Works › Prior Analytics, Books I–II
Volume 1 · pp. 689–700
Book II of the Prior Analytics, Tractate I, Chapters I-IV (part)
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LIBER II PRIORUM ANALYTICORUM.
DE POTESTATE SYLLOGISMI GENERATI.
TRACTATUS I.
DE POTESTATE SYLLOGISMI PENES PROPOSITIONES ACCEPTA.
CAPUT I.
De potestate accepta penes formam praemissarum.
In quot igitur sive quantis figuris (quia in tribus) et per quales propositiones in qualitate et quantitate conjugatas, et per quot (quia per duas propositiones) et quando quantum ad utiles conjugationes, et quomodo fit (quantum ad distinctiones modorum in figuris) omnis syllogismus. Amplius autem ad quae media antecedentia vel consequentia vel opposita perspiciendum est construenti per affirmativum syllogismum, vel destruenti per negativum, et quomodo oporteat quaerere de quolibet proposito secundum unamquamque artem syllogisticam. Amplius autem per quam viam resolutionis sumamus terminos vel propositiones quae in singulis syllogismis sunt principia ipsorum, jam in superiori libro (qui de perfecta syllogismi generatione est) secundum omnia substantialia ipsius pertransivimus sufficienter quantum ad generationem syllogismi secundum substantiam ipsius. Restat ergo nunc dicere de potestate generati syllogismi quantum ad conclusiones quas potest inferre: sicut et in naturis post rem in substantia perfectam primum consequens eam est potestas ipsius, quae consequitur perfectionem substantiae. De potestate igitur syllogismi generati deinceps dicemus. Dicemus autem primo de potestate syllogismi, quantum ad propositiones praemissas, quae accipitur ex forma ipsarum propositionum.
Incipientes igitur dicimus, quoniam syllogismorum quidam sunt universales, ex ambabus praemissis universalibus constituti: alii vero sunt particulares, ex altera particulari constituti. Universales quidem omnes habent eamdem potestatem, quod plura (hoc est, plures conclusiones) syllogizant, unam quidem immediate, aliam autem ex conversione conclusionis, quae semper suam infert conversam. Sed particularium syllogismorum illi qui sunt praedicativi sive qui concludunt affirmativas conclusiones, concludunt plures conclusiones. Illi vero qui sunt negativi concludunt unam solam conclusionem.
Et hujus causa est, quia quaedam propositiones conclusae in universalibus syllogismis et particularibus, convertuntur simpliciter, vel per accidens in terminis, sicut universalis affirmativa convertitur in particularem, et particularis affirmativa simpliciter, et universalis negativa convertitur simpliciter. Quaedam autem propositiones conclusae non convertuntur in terminis, sicut particularis negativa: conclusio enim propter hoc quod est propositio enuntians aliquid de aliquo, conversionem suscipit, sicut et alia propositio: propter quod quidam syllogismi (ut universales affirmativi et negativi, et particulares affirmativi) plures conclusiones syllogizant, quia conclusionem principalem, et conversam ipsius: cujus exemplum est, ut si ostensum sit et conclusum A omni B aut alicui B inesse simul, cum hoc ex conversione conclusionis ostensum erit B alicui A inesse. Universalis enim affirmativa convertitur in particularem, et particularis convertitur simpliciter. Similiter autem si ostensum sit et conclusum nulli B A inesse, ex conversione universalis negativae ostensum erit B nulli A inesse. Haec autem conclusio alia est a priore quam immediate concludit syllogismus: tamen aliquo modo est conclusio facti syllogismi, quia conversa substantialiter et implicite continetur in ea quae convertitur in ipsam. Si autem in particulari syllogismo aliquo conclusum est vel ostensum, quod alicui B non inest A, non est necesse per syllogismum quod alicui B non insit A, eo quod aliqua contingit omni inesse: aliquod enim animal non est homo, et tamen omnis homo est animal: et sic non potest esse vera conversa particularis negativae quae est, aliquis homo non est animal: quia contradictoria est ejus quae dicit, omnis homo est animal.
BOOK II OF THE PRIOR ANALYTICS.
ON THE POWER OF THE GENERATED SYLLOGISM.
TRACTATE I.
ON THE POWER OF THE SYLLOGISM TAKEN ACCORDING TO THE PROPOSITIONS.
CHAPTER I.
On the power taken according to the form of the premises.
Therefore in how many, or in how great, figures (namely in three), and through what propositions joined in quality and quantity, and through how many propositions (namely through two), and when with respect to useful conjunctions, and how every syllogism is made (with respect to the distinctions of modes in the figures): moreover, to what middle terms, antecedents, consequents, or opposites one must look when constructing through an affirmative syllogism, or destroying through a negative one, and how one must seek concerning any proposed matter according to each syllogistic art: moreover, by what way of resolution we take the terms or propositions which are the principles of the syllogisms in individual cases, we have already gone through sufficiently in the preceding book (which is about the completed generation of the syllogism), according to all the substantial things of it, as to the generation of the syllogism according to its own substance. Therefore it remains now to speak about the power of the generated syllogism with respect to the conclusions which it can infer, just as also in natural things, after a thing perfected in substance, the first consequent upon it is its power, which follows the perfection of the substance. Therefore next we shall speak of the power of the generated syllogism. But first we shall speak of the power of the syllogism with respect to the propositions laid down as premises, which is taken from the form of those propositions themselves.
Beginning, then, we say that some syllogisms are universal, constituted from both premises universal; others, however, are particular, constituted from one premise particular. All universal syllogisms indeed have the same power, namely that they syllogize several things (that is, several conclusions), one immediately, and another from the conversion of the conclusion, which always brings in its own converse. But among particular syllogisms, those which are predicative, or which conclude affirmative conclusions, conclude several conclusions. Those, however, which are negative conclude one conclusion only.
And the cause of this is that certain propositions concluded in universal and particular syllogisms are converted simply, or by accident in their terms, as a universal affirmative is converted into a particular, and a particular affirmative is converted simply, and a universal negative is converted simply. But certain concluded propositions are not converted in their terms, as a particular negative is not. For a conclusion, because it is a proposition enunciating something of something, admits conversion, just as another proposition does. On account of this certain syllogisms (such as universal affirmative and negative syllogisms, and particular affirmative syllogisms) syllogize several conclusions, because they syllogize the principal conclusion and its converse. An example of this is that, if it has been shown and concluded that A belongs to every B or to some B at the same time, together with this, from the conversion of the conclusion, it will have been shown that B belongs to some A. For a universal affirmative is converted into a particular, and a particular is converted simply. Similarly, if it has been shown and concluded that A belongs to no B, from the conversion of the universal negative it will have been shown that B belongs to no A. This conclusion, however, is other than the prior one which the syllogism immediately concludes; nevertheless in some way it is a conclusion of the syllogism that has been made, because the converse is contained substantially and implicitly in that which is converted into it. But if in some particular syllogism it has been concluded or shown that A does not belong to some B, it is not necessary through the syllogism that B should not belong to some A, because something can belong to every instance of something: for some animal is not a human being, and yet every human being is an animal; and thus the converse of the particular negative cannot be true, namely, some human being is not an animal, because it is contradictory to that which says, every human being is an animal.
Haec ergo causa (quod conclusio convertitur) prima et communis omnium causa est concludendi plures conclusiones: quia quicumque syllogismus concludit aliquam propositionem, ille in se substantialiter habet etiam conversam conclusionis: et ideo ex suis substantialibus concludit etiam illam. Si autem conclusio converti non potest, tunc per sua substantialia non concludit nisi unam solam conclusionem: et haec est potestas tam universalium quam particularium syllogismorum.
Si quis autem dicat quod hoc quod dictum est, quod omnes conclusiones universales tam affirmativae quam negativae convertuntur, instantiam habere videtur, quia universalis negativa de contingenti non necessario non convertitur, sicut in priori libro habitum est. Similiter et hoc quod dictum est, quod particularis negativa non convertitur, instantiam habere videtur, quia particularis negativa de contingenti non necessario convertitur.
Ad haec autem diversi diversa respondent. Dicunt enim quidam, quod ut frequentius convertuntur universalis affirmativa et negativa, et particularis affirmativa: particularis vero negativa ut frequentius non convertitur, licet quam raro et in paucis sit instantia. Alii dicunt (quod tamen in idem redit) quod in omni materia et necessaria et contingenti et impossibili in communi considerata, illae quae dictae sunt fiunt conversiones, quamvis in aliquo speciali contingenti non fiunt. Adhuc attendendum est quod cum hic dicitur, quod est eadem propositio conversa, et in quam convertitur, quando fit conversio conclusionis, non intelligitur hoc quantum ad formam propositionis quae attenditur in situ et positione terminorum, sed quantum ad terminorum substantiam: et hoc est secundum propositionum materiam: sic enim una est in alia, et conclusa una et alia conclusa est in illa.
Est autem de universalibus syllogismis adhuc aliter dicere, qualiter unus et idem syllogismus habet potestate plures conclusiones, quamvis secundum actum non concludat nisi unam. In prima enim figura in qua medium ponitur inter extrema et subjicitur in prima propositione, et praedicatur in secunda, accipiendo primo universales syllogismos primum et secundum, omnium illorum quae sunt sub medio, et omnium eorum quae sunt sub minori extremitate, quae subjicitur in secunda propositione et distribuitur universaliter, omnium illorum erit idem syllogismus: et de omnibus illis concluditur major extremitas, sicut si dicam sic, omne animal est substantia: omnis homo animal: ergo omnis homo substantia. Et accipiatur sub medio sic, omne sensibile substantia: omnis homo sensibile: ergo omnis homo substantia. Vel si accipiatur sub minori extremitate sic, omnis homo substantia: omne risibile homo: ergo omne risibile substantia. Talis autem syllogismus fit si hoc quidem quod sumitur sub medio, ponatur in medio sicut subjectum est in praedicato, ita quod sumptum sub medio subjiciatur ei quod fuit medium in primo syllogismo: tunc enim erit subjectum minoris propositionis, et erit minor extremitas de qua concluditur extremitas major. Et si illud quod sumitur sub minori extremo, ponatur subjectum conclusionis: quia tunc etiam erit minor extremitas et subjectum in minori propositione: et tunc per id quod in priori syllogismo fuit minor extremitas sumpta pro medio, concluditur major extremitas de eo quod sumptum est sub minori: et eodem modo de eo quod sumitur sub medio, per medium ipsum concluditur major extremitas: et hoc est facile.
Therefore this cause, namely that the conclusion is converted, is the first and common cause for all syllogisms of concluding several conclusions: because whatever syllogism concludes some proposition, that syllogism substantially has in itself also the converse of the conclusion; and therefore from its substantial constituents it also concludes that converse. But if the conclusion cannot be converted, then through its substantial constituents it concludes only one conclusion; and this is the power both of universal and of particular syllogisms.
But if someone says that what has been said, that all universal conclusions, affirmative as well as negative, are converted, seems to have an exception, because a universal negative concerning the contingent-not-necessary is not converted, as was held in the prior book. Similarly also what has been said, that a particular negative is not converted, seems to have an exception, because a particular negative concerning the contingent-not-necessary is converted.
To these matters different people reply in different ways. Some say that for the most part the universal affirmative and negative, and the particular affirmative, are converted, while the particular negative is for the most part not converted, although an exception is found rarely and in few cases. Others say (which nevertheless comes back to the same thing) that in every matter, necessary, contingent, and impossible, considered in common, those conversions which have been stated do occur, although in some special contingent matter they do not occur. Still one must attend to this, that when it is said here that the converted proposition and that into which it is converted are the same proposition, when conversion of the conclusion occurs, this is not understood with respect to the form of the proposition which is considered in the arrangement and position of the terms, but with respect to the substance of the terms; and this is according to the matter of the propositions. For in this way one is in the other, and when one has been concluded, the other too has been concluded in it.
Concerning universal syllogisms there is still another way to say how one and the same syllogism has several conclusions in potency, although according to act it concludes only one. For in the first figure, in which the middle is placed between the extremes and is subjected in the first proposition and predicated in the second, taking first the first and second universal syllogisms, of all those things which are under the middle, and of all those things which are under the minor extreme, which is subjected in the second proposition and distributed universally, there will be the same syllogism for all of those; and the major extreme is concluded of all those things. For example, if I say thus: every animal is a substance; every human being is an animal; therefore every human being is a substance. And let something be taken under the middle thus: every sensible thing is a substance; every human being is sensible; therefore every human being is a substance. Or if something is taken under the minor extreme thus: every human being is a substance; every risible thing is a human being; therefore every risible thing is a substance. Such a syllogism is made if that which is taken under the middle is placed in the middle as subject is in predicate, so that what is taken under the middle is subjected to that which was the middle in the first syllogism. For then it will be the subject of the minor proposition, and it will be the minor extreme of which the major extreme is concluded. And if that which is taken under the minor extreme is placed as the subject of the conclusion, then it too will be the minor extreme and the subject in the minor proposition; and then, through that which in the prior syllogism was the minor extreme taken as middle, the major extreme is concluded of that which has been taken under the minor; and in the same way, concerning that which is taken under the middle, through the middle itself the major extreme is concluded; and this is easy.
Et hujus exemplum in terminis transcendentibus est, ut si dicamus, quod haec conclusio, omne B est A, conclusa sit per C medium, quaecumque sunt sumpta sub B minori extremitate, aut sub C medio, necesse est quod de omnibus illis concludatur A dici sive praedicari, sicut si D sumatur sub B, erit D in toto B, quia omne D erit B, et B est in toto A, ita quod omne B est A, et sic concluditur quod D est in toto A per eumdem syllogismum. Rursus autem similiter erit si sub C medio accipiatur E, tunc enim erit E in toto C et C in toto A, et concluditur quod E est in toto A.
Similiter autem est in secundo primae figurae, in quo universalis et privativus fit syllogismus, sicut si dicatur, nullum animal lapis: omnis homo animal: ergo nullus homo lapis. Sive sumatur sub medio, sive sub minori extremo, sequetur remotio majoris extremitatis de omnibus illis: et est facile formare hujusmodi syllogismos.
In secunda autem figura in primo et secundo modo (qui sunt universales syllogismi) non contingit majorem extremitatem syllogizari de sumptis sub medio: eo quod medium est praedicatum, et sub praedicato secundum decursum syllogisticum nihil sumi potest: sed id solum est syllogizare ut concludatur de eo major extremitas quod est sumptum sub conclusione (hoc est, sub minori extremitate, quae subjectum est conclusionis 1) quia illa est etiam subjectum minoris propositionis quae universaliter distributa in syllogismis duobus primis secundae figurae: et ideo syllogistice aliquid potest sumi sub ipsa de quo negative concludatur major extremitas, sicut sic syllogizando in primo secundae, nullus lapis est animal: omnis homo est animal: ergo nullus homo lapis. Et sub medio accipi non potest cum sit praedicatum, et stet secundum seipsum, sed sub homine accipi potest risibile sic, nullus lapis animal: omne risibile animal: ergo nullum risibile lapis. Similiter est in secundo secundae. Patet igitur quod in secunda figura solum id quod sub conclusione (hoc est, sub minori extremo quod in conclusione est subjectum) contingit hoc modo syllogizare negative, quod de ipso negative concludetur major extremitas: medium enim in secunda figura non potest stare pro partibus quae sub ipso accipiantur.
Hujus autem exemplum in terminis generalibus sive transcendentibus est, ut si dicamus, quod A medium nulli B insit in majori propositione, conclusio erit quoniam nulli C inest B. Si autem sub C minori extremo est sumptum D, manifestum est quod etiam illi non inest B majus extremum: quia aliter non negaretur universaliter de C, quod enim universaliter negatur de superiori negatur de omni suo inferiori per syllogismum. Si autem sumantur aliqua sub A medio in secunda figura, quamvis forte de illis majus extremum removeatur et non insit eis, tamen hoc non potest esse palam sive manifestum per syllogismum, sicut si dicamus, quod E est sumptum sub A medio. Sed quod A nulli C insit, hoc est ostensum per syllogismum primum: sed quod eidem A non insit B (quod dicit conversa majoris propositionis), hoc est sumptum et non demonstratum per syllogismum: et propter hoc per syllogismum concludi non potest, quod B majus extremum non insit E quod sub medio est acceptum.
In particularibus autem syllogismis primae figurae de his qui sunt sub minori extremitate in conclusione subjecta, non est sive contingit necessarium aliquid syllogizare per syllogismum: cujus causa est: quia particularis est, et syllogistice sub particulari sumi nihil potest 2, unde minor extremitas sumpta fuerit particulariter ad ea quae possent sumi sub minori extremitate: per syllogismum enim major extremitas non potest concludi de contentis sub minori extremitate. Eorum autem quae sunt sub medio sumpta, erit major extremitas in omnibus: quia in illis qui sunt in prima figura, medium est in toto primo vel in nullo: et ideo necesse est quod de omnibus his verificetur major extremitas, vel removeatur ab omnibus illis: tamen major extremitas non concluditur inesse his quae sunt sub medio per syllogismum primum, sed potius per syllogismum in syllogismo primo implicitum, sicut in praehabitis dictum est, in quo de eo quod est sub medio per hoc quod subjicitur medio sit minor extremitas, de qua concluditur per medium major extremitas. Et hujus exemplum est in tertio primae figurae, ut si A major extremitas omni B medio dicatur inesse in majori propositione, et B medium alicui C dicatur inesse in minori: tunc enim ejus quod sub C minori extremitate positum, non erit syllogismus, quia contingit majorem esse particularem in prima figura: ejus vero quod est praesumptum sub B medio, erit quidem implicitus in primo syllogismo syllogismus: sed hoc non erit propter illum syllogismum qui prius factus est, sed (ut diximus) propter eum qui implicitus est in illo.
An example of this in transcendent terms is as follows: if we say that this conclusion, every B is A, has been concluded through C as middle, whatever things are taken under B, the minor extreme, or under C, the middle, it is necessary that A be concluded as said or predicated of all those things. Thus, if D is taken under B, D will be in the whole of B, because every D will be B, and B is in the whole of A, so that every B is A; and so it is concluded through the same syllogism that D is in the whole of A. Again it will be similar if E is taken under C as middle: for then E will be in the whole of C and C in the whole of A, and it is concluded that E is in the whole of A.
Likewise it is so in the second mode of the first figure, in which a universal and privative syllogism is made, as if it is said: no animal is a stone; every human being is an animal; therefore no human being is a stone. Whether something is taken under the middle or under the minor extreme, the removal of the major extreme from all those things will follow; and it is easy to form syllogisms of this kind.
But in the second figure, in the first and second mode (which are universal syllogisms), it is not possible for the major extreme to be syllogized of the things taken under the middle, because the middle is a predicate, and under a predicate, according to syllogistic procedure, nothing can be taken. But the only thing syllogized is that the major extreme is concluded of that which is taken under the conclusion (that is, under the minor extreme, which is the subject of the conclusion 1), because that too is the subject of the minor proposition which is universally distributed in the two first syllogisms of the second figure; and therefore something can syllogistically be taken under it, of which the major extreme is negatively concluded, as in syllogizing thus in the first mode of the second figure: no stone is an animal; every human being is an animal; therefore no human being is a stone. And something cannot be taken under the middle, since it is a predicate and stands according to itself; but under human being, risible can be taken thus: no stone is an animal; every risible thing is an animal; therefore no risible thing is a stone. It is similar in the second mode of the second figure. Therefore it is clear that in the second figure only that which is under the conclusion (that is, under the minor extreme which is the subject in the conclusion) can in this way be syllogized negatively, so that the major extreme will be concluded negatively of it; for the middle in the second figure cannot stand for the parts which are taken under it.
An example of this in general or transcendent terms is as follows: if we say that A as middle belongs to no B in the major proposition, the conclusion will be that B belongs to no C. But if D has been taken under C, the minor extreme, it is manifest that B, the greater extreme, does not belong to that either, because otherwise it would not be denied universally of C; for what is universally denied of a superior is denied of every inferior of it through a syllogism. But if some things are taken under A as middle in the second figure, although perhaps the greater extreme is removed from them and does not belong to them, nevertheless this cannot be plain or manifest through the syllogism, as if we say that E is taken under A as middle. But that A belongs to no C has been shown through the first syllogism; that B does not belong to that same A (which says the converse of the major proposition), however, has been taken and not demonstrated through the syllogism; and on account of this it cannot be concluded through the syllogism that B, the greater extreme, does not belong to E, which has been taken under the middle.
In particular syllogisms of the first figure, concerning the things which are under the minor extreme subjected in the conclusion, it is not, or it does not occur as, necessary to syllogize anything through the syllogism. The cause of this is that the proposition is particular, and nothing can be syllogistically taken under a particular 2; hence the minor extreme would have been taken particularly in relation to those things which could be taken under the minor extreme. For through the syllogism the major extreme cannot be concluded of the things contained under the minor extreme. But of the things which are taken under the middle, the major extreme will belong in all cases, because in those syllogisms which are in the first figure the middle is in the whole of the first or in none; and therefore it is necessary that the major extreme be verified of all these things, or be removed from all those things. Nevertheless the major extreme is not concluded to belong to these things which are under the middle through the first syllogism, but rather through the syllogism implicit in the first syllogism, as was said in what preceded, in which that which is under the middle, by being subjected to the middle, becomes the minor extreme, of which the major extreme is concluded through the middle. An example of this is in the third mode of the first figure: if A, the major extreme, is said to belong to every B, the middle, in the major proposition, and B, the middle, is said to belong to some C in the minor, then there will not be a syllogism of that which is placed under C, the minor extreme, because it is possible for the major premise to be particular in the first figure. But of that which is assumed under B as middle, there will indeed be an implicit syllogism in the first syllogism; but this will not be on account of that syllogism which was previously made, but, as we have said, on account of the one which is implicit in it.
Similiter autem in particularibus syllogismis aliarum figurarum: in omnibus enim figuris in particularibus syllogismis non erit syllogismus ejus quod est sub minori extremitate acceptum qui est subjectum in conclusione: alterius autem termini (qui est medium) erit quidem ad contenta syllogismus: hoc tamen non est per syllogismum: sed talia per indemonstratam et non conclusam propositionem ostendebantur, sicut et in universalibus syllogismis primae figurae dictum est: aut si erit in illis ad sumpta sub minori extremo syllogismus, tunc erit et in his qui particulares sunt syllogismis. Ista est sententia dictorum Aristotelis, et sunt in ea plures dubitationes et opiniones.
CAPUT II.
De solutione dubitationum et diversitate opinionum quae sunt circa potestatem quae inducta est.
Hic autem notandum primum, quod quaecumque dicta de potestate concludendi plures conclusiones propter conversam conclusionis, absque dubio vera sunt, et ita subjiciantur sicut probata sunt. In his autem quae de potestate concludendi majorem extremitatem de contentis sub medio vel minorem extremitatem dicta sunt, quidam dubitaverunt. Dicunt enim quidam, quod est syllogismus simpliciter, et est syllogismus implicitus in illo. Syllogismus enim simpliciter est, qui per se stat in tribus terminis et duabus propositionibus. Syllogismus autem implicitus in illo est, qui accipitur ex intellectu majoris propositionis, quae semper est universalis in prima figura. Verbi gratia, omne B A, omne C B, vel aliquod C B. Vel si major sit universalis negativa, nullum B A, omne C B, vel aliquod C B. Et hic est simpliciter syllogismus. Implicitus autem est, qui fit ex intellectu majoris propositionis: cum enim dicitur omne B A, vel in terminis ponendo, omnis homo est animal, sensus est, omne id est animal quod est homo: et haec propositio secundum hoc in se duo continet. Per hoc enim quod dicitur, omne id est animal, accipitur major propositio quae est ad majorem extremitatem. Per hoc autem quod dicitur, quod est homo, accipitur minor. Et de duabus illis propositionibus factus syllogismus dicitur implicitus syllogismus: et fit acceptio sub medio per hoc quod dicitur, quod est homo. Acceptio autem sub majori fit per hoc quod dicitur, omne id est animal.
Likewise in the particular syllogisms of the other figures: in all figures, in particular syllogisms, there will not be a syllogism of that which is taken under the minor extreme, which is the subject in the conclusion. But of the other term, which is the middle, there will indeed be a syllogism directed to the contents; nevertheless this is not through the syllogism, but such things were being shown through an indemonstrate and unconcluded proposition, just as was said also in the universal syllogisms of the first figure; or, if there will be in those a syllogism directed to things taken under the minor extreme, then there will be one also in those syllogisms which are particular. This is the meaning of Aristotle's words, and in it there are several doubts and opinions.
CHAPTER II.
On the solution of the doubts and the diversity of opinions which concern the power that has been introduced.
Here, first, it must be noted that whatever has been said about the power of concluding several conclusions on account of the converse of the conclusion is without doubt true, and should be set down as proved. But concerning those things which have been said about the power of concluding the major extreme of the things contained under the middle, or the minor extreme, some have doubted. For some say that there is a syllogism simply, and there is a syllogism implicit in it. A syllogism simply is one which stands by itself in three terms and two propositions. But a syllogism implicit in that one is one which is taken from the understanding of the major proposition, which is always universal in the first figure. For example: every B is A, every C is B, or some C is B. Or if the major is universal negative: no B is A, every C is B, or some C is B. And this is a syllogism simply. But the implicit one is the one which is made from the understanding of the major proposition: for when every B is A is said, or, placing it in terms, every human being is an animal, the sense is: everything is an animal which is a human being. And according to this, this proposition contains two things in itself. For through the fact that it is said, everything is an animal, the major proposition is taken, which is directed to the major extreme. But through the fact that it is said, which is a human being, the minor is taken. And the syllogism made from those two propositions is called an implicit syllogism; and the taking under the middle occurs through the fact that it is said, which is a human being. But the taking under the major occurs through the fact that it is said, everything is an animal.
Dicunt isti quod implicitus syllogismus idem dicitur cum syllogismo simpliciter sive explicito, per hoc quod implicitus per intellectum continetur in explicito, et quod sic unus syllogismus (sicut implicitus in explicito est unus) concludit plures conclusiones accipiendo contenta sub medio vel sub minori extremitate. Quia vero hoc modo ea quae sunt supra majorem extremitatem, non sunt implicita in majori propositione, propter hoc non dicuntur posse concludi de majori extremitate per eumdem syllogismum, quamvis concludi possint per alium syllogismum sumpto superiori pro medio, et majori extremo sumpto pro minori sic, omne corpus animatum substantia: omne animal corpus animatum: ergo omne animal substantia.
Dicunt etiam isti quod haec est causa, quod in secunda figura major per syllogismum implicitum in majori non potest concludi de contentis sub medio, non implicatur in majori propositione: quia cum dico, nullus lapis est animal, hic non significatur nisi remotio medii ab extremo et non e converso: et ideo non significatur hic removeri extremum a medio vel a contentis sub medio: sed significatur removeri a contentis sub minori extremo propter oppositionem majoris extremi ad minus extremum; et ideo virtute syllogismi impliciti ab illis removetur, sed non a contentis sub medio. Sed si convertatur major sic, nullum A est B, ibi significaretur majus extremum removeri a contentis sub medio: sed illa conversa non implicatur in majori, et ideo absque syllogismo primo quasi indemonstrata explicite vel implicite sumitur: et si syllogizatur majus removeri a contentis sub medio, hoc fiet per syllogismum implicitum in conversa majoris, et non in majori.
Si autem ab istis quaeritur, quare magis in secunda figura dicitur major sumi indemonstrata ad concludendum majorem extremitatem removeri a contentis sub medio, quam in prima, ubi etiam quando major concluditur de contentis sub medio, major propositio per syllogismum non demonstratur, sed sumitur? Dicunt quod major de ordine suorum terminorum dicit ordinem et potestatem concludendi majus extremum de medio: et quia per seipsam se habet ad hoc, propter hoc immediatius se habet ad illud virtute demonstrationis. In secunda autem figura non per ordinem suorum terminorum se habet ad illud, sed mediate, scilicet per conversam ipsius: et ideo potius dicitur major in secunda figura sumi indemonstrata, quam in prima.
Si autem adhuc quaeritur ab istis, quare haec potestas (scilicet concludendi majorem removeri a contentis sub medio ex propositione indemonstrata) potius determinatur in syllogismo habente majorem universalem negativam, sicut habet primus modus secundae, quam in secundo modo ejusdem secundae figurae in quo major est universalis affirmativa? Dicunt quod in syllogismo secundae figurae in quo major est affirmativa, non est accipere sub medio, de quo dicatur majus extremum: sed quando major est negativa, ab omnibus contentis sub medio removetur extremum: et ideo dicitur hoc de modo primo et non de secundo.
Si autem ulterius quaeritur ab istis, quare in particularibus syllogismis primae figurae dicitur major concludi de contentis sub medio, sed non per syllogismum: cum tamen in majori particularium syllogismorum implicitus sit syllogismus, et sic implicite probata sit major per explicitum, et inferri possit ex ipsa, et sic videatur per syllogismum demonstrata secundum quemdam modum? Dicunt isti quod procul dubio implicite in talibus major demonstrata est: sed quia per primum explicitum syllogismum non est conclusa, ideo dicitur non indemonstrata, sed dicitur non per eum (qui prius factus est syllogismum) conclusa. De particularibus autem secundae figurae quantum ad acceptionem sub medio idem dicunt quod in universalibus secundae figurae syllogismis dictum est, quod scilicet accipiunt majorem propositionem indemonstratam: non syllogizant autem per acceptionem conclusionis quae demonstrata est: et sic ex indemonstrata procedunt.
These authors say that the implicit syllogism is called the same as the syllogism simply, or the explicit syllogism, because what is implicit is contained by understanding in what is explicit, and that in this way one syllogism, just as the implicit is one in the explicit, concludes several conclusions by taking things contained under the middle or under the minor extreme. But because in this way those things which are above the major extreme are not implicit in the major proposition, for this reason they are not said to be able to be concluded of the major extreme through the same syllogism, although they can be concluded through another syllogism, when the superior is taken as middle and the major extreme is taken as minor in this way: every animated body is a substance; every animal is an animated body; therefore every animal is a substance.
These same authors also say that this is the cause why in the second figure the major cannot be concluded of the things contained under the middle through a syllogism implicit in the major: it is not implied in the major proposition. For when I say, no stone is an animal, here only the removal of the middle from the extreme is signified, and not conversely; and therefore here it is not signified that the extreme is removed from the middle or from the things contained under the middle. Rather it is signified that it is removed from the things contained under the minor extreme because of the opposition of the major extreme to the lesser extreme; and therefore by the force of the implicit syllogism it is removed from those things, but not from the things contained under the middle. But if the major is converted thus, no A is B, there it would be signified that the greater extreme is removed from the things contained under the middle; but that converse is not implied in the major, and therefore it is taken apart from the first syllogism as if indemonstrate, explicitly or implicitly. And if it is syllogized that the greater is removed from the things contained under the middle, this will be done through a syllogism implicit in the converse of the major, and not in the major.
But if it is asked of these authors why in the second figure the major is said to be taken as indemonstrate for concluding that the major extreme is removed from the things contained under the middle, rather than in the first figure, where even when the major is concluded of the things contained under the middle, the major proposition is not demonstrated through a syllogism, but is taken, they say that the major, from the order of its terms, states the order and the power of concluding the greater extreme of the middle; and because of itself it is related to this, for this reason it is related to that more immediately by the force of demonstration. But in the second figure it is not related to that through the order of its own terms, but mediately, namely through its converse; and therefore the major in the second figure is rather said to be taken as indemonstrate than in the first.
But if it is further asked of these authors why this power, namely of concluding that the greater is removed from the things contained under the middle from an indemonstrate proposition, is determined rather in a syllogism having a universal negative major, as the first mode of the second figure has, than in the second mode of that same second figure, in which the major is a universal affirmative, they say that in the syllogism of the second figure in which the major is affirmative there is no taking under the middle of that of which the greater extreme may be said; but when the major is negative, the extreme is removed from all the things contained under the middle. And therefore this is said of the first mode and not of the second.
But if it is further asked of these authors why in particular syllogisms of the first figure the major is said to be concluded of the things contained under the middle, but not through a syllogism, although nevertheless in the major of particular syllogisms there is an implicit syllogism, and thus the major has been implicitly proved through the explicit, and can be inferred from it, and so seems to have been demonstrated through a syllogism according to a certain mode, these authors say that without doubt in such cases the major has been implicitly demonstrated; but because it has not been concluded through the first explicit syllogism, therefore it is not called indemonstrate, but is said not to have been concluded through it, that is, through the syllogism which was previously made. Concerning particulars of the second figure, however, with respect to the taking under the middle, they say the same thing that was said in universal syllogisms of the second figure, namely that they take the major proposition as indemonstrate; they do not syllogize through the taking of the conclusion which has been demonstrated; and thus they proceed from what is indemonstrate.
Si autem ulterius quaeritur de particularibus tertiae, in quibus aliquando major est particularis: tunc enim fit syllogismus majoris extremitatis ad ea quae accipiuntur sub medio, ut videtur: et videtur, quod tunc secundum hanc responsionem major in prima figura possit esse particularis. Et dicunt ad hoc isti, quod quando major est particularis in tertia figura, non potest syllogizari major extremitas de contentis sub medio propter causam quae praedicta est: sed tantum syllogizari potest in his in quibus major est universalis. Adhuc dicunt isti, quod majori extremitate particulari existente in figura tertia, contingit syllogizare minorem extremitatem de contentis sub medio: sed in omnibus accipitur propositio major indemonstrata: et non concluditur propositum per syllogismum prius factum explicitum vel implicitum in illo qui radicaliter idem syllogismus est cum illo. Dicunt etiam isti, quod in nullo syllogismo particuli cujuscumque figurae concludi potest major extremitas de contentis sub minori extremitate: et in omnibus est eadem causa, scilicet quia major non potest esse particularis in prima figura. Haec est prima opinio circa potestatem istam.
Secunda vero est, quod quidam dicunt hanc doctrinam hujus potestatis datam esse de syllogismo ostensivo strictissime sumpto, et de syllogismo ex hypothesi sumpto communissime: hic enim solus ille syllogismus vocatur ostensivus, cujus omnes praemissae per syllogismum ostensae sunt: et omnis ille syllogismus hic vocatur ex hypothesi, cujus praemissae per syllogismum non ostenduntur 3. Et hoc modo syllogismus ille ostensivus est, qui assumpto aliquo sub conclusione primi syllogismi concludit de illo majorem extremitatem per conclusionem primi syllogismi positam pro majori, procedit enim ille ex demonstrata propositione: ille vero qui assumit sub medio ad concludendum de illo majorem extremitatem, assumit majorem praeexistentis syllogismi quae indemonstrata est, et ideo est ex hypothesi: et ideo dicitur quod talis syllogismus concludit ex indemonstrata propositione. Et isti qui sic dicunt, ponunt quod syllogismorum prosyllogismi (ex quibus ostenduntur propositiones praemissae syllogismi primi expliciti) continue procedunt usque ad principia prima, in quibus fit status: et si alicubi fit status in prosyllogismis antequam perveniatur ad principia prima, adhuc erit ex hypothesi syllogismus, donec omnia principia usque ad prima fuerint explanata.
Si autem quaeratur ab his, quare magis dicitur fieri ad contenta sub medio in secunda figura ex indemonstrata propositione, quam in prima? Dicunt quod in majori primae figurae nihil deest nisi ejus descensio. In majori autem secundae figurae deest et ostensio et conversio ad hoc quod fiat ostensivus syllogismus: et sic iste syllogismus in secunda figura magis est ex hypothesi, quam in prima. Et quando dicitur quod non fit syllogismus, eo quod accipitur indemonstrata propositio dicitur propter hoc solum quia non fit ibi syllogismus ostensivus, eo quod procedit ex propositione non ostensiva. Et hoc quidem multi et subtiliter dixerunt, et habet aliquam veritatem.
But if it is further asked about particulars of the third figure, in which sometimes the major is particular, then, as it seems, a syllogism of the major extreme is made toward those things which are taken under the middle; and it seems that then, according to this reply, the major in the first figure could be particular. To this these authors say that when the major is particular in the third figure, the major extreme cannot be syllogized of the things contained under the middle, because of the cause which has been stated before; but it can be syllogized only in those cases in which the major is universal. They further say that, when the major extreme is particular in the third figure, it is possible to syllogize the minor extreme of the things contained under the middle; but in all cases the major proposition is taken as indemonstrate, and the proposed thing is not concluded through the previously made syllogism, explicit or implicit in that one which is radically the same syllogism as that one. These authors also say that in no particular syllogism of any figure can the major extreme be concluded of the things contained under the minor extreme; and in all cases the cause is the same, namely because the major cannot be particular in the first figure. This is the first opinion concerning that power.
The second opinion is that some say this doctrine of this power has been given concerning the ostensive syllogism taken most strictly, and concerning the syllogism from hypothesis taken most broadly. For here only that syllogism is called ostensive whose premises have all been shown through a syllogism; and every syllogism whose premises are not shown through a syllogism is here called from hypothesis 3. And in this way that syllogism is ostensive which, when something has been assumed under the conclusion of the first syllogism, concludes the major extreme of it through the conclusion of the first syllogism posited as major; for that syllogism proceeds from a demonstrated proposition. But the one which assumes under the middle in order to conclude the major extreme of it assumes the major of the pre-existing syllogism, which is indemonstrate, and therefore is from hypothesis; and therefore it is said that such a syllogism concludes from an indemonstrate proposition. And those who say this hold that the prosyllogisms of syllogisms, from which the propositions that are premises of the first explicit syllogism are shown, proceed continuously up to first principles, in which there is a stopping point; and if somewhere there is a stopping point in the prosyllogisms before first principles are reached, the syllogism will still be from hypothesis, until all principles up to the first have been unfolded.
But if it is asked of these why it is rather said to be made toward the things contained under the middle in the second figure from an indemonstrate proposition than in the first, they say that in the major of the first figure nothing is lacking except its descent. But in the major of the second figure both showing and conversion are lacking for the syllogism to become ostensive; and thus that syllogism in the second figure is more from hypothesis than in the first. And when it is said that a syllogism is not made, because an indemonstrate proposition is taken, it is said for this reason alone: that an ostensive syllogism is not made there, because it proceeds from a proposition not shown ostensively. And this indeed many have said subtly, and it has some truth.
Si autem quaeritur ad quem usum est ista duplex potestas, scilicet accipiendi sub medio, et accipiendi sub minori extremitate? Dicendum quod utilis est ad exercitium et dialectico et sophistae. Secunda etiam potestas accipiendi sub minori extremitate, est utilis in parte ad demonstrationes, in quantum illae augmentur in post assumendo.
Facillimam opinionem de ista doctrina videtur ponere Alfarabius, qui dicit, quod unus est syllogismus virtute, qui per idem dici de omni vel idem dici de nullo confirmatur: et ideo in prima figura in dici de omni non includitur nisi quod est sub termino, et non quod est super ipsum: et ideo quae supra majorem extremitatem sunt, de majori extremo vel de medio vel minori per dici de omni (quod in primo syllogismo est) concludi non possunt: et si syllogizantur de majori extremo, oportet quod ex indemonstrato per dici de omni primi syllogismi, et ad virtutem concludendi (quae in illo est syllogismo) referri non possunt. Similiter in secunda figura: quia per dici de omni et dici de nullo (quod in secunda figura est) nihil potest sumi sub medio, sed tantum sub minori extremitate: et ideo in illa nihil de medio vel de his quae sunt sub medio concludi potest: et si fiat, erit ab indemonstrato: quia oportet quod non sciatur per dici de omni vel dici de nullo, quod est in primo syllogismo: quia virtute infra ipsum non continetur: et ideo ab indemonstrato assumitur.
In particularibus autem syllogismis non potest fieri syllogismus majoris extremitatis ad ea quae sunt sub minori extremitate: quia illa de contentis sub minori extremitate accipi non possunt per dici de omni, cum minor propositio sit particularis: sed potest tamen major extremitas de contentis sub medio et affirmari et negari, non tamen per id quod virtute sit in syllogismo prius facto, per dici de omni quod est in ipso: quia medium in prima quidem propositione universaliter subjicitur et in secunda propositione particulariter praedicatur: et si sub medio aliquid accipiatur de hoc non universaliter, major extremitas concluditur: et si esset directe sub medio sumptum, et medium sub majori universaliter concluderetur: et hoc non fit. Patet igitur quod non (per id quod virtute sit in primo syllogismo) id quod est majus extremum concluditur de contentis sub medio.
Et huic expositioni magis videtur consentire littera Aristotelis: si enim aliquid sumatur sub medio particulariter, de illo non concluditur major extremitas, nisi per medium subjectum majori extremitati universaliter, et praedicatum de minori particulariter. Id autem quod sumitur sub medio, erit tunc minor extremitas de qua medium particulariter oportet praedicari in particularibus syllogismis. Id autem inferius quod particulariter praedicatur de aliquo, facit suum superius particulariter concludi de illo: et si illa conclusio sumpta sit pro majori in prosyllogismo in quo majus debet concludi de contentis sub medio, tunc syllogismus erit ex particularibus ambabus, et non valebit: et ideo talis syllogismus non continetur virtute in priori: sed erit assumptus extra dici de omni, quod perficit primum syllogismum. Hoc est igitur quod de ista doctrina diversi tradiderunt.
In duabus autem his opinionibus, prima scilicet et tertia semper unus dicitur syllogismus explicitus et implicitus per virtutem in illo: quia radicaliter unus sunt, et conclusio impliciti virtute est in explicito, et quantum ad hoc dicitur, quod unius syllogismi plures sunt conclusiones.
But if it is asked to what use this double power is ordered, namely the power of taking under the middle and of taking under the minor extreme, one must say that it is useful for exercise both to the dialectician and to the sophist. The second power also, that of taking under the minor extreme, is useful in part for demonstrations, insofar as those demonstrations are increased in subsequent assuming.
Alfarabi seems to set down the easiest opinion about this doctrine. He says that a syllogism is one in power when it is strengthened through the same "being said of every" or the same "being said of none"; and therefore in the first figure, in "being said of every" there is included only what is under the term, and not what is above it. And therefore those things which are above the major extreme cannot be concluded of the major extreme or of the middle or minor through "being said of every" which is in the first syllogism; and if they are syllogized of the major extreme, this must happen from what is indemonstrate by the "being said of every" of the first syllogism, and they cannot be referred to the power of concluding which is in that syllogism. Likewise in the second figure: because through "being said of every" and "being said of none" which are in the second figure, nothing can be taken under the middle, but only under the minor extreme; and therefore in that figure nothing can be concluded of the middle or of those things which are under the middle. And if it is done, it will be from what is indemonstrate, because it must not be known through the "being said of every" or "being said of none" which is in the first syllogism, since it is not contained in power within it; and therefore it is assumed from what is indemonstrate.
In particular syllogisms, however, a syllogism of the major extreme cannot be made toward those things which are under the minor extreme, because those things contained under the minor extreme cannot be taken through "being said of every," since the minor proposition is particular. Nevertheless the major extreme can be both affirmed and denied of the things contained under the middle, yet not through that which is in the previously made syllogism in power, through the "being said of every" which is in it; because the middle in the first proposition is universally subjected and in the second proposition is particularly predicated. And if something is taken under the middle, concerning this the major extreme is not concluded universally; and if what was taken were directly under the middle, the middle would be concluded universally under the major; and this is not done. Therefore it is clear that what is the greater extreme is not concluded of the things contained under the middle through that which is in power in the first syllogism.
And the letter of Aristotle seems to agree more with this exposition. For if something is taken under the middle particularly, the major extreme is not concluded of it except through the middle subjected universally to the major extreme and predicated particularly of the minor. But that which is taken under the middle will then be the minor extreme of which the middle must be predicated particularly in particular syllogisms. But an inferior which is predicated particularly of something causes its superior to be concluded particularly of that thing; and if that conclusion has been taken as major in a prosyllogism in which the greater must be concluded of the things contained under the middle, then the syllogism will be from two particulars, and will not be valid. And therefore such a syllogism is not contained in power in the prior one, but will be assumed outside "being said of every," which perfects the first syllogism. Therefore this is what different authors have handed down concerning this doctrine.
In these two opinions, namely the first and the third, a syllogism is always said to be one, explicit and implicit, through the power in it, because they are radically one, and the conclusion of the implicit syllogism is in the explicit one in power; and in this respect it is said that there are several conclusions of one syllogism.
Secunda autem opinio est eorum, qui dicunt secundum librum Priorum dividi a primo, per hoc quod in primo determinetur de syllogismo ostensivo, in secundo vero de syllogismo ex hypothesi, quem dicunt fieri quotiescumque non a demonstrata propositione quae est conclusio primi syllogismi sumpta cum altera concluditur: sed sumitur major a positione respondentis et consensu: et deficit in ea demonstratio. Prima tamen inter has subtilior et communior est opinio. Tertia vero studio indiget ut verificetur, et praecipue in particularibus syllogismis.
CAPUT III.
De potestate quomodo secundum materiam ex falso verum est syllogizare.
Cum autem ex combinatione duarum propositionum fiat syllogismus, est vel contingit sic se habere propositiones, quod ambae verae sint per quas fit syllogismus: et est, id est, contingit eas sic se habere ut ambae falsae: et est, quod sic se habent, ut haec (una scilicet) sit vera, illa vero sive alia sit falsa, conclusio autem consequens ex omnibus his modis, aut vera aut falsa est in omnibus his modis. Cum enim quatuor modis verum et falsum in consequendo ad invicem possint comparari (scilicet quod verum ex vero, et falsum ex falso, et verum ex falso, et falsum ex vero) non oportet nos ostendere nisi qualiter falsum non sequitur ex vero, et qualiter verum sequitur ex falso: quia hoc non est notum, et est difficile, et est syllogismi potestas: quia qualiter verum ex vero, et qualiter falsum ex falso sequitur, facile est, et ex dictis in primo libro de dispositione in terminis et propositionibus satis est manifestum.
Dicendum ergo primo, quod ex veris non est falsum syllogizare. Quamvis quidam objiciant contra hoc dicentes, quod si concludatur conclusio falsa ex duabus in toto falsis in primo secundae, sumantur contrariae illarum duarum propositionum quae erunt in toto verae et syllogizabitur eadem conclusio falsa ex duabus illis in toto veris in secundo secundae: et sic ex vero sequitur falsum. Sed ad hoc dicendum quod praemissis existentibus in toto falsis in primo secundae, necesse est extrema disparata esse: et ita unum ab altero vere poterit removeri universaliter: propter quod sic se habentibus praemissis necesse est conclusionem esse veram: et sic falsum est quod in quaestione supponitur, scilicet quod ex duabus in toto falsis falsum possit syllogizari. Ex falsis autem est verum syllogizare: sed non contingit hoc quod illae propositiones quae ponuntur in syllogismo tali, sint causa verae conclusionis, propter quid dicens: sed sunt causa quia (sive quoniam sequitur conclusio vera ex falsis), nam ejus causae (qua praemissae sunt causae propter quid) non est ex falsis syllogismus qui veram autem concludit conclusionem: ob quam autem causam hoc contingit, in sequentibus dicetur.
Sed antequam determinetur qualiter, ex falso sequitur verum, determinandum est an hoc est possibile, quod ex falso verum sequatur. Videtur enim hoc esse impossibile: quia conclusio est effectus principiorum praemissorum: causa autem et effectus generis unius debent esse. Tum etiam propter hoc, quod verum est ens, et falsum non ens, et entis non potest esse causa nisi ens. Tum etiam propter hoc, quod verum et falsum sunt opposita: oppositorum autem unum non est causa alterius. Adhuc cum dicitur verum sequi ex falso, falsum non potest esse causa illati, sed illationis. Si autem est causa illationis: aut hoc est quia est causa secundum materiam: aut quia est causa illationis secundum formam. Si secundum materiam: tunc iterum non sequetur ex falso simpliciter, sed gratia materiae, et ut nunc: et hoc non est sequi semper et simpliciter. Si autem est causa illationis secundum formam: contra hoc esse videtur, quia manente eadem forma in aliis terminis erit ex falsis syllogizare falsum. Si enim sic dicam, omnis lapis est animal: omnis homo lapis: ergo omnis homo animal. Ambae praemissae sunt in toto falsae, et conclusio vera. Si autem sic proponatur, omnis lapis animal: omne lignum lapis: ergo omne lignum animal. Erunt praemissae in toto falsae, et conclusio falsa. Et tamen utrobique manet eadem forma. Idem ergo secundum formam eamdem causabit opposita.
But the second opinion belongs to those who say that the second book of the Prior Analytics is divided from the first by this: that in the first book determination is made concerning the ostensive syllogism, but in the second concerning the syllogism from hypothesis, which they say is made whenever a conclusion is reached not from a demonstrated proposition, which is the conclusion of the first syllogism, taken with another proposition, but the major is taken from the position and consent of the respondent; and demonstration is lacking in it. Nevertheless the first among these opinions is subtler and more common. But the third needs study in order to be verified, and especially in particular syllogisms.
CHAPTER III.
On the power by which, according to matter, the true is syllogized from the false.
Since a syllogism is made from the combination of two propositions, the propositions through which the syllogism is made either are, or can happen to be, disposed so that both are true; and it is, that is, it can happen, that they are so disposed that both are false; and it is also the case that they are so disposed that this one, namely one, is true, but that one, or the other, is false. But the conclusion following from all these modes is either true or false in all these modes. For since true and false in consequence can be compared with one another in four ways, namely that the true follows from the true, and the false from the false, and the true from the false, and the false from the true, we need to show only how the false does not follow from the true, and how the true follows from the false, because this is not known, and is difficult, and is the power of the syllogism. For how the true follows from the true, and how the false follows from the false, is easy and is sufficiently manifest from what was said in the first book about disposition in terms and propositions.
Therefore it must first be said that from truths it is not possible to syllogize a falsehood. Although some object against this, saying that if a false conclusion is concluded from two wholly false propositions in the first mode of the second figure, the contraries of those two propositions, which will be wholly true, should be taken, and the same false conclusion will be syllogized from those two wholly true propositions in the second mode of the second figure; and thus a falsehood follows from truth. But to this one must say that, when the premises are wholly false in the first mode of the second figure, it is necessary that the extremes be disparate; and thus one extreme will truly be able to be removed universally from the other. On account of this, with the premises so disposed, it is necessary that the conclusion be true; and so what is supposed in the question is false, namely that a falsehood could be syllogized from two wholly false premises. But from falsehoods it is possible to syllogize a truth; nevertheless it does not happen that those propositions which are put in such a syllogism are the cause of the true conclusion as one stating the reason why. Rather they are the cause because, or insofar as, a true conclusion follows from falsehoods; for in respect of the cause by which premises are causes on account of why, there is not a syllogism from falsehoods that concludes a true conclusion. But for what cause this happens will be stated in what follows.
Before it is determined how truth follows from falsehood, however, it must be determined whether this is possible, that truth follows from falsehood. For this seems impossible, because the conclusion is the effect of the principles laid down as premises, and cause and effect ought to be of one genus. Also, because truth is a being and falsehood is non-being, and nothing except being can be the cause of being. Also, because truth and falsehood are opposites, and one of opposites is not the cause of the other. Further, when it is said that truth follows from falsehood, the false cannot be the cause of what is inferred, but of the inference. But if it is the cause of the inference, this is either because it is the cause according to matter, or because it is the cause of the inference according to form. If according to matter, then again it does not follow from falsehood simply, but by reason of the matter and as now; and this is not to follow always and simply. But if it is the cause of the inference according to form, the contrary seems to be the case, because, while the same form remains in other terms, it will be possible to syllogize a falsehood from falsehoods. For if I say thus: every stone is an animal; every human being is a stone; therefore every human being is an animal. Both premises are wholly false, and the conclusion is true. But if it is proposed thus: every stone is an animal; every piece of wood is a stone; therefore every piece of wood is an animal. The premises will be wholly false, and the conclusion false. And nevertheless the same form remains in both cases. Therefore the same thing according to the same form will cause opposites.
Ad haec ergo et similia notandum, quod falsum non potest esse causa veri quantum ad rem conclusam, sicut necessario probatum est. Sed praemissae possunt esse causa illationis verae conclusionis dupliciter, scilicet aut per se, aut per accidens: et non possunt esse causa per se, sed per accidens possunt esse causa talis illationis: non enim sunt causa illationis veri in quantum sunt falsae praemissae, sed ex parte materiae, sicut duo impares numeri causa sunt paris, quia par dividitur aliquando in duos impares, et componitur ex duobus imparibus, sicut senarius ex duobus ternariis, quem non constituunt in quantum sunt impares, sed per materiam per quam sunt duae partes numeri parium. Sic praemissae falsae constituunt conclusionem veram, non in quantum sunt falsae, sed per materiam in quantum utraque per terminum in ea positum est medietas verae conclusionis. Et hoc modo loquendo causa et effectus sunt secundum aliquid unius naturae. Et hoc modo falsum non est causa veri ut constituens ipsum, sed ut habens in se aliquid per quod constituitur secundum materiam. Et hoc modo non ens habens in se aliquid entis, potest esse causa entis per accidens. Hoc etiam modo patet, quod praemissae falsae causa sunt illationis verae conclusionis, non quantum ad formam, sed quantum ad dispositionem materiae in terminis positis in propositionibus praemissis, sicut nuper dictum est. Hic autem determinari habet de syllogismo ex falsis in quantum est in potentia ad formam probabilis et apparentis, et abstrahit ab utroque: sic enim in communi consideratus pertinet ad istius libri Priorum scientiam. In materia autem probabili consideratur in Topicis, et in materia apparente consideratur in Elenchis.
Et est hic attendendum quod syllogismus ex falsis dupliciter potest considerari, scilicet respectu conclusionis in communi sive sit vera, sive falsa: et sic concludit ex necessitate syllogistica, sicut quaelibet alia species argumentationis: quandocumque enim sunt tres termini in duabus propositionibus secundum figuram et modum, necesse est aliquam sequi conclusionem. Potest etiam comparari ad conclusionem veri: et sic non concludit ex necessitate, quia peccat in materia.
Adhuc autem notandum quod syllogismi materia est duplex. Una quidem syllogismi in quantum est syllogismus quae est tres termini et duae propositiones: et haec non potest deficere syllogismo si syllogismus est. Alia est materia syllogismi ostensivi et probantis; et hoc modo syllogismus ex falsis determinata caret materia: et ideo quoad hoc est syllogismus secundum quid, et non simpliciter: habet enim formam in modo et figura ostensivi, sed non habet materiam. Unde etiam secundum materiam omni et nulli sequitur in syllogismo ex falsis in eadem figura et modo sic, omnis lapis animal: omnis homo lapis: sequitur, omnis homo animal. Nulli autem inesse sic, nullum animal lapis: omne lignum animal: ergo nullum lignum lapis.
To these and similar points, then, it must be noted that falsehood cannot be the cause of truth with respect to the thing concluded, as has been necessarily proved. But premises can be the cause of the inference of a true conclusion in two ways, namely either per se or by accident; and they cannot be the cause per se, but by accident they can be the cause of such an inference. For they are not the cause of the inference of truth insofar as they are false premises, but from the side of the matter, just as two odd numbers are the cause of an even number, because an even number is sometimes divided into two odd numbers and is composed from two odd numbers, as six from two threes; and they do not constitute six insofar as they are odd, but through the matter through which they are two parts of even number. Thus false premises constitute a true conclusion, not insofar as they are false, but through the matter insofar as each, through the term placed in it, is a middle element of the true conclusion. Speaking in this way, cause and effect are in some respect of one nature. And in this way falsehood is not the cause of truth as constituting it, but as having in itself something through which it is constituted according to matter. And in this way non-being, having in itself something of being, can be the cause of being by accident. In this way also it is clear that false premises are the cause of the inference of a true conclusion, not with respect to form, but with respect to the disposition of the matter in the terms placed in the propositions taken as premises, as was just said. Here, however, one has to determine concerning a syllogism from falsehoods insofar as it is in potency to the form of the probable and of the apparent, and abstracts from both; for thus, considered in common, it belongs to the science of this book of the Prior Analytics. But in probable matter it is considered in the Topics, and in apparent matter it is considered in the Sophistical Refutations.
And here it must be attended to that a syllogism from falsehoods can be considered in two ways: namely with respect to a conclusion in common, whether it is true or false; and thus it concludes by syllogistic necessity, just as any other species of argumentation does. For whenever there are three terms in two propositions according to figure and mode, it is necessary that some conclusion follow. It can also be compared to the conclusion of truth; and thus it does not conclude by necessity, because it errs in matter.
Again it must be noted that the matter of a syllogism is twofold. One matter belongs to a syllogism insofar as it is a syllogism, and this is three terms and two propositions; and this cannot be lacking to a syllogism if it is a syllogism. The other is the matter of an ostensive and probative syllogism; and in this way a syllogism from falsehoods lacks determinate matter, and therefore with respect to this it is a syllogism in a certain respect and not simply; for it has the form in the mode and figure of an ostensive syllogism, but it does not have the matter. Hence also according to matter there follows both "of every" and "of none" in a syllogism from falsehoods in the same figure and mode, thus: every stone is an animal; every human being is a stone; there follows, every human being is an animal. But "to belong to none" is thus: no animal is a stone; every piece of wood is an animal; therefore no piece of wood is a stone.
Ex his etiam patere potest, qualiter syllogismus ex falsis respectu conclusionis verae dicitur syllogismus quia, sive quoniam: et non dicitur syllogismus propter quid. Dicitur enim syllogismus quia: eo quod sumitur penes causam accidentalem et remotam: causa enim illationis essentialis et proxima necessariae conclusionis est praemissarum debita dispositio in figura et modo, et est causa formalis: causa autem accidentalis et valde remota ipsius illationis est potestas materialis trium terminorum in constituenda quacumque conclusione, sicut prius dictum est: et secundum primam istarum causarum non infert verum syllogismus ex falsis, sed infert secundum secundam: et ideo est syllogismus quia.
Est autem utilitas istius syllogismi in hoc quod potestas ejus ista consideratur, et res non perfecte scitur, nisi sciatur omnis potestas ipsius. Valet enim et dialectico, secundum quod falsa accipiunt probabilitatem: sic enim saepe ex falsis arguit dialecticus. Et valet sophistae, in quantum falsa habent apparentiam. Et sunt etiam ad ipsius syllogismi substantiam cognoscendam, in quantum falsa principia comparantur ad quamcumque conclusionem in communi sive veram sive falsam.
CAPUT IV.
Qualiter syllogismi universales primae figurae fiunt ex falsis, et quod ex vero non sequitur falsum.
Primo ergo ostendemus, quoniam ex veris non est possibile falsum syllogizare: hoc enim ex his quae dicemus erit manifestum. Si enim sumamus habitudinem antecedentis ad consequens, necesse est quod cum est antecedens, quod sit consequens, et destructo consequente destruitur antecedens, sicut in ante habitis ostensum est: si enim A sit antecedens, et B consequens, cum est A necesse est esse B, et cum B non est, necesse est A non esse.
Si ergo verum est A antecedens, necesse B consequens verum esse: aut si detur oppositum, accidit sive sequitur idem simul esse et non esse: hoc autem est impossibile, quia sic contradictoria essent simul vera. Si enim dicatur quod antecedente vero existente potest consequens non esse, tunc cum consequens actu et intellectu sit in antecedente, sequitur quod si est antecedens, est consequens: dictum autem est non esse: et sic simul est et non est. Adhuc si consequente non existente universaliter tollitur consequens pro omnibus contentis sub ipso: continetur autem antecedens sub consequente: ergo tollitur ipso sublato: sed ponitur esse: ergo simul est et non est. Si autem sic est cum praemissae sint sicut principium et antecedens ad conclusionem, si praemissae sunt verae, oportet conclusionem veram esse, conclusione existente falsa, oportet praemissas ambas vel alteram esse falsas.
Sed hoc cavendum est, ne (ideo quia diximus A quod est unus terminus tantum, esse principium et antecedens) aliquis opinetur quod ex uno aliquid sequatur syllogistice. Hoc enim non contingit, quia ex uno termino nihil potest sequi syllogistice: quia illud quod syllogistice contingit sive sequitur, hoc est conclusio: per quae autem hoc fit, quod sic sequitur conclusio, ad minimum sunt tres termini, et duo intervalla sive propositiones: quia duae propositiones ex ordine trium terminorum fiunt dum medium refertur ad utrumque extremorum, vel ut subjectum utrique, vel praedicatum utriusque, vel subjectum unius et praedicatum alterius. Si ergo tales praemissae verae sumantur, ita quod in majori medium sumatur sub majori extremitate, ita quod nihil sit cui inest B medium, quin eidem insit A majus extremum, ita quod omni B insit A, et minus extremum sumatur sub medio, et sit C quod sumatur sub B, ita quod cuicumque inest C illi eidem inest B, sequitur syllogistice quod cui inest C quod illi insit A, et non potest haec conclusio falsa esse, praemissis (ut dictum est) se habentibus: quia si detur quod conclusio est falsa, veris existentibus praemissis, sequitur quod idem simul erit et non erit, sicut paulo ante ostensum est: et sic se habet habitudo A ad B, quia positum est A duas propositiones colligere, hoc est, simul collectas in figura et modo significare.
From these points it can also be clear how a syllogism from falsehoods with respect to a true conclusion is called a syllogism quia, or because, and is not called a syllogism propter quid, or on account of why. For it is called a syllogism because inasmuch as it is taken according to an accidental and remote cause. For the essential and proximate cause of the inference of a necessary conclusion is the due disposition of the premises in figure and mode, and this is the formal cause; but the accidental and very remote cause of that inference is the material power of the three terms in constituting any conclusion whatever, as was said before. And according to the first of these causes, a syllogism from falsehoods does not infer truth, but it does infer according to the second; and therefore it is a syllogism quia.
The usefulness of this syllogism is in this: that this power of it is considered, and a thing is not perfectly known unless every power of it is known. For it is useful both to the dialectician, insofar as falsehoods take on probability, for in this way the dialectician often argues from falsehoods; and it is useful to the sophist, insofar as falsehoods have appearance. And these matters also belong to knowing the substance of the syllogism itself, insofar as false principles are compared to any conclusion whatever in common, whether true or false.
CHAPTER IV.
How universal syllogisms of the first figure are made from falsehoods, and that falsehood does not follow from truth.
First, therefore, we shall show that it is not possible to syllogize a falsehood from truths; for this will be manifest from the things we shall say. For if we take the relation of antecedent to consequent, it is necessary that when the antecedent exists, the consequent exists, and, when the consequent has been destroyed, the antecedent is destroyed, as was shown in what has gone before. For if A is the antecedent and B the consequent, when A exists it is necessary that B exist; and when B does not exist, it is necessary that A not exist.
If, therefore, A the antecedent is true, it is necessary that B the consequent be true. Or if the opposite is granted, it happens or follows that the same thing is and is not at the same time. But this is impossible, because then contradictories would be true at the same time. For if it is said that, while the antecedent is true, the consequent can fail to be, then, since the consequent is in the antecedent in act and in understanding, it follows that, if the antecedent exists, the consequent exists; but it has been said not to exist, and so it both is and is not at the same time. Further, if, when the consequent does not exist, the consequent is universally taken away for all things contained under it, and the antecedent is contained under the consequent, then when the consequent is removed the antecedent is removed; but it is posited to exist; therefore it both is and is not at the same time. If this is so, since the premises are like a principle and antecedent in relation to the conclusion, if the premises are true the conclusion must be true; if the conclusion is false, both premises or one of them must be false.
But this must be guarded against: lest, because we have said that A, which is only one term, is a principle and antecedent, someone think that something follows syllogistically from one thing. For this does not happen, because nothing can follow syllogistically from one term; for that which happens or follows syllogistically is the conclusion. But those things through which it happens that the conclusion follows in this way are at minimum three terms and two intervals or propositions, because two propositions are made from the ordering of three terms when the middle is referred to each of the extremes, either as subject of both, or as predicate of both, or as subject of one and predicate of the other. If, therefore, such true premises are taken, so that in the major the middle is taken under the major extreme, so that there is nothing to which B the middle belongs without A the greater extreme belonging to that same thing, so that A belongs to every B, and the lesser extreme is taken under the middle, and C is what is taken under B, so that to whatever C belongs B belongs to that same thing, it follows syllogistically that to that to which C belongs, A belongs; and this conclusion cannot be false when the premises are disposed as stated. For if it is granted that the conclusion is false while the premises are true, it follows that the same thing will be and will not be at the same time, as was shown a little before. And the relation of A to B is so disposed because A has been posited to collect two propositions, that is, to signify them as collected together in figure and mode.
Similiter autem est in syllogismis privativis quoad hoc quod per hos non contingit falsum ex veris concludere, generaliter verum est, quod ex veris non est falsum syllogistice concludere, tam in affirmativis quam in negativis syllogismis, tam universalibus quam particularibus.
Ex falsis autem sequitur verum syllogistice, et sequitur ex falso verum et utrisque propositionibus falsis et una. Sed cum sequitur ex altera falsa, non sequitur ex utralibet falsa indifferenter sumpta, sed secunda, quando tota sive in toto sumatur falsa, ita quod praedicatum nulli parti contentae sub subjecto conveniat. Si autem non tota sumatur falsa, sed pro aliqua parte: tunc sequitur verum ex falsa altera praemissarum utralibet sumpta vel majori vel minori. Hoc autem patet per singulos primae figurae syllogismos. Accipiantur enim tres termini A B C in tali habitudine se habentes ad invicem, quod secundum rem A major extremitas insit omni C minori extremitati: et idem A nulli insit quod est de numero eorum quae sunt sub B medio contenta. Accidit autem hoc in talibus terminis qui sunt ut animal, lapis, homo: quia nullus lapis animal: omnis homo animal: ergo nullus homo lapis. Si igitur tunc in primo modo primae A omni B inesse, et B dicatur inesse omni C, sequitur ex utrisque falsis vera conclusio: quia in conclusione A omni C inerit sic, omnis lapis animal: omnis homo lapis: ergo omnis homo animal.
Similiter autem ex utrisque falsis sequitur verum in secundo modo primae qui est universalis et privativus syllogismus. Insit enim C minor extremitas nulli neque A majori extremitati, neque B medio: et hoc est quando repugnat utrique; A autem major extremitas insit omni B medio: et hoc si iidem termini (qui dicti sunt) sumantur, et medium (quod prius fuit lapis) nunc ponatur homo, sic, animal, homo, lapis: lapidi enim minori extremitati neque homo medium nulli inest, neque animal quod est major extremitas: et tamen omni homini inest animal: propter quod si sumatur nulli inesse illi cui omni inest secundum rem, falsa erit propositio. Similiter si ei cui nulli inest, sumatur omni inesse, falsa erit propositio. Si autem sumptis propositionibus ex falsis utrisque vera sequitur conclusio, sic, nullus homo animal: omnis lapis homo: ergo nullus lapis animal. Sic igitur patet qualiter in ambobus universalibus syllogismis primae figurae ex utrisque falsis sequitur vera conclusio.
Ostendamus qualiter ex altera falsa vera sequitur conclusio. Dicamus igitur quod si altera propositionum praemissarum ponatur falsa, si prima quidem propositio (quae est A B) in toto, hoc est, universaliter sit falsa, non erit sive non sequitur ex taliter falsa conclusio vera. Si autem minor propositio quae est B C sit in toto falsa, sequitur conclusio vera ex taliter falsa minori. Dico autem totam sive in toto falsam, quae contraria est toti verae: cujus exemplum est, sicut si illa quae nulli inest, sumatur omni inesse: aut e converso, si id quod omni inest, sumatur nulli inesse universaliter.
Ostendatur ergo primo, quod majori in toto falsa non potest sequi conclusio vera. Ponamus enim A nulli B inesse in majori propositione, B autem ponamus omni C inesse in minori propositione. Si ergo tali facta positione, B C minorem propositionem sumo veram, A B autem majorem propositionem sumo in toto falsam, ita quod sumo omni B inesse A in majori (cum nulli insit), impossibile est conclusionem esse veram ex taliter falsa majori. Cujus causa est: quia C est sub B, et positum est A nulli inesse B, et tunc etiam nulli inest C, quia C est sub B, siquidem hoc sit verum quod positum est, quod nulli eorum quae sunt B insit A et quod B insit omni C. Manifestum est igitur quoniam prima sive majori sumpta tota falsa, et minori vera, non potest sequi vera conclusio.
It is similar in privative syllogisms with respect to this, that through these it is not possible to conclude a falsehood from truths. In general, it is true that a falsehood cannot be concluded syllogistically from truths, in affirmative as well as in negative syllogisms, in universal as well as in particular ones.
From falsehoods, however, truth follows syllogistically; and truth follows from falsehood both when both propositions are false and when one is false. But when it follows from one false premise, it does not follow from either false premise taken indifferently, but from the second, when it is wholly or entirely taken as false, so that the predicate agrees with no part contained under the subject. But if it is not wholly taken as false, but false with respect to some part, then truth follows from one false premise whether either one, the major or the minor, is taken. This is clear through the individual syllogisms of the first figure. Let three terms A B C be taken as having such a relation to one another that according to reality A, the major extreme, belongs to every C, the minor extreme, and that same A belongs to none of the number of those things contained under B as middle. This happens in such terms as animal, stone, human being: for no stone is an animal; every human being is an animal; therefore no human being is a stone. If, then, in the first mode of the first figure A is taken to belong to every B, and B is said to belong to every C, a true conclusion follows from both false premises, because in the conclusion A will belong to every C, thus: every stone is an animal; every human being is a stone; therefore every human being is an animal.
Likewise truth follows from both false premises in the second mode of the first figure, which is a universal and privative syllogism. Let C, the minor extreme, belong to neither A, the major extreme, nor B, the middle; and this is when it is repugnant to each. But let A, the major extreme, belong to every B, the middle. This is so if the same terms which have been mentioned are taken, and the middle, which before was stone, is now posited as human being: animal, human being, stone. For to stone, the minor extreme, neither human being as middle nor animal, which is the major extreme, belongs; and yet animal belongs to every human being. Therefore, if what belongs to every instance according to reality is taken as belonging to none, the proposition will be false. Similarly, if what belongs to none is taken as belonging to every instance, the proposition will be false. But if, after propositions are taken from both false premises, a true conclusion follows, it is thus: no human being is an animal; every stone is a human being; therefore no stone is an animal. Thus, therefore, it is clear how in both universal syllogisms of the first figure a true conclusion follows from both false premises.
Let us show how a true conclusion follows from one false premise. Let us say, then, that if one of the propositions laid down as premises is posited as false, and if the first proposition, which is A B, is wholly, that is, universally false, there will not be, or there does not follow, a true conclusion from a false premise of that kind. But if the minor proposition, which is B C, is wholly false, a true conclusion follows from such a false minor. I call that proposition whole or wholly false which is contrary to the wholly true proposition. An example is as when that which belongs to none is taken to belong to all, or conversely, when that which belongs to all is taken to belong to none universally.
Therefore let it first be shown that, when the major is wholly false, a true conclusion cannot follow. For let us posit that A belongs to no B in the major proposition, and let us posit that B belongs to every C in the minor proposition. If, then, with such a position made, I take the minor proposition B C as true, but I take the major proposition A B as wholly false, so that I take A to belong to every B in the major (although it belongs to none), it is impossible that the conclusion be true from such a false major. The cause of this is that C is under B, and it has been posited that A belongs to no B; and then A belongs to no C either, because C is under B, provided that what has been posited is true, namely that A belongs to none of the things which are B and that B belongs to every C. Therefore it is manifest that, when the first or major proposition is taken as wholly false and the minor as true, a true conclusion cannot follow.
Similiter autem est si A quidem omni B inest, B et omni C in minori, dummodo sumpta sit B C minor propositio vera, A B autem propositio sit sumpta in toto falsa secundum primum modum primae figurae, ita quod nulli eorum quae sunt B insit A secundum rem: quia aliter non in toto falsa major esset propositio: tunc enim ex taliter falsa majori, non vera, sed falsa erit conclusio: tali enim positione facta, omni C inerit A in conclusione quae falsa est conclusio. Cujus causa est: quia positum est quod omni illi cui inest B inest A, B autem inest omni C, necesse est igitur quod A insit omni C.
Manifestum est igitur, quoniam prima tota falsa sive sit affirmativa, sicut in primo primae: sive privativa sit, sicut in secundo primae: altera autem propositione minori sumpta vera, non fit sive non sequitur ex taliter falsa majori conclusio vera sed falsa, sicut patet in terminis, omne animal lapis: omnis homo animal: ergo omnis homo lapis. Nullum animal sensibile: omnis homo animal: ergo nullus homo sensibile. Falsae et non verae sunt ambae conclusiones.
Si autem major non in toto falsa sumatur, sed in parte, sequitur conclusio vera ex taliter falsa propositione. Si enim ponamus, quod A majus extremum omni inest C quod est minus extremum, et idem A inest alicui B medio, et B medium insit omni C minori: cujus exemplum in terminis est, sicut animal majus extremum inest omni cygno, sicut minori: albo autem quod est medium, major extremitas quod est animal inest particulariter, quia aliquod album est animal: sed album medium inest omni cygno minori extremitati. Si ergo jam positione terminorum facta sumatur A omni B inesse in majori, quae non est in toto universaliter falsa, et sumatur B omni C inesse in minori propositione, erit conclusio quod omni C inest A, et est conclusio vera ex falsis: omnis enim cygnus est animal, sic, omne album animal: omnis cygnus album: ergo omnis cygnus animal: et est vera conclusio ex majori non in toto falsa, et minori in toto vera.
Similiter autem fit in secundo primae si privativa sit A B major propositio, et non in toto falsa: cujus ratio est, quia taliter se habentibus terminis, possibile est quod major extremitas (A scilicet) insit alicui B medio, et quod A nulli insit C minori extremitati, et quod B medium insit omni C minori extremo, ut patet in his terminis, animal, album, nix: animal enim inest alicui albo: sed nulli nivi inest animal: album autem inest omni nivi. Si ergo sumatur A quidem nulli B inesse in majori, erit major non in toto falsa, B autem sumatur omni C inesse, erit minor in toto vera, sequitur quod A nulli C inerit, quae est vera conclusio.
Si autem e converso major sumatur in toto vera, et minor in toto falsa, ex taliter falsa altera propositione erit syllogismus verae conclusionis: sicut si A B propositio in toto sit vera,
It is similar if A indeed belongs to every B, and B also to every C in the minor, provided the minor proposition B C is taken as true, but the proposition A B is taken as wholly false according to the first mode of the first figure, so that according to reality A belongs to none of those things which are B; for otherwise the major proposition would not be wholly false. For then from such a false major the conclusion will not be true, but false; for when such a position has been made, A will belong to every C in the conclusion, which is a false conclusion. The cause is that it has been posited that A belongs to everything to which B belongs, and B belongs to every C; therefore it is necessary that A belong to every C.
Therefore it is manifest that when the first proposition is wholly false, whether it is affirmative, as in the first mode of the first figure, or privative, as in the second mode of the first figure, while the other, minor proposition is taken as true, no true conclusion is made or follows from such a false major, but a false one, as is clear in terms: every animal is a stone; every human being is an animal; therefore every human being is a stone. No animal is sensible; every human being is an animal; therefore no human being is sensible. Both conclusions are false and not true.
But if the major is not taken as wholly false, but in part, a true conclusion follows from a proposition false in that way. For if we posit that A, the greater extreme, belongs to every C, which is the lesser extreme, and that same A belongs to some B, the middle, and that B, the middle, belongs to every C, the example in terms is as follows: animal, the greater extreme, belongs to every swan, as to the minor; but to white, which is the middle, the major extreme, animal, belongs particularly, because some white thing is an animal; but white as middle belongs to every swan, the minor extreme. If, then, now, with the position of the terms made, A is taken to belong to every B in the major, which is not wholly and universally false, and B is taken to belong to every C in the minor proposition, there will be the conclusion that A belongs to every C, and it is a true conclusion from false premises. For every swan is an animal, thus: every white thing is an animal; every swan is white; therefore every swan is an animal. And it is a true conclusion from a major that is not wholly false and a minor that is wholly true.
Likewise this happens in the second mode of the first figure if A B, the major proposition, is privative and not wholly false. The reason is that, with the terms so disposed, it is possible that the major extreme, namely A, belongs to some B, the middle, and that A belongs to no C, the minor extreme, and that B, the middle, belongs to every C, the minor extreme, as is clear in these terms: animal, white, snow. For animal belongs to some white thing, but animal belongs to no snow; and white belongs to every snow. If, therefore, A is taken to belong to no B in the major, the major will not be wholly false, but B is taken to belong to every C, the minor will be wholly true, and it follows that A will belong to no C, which is a true conclusion.
But if, conversely, the major is taken as wholly true and the minor as wholly false, from such a false other proposition there will be a syllogism of a true conclusion, as if the proposition A B is wholly true,
Notes
- There it takes the conclusion for the minor extreme. (Ibi capit conclusionem pro minori extremitate.) ↩
- As if he were saying that it cannot be taken under the minor extreme: both because then the major would be particular in the first figure, and also because a particular is not always such that it is permissible to take something under it. (Quasi dicat, quod non potest sumi sub extremitate minori: tum quia tunc major esset particularis in prima figura: tum etiam quia particularis non est semper talis, ut sub ea liceat sumi aliquid.) ↩
- Note the strict mode of taking an ostensive syllogism, and the broad mode of taking a syllogism from hypothesis. P. J. (Nota strictum modum sumendi syllogismum ostensivum, et latum modum sumendi syllogismum ex hypothesi. P. J.) ↩
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