Authors/Buridan/Quaestiones in analytica priora/Liber 1/Q6

From The Logic Museum

Jump to: navigation, search
Q5 Q7

See also the translation in the Old Logic Museum.

Latin English
Quaestio 6a UTRUM SYLLOGISMUS EXPOSITORIUS SIT BONUS GRATIA FORMAE Question 6a (of Questions in the Prior Analytics). WHETHER THE EXPOSITORY SYLLOGISM IS A GOOD [VALID] SYLLOGISM ON ACCOUNT OF ITS FORM
Sexta quaestio est utrum syllogismus expositorius sit bonus gratia formae. The 6th question is whether the expository syllogism is a good [i.e. valid] syllogism on account of its form.
1. Et arguitur quod non: quia iste syllogismus videtur esse expositorius 'hic homo est albus, hic homo est niger; ergo nigrum est album', et tamen consequentia non est bona, quia conclusio est manifeste falsa et tamen possibile est quod ambae praemissae sint simul verae, scilicet si in maiori demonstratur Socrates et in minori Plato.
And it is argued that it is not, since the syllogism 'this man is white, this man is black, therefore a black man is a white man' seems to be expository, and yet the consequence is not valid [bonum], because the conclusion is manifestly false and yet it is possible that both premisses are true together (namely if in the major premiss Socrates is pointed-to, and in the minor, Plato).
2. Item, demonstrando eundem hominem in maiori et in minori, tamen haec est vera 'iste homo vel asinus est homo', et cum hoc ista 'iste homo vel asinus est asinus', et tamen conclusio erit falsa dicens quod asinus est homo; igitur syllogismus non valet, licet sit expositorius.
Likewise, by pointing-to the same man in the major and in the minor premiss, still the proposition 'that man or donkey is a man' is true, and with it, the proposition 'that man or donkey is a donkey', and yet the conclusion will be false, saying that a donkey is a man, accordingly the syllogism is not valid, although it is expository.
3. Item, ponendo quod Socrates videat unum equum et unum asinum, tunc est syllogismus expositorius dicendo sic 'Socrates videt equum, Socrates videt asinum', et tamen non sequitur quod equus est asinus vel asinus est equus.
Likewise, in supposing that Socrates sees one horse, and one donkey, then it is an expository syllogism speaking thus: 'Socrates sees a horse, Socrates sees a donkey', and yet it does not follow that a horse is a donkey or [that] a donkey is a horse.
4. Item, theologice, iste est syllogismus expositorius, demonstrando deum 'iste deus est pater et iste deus est filius; ergo filius est pater'*, et tamen consequentia non valet, quia praemissae sunt verae, et tamen conclusio, in divinis, est falsa et haeretica.
Likewise, theologically, it is an expository syllogism, in pointing-to [i.e. referring to] God: 'that God is the Father, and that God is the Son, therefore the Son is the Father', and yet the consequence is not valid, because the premisses are true, and yet the conclusion, in the divine [persons] is false and heretical.
5. Ultimo arguitur: quia solet dici quod omnis bonus syllogismus tenet per dici de omni vel per dici de nullo, et in syllogismis expositoriis non est dici de omni nec dici de nullo; igitur nullus syllogismus expositorius est bonus.
Finally it is argued that because it is customarily said that every valid [bonus] syllogism holds through the Dici de omni et Nullo, and in the expository syllogism it is not said [i.e. predicated] of everything, nor said of nothing. Accordingly, no expository syllogism is valid.
Oppositum arguitur: quia Aristoteles per syllogismum expositorium tamquam bonum probat, in primo huius*, conversiones et multos syllogismos. It is argued on the opposite side: for Aristotle proves through an expository syllogism as though it were valid, conversions and many syllogisms in the first book[1]
Notandum est quod syllogismus 'expositorius'* vocatur in quo medium est terminus discretus, id est singularis. Et hoc est pro tanto quia per terminum discretum exponitur propositio particularis vel indefinita sic quod ipsa sit vera; ut si tu dicas 'aliquis homo currit', petetur a te "quis est ille?", et respondendo seu exponendo dicetur "ille est Socrates" vel "hic homo", et caetera. It is to be noted that a syllogism is called 'expository' where the middle is a discrete, i.e. singular, term. And this is forasmuch as because by means of a discrete term, a particular or indefinite proposition is explained so that it is true. For example, if you say 'some man runs', and you are asked 'who is that', and in reply or explaining, it is said that 'that is Socrates', are 'this man' &c.
Deinde de syllogismo expositorio affirmativo, de quo solum intelligimus ad praesens, dicendum est quod syllogismus expositorius affirmativus tenet per istam regulam 'quaecumque sunt eadem uni et eidem in numero, illa sunt sibi invicem eadem'. Verbi gratia, si dico sic 'Socrates est albus et idem Socrates est sedens" sequitur quod sedens est albus; quia per praemissas habetur quod tam album quam sedens est idem quod Socrates, ideo oportet concludere quod album est idem quod sedens. Et ideo considerandum est de illa regula, de qua ego pono aliquas conclusiones. Next, concerning the affirmative expository syllogism (about which we should understood, only in the present) it is to be said that the affirmative expository syllogism holds via the rule 'whatever things are the same as one and the same thing in number, are mutually the same'. For example, if I say 'Socrates is white and the same Socrates is sitting', it follows that a sitting person is white, because it is maintained in the premisses that a white person as well as a sitting person is the same as Socrates. For the same reason one must conclude that a white person is the same as a sitting person. And for that reason it is to be considered concerning that rule, of which I posit some conclusions. [I have no idea what the last sentence is about].
Prima conclusio est quod ista regula 'quaecumque sunt uni et eidem in numero eadem, illa sibi invicem sunt eadem' non est vera si iste terminus 'eadem', vel etiam iste terminus 'quaecumque', quae sunt termini pluralis numeri, teneantur collective. Quia collective loquendo materia et forma sunt eadem composito, quod quidem compositum est unum et idem in numero, et tamen materia et forma non sunt sibi invicem eadem. The first conclusion [i.e. what Buridan thinks] is that the rule 'whatever are the same as one and the same thing in number, are mutually the same' is not true if the term 'the same [things]' or the term 'whatever things', which are plural terms, are taken collectively. For in speaking collectively, matter and form are according to the same composite, which composite is of course one and the same in number, and yet the matter and the form are not mutually the same.
Secunda conclusio potest poni quod nulla sunt eadem uni et eidem in numero divisim loquendo. Quia nulla sunt si ipsa non sunt plura et diversa ab invicem; sed si ipsa sunt plura et diversa ab invicem, impossibile est quod aliquod idem sit quodlibet illorum; igitur. The second conclusion can be put: that no things are the same as one and the same thing in number, divisively speaking. For they are none, if those very things are not several and different from one another. But if those very things are several and diverse from one another, it is impossible that the same thing should be the same as any [i.e. every] one of them whatever, accordingly.
Sed tunc statim dubitatur quo modo illud principium possit habere veritatem, scilicet 'quaecumque uni et eidem sunt eadem ...' et caetera. Ad hoc respondendum est ponendo tertiam conclusionem, quae est talis: plura nomina divisim loquendo dicuntur eadem eidem termino discreto, id est de quolibet illorum nominum vere praedicatur hoc nomen 'idem' cum additione eiusdem termini discreti. Sic enim dicimus quod animal et homo sunt idem Socrati*, quia verum est dicere 'animal est idem Socrati' et 'homo est idem Socrati'. Et quando dico 'animal et homo sunt idem Socrati', ego non intelligo quod homo et animal sint plura quorum quodlibet sit idem Socrati, quia hoc est impossibile, ut dicebat secunda conclusio, sed haec nomina 'homo' et 'animal' sunt plura, quorum quodlibet dicitur idem Socrati. Non dico 'est idem Socrati', sed dico 'dicitur idem Socrati' ita quod haec dictio 'dicitur' designat solum quod hoc praedicatum 'idem Socrati' vere praedicatur de utroque illorum nominum. But then it will straightaway be doubted in what way the principle (i.e. 'whatever things are the same as one and the same thing in number &c' could be true. The reply to this, is to put forward the third conclusion, which is such: several names, speaking divisively, are said to be the same as the same discrete term, i.e. of whatever of those names the name 'the same' is truly predicated, with the addition of the same discrete term. For thus we say that an animal and a man are the same as Socrates, since it is true to say 'an animal is the same as Socrates', and 'a man is the same as Socrates'. And when I say 'an animal and a man are the same as Socrates', I do not understand that a man and an animal are several things, of which any of them whatever is the same as Socrates, for this is impossible, [just] as the second conclusion said. But the names 'man' and 'animal' are several, of which any whatever can be said to be the same as Socrates. I do not say 'is the same as Socrates', but I do say 'is said to be the same as Socrates', so that the expression 'is said' signifies only that the predicate 'the same as Socrates' is truly predicated of both of those names.
Et ideo debetis notare quod non sequitur 'A et B sunt; ergo A et B sunt aliqua'. Quia si imponantur isti termini 'A' et 'B' ad significandum eandem rem simplicem, tunc verum est dicere quod A et B sunt, et tamen non sunt aliqua sed aliquod unum indivisibile. Et ideo iste terminus 'sunt', qui est pluralis numeri, non ponitur in plurali nisi propter plura nomina, sic pro eodem supponentia, et non propter plures res significatas. And for that reason you should note that 'A and B are, therefore A and B are something' does not follow. For if the terms 'A' and 'B' are imposed to signifying the same simple thing, then it is true to say that A and B are, and yet they are not some things, but some one indivisible thing. And for that reason the term 'are', which is plural in number, is not put in the plural except on account of several [plura] names, thus standing for the same thing, and not for several things that are signified.
Alia conclusio ponitur quod ista regula est vera 'quaecumque nomina divisim dicuntur eadem eidem termino discreto, illa dicuntur sibi invicem eadem', ad istum sensum quod si de utroque duorum nominum praedicetur vere hoc nomen 'idem' cum additione eiusdem termini discreti, tunc illa nomina vere dicuntur de se invicem, ut si animal est idem Socrati et homo est idem Socrati, oportet quod homo sit idem quod animal. Et causa huius est quod impossibile est aliquod unum et idem esse hoc et esse aliud quam hoc. Another conclusion is put forward, that the rule 'whatsoever names are said divisively to be the same as one and the same thing, are said mutually of the same thing' is true, asmuch as the sense that if of both of two names the name 'same' is truly predicated, with the addition of a discrete term, then those names are truly said mutually of themselves, such as if an animal is the same as Socrates, and a man is the same as Socrates, it must be that a man is the same as an animal. And the cause of this is that it is impossible that something be one and the same as this, and to be other than this.
Ex istis sequitur alia conclusio, responsalis, scilicet quod syllogismus expositorius est bonus affirmative in qualibet figura. Quia idem valet dicere 'Socrates est animal et Socrates est homo' sicut dicere 'Socrates est idem* animali et Socrates est idem homini', ex quo oportet concludere quod homo est idem animali, et hoc designatur dicendo quod homo est animal. And from these, the other conclusion follows of the responalis [?], namely that the expository syllogism is valid, affirmativel, in any figure. For it is as valid to say 'Socrates is an animal and Socrates is a man' as it is to say 'Socrates is the same as an animal & Socrates is the same as a man', from which one must conclude that a man is the same as an animal, and this is designated by saying a man is an animal.
Sed ab ista conclusione debemus excipere terminos divinos. Et causa huius est quia in divinis eadem res simplex est una res et alia res, scilicet una persona et alia persona. Sed Aristoteles et alii, solum de hoc naturaliter loquentes, crediderunt universaliter esse impossibile quod eadem res esset plures res, divisim loquendo, ita quod esset quaelibet earum. Et verum est quod hoc est omnino impossibile in creaturis; ideo crediderunt syllogismum expositorium in omnibus terminis esse bonum, quod non est verum, saltem sub forma sub qua ut in pluribus formatur. But from this conclusion we should exclude divine terms. And the cause of this is that in the divine [persons] the same simple thing is one thing and another thing, namely one person and another person. But Aristotle and others, speaking only of this naturally, believed universally it was impossible that the same thing be many things, divisively speaking, so that it would be any of them. And it is true that this is altogether impossible in created things. For that reason they believed the expository syllogism was valid for all terms, which is not true, at least under forms under which are formed as in many [?].
Ad rationes. Reply to the arguments:
1. Ad primam, dicendum est quod si aliud suppositum significetur in maiori et aliud in minori, medium variatur; et cum medium varietur, non est bonus syllogismus, nec est bonus syllogismus expositorius.
To the first, it is to be said that if one suppositum is signified in the major premiss and another in the minor, the middle is varied, and since the middle is varied, it is not a valid syllogism, and neither is it a valid expository syllogism.
2. Ad aliam, quando tu dicis "significando eundem hominem, 'iste homo vel asinus est homo*' ... ", dico quod illa propositio est duplex. Quia vel illa propositio est intelligenda in isto sensu, scilicet 'iste, qui est homo vel asinus, est homo'; et tunc esset bonus syllogismus expositorius et sequeretur quod asinus esset homo, sed minor est manifeste falsa. Aliter potest exponi quod quaelibet illarum propositionum sit una disiunctiva; verbi gratia, sic dicendo quod iste homo vel asinus est homo, si ponatur disiunctiva, sensus erit quod iste homo est homo vel asinus est homo, et minor erit quod iste homo est asinus vel asinus est asinus; et tunc ambae praemissae essent verae, sed non esset syllogismus expositorius, quia ponuntur ibi quaedam propositiones indefinitae cum propositionibus singularibus, et illae impediunt formam syllogismi expositorii.
To the second, when you say 'in signifying the same man, "that man is either a donkey or a man" … ' – I say that this proposition is twofold. For either that proposition is to be understood in the sense, namely 'that thing, which is a man or a donkey, is a man'; and then it would be a valid expository syllogism and it would follow that a donkey was a man, but the minor is manifestly false. Otherwise, it could be explained that either of those propositions was a disjunctive one, for example, if in saying that that man or a donkey is a man, if put forward as disjunctive, the sense will be that that man is a man or a donkey is a man, and the minor will be that that man is a donkey or a donkey is a donkey, and then both premisses would be true, but it would not be an expository syllogism, because there certain indefinite propositions are put forward with the singular propositions, and those would impede the form of the expository syllogism.
3. Ad aliam, dico quod ponendo quod Socrates videt equum et quod Socrates videt asinum est bonus syllogismus, sed debet inferri 'ergo videns asinum est videns equum', quia in ista propositione 'Socrates videt equum' praedicatum non est iste terminus 'equum', sed hoc totum 'uidens equum'.
To the third, I say that in supposing that 'Socrates sees a horse' and 'Socrates sees a donkey' is a valid syllogism, but one ought to infer 'therefore someone seeing a donkey is someone seeing a horse', because in the proposition 'Socrates sees a horse', the predicate is not the term 'horse', but the whole thing 'seeing a horse'.
4. Ad aliam, concessum est quod forma syllogismi expositorii ut communiter solet formari non tenet in terminis divinis, propter causam prius dictam.
To the fourth, it is conceded that the form of an expository syllogism as customarily and commonly is formed does not hold in divine terms, for the reason given above.
5. Ad ultimam, respondeo quod solummodo syllogismi ex terminis communibus sunt qui tenent per dici de omni et per dici de nullo.
To the final argument, I reply that only syllogisms from common terms hold via dici de omni and dici de nullo.

Notes

  1. Presumably the example at the end of Prior Analytics 1, 70 a 16 (Pittacus is wise, Pittacus is good, therefore some wise man is good).
  • [[]]
Personal tools