Authors/Thomas Aquinas/posteriorum/L1/Lect26

Lecture 26 Demonstrative syllogisms best made in the first figure. On mediate and immediate negative propositions

Latin	English
	Lecture 26 (79a17-b22) DEMONSTRATIVE SYLLOGISMS BEST MADE IN THE FIRST FIGURE. ON MEDIATE AND IMMEDIATE NEGATIVE PROPOSITIONS
lib. 1 l. 26 n. 1 Postquam philosophus determinavit de materia syllogismi demonstrativi, hic determinat de forma ipsius, ostendens in qua figura praecipue fiat syllogismus demonstrativus. Et dividitur in duas partes. In prima ostendit quod syllogismus demonstrativus maxime fit in prima figura. Et quia in prima figura proceditur etiam ex negativis, et oportet demonstrationem ex immediatis procedere, ostendit in secunda parte quomodo contingit propositionem negativam esse immediatam; ibi: sicut autem esse a in b et cetera.	After determining about the material of the syllogism, the Philosopher here determines about its form, showing in which figure chiefly the, demonstrative syllogism is formed. His treatment is divided into two parts. In the first he shows that the demonstrative syllogism is formed first and foremost in the first figure. In the second, because it is possible in the first figure to proceed from negatives and because a demonstration must proceed from things immediate, he shows how a negative proposition happens to be immediate (79a33).
lib. 1 l. 26 n. 2 Primum ostendit tribus rationibus, quarum prima talis est. In quacunque figura maxime fit syllogismus propter quid, illa figura maxime est faciens scire, et propter hoc est magis accommoda demonstrationibus; cum demonstratio sit syllogismus faciens scire. Sed in prima figura maxime fit syllogismus propter quid (quod patet ex hoc quod mathematicae scientiae, ut arithmetica et geometria, et quaecunque aliae propter quid demonstrant, ut plurimum prima figura utuntur); ergo prima figura est maxime faciens scire et maxime accommoda demonstrationibus.	He shows the first with three reasons, the first of which (79a17) is this: In whatever figure the propter quid syllogism is best made, that figure is the best for causing scientific knowledge and for that reason is most suitable for demonstrations, since demonstration is a syllogism which causes scientific knowledge. But a syllogism propter quid is best made in the first figure, and this is evidenced by the fact that the mathematical sciences of arithmetic and geometry and all other sciences which demonstrate propter quid employ the first figure in most cases. Therefore, the first figure is the one which first and foremost causes scientific knowledge and is most suitable for demonstrations.
Causa autem, quare demonstratio propter quid maxime fit in prima figura, haec est. Nam in prima figura medius terminus subiicitur maiori extremitati, quae est praedicatum conclusionis, et praedicatur de minori termino, qui est subiectum conclusionis. Oportet autem in demonstratione propter quid medium esse causam passionis, quae praedicatur in conclusione de subiecto. Et unus modus dicendi per se est quando subiectum est causa praedicati, ut interfectum interiit, sicut supra dictum est; et hoc competit primae figurae, in qua medium subiicitur maiori extremitati, ut dictum est.	But the reason why demonstration propter quid is best made in the first figure is this: in the first figure the middle term is both subjected, to the major extreme, which is the predicate of the conclusion, an(I predicated of the minor extreme, which is the subject of the conclusion. Now in demonstrations propter quid the middle must be the cause of the proper attribute which is predicated of the subject in the conclusion. Furthermore, one of the modes of “saying per se” is when the subject is the cause of the predicate, as “being butchered, he died,” as has been explained above; and this is verified in the first figure in which the middle is subject to the major extreme, as has been said.
lib. 1 l. 26 n. 3 Secundam rationem ponit; ibi: postea ipsius quod quid est etc., quae talis est. Quod quid est potissimum locum in demonstrativis scientiis habet, quia, sicut dictum est, definitio aut est principium demonstrationis, aut conclusio, aut demonstratio positione differens. Ad investigandum autem definitionem sola prima figura convenit. Nam in sola prima figura concluditur universalis affirmativa, quae sola competit ad scientiam quod quid est. Nam quod quid est per affirmationem cognoscitur: praedicatur enim definitio de definito affirmative et universaliter; non enim quidam homo est animal bipes, sed omnis homo. Ergo prima figura maxime est faciens scire et accommoda demonstrationibus.	The second reason (79a23) is this: the quod quid est [i.e., the definition as signifying the essence] plays a most important role in demonstrative sciences because, as has been said, a definition is either the principle of a demonstration or the conclusion or a demonstration differing in the position of its terms. Now when it is a question of formulating a definition the first figure alone is suitable. For that is the only figure in which a universal affirmative is concluded, which alone produces science of the quod quid est. For the quod quid est is known through an affirmation. Furthermore, the definition is predicated affirmatively and universally of the defined: for it is not some man that is a two-legged animal, but every man. Therefore, the first figure is foremost in causing scientific knowledge and is best accommodated to demonstrations.
lib. 1 l. 26 n. 4 Tertiam rationem ponit; ibi: amplius haec quidem etc., quae talis est. Aliae figurae in demonstrationibus indigent prima; prima autem non indiget aliis; ergo prima figura efficacius facit scire quam aliae. Quod autem aliae figurae indigeant prima ex hoc manifestum est, quod oportet ad perfectam scientiam habendam, quod propositiones mediatae, quae sumuntur in demonstrationibus, ad immediata reducantur. Quod quidem fit dupliciter, scilicet densando media et augmentando. Densando quidem, quando medium acceptum mediate coniungitur utrique extremorum, vel alteri.	Then (79a30) he gives the third reason which is this: For purposes of I demonstration the other figures need the first, but the first does not need them. Therefore, the first figure is better equipped for causing scientific knowledge than the others. That the others need the first is evidenced by the fact that if complete scientific knowledge is to be had, the mediate propositions present in demonstrations must be reduced to immediate ones. But this reduction is made in two ways, namely, by condensing middles [i.e., by inserting fresh middles, the movement proceeding from the extremes toward the middle first employed] and by expanding outwards [i.e., by going from the middle toward the remote extreme].
Unde, quando accipiuntur media alia inter medium primum et extrema, fit quasi quaedam condensatio mediorum. Sicut si acciperetur primo sic: omne e est c; omne c est a: et deinde inter c et e, sumatur medium d; et inter c et a medium b. Augmentando autem, quando medium est immediatum minori extremitati, et mediatum maiori. Tunc enim oportet accipere plura media alia supra medium primo acceptum. Ut si dicatur: omne e est d; omne d est a; et postea supra d accipiantur alia media.	It is done by condensing when the middle actually employed is joined mediately to each of the extremes or only to the minor extreme. Hence when other middles are introduced between the first middle and the extremes, the middles, as it were, close in. Thus, if someone first says, “Every E is C,” [minor], “Every C is A,” [major], and then a middle, say D, is introduced between C and E, and a middle B between C and A. It is done by expanding when the middle is immediate to the minor extreme and mediate to the major: for then it is necessary to introduce several other middles more general than the middle first taken. Thus, if one says, “Every E is D,” “Every D is A,” and the later other middles more general than D are introduced [between D and A].
Haec autem condensatio et augmentatio mediorum fit solum per primam figuram: tum, quia solum in prima figura concluditur universalis affirmativa; tum, quia solum in prima figura medium sumitur inter extrema. In secunda autem figura medium accipitur extra extrema, quasi praedicatum de eis. In tertia vero figura, infra extrema, quasi subiectum de eis.	Now these processes of condensing and expanding can be performed only in the first figure, both because the first figure is the only one which yields a universal affirmative conclusion, and because it is only in the first figure that the middle lies between both extremes. For in the second figure the middle lies outside the extremes, as being predicated of them; in the third figure [the middle] is below each of the extremes, as being subjected to them.
lib. 1 l. 26 n. 5 Deinde cum dicit: sicut autem esse etc., docet quomodo propositio negativa possit esse immediata. Et circa hoc duo facit. Primo, proponit intentum, dicens quod sicut contingit a esse in b individualiter, idest immediate, sic et conceditur non esse, idest ita potest concedi quod propositio significans a non esse in b sit immediata. Unde exponit, quid est individualiter esse vel non esse, scilicet quando affirmativa vel negativa non habet medium per quod probetur.	Then (79a33) he teaches how a negative proposition can be immediate. In regard to this he does two things. First (79a33), he states his intention, saying that “just as it is possible for every A to be in B atomically,” i.e., immediately, “so too not to be,” i.e., so too it is possible for a proposition signifying that A is not in B to be immediate. Then he goes on to explain what it is to be or not to be atomically, namely, when the affirmation or negation does not have middle through which it might be proved.
lib. 1 l. 26 n. 6 Secundo; ibi: cum igitur aut a quidem etc., manifestat propositum. Et circa hoc duo facit: primo, ostendit quomodo propositio negativa sit mediata; secundo, quomodo sit immediata; ibi: si vero neutrum et cetera. Circa primum duo facit: primo, manifestat propositum; secundo, ostendit quoddam quod supposuerat; ibi: quod autem contingit b non esse et cetera.	Secondly (79a36), he elucidates his proposition. In regard to this he does two things. First, he shows when a negative proposition is mediate. Secondly, when immediate (79b12). Concerning the first he does two things. First, he clarifies his proposition. Secondly, he proves something he had presupposed (79b5).
Dicit ergo primo quod cum a, idest maior terminus, aut b, idest minor terminus, sunt in quodam toto, sicut species in genere, aut etiam ambo sunt sub aliquo genere, non contingit a non esse in b primo, idest non contingit quod haec propositio, nullum b est a, sit immediata. Et primo manifestat hoc quando a est in quodam toto, scilicet c; b autem in nullo; ut puta, si a sit homo, c substantia, b quantitas: potest enim syllogismus fieri ad probandum quod a nulli b insit per hoc, quod c omni a inest, b autem nulli; ut si fiat syllogismus in secunda figura, talis: omnis homo est substantia; nulla quantitas est substantia; ergo nulla quantitas est homo.	He says therefore first (79a36), that when A, i.e., the major term, or B, i.e., the minor term, is in some whole as a species in its genus, or both are under diverse genera or predicaments, it does not occur that A is not in B first, i.e., it does not occur that this proposition, “No B is A,” is immediate. First, then, he manifests this when A is in some whole, say in Q and B is in no whole. For example, if A is “man,” C is “substance,” and B is “quantity,” it is possible to form a syllogism to prove that A is in no B on the ground that C is in every A and in no B. Thus we get a syllogism in the second figure: Every man is a substance; No quantity is a substance: Therefore, no quantity is a man.
Et similiter est, si b, idest minor terminus, sit in quodam toto, ut in d, a autem non sit in aliquo toto; syllogizari poterit quod a sit in nullo b. Ut sit a substantia, b linea, d quantitas; et fiat syllogismus in prima figura sic: nulla quantitas est substantia; omnis linea est quantitas; ergo nulla linea est substantia.	In like manner, if B, i.e., the minor term, is in some whole, say D, but A is not in that whole, it is possible to syllogize that A is in no B. For example if A is “substance,” B “line,” and D “quantity,” we get a syllogism in the first figure: No quantity is a substance; Every line is a quantity; Therefore, no line is a substance.
Eodem autem modo poterit demonstrari conclusio negativa, si utrumque sit in quodam toto; ut si sit a linea, c quantitas, b albedo, et d qualitas; potest syllogizari in secunda figura, et in prima. In secunda figura sic: omnis linea est quantitas; nulla albedo est quantitas; ergo nulla albedo est linea. In prima figura sic: nulla qualitas est linea; omnis albedo est qualitas; ergo nulla albedo est linea. Est autem intelligendum, propositionem negativam esse mediatam, utroque terminorum existente in quodam toto, non quidem in eodem, sed in diversis. Si enim sint in eodem toto, erit propositio immediata, sicut, nullum rationale est irrationale, vel nullum bipes est quadrupes.	In the same way, a negative conclusion could be demonstrated if either is in some whole. For example, if A is “line,” C “quantity,” B “whitenem” and D “quality,” it is possible to form a syllogism in the first and in the second figure. In the second figure thus:Every line is a quantity; No whiteness is a quantity: Therefore, no whiteness is a line.And in the first figure thus: No quality is a line; Every whiteness is a quality: Therefore, no whiteness is a line. We should understand, however, that a negative proposition is mediate, when both terms exist in some whole which is not the same but different for each. For if they are in the same whole, the proposition will be immediate, as “No rational being is irrational,” or “No biped is a quadruped.”
lib. 1 l. 26 n. 7 Deinde cum dicit: quod autem contingit etc., manifestat quod supposuerat, scilicet quod, altero extremorum existente in aliquo toto, alterum non sit in eodem, dicens quod manifestum est ex coordinationibus, scilicet praedicamentorum diversorum, quae non commutantur ad invicem. Scilicet quia id quod est in uno praedicamento, non est in altero, manifestum est quod contingat b non esse in toto, in quo est a, aut e converso, quia videlicet contingit unum terminorum accipi in uno praedicamento, in quo non est alius. Sit enim una coordinatio praedicamenti acd, puta praedicamentum substantiae; et alia coordinatio sit bef, puta praedicamentum quantitatis. Si ergo nihil eorum, quae sunt in coordinatione acd, de nullo praedicatur eorum, quae sunt in coordinatione bef; a autem sit in p, quasi in quodam generalissimo, quod sit principium totius primae coordinationis; manifestum est quod b non erit in p, quia sic coordinationes, idest praedicamenta, commutarentur. Similiter autem est si b sit in quodam toto, ut puta in e; manifestum est quod a non erit in e.	Then (79b5) he explains something he had presupposed, namely, “on condition that one of the extremes exist in some whole and that the other be not in the same,” saying that it is “clear from the ‘orderings’ of the various predicaments, which are” not mutually interchangeable. In other words, because that which is in one predicament is not in another, it is plain that B happens not to be in the whole in which A is, or vice versa, because one of the terms happens to be taken from one predicament in which the other is not found. Thus, let one ordering of the predicaments be ACD, say the predicament of substance, and another ordering be BEF, say the predicament of quantity. Then if none of those in the ordering ACD be predicated of none in the ordering BEF, while A is in P as in that most general item which is the principle of the whole first ering, it is plain that B is not in P, because then the orderings, i.e., the predicaments, would be interchanged. Similarly, if B is in some whole, say in E, it is plain that A is not in E.
lib. 1 l. 26 n. 8 Deinde cum dicit: si vero neutrum etc., ostendit quomodo propositio negativa sit immediata dicens quod, si neutrum sit in toto aliquo, scilicet, neque a neque b; et tamen a non sit in b, necesse est quod haec sit immediata, nullum b est a. Quia si acciperetur aliquod medium ad syllogizandum eam, oporteret quod alterum ipsorum esset in aliquo toto; oporteret enim syllogismum fieri, aut in prima figura, aut in secunda. In tertia enim figura non potest concludi universalis negativa, qualem oportet esse propositionem immediatam. Si quidem syllogismus fit in prima figura, oportet quod b sit in quodam toto, quia b est minor extremitas, et in prima figura oportet semper minorem propositionem esse affirmativam. Non enim fit syllogismus in prima figura ex maiori affirmativa et minori negativa.	Then (79b12) he indicates how a negative proposition may be immediate, saying that “if neither is in some whole,” i.e., neither A nor B, and A is not in B, it is necessary that this proposition, “No B is A,” be immediate. Because if a middle were taken to syllogize it, then one of them would have to be in some whole, for the syllogism would have to be made either in the first figure or in the second, since in the third figure a universal negative cannot be concluded, as is required for an immediate proposition. However, if it is made in the first, B would have to be in some whole, because B is the minor extreme, and in the first figure the minor proposition must always be affirmative. For a syllogism with the major affirmative and the minor negative cannot be formed in the first figure.
Sed si syllogismus erit in media figura, contingit quodcunque, idest vel a vel b, esse in toto quodam; quia in media figura potest esse negativa tam prima quam secunda propositio. Nunquam tamen potest esse, neque in prima neque in secunda, utraque propositio negativa. Et ideo oportet quod, altera existente affirmativa, alterum extremorum sit in quodam toto. Sic igitur patet quod propositio negativa est immediata, quando neutrum terminorum est in quodam toto. Non autem potest dici quod quamvis neutrum sit in quodam toto, potest tamen accipi medium ad ipsam concludendam, scilicet si accipiatur medium convertibile: quia oportet tale medium esse quod sit prius et notius; et hoc est vel genus vel definitio, quae non est sine genere. Deinde cum dicit: manifestum igitur est etc., concludendo epilogat quod dictum est. Et litera plana est ex dictis.	But if it be in the second figure, either may, i.e., A or B, may be in a whole, because in the second figure the first proposition may be negative in some moods and the minor in other moods. Of course it is never permitted, neither in the first nor the second, to have both propositions negative. And so it is required that when either proposition is affirmative, one of the extremes must be in some whole. Thus it is clear that a negative proposition is immediate, when neither of its terms is in some whole. This does not mean, however, that although neither is in some whole, a middle could be found to conclude it, namely, if one were to take a convertible middle, because it is necessary that such a middle be prior and better known. And this is either the genus itself or the definition, which is not without a genus. Then (79b21) he concludes and summarizes what has been said. Here the text is sufficiently clear.