Authors/Buridan/Quaestiones in analytica priora/Liber 1/Q5

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Q4 Q6

 

Latin English
[Quaestio 5a UTRUM OMNIS BONUS SYLLOGISMUS TENEAT PER DICI DE OMNI VEL PER DICI DE NULLO] [Question 5.  Whether every good syllogism holds through dici de omni or by dici de nullo]
Quinta quaestio est utrum omnis bonus syllogismus teneat per dici de omni* vel per dici de nullo*. The fifth question is whether every good syllogism holds through dici de omni or by dici de nullo.
1. Arguitur quod non: quia dici de omni non est principium incomplexum, ut de se notum est; nec est principium complexum, quia non est oratio perfecta, et ideo neque vera neque falsa, et tamen principia complexa debent esse primo vera et per se nota: ergo dici de omni non est aliquod principium; ideo per ipsum non tenent syllogismi.
It is argued that not, for dici de omni is not an incomplex principle, such as it is known of itself, nor is it a complex principle, for it is not a complete speech, and is therefore neither true nor false, and yet complex principles ought to be primarily true and known per se.  Therefore dici de omni is not a principle, therefore syllogisms do not hold through it.
2. Item, syllogismus expositorius est bonus syllogismus, et tamen in eo non est dici de omni vel de nullo; ergo non omnis bonus syllogismus tenet per dici de omni vel de nullo.
Likewise, an expository syllogism is a good syllogism, and yet there is no dici de omni or de nullo in it.  Therefore not every syllogism holds through dici de omni or dici de nullo.
3. Item, si per dici de omni tenerent syllogismi, sequeretur quod ex puris particularibus valeret syllogismus; consequens est falsum, ut patet primo huius. Consequentia probatur: quia in propositione particulari salvatur dici de omni; verbi gratia, in hac propositione 'quidam homo est animal' salvatur dici de omni: quia nihil est sumere sub subiecto, scilicet sub 'homine', de quo non vere dicatur praedicatum, et hoc est dici de omni, ut patet per descriptionem eius.
Likewise, if syllogisms held through dici de omni, it would follow that a syllogism would be valid from pure particulars.  The consequent is false, as is clear from the first [question of] this [book?].  The consequence is proved, for dici de omni is preserved in a particular proposition - for example, in the proposition 'some man is an animal' dici de omni is preserved, for there is nothing to take under the subject of which the predicated is not truly predicated, and this is dici de omni, as is clear from its description.
4. Item, multae sunt coniugationes inutiles in quibus salvatur dici de omni et de nullo: ergo propter dici de omni vel de nullo non redduntur syllogismi boni. Consequentia videtur nota de se. Et antecedens manifestum est: quia si in prima figura maior sit universalis affirmativa et minor universalis negativa, ibi erunt dici de omni et dici de nullo, et tamen syllogismus non valebit.
Likewise, there are many useless combinations in which dici de omni or de nullo is preserved. Therefore, it is not because of dici de omni or de nullo that good syllogisms are returned.  The consequent is evident per se, and the antecedent is manifest, for if in the first figure the major is universal affirmative and the minor universal negative, there will in that case be dici de omni or de nullo, and yet the syllogism will not be valid.
5. Item, syllogismi tenentes per dici de omni vel de nullo dicuntur perfecti; sed non omnes syllogismi dicuntur perfecti; immo in secunda figura et in tertia nulli sunt perfecti, ut dicit Aristoteles, et tamen sunt boni; ergo non omnes syllogismi boni tenent per dici de omni vel de nullo.
Likewise, syllogisms holding through dici de omni or de nullo are called perfect, but not all syllogisms are called perfect. Indeed, in the second and third figure none are perfect, and yet they are good. Therefore not all syllogisms hold through dici de omni or de nullo.
Oppositum arguitur. Et dicitur communiter, et apparet manifeste, quod syllogismi primae figurae tenent manifeste per dici de omni vel de nullo, ut vult Aristoteles; syllogismi autem secundae figurae et tertiae tenent in virtute syllogismorum primae figurae (primo enim declarantur per reductionem ad primam figuram); ideo, de primo ad ultimum, omnes syllogismi tenent in virtute dici de omni vel dici de nullo. The opposite side is argued.  And it is commonly said, and manifestly appears, that the syllogisms of the first figure hold manifestly through dici de omni or de nullo, as Aristotle would have it. But syllogisms of the second and third figure hold in virtue of syllogisms of the first figure (for they are made clear by reduction to the first figure). Therefore, 'from first to last', all syllogisms hold in virtue of dici de omni or de nullo.
Item, nisi syllogismi deberent tenere per dici de omni aut de nullo, sequeretur quod ita bene fierent syllogismi ex puris particularibus vel indefinitis sicut fiunt ex universalibus; modo consequens est falsum, ut apparet primo huius*. Likewise, unless syllogisms had to hold through dici de omni or de nullo, it would follow that syllogisms would well be made from mere particulars or indefinites, just as they are made from universals.  But the consequence is false, as is apparent from the first [question?] of this book.
Primo videndum est quid debeamus intelligere per dici de omni vel de nullo, secundo videndum est de descriptionibus eorum, et tertio dicetur directe ad quaesitum. First, we should see what we ought to understand by dici de omni or de nullo. Second, we should see about their descriptions, and third, we should speak directly to the question.
Quantum ad primum videtur mihi quod haec oratio 'dici de omni' est una oratio truncata, indigens supplemento. Unde haec oratio 'dici de omni' capitur loco huius orationis 'praedicatum dici affirmative de subiecto distributo', et haec oratio 'dici de nullo' capitur loco huius orationis 'praedicatum dici negative de subiecto distributo'. As far as the first, it seems to me that the expression 'dici de omni' is a truncated expression, requiring a supplement.  Hence the expression 'dici de omni' takes the place of the expression 'a predicate being said affirmatively of a distributed subject', and the expression 'dici de nullo' takes the place of the expression 'a predicate being said negatively of a distributed subject'.
Sed aliqui* dubitant quae res est praedicatum dici affirmative de subiecto distributo; et haec dubitatio est ac si dubitaremus quae res est hominem bibere vinum. Et aliqui dicunt quod hoc non est nisi una propositio, ita scilicet quod haec oratio 'hominem bibere vinum' supponit pro ista propositione 'homo bibit vinum'. Alii autem dicunt quod hominem bibere vinum est quoddam significabile complexum, correspondens a parte rei huic corruptibili propositioni 'homo bibit vinum'. Alii autem dicunt quod hominem bibere vinum non est aliud quam homo taliter se habens ad vinum. Alii autem dicunt quod est quoddam accidens inhaerens homini ut taliter se habeat ad vinum. Et proportionaliter diceretur in proposito. Et non est in hoc loco discutiendum quid illorum sit verum, immo pertinet ad quartum Metaphysicae*.
But some persons doubt what thing is the predicate being said of a distributed subject, and this doubt is as if we were to doubt what a man drinking wine is.  And some say that it is only a proposition, namely, so that the expression 'a man drinking wine' supposits for the proposition 'a man drinks wine'.  But others say that a man drinking wine is a sort of complex signifiable, corresponding on the part of reality to the corruptible proposition 'a man drinks wine'.  And others say that a man drinking wine is nothing other than a man related in such a way to wine.  Still others say that it is a sort of accident inhering in a man so that he is related in such a way to wine.  And it would be said in a corresponding way to the case in hand.  And it should not be discussed in this place which of those is true. Rather, it pertains to the fourth book of the Metaphysics.
Tunc venio ad secundum. Et est dicendum quod tale complexum non proprie definitur vel describitur, sed talis oratio per orationem manifestiorem explicatur vel interpretatur. Et Aristoteles ponit interpretationem talem "dici de omni est quando nihil est sumere sub subiecto de quo non dicatur praedicatum, et dici de nullo est quando nihil est sumere sub subiecto a quo non removeatur praedicatum*", id est: quandocumque praedicatum dicitur de subiecto affirmative et universaliter, per talem propositionem designatur quod ipsum praedicatum vere dicitur de omni eo de quo subiectum vere dicitur (verbi gratia, si dico 'omne B est A', ego designo quod hoc praedicatum 'A' vere dicitur de omni eo de quo 'B' vere praedicatur), et quando praedicatum negatur de subiecto universaliter, per talem propositionem designatur quod praedicatum vere negatur de omni eo quod sub subiecto sumeretur sive de quo subiectum vere diceretur. Then I turn to the second.  And it should be said that such a complex is not properly defined or described, but rather that such an expression is explicated or interpreted through a more manifest expression.  And Aristotle gives such an interpretation, saying "dici de omni is when there is nothing to take under the subject of which the predicated is not predicated, and dici de nullo is when there is nothing to take under the subject from which the predicated is not removed'.  That is, whenever the predicate is predicated of the subject affirmatively and universally, it is designated through such a proposition that this predicate is truly predicated of all that of which the subject is truly predicated. For example, if I say 'every B is A', I designate that the predicate 'A' is truly predicated of all that of which 'B' is truly predicated.  And when the predicate is denied of the subject universally, it is designated through such a proposition the predicate is truly denied of all that of which is taken under the subject, or of which the subject is truly predicated.
Postea respondendum est directe ad quaesitum. Et dico primo quod syllogismi primae figurae ex terminis communibus tenent manifeste per dici de omni vel per dici de nullo. Quia in primo modo et tertio, <in maiore> praedicatum affirmatur universaliter de subiecto, et postea, in minore, illud subiectum dicitur de quodam tertio; ergo, per regulam datam, oportet quod primum praedicatum dicatur de illo tertio, quia regula erat quod si praedicatum dicitur universaliter de subiecto, ipsum dicitur de omni illo de quo subiectum vere dicitur; hoc enim significat 'dici de omni'. Et eodem modo apparet quod secundus modus et quartus tenent directe per dici de nullo. Afterwards, I should speak directly to the question.  And I say first that syllogisms of the first figure [formed] from common terms hold manifestly from dici de omni or from dici de nullo.  For in the first and third mood, in the major the predicate is affirmed universally of the subject, and afterwards, in the minor, that subject is predicated of some third.  Therefore, through the rule given, it has to be that the first predicate is predicated of that third, for the rule was that if the predicate is predicated universally of the subject, it is predicate of all that of which the subject is predicated, for that is what dici de omni signifies. And in the same way it is apparent that the second and fourth mood hold directly through dici de omni.
Secunda conclusio est quod syllogismi secundae figurae et tertiae non tenent manifeste per dici de omni vel per dici de nullo. Et causa est quia in illis duabus figuris subiectum primo distributum non ponitur dici de aliquo alio universaliter. Verbi gratia, in secunda figura fiat syllogismus sic 'nullum B est A, omne C est A; ergo nullum C est B'; verum est quod in maiore 'A' dicebatur de nullo B, sed postea, in minore nihil sumebatur sub 'B' quod tamen oporteret fieri si processus manifeste teneret per dici de nullo. Ita in tertia figura fiat syllogismus 'omne C est A, omne C est B; ergo quoddam B est A'; patet quod in maiore 'A' dicebatur de omni C, sed in minore non accipiebatur 'C' praedicari de aliquo alio, quod tamen oporteret si talis processus teneret manifeste per dici de omni. The second conclusion is that syllogisms of the second and third figure do not hold manifestly through dici de omni or through dici de nullo.  And the cause is that in those two figures the subject first distributed is not given to be predicated of some other universally.  For example, in the second figure we make the syllogism 'no B is A, every C is A, therefore no C is B'. It is true that in the major, 'A' was predicated of no B, but afterwards in the minor nothing was taken under 'B', which nonetheless would have to happen if the process were manifestly to hold through dici de nullo.  So in the third figure we make that syllogism 'every C is A, every C is B, therefore some B is A'. It is clear that in the major 'A' was predicated of every C, but in the minor 'C' was not taken to be predicated of some other, which nonetheless would have to be is such a process were manifestly to hold through dici de omni.
Et ab hoc concludit Aristoteles quod omnes syllogismi primae figurae sunt perfecti, quia evidenter tenent per dici de omni vel de nullo, loquendo tamen de directe concludentibus; sed syllogismi secundae et tertiae figurae dicuntur imperfecti. And from this, Aristotle concludes that all syllogisms of the first figure are perfect, because they evidently hold through dici de omni or de nullo.  But syllogisms of the second and third figure are called imperfect.
Ultima conclusio potest poni quod syllogismi secundae figurae et tertiae facti ex terminis communibus tenent per dici de omni vel de nullo, licet occulte: quia aliter contingeret syllogizare ex praemissis particularibus vel indefinitis sicut contingit syllogizare ex universalibus. Et illud declaratur per reductiones secundae figurae et tertiae ad primam. Verbi gratia, syllogismus secundae figurae est talis 'nullum B est A, omne C est A; ergo nullum C est B'; modo maior propositio, propter eius conversionem, valet istam 'nullum A est B', et tunc directe in minori propositione fiet sumptio sub termino distributo. The final conclusion is that syllogisms of the second and third figure made from common terms hold through dici de omni or de nullo, although obscurely. For otherwise, it would be possible to syllogise from particular premisses, or indefinites, just as it is possible to syllogise from universals.  And that is made clear through the reductions of the second and third figure to the first.  For example, a syllogism of the second figure is 'no B is A, every C is A, therefore no C is B'.   But the major proposition, because of its conversion, validates 'no A is B', and then directly in the minor proposition there happens a subsumption under a distributed term.
Ita, similiter, in tertia figura fiat syllogismus sic 'omne C est A, omne C est B; ergo quoddam B est A'; modo ad istam minorem universalem 'omne C est B' sequitur per conversionem ista propositio 'quoddam B est C', et tunc directe B sumitur sub termino distributo in maiori propositione. Et sic patet quod, licet in istis figuris non fiat sumptio sub subiecto distributo manifeste, tamen fit virtualiter et occulte. Thus, similarly, we make a syllogism of the third figure 'every C is A, every C is B, therefore some B is A'.  But from the universal minor 'every C is B' there follows the proposition 'some B is C' by conversion, and then directly B is taken under the term distributed in the major proposition.  And thus it is clear that, although in those figures there is no subsumption under a distributed subject manifestly, still it happens in a virtual way, and obscurely.
De syllogismis autem qui formantur ex terminis singularibus, qui vocantur 'syllogismi expositorii', dicetur in alia quaestione. But syllogisms which are formed from singular terms, which are called 'expository syllogisms', we will talk about in another question [*].
Et tunc ad rationes principales. And then to the main arguments.
1. Ad primam dico quod per istam orationem truncatam 'dici de omni' nos intelligimus unam orationem perfectam quae est unum principium complexum, scilicet quod quandocumque praedicatum dicitur universaliter de subiecto, designatur quod ipsum vere dicitur de omni eo de quo illud subiectum vere dicitur; et hoc principium est supponendum ex significatione nominis, quoniam in omni doctrina oportet illam praesupponere.
To the first I say that by the truncated expression dici de omni we understand a single perfected expression which is a single complex principle, namely that whenever the predicate is predicated universally of the subject, it is designated that it is truly said of all that of which that subject is truly predicated, and this principle is to be supposed from the signification of a name, since in every doctrine one must presuppose that.
2. Ad aliam, de syllogismis expositoriis, dicetur in alia quaestione.
To the second, about the expository syllogism, I will speak to that in another question.
3. Ad aliam, quando dicitur quod in propositione particulari salvatur dici de omni, respondeo quod quamvis praedicatum possit vere dici de subiecto et de omnibus contentis sub eo, tamen per propositionem universalem hoc non designatur. Modo, ad dici de omni, prout de eo intenditur in hoc libro, sufficit et requiritur quod designetur praedicatum dici de omni de quo dicitur subiectum, quae designatio fit per distributionem* subiecti, et non curatur utrum sit verum vel non verum. Unde hic est dici de omni 'omnis asinus est homo' prout in hoc libro loquimur de dici de omni. Et ideo descriptio quam ponit Aristoteles debet sic glossari "dici de omni est quando nihil est sumere ..." et caetera, id est dici de omni est quando designatur quod nihil est sumere et caetera; hoc enim designatur per signum distributivum.
To the third, when it is said that in a particular proposition dici de omni is preserved, I reply that although the predicate could be truly predicated of the subject and of all contained under it, still this is not what is designated by a universal [?] proposition.  But, for dici de omni, as meant in this book, it is sufficient, and it is necessary that it is designatedthat the predicated is predicated of all which the subject is predicated, which designation happens by the distribution of the subject, and it does not matter whether the proposition is true or false.  Hence 'every donkey is a man' is dici de omni, as we speak of dici de omniin this book. And therefore the description which Aristotle gives ought to be glossed as follows. "Dici de omni is when there is nothing to take under ..." etc., that is, dici de omni is when it is designated that there is nothing to take under etc, for this is designated by the distributive sign.
4. Ad aliam, concedo quod in multis coniugationibus inutilibus est dici de omni vel de nullo, sed non sumitur sub subiecto distributo, et ideo non habet ibi locum principium prius positum.
To the fourth, I concede that in many useless conjunctions there is dici de omni or de nullo, but it is not taken under a distributed subject, and therefore the principle given above does not have a place there.
5. Ad ultimam, concedo, et dico quod non omnes syllogismi sunt perfecti qui tenent per dici de omni, sed solum illi qui manifeste tenent per dici de omni.
To the last, I concede it, and I say that not all syllogisms which hold under dici de omni are perfect, but only those which manifestly hold through dici de omni.

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