Works › Posterior Analytics, Books I–II
Volume 2 · pp. 170–173
Chapter III. Whether the mode of introduction into definition can be a syllogism.
CAPUT III. An modus introductionis in diffinitione possit esse syllogismus. At vero neque per divisionem (hoc est, per divisivum syllogismum) via est syllogizare diffinitionem, sicut et in prioribus resolutoriis quae circa figuras syllogismorum sunt (hoc est in primo Priorum, ubi de figuris agitur et de resolutione figurarum ad invicem) dictum est, ubi docetur inventio medii, et ubi docetur resolvi syllogismus ad propositum. Quod autem per divisivum syllogismum probari non possit, ratio quidem prima est ad hoc: quia in divisivo syllogismo nequaquam fit vel sequitur tunc illam rem esse quae conclusa est his entibus, hoc est, cum haec sint quae praemissa sunt in praemissis, hoc est, conclusio non sequitur neque probatur ex praemissis. Si autem debeat concludi diffinitio in eo quod quid est, oportet quod fiat per syllogismum probantem qui sit causa conclusionis: divisivus autem syllogismus non demonstrat, hoc est, non probat, quia ex prioribus non procedit: sicut neque inducens probat, eo quod ex prioribus non procedit: et ideo potius colligit universale quam probet: singularia enim non sunt causa universalis, sed potius per illa colligitur sicut mixtum et confusum in ipsis. In his enim quae vera et completa ratione probantur, non oportet conclusionem (postquam conclusa est) interrogare ac si non sit probata: neque oportet eam esse in concedendo, et praecipue in demonstratione per immediata facta, sive respondens concedat talem conclusionem sive non, semper erit probata et vera: sed necesse est esse conclusionem et sequi cum illa sint quae praemissa sunt, etiam si non dicat hoc concedendo respondens. Cujus exemplum est si aliquis dividens ita procedat quaerens hominis diffinitionem, et dicat primo dividendo, homo est et est animal vel non est animal, sive est animal vel inanimatum. Et postea sic arguat: sed non est non animal: ergo est animal. Sive sic: sed non est inanimatum: ergo est animatum sive animal (quia accipitur hic pro animato): tunc enim accipit quod non est non animal, et non probat: et ex hoc non probato infert quod est animal per divisionem a partibus sufficienter enumeratis: unde id quod postea accipit animal, non est syllogizatum syllogismo probante, licet aliquo modo syllogismo divisivo probatum sit: habens autem quod homo est animal, et volens ulterius procedere ad hominis diffinitionem, dividendo animal dicit: si homo est animal, aut ergo est gressibile animal, aut aquaticum sive natabile: et tunc iterum per negationem aquatilis accipit, et non probat quod homo est animal gressibile: et sic dicit hominem totum (hoc est, secundum totum esse) per diffinitionem explicantem esse animal gressibile concludens sic: homo est animal, et non animal: et homo est animal gressibile, et non aquaticum: ergo homo est per diffinitionem et in eo quod quid est, animal gressibile: hoc enim non est necesse sequi ex dictis sive praemissis: sed accipit illud sine probatione. Et hoc quia ante diximus divisionem producendo ad omnes differentias imponendas in hominis diffinitione, ut ulterius divideremus gressibile in bipes et quadrupes, et hoc ulterius in rationale vel irrationale, et hoc iterum in mortale et immortale, ut sic usque ad ultimum indivisibile deduceretur divisio, nemo calumnietur: quia quoad propositam intentionem, utrum in paucis vel in multis deducatur divisio, nihil differt: quia in omnibus est una et eadem ratio, et semper alterum dividentium accipit sine probatione: unde idem est in paucis et in multis dividere: et in sic procedentibus non fit usus syllogisticus: quia in usu syllogistico nihil accipitur, nisi quod probatur ex praemissis 1. Ratio autem hujus est: quia cum dicitur, homo est animatum vel non animatum, et negatur altera sic, non est inanimatum, tunc commune divisum cum negatione alterius dividentis ipsum idem alteri fit penitus. Quod sic patet: homo est animal vel non animal: et dicatur, homo non est non animal, idem est ac si dicatur, homo est animal: et sic ex ista, non est non animal, non probatur ista secundum rem, sed est idem illi et petitur in illa, et non probatur. Qui enim diffinitionem vult syllogizare, oportet quod syllogizet eam ex convenientibus diffinitioni: et hae sunt causae concludentes eam in eo quod quid est: et hoc non facit syllogismus divisivus. Cujus ratio est, quia quaeramus quid prohibet esse quod quidem per divisionem acceptum est, praedicari de homine: et tamen non divisim nec simul necesse est praedicari in eo quod quid est: neque propter hoc quod sic praedicantur, sunt diffinitiones ostendentes quid erat esse: non enim quidquid praedicatur de aliquo per divisionem acceptum, est diffinitio ejus. Amplius ad idem ratio est alia: quia quaeramus quid prohibet aut in divisione apponere aliquid quod non est in diffinito sicut diffiniens, et quid prohibet etiam per divisionem auferre vel omittere aliquid, quod tamen est in diffinito sicut diffiniens ipsum, quamvis in diffinitione non sit acceptum: aut quid prohibet etiam in divisione excellere, hoc est, per excellentiam dividere substantias, ut si dicatur, homo est ens. Entium autem aliud actu et aliud potentia: cum tamen excellentia non sint ponenda in diffinitione. Patet igitur quod via veniendi in diffinitionem non est syllogismus divisivus. Haec quidem igitur dimittantur, quia ad probationem propositi sufficiunt ea quae dicta sunt. Contingit solvere, ita quod dicunt per divisionem concludi diffinitionem in accipiendo omnia adjacentia in eo quod quid est praedicari de diffinito et essentialiter, et quod est sic facere divisionem in proximum id quod consequenter est priori accepto, et quod divisio fiat per substantialia et immediata, et tertio quod nihil relinquatur indivisum usque ad ultimum indivisibile in quo stat divisio quod ulterius dividi non potest. Hoc autem est necessarium, quod sic fiat et ducatur divisio, quia id in quo ultimo stat, jam oportet esse individuum sive indivisibile specie, hoc est, secundum formam, quod formaliter ulterius non possit dividi. Sed haec solutio nulla est, quia omnibus quae dicta sunt observatis, non habet divisio formam syllogismi probantis diffinitionem de diffinito esse in eo quod quid est. Syllogismus enim non ponit, neque accipit quod non est per se notum vel notius: divisio autem accipit non probatum, ut dictum est. Sed si divisio vel divisivus syllogismus verus est, cognoscere facit diffinitionem: tamen alio modo quam probando via syllogistica facit hoc: et hoc quidem non est inconveniens, neque contra ea quae dicta sunt: quia ratio inducta non dicit, quod nihil faciat ad diffinitionem, sed quod via syllogistica diffinitio ut diffinitio de diffinitione probari non potest. Hoc autem patet in syllogismo, quod etiam inducens et concludens ex inductione fortasse non demonstrat (hoc est, non vere probat) cum ex posterioribus procedat: et tamen ostendit aliquid quocumque modo ostensionis ex notis quoad sensum: unde quamvis aliquid faciat dividens ad diffinitionem, tamen syllogismum non dicit ille, qui ex divisione vult probare diffinitionem. Et hujus adhuc aliud est simile: quia sicut in conclusionibus quae concluduntur enthymematice sine mediis in quibus deest aliquid quod facit evidentiam ostensionis, si aliquis dicat, quoniam his existentibus (quae enthymematice praemissa sunt) necesse est hoc esse quod conclusum est, post conclusionem factam contingit adhuc interrogare, propter quid sequitur conclusio? eo quod medium et ordinatio propositionum in figuram et modum differunt, quae faciunt consequentiae evidentiam. Sic etiam aliquo accepto per divisionem, et conclusa tandem diffinitione contingit interrogare, propter quid sequitur conclusio? quia in divisione non sunt ea ex quibus de necessitate via syllogismi concludatur diffinitio, eo quod haec sunt sicut dictum est: unde in terminis divisis (hoc est, per divisionem acceptis) cujuslibet illationem post conclusionem contingit interrogare, propter quid sequitur conclusio? quia non est probata per praemissa, sicut patet in exemplo. Ut si quis volens diffinitionem hominis colligere, quaerit quid est homo per diffinitionem, et accipit per divisionem hanc: aut animatum, aut inanimatum: et non est inanimatum: ergo est animal: et habito quod est animal, accipiat per eumdem modum divisionis, quod est mortale: et ulterius dicendo accipiat quod est pedes habens, gressibile scilicet et non volatile, nec natatile, et hoc sine pennis, secundum unamquamque quidem appositionem differentiae per divisionem acceptae contingit quaerere, propter quid sequitur? et ideo non est probata. Dividens enim sic dicet et demonstrabit sive ostendet divisione (hoc est, quod opinatur ex divisione) ostendendo quod scilicet omne animal mortale aut immortale sit: hoc autem facit accipiendo et supponendo. Haec autem ratio omnis (hoc est, tota) sic per divisionem collecta, non est diffinitio conclusa et probata per syllogismum dico divisivum: quia non probat diffinitionem propter quid, quamvis divisione demonstravit (hoc est, aliquo modo declarationis ostendit) ea quae ponuntur in diffinitione: sed tamen diffinitio non fit syllogismus concludens diffinitionem in eo quod quid est esse. Unde in Arabica translatione illud sic est: jam ergo manifestum est quod diffinitio possibile est ut extrahatur per viam divisionis, et quia impossibile est ut sciatur per viam syllogismi. Attendendum autem est hic, quod cum syllogismus divisivus sit syllogismus dialecticus, non videtur esse peccatum in ipso, praecipue cum utraque praemissarum notior sit conclusione, cum sic dicitur, homo est animal, vel non est animal: sed non est non animal: ergo est animal: et sic non erit ibi petitio principii, ut in praehabitis dictum est. Adhuc autem communiter dicitur quod si in syllogismo divisivo probarentur praemissae, non esset petitio principii: cum autem non probatur, tunc est principii petitio: quia commune quod dividitur, est negatione alterius dividentis idem cum reliquo: et ideo petitur in ipso, ut ante dictum est. Et quamvis in tali processu non est peccatum contra syllogismum dialecticum, tamen est peccatum contra demonstrationem, quia non est per causam: cum enim sic proceditur: homo est animal, vel non animal, haec vera: et cum assumitur: sed non est non animal: ergo est animal: haec propositio, non est non animal, non est causa conclusionis: non enim est ideo animal, quia non est non animal: sed si una est causa alterius, potius e converso ideo non est non animal, quia est animal 2. <marginal-label>Quare in diffinitione ponendum sit genus proximum.</marginal-label> Attendendum etiam quod si aliquis dividendo percurrat per proximas differentias dividens prius acceptum et omittat aliquid, et primum postea conjungat sequentibus, non faciet diffinitionem explicantem totum esse rei proprie: ut si aliquis diffiniens hominem dicat, quod homo est corpus rationale mortale: multa enim inter corpus et rationale omissa sunt, quae non explicantur in diffinitione. <marginal-label>Objectio.</marginal-label> Et si objicitur quod est oratio explicans esse et convertibilis: ergo est diffinitio. <marginal-label>Solutio.</marginal-label> Respondetur quod non est proprie diffinitio, quia non potest explicari quod est in esse ipso vel quidditate; et ideo extenso nomine et non proprie dicitur diffinitio. <marginal-label>Objectio.</marginal-label> Si autem objicitur quod in qualibet diffinitione explicite secundum hoc oportet ponere omnia superiora genera usque ad ultimum. <marginal-label>Solutio.</marginal-label> Dicendum quod hoc non sequitur: quia posito genere subalterno ponuntur omnia superiora quae actu et intellectu sunt in ipso: sed non est sic de differentia, quia inferior differentia non continet in se superius genus, eo quod differentia non dicit aliquid conjunctum ex genere et differentia: et ideo non ita intelligitur genus in differentia, sicut significatur in ipsa secundum intellectum. Sed si intelligitur genus posita differentia, hoc sic intelligitur, ut potentia intelligatur posito actu: non tamen sic, quod potentia aliquis sit actus: et ideo ex genere remoto et differentiis ultimis et proximis diffinito, proprie loquendo diffinitio fieri non potest.
CHAPTER III. Whether the mode of introduction into definition can be a syllogism. But truly neither through division, that is, through a divisive syllogism, is there a way to syllogize definition, just as was said in the prior resolutory books which are about the figures of syllogisms, that is, in the first book of the Prior Analytics, where the figures are treated and the resolution of figures to one another, where the discovery of the middle is taught and where a syllogism is taught to be resolved to the proposed thing. But that it cannot be proved through a divisive syllogism, the first reason indeed is for this: because in a divisive syllogism in no way is it made or does it follow then that the thing which is concluded exists, given these beings, that is, when these are the things set forth in the premises, that is, the conclusion does not follow nor is it proved from the premises. But if a definition ought to be concluded in that which is what it is, it must be done through a proving syllogism which is the cause of the conclusion; but a divisive syllogism does not demonstrate, that is, it does not prove, because it does not proceed from prior things, just as neither does one inducing prove, because he does not proceed from prior things, and therefore he rather gathers the universal than proves it. For singulars are not the cause of the universal, but rather through them it is gathered as mixed and confused in them. For in those things which are proved by true and complete reason, one need not question the conclusion after it has been concluded as if it has not been proved; nor is it necessary that it be in conceding, and especially in a demonstration made through immediates, whether the one responding concedes such a conclusion or not, it will always be proved and true. But it is necessary for the conclusion to be and to follow when those things which are the premises are so, even if the respondent does not say this by conceding. An example of this is if someone dividing proceeds thus while seeking the definition of human being, and first by dividing says, human being is and is animal or is not animal, or is animal or inanimate. And afterward he argues thus: but it is not non-animal; therefore it is animal. Or thus: but it is not inanimate; therefore it is animate or animal, because this is here taken for animate. For then he accepts that it is not non-animal and does not prove it; and from this unproved thing he infers that it is animal through division from the parts sufficiently enumerated. Hence what he afterward accepts, animal, has not been syllogized by a proving syllogism, although in some way it has been proved by a divisive syllogism. But having that human being is animal, and wishing to proceed further to the definition of human being, by dividing animal he says: if human being is animal, then either it is a walking animal or aquatic or able to swim. And then again through the negation of aquatic he accepts and does not prove that human being is a walking animal. And thus he says the whole human being, that is, according to its whole being, by definition explaining it to be a walking animal, concluding thus: human being is animal and not non-animal; and human being is walking animal and not aquatic; therefore human being is by definition and in that which is what it is a walking animal. For this does not necessarily follow from the things said or from the premises; rather he accepts it without proof. And as to this, because before we said that division is produced to all the differences to be placed in the definition of human being, so that further we would divide walking into two-footed and four-footed, and this further into rational or irrational, and this again into mortal and immortal, so that thus division would be led down to the ultimate indivisible, let no one complain, because with respect to the proposed intention, whether division is led down in few or in many, makes no difference; for in all there is one and the same reason, and always one of the dividing members he accepts without proof. Hence it is the same to divide in few and in many; and in those proceeding thus no syllogistic use is made, because in syllogistic use nothing is accepted unless it is proved from the premises 1. But the reason for this is that when it is said, human being is animate or inanimate, and one of them is denied thus, it is not inanimate, then the common thing divided, with the negation of one of those dividing it, becomes entirely the same with the remaining one. This is clear thus: human being is animal or non-animal; and let it be said, human being is not non-animal. This is the same as if it were said, human being is animal. And thus from this, it is not non-animal, the other is not proved according to the thing, but it is the same as that and is begged in that, and it is not proved. For one who wishes to syllogize a definition must syllogize it from things fitting the definition; and these are causes concluding it in that which is what it is. And the divisive syllogism does not do this. The reason for this is that we ask what prevents what has been accepted through division from being predicated of human being, and nevertheless it is not necessary that it be predicated dividedly or at once in that which is what it is; nor because they are thus predicated are they definitions showing what it was to be. For not whatever is predicated of something, having been accepted through division, is its definition. Further, another reason for the same point is that we ask what prevents either placing in division something that is not in the defined thing as defining it, and what also prevents removing or omitting through division something which nevertheless is in the defined thing as defining it, although it has not been accepted in the definition, or what also prevents exceeding in division, that is, dividing substances by excess, as if it is said, human being is a being. But of beings one is actual and another potential, although excessive things are not to be placed in definition. Therefore it is clear that the way of coming into definition is not the divisive syllogism. Therefore let these things be left, because the things that have been said suffice for proof of the proposed thing. A solution can be made, so that they say that through division definition is concluded by accepting all adjacent things to be predicated of the defined in that which is what it is and essentially, and that it is thus to make division into the proximate thing which is consequently after what was previously accepted, and that division is made through substantial and immediate things, and third, that nothing be left undivided all the way to the ultimate indivisible in which division stops, which cannot be further divided. But it is necessary that division be made and led in this way, because that in which it finally stops must now be individual or indivisible in species, that is, according to form, which cannot formally be divided further. But this solution is nothing, because, when all the things that have been said have been observed, division does not have the form of a syllogism proving definition to be of the defined in that which is what it is. For a syllogism does not posit nor accept what is not per se known or better known; but division accepts what is not proved, as has been said. But if division or the divisive syllogism is true, it makes definition known, yet in another way than by proving by the syllogistic way it does this. And this indeed is not unsuitable, nor against the things that have been said, because the reason brought in does not say that nothing contributes to definition, but that by the syllogistic way definition as definition cannot be proved of definition. But this is clear in the syllogism, because also the one inducing and concluding from induction perhaps does not demonstrate, that is, does not truly prove, since he proceeds from posterior things; and nevertheless he shows something by whatever mode of showing from things known as to sense. Hence, although one dividing contributes something to definition, nevertheless the one who wishes to prove definition from division does not state a syllogism. And another thing is still similar to this: because just as in conclusions which are concluded enthymematically without middles, in which something is lacking that makes the evidence of the showing, if someone says that, with these things existing, namely the things premised enthymematically, it is necessary for this which has been concluded to be, after the conclusion has been made it still happens to ask, on account of what does the conclusion follow? because the middle and the ordering of propositions into figure and mode differ, which make the evidence of consequence. Thus also, when something has been accepted through division and definition finally concluded, it happens to ask, on account of what does the conclusion follow? because in division there are not those things from which definition is concluded of necessity by the way of syllogism, because these are as has been said. Hence in divided terms, that is, accepted through division, after the conclusion it happens to ask the inference of any of them, on account of what does the conclusion follow? because it has not been proved through the premises, as is clear in the example. As if someone wishing to gather the definition of human being asks what human being is through definition, and accepts through division this: either animate or inanimate; and it is not inanimate; therefore it is animal. And when it has been had that it is animal, let him accept by the same mode of division that it is mortal; and further by speaking let him accept that it has feet, namely walking and not flying nor swimming, and this without wings. According to each placing of a difference accepted through division, it happens to ask, on account of what does it follow? and therefore it is not proved. For one dividing thus will say and demonstrate or show by division, that is, what he opines from division, by showing namely that every animal is mortal or immortal; but he does this by accepting and supposing. But this whole account, that is, the total account, thus gathered through division, is not a definition concluded and proved through a syllogism, I say a divisive one, because it does not prove the definition on account of what, although by division he demonstrated, that is, showed by some mode of declaration, those things which are placed in the definition. But nevertheless the definition does not become a syllogism concluding definition in that which is what it is to be. Hence in the Arabic translation that passage is thus: now therefore it is manifest that it is possible for definition to be extracted through the way of division, and that it is impossible for it to be known through the way of syllogism. But it must be attended to here that, since a divisive syllogism is a dialectical syllogism, there does not seem to be a fault in it, especially since each premise is better known than the conclusion, when it is said thus: human being is animal or is not animal; but it is not non-animal; therefore it is animal. And thus there will not be begging the principle there, as was said in the things previously had. Moreover it is commonly said that if the premises were proved in a divisive syllogism, there would not be begging the principle; but when it is not proved, then there is begging of the principle, because the common thing which is divided, by the negation of one of those dividing it, is the same as the remaining one; and therefore it is begged in it, as was said before. And although in such a process there is not a fault against the dialectical syllogism, nevertheless there is a fault against demonstration, because it is not through a cause. For when it is proceeded thus: human being is animal or non-animal, this is true; and when it is assumed, but it is not non-animal; therefore it is animal, this proposition, it is not non-animal, is not the cause of the conclusion. For it is not animal because it is not non-animal, but if one is the cause of the other, rather conversely it is therefore not non-animal because it is animal 2. <marginal-label>Why the proximate genus must be placed in definition.</marginal-label> It must also be attended to that if someone by dividing runs through the proximate differences, dividing what was previously accepted, and omits something, and afterward joins the first thing to the following things, he will not make a definition properly explaining the whole being of the thing, as if someone defining human being says that human being is rational mortal body; for many things have been omitted between body and rational, which are not explained in the definition. <marginal-label>Objection.</marginal-label> And if it is objected that it is a speech explaining being and convertible; therefore it is a definition. <marginal-label>Solution.</marginal-label> It is responded that it is not properly a definition, because what is in the very being or quiddity cannot be explained; and therefore by an extended and not proper name it is called definition. <marginal-label>Objection.</marginal-label> But if it is objected that in any definition it is necessary according to this explicitly to place all superior genera all the way to the ultimate one. <marginal-label>Solution.</marginal-label> One must say that this does not follow, because when the subalternate genus has been posited, all superior things which are actually and intellectually in it are posited; but it is not thus with difference, because an inferior difference does not contain in itself the superior genus, because difference does not state something conjoined from genus and difference. And therefore genus is not understood in difference in the way in which it is signified in it according to understanding. But if genus is understood when difference has been posited, this is understood in such a way that potency is understood when act has been posited, yet not in such a way that potency is somehow act. And therefore from a remote genus and from ultimate and proximate differences to the defined thing, properly speaking, definition cannot be made.
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