Authors/Buridan/Quaestiones in analytica priora/Liber 1/Q7

 

Latin	English
Quaestio 7a UTRUM SYLLOGISMI EXPOSITORII NEGATIVI VALEANT GRATIA FORMAE	Question 7.  Whether a negative expository syllogism is valid in virtue of its form
Septima quaestio est utrum syllogismi expositorii negativi valeant gratia formae.	The seventh question is whether a negative expository syllogism is valid in virtue of its form
1. Et arguitur quod non: quia vel exigeretur quod praemissae essent simul verae, vel sufficeret quod essent successive verae sicut successive proponuntur; hoc patet quia est sufficiens divisio; sed neutrum illorum potest dici. Probatio. Probatur quod non oportet praemissas simul esse veras: quoniam hoc est impossibile; non enim possunt simul esse ab eodem homine prolatae; ideo non possunt simul esse verae. Deinde declaratur alia pars, scilicet quod non sufficit eas esse veras successive, sicut successive proponuntur: quia tunc esset syllogismus talis 'Socrates non movetur et Socrates currit; ergo currens non movetur'; constat quod praemissae essent successive verae posito casu possibili, scilicet quod dum prima pars proponebatur, Socrates quiescebat et immediate post incepit currere, et tamen conclusio erit falsa et impossibilis; ideo syllogismus talis non valebat.	And it is argued that it is not. For either it is required that the premisses would be true at the same time, or it would be sufficient that they would be successively true, or successively put forward.  This is clear because it is a sufficient division, but neither of these can be said.  It is proved that both premisses do not have to be true at the same time, for this is impossible, for they cannot be uttered by the same man at the same time, therefore they cannot both be true at the same time. Next we clarify the other part, namely that it is not sufficient for them to be true successively, as successively put forward, for then there would be a syllogism such as 'Socrates does not move and Socrates runs, therefore a running thing does not move'.  It is plain that the premisses would be successively true in the possible case, namely that while the first part was put forward, Socrates was resting and immediately afterwards began to run, and then the conclusion will be false and impossible.  Therefore such a syllogism would not be valid.
2. Item, hic est syllogismus expositorius negativus 'Socrates est animal, Socrates non est asinus; ergo asinus non est animal'; et tamen constat quod ille syllogismus non valet: quia praemissae sunt verae, casu posito, et conclusio falsa.	Likewise, 'Socrates is an animal, Socrates is not a donkey, therefore a donkey is not an animal' is a negative expository syllogism, and yet it is plain that this syllogism is not valid, for the premisses are true, in the case in hand, and the conclusion false.
3. Item, in divinis*, invenitur manifeste instantia: quia significata persona patris, erit syllogismus expositorius sic 'iste pater non est filius et iste idem pater est deus; ergo deus non est filius', et tamen syllogismus non valet, quia ex fide praemissae sunt verae et conclusio falsa.	Likewise, in the divine persons we have a manifest counterexample, for when the person of the father is signified, there will be the following expository syllogism.  'This Father is not the Son and this same father is God, therefore God is not the Son', and yet the syllogism is not valid, for (from faith) the premisses are true and the conclusion false.
4. Item, dubitatur quae conclusio concluderetur per istum syllogismum expositorium 'Socrates est animal, Socrates est non omnis homo*'; illae praemissae sunt verae, et tamen videtur quod tu non posses concludere conclusionem veram: quia si tu concludis 'ergo non omnis homo est animal' vel 'ergo homo non est animal', constat quod totum est falsum; et si velles concludere affirmativam, dicendo 'ergo homo est animal', non sequeretur gratia formae: quia in eadem dispositione acciperem praemissas veras et conclusionem falsam, scilicet dicendo sic 'Socrates est animal, Socrates est non omnis lapis'; conclusio esset falsa dicens quod lapis est animal; ergo manifestum est quod ille syllogismus, quamvis esset expositorius, tamen non valebat.	Likewise, it is doubtful which conclusion would be concluded from the expository syllogism 'Socrates is an animal, Socrates is not every man'.  The premisses are true, and yet it seems that you cannot conclude a true conclusion, for if you conclude 'therefore not every man is an animal', or 'therefore a man is not an animal', it is plain that the whole expression is false. And if you wished to conclude the affirmative, saying 'therefore a man is an animal', it would not follow in virtue of its form, for in the same disposition I would accept true premisses and a false conclusion, namely saying 'Socrates is an animal, Socrates is not every stone' - the conclusion saying 'a stone is an animal' would be false. Therefore it is manifest that the syllogism, although expository, was nonetheless not valid.
Oppositum arguitur per Aristotelem; quia Aristoteles, in isto libro*, ad probandum multos syllogismos utitur syllogismis expositoriis, non solum affirmativis sed etiam negativis, tamquam utrisque exsistentibus bonis.	The opposite is argued through Aristotle. For Aristotle, in this book, uses the expository syllogism for proving many syllogisms - not only affirmative but negative, as though both were good.
Notandum est quod syllogismus expositorius negativus tenet per istam regulam 'quaecumque sibi invicem sunt eadem, a quocumque unum eorum est diversum ab eodem reliquum est diversum', ut si Marcus est idem quod Tullius, a quocumque Marcus differt ab eodem Tullius differt.	It should be noted that a negative expository syllogism holds by the rule 'whatever are the same as each other, from whatever one of them is different, so the other is different from the same thing'. So that if Marcus is the same as Tully, from whatever Marcus is different from, Tully is different from the same thing.
Et ista regula, sicut regula de affirmativis, debet intelligi sane. Quoniam impossibile est quod aliqua sint sibi invicem eadem, quoniam aliqua non sunt nisi sint plura et ab invicem diversa; et si sint plura et ab invicem diversa, tunc non sunt sibi invicem eadem. Et ideo regula, si volumus loqui de virtute sermonis, debet sic exponi quod si duo nomina dicuntur sibi invicem eadem, cuicumque unum illorum nominum dicitur diversum, reliquum eidem dicitur diversum.	And this rule, just as the rule of affirmative [expository syllogisms], ought to be reasonable understood.  For it is impossible that some things are the same as one another, since some things do not exist unless they are several and different from one another, and if they are several and different from one another, then they are not the same as one another.  And therefore the rule (if we wish to speak literally) ought to be explained as follows: that if two names 'are predicated the same' as one another, then to whatever thing one of those names is predicated as different, the other is [also] predicated as different.
Unde debetis scire quod aliqua nomina bene dicuntur sibi invicem eadem. Non dico 'sunt sibi invicem eadem', sed 'dicuntur sibi invicem eadem', hoc est dictum quod de utroque ipsorum vere dicitur hoc praedicatum 'idem' cum additione reliqui nominis.	Hence, you ought to know that some names are properly predicated the same as one another. I do not say 'are the same as one another' but "are predicated the same as one another", that is, said that of each of them the predicate 'the same' is truly predicated, with the addition of the other name.
Sic enim ista nomina 'animal' et 'homo' dicuntur sibi invicem eadem, quia vere dicimus 'animal est idem homini' et 'homo est idem animali'; et huius modi identitas designatur per propositionem affirmativam; unde si ego dico 'homo est animal', ego designo quod homo est idem animali. In hoc ergo sensu dicta regula est vera; et ex hoc concludendum est quod syllogismus expositorius negativus est verus et bonus, cum teneat per illam regulam, veram et bonam. Tamen, ut videatis qualiter ille syllogismus debeat fieri oportet scire quod tres sunt figurae; ideo pono aliquas conclusiones.	For in this way the names 'animal' and 'man' are predicated the same as one another, for we truly say 'an animal is the same as a man', and 'a man is the same as an animal', and identity of this sort is designated by an affirmative proposition. Hence, if I say 'a man is an animal', I designate that a man is the same as an animal.  Therefore in this sense the said rule is true, and from this it should be concluded that a negative expository syllogism is true and good, since it holds by that rule, true and good. Yet, so as you may see how that syllogism ought to be constructed you have to know that there are three figures, therefore I give some conclusions.
Prima conclusio est ista quod in prima figura non valet syllogismus expositorius si minor sit negativa. Verbi gratia, 'Socrates est animal, asinus non est Socrates', non potest inferri 'ergo asinus non est animal', quia praemissae sunt verae et conclusio falsa. Et causa huius est quia in maiori propositione Socrates ponebatur esse idem animali, non tamen omni animali; modo in conclusione tu concludis asinum non solum ab animali sed ab omni animali esse diversum, quia dicendo sic 'asinus non est animal' iste terminus 'animal' stat* confuse et distributive.	The first conclusion is that in the first figure the expository syllogism is not valid if the minor is negative.  For example, 'Socrates is an animal, a donkey is not Socrates' does not imply 'therefore a donkey is not an animal', for the premisses are true and the conclusion false.  And the cause of this is that in the major proposition, Socrates was said to be the same as an animal, yet not any animal, whereas in the conclusion you conclude the donkey to be different not just from an animal but from any animal, for in saying 'a donkey is not an animal', the term 'animal' stands confusedly and distributively.
Debetis ergo notare istam regulam quod ex termino distributo sequitur bene ipse non distributus (sequitur enim bene 'omnis homo est animal; ergo homo est animal'), sed numquam ex termino non distributo sequitur ipse distributus. Et ideo praedictus syllogismus erat malus, quia 'animal' in maiori propositione sumebatur sine distributione et in conclusione distribuebatur. Et ista regula non habet solum veritatem quoad primam figuram sed bene quoad secundam et tertiam. Tamen vos debetis scire quod praedictus syllogismus, scilicet ex minore negativa bene valebat indirecte; exemplum 'Socrates est animal, asinus non est Socrates', bene sequitur 'ergo animal non est asinus', quoniam in conclusione nihil distribuitur quod non erat distributum in praemissis.	Therefore you ought to note the rule that from a distributed term, there follows well that term not distributed (for 'every man is an animal therefore a man is an animal' follows well); but never from a term that is not distributed does the distributed term follow.  And therefore the syllogism above was bad, for 'animal' in the major proposition was taken without distribution, but in the conclusion it was distributed. And that rule does not only have truth in respect of the first figure, but well in respect of the second and third.  Yet you ought to know that the previous syllogism, namely from the negative minor, it followed well indirectly.  Example: [from] 'Socrates is an animal, a donkey is not Socrates', the conclusion 'therefore an animal is not a donkey' follows well, for in the conclusion nothing is distributed that was not distributed in the premisses.
Secunda conclusio est quod in secunda figura valet syllogismus expositorius affirmativus, propter illam regulam datam in alia quaestione, sed in secunda figura non valet syllogismus expositorius negativus nisi maior extremitas acciperetur universaliter. Exemplum 'homo est Socrates, risibile non est Socrates', non sequitur 'ergo risibile non est homo'; et similiter est si ponatur maior negativa, quia non sequitur 'homo non est Socrates, risibile est Socrates; ergo risibile non est homo'. Quoniam utrobique praemissae sunt verae et conclusio est falsa; et hoc est quia maior extremitas distribuitur in conclusione quae non distribuebatur in praemissis. Sed bonus esset syllogismus dicendo sic 'nullus homo est Socrates, quoddam risibile est Socrates; ergo quoddam risibile non est homo'; si enim conclusio est falsa, hoc est propter falsitatem maioris.	The second conclusion is that in the second figure an affirmative expository syllogism is valid, on account of the rule given in the other question, but in the second figure a negative expository syllogism is not valid unless the major extremity is taken universally.  Example: [from] 'a man is Socrates, a thing capable of laughter is not Socrates', it does not follow 'therefore a thing capable of laughter is not a man', and it is similar if the major is negative, for 'a man is not Socrates, a thing capable of laughter is Socrates, therefore a thing capable of laughter is not a man'. For both premisses are true and the conclusion false, and this is because a major extremity is distributed in the conclusion which is not distributed in the premisses.  But a good syllogism would be 'no man is Socrates, something capable of laughter is Socrates, therefore something capable of laughter is not a man'.  For if the conclusion is false, this is because of the falsity of the major.
Tertia conclusio est quod in tertia figura non valet syllogismus expositorius negativus si minor sit negativa, ut 'Socrates est animal, Socrates non est asinus; ergo asinus non est animal'. Dico ergo quod ille syllogismus non valebat quia maior extremitas distribuitur in conclusione et in praemissis non distribuebatur. Sed si minor sit affirmativa et maior negativa, erit bonus syllogismus expositorius. Unde quidquid dicebatur de prima figura debet dici et concedi de tertia figura.	The third conclusion is that in the third figure a negative expository syllogism is not valid if the minor is negative, such as 'Socrates is an animal, Socrates is not a donkey, therefore a donkey is not an animal'.  Therefore I say that this syllogism was not valid because the major extremity was distributed in the conclusion and is not distributed in the premisses.  But if the minor is affirmative and the major negative, it will be a good expository syllogism. Hence, whatever was said of the first figure ought to be said and conceded of the third figure.
Ultimo potest dici, sicut dicebam de affirmativis, quod syllogismi expositorii negativi secundum illam formam secundum quam ut in pluribus formantur non valent in terminis divinis, propter hoc quod in divinis utraque plurium rerum ab invicem diversarum est uni et eidem rei simplici eadem. Sed hoc non crediderunt plures auctores esse possibile; ideo crediderunt syllogismos expositorios in omnibus terminis esse bonos. Et verum est quod sunt in omnibus terminis boni exceptis terminis divinis, quia in creaturis impossibile est quod uni et eidem rei simplici quaelibet diversarum rerum sit eadem.	Finally, it can be said that, just as was said of affirmatives, that of a negative expository syllogism, according to the form in which ut in pluribus formantur, are not valid in divine terms, because of the fact that in the divine persons each of several things different from one another is the same as one and the same thing simplici.  But several authors did not believe this was possible, therefore they believed expository syllogisms to be good in all terms.  And it is true that they are good in all terms, but with the divine terms excepted, for it is impossible in created things that to one and the same thing simplici, each one of different things is the same.
Istis visis respondendum est ad rationes.	Having examined this, we should reply to the arguments.
1. Ad primam, concedo quod in syllogismo vocali praemissae non sunt simul verae, quia non sunt simul. Tamen debent sic capi ac si eodem tempore et pro eodem tempore proferrentur; et sic praemissae in syllogismo qui fiebat non sunt concedendae. Unde si dico sic 'Socrates non movetur, Socrates currit; ergo currens non movetur', syllogismus non valet nisi intelligendo minorem et conclusionem ac si eodem tempore et pro eodem tempore proferrentur cum maiori. Et ad illum intellectum si maior erat vera, scilicet 'Socrates non movetur', minor erat falsa, scilicet 'Socrates currit', et praemissae debent esse una copulativa; modo illa est impossibilis quae est composita ex illis praemissis, et ergo sunt incompossibiles.	To the first, I concede that in a verbal syllogism the premisses are not true at the same time, for they do not exist at the same time.  Yet they ought to be grasped as if they were put forward at one time, and for the same time, and so the premisses in the syllogism which was made [in the argument] should not be conceded.  Hence, if I say 'Socrates does not move, Socrates runs, therefore a running thing does not move', the syllogism is not valid except by understanding the minor and the conclusion as they were put forward as if at the same time, and for the same time, as the major. And in that understanding, if the major was true, namely 'Socrates does not move', the minor was false, namely 'Socrates runs', and the premisses ought to be one conjunction. But that is impossible when it is composed from those premisses, and therefore they are not co-possible.
2. Ad aliam, concedo quod syllogismus qui fuit formatus non valebat, quia minor erat negativa in tertia figura.	To the second, I concede that the syllogism which was formed was not valid, for the minor was negative in the third figure.
3. Ad aliam, quae arguit de terminis divinis, dictum est in positione.	To the third, which argued about the divine terms, this was discussed in the determination.
4. Ad ultimam, dico quod ille syllogismus erat affirmativus, quia ambae praemissae erant affirmativae. Ista enim est affirmativa 'Socrates est non omnis homo', quia haec negatio 'non' non cadit super copulam, et est de praedicato infinito. Et ideo debet inferri conclusio affirmativa, scilicet ista 'ergo non omnis homo est animal*', ponendo quod negatio solum sit infinitans, et non negans verbum, ad istum sensum 'non omnis homo', id est 'aliquod quod est non omnis homo', 'est animal'; sic enim sumebatur in praemissa, quoniam ista 'Socrates est non omnis homo*' valet istam 'Socrates est aliquid quod est non omnis homo'.	To the last, I say that the syllogism was affirmative, for both premisses were affirmative. For 'Socrates is not every man' is affirmative, because the negation 'not' does not fall over the copula, and it is of the infinite predicate.  And therefore an affirmative conclusion ought to be inferred, namely 'therefore not every man is an animal', by positing that the negation is only infinitising, and not negating the verb, in the sense 'not every man', that is 'something that is not every man', 'is an animal'. For thus it was taken in the premisses, since 'Socrates is not every man' validates 'Socrates is something that is not every man'.