Authors/Buridan/Quaestiones in analytica priora/Liber 1/Q12

 

Latin	English
[Quaestio 12a UTRUM PARTICULARIS NEGATIVA POSSIT CONVERTI]	[Question 12: whether the particular negative can be converted]
Duodecima quaestio est utrum particularis negativa possit converti.	The twelfth question is whether the particular negative can be converted.
1.Et arguitur quod sic per simile: quia sicut affirmativa se habet ad affirmativam, ita negativa ad negativam; sed affirmativa convertitur in affirmativam, quamvis sit particularis; ergo ... et caetera.	And it is argued that it is 'by simile', for just as the affirmative stands to the affirmative, so the negative to the negative.  But an affirmative is converted to an affirmative, although it is particular, etc.
2. Item, haec est bona consequentia 'quidam homo non est risibilis; ergo quoddam risibile non est homo', et tamen ista est conversio particularis negativae. Et probo quod illa consequentia sit bona: quia sequitur 'quidam homo non est risibilis; ergo quidam homo non est', et ultra sequitur 'quidam homo non est; ergo nullus homo est', et sequitur ultra 'nullus homo est; ergo nullum risibile est homo', et postea convertitur 'ergo quoddam risibile non est homo', et sic, de primo ad ultimum, concluditur propositum. Et eodem modo argueretur quod esset bona consequentia 'quidam homo non est animal; ergo quoddam animal non est homo'.	Likewise, the consequence 'some man is not capable of laughter, therefore something capable of laughter is not a man' is good, and yet is is a conversion of the particular negative.  And I prove that the consequence is good, for 'some man is not capable of laughter, therefore some man is' follows, and furthermore 'some man is not', therefore no man is' follows, and furthermore 'no man is, therefore nothing capable of laughter is a man', and afterwards 'therefore something capable of laughter is not a man' is converted, and 'from first to lastthe proposal is concluded. And in the same way it would be argued that 'some man is not an animal, therefore some animal is not a man' would be a good consequence.
3. Item, haec est particularis negativa 'quoddam B A non est', et tamen convertitur simpliciter, scilicet in istam 'quoddam A B non est'; ergo particularis negativa convertitur. Probo minorem: quia ista 'quoddam B A non est' potest habere duas causas veritatis, scilicet unam quia aliquis illorum terminorum pro nullo supponit, et tunc statim sequitur quod sicut haec est vera 'B A non est', ita haec est vera 'A B non est'; nam sicut homo chimaera non est, ita chimaera homo non est; alia causa veritatis potest esse quia licet sit aliquod B et aliquod A, tamen hoc non est illud; et sic adhuc utraque erit vera; ideo, quocumque modo, una sequitur ad aliam.	Likewise, 'some B-A is not' is a particular negative, and yet it is converted simply, namely to 'some A-B is not', therefore the particular negative is converted.  I prove the minor, for 'some B-A is not' can have two causes of truth, namely one because one of the terms supposits for nothing, and then it immediately follows that just as 'B-A is not' is true, so 'A-B is not' is true. For just as a man-chimaera is not, so a chimaera-man is not.  The other cause of truth can be that although there is some B and some A, yet one is not the other, and thus both will still be true.  Thus, either way, one follows from the other.
4. Item, sicut se habet ista 'nullum B est A' ad istam 'quoddam A non est B', ita se habet ista 'nullum A est B' ad istam 'quoddam A est B'; ergo, per locum a transmutata proportione, sicut se habet ista 'nullum B est A' ad istam 'nullum A est B', ita se habet ista 'quoddam B non est A' ad istam 'quoddam A non est B'; sed ista 'nullum B est A' infert istam 'nullum A est B'; ergo ista 'quoddam B non est A' infert istam 'quoddam A non est B', et sic habetur propositum.	Likewise, just as 'no B is A' stands to 'some A is not B', so 'No A is B' stands to 'some B is not A'. Therefore, by the topic from transformed proportion, just as 'no B is A' stands to 'no A is B', so 'some B is not A' stands to 'some A is not B'.  But 'no B is A' implies 'no A is B', therefore 'some B is not A' implies 'some A is not B', and thus we have the case in point.
5. Item, regula est in logica quod quidquid repugnat consequenti alicuius consequentiae repugnat antecedenti; modo particularis negativa est consequens ad universalem negativam; ergo si particulari negativae repugnaret converti, hoc etiam repugnaret universali negativae, quod est falsum.	Likewise, it is a rule in logic that whatever is inconsistent with the consequent is inconsistent with the antecedent. But the particular negative is the consequent of the universal negative, therefore if it were inconsistent for the particular negative to be converted, it would also be inconsistent for the universal negative [to be converted], which is false.
6. Item, auctor Summularum ponit eam converti per contrapositionem; ergo potest converti.	Likewise, the author of the Summulae supposes that it is converted by contraposition, therefore it can be converted.
7. Et etiam auctor Summularum ponit quod idem est iudicium de particularibus, indefinitis et singularibus; sed singularis negativa bene convertitur; ergo similiter particularis negativa.	And also the author of the Summulae supposes that the same thing is to be judged of particulars, indefinites and singulars. But the singular negative is well converted, therefore similarly the particular negative.
Oppositum determinat Aristoteles.	Aristotle determines the opposite.
Sciendum est primo ad praesens quod solum de illis propositionibus de quibus dictum est in tribus quaestionibus praecedentibus, scilicet de inesse et de praesenti, hic etiam dicetur. Et tunc pono conclusiones.	It should first be known at present that only of the propositions which were talked about in the three preceding questions, namely assertoric and present tense, this will also be said [?].  And then I give the conclusions.
Prima conclusio est ista quod particularis negativa de praedicato non distributo convertitur simpliciter, ut 'quoddam B A non est; ergo quoddam A B non est', sicut probatum fuit in argumento.	The first conclusion is that the particular negative of the predicate non-distributed is simply converted, e.g 'some B-A is not, therefore some A-B is not', just as was proved in the argument.
Secunda conclusio est ista, quod aliquae particulares negativae, quamvis sint de praedicato distributo, convertuntur simpliciter gratia materiae ut 'homo non est animal; igitur animal non est homo'; sequitur enim 'homo non est animal; ergo homo non est', et ultra 'ergo nullus homo est', et ultra 'ergo animal non est homo'; ergo, de primo ad ultimum, erit bona consequentia. Similiter sequitur 'quidam homo non est asinus; ergo quidam asinus non est homo'; probatio: quia ex opposito consequentis sequitur oppositum antecedentis; verbi gratia, sequitur 'omnis asinus est homo; ergo omnis homo est asinus', quia prima illarum est impossibilis, et ad impossibile sequitur quodlibet.	The second conclusion is that some particular negatives, although they are of the distributed predicate, are converted simply in virtue of the material, e.g. 'a man is not an animal, therefore an animal is not a man', and also 'therefore no man is', and also 'therefore an animal is not a man'. Therefore, from 'first to last', it will be a good consequence.  Similarly 'some man is not a donkey, therefore some donkey is not a man'.  Proof: because from the opposite of the consequent there follows the opposite of the antecedent. For example, 'every donkey is a man, therefore every man is a donkey' follows, because the first is impossible, and anything follows from the impossible.
Tertia conclusio est quod nulla particularis negativa de praedicato communi distributo convertitur in aliam quae etiam sit de praedicato distributo, et hoc gratia formae. Quia consequentia gratia formae debet tenere in omnibus terminis retenta consimili forma; ideo si in aliquibus terminis invenitur instantia, statim sequitur quod consequentia non erat formalis. Sed instantia statim invenitur in proposito, quia haec est vera 'quoddam animal non est homo', et tamen convertens esset falsa, scilicet 'quidam homo non est animal'. Et causa huius est quia in convertente distribuitur iste terminus 'animal', qui in antecedente non erat distributus; modo terminus non distributus non potest inferre se ipsum distributum; non enim sequitur 'quidam homo currit; igitur omnis homo currit'.	The third conclusion is that no particular negative with a common distributed predicate is converted into another which also has a distributed predicate, and this is in virtue of its form.  For a consequence 'in virtue of form' ought to hold in all terms keeping a similar form, therefore if in some terms a counter-instance were found, it would immediately follow that the consequence was not formal.  But a counter-example is immediately found in the case at hand, for 'some animal is not a man', and yet converting it would be false, namely 'some man is not an animal'.  And the cause of this is that in the converting the term 'animal' is distributed, which in the antecedent was not distributed. But a term that is not distributed cannot imply itself distributed, for 'some man runs, therefore every man runs' does not follow.
Deinde, quia in uno argumento locutum est de singularibus, pono de eis conclusiones. Prima conclusio est quod singularis negativa, si sit de praedicato singulari, convertitur simpliciter, ut 'hoc B non est hoc A; ergo hoc A non est hoc B'; oportet enim si Socrates sit diversus a Platone quod Plato sit diversus a Socrate. Et sic etiam affirmativa convertitur, ut 'hoc A est hoc B; ergo hoc B est hoc A'; quia si hoc est idem illi, oportet quod illud sit idem huic.	Next, because in one argument we spoke of singulars, I give conclusions about them.  The first conclusion is that the singular negative, if it is of a singular predicate, is simply converted. E.g. 'this B is not this A, therefore this A is not this B', for it must be that if Socrates is different from Plato, that Plato is different from Socrates'. And so also the affirmative is converted, e.g. 'this A is this B, therefore this B is this A', for if this is the same as that, it must be that that is the same as this.
Secunda conclusio est ista, quod singularis de praedicato non distributo convertitur in particularem vel indefinitam, ut 'Socrates est albus; ergo album est Socrates', vel etiam, negative, ut 'Socrates homo non est' (quia Socrates Plato non est) 'ergo homo Socrates non est', vel 'homo non est Socrates'.	The second conclusion is that a singular with the predicate not distributed is converted into a particular or indefinite, e.g. 'Socrates is white, therefore a white thing is Socrates', or also negative, e.g. 'Socrates is not a man' (because Socrates is not Plato) 'therefore a man Socrates is not' or 'a man is not Socrates'.
Tertia conclusio est quod singularis de praedicato communi distributo convertitur in universalem, sive sit affirmativa sive negativa. Sequitur enim 'Socrates est omnis homo; ergo omnis homo est Socrates'; sequitur etiam 'Socrates non est albus; ergo nullum album est Socrates'. Et causa est quia non mutatur suppositio alicuius termini; suppositio enim termini singularis non mutatur sive negatio praecedat sive sequatur ipsum*, quia non potest distribui, propter quod istae aequipollent 'Socrates non currit' et 'non Socrates currit'.	The third conclusion is that a singular with a common distributed predicate is converted into the universal, whether it is affirmative or negative.  For 'Socrates is every man, therefore every man is Socrates' follows, and also 'Socrates is not white, therefore no white thing is Socrates'. And the cause is that the supposition of a term is not changed, for the supposition of a singular term is not changed whether negation precedes it or follows it, because it cannot be distributed.  Because of this 'Socrates does not run' and 'it is not the case that Socrates runs' are equipollent.
Ultimo, de dictis auctoris Summularum, dicendum est quod non est verum quod idem sit iudicium de particularibus, indefinitis et singularibus, nec in convertendo, nec in syllogizando, nec in modo concludendi, sed est idem iudicium de particularibus et indefinitis.	Finally, of the sayings of the author of the Summulae, it should be said that it is not true that the judgment is the same for particulars, indefinites and singulars, nor in converting, nor in syllogising, nor in the mode of concluding, but it is the same judgment for particulars and indefinites [?]
Dicendum est etiam quod conversio per contrapositionem non est proprie conversio. Quia non manent idem termini, sed mutantur termini finiti in terminos infinitos; ideo non fit de subiecto praedicatum nec e converso. Et ultra si volumus illas conversiones per contrapositionem vocare 'conversiones', tamen diceremus quod non sunt consequentiae formales.	It should be said also that conversion by contraposition is not conversion proper.  For they do not remain the same terms, but rather definite terms are changed into indefinite ones, and so a predicate is not made from a subject, nor conversely. And furthermore, if we wish to call those conversions by contraposition 'conversions', still we would say that they are not formal consequences.
Quoniam conversio universalis affirmativae esset falsa ubi terminus infinitus pro nullo supponeret; verbi gratia, non est bona consequentia 'omnis homo est ens; ergo omne non ens est non homo', quia prima est vera et secunda falsa; est enim affirmativa, quae non potest esse vera si aliquis terminus pro nullo supponit; modo iste terminus 'non ens' pro nullo supponit; ergo sequitur quod ipsa est falsa.	Since [?] conversion of the universal affirmative would be false where an indefinite term supposited for nothing, for example, 'every man is a being, therefore every non being is a non man', is not a good consequence, for the first is true and the second false, for it is an affirmative proposition, which cannot be true if any term [in it] supposits for nothing. But the term 'non being' supposits for nothing, therefore it follows that the second is false.
Conversio autem particularis negativae esset falsa ubi terminus finitus pro nullo supponeret: quia non sequitur 'quaedam chimaera non est homo; ergo quidam non homo non est non chimaera'; quia prima est vera et secunda falsa eo quod sua contradictoria est vera, scilicet ista 'omnis non homo est non chimaera', quod patet per inductionem.	But conversion of the particular negative would be false where the definite term supposited for nothing, for 'some chimaera is not a man, therefore some non man is not a non chimaera' does not follow, for the first is true and the second false because its contradictory is true, namely 'every non man is a non chimaera', which is clear by example [per inductionem].
His visis, respondeo ad rationes.	Having seen these, I reply to the arguments.
1. Ad primam, dico quod non est simile de particularibus affirmativis et de particularibus negativis ad invicem in convertendo ubi praedicata distribuuntur, sicut est modus consuetus formandi particulares negativas. Et est dissimilitudo quia in conversione affirmativarum non mutatur suppositio alicuius termini, sed in conversione negativae mutatur suppositio non distributa in distributam, ubi non est bona consequentia.	To the first, I say there is no similarity between particular affirmatives and particular negatives in conversion where the predicates are distributed, as is the customary way of forming particular negatives.  And there is a dissimilarity because in the conversion of affirmatives the supposition of a term is not changed, but in the conversion of negatives non-distributed supposition is changed into distributed, where there is not a good consequence.
2. Ad aliam, concedo quod ista 'quidam homo non est risibilis' bene convertitur gratia materiae, sed non gratia formae.	To the second, I concede that 'some man is not capable of laughter' is well converted in virtue of its material, but not in virtue of its form.
3. Ad aliam, concessum est quod ista bene convertitur 'quoddam B A non est'.	To the third, it is conceded that 'some B-A is not' is well converted.
4. Ad aliam, dico quod locus a transmutata, vel commutata, proportione non habet suam necessitatem nisi in subiectis quantitativis et in subiectis extensis.	To the fourth, I say that the topic from the transformed (or commuted) proportion does not have its necessity except in quantitative subjects and in extended subjects.
5. Ad aliam, concedo istam regulam 'quidquid repugnat consequenti repugnat antecedenti' ad talem sensum quod propositio repugnans secundum oppositionem consequenti non potest stare in veritate cum antecedente. Tamen aliquod praedicatum bene repugnat termino significanti consequens quod non repugnat termino significanti antecedens; verbi gratia, istud praedicatum 'converti' bene repugnat isti termino 'particularis negativa'; dico quod sic repugnat quod non possit vere praedicari de eo; tamen non oportet quod propter hoc repugnet isti termino 'universalis negativa'.	To the fifth, I concede the rule 'whatever is inconsistent with the conseequent, is inconsistent with the antecedent', in the sense that a proposition that is inconsistent by opposition to the consequent cannot stand in truth with the antecedent.  But some predicate is rightly inconsistent with a term signifying the consequent that is not inconsistent with a term signifying the antecedent. For example, the predicate 'to be converted' is rightly inconsistent with the term 'particular negative'.  I say that it is inconsistent so that it cannot be truly predicated of it, yet it does not have to be that because of this it is inconsistent with the term 'universal negative'.
6. Ad auctorem Summularum dictum est in positione.	The reply to the argument of the Summulae was stated in the determination [positione].