Works › Posterior Analytics, Books I–II
Volume 2 · pp. 169–170
Chapter II. Whether the syllogistic way is the way of coming into cognition of definition.
a de B praedicari cum reduplicatione de omnibus de quibus dicitur B, ut si sic syllogizetur: omne B A: omne C B in eo quod quid est: ergo omne C A in eo quod quid est. Non enim sequitur: omne C A in eo quod quid est, nisi reduplicatio in utraque ponatur praemissarum: si enim debeat sequi conclusio cum reduplicatione ejus quod quid est, oportet quod utraque praemissarum hanc eamdem habeat reduplicationem: oportet igitur, quod sicut A de B est cum reduplicatione, insit etiam in minori B de C cum reduplicatione ejus quod quid est: quia cum conclusio sit utriusque praemissarum medietas, et a majori quidem habet praedicatum, et a minori subjectum, si reduplicatio debeat esse in conclusione, oportet quod in majori sit reduplicatio ad praedicatum, et in minori ad subjectum: et tunc in conclusione erit ad utrumque. Si igitur istam reduplicationem quod quid est et quod quid erat esse, utraque praemissarum habuerit, tunc prius in praemissis in medio (quod subjicitur in prima et praedicatur in secunda) erit ista reduplicatio quod quid est quam in conclusione: et sic in praemissa petitur id quod est in principio, et sic non potest concludi quid est secundum quod quid est, impediente peccato quod est petitio principii. In praemissa enim petitur id quod est in conclusione. Non ergo potest concludi quid est in eo quod quid est per medium aliquod. Sicut in terminis specialibus hoc apparet: quia est vel contingit monstrare syllogistice quid est homo secundum quod quid est: sit enim C minor extremitas homo, A autem major extremitas sit quod quid est homo, hoc est, hominis diffinitio, sive haec diffinitio sit animal bipes, sive aliud aliquid quod sit diffinitio hominis. Si igitur syllogizatur, hoc est, debeat esse syllogismus in quo A diffinitio hominis per medium D de E, hoc est, homine debeat syllogizari, necesse est quod de omni B medio praedicetur A, quod est diffinitio hominis, et B de omni C, et tunc oportet quod et hujus praedicationis in majori et minori sit ad medium ratio (hoc est, alia diffinitio) quae etiam dicit quid est homo, sic: omne animal bipes in eo quod quid est, animal rationale mortale in eo quod quid est: omnis homo est animal bipes in eo quod quid est: ergo omnis homo est animal rationale mortale in eo quod quid est. Et sic diffinitio concluditur per diffinitionem: oportet enim reduplicationem ejus quod quid est in duabus propositionibus et primis sive praemissis considerare si debeat concludi in conclusione: et tunc incidet petitio principii. Hoc autem quod dicit hic, maxime manifestum est per conversionem, hoc est, si aliquis per convertibilia (quae tota subjecta sunt) syllogizet: quia tunc prius petitur in praemissis quam concludatur ex praemissis in conclusione si praedicto modo diffinitio de diffinito debeat concludi in eo quod quid est: si enim per conversionem (hoc est, per convertibilia) simus demonstrantes quid est animal et quid est homo, aut aliud aliquid quodlibet de numero eorum quae sunt diffinibilia (quasi diffinitio de diffinito concludi debeat) oportet quod medium sit diffinitivum: et tunc reduplicatio in majori et minori repeteret hoc quod est ex principio. Ut si aliquis diffiniat animam sic dicens, quod anima est id quod est sibi causa vivendi: et hujus daret aliam diffinitionem quae de ista concluderetur, vel e converso: et diceret, quod illud quod sibi ipsi est causa vivendi est numerus seipsum movens, sicut dixit Plato: et secundam diffinitionem dixit esse causam primae tunc syllogizando, necesse est repetere animam quae medium erit cum reduplicatione utriusque diffinitionis: quod vere (hoc est, in quantum quod vere est per diffinitionem) et sic repetitur sicut idem in praemissis et in conclusione, sic: omnis anima est numerus seipsum movens in eo quod quid est, vel in eo quod vere: omne quod est sibi ipsi causa vivendi est anima in eo quod quid est: ergo omne quod est sibi ipsi causa vivendi est numerus seipsum movens in eo quod quid est. Non enim sequitur conclusio cum reduplicatione ejus quod dicitur in eo quod quid est, si simpliciter et sine reduplicatione accipiantur praemissae: si enim B praedicatur simpliciter de C in minori propositione, ut dicatur, omne C B, tunc non erit conclusio quod A de C in conclusione dicatur in eo quod quid est: quia non sequitur: omne B A, omne C B, ergo omne C A in eo quod quid est. Sed verum erit dicere sive concludere, quod erit solum sine reduplicatione A de C conclusum, et non concludetur in eo quod quid est. Neque iterum conclusio cum reduplicatione in terminis generalibus sequitur, si dicatur A major extremitas de medio B, cum in eo quod quid est: et non fit eadem reduplicatio in minori: non sequitur conclusio cum reduplicatione medii. Quod patet, quia animal esse (hoc est, animalis diffinitio) praedicatur de hominis esse (hoc est, de hominis diffinitione) sicut etiam praedicatur animal de homine, cum dicitur omnem hominem esse animal: sed non praedicatur sic sicut ea praedicantur de se invicem quae convertibilia sunt in eo quod quid sunt, quorum unum et idem est esse per diffinitionem: et ideo una de alia concludi non potest in eo quod quid erat esse. Si quidem igitur non sic (hoc est, cum reduplicatione) accipiat in praemissis, non syllogizatur quod in conclusione A sit in C secundum hoc quod quid erat esse in substantia sive substantiali diffinitione. Si vero sic cum reduplicatione accipiat utrasque praemissarum, tunc prius erit accipiens in minori propositione quod C est in B in eo quod quid est, quam demonstretur in conclusione propter quid, cum sit de quaesitis et non de notis et notioribus: sed potius accipit et petit id quod in principio est. Sic ergo patet quod diffinitio non potest per demonstrationem vel syllogismum concludi ut diffinitio: non ergo modus introductionis et diffinitione est via syllogistica. Notandum autem quod in processu qui habitus est, petitur id quod est in principio: quia in tali processu A et B sunt idem, cum unum sit diffinitio alterius: quod significat reduplicatio facta in majori propositione: diffinitionis autem non est diffinitio, nisi diffinitio dicatur tantum aliorum nominum magis notorum positio: et sic supponere B de C in minori propositione praedicari, est idem quod supponere A de C praedicari. Supponere autem A de C praedicari, est supponere ipsum quod probare intendit: et ita petit in minori id quod est in principio. Notandum etiam quod cum dicitur, B est A in eo quod quid est, non intelligitur aliud per tales sermones nisi quod non praedicatur solum unum de altero, sed in se habet modum, quod praedicatur ut diffinitio et idem secundum esse. Adhuc autem notandum, quod cum sic syllogizetur: omne B est A in eo quod quid est: bene sequitur syllogistice, quod omne C est A in eo quod quid est: et tamen est petitio principii: nec est contra consequentiam syllogismi, sed contra probationem: non enim impedit quin sequatur conclusio, sed facit ad hoc quod non probat propositum 1.
for A to be predicated of B with reduplication concerning all things about which B is said, as if it is syllogized thus: every B is A; every C is B in that which is what it is; therefore every C is A in that which is what it is. For it does not follow, every C is A in that which is what it is, unless reduplication is placed in each of the premises; for if the conclusion with reduplication of that which is what it is ought to follow, each of the premises must have this same reduplication. Therefore it is necessary that, just as A is of B with reduplication, so in the minor B also belongs to C with the reduplication of that which is what it is; because, since the conclusion is the middle state of each premise, and from the major indeed it has the predicate, and from the minor the subject, if reduplication ought to be in the conclusion, it is necessary that in the major there be reduplication toward the predicate, and in the minor toward the subject; and then in the conclusion it will be toward each. Therefore, if each of the premises has this reduplication what it is and what it was to be, then in the premises, in the middle, which is subjected in the first and predicated in the second, this reduplication what it is will be prior than in the conclusion; and thus in the premise that which is in the principle is begged, and thus what it is cannot be concluded according as it is what it is through some middle, with the fault which is begging the principle impeding it. For in the premise that which is in the conclusion is begged. Therefore what it is in that which is what it is cannot be concluded through any middle. This appears in special terms, because it is or happens to show syllogistically what a human being is according as it is what it is. For let C, the minor extreme, be human being, but let A, the major extreme, be what human being is, that is, the definition of human being, whether this definition is two-footed animal or some other thing that is the definition of human being. Therefore if it is syllogized, that is, if there ought to be a syllogism in which A, the definition of human being, ought to be syllogized through middle D of E, that is, of human being, it is necessary that A, which is the definition of human being, be predicated of every middle B, and B of every C; and then it is necessary that for this predication in the major and minor there be an account toward the middle, that is, another definition, which also says what human being is, thus: every two-footed animal, in that which is what it is, is rational mortal animal in that which is what it is; every human being is two-footed animal in that which is what it is; therefore every human being is rational mortal animal in that which is what it is. And thus definition is concluded through definition; for it is necessary to consider the reduplication of that which is what it is in the two propositions and the first propositions or premises, if it ought to be concluded in the conclusion; and then begging the principle occurs. But what he says here is especially manifest through conversion, that is, if someone syllogizes through convertible things, which are total subjects, because then something is begged in the premises before it is concluded from the premises in the conclusion, if in the aforesaid way definition ought to be concluded of the defined in that which is what it is. For if through conversion, that is, through convertible things, we are demonstrating what animal is and what human being is, or any other thing whatever from the number of those things which are definable, as if definition ought to be concluded of the defined, the middle must be definitive; and then the reduplication in the major and minor would repeat that which is from the principle. As if someone defines soul thus, saying that soul is that which is for itself the cause of living, and he gives another definition of this which would be concluded from that one, or conversely, and says that that which is for itself the cause of living is a number moving itself, as Plato said; and then, by syllogizing, he said that the second definition was the cause of the first, it is necessary to repeat soul, which will be the middle with the reduplication of each definition, which truly, that is, insofar as what truly is through definition, is thus repeated as the same in the premises and in the conclusion, thus: every soul is a number moving itself in that which is what it is, or in that which is truly; everything that is for itself the cause of living is soul in that which is what it is; therefore everything that is for itself the cause of living is a number moving itself in that which is what it is. For a conclusion with reduplication of that which is said in that which is what it is does not follow if the premises are taken simply and without reduplication. For if B is predicated simply of C in the minor proposition, so that it is said, every C is B, then there will not be the conclusion that A is said of C in the conclusion in that which is what it is, because it does not follow: every B is A, every C is B, therefore every C is A in that which is what it is. But it will be true to say or conclude that only A will be concluded of C without reduplication, and it will not be concluded in that which is what it is. Nor again does a conclusion with reduplication in general terms follow if A the major extreme is said of the middle B with in that which is what it is, and the same reduplication is not made in the minor; a conclusion with reduplication of the middle does not follow. This is clear, because to be animal, that is, the definition of animal, is predicated of the being of human being, that is, of the definition of human being, just as animal is also predicated of human being when every human being is said to be animal; but it is not predicated in the way in which those things are predicated of one another which are convertible in that which they are, of which there is one and the same being through definition. And therefore one cannot be concluded of the other in that which it was to be. If therefore he does not take it thus, that is, with reduplication, in the premises, it is not syllogized that A is in C in the conclusion according to this, what it was to be in substance or in substantial definition. But if he takes each premise thus with reduplication, then he will be accepting in the minor proposition that C is in B in that which is what it is before it is demonstrated in the conclusion on account of what, since it belongs to the things asked and not to the known and more known things. But rather he accepts and begs that which is in the principle. Thus, therefore, it is clear that definition cannot be concluded as definition through demonstration or syllogism; therefore the mode of introduction and of definition is not the syllogistic way. But it must be noted that in the process that has been had, that which is in the principle is begged, because in such a process A and B are the same, since one is the definition of the other; and the reduplication made in the major proposition signifies this. But there is not a definition of definition, unless definition is said only to be the position of other better-known names; and thus to suppose B to be predicated of C in the minor proposition is the same as to suppose A to be predicated of C. But to suppose A to be predicated of C is to suppose the very thing that he intends to prove; and thus he begs in the minor that which is in the principle. It must also be noted that when it is said, B is A in that which is what it is, nothing else is understood through such speeches except that one is not predicated only of the other, but in itself it has the mode that it is predicated as definition and the same according to being. Moreover it must be noted that when it is syllogized thus: every B is A in that which is what it is, it follows well syllogistically that every C is A in that which is what it is; and nevertheless it is begging the principle. Nor is it against the consequence of the syllogism, but against the proof; for it does not prevent the conclusion from following, but makes for this, that it does not prove the proposed thing 1.
Notes
- From this it is clear that begging the principle does not sin against the syllogism. P. J. (Ex quo patet quod petitio principii non peccat contra syllogismum. P. J.) ↩
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