Volume 2 · pp. 193–196

Chapter XII. Whether definition and demonstration are in some way the same, and how definition is related to demonstration.

Latin (Borgnet)English

pp. 193–196

CAPUT XII. An idem sit diffinitio et demonstratio aliquo modo, et qualiter se habeat diffinitio ad demonstrationem. Nunc consequens est determinare an idem sit diffinitio et demonstratio, an non, et quomodo se habet diffinitio ad demonstrationem. Adhuc autem praemittere oportet quot et quae sunt genera diffinitionum, ut de quolibet genere sciatur qualiter se habeat ad demonstrationem. Dabimus igitur primo quatuor diffinitionum genera, et sumemus omnia illa secundum illam rationem diffinitionis de qua dicit Aristoteles, quod diffinitio generaliter dicitur ratio ipsius quod quid est, hoc est, ratio quidditatem significans: quia enim est diffinitio aliquid rei quae significatur per nomen, manifestum est quoniam etiam aliqua erit ratio ipsius communis, qua dicitur quid significat ipsum nomen: aut etiam quae est ratio altera nomina ponens ad nominis declarationem: quod idem est cum eo quod dictum est, oratio explicans nominis significationem: nomen enim habet implicite idem quod explicat oratio significationem nominis declarans, et hoc sub aliis nominibus positis quae magis nota sunt quam ipsum nomen. Haec igitur est diffinitio quaedam significans id quod dicitur per nomen, ut quid significat illud nomen quod datur triangulo secundum quod triangulus est, ab ipsius rei forma impositum: si enim esset nomen ab accidente impositum, non daretur de ipsius significatione talis ratio sive diffinitio: haec autem significat quoddam quid est, quod (hoc est, quam diffinitionem) vere habentes (in quantum per ipsam innotescit nomen) et quod genus diffinitionis vere habentes, quaerimus ulterius, quia est, vel si est: et quaerimus propter quid, quando accipimus si est. Difficile autem est per talem diffinitionem accipere: quia est res de his quae nescimus alio modo quam per nominis expositionem, quia sunt, et an sunt. Causa autem hujus difficultatis est dicta prius: quia per talem nominis expositionem de re quacumque neque scimus si est vere, neque scimus vere si non est: sed aut (hoc est tantum) secundum accidens scimus per talem rationem nominis de re si est, aut si non est. Hoc autem accidens est, quia nescimus nisi in quantum in apprehensione cadit per nomina, et non scimus per rei essentialia. Haec igitur nominis declaratio est una. Ratio autem una, hoc est, altera de re ipsa data, est duplex, secundum quod duplex est unum: est enim unum ordine et connexione multorum: unde sicut unum dicitur Ilias, hoc est, versus Homeri de historia Trojana, quae connexio est multorum, et ordine unum: et haec unitas vocatur conjunctio multorum ad invicem: et huic similis est ratio subjecti, quae datur ex genere et differentiis, ad unum ultimum complementum ordinata per modum ordinis quo potentiae plures ordinantur ad actum unum: et haec est diffinitio quae extra stat, et non ingreditur demonstrationem, ut in ante habitis diximus, et est principium demonstrationis extrinsecum. Alia vero ratio est unius vere: et hoc est unum de uno ostendens, et non est, secundum accidens (hoc est, secundum accidentalia data, sed per substantialia dicentia et quid et propter quid) sicut est diffinitio passionis, quae dicit esse unius de uno subjecto, in quo et per quod diffinitur. Una quidem harum diffinitionum est terminus, et haec est diffinitio subjecti conjungens substantialia subjecti usque ad terminum qui est ultima differentia. Unde dicitur terminus: quia est termini (hoc est, subjecti) usque ad ultimum actu terminati. Alia vero (quae est passionis terminus) est etiam passionis ratio demonstrans passionem de subjecto, et est propter quid dicens causam propter quam passio est in subjecto. Propter quod prima quidem diffinitio significat quid est subjectum, sed non demonstrat sicut ingrediens per substantivam demonstrationem, sed est principium demonstrationis stans extra et statuens subjectum et confirmans illud contra illum qui forte diceret subjectum proprium non esse. Illa vero diffinitio passionis quae posterius et post subjecti diffinitionem dicens quid et propter quid, manifestum est quoniam erit ut demonstratio ejus diffinitionis quod quid est, hoc est, illius diffinitionis quae solum dicit quid est passio: quia illa concluditur sicut et ipsa passio. Manifestum quia illa quae dicit quid et propter quid, erit ut demonstratio, positione differens a demonstratione. Hoc autem diversi diversimode exponunt. <marginal-label>Prima opinio.</marginal-label> Dicunt enim quidam breviter se absolventes, quod positione differre est per concretum et abstractum differre: quia cum in demonstratione concluditur, ut in subjecto est, oportet eam accipere in concreto sic, ignis extinctus in nube tonat. Cum autem sumitur ut diffinitio (eo quod diffinitio significat quidditatem) oportet quod significetur ut in abstracto sic, tonitru est ignis extinctio in nube, vel sonitus extincti ignis. <marginal-label>Secunda.</marginal-label> Aliter dicunt alii et subtilius, quod talis diffinitio dicens quid et propter quid, continet omnia quae sunt in demonstratione alio ordine positionis, quam in demonstratione sunt: dicendo enim sic, tonitru est in nube aquosa ignis extincti sonus continuus, ibi est subjectum demonstrationis nubes, et medium demonstrationis ignis extinctus, et major extremitas sonus continuus. Sed in hoc differt, quod extremitas quae in diffinitione est ultima, in demonstratione est prima: et subjectum quod primum est in diffinitione, est tertium in demonstratione: et minor extremitas de qua major extremitas est concludenda, et medium est positione medium. <marginal-label>Tertia.</marginal-label> Ista ergo quae dicunt, Alfarabius dicit (ut in ante habitis expositum est) quod differt positione: quia talis diffinitio in demonstratione partim ponitur in majori propositione, partim in minori, et partim in conclusione. Id enim quod dicit quid passionis tantum (quod est major extremitas) ponitur in majori: medium autem dicens propter quid, ponitur in minori cum subjecto: et subjectum et id quod dicit quid passionis, ponitur in conclusione: et ita quod continue positum est in diffinitione, interruptam et discontinuam positionem habet in demonstratione, et sic positione differt a demonstratione in qua ponitur: ita quod praepositio a dicat causam differentis positionis: quia demonstratio hoc exigit in ordine praemissarum ut sic differentem accipiat (ad ea quae in diffinitione continua sunt) positionem. Differt enim dicere in demonstratione et demonstrare id quod tonat (hoc est, quod alicui tonus inest ut passio et praedicatum) et dicere diffiniendo quid est tonitru: differunt enim dicere id quod tonat in eo quod tonat, et dicere quid est tonitru. Dicet enim sic ille qui dicit quod hoc tonat, et demonstrat quod hoc tonat, sic, quod propter hoc tonat hoc vel illud, quod extinguitur ignis in nubibus. Dicens autem diffinitive quid est tonitru, dicet quod tonitru est extinctio ignis in nubibus, hoc est, sonus extinctionis ignis in nube: quid enim passionis aliquando subticetur, eo quod manifestum est, sicut in ante habitis dictum est. Propter quod patet quod eadem ratio (hoc est, diffinitio dicens quid et propter quid) alio modo (hoc est, diverso modo) dicitur: et sic quidem demonstratio continua, hoc est, omnia habens quae diffinitio continua habet. Sic autem (hoc est, alio modo sumpta secundum positionem) continua diffinitio et dicens quid et propter quid. Tres igitur jam sunt determinatae diffinitiones, nominis scilicet et subjecti, et passionis, quae dicit quid et propter quid. Amplius adhuc praeter dictos terminos est alius terminus qui est dicens quid passionis ex solis essentialibus passionum: sicut si dicatur, quod tonitru est continuus sonus in nubibus: et talis terminus est qui est ipsius demonstrationis conclusio, quia concluditur sicut passio. Illa vero quae est in medio inter hanc et illam, quae dicit quid et propter quid, est diffinitio ipsius, quid est subjecti et est indemonstrabilis: quia neque concluditur, neque demonstrationem ingreditur. Una (hoc est, altera) quae est passionis dicens quid et propter quid, sicut syllogismus demonstrativus casu differens a demonstratione in hoc quod una pars cadit in diversum cum alia. Tertium autem terminorum genus est, quod est ipsius demonstrationis conclusio. Diffinitio igitur nominis demonstrat quid significat id quod dicitur. Diffinitio passionis dicens quid et propter quid, principium est demonstrationis ingrediens in substantiam ejus. Diffinitio autem passionis dicens quid, est sicut id quod concluditur. Diffinitio autem subjecti dicens quid subjectum, neque ingreditur, neque concluditur: et ideo medium istorum dicitur sicut dicitur medium per abnegationem extremorum. Manifestum igitur ex dictis est, et qualiter ipsius quod quid est, est demonstratio, hoc est, diffinitionis, et qualiter non: et quorum sive quarum diffinitionum sive terminorum est demonstratio, et quorum terminorum non est demonstratio. Amplius autem ulterius manifestum est ex dictis, diffinitio quot modis dicitur, et qualiter quod quid est (sive diffinitio) demonstratur (hoc est, demonstratione concluditur) et quomodo non demonstratur: quia diffinitio subjecti et passionis quae dicit quid et propter quid, non demonstratur: sed illa quae dicit quid tantum passionis demonstratur, et quorum terminorum est demonstratio, et quorum non est demonstratio. Adhuc autem ex dictis manifestum est etiam, quomodo se habet diffinitio ad demonstrationem, et quomodo contingat ejusdem esse diffinitionem et demonstrationem, quia incomplexi ejusdem sunt sicut passionis, et complexi quod est passionis dicens quid tantum diffinitio: et qualiter non contingat ejusdem esse diffinitionem et demonstrationem: et sic quae quaesita sunt in praecedentibus soluta sunt.

CHAPTER XII. Whether definition and demonstration are in some way the same, and how definition is related to demonstration. Now it is consequent to determine whether definition and demonstration are the same thing or not, and how definition is related to demonstration. Moreover one must premise how many and what the genera of definitions are, so that concerning each genus it may be known how it is related to demonstration. Therefore first we shall give four genera of definitions, and we shall take all those according to that account of definition concerning which Aristotle says that definition is generally called the account of what it is itself, that is, an account signifying quidditas. For because definition is something of the thing which is signified by the name, it is manifest that there will also be some common account of it by which it is said what the name itself signifies; or also which is an account positing other names for the declaration of the name, which is the same as what was said, an expression explaining the signification of the name. For a name implicitly has the same thing that an expression declaring the signification of the name explains, and this under other names posited which are better known than the name itself. Therefore this is a certain definition signifying that which is said through the name, as what that name signifies which is given to triangle according as it is triangle, imposed from the form of the thing itself. For if the name were imposed from an accident, such an account or definition would not be given concerning its signification. But this signifies a certain what it is, which, that is, which definition, when we truly have it, insofar as through it the name becomes known, and when we truly have that genus of definition, we ask further that it is or whether it is; and we ask on account of what when we receive whether it is. But it is difficult to receive through such a definition that the thing is from those things which we do not know in any other way than through exposition of the name, that they are and whether they are. But the cause of this difficulty was stated before, because through such an exposition of a name, concerning any thing whatever, we neither know whether it truly is, nor do we truly know whether it is not; but either, that is, only according to accident, through such an account of the name we know concerning the thing whether it is or whether it is not. But this is accidental, because we know only insofar as it falls into apprehension through names, and we do not know through the essentials of the thing. Therefore this declaration of a name is one. But one account, that is, another account given concerning the thing itself, is twofold, according as one is twofold. For there is one thing by order and connection of many things; hence just as the Iliad, that is, the verses of Homer about the Trojan history, is called one thing, whose connection is of many things and one in order, and this unity is called a conjunction of many things to one another. And similar to this is the account of the subject, which is given from genus and differences, ordered to one ultimate completion through the mode of order by which many potencies are ordered to one act. And this is the definition which stands outside and does not enter demonstration, as we have said in what was had before, and is an extrinsic principle of demonstration. But another account is of what is truly one, and this shows one thing of one thing, and is not according to accident, that is, according to accidental things given, but through substantial things saying both what and on account of what, as is the definition of a passion, which says the being of one thing concerning one subject in which and through which it is defined. One indeed of these definitions is a term, and this is the definition of the subject, joining the substantial things of the subject up to the term which is the ultimate difference. Hence it is called a term, because it is of a term, that is, of the subject, terminated in act up to the ultimate. But the other, which is the term of the passion, is also the account of the passion demonstrating the passion of the subject, and is the on-account-of-what saying the cause on account of which the passion is in the subject. For this reason the first definition indeed signifies what the subject is, but it does not demonstrate as entering through substantive demonstration; rather, it is a principle of demonstration standing outside and establishing the subject and confirming it against the one who perhaps would say that the proper subject does not exist. But that definition of the passion which is posterior and after the definition of the subject, saying what and on account of what, is manifestly as a demonstration of that definition of what it is, that is, of that definition which says only what the passion is, because that is concluded just as the passion itself also is. It is manifest that that which says what and on account of what will be as demonstration, differing from demonstration in position. But different persons expound this differently. <marginal-label>First opinion.</marginal-label> For certain people, absolving themselves briefly, say that to differ in position is to differ through the concrete and the abstract, because when it is concluded in demonstration as it is in a subject, one must receive it in the concrete thus: fire extinguished in a cloud thunders. But when it is taken as definition, because definition signifies quidditas, it must be signified as in the abstract thus: thunder is extinction of fire in a cloud, or the sound of extinguished fire. <marginal-label>Second.</marginal-label> Others speak otherwise and more subtly, that such a definition saying what and on account of what contains all things which are in demonstration in another order of position than they are in demonstration. For by saying thus, thunder is in a watery cloud the continuous sound of extinguished fire, there the subject of demonstration is cloud, and the middle of demonstration is extinguished fire, and the greater extremity is continuous sound. But it differs in this, that the extremity which is last in the definition is first in the demonstration; and the subject which is first in the definition is third in the demonstration; and the lesser extremity concerning which the greater extremity is to be concluded, and the middle, is a middle in position. <marginal-label>Third.</marginal-label> Therefore these things which they say, Alfarabi says, as has been expounded in what was had before, that it differs in position, because such a definition in demonstration is posited partly in the major proposition, partly in the minor, and partly in the conclusion. For that which says only what the passion is, which is the greater extremity, is posited in the major; but the middle saying on account of what is posited in the minor with the subject; and the subject and that which says what the passion is are posited in the conclusion. And so that which is posited continuously in definition has an interrupted and discontinuous position in demonstration, and thus it differs in position from the demonstration in which it is posited, so that the preposition from may state the cause of the differing position, because demonstration requires this in the order of the premises, that it receive a position thus different from those things which are in the continuous definition. For to say in demonstration and to demonstrate that which thunders, that is, that sound belongs to something as passion and predicate, and to say by defining what thunder is, differ. For saying that which thunders in that it thunders and saying what thunder is differ. For the one who says that this thunders and demonstrates that this thunders will speak thus: that because of this, this or that thunders, namely because fire is extinguished in clouds. But the one speaking definitively what thunder is will say that thunder is extinction of fire in clouds, that is, the sound of the extinction of fire in a cloud; for what belongs to the passion is sometimes left unspoken because it is manifest, as was said in what was had before. For this reason it is clear that the same account, that is, the definition saying what and on account of what, is said in another mode, that is, in a diverse mode; and thus indeed a continuous demonstration, that is, having all things which a continuous definition has. But thus, that is, taken in another mode according to position, it is a continuous definition and one saying what and on account of what. Therefore three definitions have now been determined, namely of the name, of the subject, and of the passion which says what and on account of what. Moreover, besides the terms already mentioned there is still another term which says what the passion is from the essentials of the passions alone, as if it is said that thunder is continuous sound in clouds. And such a term is the conclusion of the demonstration itself, because it is concluded just as the passion is. But that which is in the middle between this and that which says what and on account of what is the definition of it, what the subject is, and is indemonstrable, because it is neither concluded nor enters demonstration. One, that is, the other, which belongs to the passion and says what and on account of what, is like a demonstrative syllogism differing from demonstration by case in this, that one part falls differently with another. But the third genus of terms is that which is the conclusion of the demonstration itself. Therefore the definition of the name demonstrates what that which is said signifies. The definition of the passion saying what and on account of what is a principle of demonstration entering into its substance. But the definition of the passion saying what is as that which is concluded. But the definition of the subject saying what the subject is neither enters nor is concluded; and therefore it is called a middle among these in the way in which a middle is called so through the denial of extremes. Therefore from what has been said it is manifest both how there is demonstration of what-it-is itself, that is, of definition, and how there is not; and of which things, or of which definitions or terms, there is demonstration, and of which terms there is not demonstration. Moreover, further from what has been said it is manifest in how many ways definition is said, and how what it is, or definition, is demonstrated, that is, concluded by demonstration, and how it is not demonstrated, because the definition of the subject and of the passion which says what and on account of what is not demonstrated; but that which says only what the passion is is demonstrated, and of which terms there is demonstration and of which there is not demonstration. Moreover, from what has been said it is also manifest how definition is related to demonstration, and how it happens that there is definition and demonstration of the same thing, because they are of the same incomplex thing, as of a passion, and of the complex thing which belongs to the passion, the definition saying only what; and how it does not happen that there is definition and demonstration of the same thing. And thus the things which were asked in the preceding matters have been solved.