Volume 2 · pp. 177–180

Chapter V. Whether definition according to itself is demonstrable or not.

Latin (Borgnet)English

pp. 177–180

CAPUT V. Utrum diffinitio secundum se sit demonstrabilis vel non. Superius autem quatuor quaesitae sunt quaestiones, scilicet quomodo et quid est quod demonstratur, et quis modus introductionis, et quid est diffinitio, et quorum: et jam habitum est quid et quorum est diffinitio, et quis est modus introductionis: restat determinare primam quaestionem, quomodo scilicet quid est demonstretur, et an ipsa diffinitio secundum se et in eo quod quid sit demonstrabilis vel non. Et de hac quaestione prima determinantes dicimus amplius quomodo aliquis monstrabit vel demonstrabit quod quid est (hoc est, diffinitionem) in eo quod quid est: hoc enim est quaerere, utrum ipsa diffinitio secundum se demonstrabilis est, vel non? Et hic attendendum est diligenter, quoniam in hoc capitulo et translationes et verba Commentatorum valde sunt varia: et nos tres (quae magis videntur) prosequemur expositiones. Si enim sic demonstretur de aliquo, necesse est prius scire de ipso quia est, antequam sciatur quid est de ipso. Si enim nesciatur quia est, tunc non potest sciri quid est: quia esse aliquid est antequam sit quid vel quidditas ipsius: et haec duo se habent sicut esse simpliciter et esse quid: esse autem diffinitionem, ut dicit communiter Commentum Arabicum, est esse diffinitionem cujus est diffinitio. Cujus exemplum est: quia in eo quod est de homine, necesse est prius scire quia est homo, antequam sciatur quid est homo. Nisi enim sit homo in suis essentialibus principiis, sciri non potest quid sit: et ideo prius necesse est scire quia est in talibus principiis, antequam sciatur quid est: et ideo hae duae quaestiones, quia est, et quid est, ordinantur, quod quaestione quia est, oportet primum scire, utrum scilicet est in suis principiis, aut non: et tunc post hoc scietur quaestio quid est, sicut si est homo, vel non est, vel aliud quodlibet de quo scire volumus quid est. Hujus autem causa et ratio est, quia quod non est, et esse non habet in suis principiis constituentibus ipsum, nullus sciet quid est: quia ex suis principiis in quibus est, habet determinari quaestio quid est per diffinitionem. Aliquid enim significat ratio, quae, inquam, ratio est vel diffinitio secundum rei substantiam data, vel est nomen (hoc est, nominis interpretatio) quod implicite dicit esse diffiniti: sicut cum dico, tragelaphus (hoc est, hircocervus) a tragos quod est hircus, et elaphos quod est cervus: hoc enim habet nominis interpretationem ad minus: et ideo oportet, quod habeat esse secundum imaginationem in suis componentibus ipsum, ex quibus scitur quid est ipsum, quoniam est quid imaginatione hirci et cervi confictum. Quid autem sit tragelaphus secundum esse et naturae veritatem, impossibile est scire: quia secundum modum esse, qui respondet quaestioni quia est, nec habet nec habere poterit. At vero si haec quae dicta sunt ita se habent, si aliquis demonstrabit quid est in eo quod quid est, oportet supponere quia est: quia utrumque simul una demonstratione demonstrare non poterit. Detur enim quod utrumque demonstret una demonstratione: tunc qualiter hoc potest esse, quod utrumque una poterit demonstratione demonstrare? diversae enim viae sunt ostendendi haec duo: diffinitio enim dicit quid est, et demonstratio quia est, hoc de hoc (ut ante dictum est) demonstrabit quia est: et diffinitio est unum quod est via in quid est, et aliud est demonstratio quod est via in quia est cognoscendo: et ideo non potest videri qualiter eadem ratione utrumque istorum aliquis demonstrabit. Id autem quod quid est homo, et esse hominem, sive quia homo est, aliud et aliud in numero quaestionum: et alia est via ad terminandum quaestionem unam, et alia ad determinandum quaestionem aliam: et haec simul sciri non possunt: quia prius oportet scire quia est in suis principiis, antequam sciatur quid est: nec potest scire aliquis quid, nisi prius sciat quia est: et quid est scitur diffinitione, et quia est scitur demonstratione: et aliud est diffinitionis via notificans quidditatem incomplexi secundum quod quid est, et aliud demonstratio notificans et demonstrans quia est. Id autem quod quid est homo, et esse hominem, aliud quia quid est homo, significat quidditatem hominis: et esse hominem, sive etiam quia est homo, dicit hominem habere esse per praedicatum de ipso, vel negatum ab ipso ¹. Patet igitur quod in omni quod est, quia est vel esse illud, praecedit scire quid est illud, et non possunt esse simul, et unum antecedit aliud necessario. Hoc autem sic habito et supposito, postea ulterius ratiocinando procedimus et dicimus, quod necesse est quod per demonstrationem demonstretur de omni re demonstrabili quia est, nisi sit substantia quae demonstrari non potest: quia esse et ens nulla est substantia: et substantia si demonstrari posset, non demonstraretur nisi per ens: et hoc est ideo quia quid est (hoc est ens) non est genus, sed transcendens quod de substantia non ut genus praedicatur: quod si genus esset, substantia esset compositum ex genere et differentia, et haberet esse in differentiis et passionibus, et hoc esset demonstrabile de substantia per substantiae diffinitionem. Ex his igitur sequitur quod pro certo demonstratio est via ad hoc quod quid (hoc est, quod aliquid est), hoc est, qua probatur quod aliquid est, sive qua probatur quia est aliquid, et non diffinitur. Cujus signum est, quia hoc vere et nunc quibus utimur, faciunt scientiae demonstrativae mathematicae: per demonstrationem enim non demonstrat geometer quid est per diffinitionem quod significat triangulus (hoc est, trianguli diffinitionem), sed accipit illud per diffinitionem: sed quod hoc quid quod accipit, aliquid est, et quia est, demonstrat per syllogismum demonstrativum. Quaeramus igitur quid demonstrabit diffiniens, et quaeramus utrum diffiniendo monstrabit quid est, vel quia est? velut si dicam gratia exempli, utrum de triangulo diffiniens monstrabit quia est, vel quid est? Et si dicatur quod demonstrat quid est, quia aliud non potest monstrare diffiniens: cum non sit monstratum quia est, tunc sequitur quod aliquis sciens aliquid quod quid est, et secundum quod quid est diffinitione, nesciet ipsum si est: quod falsum est, quia probatum est quod quia est (quod determinat quaestionem si est) prius oportet scire: unde hoc est impossibile: et sic videtur quod diffiniens non possit demonstrare vel ostendere quid est, nisi prius ostendat quia est: sed quia est non potest ostendere: ergo nec quid est circa diffinitionem. Et ut hoc melius intelligatur, dictum sit Alfarabii in Commento Arabico est attendendum, quod quid est ostendere circa diffinitionem, est demonstrare diffinitionem: quod facere non potest diffiniens, ut praehabitum est: quia diffiniens nullo modo neque per syllogismum ostensivum, neque divisivum, neque per diffinitionem contrarii potest ostendere diffinitionem quia est. Aut ostendere diffinitionem, est ostendere quia diffinitio est hujus diffinitio. Et hoc iterum non potest facere diffiniens: quia non ponit intentionem suam circa hoc cujus sit diffinitio, sed tantum quid sit diffinitio, quod sit ex essentialibus collecta: et non studet circa hoc cujus sit vel quia sit. Hoc autem manifestum est secundum modum terminorum (hoc est, diffinitionum) quibus nunc utimur in diffinitivis: quia diffinientes non demonstrant quod quid est (hoc est, quid sit hujus vel illius diffinitio) hoc est enim demonstrare quid quod sic sit, sive quia sit, quando ostenditur cujus sit ut diffinitio. Si enim diffiniatur circulus, quod est id ex cujus medio aliquid semper est aequale: ubique enim medium circuli aequaliter distat a circumferentia, quod non convenit alicui figurae angulari: sed tunc datur diffinitio formalis circuli, quae dicit propter quid est id quod diffinitur in tali esse et quidditate, hoc est, propter quid est circulus: quia hoc directe dicit causam et esse circuli, quod medium aequaliter undique distat: et tunc sic diffiniens non demonstrat, cujus sit ista diffinitio, vel cui insit ut diffinitio, sed tantum, quod circulus tale quid sit secundum se, et secundum sui quidditatem: si enim demonstraret cujus sit ista diffinitio ut quid est, tunc diceret utrum esset aenei circuli, vel lignei: et tunc esset ipsam dicere montis aenei qui in convexo circularis est. Arabica translatio non habet montis, sed dicit, quod esset ipsum dicere, quod est ens: neque enim considerat diffiniens quando dicit quid est secundum quod quid est considerat, quia possibile sit esse in aliquo subjecto, sicut diffinit quando assignantur termini sive diffinitiones. Neque considerat diffiniens, quia illud est (hoc est, esse habet) quod diffinit (hoc est, quod sit alicujus subjecti in quo esse habeat) quando dicuntur a diffinientibus diffinitiones. Sed semper in talibus diffinitionibus formalibus licet et oportet dicere causam propter quid: quia illa est quid in talibus: et sic nunquam demonstrat quia, et non potest demonstrare quid nisi per demonstrationem sciat quia: ergo diffiniens non demonstrat quid, sed sumit ipsum. Patet ergo quod quid est in eo quod quid est, secundum se est indemonstrabile. Hujus enim est expositio Commenti Arabici: et in hanc magis consentit Boetii translatio, et etiam translatio Joannis. <marginal-label>Expositio aliorum.</marginal-label> Sunt tamen qui parum ab ista deviant expositione, in eo quidem quod quid, et quia est non sic exponunt ut dictum est: sed de quolibet dicunt oportere prius sciri quia est, quam quid est: et non est possibile, quod quia est: vel cum quid est, sciatur vel post ipsum, et hoc quidem est verum: sed cum ad hoc quod ad diffinitionem refertur quid sit, scilicet diffinitio, et quia est, magis videtur facere ad propositum: et quod quia est diffinitio sic demonstraretur cujus est, et cui inest ut diffinitio. In hoc enim est quod est ipsa diffinitio. <marginal-label>Alia expositio.</marginal-label> Alius modus est expositionis et satis conveniens, quod cum dicitur quod dicimus per demonstrationem demonstrari esse quia nisi sic dicatur substantia: substantia subjectum quod subjicitur passionibus et differentiis sicut genus substat differentiis. Talis autem substantia non demonstratur, sed esse ipsius quod est secundum aliquod praedicatum quod inest ei ut passio vel differentia quae est substantialis qualitas ipsius: esse autem tale non est substantia: eo quod non est sicut genus subjectum differentiis et passionibus. Et ex his tunc patet, quod demonstratio erit de hoc quod aliquid est, hoc est, quia aliquid est esse habet per diffinitionem: quod vere et nunc faciunt scientiae. Et per hoc probatur sicut per signum, quod ita sit: quia in scientia demonstrativa ita procedit geometer, qui accipit et supponit quid est quod per diffinitionem significat triangulus: sed quod triangulus est quid, secundum illam diffinitionem demonstrat: et sic demonstrat quia et non quid. Quaeramus igitur, quid monstrabit diffiniens? Monstrabitne quid est, vel monstrabitne quia est, velut triangulum ostendat secundum quid est? et si conceditur quod demonstrat quid est, sequitur impossibile: quia sciens quid est non demonstraret nisi sciret: et sic sciens quid est, ignorabit si est: et hoc est impossibile. Et tunc manifestum est quod diffinientes non demonstrant quid est secundum modos terminorum (hoc est, diffinitionum) qui nunc dicti sunt. Hoc autem dicimus: quia est alius modus terminorum secundum quem modum expositio nominum dicitur diffinitio, de quo in sequenti inquirimus capitulo. Hujus exemplum est, quod si circulus dicatur, quod ex medio, hoc est, a medio est aequale per differentiam, et sit convertibile cum circulo: et hoc demonstrator probat adhuc, tali ratione vel diffinitione conclusa contingit quaerere propter quid est diffinitum? si est vel propter quid est circulus? quia per illud quod sic diffinitur, non ostenditur esse: quia quod est vel esse oportet sciri ante quid est: propter quod talis diffinitio est non dicens esse quid: sicut si diceretur diffinitio montis aenei qui esse non habet. Et attende semper quod quia est non praesumitur nec praescitur ante quid est: ita quod sit in actu et secundum naturam in rebus naturalibus extra, sed quia est ante in suis principiis essentialibus: et non in illis sic sciatur, quia sic in illis non potest aliquo modo diffiniri per quid est. Mons autem aeneus et alia impossibilia simpliciter non habent esse in principiis aliquibus: et ideo talia realiter non diffiniuntur: et ideo cum tales termini assignantur a diffinientibus, non determinatur quia possibile sit esse quod dicitur cum assignant termini: neque probant quod illud est, cujus dicunt esse diffinitiones ipsi diffinientes: sed semper adhuc licet quaerere propter quid, si est quod diffinitur. Diffinitio ergo per seipsam non demonstratur. Primum quod positum est melius est, et hoc est in commento.

CHAPTER V. Whether definition according to itself is demonstrable or not. But above four questions were asked, namely how and what it is that is demonstrated, and what is the mode of introduction, and what definition is, and of what things it is; and now what definition is and of what things it is, and what the mode of introduction is, have been had. It remains to determine the first question, namely how what it is is demonstrated, and whether definition itself according to itself and in that which is what is demonstrable or not. And determining first about this question, we say further how someone will show or demonstrate what it is, that is, definition, in that which is what it is; for this is to ask whether definition itself according to itself is demonstrable or not. And here one must diligently attend, because in this chapter both the translations and the words of the Commentators are very varied; and we will pursue three expositions, those which seem better. For if it is thus demonstrated about something, it is necessary first to know about it that it is, before what it is about it is known. For if that it is is not known, then what it is cannot be known, because something's being is before it is what or its quiddity; and these two are related as being simply and being what. But to be a definition, as the Arabic Commentary commonly says, is to be a definition of that of which it is the definition. The example of this is that in that which concerns a human being, it is necessary first to know that human being is before it is known what human being is. For unless a human being is in his essential principles, it cannot be known what he is; and therefore it is first necessary to know that he is in such principles before it is known what he is. And therefore these two questions, that it is and what it is, are ordered so that by the question that it is one must first know whether namely it is in its principles or not; and then after this the question what it is will be known, as whether human being is or is not, or anything else about which we wish to know what it is. But the cause and reason of this is that no one will know what that is which is not and does not have being in its principles constituting it, because the question what it is has to be determined by definition from its principles in which it is. For an account signifies something, which account, I say, is either a definition given according to the substance of the thing, or is a name, that is, an interpretation of the name, which implicitly states the being of the defined thing; as when I say tragelaphus, that is, goat-stag, from tragos, which is goat, and elaphos, which is stag. For this has at least the interpretation of a name; and therefore it must have being according to imagination in its components, from which what it is is known, since it is some what fashioned by imagination from goat and stag. But what tragelaphus is according to being and the truth of nature, it is impossible to know, because according to the mode of being which answers to the question that it is, it neither has nor will be able to have being. But truly if these things that have been said hold in this way, if someone will demonstrate what it is in that which is what it is, he must suppose that it is, because he will not be able to demonstrate each at once by one demonstration. For let it be granted that he demonstrates each by one demonstration; then how can this be, that he will be able to demonstrate each by one demonstration? For there are diverse ways of showing these two. For definition says what it is, and demonstration that it is will demonstrate that it is, this of this, as was said before; and definition is one thing, which is the way into what it is, and demonstration is another thing, which is the way in knowing that it is; and therefore it cannot be seen how someone will demonstrate both of these by the same reason. But what human being is, and to be a human being, or that human being is, are one and another in the number of questions. And one way is for terminating one question, and another for determining another question; and these cannot be known at once, because one must first know that it is in its principles before what it is is known. Nor can someone know what unless he first knows that it is. And what it is is known by definition, and that it is is known by demonstration; and one is the way of definition making known the quiddity of the incomplex according to what it is, and another is demonstration making known and demonstrating that it is. But what human being is and to be a human being differ, because what human being is signifies the quiddity of human being; and to be a human being, or also that human being is, says that human being has being through a predicate concerning him, or negated from him ¹. Therefore it is clear that in everything that is, that it is or the being of it precedes knowing what that is, and they cannot be at once, and one necessarily precedes the other. But when this has been had and supposed thus, afterward proceeding further by reasoning we say that it is necessary that, by demonstration, that it is be demonstrated concerning every demonstrable thing, unless it is substance, which cannot be demonstrated, because being and ens is no substance. And if substance could be demonstrated, it would not be demonstrated except through ens; and this is because what it is, that is, ens, is not a genus, but a transcendent which is not predicated of substance as genus. But if it were a genus, substance would be a composite from genus and difference, and would have being in differences and properties, and this would be demonstrable of substance through the definition of substance. Therefore from these things it follows that for certain demonstration is the way to this what, that is, that something is, that is, the way by which it is proved that something is, or by which it is proved that something is, and it is not defined. The sign of this is that the mathematical demonstrative sciences, which we truly and now use, do this. For through demonstration the geometer does not demonstrate what it is through definition that triangle signifies, that is, the definition of triangle, but he accepts that through definition; but that this what which he accepts is something, and that it is, he demonstrates through a demonstrative syllogism. Therefore let us ask what the one defining will demonstrate, and let us ask whether by defining he will show what it is or that it is; as if, for the sake of example, I say whether one defining about triangle will show that it is or what it is. And if it is said that he demonstrates what it is, because the one defining cannot show anything else, since it has not been shown that it is, then it follows that someone knowing something as to what it is, and according to what it is by definition, will not know whether it is; which is false, because it was proved that that it is, which determines the question if it is, must first be known. Hence this is impossible; and thus it seems that one defining cannot demonstrate or show what it is unless he first shows that it is. But he cannot show that it is; therefore neither can he show what it is concerning definition. And so that this may be better understood, the saying of Alfarabi in the Arabic Commentary must be attended to: that to show what it is concerning definition is to demonstrate definition, which the one defining cannot do, as was previously had, because the one defining in no way can show definition that it is, neither through an ostensive syllogism, nor through a divisive one, nor through the definition of the contrary. Or to show definition is to show that the definition is the definition of this. And again the one defining cannot do this, because he does not place his intention around this, of what it is the definition, but only what definition is, namely that it is gathered from essential things; and he does not study around this, of what it is or that it is. But this is manifest according to the mode of terms, that is, definitions, which we now use in definitives, because those defining do not demonstrate what it is, that is, what the definition of this or that is; for this is to demonstrate the what, that it is thus, or that it is, when it is shown of what it is as definition. For if circle is defined, that it is that from whose middle something is always equal, for everywhere the middle of a circle is equally distant from the circumference, which does not belong to any angular figure; but then the formal definition of circle is given, which states on account of what that which is defined is in such being and quiddity, that is, on account of what circle is, because this directly states the cause and being of circle, that the middle is equally distant on every side; and then one defining thus does not demonstrate of what this definition is, or to what it belongs as definition, but only that circle is such a what according to itself and according to its quiddity. For if he demonstrated of what this definition is as what it is, then he would say whether it were of a bronze circle or a wooden one; and then it would be to say it of a bronze mountain which is circular on the convex surface. The Arabic translation does not have mountain, but says that it would be to say this, that it is being. For the one defining, when he says what it is according as he considers what it is, does not consider that it is possible for it to be in some subject, just as he defines when terms or definitions are assigned. Nor does the one defining consider that the thing is, that is, that it has being, which he defines, that is, that it belongs to some subject in which it has being, when definitions are stated by those defining. But always in such formal definitions one may and must state the cause on account of what, because that is the what in such matters; and thus he never demonstrates that it is, and he cannot demonstrate what unless he knows that through demonstration; therefore the one defining does not demonstrate what, but takes it. Therefore it is clear that what it is in that which is what it is is indemonstrable according to itself. For this is the exposition of the Arabic Commentary; and with this Boethius's translation agrees more, and also John's translation. <marginal-label>Exposition of others.</marginal-label> Nevertheless there are some who deviate a little from that exposition, in this indeed, that they do not expound what and that it is in the way that has been said, but say that concerning anything whatever one must first know that it is before what it is; and it is not possible that that it is be known either with what it is or after it. And this indeed is true; but since, for this which is referred to definition, what it is, namely definition, and that it is, seem more to contribute to the proposed matter, and because that it is a definition would thus be demonstrated, of what it is and to what it belongs as definition. For in this is what the definition itself is. <marginal-label>Another exposition.</marginal-label> Another mode of exposition is also quite fitting: that when it is said that we say being-that to be demonstrated through demonstration, unless substance is said in this way: substance is the subject that is subjected to properties and differences, just as genus stands under differences. But such substance is not demonstrated, but the being of it which is according to some predicate which belongs to it as a property or difference which is its substantial quality. But such being is not substance, because it is not like a genus subjected to differences and properties. And from these things it is then clear that demonstration will be about this, that something is, that is, because something has being through definition, which the sciences truly and now do. And through this it is proved as through a sign that it is so, because in demonstrative science the geometer proceeds thus, who accepts and supposes what it is that triangle signifies through definition; but he demonstrates that triangle is something according to that definition. And thus he demonstrates that it is and not what it is. Therefore let us ask, what will the one defining show? Will he show what it is, or will he show that it is, as if he should show triangle according to what it is? And if it is conceded that he demonstrates what it is, an impossibility follows, because one knowing what it is would not demonstrate unless he knew; and thus one knowing what it is will be ignorant if it is; and this is impossible. And then it is manifest that those defining do not demonstrate what it is according to the modes of terms, that is, definitions, which have now been stated. But we say this because there is another mode of terms according to which the exposition of names is called definition, about which we inquire in the following chapter. The example of this is that if circle is said to be what is equal from the middle, that is, from the center, through difference, and is convertible with circle, and the demonstrator proves this still, when such an account or definition has been concluded it happens to ask on account of what the defined thing is, if it is or on account of what circle is, because through that which is thus defined, being is not shown. For what is or being must be known before what it is; for this reason such a definition is not saying what being is, as if the definition of a bronze mountain, which does not have being, were stated. And always attend that that it is is not presumed or foreknown before what it is in such a way that it is in act and according to nature in external natural things, but that it is before in its essential principles. And it is not known in those principles in such a way, because thus in those principles it cannot in any way be defined through what it is. But a bronze mountain and other impossibles simply do not have being in any principles; and therefore such things are not really defined. And therefore, when such terms are assigned by those defining, it is not determined that what is said can possibly be, when they assign terms; nor do those defining themselves prove that that exists of which they say these are the definitions. But it is always still permitted to ask on account of what, if that which is defined exists. Therefore definition is not demonstrated through itself. The first thing that was posited is better, and this is in the commentary.

Notes

According to that passage of the first part of this treatise, chapter 5. For what unity is and unity's being are not the same. P. J. (Juxta illud primi hujus tract. cap. 5. Id enim quod quid est unitas et unitatem esse non est idem. P. J.) ↩