Authors/Thomas Aquinas/posteriorum/L1/Lect28

Lecture 28 How by syllogizing in the first or second figure a false negative is concluded contrary to an immediate affirmative

Latin	English
	Lecture 28 (80a8-b16) HOW BY SYLLOGIZING IN THE FIRST OR SECOND FIGURE A FALSE NEGATIVE IS CONCLUDED CONTRARY TO AN IMMEDIATE AFFIRMATIVE
lib. 1 l. 28 n. 1 Postquam philosophus ostendit quomodo concludatur per syllogismum affirmativa falsa, contraria negativae immediatae, hic ostendit quomodo per syllogismum concludatur negativa falsa, contraria affirmativae immediatae. Et primo, in prima figura; secundo, in secunda; ibi: sed in media figura et cetera. Circa primum duo facit. Primo, ostendit de quo est intentio. Et dicit quod cum negativa universalis concludi possit in prima et in secunda figura, primo dicendum est quot modis syllogismus ignorantiae fiat in prima figura, et qualiter se habentibus propositionibus in veritate et falsitate. Secundo; ibi: contingit quidem etc., prosequitur propositum. Et primo, ostendit quomodo fiat talis syllogismus in prima figura ex duabus falsis; secundo, quomodo fiat ex altera vera et altera falsa; ibi: contingit autem et altera et cetera.	After showing how a false affirmative conclusion contrary to an immediate negative is obtained by syllogizing, the Philosopher here shows how by syllogizing a false negative is concluded contrary to an immediate affirmative. First, in the first figure. Secondly, in the second (8048). Concerning the first he does two things. First (80a8), he states his intention and says that since a universal negative may be concluded in the first as well as in the second figure, we must first show in which moods a syllogism of ignorance is formed in the first figure and under which conditions of truth and falsity in the propositions. Secondly (80a11), he establishes his proposition. First, he shows how such a proposition is formed from two false premises in the first figure. Secondly, how it is formed from one false and one true premise (80a14).
lib. 1 l. 28 n. 2 Dicit ergo primo quod praedictus syllogismus fieri potest ex utrisque falsis. Quod patet si a sit et in c et in b individualiter, idest immediate. Est autem immediate genus in proximis speciebus, in quas primo dividitur, sicut color in albedine et nigredine. Genus enim per se praedicatur de specie, quia primo ponitur in eius definitione; et immediate praedicatur de specie proxima, quia immediate in eius definitione ponitur, non autem ex hoc, quod ponatur in definitione alicuius partis definientis, sicut se habet genus remotum ad ultimam speciem. Sint ergo termini, color, albedo, nigredo. Si ergo accipiatur a quidem in nullo c esse, utpote si dicamus: nulla albedo est color; c autem in omni b, ut puta si dicamus: omnis nigredo est albedo; falsae sunt ambae propositiones, et falsa est conclusio, scilicet: nulla nigredo est color.	He says therefore first (80a11) that the aforesaid syllogism can be formed from premises, both of which are false. This is clear if A is both in B and in C individually, i.e., immediately. It is thus that a genus is immediately in the proximate species into which it is first divided, as color into blackness and whiteness. For the genus is predicated per se of the species, because the former is placed first in the definition of the latter; and it is predicated immediately of a proximate species, because it is put in its definition immediately and not in the way that a remote genus-which is put in the definition of a defining part-is related to an ultimate species. Therefore, let the terms be “color,” “whiteness” and “blackness.” If, then, we assume that A is in no C, for example, if we say, “No whiteness is a color,” but C is in every B, say “All blackness is whiteness,” both propositions are false, as is the conclusion, “No blackness is a color.”
lib. 1 l. 28 n. 3 Deinde cum dicit: contingit autem etc., ostendit quomodo possit esse in praedicto syllogismo altera vera et altera falsa. Et primo ostendit quomodo possit esse maior vera et minor falsa; secundo, quomodo contingit e converso; ibi: sed et eam quae est et cetera.	Then (80a14) he shows how there can be one false and one true premise in the syllogism under discussion. First, he shows how the major can be true and the minor false. Secondly, how it might be the reverse (8040).
Dicit ergo primo quod contingit syllogismum ignorantiae negativum fieri in prima figura, falsa existente altera propositionum indifferenter, quaecunque sit illa. Potest enim contingere quod haec propositio a.c, quae est maior, sit vera, et propositio, quae est b.c, sit falsa, quae est minor. Et quod propositio maior possit esse vera, probat per hoc, quod iste terminus a, quicunque sit ille, non est necesse quod insit omnibus, sicut color non praedicatur de omnibus entibus. Quod autem minor sit falsa, probat per hoc, quia non potest accipi aliquis terminus, a quo universaliter negetur a, qui quidem terminus praedicetur de b: supponimus enim quod haec sit vera et immediata: omne b est a. Si ergo aliquid universaliter praedicetur de b, ita quod haec sit vera, omne b est c, non potest esse quod de illo universaliter negetur a.	He says therefore first (80a14) that a negative syllogism of ignorance can be formed in the first figure no matter which one of the propositions happens to be false. For it might happen that the proposition AC, which is the major, is true, and the proposition BC, which is the minor, is false. That the major proposition could be true he proves by the fact that the term A, whatever it be, need not be in all things, as color is not predicated of all beings. That the minor would be false he proves on the ground that it is not possible to assume a term of which A would be universally denied and which would also be predicated of B: for we are supposing that the proposition, “Every B is A,” is true and immediate. Therefore, if something were universally predicated of B, so that “Every B is C” would be true, then A cannot be universally denied of C. Consequently, this proposition, “No C is A,” which was the major, will not be true. For if every B is A, as we supposed, and every B is C, as we are now assuming, it follows in the third figure that some C is A, which contradicts the major.
Et ita haec propositio: nullum c est a, non erit vera; quae erat maior. Si enim omne b est a, ut supponitur, et omne b est c, ut assumitur, sequitur in tertia figura: quoddam c est a, quae est contradictoria maioris. Falsa ergo erit ista: nullum c est a. Si ergo haec sit vera, quae est maior, necesse est quod haec sit falsa, quae est minor: omne b est c. Secundo, probat per hoc quod ex duabus veris non potest concludi falsa, ut supra probatum est. Datur autem haec esse vera: nullum c est a. Si ergo etiam haec sit vera: omne b est c; sequitur quod conclusio sit vera: nullum b est a; quae tamen supponitur esse falsa, utpote contraria huic immediatae propositioni: omne b est a.	Therefore the proposition, “No C is A,” will be false. Hence if this is true, which is the major, it is required that this be false, which is the minor, i.e., “Every B is C.” Then he proves the same thing on the ground that if both premises are true, then as has been proved above, a false conclusion cannot follow—which is out of place in a syllogism of ignorance, which ought to conclude to a false conclusion. But it was given that this is true, namely, “No C is A”’: if then it is also true that “Every B is C,” it follows that the conclusion, “No B is A,” is true, whereas it is supposed to be false, being contrary to this immediate proposition, “Every B is A.”
lib. 1 l. 28 n. 4 Deinde cum dicit: sed et eam etc., ostendit quomodo minor sit vera, maiori existente falsa. Et dicit quod propositio c.b, scilicet minor, potest esse vera, cum maior sit falsa. Quia enim haec propositio: omne b est a, cuius contraria debet concludi, est immediata, necesse est quod b sit in a sicut pars in toto, sicut albedo in colore. Potest autem accipi aliquid aliud, in quo etiam sit b sicut in toto, non tamen immediate, et sit illud qualitas quae sit c. Necesse est ergo, secundum praedicta, quod horum duorum, scilicet a et c, alterum sit sub altero, idest color sub qualitate. Si ergo aliquis accipiat a in nullo c esse, ut puta, si dicat: nulla qualitas est color, falsa erit propositio. Minor autem erit vera, scilicet: omnis albedo est qualitas. Conclusio autem erit falsa, et immediatae contraria, scilicet: nulla albedo est color. Sic ergo manifestum est quod potest fieri syllogismus ignorantiae negativus in prima figura, et altera propositione falsa et utrisque.	Then (80a20) he shows how the minor can be true, the major being false. And he says that the proposition CB, namely, the minor, can be true, while the major is false. For since this proposition, “Every B is A,” whose contrary is to be concluded, is immediate, it is necessary that B exist in A as a part in a whole, as “whiteness” in “color.” But it is possible to take something else in which B also exists as in a whole, though not immediately—let this other thing be “quality,” i.e., C. It is necessary, therefore, according to the aforesaid, that as between these two, namely, A and C, one should be under the other, i.e., color under quality. Now if someone assumes that A is in no C and says, “No quality is a color,” the proposition will be false. But the minor will be true, namely, “Every whiteness is a quality.” The conclusion, however, “No whiteness is a color,” will be false and contrary to an immediate proposition. And so it is clear that a negative syllogism of ignorance can be formed in the first figure when either one or both of the premises are false.
lib. 1 l. 28 n. 5 Deinde cum dicit: sed in media figura etc., ostendit quomodo syllogismus ignorantiae negativus fiat in secunda figura. Et primo, quando utraque est falsa; secundo, quando altera tantum; ibi: similiter autem et alteram esse falsam et cetera. Dicit ergo primo quod in media figura non contingit utrasque propositiones esse totas falsas. Et dicit totas falsas illas, quae sunt contrariae propositionibus veris. Et hoc probat. Quia cum debeamus concludere negativam falsam contrariam affirmativae immediatae, necesse est accipere quod haec sit vera et immediata, omne b est a, puta, omnis albedo est color. Sic autem se habentibus terminis, non potest inveniri aliquis medius terminus, qui universaliter praedicetur de uno termino, et universaliter removeatur ab altero. Detur enim quod ille terminus c universaliter removeatur ab a, et universaliter praedicetur de b; erit ergo haec vera: nullum a est c; quare et conversa erit vera: nullum c est a; sed omne b est c, ergo nullum b est a; cuius contrarium fuit suppositum.	Then (8047) he shows how a negative syllogism of ignorance is formed in the second figure. First, when both are false. Secondly, when one or the other is false (80a38). He says therefore first (8047) that in the second figure it does not happen that both propositions are entirely false. And he calls those propositions entirely false which are contrary to true propositions. He proves this: For since we are trying to conclude a false negative contrary to an immediate affirmative, we must assume that this proposition, “Every B is A,” is true and immediate, say, “Every whiteness is a color.” But with terms so related it is impossible to find a middle term which would be predicated universally of one and universally removed from the other. For suppose that the term C could be universally removed from A and universally predicated of B. Then the proposition, “No A is C,” will be true; consequently, its converse, “No C is A,” will also be true. But every B is C. Therefore, no B is A, the contrary of which was supposed.
Similiter etiam non potest esse quod universaliter removeatur a b, et universaliter praedicetur de a; quia si haec est vera: omne a est c, et conversa erit vera: quoddam c est a. Si autem haec est vera: nullum b est c, et conversa erit vera: nullum c est b. Sic ergo ex his duabus propositionibus: quoddam c est a; nullum c est b; sequitur, quoddam b non est a, quae est contradictoria eius, quae supponebatur, omne b est a. Relinquitur ergo quod impossibile est inveniri aliquod medium, quod, praedicto modo se habentibus a et b, de uno praedicetur, et ab alio removeatur. Et tamen oportet, si debeat fieri syllogismus in secunda figura, ut medium de uno extremorum praedicetur, et de alio negetur. Et ideo si ambae sunt falsae totaliter, oportet quod earum contrariae sint verae; quod est impossibile, ut probatum est.	Similarly, it cannot be universally removed from B and universally predicated of A. For if it is true that every A is C, the converse, “Some C is A,” will be true. But if it is true that no B is C, its converse, “No C is B,” will be true. So, then, from these two propositions, “Some C is A” and “No C is B,” there follows, “Some B is not A,” which is the contradictory of what was supposed, namely, that “Every B is A.” What remains, therefore, is that it is impossible to find any middle which, A and B being related in the way we have supposed, can be predicated of one and removed from the other. Yet if a syllogism is to be formed in the second figure, the middle must be predicated of one of the extremes and denied of the other. Therefore, if both are totally false, the contraries would have to be true, which is impossible as has been proved.
Nihil tamen prohibet utramque propositionem esse falsam particulariter. Puta, si accipiamus quoddam medium, quod particulariter praedicetur de a et de b, puta masculus, quod particulariter praedicatur de animali et de homine. Si ergo accipiatur c esse in omni a, puta, si accipiamus: omne animal esse masculum; et accipiamus c in nullo b esse, puta si dicamus: nullus homo est masculus; utraque propositio est falsa, non tamen totaliter, sed particulariter. Et eadem ratio est, si e converso maior sit negativa, et minor affirmativa. Ut si dicamus: nullum animal est masculum; omnis homo est masculus.	However, nothing prevents both from being false particularly: thus we may take some middle which is predicated particularly of A and of B, say “male,” which is predicated particularly of animal and of man. Now if C is taken in every A, say “Every animal is male,” and in no B, say “No man is male,” each proposition will be false, not entirely but particularly. And the same holds if, conversely, the major is negative and the minor affirmative, i.e., if we should say, “No animal is male” and “Every man is male.”
lib. 1 l. 28 n. 6 Deinde cum dicit: similiter autem alteram etc., ostendit quomodo contingit alteram esse falsam. Et primo in secundo modo secundae figurae; secundo in primo; ibi: similiter autem fit transposito et cetera. Dicit ergo primo quod contingit in hac figura alteram propositionem esse falsam indifferenter, quaecunque sit illa. Quod patet ex hoc, quia cum supponatur a per se et immediate praedicari de b, quidquid est in omni a est in omni b; sicut omne quod universaliter praedicatur de animali, praedicatur universaliter de homine. Si ergo accipiatur aliquod medium c, quod universaliter praedicetur de a, ut si dicamus: omne animal est vivum; et universaliter removeatur a b, ut si dicamus: nullus homo est vivus: patet quod a.c, quae est maior propositio, erit vera; sed b.c quae est minor, erit falsa.	Then (80a38) he shows how it happens when one is false. First, in the second mode of the second figure. Secondly, in the first mode (80b6). He says therefore first (80a38) that in this figure it occurs that either proposition may be false. This is clear from the fact that if A is supposed to be predicated per se and immediately of B, whatever is in every A is in every B, as whatever is predicated universally of animal is predicated universally of man. Therefore, if some middle, C, be taken which is universally predicated of A, say “Every animal is living,” and universally removed from B, say “No man is living,” it is evident that AC, which is the major proposition, will be true, but BC, which is the minor, will be false.
Et similiter probat quod e converso contingit maiorem esse falsam. Non enim potest esse quod aliquid universaliter removeatur a b, et universaliter praedicetur de a, terminis sic se habentibus. Dictum est enim quod si aliquid est in a universaliter, sequitur quod sit in b. Si ergo aliquid removeatur a b universaliter, non potest esse quod universaliter praedicetur de a. Sicut quod universaliter removetur ab homine, non potest universaliter praedicari de animali. Si ergo accipiatur aliquid, quod universaliter removeatur ab homine, puta, irrationale, et dicatur sic: omne animal est irrationale; nullus homo est irrationalis; sequitur quod minor propositio sit vera, et maior falsa. Sed in his terminis, maior propositio non est totaliter falsa. Potest autem accipi terminus in quo sit totaliter falsa, puta si accipiamus inanimatum pro medio.	Similarly, he proves that the converse occurs when the major is false. For it cannot be that something be universally removed from B and universally predicated of A, when the terms have that position. For it has been stated that if something is in A universally, it follows that it is also in B. Consequently, if something be removed universally from B, it cannot be that it is predicated universally of A. For example, anything universally removed from “man” cannot be universally predicated of “animal.” Therefore, if something is taken which is universally removed from man, say “irrational,” and you state that “Every animal is irrational” and “No man is irrational,” it follows that the minor proposition is true and the major false. But in these terms the major premise is not totally false. However, one can take a term in which it is totally false, for example, if we should take “inanimate” as the middle.
lib. 1 l. 28 n. 7 Deinde cum dicit: similiter autem fit etc., ostendit idem in primo modo secundae figurae, in quo maior est negativa. Manifestum est enim quod, praedictis terminis, scilicet a et b, sic se habentibus ut dictum est, quod universaliter removetur ab a, non poterit esse in nullo b. Si ergo accipiatur c medium, quod universaliter removetur ab a, et universaliter praedicetur de b; erit maior propositio vera et minor falsa. Puta si sint isti termini, inanimatum, animal, homo.	Then (80b6) he shows the same in the first mode of the second figure, where the major is negative. For it is clear that with the terms A and B so related, as was said, something universally removed from A cannot be in any B. Therefore, if a middle, C, be taken which is universally removed from A and universally predicated of B, the major will be true and the minor false. For example, if the terms are “inanimate,” “animal” and “man.”
Et similiter ostendit quod potest esse minor vera, et maior falsa. Manifestum est enim, secundum praedicta, quod id quod universaliter praedicatur de b, non potest removeri universaliter ab omni a: quia quod universaliter praedicatur de b, ad minus oportet in quodam a esse. Si ergo accipiatur c medium, quod universaliter praedicetur de b, puta, rationale, vel vivum, et universaliter negetur de a; minor propositio erit vera, scilicet: omnis homo est rationale, vel vivum. Maior autem: nullum animal est rationale, est falsa in parte; nullum animal est vivum, est falsa in toto. Deinde epilogando concludit quod syllogismus deceptivus potest fieri in immediatis, utrisque propositionibus existentibus falsis, vel altera tantum.	Similarly, he shows that the minor can be true and the major false. For it is clear, according to the aforesaid, that that which is universally predicated of B cannot be universally removed from every A, because what is universally predicated of B must be in some A at least. Therefore, if C be taken as a middle which is universally predicated of B, say, “rational” or “living,” and universally denied of A, there will be a true minor proposition, namely, “Every man is rational” or “living.” But the major, namely, “No animal is rational,” is false in part, while “No animal is living,” is false entirely. Then summarizing (80b14) he concludes that a deceptive syllogism can be formed in immediates, when both propositions are false or only one is false.