every man is just' seems the same as 'a certain man is not just', and even Boethius takes both to be one and the same, yet nevertheless a different meaning appears to those who examine it more carefully [*]. ||           For much is of consequence to the meaning of the assertion, since the negative particle drives out and destroys the whole affirmation when placed before, [but] brings about a separation of the terms when placed in between [*], as indeed is also shown in hypothetical propositions. For the sense of 'if it is a man, it is not just' and 'it is not the case that if it is a man, it is just' is not the same. For the former shows the statement of 'man' is not compatible with 'just', but the latter does not necessarily exclude 'just'; and it is true, but the former is false. And of course the latter which extinguishes the whole hypothetical (i.e. 'if it is a man, it is just') with negation sent before, is called its proper negation, and is strictly dividing, i.e. can neither be true nor false with it at the same time, in fact destroys its sense absolutely. But the former can be false at the same time, though they can never at the same time be true. Wherefore it seems to be contrary to it rather than contradictory. ||           Thus also, in categorical propositions, the only proper and strictly dividing contradiction to any affirmation seems to be that which destroys its sense when the negation is placed before [*], as 'it is not the case that every man is a man', [but] not 'a certain man is not a man' is of 'every man is a man', for the one can perhaps be false with the other. For with absolutely no man existing, neither the proposition 'every man is a man' is true nor 'some man is not a man' (i.e. a certain thing that is a rational mortal animal, is not a rational mortal animal), for the name of man was imposed from the presence of an animal informed by rationality and mortality. Anyone who says this, states that that it is an animal informed by rationality and mortality. ||           Hence 'a certain man is not a man', i.e. 'a certain thing which is a rational mortal animal is not a rational mortal animal or animal absolutely', is always false, for it is altogether impossible that what this very proposition says can happen either at any time or that nature allows an instance of it. For in what time could we show in something that what is not a man is a man? For of course it does not happen that a man at the same time is and not is, for what is not enclosed in negation, but is posited outside it, is permanently established as it were. But since 'a certain man is not a man' is always false and also 'every man is a man' (when a man does not exist) it is clear they are false at the same time, wherefore they could not be called strictly dividing. ||           Thus also with man destroyed, both 'every white man is white' is false, and 'a certain white man is not white', i.e. 'a certain man who is informed by whiteness is not informed by it, indeed lacks it'. For by the removal of the predicate, the determination of the subject, in which the very predicate, that is not found in that subject, is left in the subject, makes the assertion false. Just as also the determination of the subject prevents 'man in his native state is an animal' being true, which perhaps with the determination taken away would remain true.
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 * SOURCE: L. M. De Rijk (ed.), Petrus Abaelardus Dialectica, Assen: Van Gorcum 1970. PETRI ABAELARDI DIALECTICA PRAEDICAMENTA DE PRAEDICAMENTIS ARISTOTELIS LIBER PRIMUS DE SUBSTANTIA […] LIBER SECUNDUS DE SPECIERUM DIFFERENTIIS CATEGORICARUM
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 * DE AFFIRMATIONE ET NEGATIONE
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 * Est autem affirmatio enuntiatio affirmativa, ut 'omnis homo est animal', 'quidam homo est animal'; negatio vero enuntiatio negativa, ut 'quidam homo non est animal', 'nullus homo est animal'. Habet autem omnis affirmatio unam tantum propriam negationem secundum contradictionis oppositionem. Alia autem est contradictionis oppositio, alia contrarietatis. Quae enim invicem sunt contrariae propositiones, oppositione contrarietatis sibi maxime adversantur, veluti istae: 'omnis homo iustus est', 'nullus homo iustus est'; quae vero contradictoriae sunt atque inter se verum falsumque semper dividentes, contradictionis oppositione sibi repugnant, ut 'omnis homo iustus est', 'non omnis homo iustus est, et rursus 'nullus homo iustus est', 'quidam homo iustus est'; sic etiam singulares 'Socrates est iustus', 'non est Socrates iustus'.
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 * Quae autem invicem contrariae propositiones vel contradictoriae, quae etiam subalternae vel subcontrariae dicantur, aut quas ad invicem inferentias vel differentias [174] qualesque conversiones habeant, in his Introductionibus diligentius patefecimus quas ad tenerorum dialecticorum eruditionem conscripsimus.
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 * Nec in his rursus nobis immorandum est, sed ad altiora tractatum transferamus atque affirmationum et negationum proprietates subtilius distinguamus. Cum enim singulare subiectum ponitur, unam tantum negationem vel affirmationem una acceptio subiecti facit; cum autem universale subicitur, multas affirmationes vel negationes subiecti variatio secundum signa tenet. Eius namque affirmationis quae dicit: 'omnis homo iustus est', cum ea videtur negatio quae ait: 'nullus homo iustus est', tum illa quae proponit: 'quidam homo iustus non est', vel 'non omnis homo iustus est'. Eius quoque negationis: 'nullus homo iustus est', duae videntur affirmationes, vel [et] 'omnis homo iustus est', vel 'quidam homo iustus est'.
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 * Cumque eidem affirmationi vel negationi duae sint oppositae, quae videlicet simul cum ea verae esse non possint, altera contrarietatis oppositione quam longissime ab ea recedit, altera vero contradictionis oppositione, ut quod ea proponebat tantum perimit ac simpliciter ei contradicit.
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 * Cum enim huic propositioni: 'omnis homo iustus est' haec contrarie opponatur: 'nullus homo iustus est', illa vero contradictorie: 'non omnis homo iustus est', atque utraque ipsius sententiam perimat, haec quidem: 'non omnis homo iustus est' simpliciter priori contradicit, illa vero: 'nullus homo iustus est', plus facit, quae non tantum ostendit non omni homini iustum convenire, verum etiam ab omni removeri.
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 * UNDE MAGIS OPPOSITAE SINT CONTRARIAE QUAM CONTRADICTORIAE 
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 * Merito ergo haec tamquam contraria priori opponitur quae ei maxime est adversa. Ea namque opposita contraria definiunt quae prima fronte sibi opponuntur, hoc est quae maxime sibi repugnant, velut album et nigrum, quae nullo modo eidem simul inesse possunt. Plus autem adversa est, hoc est opposita, 'nullus homo iustus est' ei quae est 'omnis homo iustus est' quam 'non omnis homo iustus est'; magis enim consentit ei 'non omnis homo iustus est' quam 'nullus homo iustus est'; haec enim propter unum vera est, si iustitia careat, illa vero non nisi omnes careant. Facilius autem uno non existente iusto contingere posset quod universalis affirmatio dicit quam nullis existentibus iustis. Unde manifestum est universalem negationem magis adversari universali affirmationi [175] quam particularem negationem; quippe haec omnibus aufert quod illa omnibus attribuit.
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 * Quod autem dicitur particularis nec secum in falsitate posse pati universalem, sed, si haec falsa sit, illam necessario veram, hoc ad oppositionem non pertinet contrarietatis, immo ad dividentiam contradictionis. Quod enim falsae non possunt simul esse {id est quod non possunt simul abesse}, ea quae dicunt, ad immediationem potius attinet quam ad contrarietatem. Quod autem verae non possunt simul esse, id est quod non possunt simul esse ea quae dicunt, id solum ad oppositionem pertinet vel contrarietatem. Nulla enim contraria ex natura contrariorum destructa se ponunt, sed omnia posita sese mutuo auferunt; quod tam in complexis quam in incomplexis licet inspicere.
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 * Quod itaque simul abesse non possunt, oppositionem non exigit, sed dividentiam seu immediationem; immediatio autem oppositionem non exigit. Sunt enim multa immediatorum non opposita, sicut infinitum speciei et finitum nomen generis, sicut 'non-homo' et 'animal'. Nec in his etiam, ubi immediatio compositionem incumbit, immediatio oppositionem facit maiorem; quod ex 'albo' et 'non-albo' et 'nigro' perpenditur. Non enim tantum adversa sunt album et non-album, quamvis nec simul absint, quantum album et nigrum quae simul abesse contingit. Quae enim non alba sunt, non est necesse contrarium albi dicere, id est nigrum, sed crocea esse possunt vel alterius coloris.
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 * Quod itaque quaelibet simul esse non possunt, ad oppositionem pertinet; quod autem simul abesse nequeunt, ad immediationem. Unde, etsi subcontrariae simul abesse non possint, non tamen oppositae videntur, eo videlicet quod simul possint adesse, in contingenti scilicet materia propositionum, sicut earum dividentes abesse, universales scilicet affirmativa et negativa, quas ex maxima oppositione, ut ostensum est, contrarias convenit appellari, caeteras vero contradictorias.
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 * Ex his itaque manifestum est ei quae dicit: 'omnis homo iustus est' magis repugnare 'nullus homo iustus est' quam 'non omnis homo iustus est'. Unde merito ab universali affirmativa illa contraria ponitur quae universalis est negativa, haec vero contradictoria quae particularis dicitur. Eadem enim haec: 'non omnis homo iustus est' cum ea videtur quae proponit: 'quidam homo iustus non est'; atque pro una et eadem utramque Boethius accipit, cum tamen earum sententia diversa appareat his qui eam perspicacius inspiciunt.
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 * Multum enim refert ad sententiam enuntiationis, [176] cum praeposita negativa particula totam exigit et destruit affirmationem, et cum eadem interposita terminorum separationem facit, quod quidem ex hypotheticis quoque enuntiationibus ostenditur. Non enim eadem est sententia istarum: si est homo, non est iustus et non si est homo, est iustus. Illa namque demonstrat 'hominis' positionem non pati 'iustum', haec vero non necessario exigere 'iustum'; quod verum est, illud autem falsum. Et haec quidem quae negatione[m] praemissa totam hypotheticam perimit, hanc scilicet: si est homo, est iustus eius propria negatio dicitur ac recte dividens, quae scilicet nec vera simul cum ea nec falsa esse potest, quippe eius sensum simpliciter destruit. Illa vero simul esse falsa potest, numquam autem simul vera. Unde potius contraria ei videtur quam contradictoria.
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 * Sic quoque in categoricis propositionibus ea tantum propria contradictio ac recte dividens cuilibet affirmationi videtur quae negatione[m] praeposita totam eius sententiam destruit, ut eius quae est: 'omnis homo est homo' ea quae est: 'non omnis homo est homo', non ea quae est: 'quidam homo non est homo'; haec enim fortasse simul erit falsa cum ea. Re enim hominis prorsus non existente neque ea vera est quae ait: 'omnis homo est homo' nec ea quae proponit: 'quidam homo non est homo', hoc est 'quaedam res quae est animal rationale mortale, non est animal rationale mortale'; 'hominis' enim nomen nonnisi ex praesentia animalis rationalitate et mortalitate informati impositum fuit. Qui ergo hanc dicit, id proponit quod est animal rationalitate {et} mortalitate informatum.
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 * Haec igitur: 'quidam homo non est homo', id est 'quaedam res quae est animal rationale mortale' non est animal rationale mortale vel animal simpliciter', semper falsa est; est enim omnino impossibile quod ipsa dicit nec ullo tempore contingere potest nec eius exemplum natura patitur. Quo enim tempore in aliquo ostendere possemus quod {id} quod est homo, non est homo?: quippe ipsum simul esse hominem et non esse non contingit; quod enim in negatione non clauditur sed extra eam ponitur, quasi permanens constituitur. Cum autem 'quidam homo non est homo' semper falsa sit atque, 'omnis homo est homo' homine non existente, patet simul easdem falsas esse; unde nec recte dividentes dici poterunt.
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 * Sic quoque homine destructo et quae ait: 'omnis homo [est] albus est albus' falsa est, et quae [177] dicit: 'quidam homo albus non est albus', hoc est 'quidam homo qui est informatus albedine non est ipsa informatus', immo caret ea'. Remotione namque praedicati determinatio subiecti, in qua praedicatum ipsum subiecto relinquitur, quod in ipso subiecto non invenitur, falsam facit enuntiationem. Sicut et istam subiecti determinatio impedit: 'homo rudibilis est animal'; quae fortasse determinatione subtracta vera remaneret.
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 * Patet itaque ei quae dicit:

omnis homo est homo vel omnis homo albus est homo albus

eam tamquam rectam dividentem opponi quae negatione {prae}posita totum eius sensum exstinguit, hoc modo:

non omnis homo est homo, non omnis homo albus est albus,

non eam scilicet quae negationem interponit ad praedicatum disiungendum a subiecto. Aliud autem est res a se invicem disiungere, aliud ostendere non omnes sibi eas convenire. ||           Hence it is clear that to

every man is a man or every white man is a white man

there is opposed, as a strictly dividing proposition, one that extinguishes its entire sense by the negation placed before it as follows

not every man is a man not every white man is white

i.e. not the proposition in which negation is placed so as to disconnect predicate from subject. For the one is to disjoin things from one another, the other to show that not all things belong to them [*]. ||           For anyone who treats these as disjoined from one another, accepts them as existing [*], but anyone who treats as not belonging to them, no more implies their existence than their non existence, but rather states only that they do not inhere in them [*]. Negation accordingly has one force when placed before, another when placed in between. Wherefore also 'every man is not white' does not seem the same as 'not every man is white', and 'a certain man is not white' is not the same as 'it is not the case that a certain man is white'. For anyone who says 'every man is not white' removes whiteness [*] from every man, as if he brings about the removal of the universal saying that every one lacks whiteness [*], but anyone who extinguishes the sense of the universal affirmation, shows only that it does not belong to every one, not also that it is separated from all, for the former [i.e. the negation of the affirmation] is true, even if one is not white. ||           Also that which simply asserts 'a certain man is not white', removes whiteness from a certain [man] [*]. But anyone who states 'it is not the case that a certain man is white' and removes the sense of the particular affirmative, cuts [it] into its contradictory, namely the universal negative, as if he had said that none is white. For anyone who extinguishes the sense of the proposition by putting negation before, assuredly presents it as false. But if 'a certain man is white' is false, the truth of its contradictory 'no man is white' is left over. ||           Therefore 'it is not the case that a certain man is white' states just as much as 'no man is white', and deservedly so. For 'no man' is such as 'any man', and anyone who denies [negat] that a certain man is white, also removes all accidents from [man], i.e. wholly denies [denegat] that Socrates is white, that Plato is white, and that anyone else is white. For as much as it has either predication or consequence for a number of things, by so much many things are removed from them. Wherefore also anyone who says 'Socrates is not a certain man', removes every man, since 'a certain [man]' is each man, as if he said 'he is not a man'. But anyone who states that he is not every [man], excludes none - assuredly no one is everyone. ||           But perhaps it is said that the the remotion in which 'every' is stated, is more than that in which 'a certain' is stated, indeed in one 'a certain' is excluded, in the other 'every'. Besides, if we think more of the remotion of words than of things, in the one the expression 'a certain man' is supposed, in the other 'every man', and by negation it is removed. But if we think of the remotion of the thing designated, since 'a certain man' has predication to each man, but 'man' to none, with 'a certain man', each man is taken away, whereas none [is taken away] with 'every'. But whoever says that 'a certain' is removed, excludes all, if here he accepts the sense of negation in 'it is not the case that a certain', but [excludes] no one if in the sense of 'it is not the case that every'. ||           But if he understands these as affirmatives, i.e. when either 'a certain' is removed or 'every', here it is separated and diverse, nothing to the explanation of negations. In negation, accordingly, as many things are contained in what is predicated, as there are many excluded in it, i.e. all which are enclosed by it. For just as in affirmation one thing out of all is attributed, thus in negation 'every' is removed. For example, if we say 'Socrates is a man', he is said to be some man, but we say he is not a man, we remove 'every' from him. ||           Wherefore, while an affirmation is inferred from one thing, yet from one thing a negation cannot be shown. For if someone was this man, there is a man, but if someone was not this man, there is not a man. Accordingly, what is predicated of something in affirmation, is removed in negation of all things, yet with the sense of the predicated expression remaining the same in both. For since the affirmation seems to say that there is someone who is a man, the negation takes away the same thing, i.e. that there is not some one, i.e. where each one, when there is someone, is excluded. ||           Now it is manifest from the above that to every affirmation there is a negation strictly opposed in contradiction, such as is properly dividing and which with negation placed before it removes its entire sense, so that to 'Socrates is a man', there is opposed 'it is not the case that Socrates is a man', and not 'Socrates is not a man'. And to 'every man is a man' there is opposed 'not every man is a man', not 'a certain man is not a man'. But of 'a certain man is a man', there is opposed 'it is not the case that a certain man is a man', not 'no man is a man' [*]. ||           But because these negations are remotive, nothing prevents them also having other other negations such as are properly dividing, and which are destructive of them, so that to 'Socrates is not a man' there is 'it is not the case that Socrates is not a man', which destroys that which was first being stated, i.e. as if it were to show it false. ||           And thus also of 'some man is not a man' the proper destructive negation is 'it is not the case that some man is not a man', which says there is not in reality what the first thing was saying, i.e. that 'man' is disjoined from a certain man. Thus also in hypothetical propositions, to the negations which are separative, other negations are applied which may be destructive of them, so that to 'if there is a man, there is not a stone', there is opposed 'it is not the case that if there is a man, there is not a stone', i.e. which totally denies its whole sense, as if we were saying it is false, showing in fact there is nothing in reality which it states. ||           Now destructive and strict negations can be suited not only to these negations which we have called separative, but perhaps also in those which are destructive, i.e. which extinguish and falsify their entire sense. For example, when we say 'it is not the case that it is not the case that every man is an animal', as if it were said openly that there does not exist in reality what 'not every man is an animal' says negatively. But of course a negation of this sort is equipollent to the universal affirmation 'every man is an animal', in a sense that seems rather to be affirmative, for what takes away one [of two] dividing [assertions], seems to constitute the other. ||           But although it has a certain equipollence to it, yet in sense it has a very great difference, i.e. since the latter is stated in affirmation, but the former in negation, as if they always seemed to accompany one another, yet they do not guard an inference from one to the other. ||           Accordingly, every proposition seems to have a proper negation, which absolutely destroys and removes its sense with the negation placed before, so that to 'every man is white', there is opposed the negation 'not every man is white', or to 'a certain man is white' there is opposed 'no man is white', which is the same as 'it is not the case that a certain man is white' [*], and to 'a man is white' there is opposed 'it is not the case that a man is white', to 'Socrates is white', 'it is not the case that Socrates is white'. ||           Proper negations then are those negations which take away absolutely the sense of an affirmation, i.e. so as wholly to deny no more and no less than what the affirmation stated [*]. For when it is asserted of the same universal subject in different ways, many affirmations and negations arise in this way: 'every man is white', 'no man is white', 'a certain man is white', 'a certain man is not white' or 'not every man is white' which is alone the proper and strict negation of 'every man is white', which absolutely takes away what it was saying, thus: 'not every man is white', i.e. not 'no man is white', which removes whiteness from all those things, to which the former was attributing whiteness, [*]. For the latter denies more than a strict negation, i.e. it not only denies what the affirmation was stating, that is, it not only shows that not everything is white, but on the contrary that none is, where a greater negation is stated. ||           For with any one thing not being white, the former is true. But the latter is not [true] unless all things lack whiteness [*], therefore more is wholly denied in the latter than in the former, and it takes more away than absolutely removes the sense of the affirmation, in this way 'not every man is white'. ||           Wherefore 'not every man is white' is the only properly dividing and strict negation of what 'every man is white' was saying, and not of 'no man is white', which can be false with it at the same time and denies more than what the former was stating, or also, as some please, the separative particular [*] 'a certain man is not white', which also, as was shown, could be false at the same time. Wherefore Aristotle distinguished universal negation more subtly than Boethius. For rightly he always opposes 'not every man is white', but Boethius opposes 'a certain man is not white', the particular separative in negation, which he judged to be the same as the destructive negation, falsely, as was shown, i.e. since sometimes the particular is found to be false at the same time as the universal, as we have taught above. ||           But of the dividings of affirmation and negation, when one is true, the other necessarily is false, and when one is false, the other is true, i.e. either the thing itself exists of which it concerns, or it does not exist, just as Aristotle taught of the opposition of affirmation and negation. For whether Socrates exists, or not exists, there exists always in reality what one of the dividing propositions asserts, and what the other states does not exist in reality, i.e. of 'Socrates exists' and 'Socrates does not exist'. For when he exists, the affirmation is true and the negation false. But when he does not exist, the converse is true. ||           Yet perhaps it will be objected, that after Socrates has perished, 'it is not the case that Socrates is Socrates' is neither true nor false, since clearly the proper sense of the proposition is lost because the subject expression, which is now neither significative nor even predicative. For if with Socrates destroyed, his name retains its earlier and proper imposition, which was made with him existing, also when he is destroyed, 'Socrates' is said, wherefore also man, indeed the name of him, as a man, was such as before. ||           But what does not exist, cannot be called 'man'. For if what does not exist were called a man, an equivocation would be transferred to a non-existing thing. At one time the true negation by which it was dealing with an existing thing, was not of the affirmation stated, which was false, nor at another even the truth which by the imposition of the voice removes the same thing from itself, as 'this body' would disjoin him from himself. ||           It is necessary therefore that the name of Socrates is taken in the same signification as much in affirmation as in negation, i.e. in the designation of the person as existing who perished, otherwise it is not an opposition of contradiction, i.e. unless you accept [them] in the same sense. Wherefore Aristotle himself in I Perihermaneias [says] ' We will call such a pair of propositions a pair of contradictories. Those positive and negative propositions are said to be contradictory when they have the same subject and predicate. The identity of subject and of predicate must not be 'equivocal'. Indeed there are definite qualifications besides this, which we make to meet the casuistries of sophists'. As if he were openly saying, if you wish to state a contradiction of divided propositions, you must take the terms of both propositions in the same sense, namely with every kind of sophism excluded. ||           But in the second edition of the Perihermaneias, Boethius records that Aristotle set down six kinds of sophisms in his Sophisticis Elenchis, all of which in fact prevent the opposition of contradiction. Now he called these: univocation, different part, different time, different relatum, different manner. But he misses the opposition of contradiction with the terms equivocally taken, as for example 'Alexander seized Helen', 'Alexander did not seize [Helen]', for both are true - the affirmation, of the son of Priam, of course, whereas the negation is of course true of the great king of the Macedonians. For with a word accepted of different things of which it is said univocally, a contradiction often disappears, as when someone says that Socrates is a man (where the name 'of man' is understood of inferiors) he states the truth. But if that name relates to that species of man which they make up purely by the abstraction of accidents, the negation 'Socrates is not a man' will also be true.
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 * Qui enim de eis ut de disiunctis ab invicem agit, eas tamquam existen{te}s accipit; qui autem ut de non convenientibus sibi, non magis earum existentiam quam non-existentiam innuit, sed [non] solum quod non sibi inhaereant proponit. Aliam itaque vim negatio habet praeposita, aliam interposita. Unde et quae dicit: 'omnis homo non est albus' non eadem videtur cum ea: 'non omnis homo est albus' et quae proponit: 'quidam homo non est albus' non eadem est cum ea: 'non quidam homo est albus'. Qui enim dicit: 'omnis homo non est albus' ab omni homine albedinem removet ac si universalem faciat remotionem dicens omnem carere albedinem; qui autem universalis affirmationis sensum exstinguit, id solum demonstrat quod non omni conveniat, non etiam quod ab omni separata sit; illa enim vera est, etsi unus albus non sit.
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 * Ea quoque quae ait simpliciter: 'quidam homo non est albus', albedinem a quodam removet. Qui vero proponit: 'non quidam homo est albus' sensumque particularis affirmativae tollit, in contradictoriam eius incidit, universalem scilicet negativam, ac si diceret nullum esse album. Qui enim negatione praeposita sensum propositionis exstinguit, ipsam profecto falsam esse ostendit. Si autem falsa sit 'quidam homo est albus', vera ipsius contradictoria relinquitur 'nullus homo est albus'.
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 * Tantumdem ergo proponit 'non quidam homo est albus', quantum 'nullus homo est albus'; et merito. Quod enim dicit[ur] 'nullus homo' tale est quale etiam 'ullus homo' et qui negat quemdam hominem esse album, omnia quoque eius accidentia perimit, id est et Socratem esse album denegat et Platonem et quemcumque alium. Quanto enim ad plura vel praedicatio vel consecutio se habuit, tanto plura in ipsis perimuntur. Unde et qui dicit: 'Socrates non [178] est quidam homo', cum unusquisque quidam sit, omnem hominem aufert, ac si diceret: 'non est homo'. Qui vero ipsum non omnem esse proponit, nullum excludit, quippe nullus est omnis.
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 * Sed fortasse dicitur haec remotio in qua 'omnis' ponitur, maior esse quam ea in qua 'quidam', quippe hic 'quidam', ibi 'omnis' excluditur. At si vocum remotionem magis quam rerum pensemus, ibi quidem 'quidam homo' ista vox, hic vero 'omnis homo' ponitur atque negatione removetur. Si vero rei designatae remotionem pensemus, cum 'quidam homo' ad unumquemque hominem praedicationem habeat, 'homo' vero ad nullum, hic in 'quidam homo' unusquisque aufertur, nullus vero in 'omnis'. Qui vero dicit 'quidam' removeri, si sensum negationis hic accipiat quod non sit quidam, omnes exclusit, si vero quod non sit omnis, neminem.
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 * Si vero affirmativas easdem intelligat, cum scilicet aut 'quidam' removetur vel 'omnis', hoc est separatus ac diversus, nihil ad expositionem negationum. In negatione itaque quanto plura in praedicato continentur, tanto in ipso excluduntur, omnia scilicet quae ab ipso clauduntur. Nam sicut in affirmatione unum ex omnibus attribuitur, ita in negatione 'omnis' removetur: veluti si dicatur: 'Socrates est homo', tale est tamquam aliquis homo [non] esse dicatur; si vero ipsum non esse hominem dicamus, 'omnis' ab ipso removeremus.
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 * Unde cum ex uno affirmatio inferatur, ex uno tamen negatio non potest monstrari. Si quis enim hic homo fuerit, homo est, sed si non sit hic homo, non est homo. Quod itaque in affirmatione circa aliquem praedicatur, in negatione circa omnes removetur, sensu tamen praedicatae dictionis eodem in utraque remanente. Cum enim affirmatio dicere videatur quod sit aliquis hominum, negatio idem aufert, quod videlicet non sit aliquis, in quo scilicet unusquisque, cum aliquis sit, excluditur.
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 * Manifestum est autem ex suprapositis omni affirmationi eam in contradictionem recte opponi negationem tamquam propriam dividentem quae negatione praeposita totam eius sententiam perimit, ut ei quae est: 'Socrates est homo' ea quae est: 'non Socrates est homo', non ea quae dicit: 'Socrates non est homo'; et ei quae est: 'omnis homo est homo, ea quae est: 'non omnis homo est homo', non ea quae est: 'quidam homo non est homo'; eius vero quae est: 'quidam homo est homo' ea quae est: 'non quidam homo est homo', non ea quae est: 'nullus homo est homo'.
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 * Quae vero remotivae sunt negationes, nihil prohibet eas quoque alias, quae earum destructivae sunt, negationes habere tamquam proprias [179] dividentes, ut eam quae dicit: 'Socrates non est homo' ea quae proponit: 'non Socrates non est homo', quae id quidem destruit quod prima proponebat, ac si scilicet eam falsam esse ostenderet.
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 * Sic quoque et eius quae est: 'quidam homo non est homo' ea est propria negatio destructiva: 'non quidam homo {non} est homo', quae quidem dicit non esse in re quod prima dicebat, id est quod 'homo' a quodam homine disiungatur. Sic quoque et in hypotheticis propositionibus his negationibus quae separativae sunt, aliae quae earum destructivae sint negationes applicantur, ut ei quae est: si est homo, non est lapis ea quae est: non si est homo, non est lapis quae scilicet eius totam sententiam denegat, ac si ipsam falsam esse diceremus, ostendentes quidem non esse in re quod ipsa dicit.
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 * Nec solum autem his negationibus quas separativas diximus, destructivae ac rectae negationes possunt aptari, verum etiam fortasse his quae destructivae sunt, quae scilicet totam earum sententiam exstinguant ac falsificent. Veluti cum dicitur: 'non non omnis homo est animal', ac si aperte diceretur non esse in re quod negativa illa dicit: 'non omnis homo est animal'. Sed huiusmodi quidem negatio eoquod universali affirmationi quae ait: 'omnis homo est animal' aequipolleat, in sensu potius affirmativa videtur; qui enim unam dividentium aufert, alteram constituere videtur.
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 * Sed licet quamdam ad ipsam habeat aequipollentiam, in sensu tamen maximam habet differentiam, cum haec scilicet in affirmatione, illa vero in negatione proponatur, ac si sese semper comitari videntur, non tamen mutuam ad se inferentiam custodiunt.
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 * Omnis itaque propositio propriam videtur habere negationem, quae sensum eius simpliciter destruit ac praeposita negatione perimit. Ut ei quae dicit: 'omnis homo est albus' ea opponatur negatio quae ait: 'non omnis homo est albus' vel ei quae dicit: 'quidam homo est albus', 'nullus homo est albus', quae eadem est cum ista: 'non quidam homo est albus'; et ei quae est: 'homo est albus', 'non homo est albus', 'Socrates est albus', 'non Socrates est albus'.
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 * Propriae ergo illae sunt negationes quae affirmationis sententiam simpliciter auferunt, ut scilicet non plus aut minus in eis denegetur quam affirmatio proponebat. Cum enim de eodem subiecto universali diversis modis enuntiato multae fiant affirmationes et negationes hoc modo: 'omnis homo est albus', 'nullus est albus', 'quidam est albus', 'quidam [180] non est albus' vel 'non omnis est albus', eius quae est: 'omnis homo est albus', ea sola propria est et recta negatio {quae} simpliciter id aufert quod illa dicebat, hoc modo: 'non omnis homo est albus', non illa scilicet quae ab omnibus albedinem removet quibus illa albedinem attribuebat, quae scilicet ait: 'nullus homo est albus'; plus enim haec negat quam recta negatio, quae scilicet non solum negat quod affirmatio proponebat, hoc est non solum ostendit non omne esse album, immo nullum esse; in quo maior negatio proponitur.
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 * Illa enim unoquoque non existente albo vera est, ista autem non nisi omnes albedine careant; plus itaque in ista quam in illa denegatur ac plus ista tollit quam ea quae sensum affirmationis simpliciter perimit, hoc modo: 'non omnis homo est albus'.
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 * Unde ea sola est: 'non omnis homo est albus' proprie dividens et recta negatio eius quae dicebat: [non] 'omnis homo est albus', non ea quae est: 'nullus homo est albus', quae et simul cum ea falsa potest esse plusque denegat quam illa proponebat; vel ea etiam, ut quibusdam placet, separativa particularis quae dicit: 'quidam homo non est albus', quae etiam, ut ostensum est, simul falsa esse poterit. Unde subtilius Aristoteles negationem universalem quam Boethius distinxit. Hic enim 'non omnis homo est albus, recte semper opponit, Boethius autem 'quidam homo non est albus', particularem negatione{m} separativam, quam eamdem esse cum ea quae destructiva, falso, ut ostensum est, arbitratur, cum scilicet aliquando simul falsa cum universali reperiatur particularis, ut supra docuimus.
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 * Dividentium autem affirmationis et negationis cum una vera sit, aliam necesse est falsam esse, et cum falsa sit, veram, sive scilicet res ipsa sit de qua agitur, sive non sit, sicut in oppositione affirmationis et negationis Aristoteles docuit. Sive enim Socrates sit, sive non sit, semper in re est quod una dividentium dicit, et non est in re quod altera proponit, harum scilicet: 'Socrates est', 'non Socrates est'. Cum enim ipse est, vera est affirmatio et falsa negatio; cum autem non est, econverso.
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 * Fortasse tamen opponitur, postquam Socrates perierit, nec veram nec falsam esse 'non Socrates est Socrates', cum videlicet propositionis amittat proprietatem pro subiecta voce, quae iam significativa non est sive etiam praedicativa. Si enim destructo Socrate ipsius nomen priorem et propriam impositionem retineat, quae in ipso tamquam existente facta est, profecto ipso quoque destructo, Socrates dicitur; unde etiam homo, quippe ipsius nomen, ut hominis, tale quod ante fuit.
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 * At vero [181] quod non est, homo dici non potest. Si enim quod non est, homo diceretur, aequivocatio ad non-existentem rem transferatur; iam non erat {pro}positae affirmationis, quae falsa erat, negatio {vera} qua de existente agebatur, nec iam etiam vera[m] quae vocis impositione mutata idem a se removet, tamquam 'hoc cadaver' a se ipso disiungeret.
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 * Oportet itaque 'Socratis' nomen tam in affirmatione quam in negatione in eadem significatione accipi, in designatione scilicet eius qui periit tamquam existentis; alioquin non ess{et} oppositio contradictionis, nisi scilicet in eodem sensu acceptis. Unde ipse Aristoteles in Primo Periermenias, cum contradictionem affirmationis et negationis describeret, ait: " sit haec contradictio: affirmatio et negatio oppositae; dico autem opponi eiusdem de eodem, non autem aequivoce et quaecumque caetera talium determinauimus contra argumentorum sophisticas importunitates." Ac si aperte diceret: si contradictionem dividentium propositionum proponere velis, oportet utriusque propositionis terminos in eodem sensu accipi, omni videlicet genere sophismatis excluso.
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 * Sex autem sophismatum genera Aristotelem in Sophisticis Elenchis suis posuisse Boethius in Secunda Editione Periermenias commemorat, quae quidem omnia contradictionis oppositionem impediunt. Haec autem ipse dixit aequivocationem, univocationem, diversam partem, diversum tempus, diversum relatum, diversum modum. Deficit autem oppositio contradictionis terminis aequivoce sumptis, cum scilicet {dicimus}: 'Alexander rapuit Helenam', 'Alexander non rapuit': utraque enim vera est, affirmatio quidem de filio Priami, negatio vero de rege magno Macedonum. Saepe enim voce in diversis accepta de quibus univoce dicitur, contradictio perit; ut si quis dicat Socratem esse hominem 'hominis' que nomen circa inferiora intelligat, verum proponit; quodsi ad speciem illam hominis quam fingunt puram per abstractionem accidentium, ipsum nomen referat, vera quoque erit negatio 'Socrates non est homo'.

||           For Socrates is both one an individual man, and is truly denied to be the species which man is, but of both 'men' the name of 'man' is said as much of a simple thing as of an individual, i.e. with the definition 'rational mortal animal'. They do not say 'univocation' because a word is taken to mean the same thing, but 'identity'. For just as 'equivocal' is said of many, so 'univocal', wherefore the name 'Socrates', if it is not common, is called neither 'equivocal' nor 'univocal'. The acceptance of the different part hinders the contradiction, for example, if the eye were said both to be white on account of this part, and not to be white on account of that part, they will both be true. But also a different time can remove a contradiction, for example if it be said 'I read but not read' [*], where 'read' is meant in the past tense, but in the latter is taken in the present tense. ||           Also in a different report a contradiction is called false, for example if we say 'Anchises is a father', and this is understood 'in respect of Aeneas', it is true, and also if the same person is said not to be the father in respect of Priam, this is also true. Also a different mode of assertion is said to take away a contradiction. For if 'a countryman and a bishop' is said, and that is taken according to potentiality, it is true. But if the negation 'not being a bishop' relates to an actual state of affairs, this also is true. ||           But it appears from the above determinations, that Aristotle demonstrated the contradiction of affirmation and negation not according to sense but according to the material of constitution. For if the sense were accepted in the things themselves, he would have said that in negation the same thing is taken away from the same thing that was stated in the affirmation, and he would have said that the same thing was removed from the same thing. The exclusion of equivocation, which pertains to spoken words, would seem to be useless. ||           For what takes away the same from the same, has the sense of negation, although sometimes it is lacking in the constitution, for example when we say 'Socrates is a sword', 'it is not the case that Socrates is sharp', 'Socrates is a man', 'Socrates is not a rational mortal animal'. For these guard a contradiction in sense, but do not state it in the sound, since they change completely the material of the sounds. But because Aristotle meant to show not only the sense of the contradiction, but also the true constitution, which consists of the same spoken terms, he rightly said afterwards that the same terms have negation according to presentation, the rest seemed to be determined according to the sense. ||           But those kinds of sophisms of different ways or different reports, which Boethius adnumerates, seem uselessly adjoined to those who examine the reason well. And he understands a different mode of assertion in 'an egg is an animal', 'an egg is not an animal', relating the one to potentiality, the other to actuality. For in the affirmation ['an egg is an animal'], to maintain its truth, the signification of the word 'is' is taken according to potentiality, yet this [idea] not found in any authority, nor does reason hold it. For if it is not posited substantively, what he adds, i.e. the predicate 'animal', he will not join by the copula ['is']. But if 'animal' is the whole name, it does not contain anything that is not now animated, but an egg will not be one of those things which are now animated. ||           Also the negation 'Aeneas is not a father', cannot express without qualification that he is not a father either of Priam or of some other, but rather it altogether denies that he is a father and excludes everyone who falls under the name 'father'. Nor does anyone who says that he is a father, show of whom he is a father, but asserts without qualification that he is a father. For the demonstration of he of whom he is the father does not happen, when his name is withheld. ||           And although according to the truth of the matter, determinations of this sort were not attached, they were mentioned on account of the casuistries of the sophists, which were settled not so much by reason but by opinion and use. Wherefore Aristotle himself also says 'which we make to meet the casuistries of sophists'. It is therefore right and proper as much as verbally as in meaning, that negation extinguishes the sense of the assertion when it is prefixed to the proposition. Now since it removes that sense, the signification of the words is not changed. ||           From this it is manifest that Aristotle considered the negation of a universal affirmation in a more subtle way [*] than Boethius. For Boethius opposes to 'every man is just' the particular separative proposition 'a certain man is not just', when nonetheless both may be false at the same time, as was shown. But Aristotle assigns to it the proposition 'not every man is just', which can never be true or false at the same time as [the other]. Rather, the true and the false always divide among them so that, whenever the former is true, the latter is false, and conversely, whether there are things that correspond, or not [*]. ||           Yet when there are no things, they do not seem to have the constitution of a sentence, since now the signification of the parts will have perished, as we have also taught above [*]. But if propriety of constitution is sometimes missing in them, the division of sense is never taken away, for always one that was uttered will be the case, the other will not. For at any time it is indisputable that either what 'every man is just' states is the case, or what 'not every man is just' says, or similarly not to be the case. Wherefore they make a strict contradiction. ||           Now they will perhaps ask what proposition is expressed by a negation such as 'not every man is just', since it does not have the sense of the particular (i.e. of 'a certain man is not just'). But we call it neither properly a particular nor a universal negative, but properly the negation of a universal. Therefore it is not necessary that what are destructive and proper negations fall under the division of categoricals which Boethius states through a universal and particular material and sense, in which he nonetheless includes all categoricals, being of the view, as was shown, that 'not every man is just' has a particular sense, namely of 'a certain man is not just'. [*].              ||            But since signs of quantity that are attached or removed make many differences of affirmation and negation, since clearly universal, particular, or indefinite [propositions] come about [as a result], we must distinguish their functions more subtly and consider how much force of signification and place they possess in a statement. ||                          ||            Now the signs 'every', 'a certain', 'no', are not acknowledged in the constitution of the proposition. For they assert that the only parts of the categorical proposition are what we call terms, i.e. subject and predicate, though they concede that the verb itself, which is designative of inherence, is a part, i.e. where it is predicated in the second place. But as we said above, there can be parts of the proposition which are not terms or principals as predicate and subject, without which the proposition in no way could stand, since it expresses their attachment or removal. ||           And also we can firmly establish that signs are parts of the proposition as well, as much from reason as from authority. For 'every man is white' is an entire statement, because it is a sentence signifying the true or the false. And the universal assertion that the attachment of the sign makes of what it is attached to, extends and fills out the sense, since it gathers 'man' around all things. Thus also the determinations of the either subject or predicate can be mixed together in the parts of propositions according to place, for example when we say 'Socrates does not see Plato'. For that is one entire truth and to the truth which especially the determination of the oblique case very often falsifies, which having been removed, the proposition remains false. ||           Moreover, authority allows that signs are among the parts of the proposition, since in his Categories Boethius divides the proposition 'every man is an animal' into 'every man' and 'is an animal'. So also [such] signs are parts of speech and are designative by imposition. For words, which do not mean the same to all, are not natural, but are devised for forming locutions that are both tenseless and simple. Nor of infinite signification nor of oblique proposition, for of the same thing are the cases of the very thing to which the subject is attached, as if adjectives of it, and it is established that they stick fast to them and are called names. This follows whether they are proper or appellative names. ||                          ||            But 'every' cannot be appellative, since clearly it could not be suited to many things individually. For of nothing can it be said that it is everything, indeed 'everything' is not imposed on 'something' as if it were said 'that thing is everything'. Further, it is not appellative since it is not universal. Wherefore Aristotle says '"every" is universal, but according as it consignifies universally'. It cannot be a proper name either, since it forms a plural, nor can we show a singular signification of it. Yet it is said by some that the signification of it is of all things at the same time taken as a collection, as such also could be made a predication [such as] 'everything is 'everything', that is, 'a collection of all things is a collection of all things'. ||           But of course in this signification, if perhaps it could be taken in this way, in the same way that a whole [quantity] collects together the parts of quantity, when we say 'everything is 'everything', that is 'a whole collection of things is a whole collection of things', in no way is it understood as the sign of universality, nor does it send us to the inferiors of the universal. For 'whole' and 'every' differ in that 'every' is applied to the species, that is to the inferiors, but 'whole' to the parts, i.e. the constituents. And either can in fact be a sign of quantity, in fact the latter of the universal quantity of a thing according to comprehension of the singulars of a species, but the former of the individual composed according to the constitution of component parts. Wherefore also 'all Socrates' can be said, but not 'every [Socrates]'. ||           But there are some whom it pleases that 'every' and 'a certain', according as they are called signs of quantity, are taken from the universality and unity of quantities, which they determine when adjoined to the subjects around them. But falsely. For if 'every' were taken from universality, and from the unity of quantities, thus 'universal' would say the same as 'every', and 'universal man is a species'would be just as valid as 'every man is a species', which is plainly false.
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 * Nam et Socrates aliquod est de individuis hominis, et illa species quae homo est, vere denegatur esse; de utroque autem homine tam de simplici quam {de} individuo univoce nomen 'hominis' dicitur, cum ea scilicet definitione quae est animal rationale mortale. Univocationem non dicunt cum circa eamdem rem vox accipitur, sed identitatem. Sicut enim aequivocum ad multa dicitur, ita univocum; unde 'Socratis' nomen, si commune non sit, neque aequivocum neque univocum dicitur. Diversae partis acceptio [182] contradictionem impedit, veluti, si oculus et albus esse dicatur propter hanc partem et non esse albus propter illam, verae utraeque erunt. Sed et diversum tempus contradictionem potest perimere, veluti si dicatur: 'iste legit ac non legit' ibique 'legit' praeteriti temporis designativum, hic vero praesentis accipiatur.
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 * In diverso quoque relatu contradictio falsa dicitur veluti si dicatur: 'Anchises {est} pater, et intelligatur 'Aeneae respectu', {uerum est; atque {si} idem non esse pater intelligatur respectu} Priami, hoc quoque verum est. Diversus quoque modus enuntiationis contradictionem auferre dicitur. Si enim dicatur: 'rusticus est episcopus' et id secundum potentiam sumatur, verum est; si vero non esse episcopus et ad actum negatio referatur, haec quoque vera est.
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 * Apparet autem ex suprapositis determinationibus Aristotelem contradictionem affirmationis et negationis non {tam} secundum sententiam quam secundum constitutionis materiam demonstrasse. Si enim sententiam in rebus ipsis acciperet, dixisset idem in negatione de eodem auferri quod in affirmatione proponebatur, remque eamdem ab eadem re dixisset removeri. Aequivocationis exclusio, quae ad voces pertinet, inutilis videretur.
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 * Quae enim eamdem rem ab eadem aufert, negationis sententiam tenet, etsi quandoque in constitutione deficiat, veluti cum dicitur: 'Socrates est ensis', 'non est Socrates mucro'; 'Socrates est homo', 'non Socrates est animal rationale mortale'. Hae enim contradictionem in sensu custodiunt, sed non in voce proponunt, cum vocum materiam permutent. Quia vero Aristoteles non solum sententiam contradictionis, verum etiam constitutionem demonstrare intendit, quae in eorumdem terminorum voce consistit, recte postquam eosdem terminos negationem habere dixit secundum prolationem, caetera secundum sententiam determinanda videbantur.
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 * At vero illa sophismatum genera de diverso modo vel diverso relatu, quae Boethius annumerat, his qui rationem bene perspiciunt inutiliter adiuncta videntur. Diversum autem enuntiandi modum in eo intellexit quod ait: 'ovum est animal', 'ovum non est animal', {illud} ad potentiam, hoc ad actum referens. Nam in affirmatione, ut veritatem conservet, 'est' verbi significationem secundum potentiam sumit; quod tamen nec in a[u]ctoritate inveni, nec ratio tenet. Si enim substantive non ponitur, quod subditur, animal scilicet praedicatum, non copulabit; [183] quodsi est 'animal' totum nomen, nonnisi ea quae iam animata sunt continet, ovum vero non erit aliquid horum quae iam animata sunt.
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 * Ista quoque negatio: 'Aeneas non est pater', non potest simpliciter ostendere ipsum non esse patrem vel Priami vel alicuius alterius, sed omnino eum esse patrem denegare atque omnem qui in 'patris' nomine continetur, excludere. Nec qui dicit ipsum esse patrem, cuius sit pater [non] monstrat, sed simpliciter quod sit pater enuntiat. Non enim demonstratio fit eius cuius pater est, cum nomen eius reticetur.
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 * At licet secundum rei veritatem determinationes huiusmodi non essent apponendae, propter importunitates tamen sophistarum fuerant tangendae, qui non tam rationem quam opinionem usumque sectantur. Unde et ipse Aristoteles: "quae nos, inquit, determinamus contra sophisticas argumentorum importunitates." Est itaque recta ac propria tam voce quam sensu negatio, quae negatio praeposita propositae enuntiationi sententiam eius exstinguit. Cum autem sententia eadem perimitur, vocum significatio non mutatur. In his autem recta contradictio continetur.
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 * Ex his itaque manifestum est subtilius Aristotelem considerasse negationem universalis affirmationis quam Boethium. Illi enim quae ait: 'omnis homo iustus est' particularem illam separativam quae ait: 'quidam homo non est iustus' Boethius opponit; cum tamen utrasque, ut ostensum est, falsas simul esse contingat. Aristoteles autem eam assignat quae dicit: 'non omnis homo iustus est', quae numquam simul vera est vel falsa; sed semper invicem ita verum et falsum dividit quod, quotiens haec vera est, illa falsa est, et econverso, sive scilicet res earum sint, sive non sint.
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 * Cum tamen res non sunt, non videntur orationis constitutionem habere, cum iam partium significatio perierit, ut supra quoque docuimus. Sed si eis constitutionis proprietas quandoque deficiat, divisio sensus numquam deest; semper enim alterum erit quod dicitur, alterum non erit. Omni enim tempore constat esse vel id quod 'omnis homo iustus est' proponit, vel quod 'non omnis homo iustus est' dicit, ac similiter non esse; unde rectam contradictionem faciunt.
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 * Quaerent autem fortasse de huiusmodi negatione: 'non omnis homo iustus est', cum particularis sententiam non teneat, -- eius scilicet quae ait: 'quidam homo non est iustus' -- quae sit propositio dicenda. Nos vero nec particularem eam proprie nec universalem dicimus negativam, [184] sed propriam universalis negationem. Non itaque necesse est eas quae destructoriae sunt ac propriae negationes, sub ea divisione categoricarum cadere quam Boethius per universalis ac particularis materiam ac sententiam proponit, in qua tamen omnes conclusit categoricas, opinans, ut ostensum est, 'non omnis homo iustus est' particularem sententiam habere, eius scilicet: 'quidam homo iustus non est'.
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 * Quoniam autem signa quantitatis subiectis apposita vel subtracta multas faciunt differentias affirmationum et negationum, cum videlicet alias universales, alias particulares, vel indefinitas esse secundum ea contingat, oportet eorum officia subtilius distinguere et quam in {pro}positione vim significationis et locum obtineant, considerare.
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 * DE SIGNIS QUANTITATIS
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 * Quidam autem nec in constitutionem propositionis signa recipiunt, haec scilicet 'omnis', 'quidam', 'nullus'. Aiunt enim categoricae propositionis solas esse partes quas terminos dicimus, id est praedicatum et subiectum. Sed hi quidem nec ipsum verbum, quod inhaerentiae designativum est, partem concedunt esse, ubi scilicet secundo loco praedicatur. At vero, ut supra diximus, partes propositionis esse possunt quae termini non sunt aut principales tamquam praedicatum et subiectum, sine quibus propositio nullo modo potest consistere, cum eorum cohaerentiam vel remotionem demonstret.
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 * Et nos quoque tam ex ratione quam ex auctoritate signa quoque propositionis partes esse possumus convincere. Hoc enim totum {pro}positio est: 'omnis homo est albus', quia est oratio verum vel falsum significans; ac quidem universalis enuntiatio, quod signi appositio facit quod cui apponitur, sensum extendit atque implet, cum hominem circa omnia colligit. Sic etiam determinationes vel subiecti vel praedicati propositionum partibus secundo loco possunt admisceri, veluti cum dicimus: 'Socrates non videt Platonem,. Id enim totum unum verum est et ad veritatem quam maxime obliqui determinatio saepissime vitiat, qua substracta falsa remanet propositio.
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 * Recipit autem auctoritas inter partes propositionis signa, cum in Categoricis suis Boethius huius propositionis: 'omnis homo est animal, divisionem fecit in 'omnis homo' et 'est animal'; sicut etiam signa sunt partes orationis ac per impositionem designativa. Neque enim voces sunt naturales, quae omnibus eaedem non sunt, sed inventae ad formandas [185] locutiones et sine tempore ac simplices; nec infinitae significationis nec obliquae positionis: eiusdem enim sunt casus cuius est ipsum cui apponitur subiectum, ac quasi eius adiectiva constat ea adhaerere {et} nomina dici; sed utrum propria vel appellativa, consequitur.
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 * {DE 'OMNIS'}
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 * Sed 'omnis' quidem appellativum esse non potest, cum videlicet multis singillatim non possit aptari. De nullo enim dici potest quod sit omne, quippe nec omne alicui sic impositum est ut diceretur: 'istud sit omne'. Amplius appellativum non est, cum universale non sit. Unde Aristoteles: "'omnis', inquit, universaliter est, sed quoniam universaliter consignificat." Proprium quoque esse non potest cum plurale faciat nec singularem eius significationem ostendere possimus. Dicitur tamen a quibusdam quod eius significatio sit omnium rerum simul acceptarum collectio, ut talis etiam possit fieri praedicatio: 'omne est omne', id est 'collectio omnium rerum est collectio omnium rerum'.
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 * Sed in hac quidem significatione, si forte ita possit accipi ut etiam partes quantitatis sicut totum colligat -- cum dicitur: 'omne est omne', id est 'tota collectio rerum est tota collectio rerum' -- nullo modo ut signum universalitatis accipitur nec ad inferiora universalis nos mittit. In hoc enim 'totum' et 'omne' discrepant quod 'omne' ad species, id est ad inferiora, 'totum' vero ad partes, scilicet constituentes, ponitur. Et utrumque quidem quantitatis signum esse potest, illud quidem quantitatis universalis rei secundum comprehensionem singularum specierum, hoc vero individui compositi secundum constitutionem componentium partium. Unde et totum Socrates dici potest, sed non omnis.
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 * Sunt autem quibus placet 'omnis' et 'quidam', eoquod quantitatis signa dicantur, sumpta esse ab universalitate et unitate quantitatibus, quas ipsa subiectis adiuncta circa ipsa det{erm}inent. Sed falso. Si enim 'omne' sumptum esset ab universalitate [et unitate quantitatibus], sic 'universalis' idem diceret quod 'omnis', ac tantumdem valeret 'homo universalis est species' quantum 'omnis homo est species'; quod aperte falsum est.

||                          ||            But if 'a certain' is taken to be a sign of particularity from unity, assuredly when 'a certain man' is said, it is just as valid as 'one man', that is, the unity of a man. And now it will not be a particular, but more an indefinite proposition, as if it were said 'a man is white'. And besides, just as it can be said 'every or a certain white thing' or 'every white man or some [white man]', thus both 'every certain or a certain certain white thing' or 'every certain or a certain certain man'. Accordingly it seems to me that the particular sign is not taken from unity, but rather that being a discrete thing is of the essence of the particular, just as 'someone', which is the name of an indefinite and indeterminate substance, is made from 'some' by adjoinment. It is also clear from this that it is not taken from unity, but that it is attached to unity, since we say 'a certain unity', yet reason does not allow unity to be formed with unity. ||                          ||            But now 'every' is comprehensive of many things individually, and collects individually the same things together which the very sound to which it is attached [applies to?], and the sign of universality is uttered according to the comprehension of all the inferior singulars. For the quantity of a universal thing consists in its diffusion through inferiors. And since it is always collective of singulars, it can be asserted of none, because there are none to which different singulars may belong, nor was it ever imposed in such a way as to say 'this thing is every thing'.
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 * DE 'QUIDAM'
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 * Si vero et 'quidam' signum particularitatis sumptum sit ab unitate, [186] profecto cum dicitur: 'quidam homo', tantumdem valet quantum 'unus homo', id est hominis unitatem; ac iam non particularis, sed magis indefinita propositio erit, ac si diceretur: 'homo {est} albus'. Ac sicut potest dici 'omne vel quoddam album' vel 'omnis homo albus vel quidam', sic et 'omne quoddam vel quoddam quoddam {album}' vel 'omnis quidam vel 'quidam quidam homo'. Videtur itaque mihi quod signum particulare non sumptum esse ab unitate, sed discretivum esse particularis essentiae, sicut 'aliquis', quod indefinitae atque indeterminatae substantiae nomen est, tamquam '{ali}quis' ex 'quis' per adiectionem factum est. Patet hinc quoque ab unitate ipsum sumptum non esse, quod et ipsum unitati quoque apponitur, cum dicitur 'quaedam unitas', {unitas} tamen ipsa cum unitate formari ratio non permittat.
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 * 'Omnis' autem multorum est singillatim comprehensivum et eadem singillatim colligit quae vox ipsa [apposita est] cui apponitur, signumque universalitatis secundum comprehensionem omnium singulorum inferiorum dicitur. Nam universalis rei quantitas in diffusione sua per inferiora consistit. Ac quoniam singulorum semper est collectivum, de nullo enuntiari potest, quia nulla sunt quibus diversa conveniant singula nec numquam ita impositum fuit ut diceretur de aliquo: 'istud sit omne'.
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 * Sic et 'uterque', cum duo quaelibet singillatim accepta colligat, de nullo enuntiari valet; inventum tamen est ut per ipsum de quibuslibet duobus singillatum acceptis agatur. Sicut autem circa quotlibet 'omnis' et 'nullus' et 'quidam' se habent et universales ac particulares tam affirmativas quam negativas faciunt enuntiationes, ita 'uterque' et 'neuter' et 'alter' circa duos. Sunt enim contrariae 'uterque currit' et 'neuter'. Sub his autem velut earum contradictoriae angulariter acceptae atque subalternae ad supra se positas et invicem subcontrariae 'alter currit' et 'alter non currit' continentur; ut subiectae descriptionis formula monstrat:

uterque eorum currit  --- contrariae   ---  neuter currit / X / alter currit  subcontrariae    alter non currit

[187]              ||            And thus 'both', since it gathers together any two taken individually, is validly asserted of none; yet it is found that it deals per ipsum with any two things whatever taken singly. And just as 'every' and 'no' and 'a certain' make universal and particular assertions, affirmative as well as negative, about as many things as you like, so for 'each' and 'neither' and 'one of' about two things. For there are contraries - 'both run' and 'neither [runs]'. Moreover under these, for instance, their contradictories are contained diagonally opposite, and subalternates to the ones above, and among them the subcontraries 'one of them runs' and 'one of them does not run', as the form of the description below shows:

both run ---  contraries --- neither runs / X / one of them runs  --- subcontraries --- one does not run ||           Now just as 'every' is comprehensive of the singulars which [are] named by the word to which it is attached, and also 'no' (although the latter is collective with the remotion of the singulars, whereas the former is not), so 'a certain' is designative of one indeterminately, thus 'both', 'neither' and 'one or the other' of two. Wherefore also according to the adjoinment of the subject, as was shown, contraries, subcontraries, subalternates or contradictories make assertions. ||           But what kind of name 'every' is acknowledged to be, i.e. whether proper or appellative, is not easy to make precise, on account of the reasons given above. Yet we observe more the nature of proper names than of universals in it, if we were to hold to the first imposition of it. For thus it seems to have been given in all things, as much as in singulars, so as to gather together the singulars as if it were proper names of them. As the voice may seem one in sound, nonetheless it holds the signification of many proper names [*], as if 'this thing and this ...' were said, and however many are similar, we would gather together the singulars. ||           But that it makes a plural, happens according to the multiplicity of equivocation, according to which we call many people Ajaxes or Alexanders. Perhaps also the difference between 'every' and the proper names of all things would be this: that in 'every' not only the singulars are collected together, but also it is suggested that nothing is excepted. But in 'everything' the singulars can be collected together, though it is not suggested that nothing remains from them, but more that if it were to happen that the singulars were presented, a certain number of things would be referred to according to words. But with 'every', since it collects together all things, a certain number is not made explicit, but rather however many are singular, it collects in a way so as to suggest nothing left out. ||           But from names, according to their imposition, we do not hold that none is left over, but perhaps we notice this more in some things from our choice than from our imposition - for example, if all subjects of the same name fall under our notice and we present all their names, that we would collect all things, i.e. with none left out, by our choice more than by the imposition of the names we hold, i.e. that we would know nothing else than what are named are contained in the name itself. But since the collection of singular things which 'every' refers to is not definite according to number, but however many things it collects are singular, it is appended not only to these names which contain all things, but also to all appellatives comprehensive of as many things. ||           For just as we say 'a collection of all things', so also we say 'every man' and 'every white thing'. Even if in this case there is not as much a comprehension of things as there is according to the difference of names in the previous case, yet the same sense of the universal sign seems to persist. For as much as it pertains to it, no object is left over, but the subject to which the name is appended, either 'man' or 'white', contains some things for its imposition which are determined in it. But as far as it pertains to the sense of the sign, nothing is the determination of its essence, but it puts forward just as much here as there, i.e. leaving out no object. For when in 'every man', 'every' precedes, if per se ipsum is accompanied, no object is excluded in it, just as when 'every object' is said. For it is such as if it were said 'every object which is a rational mortal animal'. ||           Since therefore the imposition of 'every' which precedes [a name], would like to send us to 'all things', the dropping of the adjoined name brings back the understanding to it, and corrects and binds fast the comprehension of 'every' in some way. Since of course the dropping of the name according to one, not a multiple, signification of the sense, in which all men are in fact united according to the same nature, makes the proposition one, not multiple, and also Aristotle calls such a thing a proposition.
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 * Sicut autem, ut 'omnis' comprehensivum singulorum quae nomina{n}tur a voce cui apponitur, et 'nullus', -- sed id quidem in remotione singulorum est collectivum, illud autem non --, 'quidam' autem unius indeterminate designativum est, ita 'uterque' et 'neuter' et 'alter' circa duos. Unde et secundum adiectionem subiecti, ut ostensum est, contrarias, subcontrarias, subalternas sive contradictorias faciunt enuntiationes.
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 * Quale autem nomen 'omnis' esse confiteatur, utrum scilicet proprium an appellativum, propter suprapositas rationes non est facile definire. Magis tamen propriorum naturam quam universalium in ipso percipiemus, si primam ipsius inventionem tenuerimus. Sic enim omnibus rebus tamquam singulis datum fuisse videtur, ut singula sic colligeret quasi propria ipsarum nomina. Ut in sono vox una videatur, significatione{m} tamen multorum propriorum nominum tenet; ac si 'haec res et haec' diceretur ac quotcumque sunt similiter, singula colligeremus.
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 * Quod autem plurale facit, secundum multiplicitatem aequivocationis contingit, secundum quam plures Aiaces vel plures Alexandros dicimus; ac fortasse haec erit {differentia} inter 'omnis' et omnium rerum propria nomina, quod in 'omnis' non solum singula colliguntur, verum etiam innuitur quod nullum excipiatur. In 'omne' vero singula possunt colligi, sed quod nullum remaneat ex ipsis non innuitur, sed magis si singula proferri contingeret, certus rerum numerus secundum vocabula monstraretur; 'omnis' vero, cum omnia colligat, certum numerum non explicat, sed quotcumque sint ea singula, ita colligit ut nullum praetermissum esse innuat.
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 * Ex nominibus autem secundum ipsorum inventionem non tenemus quod nullum relinquitur, sed magis fortasse in quibusdam ex discretione nostra quam ex impositione nostra hoc anima{d}vertimus, veluti, si omnia eiusdem nominis subiecta notitiae nostrae subiaceant eorumque nomina omnia proferamus, quod omnia collegerimus, nullo scilicet praetermisso, discretione nostra magis quam nominum impositione teneamus, eo scilicet quod scierimus nihil aliud quam ea quae nominata sunt in nomine ipso contineri. Quoniam autem non est definita secundum numerum ea singularum rerum collectio quam 'omnis' demonstrat, sed quotcumque sunt singula colligit, non solum his nominibus quae omnia continent, apponitur, verum etiam omnibus appellativis quotcumque rerum comprehensivis.
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 * Sicut enim '{collectio} omnium rerum', ita et 'omnis homo' et 'omne albam' dicimus; etsi hic non sit tanta rerum comprehensio quanta ibi secundum [188] nominum differentiam, signi tamen universalis eadem sententia videtur persistere. Quantum enim ad ipsum pertinet, nulla res relinquitur, verum subiectum nomen cui apponitur, vel 'homo' vel 'album', pro inventione sua quaedam tamen continet quae in ipso determinantur. Quantum vero ad sententiam signi pertinet, nulla est determinatio essentiae, sed tantumdem hic quantum et ibi proponit, nullam scilicet rem praetermittens. Cum enim in 'omnis homo' 'omnis' praecedit, si per se ipsum attendatur, nulla res in ipso excluditur, sicut et cum dicitur: 'omnis res'. Tale est enim ac si diceretur: 'omnis res quae est animal rationale mortale'.
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 * Cum ergo 'omnis' impositio quae praecedit, ad 'omnia' nos mittere vellet, submissio adiuncti nominis ad ea intellectum reducit atque 'omnis' comprehensionem quodammodo castigat ac restringit. Cum quidem submissi{o} nominis secundum unam, non multiplicem, significationem sententiae, qua omnes quidem homines secundum eamdem naturam uniuntur, unam, non multiplicem, {propositionem faciat, unam, non multiplicem,} huiusmodi quoque propositionem Aristoteles dicit.

||           Accordingly, although 'every' is appended to different and opposite names (since we say either 'every horse' or 'every man') yet their sense, for example of 'animal', continues the same, since we call 'rational animal' an expression, not a name, since we say 'irrational animal' and also since we say 'a horse is an animal' (or 'a man is an animal'). For even if another thing than a horse is an animal, and there is another thing than a man, yet there is not another name than that of 'animal' that is said there. Thus also when we say 'a horse is not a rational animal', the 'animal' that [comes after 'rational'] they concede is determined broadly as taken by 'rational', lest the assertion becomes false.
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 * Cum itaque vel 'omnis equus' vel 'omnis homo' dicitur, licet diversis et oppositis nominibus 'omnis' apponatur, eadem tamen eius sententia permanet, sicut 'animalis', cum dicimus vel 'animal rationale' orationem, non nomen, proferentes vel 'animal irrationale' vel cum etiam proponitur: 'equus est animal' {uel 'homo est animal'}. Etsi enim aliud sit animal quam equus et aliud quam homo est, non aliud tamen hic nomen 'animalis' quam ibi dicit. Sic quoque et cum dicitur: 'equus non est animal rationale' 'animal' quod praecedit large sumptum per 'rationale' determinari concedunt, ne falsa fiat enuntiatio.

||           But perhaps we would resolve [this] more easily, if we took the the sign of 'every' with the adjoined name as a composite expression, not of course deciding this by authority but by reason. For example, when we say 'every man', by 'every man' we would deal with single men in what was called a universal proposition, just as with a composite name, so that it would state something of everything, with none left out, whereas the particular or singular, would state [something] about something indeterminately or determinately.
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 * Fortasse autem facilius nos absolveremus, si 'omnis' signum cum adiuncto nomine tamquam compositam dictionem acciperemus, non tam quidem auctoritatem quam rationem sectantes. Veluti cum dicitur 'omnis homo', per 'omnis homo' tamquam per compositum nomen de singulis hominibus ageremus in ea quae universalis propositio diceretur, quod de omnibus nullo excluso proponeretur aliquid, particularis vero vel singularis, quod de aliquo indeterminate vel determinate proponeret.

||           But there are those who would not properly allow signs of this sort among expressions, nor may they say that a proper significant speech holds from imposition, but it makes a certain indication by representation of the spoken subject, as it is taken, i.e. about all things, not about one thing only, according as Boethius in the secundo divisionum calls signs of this sort determinations. For since 'man' can be taken both concerning one per se and concerning all, when 'every' or 'a certain' is given, they determine in some way how many are taken in the name itself, and here it is said to signify, not through the proper imposition of the sound, but as through a real representation, in which and a circle. ||           But signs of quantity are not called for any other reason than from the comprehension of the signification of the spoken subject which they determine, i.e. whether every subject is comprehended a thing in itself, or whether a certain thing. Just as 'every' in the singular number directs us to singulars individually taken in a singular way, thus 'all' in the plural directs us to singulars taken in a plural way. For example when it we say 'all men', assuredly we collect together both these two and those three and any number whatever according to any number of them whatever. ||           For just as 'man' names anything whatever taken per se, so 'men' comprehends whatever number collected at the same time. Wherefore according as from 'every man is white', 'Socrates is white' is implied, thus from 'all men are white', 'these two are white', or 'these three', i.e. when 'all', just as with 'every', is brought back to divisible parts, i.e. to those which take the predication of all singulae. For just as this man is called 'this man', so these two men or these three men are called 'men'. ||           But if 'all' is taken more collectively than individually, singulars do not seem to be inferred. For example when we say 'all the generalissima are ten', clearly they are taken at the same time, from which in no way is it conceded to be inferred that Substance and Quality are ten, for indeed to the singulars which are general are called, that word 'all' was not sending us, but rather more to the whole collection of the generalissima taken together, as when we say 'all the world'. ||                          ||            'No' is also called a sign of universality, gathering together singulars in remotion, which is well composed from 'not' and 'any'. For when there is not any left, the removal of all comes about, in fact each one is any, i.e. some, for either each one is any, or some is not some, but the last is false, the first is true. ||           But when the signs in subjects only appended to universals or particulars make propositions, still they can be appended not only in subject, but also in predicates, as also in singular propositions, to contraries, subcontraries, subalternates, or contradictories according to the assertion of the predicate we can assign. ||           For there are contraries also vehemently opposed, [e.g.] 'Socrates is every man', 'Socrates is not some man'. Moreover under these which are contained 'Socrates is some man', 'Socrates is not every man', subcontraries are said among them. But subalternates are of course on the one hand 'Socrates is every man', 'Socrates is some man', on the other 'Socrates is not some man', 'Socrates is not every man'. But contradictories are of course on the one hand 'Socrates is every man', 'Socrates is not every man', on the other 'Socrates is not some man', 'Socrates is someone'. ||           Now there appear in these properties of contraries, subcontraries, subalternates, contradictories from it also equippollence of conversion. For 'Socrates is every man' and 'every man is Socrates' are equal. Again, 'Socrates is not some man' and 'no man is Socrates'. For whoever says that Socrates is not someone, since each person is someone, excludes every man from him. Also these are equipollent among one another: 'Socrates is some man' and 'some man is Socrates', and those also 'it is not the case that Socrates is every man' and 'it is not the case that every man is Socrates'. ||           A twofold universality or particularity can also be taken in propositions in signs of quantity appended to the subject just as to the predicate and then also a twofold nature [can] be observed of the propositions above. For just as universals seem double 'every man is every animal' and 'no man is every animal', thus also twofold contraries are said. But subcontraries 'a certain man is some animal', 'a certain man is not every animal'. ||           But subalternates of course on the one hand 'every man is every animal', 'a certain man is some animal', but on the other 'no man is some animal', 'a certain man is every animal [?]'. Contradictories 'every man is every animal', 'a certain man is not every animal' or rather 'it is not the case that every man is every animal'. Again 'no man is some animal', and 'a certain man is some animal' ||           But since properties of propositions in these we show in propositions which de puro inesse they were stated and without mode assert something, as 'Socrates reads', for here the reading of Socrates is absolutely asserted, to those they call modals, we descend, which of course are not absolute, but with mode and determination predicate something, as 'Socrates reads well', and thence of course, that is from the modification of the predicate, are called modals.
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 * Sunt autem qui nec inter dictiones signa huiusmodi proprie velint admittere nec ipsa dicant propriam vocum significationem ex impositione tenere, sed quamdam indicationem {per repraesentationem} facere de voce subiecta, qualiter ipsa accipiatur, circa omnes scilicet, non circa unum tantum, secundum quod Boethius in Secundo Divisionum [189] huiusmodi signa determinationes appellat. Cum enim 'homo' et circa unum per se et circa omnes possit accipi, cum 'omnis' aut 'quidam' ponitur, quodammodo determinant quot in nomine ipso accipiantur, hoc quoque signare dicitur, non per propriam vocis impositionem, sed tamquam per realem repraesentationem, qua et circulus.
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 * Quantitatis autem signa non aliunde dicuntur nisi quia ex comprehensione significationis subiectae vocis [quam] determinant, utrum scilicet omnis subiecta res in ipso comprehendatur an quaedam. Sicut autem 'omnis' singularis numeri ad singulos singillatim singulariter acceptos nos mittit, ita 'omnes' plurale ad singulos pluraliter acceptos. Veluti cum dicitur: 'omnes homines', profecto et hos duo et illos tres et quotlibet colligimus secundum quemlibet eorum numerum.
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 * Sicut enim 'homo' quemlibet per se acceptum nominat, ita 'homines' quotcumque simul collectos comprehendit. Unde quemadmodum ex 'omnis homo est albus', 'Socrates est albus' innuitur, ita ex 'omnes homines sunt albi', 'hi duo sunt albi' vel 'hi tres', quando scilicet 'omnes' ad divisibiles partes, sicut 'omnis', reducitur, ad eas scilicet quae singulae praedicationem totius accipiunt. Sicut enim hic homo dicitur hic homo, ita hi duo homines vel hi tres homines dicuntur homines.
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 * Si autem 'omnes' {magis} collective quam individue accipiatur, non videntur singula inferri; veluti cum dicitur: 'omnia generalissima sunt decem', simul videlicet accepta, ex quo inferri nullo modo conceditur quod Substantia et Quantitas sint decem, quippe iam ad singula quae generalissima nominantur, illud 'omnia' nos non mittebat, sed ad totam magis simul generalissimorum collectionem, sicut et 'omnis', ut cum dicitur: 'omnis mundus'.
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 * DE 'NULLUS'
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 * 'Nullus' quoque singulos in remotione colligens universalitatis signum dicitur, quod bene ex 'non' et 'ullo' compositum est. Cum enim nec ullus relinquitur, omnium fit remotio, quippe unusquisque est ullus, id est aliquis; aut enim unusquisque in se est aliquis aut aliquis non est aliquis; sed falsa ultima, vera fuit prima.
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 * Cum autem signa subiectis tantum apposita universales aut particulares faciant propositiones, non tamen tantum subiectis, verum etiam praedicatis apponi possunt, ut etiam in singularibus propositionibus contrarias, subcontrarias, subalternas, seu contradictorias secundum enuntiationem praedicati possimus assignare.
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 * Sunt namque contrariae ac vehementer oppositae: 'Socrates est omnis homo', 'Socrates non est aliquis [190] homo'. Sub his autem quae continentur 'Socrates est aliquis homo', 'Socrates non est omnis homo' subcontrariae invicem dicuntur. Subalternae vero sunt hinc quidem: 'Socrates est omnis homo', 'Socrates est aliquis homo', illinc vero: 'Socrates non est aliquis homo', 'Socrates non est omnis homo'. Contradictoriae vero: sunt hinc quidem: 'Socrates est omnis homo', 'Socrates non est omnis homo', illinc vero: 'Socrates non est aliquis homo', 'Socrates est aliquis'.
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 * Apparent autem in his contrariarum, subcontrariarum, subalternarum, contradictoriarum proprietates ex ipsa quoque conversionis aequipollentia. Sunt namque pares 'Socrates est omnis homo' et 'omnis homo est Socrates'; rursus 'Socrates non est aliquis homo' et 'nullus homo est Socrates'. Qui enim nec aliquem esse Socratem dicit, cum unusquisque sit aliquis, omnem hominem ab eo excludit. Sunt hae quoque invicem aequipollentes: 'Socrates est aliquis homo' et 'aliquis homo est Socrates', et hae quoque ad invicem: 'non est Socrates omnis homo' et 'non omnis homo est Socrates'.
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 * Potest quoque in propositionibus duplex universalitas aut particularitas accipi signis quantitatis tam subiecto quam praedicato appositis et tunc quoque suprapositarum propositionum nat{ur}a dupliciter servari. Sicut enim dupliciter universales videntur 'omnis homo est omne animal' et 'nullus homo est omne animal', ita et dupliciter contrariae dicendae sunt. Subcontrariae vero 'quidam homo est aliquod animal', 'quidam homo non est omne animal'.
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 * Subalternae vero hinc quidem: 'omnis homo est omne animal', 'quidam homo est aliquod animal', illinc vero: 'nullus homo est aliquod animal', 'quidam homo est omne animal'. Contradictoriae: 'omnis homo est omne animal', 'quidam homo non est omne animal, vel potius 'non omnis homo est omne animal'; rursus 'nullus homo est aliquod animal' et 'quidam homo est aliquod animal'.
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 * Quoniam autem propositionum proprietates in his ostendimus propositionibus quae de puro inesse proponuntur et sine modo aliquid enuntiant, ut 'Socrates legit' -- hic enim lectio de Socrate simpliciter enuntiatur --, ad eas quas moda1es appellant, descendamus; quae quidem non simpliciter, sed cum modo et determinatione aliquid praedicant ut 'Socrates bene legit', et inde quidem, hoc est ex modificata praedicatione, modales nominantur.