Works › Posterior Analytics, Books I–II
Volume 2 · pp. 97–99
Treatise IV, Chapter III Continuation. How A Syllogism Of Ignorance Is Made In The First Figure Concerning Immediate Negatives
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est A C sit falsa. Hoc autem contingit. Et si dicatur quod B quod est postremum, et in A primo et in C medio erit, ita scilicet quod B postremum sit sub A primo et C medium scilicet sub B postremo: tunc enim necesse est quod A sit sub C, vel e converso: sic enim necesse est alterum sub altero esse. Tali autem facta terminorum dispositione, si accipiat aliquis A majorem extremitatem in nullo C esse medio, falsa erit propositio major quae est, nullum C est A, et est immediate falsa: et quia aliquando A sub C est, ideo aliquod C est A, propter quod haec falsa erit, nullum C est A, quae est major et minor vera: omne B est C, et sequitur conclusio falsa, ergo nullum B est A. Termini autem in quibus hoc declaratur, sunt generalissimum, et hujus principium dividens ipsum in species cum tertio proprie proprio ejusdem generis, sic in secundo primae: nullum susceptibile contrariorum est substantia: omne corporeum est susceptibile contrariorum: ergo nullum corporeum est substantia. Manifestum est igitur quoniam et cum altera, quaecumque sit falsa, et etiam utrisque falsis existentibus, erit in prima figura talis ignorantiae syllogismus.
Notandum est autem quod haec negativa, nullum B est A, potest esse immediate falsa, B minori extremitate existente in aliquo toto: non tamen potest esse vera, B minori extremitate existente in aliquo toto: quia sicut affirmativa est immediate vera, sic sua negativa est immediate falsa: sed affirmativa non est immediate vera, nisi suum subjectum sit in aliquo toto immediate: ergo negativa non potest esse immediate falsa, nisi subjectum sit in aliquo toto. Manifestum est igitur quoniam et cum altera falsa sit, et etiam in utrisque falsis erit syllogismus falsus secundum hanc ignorantiam.
Qualiter autem talis ignorantiae syllogismus fiat in media figura ut intelligatur, praemittere oportet quod in media figura in duobus primis modis qui sunt universales, concluditur negativa universalis quae cum sit ignorantiae syllogismus, contraria contra quam concludit erit universalis affirmativa. Hoc autem supposito, dicimus quod in media figura tali hypothesi facta qualis a principio istius capituli facta est (quod scilicet A et in C et in B sit) totas propositiones praemissas sive universaliter non contingit esse falsas, ita quod utraque sit tota falsa: cum enim A in omni B sit, ut dicit hypothesis, ut scilicet illa propositio sit vera, omne B est A, tunc nihil potest accipi pro medio quod in altero quidem omni, in altero autem nullo sit: quod tamen exigitur in primis duobus modis secundae figurae, in quibus solum potest esse syllogismus ignorantiae: si enim omne B est A, sequitur quod quidquid inest A hoc inest B, quia quando alterum de altero dicitur ut de subjecto, quidquid dicitur de praedicato, dicitur etiam de subjecto: et sic nihil dicibile est de praedicato universaliter, quod de subjecto universaliter removeatur.
Adhuc si omne B est A, tunc per tertiam figuram sequitur quod inest B particulariter alicui A, et sic quod universaliter inest B non potest universaliter removeri ab A, ergo nihil erit accipere quod in altero quidem sit omni, in altero autem nullo sit: et sic in duobus primis modis secundae figurae, in quibus una est universalis affirmativa et altera universalis negativa, non possunt esse propositiones praemissae in toto falsae: sicut enim in Prioribus Analyticis dictum est, in duobus primis modis secundae figurae oportet recipere sic propositiones praemissas, quod in una earum medium in hoc quidem uno extremo in toto sit, in alio autem extremo in toto non sit: quia uterque illorum modorum constat ex una universali affirmativa, et altera universali negativa: et ideo dicto modo oportet accipere propositiones si vere debeat in primis duobus modis in secunda figura fieri syllogismus. Sit enim A major extremitas, et C sit medium, et B sit minor extremitas, sicut in ante habitis positum est: tunc si ambae praemissae sunt in toto falsae, hae scilicet, omne A est C, nullum B est C, tunc contrariae earum erunt in toto verae, hae scilicet, nullum A est C, omne B est C: sed in istis veris contrariis jam primo removetur C ab A universaliter et de omni, in secunda significatur inesse omni A universaliter: et sic idem vere erit dicibile de altero omni et de reliquo nullo: quod impossibile est, cum jam positum sit omne B esse A.
the one which is A C is false. But this happens. And if it is said that B, which is the last, will be both in A the first and in C the middle, namely in such a way that B the last is under A the first and C the middle is under B the last, then it is necessary that A be under C, or conversely; for in this way it is necessary that one be under the other. But with such a disposition of terms made, if someone accepts A the major extreme as being in no C the middle, the major proposition which is "no C is A" will be false, and it is immediately false. And because sometimes A is under C, therefore some C is A; on account of this this proposition, "no C is A," will be false, and it is the major, while the minor is true: every B is C; and the false conclusion follows: therefore no B is A. But the terms in which this is declared are a most general thing, and the principle of this dividing it into species, together with the third thing, the proper property of the same genus, thus in the second mode of the first figure: no thing susceptible of contraries is substance; every corporeal thing is susceptible of contraries; therefore no corporeal thing is substance. Therefore it is manifest that both when one premise, whichever one is false, and also when both are false, such a syllogism of ignorance will exist in the first figure.
But it must be noted that this negative, no B is A, can be immediately false while B, the minor extreme, exists in some whole; nevertheless it cannot be true while B, the minor extreme, exists in some whole, because just as the affirmative is immediately true, so its negative is immediately false. But the affirmative is not immediately true unless its subject is immediately in some whole; therefore the negative cannot be immediately false unless the subject is in some whole. Therefore it is manifest that both when one premise is false, and also when both are false, there will be a false syllogism according to this ignorance.
But in order that one may understand how such a syllogism of ignorance is made in the middle figure, it is necessary to premise that in the middle figure, in the first two modes which are universal, a universal negative is concluded; and since this is a syllogism of ignorance, the contrary against which it concludes will be a universal affirmative. But with this supposed, we say that in the middle figure, when such a hypothesis has been made as was made from the beginning of this chapter, namely that A is both in C and in B, the premise propositions cannot be wholly or universally false, so that each is wholly false. For since A is in every B, as the hypothesis says, namely so that this proposition is true, every B is A, then nothing can be accepted for a middle which is in the one extreme universally and in the other extreme not at all. Nevertheless this is required in the first two modes of the second figure, in which alone there can be a syllogism of ignorance. For if every B is A, it follows that whatever is in A is in B, because when one thing is said of another as of a subject, whatever is said of the predicate is also said of the subject; and so there is nothing sayable of the predicate universally that is universally removed from the subject.
Moreover, if every B is A, then through the third figure it follows that B is particularly present in some A; and thus what is universally present to B cannot be universally removed from A. Therefore there will be nothing to accept which is in one of them universally and in the other not at all. And so, in the first two modes of the second figure, in which one premise is a universal affirmative and the other a universal negative, the premise propositions cannot be false in whole. For, as was said in the Prior Analytics, in the first two modes of the second figure it is necessary to receive the premises in such a way that in one of them the middle is in this one extreme in the whole, but is not in the whole of the other extreme, because each of those modes consists of one universal affirmative and the other universal negative. And therefore the propositions must be accepted in the aforesaid way if a syllogism truly ought to be made in the first two modes in the second figure. For let A be the major extreme, and let C be the middle, and let B be the minor extreme, as was posited in the preceding matters. Then if both premises are wholly false, namely these, every A is C, no B is C, then their contraries will be wholly true, namely these: no A is C, every B is C. But in these true contraries, first C is already removed from A universally and of every one, and in the second it is signified to be present to every A universally. And thus the same thing will truly be sayable of the whole of one and of none of the remaining one, which is impossible, since it has already been posited that every B is A.
Sed utramque propositionem nihil prohibet in quodam esse falsam in primis duobus modis secundae figurae in ignorantiae syllogismo, ut scilicet si C medium tam in A majori extremitate, quam in B minori extremitate sit quodam, hoc est, particulariter et non universaliter: si enim tunc C accipiatur esse in omni A et universaliter, et idem C medium accipiatur in nullo B esse universaliter, utraeque propositiones erunt falsae in parte: non tamen totae sive universaliter erunt falsae, sed non in toto falsae erunt, sed in quodam sive particulariter: et hoc est in secundo secundae.
Similiter autem potest fieri in primo secundae si e converso secundo modo ponatur privativa propositio pro majori, et universalis affirmativa pro minori propositione, alteram falsam in toto et alteram veram in toto quamlibet sive majorem sive minorem contingit ad concludendum ignorantiae syllogismum contra universalem affirmativam. Et hoc ostendamus primo in secundo secundae quomodo fit ex majori vera et ex minori falsa: si enim C medium insit et omni B, quia quod inest in omni A hoc etiam est in omni B, quod B est sub A, ut dicit hypothesis. Tali igitur facta dispositione, si accipiatur C omni A inesse in majori propositione quae dicit quod omne A est C (tunc enim C in toto est A) et accipiatur idem C medium in B toto non inesse, sic, nullum B est C, et concludatur quod nullum B est A, quae est contraria illi, omne B est A, tunc propositio illa major quae quidem est A C erit vera: sed minor quae est B C erit falsa. Termini autem in quibus hoc est manifestum, sunt generalissimum, et ejus species contenta, et propria passio ipsius generis, sic, omnis substantia susceptibilis contrariorum: nullum corpus susceptibile contrariorum: ergo nullum corpus substantia.
But nothing prevents each proposition from being false in a certain respect in the first two modes of the second figure in a syllogism of ignorance, namely if C the middle is in some respect both in A the major extreme and in B the minor extreme, that is, particularly and not universally. For if C is then accepted as being in every A and universally, and the same C the middle is accepted as being in no B universally, each proposition will be false in part. Yet they will not be wholly or universally false, but they will be false not in the whole, but in a certain respect or particularly; and this is in the second mode of the second figure.
Similarly, however, this can be done in the first mode of the second figure if, conversely to the second mode, a privative proposition is posited for the major, and a universal affirmative for the minor proposition. It happens that either one, whether the major or the minor, is false in whole and the other true in whole for concluding a syllogism of ignorance against a universal affirmative. And let us show this first in the second mode of the second figure, how it is made from a true major and from a false minor. For if C the middle is present also to every B, because what is present in every A is also present in every B, because B is under A, as the hypothesis says. Therefore with such a disposition made, if C is accepted as being present to every A in the major proposition, which says that every A is C, for then C is in the whole A, and the same C the middle is accepted as not being in the whole B, thus, no B is C, and it is concluded that no B is A, which is contrary to that proposition, every B is A, then that proposition which is the major, A C, will indeed be true; but the minor which is B C will be false. But the terms in which this is manifest are a most general thing, its contained species, and the proper property of the genus itself, thus: every substance is susceptible of contraries; no body is susceptible of contraries; therefore no body is substance.
Item in eodem modo ostenditur, quod fit ignorantiae syllogismus contra universalem affirmativam majori existente falsa et minori vera. Si enim accipiatur minor universalis negativa, ita quod C in nullo sit B. Si enim hoc ponitur, tunc sequitur quod non in omni sit A, quia omne B est A, sicut dixit hypothesis. Unde si in A est C, sequitur quod etiam sit in B: sed jam datum erat quod non erat in B, hoc est, quod C nulli inerat B, patet ergo quod id quod nulli inest B non omni inerit A. Si igitur universaliter et affirmative accipiatur C in toto esse A, sic, omne A est C in majori propositione: et accipiatur idem C in toto B non inesse, ita quod nullum B est C, sequitur quod nullum B est A in secundo modo secundae figurae, sicut prius: et erit propositio minor quae est B C vera: altera autem quae est A C erit falsa. Termini autem in quibus hoc est manifestum, sunt duo generalissima, et proprium alterius eorum, sic, omnis substantia est quantitas: nullum susceptibile contrariorum est quantitas: ergo nulla substantia est susceptibilis contrariorum.
Similiter autem fit iste ignorantiae syllogismus in primo secundae figurae transposito privativo termino: ita quod major sit negativa universalis, et minor affirmativa: ita quod major sit vera, et minor falsa. Prima enim hypothesi servata, quod B sit sub A, sequitur necessario quod id quod universaliter in nullo non est A quod hoc idem in nullo B est. Si igitur taliter se habentibus terminis accipiatur C medium in toto quidem A non esse, sic, nullum A est C, et accipiatur in toto B esse, sic, omne B est C, concludetur quod nullum B est A, et erit quae est A C major propositio vera: alia autem quae est B C minor propositio, erit falsa. Termini autem iidem sunt qui proxime superius suppositi sunt, sic, nulla substantia est quantitas: omne susceptibile contrariorum est quantitas: ergo nullum susceptibile contrariorum est substantia.
Et iterum in eodem modo fit ignorantiae syllogismus ex majori falsa in minori vera: hypothesi enim prima servata, quod omne B sit A, contra hanc debet fieri ignorantiae syllogismus: positione enim servata tali, tunc C medium quod in omni B est non potest vere accipi in nullo A inesse: quia aliquod A est B, unde in nullo A illud accipere est falsum: necesse est enim si in omni A est, etiam in quodam A esse. Si igitur accipiatur C medium in omni quidem esse B in minori propositione: et accipiatur idem C in nullo esse A, tunc propositio minor quae est B C vera erit: major autem quae est A C erit falsa: et erit idem qui prius syllogismus. Termini sunt generalissimum, et ejus species sub ipso contenta, et proprium ejusdem, sic, nulla substantia est susceptibilis contrariorum: omne corpus est susceptibile contrariorum: ergo nullum corpus est substantia. Manifestum est igitur quod et utrisque falsis propositionibus praemissis, et altera tantum falsa potest fieri, et erit syllogismus deceptivus sive ignorantiae in individuis, hoc est, immediatis.
Likewise, in the same mode it is shown that a syllogism of ignorance against a universal affirmative is made when the major exists as false and the minor as true. For if a universal negative minor is accepted, so that C is in no B, then if this is posited, it follows that A is not in every one, because every B is A, as the hypothesis said. Hence if C is in A, it follows that it also is in B; but it had already been granted that it was not in B, that is, that C was present to no B. Therefore it is clear that that which is present to no B will not be present to every A. Therefore if C is accepted universally and affirmatively as being in the whole A, thus, every A is C in the major proposition, and the same C is accepted as not being in the whole B, so that no B is C, it follows that no B is A in the second mode of the second figure, as before. And the minor proposition which is B C will be true, but the other, which is A C, will be false. But the terms in which this is manifest are two most general things and the proper property of one of them, thus: every substance is quantity; nothing susceptible of contraries is quantity; therefore no substance is susceptible of contraries.
Similarly also this syllogism of ignorance is made in the first mode of the second figure, with the privative term transposed, so that the major is a universal negative and the minor affirmative, so that the major is true and the minor false. For with the first hypothesis preserved, that B is under A, it follows necessarily that what is universally not in no A, this same thing is in no B. Therefore, with the terms related in this way, if C the middle is accepted as not being in the whole A, thus, no A is C, and is accepted as being in the whole B, thus, every B is C, it will be concluded that no B is A; and the proposition which is A C, the major proposition, will be true, while the other, which is the B C minor proposition, will be false. The terms are the same as those supposed immediately above, thus: no substance is quantity; every thing susceptible of contraries is quantity; therefore nothing susceptible of contraries is substance.
And again in the same mode the syllogism of ignorance is made from a false major and a true minor. For when the first hypothesis is preserved, that every B is A, a syllogism of ignorance ought to be made against this. For when such a position is preserved, then C the middle, which is in every B, cannot truly be accepted as being in no A, because some A is B; whence to accept that thing as being in no A is false. For it is necessary, if it is in every A, that it also be in some A. Therefore if C the middle is accepted as indeed being in every B in the minor proposition, and the same C is accepted as being in no A, then the minor proposition which is B C will be true, but the major which is A C will be false, and it will be the same syllogism as before. The terms are a most general thing, and its species contained under it, and its proper property, thus: no substance is susceptible of contraries; every body is susceptible of contraries; therefore no body is substance. Therefore it is manifest that both with both premise propositions false, and with only one false, there can be, and there will be, a deceptive syllogism or syllogism of ignorance in individual things, that is, immediate things.
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