Works › Prior Analytics, Books I–II
Volume 1 · pp. 672–674
Chapter XIV. That syllogisms from hypothesis cannot be reduced into terms in this way.
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CAPUT XIV. Quod syllogismi ex hypothesi sic in terminos reduci non possunt.
Amplius autem quia syllogismi ex hypothesi ex habitudine locali suam habent consequentiam, et non ex ordine terminorum et positione propositionum in syllogismo, ideo syllogismos ex hypothesi non est tentandum hoc modo in tres terminos reducere. In syllogismis enim ex hypothesi non est sive contingit reducere ex his quae posita sunt in syllogismo: quia non sunt posita ex ordine trium terminorum, sed potius ex habitudine locali. Tales enim syllogismi ex hypothesi non sunt ostensi per habitudinem terminorum per syllogismum ostensivum, qui solus veram habet formam syllogismi. Sed potius in his qui fiunt per habitudines, sunt concessiones quaedam ad placitum respondentis, sicut quando concessum est quod si in uno se sic habet, in omnibus similiter esse. Sicut si aliquis ponat, quod si una quaedam potestas non sit aliquorum contrariorum, quod sequatur ad hoc neque unam aliquam non esse disciplinam contrariorum: et hoc concesso disputet aliqua inducendo contraria, ut sanum et aegrum, sive sanativum et aegrotativum non esse unius potestatis: quia si essent unius potestatis, essent unius actionis: et si essent unius actionis essentialis, sequeretur quod essent idem: et sic idem simul esset sanativum et aegrotativum: et ex hoc dicat esse ostensum, quoniam non omnium contrariorum est una potestas: quia instantia est in sano et aegro. Sed non adhuc est ex hoc ostensum, quod non sit una disciplina contrariorum, quamvis ex ipsa rei habitudine confiteri sit necesse, quod quorum non est potestas, quod illorum non sit etiam una disciplina: sed hoc confiteri non cogitur ex syllogismo, sed potius ex conditione, hoc est, confessione dicta, hac scilicet, quod si probetur non esse unam potestatem contrariorum, quod probatum sit non esse unam disciplinam. Talem igitur rationem non est reducere illa reductione, quae resolutio est propositionum in tres terminos. Sed bene probatur syllogistice, quod si sanativi et aegrotativi non est una potestas, quod non omnium contrariorum est una potestas: sic enim fortasse fuit et fit syllogismus ostensivus hoc concludens. Illud autem quod ex hoc infertur, quod non omnium contrariorum sit una disciplina, est conditio ex confessione et habitudine locali et non ex consequentia syllogistica.
Similiter autem est etiam in his syllogismis qui per impossibile datum a respondente in opposito conclusionis vere per syllogismum ostensivum syllogizatae, per quod oppositum sumptum cum majori vel minori deducitur ad oppositum alterius praemissarum, quod est etiam impossibile. Hos enim utiles syllogismos (cum non inferant ex dispositione terminorum in figura, et ex modo combinationis propositionum, sed arguant ex positione dantis oppositum) non est vel contingit resolvere tali resolutione, qua propositiones in terminos resolvuntur, et alterum praemissorum, quod datum est in opposito conclusionis, et pro altera propositione ponitur in syllogismo deducente ad impossibile, non est secundum rem et dispositionem figurae et modi secundum realem ordinem medii ad extrema: sed in tali syllogismo semper concluditur ex conditione data in opposito conclusionis, quod cum praemissis eumdem terminorum non habuit ordinem, ut medium vel esset inter extrema, vel ante ea, vel posterius eis.
CHAPTER XIV. That syllogisms from hypothesis cannot be reduced into terms in this way.
Furthermore, because syllogisms from hypothesis have their consequence from a local relation, and not from the order of terms and the position of propositions in a syllogism, therefore one must not try to reduce syllogisms from hypothesis into three terms in this way. For in syllogisms from hypothesis there is not, or it does not happen, to reduce from those things which are posited in the syllogism, because they are not posited from the order of three terms, but rather from a local relation. For such syllogisms from hypothesis have not been shown through the relation of terms by an ostensive syllogism, which alone has the true form of syllogism. Rather, in those which are made through relations, there are certain concessions according to the pleasure of the respondent, as when it has been conceded that if in one thing it has itself so, it is so similarly in all. For example, if someone posits that, if some one power is not of certain contraries, it follows from this that there is not some one discipline of contraries either; and, with this conceded, he disputes by introducing certain contraries, as the healthy and the sick, or the healing and the sickening, that they are not of one power, because if they were of one power, they would be of one action; and if they were of one essential action, it would follow that they were the same; and so the same thing would at once be healing and sickening; and from this he says that it has been shown that there is not one power of all contraries, because there is an instance in the healthy and the sick. But from this it has not yet been shown that there is not one discipline of contraries, although from the very relation of the thing it is necessary to confess that of those things of which there is not a power, of those there is not also one discipline. Yet one is not compelled to confess this from a syllogism, but rather from the condition, that is, from the confession stated, namely this, that if it is proved that there is not one power of contraries, it has been proved that there is not one discipline. Therefore such a reasoning must not be reduced by that reduction which is the resolution of propositions into three terms. But it is proved well syllogistically that if there is not one power of the healing and the sickening, then there is not one power of all contraries; for thus perhaps there was and is an ostensive syllogism concluding this. But that which is inferred from this, that there is not one discipline of all contraries, is a condition from confession and local relation, and not from syllogistic consequence.
It is similar also in those syllogisms which, through an impossible given by the respondent in the opposite of a conclusion truly syllogized through an ostensive syllogism, by which opposite, taken with the major or minor, it is led to the opposite of the other premise, which also is impossible. For these useful syllogisms, since they do not infer from the disposition of terms in a figure and from the mode of combination of propositions, but argue from the position of the one giving the opposite, are not, or cannot be, resolved by such a resolution by which propositions are resolved into terms. And one of the premises, which has been given in the opposite of the conclusion and is placed as the other proposition in the syllogism leading to the impossible, is not according to reality and the disposition of figure and mode according to the real order of the middle to the extremes; but in such a syllogism the conclusion is always drawn from a condition given in the opposite of the conclusion, which did not have the same order of terms with the premises, such that the middle either was between the extremes, or before them, or after them.
Isti tamen syllogismi qui ducunt ad impossibile, differunt a prius dictis syllogismis ex hypothesi, qui fundantur super simile (sicut prius dictum est) in hoc, quoniam in illis qui sunt per similitudinem oportet respondentem prius confiteri positionem, quod sicut est in uno, ita sit in aliis: eo quod secundum rem hoc non habet necessitatem: et ideo ad positionem respondentis tunc syllogizatur: oportet igitur in illis respondentem prius confiteri si debeant concedere vel non debeant ipsius respondentes. Cujus exemplum est, quod si debeat concludi unam esse disciplinam contrariorum per hoc quod una est potestas eorum, tunc enim prius confiteri oportet quod una sit potestas, et concedere oportet esse unam disciplinam omnium contrariorum per hoc, quod quorumdam est una potestas et una disciplina per hoc quod similiter se habet in omnibus, sicut in uno. Hoc autem in syllogismo ducente ad impossibile de necessitate concedent, etiamsi non confiteantur: quia coguntur per hoc principium, quod contradictoria non sunt simul vera, et quod de omnibus alterum eorum est verum. Concedent igitur necessario: eo quod ex ipsa oppositione contradictionis falsum statim ex ipsa re manifestum sit: ideo enim non stat cum altera praemissarum, quia contradictoria simul vera esse non possunt. Cujus exemplum, quod si detur hoc inconveniens quod diameter est simeter, quod oppositum est huic verae, diameter non est simeter, deducens ad hoc manifeste falsum, quod imparia in numeris sunt aequalia paribus, sive fiunt paria, quod est impossibile secundum rem et non tantum secundum concessionem.
Sunt plures modi syllogismorum ex hypothesi, sicut in parte in ante habitis dictum est, et sunt modi illi diversi in quibus concluditur ex conditione, et non ex dispositione terminorum in figura et modo: et omnes istos modos oportet diligenter perspicere, et pernotare diligenter differentias in quibus differunt a se invicem et ab ostensivo syllogismo, et videre qui in terminos possint reduci, et qui non. Quae autem sint horum syllogismorum differentiae, et quoties sive quot modis utiliter fiunt syllogismi qui sunt ex hypothesi, postea in secundo istius scientiae libro, et in proprio de syllogismis hypotheticis libro dicemus. Nunc autem quantum ad praesentem intentionem pertinet, tantum sit nobis manifestum, quoniam hujusmodi syllogismos hypotheticos non est resolvere in terminos secundum figurae dispositionem: et jam diximus ob quam causam hujusmodi resolutio fieri non potest.
Yet these syllogisms which lead to the impossible differ from the previously mentioned syllogisms from hypothesis, which are founded upon likeness, as was said before, in this: that in those which proceed through likeness the respondent must first confess the position, that as it is in one case, so it is in the others, because according to reality this does not have necessity; and therefore then one syllogizes toward the respondent's position. Therefore in those, the respondent must first confess whether they ought to concede or ought not, the respondents themselves. An example of this is that, if it ought to be concluded that there is one discipline of contraries through this, that there is one power of them, then one must first confess that there is one power, and one must concede that there is one discipline of all contraries through this, that of certain things there is one power and one discipline through the fact that it has itself similarly in all, as in one. But in a syllogism leading to the impossible they will concede this of necessity, even if they do not confess it, because they are compelled through this principle, that contradictories are not true at the same time, and that of all things one of them is true. Therefore they will concede necessarily, because from the very opposition of contradiction the false is immediately manifest from the thing itself; for it does not stand with the other of the premises, because contradictories cannot be true at the same time. The example is that, if this unsuitable thing is granted, that a diameter is commensurable, which is the opposite of this true statement, a diameter is not commensurable, this leads to the manifestly false result that odd numbers are equal to even numbers, or become even, which is impossible according to reality and not only according to concession.
There are several modes of syllogisms from hypothesis, as was said in part in the preceding matters, and those are diverse modes in which the conclusion is reached from a condition and not from the disposition of terms in figure and mode. And all those modes must be diligently examined, and the differences in which they differ from one another and from an ostensive syllogism must be diligently noted, and one must see which can be reduced into terms and which cannot. But what the differences of these syllogisms are, and how often or in how many modes syllogisms which are from hypothesis are usefully made, we shall say later in the second book of this science and in the proper book On Hypothetical Syllogisms. But now, as much as pertains to the present intention, let only this be manifest to us: that hypothetical syllogisms of this kind are not to be resolved into terms according to the disposition of figure; and we have already said for what cause resolution of this kind cannot be made.
Si autem aliquis quaerat, propter quid hoc sit, quod in syllogismo hypothetico (qui fit per similitudinem ad constructionem universalis per particularem) oporteat uti praeconfessione, in syllogismo autem ad impossibile quoad destructionem particularis non oportet uti praeconfessione aliqua? Sed hujus plana est ratio, haec scilicet, quod destructo particulari necessario destruitur universale, sive quis confiteatur, sive non: sed positio particularis non de necessitate ponit universale: et ideo in illo oportet uti praeconfessione, vel non sequitur conclusio.
Si quis autem iterum obviet et dicat, quod omne genus argumentationis reduci habet ad syllogismum: est autem ex hypothesi syllogismus quoddam genus argumentationis: ergo reducitur in syllogismum. Adhuc autem arguatur: quorumcumque oppositorum non est una potestas, non est eadem disciplina: contrariorum non est una potestas: ergo nec una disciplina: hic est syllogismus ex hypothesi in formam ostensivi syllogismi reductus. Et si dicat aliquis, quod non est syllogismus in prima figura, quia minorem habet negativam, formetur idem in similitudine affirmationis, sic, quorumcumque est idem sensus, horum est una disciplina: oppositorum autem est idem sensus: ergo una disciplina.
Ad haec autem et omnia similia dicendum, quod omnis verus syllogismus infert ex his quae posita sunt in syllogismo in terminorum dispositione et modo combinationis propositionum, et non ex aliqua conditione vel locali habitudine antecedentis ad consequens, vel e converso: et ideo syllogismus ex hypothesi secundum hunc modum syllogismi non est vere syllogismus: quia talem non habet terminorum dispositionem et propositionum complexionem: et ideo etiam hac reductione reduci non potest. Et quod objicitur quod omne genus argumentationis reducitur in syllogismum, Dicendum quod verum est: sed quodlibet genus argumentationis reducitur in suum syllogismum sibi appropriatum: et ideo argumentatio quae vim habet ex hypothesi, reducitur in syllogismum hypotheticum; et alia quae habet virtutem ex dispositione terminorum, reducitur in syllogismum categoricum sive ostensivum. Et per hoc patet quod ex argumentatione quam inducit, non formatur nisi syllogismus hypotheticus immediate, sic, quorumcumque est idem sensus, horum est eadem disciplina: sed contrariorum est idem sensus: ergo eadem disciplina: ibi enim arguitur a positione antecedentis: et ideo tales conclusiones dicuntur non esse syllogizatae syllogismo, qui vere syllogismi formam habet.
But if someone asks why this is, that in a hypothetical syllogism, which is made through likeness for the construction of a universal through a particular, one must use a preconfession, whereas in a syllogism to the impossible, with respect to the destruction of a particular, one need not use any preconfession, the reason for this is plain, namely this: that when the particular has been destroyed, the universal is necessarily destroyed, whether someone confesses it or not; but the positing of a particular does not of necessity posit the universal, and therefore in that case one must use a preconfession, or the conclusion does not follow.
But if someone again objects and says that every genus of argumentation has to be reduced to syllogism, but a syllogism from hypothesis is a certain genus of argumentation, therefore it is reduced to syllogism. Again let it be argued: of whatever opposites there is not one power, there is not the same discipline; of contraries there is not one power; therefore neither is there one discipline. Here there is a syllogism from hypothesis reduced into the form of an ostensive syllogism. And if someone says that it is not a syllogism in the first figure because it has the minor negative, let the same thing be formed in likeness to affirmation, thus: of whatever things there is the same sense, of these there is one discipline; but of opposites there is the same sense; therefore there is one discipline.
But to these and all similar things it must be said that every true syllogism infers from those things which are posited in the syllogism in the disposition of terms and the mode of combination of propositions, and not from some condition or local relation of antecedent to consequent, or conversely. And therefore a syllogism from hypothesis, according to this mode of syllogism, is not truly a syllogism, because it does not have such a disposition of terms and complexing of propositions; and therefore it also cannot be reduced by this reduction. And as to what is objected, that every genus of argumentation is reduced into syllogism, it must be said that it is true, but each genus of argumentation is reduced into its own syllogism appropriated to it. And therefore argumentation which has force from hypothesis is reduced into a hypothetical syllogism, and another, which has its power from the disposition of terms, is reduced into a categorical or ostensive syllogism. And through this it is plain that from the argumentation which he introduces, nothing is formed immediately except a hypothetical syllogism, thus: of whatever things there is the same sense, of these there is the same discipline; but of contraries there is the same sense; therefore there is the same discipline. For there the argument proceeds from the positing of the antecedent; and therefore such conclusions are said not to be syllogized by a syllogism which truly has the form of a syllogism.
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