Works › Prior Analytics, Books I–II
Volume 1 · pp. 491–493
Chapter IV. On the formation of syllogisms concluding particularly in the first figure according to useful and useless conjugations.
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CAPUT IV. De formatione syllogismorum particulariter concludentium in prima figura secundum utiles conjugationes et inutiles.
Syllogismi autem particulariter concludentes sic fiunt in hac figura. Si enim hic terminus qui est major extremitas se habeat ad medium universaliter, ita quod universaliter praedicetur de ipso: iste vero qui est minor extremitas, particulariter se habeat ad medium, ita quod medium particulariter praedicetur de minori extremitate: quando quidem id quod est vel ponitur ad majorem extremitatem, ita quod major propositio in qua praedicatur major extremitas sit universalis affirmativa vel negativa, et minor particularis affirmativa, sive praedicativa, quod idem est: tunc necesse est syllogismum fieri perfectum particulariter concludentem. Quando autem ad minorem extremitatem ponitur universalis, et ad majorem ponitur particularis: vel etiam quando negativa ponitur ad minorem, vel quocumque alio modo disponantur propositiones quam dictum est, est inutilis conjugatio et non fit syllogismus. Dico autem majorem quidem extremitatem, in qua medium sicut subjectum in praedicato: minorem autem extremitatem, quae est sumpta sub medio, et de qua medium praedicatur. Cujus exemplum est, quod A insit omni B, B autem medium insit alicui C, sequitur quod necesse est A alicui C inesse, sic formando syllogismum: omne B est A, quoddam C est B, ergo quoddam C est A. Et confirmatur per dici de omni, a quo fit decursus syllogisticus: quia ex quo A inest omni B universaliter, tunc oportet quod insit omni parti ejus quod est B: C autem aliquod est aliqua partium B, oportet igitur quod illi insit A: per id quod in Praedicamentis habitum est, quando alterum de altero ut de subjecto, quaecumque de praedicato dicuntur, omnia de subjecto dici necesse est.
Similiter formatur syllogismus particulariter et negative concludens, si ponatur universalis negativa ad majorem, et particularis affirmativa ad minorem, ut si A quidem nulli B inest, B autem inest alicui C, sequitur enim quod necesse est A alicui C non inesse, sic formando syllogismum: nullum B est A, quoddam C est B, ergo quoddam C non est A.
Et isti duo particulariter concludentes syllogismi formantur a duobus universaliter concludentibus: primus a primo, et secundus a secundo: et per idem principium confirmantur, per quod confirmantur universaliter concludentes, et hoc est per dici de omni, et dici de nullo. Jam enim determinatum est qualiter dicimus de omni dici et de nullo. Talis igitur syllogismus perfectus est, nullo indigens praeter id quod habet et claudit in seipso. Eodem autem modo et idem fit syllogismus tam negative quam affirmative concludens, quando non particularis, sed indefinita affirmativa sive praedicativa ponitur minor propositio quae designatur per B C. Idem enim erit syllogismus ex indefinito et ex particulari sumpto: quia indefinitum aequipollet particulari.
Inutiles autem fiunt conjugationes, quocumque alio modo termini et propositiones disponantur. Si enim ad minorem extremitatem ponatur universale, ita quod minor sit universalis sive praedicative, sive privative, et particularis ponatur ad majorem, non erit syllogismus nec praedicativae nec negativae conclusionis, sive indefinita sit, sive particularis quae ponitur ad majorem. Hujus autem exemplum est, sicut si A inest alicui B vel alicui B non inest, B autem omni C inest, non fit syllogismus: nihil enim sequitur ex tali complexione, quoddam B est A, omne C est B. Similiter nec ex tali, quoddam B non est A, omne B C: sequitur enim inesse omni et nulli. Termini quidem in quibus sequitur omni inesse, sunt bonum, habitus, prudentia, sic, quidam habitus bonum: omnis prudentia habitus: ergo quaedam prudentia bonum: quod est verum, omnis enim prudentia bonum. Exemplum autem ubi sequitur nulli inesse, est in his terminis, bonum, habitus, indisciplina, sic, quidam habitus bonum: omnis indisciplina habitus: ergo quaedam indisciplina bonum: quod non valet, quia nulla indisciplina bonum.
CHAPTER IV. On the formation of syllogisms concluding particularly in the first figure according to useful and useless conjugations.
But syllogisms concluding particularly are made in this figure in this way. For if this term which is the greater extreme has itself to the middle universally, so that it is predicated universally of it, but that which is the lesser extreme has itself particularly to the middle, so that the middle is predicated particularly of the lesser extreme; when what is or is posited is at the greater extreme, so that the major proposition in which the greater extreme is predicated is universal affirmative or negative, and the minor is particular affirmative, or predicative, which is the same thing, then a perfect syllogism concluding particularly must be made. But when a universal is posited at the lesser extreme and a particular is posited at the greater, or also when a negative is posited at the lesser, or the propositions are disposed in any other way than has been said, there is a useless conjugation and no syllogism is made. Now I call the greater extreme that in which the middle is as a subject in a predicate; and the lesser extreme that which is taken under the middle and of which the middle is predicated. An example of this is that A belongs to every B, but B, the middle, belongs to some C; it follows that A must belong to some C, forming the syllogism thus: every B is A; some C is B; therefore some C is A. And it is confirmed through being-said-of-every-one, from which the syllogistic running-through is made, because from the fact that A belongs to every B universally, then it must belong to every part of what is B. But some C is one of the parts of B; therefore A must belong to that. This is through what was held in the Categories: when one thing is said of another as of a subject, whatever is said of the predicate must all be said of the subject.
Similarly a syllogism concluding particularly and negatively is formed if a universal negative is posited at the major and a particular affirmative at the minor, as if A indeed belongs to no B, but B belongs to some C; for it follows that A must not belong to some C, forming the syllogism thus: no B is A; some C is B; therefore some C is not A.
And those two syllogisms concluding particularly are formed from the two that conclude universally: the first from the first, and the second from the second; and they are confirmed through the same principle through which the universal-concluding ones are confirmed, and this is through being-said-of-every-one and being-said-of-none. For it has already been determined how we say "to be said of every one" and "of none." Therefore such a syllogism is perfect, needing nothing beyond what it has and encloses in itself. But in the same way, and the same syllogism, both negatively and affirmatively concluding, occurs when not a particular but an indefinite affirmative or predicative is posited as the minor proposition which is designated through B C. For the syllogism will be the same from the indefinite and from the particular taken, because the indefinite is equivalent to the particular.
But conjugations become useless in whatever other way terms and propositions are disposed. For if a universal is posited at the lesser extreme, so that the minor is universal either predicatively or privatively, and a particular is posited at the greater, there will be no syllogism of either a predicative or a negative conclusion, whether it is an indefinite or a particular which is posited at the greater. An example of this is as if A belongs to some B or does not belong to some B, but B belongs to every C: no syllogism is made; for nothing follows from such a complexion, "some B is A; every C is B." Similarly neither from such a one, "some B is not A; every B C"; for belonging to every one and belonging to no one follow. The terms, indeed, in which belonging to every one follows are good, habit, prudence, thus: some habit is good; every prudence is a habit; therefore some prudence is good; which is true, for every prudence is good. But an example where belonging to no one follows is in these terms: good, habit, lack of discipline, thus: some habit is good; every lack of discipline is a habit; therefore some lack of discipline is good; which does not hold, because no lack of discipline is good.
Rursum autem inutilis conjugatio est si minor ponatur universalis negativa, ut si B nulli C ponatur inesse, et major ponatur particularis affirmativa, ut si ponatur A alicui B inesse vel non inesse: eo quod particularis potest esse affirmativa vel negativa: vel in majori ponatur A non omni B inesse: non omne enim aequipollet ad aliquod non: quia negatio formaliter respicit distributionem: nec potest fieri syllogismus, quia sequitur omni et nulli inesse. Et termini in quibus sequitur omni inesse in tali dispositione, sunt album, equus, cygnus, sic, quoddam album equus, vel quoddam album non est equus: omnis cygnus est albus: ergo quidam cygnus equus. Et constat, quod nullus cygnus est equus. Vel sic, quidam equus albus: quidam cygnus vel nullus cygnus equus: ergo quidam cygnus non est albus; cum constet omnem cygnum album esse. Termini autem in quibus sequitur nulli inesse sunt isti, album, equus, corvus, sic, quidam equus albus: nullus corvus equus, vel quidam corvus non est equus: ergo quidam corvus non est albus, cum constet nullum corvum album esse. Idem autem est per omnia si propositio A B, quae est major, sit indefinita: quia, sicut diximus, indefinitum aequipollet particulari.
Similiter autem inutilis est conjugatio, quando ad majorem extremitatem sive ad majorem propositionem ponitur universalis sive sit affirmativa sive negativa, et ad minorem ponitur particulare negativum: quia minori existente negativa nihil sequitur in prima figura1: nec in tali complexione fit syllogismus, sive indefinita sive particularis negativa ponatur ad minorem extremitatem. Hujus autem exemplum est: si A quidem quod est major extremitas dicatur omni B inesse, quod est medium; B autem dicatur non inesse, vel per aequipollentiam dicatur non omni B inesse. Causa autem hujus est: quia aliquid acceptum cui alicui medium non inest, hoc et omne et nullum, sequitur ad primum, quod est major extremitas: et sic et omni et nulli inest major extremitas minori in conclusione. Ponantur enim termini tales, animal, homo, album, sic, omnis homo est animal: quoddam album non est homo: deinde sub albo accipiantur alba de quibus homo non praedicatur, nix scilicet, sic et cygnus: de neutro enim illorum nec universaliter nec particulariter affirmative praedicatur homo: et fiat primo talis syllogismus, omnis homo animal: cygnus non est homo: ergo quidam cygnus non est animal. Patet autem quod omnis cygnus est animal. Deinde fiat alius syllogismus in eadem complexione, omnis homo animal: quaedam nix non est homo: ergo quaedam nix non est animal. Et patet quod nulla nix est animal: propter quod etiam secundum talem complexionem non fit syllogismus.
Again, a conjugation is useless if the minor is posited as a universal negative, as if B is posited as belonging to no C, and the major is posited as a particular affirmative, as if A is posited as belonging or not belonging to some B; because the particular can be affirmative or negative; or in the major A is posited as not belonging to every B. For "not every" is equivalent to "some not," because negation formally regards distribution; nor can a syllogism be made, because belonging to every one and belonging to no one follow. And the terms in which belonging to every one follows in such a disposition are white, horse, swan, thus: some white thing is horse, or some white thing is not horse; every swan is white; therefore some swan is horse. And it is agreed that no swan is a horse. Or thus: some horse is white; some swan, or no swan, is horse; therefore some swan is not white, although it is agreed that every swan is white. But the terms in which belonging to no one follows are these: white, horse, raven, thus: some horse is white; no raven is horse, or some raven is not horse; therefore some raven is not white, although it is agreed that no raven is white. But the same holds in all respects if proposition A B, which is the major, is indefinite, because, as we have said, the indefinite is equivalent to the particular.
Similarly the conjugation is useless when a universal, whether affirmative or negative, is posited at the greater extreme or at the major proposition, and a particular negative is posited at the minor, because, when the minor is negative, nothing follows in the first figure1; nor in such a complexion is a syllogism made, whether an indefinite or a particular negative is posited at the lesser extreme. An example of this is: if A, which is the greater extreme, is said to belong to every B, which is the middle; but B is said not to belong, or by equivalence is said not to belong to every B. The cause of this is that something accepted to which the middle does not belong in some case, both every one and no one follow upon the first, which is the greater extreme; and thus the greater extreme belongs both to every one and to no one of the lesser in the conclusion. Therefore let such terms be posited: animal, man, white, thus: every man is animal; some white thing is not man; then under white let white things be accepted of which man is not predicated, namely snow, and so too a swan; for man is predicated of neither of them, neither universally nor particularly affirmatively. And first let such a syllogism be made: every man is animal; swan is not man; therefore some swan is not animal. But it is clear that every swan is animal. Then let another syllogism be made in the same complexion: every man is animal; some snow is not man; therefore some snow is not animal. And it is clear that no snow is animal; on account of which, even according to such a complexion, no syllogism is made.
Rursum si ponatur major universalis negativa, et minor particularis negativa, ut si A quidem nulli B insit, B autem alicui C non insit, sequitur omni et nulli inesse majorem extremitatem minori: et sint termini, inanimatum, homo, album, et sub albo sumantur aliqua alba de quibus homo non praedicatur, cygnus scilicet et nix: in tali enim dispositione complexionis inanimatum praedicatur de uno, scilicet nive: de altero vero nullo, scilicet cygno: et sic sequitur omni inesse sic, nullus homo inanimatum: quaedam nix non est homo: ergo nulla nix inanimatum: patet enim omnem nivem esse inanimatam. Quod sequitur etiam nulli sic, nullus homo inanimatum: quidam cygnus non est homo: ergo quidam cygnus non est inanimatum: et patet quia nullus cygnus est inanimatum.
Amplius autem: quia cum dicitur quod alicui eorum quae sunt accepta sub minori extremitate non inest medium, sicut cum dicitur, quod alicui eorum quae sunt accepta sub C, non inest B, hoc est indefinitum: quia nec universali signo nec particulari determinatur et ideo duobus modis verificatur, si dicatur B alicui C non inesse: est enim hoc verum si nulli C inest B, et est iterum verum si non omni C inest B: sumptis autem terminis talibus in quibus B nulli insit C in minori propositione, non fit syllogismus: hoc enim jam dictum et ostensum est prius. Manifestum est ergo quod in eo quod sic se habent termini, quod minor scilicet sit particularis negativa, non fit syllogismus. Si enim ex tali complexione universaliter fieret syllogismus, tunc etiam esset syllogismus in terminis praedicto modo se habentibus, quando scilicet minor esset universalis negativa.
Similiter autem in terminis ostendetur, quod non fit syllogismus si universalis propositio ponatur privativa, dum etiam minor sit privativa.
Nec iterum fit syllogismus si ambo intervalla (hoc est, propositiones in figuram et modum intervenientes) dicuntur esse particularia: quia ex utraque particulari non fit syllogismus, sive affirmativae sint ambae, sive negativae: sive una affirmativa, et altera negativa quocumque modo.
Adhuc si una propositionum sit indefinita, alia vero definite particularis, vel ambo intervalla sint indefinita, nullo istorum modorum fit syllogismus. Termini vero communes omnium istarum inutilium conjugationum, in quibus ostenditur omni et nulli inesse, sunt animal, album, homo: in his sequitur animal universaliter ad hominem. Ad nulli autem inesse sunt termini communes animal, album, lapis: animal enim sequitur nulli lapidi inesse.
Manifestum est igitur ex his quae dicta sunt, quoniam si fit syllogismus in hac prima figura particularis, necesse est quod termini sic se habeant ut diximus: aliter autem habentibus terminis nullo modo fit syllogismus.
Again, if the major is posited as a universal negative and the minor as a particular negative, as if A indeed belongs to no B, but B does not belong to some C, it follows that the greater extreme belongs both to every one and to no one of the lesser. And let the terms be inanimate, man, white, and under white let some white things be taken of which man is not predicated, namely swan and snow. For in such a disposition of complexion, inanimate is predicated of one, namely snow, but of the other not at all, namely swan; and thus belonging to every one follows in this way: no man is inanimate; some snow is not man; therefore no snow is inanimate; for it is clear that all snow is inanimate. That belonging to no one also follows thus: no man is inanimate; some swan is not man; therefore some swan is not inanimate; and it is clear that no swan is inanimate.
Moreover, because when it is said that the middle does not belong to some of those which are accepted under the lesser extreme, as when it is said that B does not belong to some of those which are accepted under C, this is indefinite, because it is determined by neither a universal sign nor a particular sign, and therefore is verified in two ways if it is said that B does not belong to some C. For this is true if B belongs to no C, and it is again true if B does not belong to every C. But with such terms taken in which B belongs to no C in the minor proposition, no syllogism is made, for this has already been said and shown before. Therefore it is manifest that in the case in which the terms have themselves in such a way that the minor is a particular negative, no syllogism is made. For if a syllogism were made universally from such a complexion, then there would also be a syllogism in terms having themselves in the aforesaid manner, namely when the minor was a universal negative.
Similarly, it will be shown in terms that no syllogism is made if the universal proposition is posited as privative while the minor also is privative.
Nor again is a syllogism made if both intervals (that is, the propositions intervening in figure and mode) are said to be particular, because from both particular propositions no syllogism is made, whether both are affirmative, or negative, or one affirmative and the other negative in whatever way.
Again, if one of the propositions is indefinite and the other definitely particular, or both intervals are indefinite, in none of those ways is a syllogism made. But the common terms of all those useless conjugations, in which belonging to every one and belonging to no one is shown, are animal, white, man; in these, animal follows universally upon man. But for belonging to no one the common terms are animal, white, stone; for animal follows as belonging to no stone.
Therefore it is manifest from these things that have been said that, if a particular syllogism is made in this first figure, the terms must have themselves as we have said; but when the terms have themselves otherwise, a syllogism is made in no way.
Notes
- Note that this rule is also true universally concerning the third figure, as is clear below. (Nota quod haec regula vera est etiam universaliter de tertia figura, ut patet infra.) ↩
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