Authors/Thomas Aquinas/posteriorum/L1/Lect37

Lecture 37 Whether universal demonstration is stronger than particular demonstration

Latin	English
	Lecture 37 (85a12-b21) WHETHER UNIVERSAL DEMONSTRATION IS STRONGER THAN PARTICULAR DEMONSTRATION
lib. 1 l. 37 n. 1 Postquam philosophus determinavit de syllogismo demonstrativo, hic agit de comparatione demonstrationum ad invicem. Et quia scientia ex demonstratione causatur, ideo dividitur pars ista in duas partes: in prima, agit de comparatione demonstrationis; in secunda, de comparatione scientiae; ibi: certior autem scientia est et cetera. Circa primum tria facit: primo, movet dubitationem de comparatione demonstrationum; secundo, dicit quo ordine sit procedendum; ibi: primo quidem igitur etc.; tertio, prosequitur dubitationes motas; ibi: videbitur quidem igitur et cetera.	After determining about the demonstrative syllogism, the Philosopher now treats of the comparison of demonstrations one to another. And because science is caused by demonstration, his treatment is divided into two parts. In the first he treats of the comparison of demonstrations. In the second of the comparison of sciences (87a31) [L. 41]. In regard to the first he does three things. First, he raises a doubt concerning the comparison of demonstrations. Secondly, he lays down the order of procedure (85a17). Thirdly, he deals with the doubts raised (85a20).
lib. 1 l. 37 n. 2 Dicit ergo primo quod demonstratio tripliciter dividitur: uno enim modo dividitur in universalem et particularem; alio autem modo dividitur in categoricam et privativam, idest affirmativam et negativam; tertio modo dividitur in eam quae demonstrat ostensive, et in eam quae ducit ad impossibile. Est ergo quaestio in singulis divisionibus qualis potior sit.	He says therefore first (85a12) that demonstration is divided in three ways: for in one way it is divided into universal and particular; in another way into categorical and privative, i.e., affirmative and negative; in a third way into that which demonstrates ostensively and that which leads to the impossible. In each division, therefore, the question arises as to which is the stronger.
lib. 1 l. 37 n. 3 Deinde cum dicit: primum quidem igitur etc., ostendit quo ordine sit agendum; et dicit quod primo agendum est de comparatione universalis et particularis demonstrationis. Et cum hoc fuerit ostensum, tunc dicemus et de demonstratione, quae demonstrat aliquid affirmative, et de ea quae demonstrat ad impossibile; utrum scilicet affirmativa sit potior, et utrum ea quae est ad impossibile sit potior.	Then (85a17) he shows what order should be followed, saying that the comparison of universal to particular demonstration should be treated first. And when this has been done, we shall speak of demonstrations which demonstrate something affirmatively and of those which demonstrate to the impossible, namely, whether the affirmative is stronger and whether the demonstration to the impossible is stronger.
lib. 1 l. 37 n. 4 Deinde cum dicit: videbitur quidem igitur etc., prosequitur dubitationes propositas. Et primo, de comparatione demonstrationis particularis et universalis; secundo, de comparatione affirmativae et negativae; ibi: quod autem affirmativa etc.; tertio, de comparatione ostensivae et ducentis ad impossibile; ibi: quoniam autem categorica et cetera. Circa primum tria facit: primo, proponit rationes ad ostendendum quod particularis demonstratio sit potior quam universalis; secundo, solvit eas; ibi: aut primum quidem etc.; tertio, ponit rationes in contrarium; ibi: amplius si demonstratio et cetera.	Then (85a20) he deals with the problems he has proposed. First, of the comparison of the particular with the universal. Secondly, of the comparison of the affirmative with the negative (86a32) [L. 39]. Thirdly, of the comparison of the ostensive with that which leads to the impossible (87a1) [L. 40]. Concerning the first he does three things. First, he proposes reasons to show that the particular demonstration is more powerful than the universal. Secondly, he solves them (85b4). Thirdly, he gives reasons to the contrary (85b22) [L. 38].
lib. 1 l. 37 n. 5 Circa primum ponit tres rationes, dicens quod quibusdam forte videbitur per has rationes immediate ponendas, quod particularis demonstratio sit dignior quam universalis. Et prima ratio talis est. Illa demonstratio est potior, per quam maxime scimus. Et hoc sic probat, quia virtus demonstrationis est scire. Dicitur enim virtus uniuscuiusque id quod ultimum potest, sicut hominis qui potest ferre centum libras, virtus non est quod ferat decem, sed quod ferat centum, quod est ultimum suae potentiae, ut dicitur in I de coelo et mundo. Hoc autem est maximum quod potest facere demonstratio, scilicet quod faciat scire. Unde haec est virtus demonstrationis. Unumquodque autem tanto perfectius est, quanto magis attingit ad propriam virtutem, ut patet in VII Physic. Unde manifeste patet haec propositio, quod tanto est demonstratio potior, quanto magis facit scire. Assumit autem quod magis scimus unumquodque cum cognoscimus ipsum secundum se, quam quando cognoscimus ipsum secundum aliud: ut puta, cum cognoscimus de Corisco quod ipse Coriscus est musicus, magis hoc scimus quam si sciamus solum quod homo est musicus. Et ista etiam propositio simpliciter vera est, quia semper id quod est per se, prius est eo quod est per aliud et causa eius, ut habetur in VIII Physic.	In regard to the first he sets forth three reasons, remarking that in virtue of these reasons to be set down forthwith, it will perhaps seem to some that a particular demonstration is of more value than a universal one.The first reason (85a20) is this: That demonstration is stronger through which we know best in a scientific way. And he proves it on the ground that the strength of a demonstration consists in knowing in a scientific way. For the most that a thing can do is called its strength: for the strength of a man able to carry 100 pounds is not that he can carry ten but that he can carry 100, which is the limit of his power, as it is stated in On the Heavens I. Now the most that a demonstration can do is to cause scientific knowledge; consequently, that is the strength of a demonstration. But a thing is more perfect to the extent that it attains the strength appropriate to it, as is clear from Physics VII. Hence this proposition is quite evident, namely, that the better a demonstration causes scientific knowledge, the stronger it is. (He assumes that we know a thing better when we know it according to itself than when we know it according to something else: thus we know more in regard to Coriscus when we know that Coriscus himself is a musician than when we merely know that some man is a musician). And this proposition is true, absolutely speaking, because that which is per se is always prior to and the cause of that which is through something else, as it is stated in Physics VIII.
Ex his autem subintelligitur conclusio, quod potior est demonstratio, quae facit scire aliquid secundum se, quam quae facit scire aliquid secundum aliud. Demonstratio autem universalis demonstrat aliquid et facit scire non secundum ipsum, sed secundum aliud, scilicet secundum universale; sicut quod triangulus duorum aequalium laterum, qui est isosceles, habet tres, non quia est isosceles, sed quia est triangulus. Particularis autem demonstratio demonstrat de aliqua re particulari secundum seipsam. Unde sequitur, secundum praemissa, quod particularis demonstratio sit potior quam universalis.	From these facts the conclusion is gathered that a demonstration which makes one know something according to itself is stronger than one which makes one know something according to something else. But a universal demonstration demonstrates and makes one know something not according to itself, but according to something else, namely, according to the universal, as that a triangle with two equal sides, i.e., an isosceles, “has three,” not because it is isosceles but because it is a triangle. A particular demonstration, on the other hand, demonstrates about a particular thing according to itself. Hence according to this it follows that a particular demonstration is stronger than a universal.
lib. 1 l. 37 n. 6 Secundam et tertiam rationem ponit ibi: amplius si universale quidem etc., quae talis est. Universale non est aliquid praeter singularis, ut probatur in VII Metaphys. Demonstratio autem universalis facit opinionem, ex ipso modo suae demonstrationis, quod sit aliquid et quaedam natura in entibus; puta cum demonstrat aliquid de triangulo praeter particulares triangulos, et de figura praeter particulares figuras, et de numero praeter particulares numeros.	Then (85a31) he gives a second reason. It is this: The universal is not something apart from singulars, as was proved in Metaphysics VII. But a universal demonstration leads one to think, from the very manner of its demonstration, that the universal is “something,” i.e., a certain nature in the realm of beings: for example, when it demonstrates something of triangle apart from particular triangles, and of number apart from particular numbers.
Praemissis autem duabus propositionibus addit alias duas. Nam primae propositioni, quae dicebat quod universale non est aliquid praeter singularia, addit hanc propositionem, quod potior est demonstratio, quae est de ente, quam illa quae est de non ente. Secundae autem propositioni, quae dicebat quod demonstratio universalis facit opinionem quod universale sit aliquid in rerum natura, addit aliam propositionem, scilicet quod demonstratio, quae non facit errare, est potior quam ea per quam erratur.	To these two propositions he adds two others: to the first one, which stated that the universal is not something apart from the singulars, he adds this proposition, namely, that a demonstration concerned with being is stronger than one concerned with non-being. But to the second proposition, which stated that a universal demonstration leads one to think that a universal is something existing as a real nature, he adds another proposition, namely, that a demonstration which does not cause error is stronger than one which leads to error.
Et ostendit quod propter demonstrationem universalem erratur, quia procedentes secundum demonstrationem universalem demonstrant de aliquo universali sicut de quodam analogo; idest sicut de quodam communi, quod proportionaliter se habet ad multa, quasi sit aliquid commune, quod neque est linea, neque numerus, neque solidum, idest corpus, neque planum, idest superficies, sed aliquid praeter haec, idest ipsa quantitas universalis; vel, aliquid propter haec, idest quod necesse est ponere ad hoc quod ista habeant rationem quantitatis.	Then he shows that one is led into error on account of a universal demonstration, because one who proceeds according to a universal demonstration demonstrates concerning some universal as of some analogue, i.e., as of something common which is referred to many things proportionally, as though there existed something common which is neither a line nor a number nor a solid, i.e., a body, nor a plane, i.e., a surface, but “something apart from these,” i.e., a universal quantity; or “something owing to them,” i.e., something which must be posited, if they are to have the formality of quantity.
Sic igitur secundum duo media, quasi duplici ratione concludit unam conclusionem, dicens quod si universalis demonstratio ita se habet, quod minus est de ente quam particularis, et magis facit opinionem falsam quam particularis; sequitur ex his duobus mediis quod universalis sit indignior quam particularis.	Thus, therefore, in virtue of two middles, equivalent as it were to two arguments, he concludes to one conclusion, saying that if the universal demonstration is as described, i.e., is less an entity than the particular, and more likely to create a false opinion than the particular, it follows from these two middles that the universal ranks lower than the particular.
lib. 1 l. 37 n. 7 Deinde cum dicit: aut primum quidem nihil etc., solvit praedictas rationes per ordinem. Et primo primam, dicens quod primum quidem, idest secundum quod procedebat prima ratio, non habet aliam rationem in universali quam in particulari; quia utrobique invenitur secundum se et secundum aliud. Et manifestat quod in universali inveniatur secundum se. Habere enim tres angulos aequales duobus rectis non convenit isosceli secundum se, idest secundum quod isosceles est, sed secundum quod est triangulus; et ideo qui cognoscit quemdam triangulum habere tres, scilicet isoscelem, minus habet cognitionem de eo quod est per se, quam si cognoscat quod triangulus habet tres. Et hoc est universaliter dicendum, quod si aliquid non insit triangulo secundum quod est triangulus, et demonstretur de eo, quidquid sit illud, non erit vera demonstratio. Si autem insit ei secundum quod est triangulus, cognoscens in universali de triangulo secundum quod huiusmodi, perfectiorem cognitionem habet.	Then (85b4) he solves these reasons in order. First, he solves the first one, saying that the first, i.e., the ground on which the first reason rests, is no different in the universal than in the particular, because in both cases we find something which is according to itself and something according to something else. And he shows that something which is according to itself is found in the universal. For “to have three angles equal to two right angles” does not belong to isosceles according to itself, i.e., precisely as isosceles, but according as it is a triangle. Consequently, one who knows that a certain triangle, namely, the isosceles, “has three,” has less knowledge of that which is per se than if he knew that a triangle “has three.” And it must be admitted universally that if there be any characteristic which does not belong to triangle as triangle, but that characteristic is nevertheless demonstrated of it, the demonstration will not be true. But if it is in it precisely as it is a triangle, then by knowing it in a universal way of triangle precisely as of triangle, he has a more perfect knowledge.
Ex his igitur concludit quamdam conditionalem, in cuius antecedenti tria ponuntur. Quorum unum est quod triangulus sit in plus quam isosceles; secundum est quod triangulus praedicetur de isoscele et aliis secundum eamdem rationem et non aequivoce; tertium est quod habere tres angulos aequales duobus rectis insit omni triangulo. Et his tribus suppositis, consequens est quod habere tres non conveniat triangulo in quantum est isosceles, sed e converso.	From these facts, therefore, he concludes a conditional statement in whose antecedent three things are placed: one is that “triangle” is in more things than isosceles is; the second is that “triangle” is predicated of isosceles and of those others according to the same formality and not equivocally; the third is that “having three angles equal to two right angles” is present in every triangle. With these three suppositions, the consequent is that “the having of three” does not belong to triangle precisely as it is isosceles, but vice versa.
Apposuit autem prima duo in antecedente, quia si triangulus non esset in plus, vel si aequivoce praedicaretur de pluribus, non compararetur ad isoscelem sicut universale ad particulare. Tertium autem addit, quia si habere tres non conveniret omni triangulo, non conveniret ei in quantum triangulus, sed in quantum aliquis triangulus. Sicut hoc ipsum quod est habere tres, quia non convenit omni figurae, non convenit figurae in quantum est figura, sed in quantum est figura quaedam, quae est triangulus.	Now the first two were put in the antecedent on the ground that if “triangle” were not the wider term or if it were predicated equivocally of its several inferiors, it would not be compared to “isosceles” as universal to particular. But he added the third, because if “having three” did not belong to every triangle, it would not belong to isosceles precisely as triangle, but in virtue of being a certain triangle; just as the characteristic of “having three” does not belong to every figure precisely as figure, but because it is a certain figure which is a triangle.
Ex his igitur concludit oppositum eius quod obiectio supponebat, scilicet quod ille qui scit in universali, magis cognoscit rem per se et in quantum huiusmodi, quam ille qui cognoscit in particulari. Et ex hoc ulterius concludit principale propositum, scilicet quod potior sit demonstratio universalis quam particularis.	From these statements, therefore, he concludes to the opposite of that which the objection presupposed, namely, he concludes that one who knows in the universal knows the thing per se and as such in a better way than one who knows in the particular. And from this he further concludes his chief proposition, namely, that universal demonstration is stronger than particular.
lib. 1 l. 37 n. 8 Secundam rationem solvit ibi: amplius si quidem sit quaedam etc., et dicit quod si universale praedicatur de pluribus secundum unam rationem et non aequivoce, universale quantum ad id quod rationis est, idest quantum ad scientiam et demonstrationem, non erit minus ens quam particulare sed magis: quia incorruptibile est magis ens quam corruptibile; ratio autem universalis est incorruptibilis; particularia autem sunt corruptibilia, quibus accidit corruptio secundum principia individualia, non secundum rationem speciei, quae communis est omnibus et conservatur per generationem. Sic igitur quantum ad id quod rationis est, universalia magis sunt entia quam particularia. Quantum vero ad naturalem subsistentiam, particularia magis sunt entia, quae dicuntur primae et principales substantiae.	Then (85b15) he answers the second reason, saying that if the universal is predicated of several according to one formality and not equivocally, the universal, so far as its formality is concerned, i.e., so far as science and demonstration are concerned, will not be less of an entity than the particular, but more. For the incorruptible is more a being than the corruptible; but the formality of a universal is incorruptible, whereas particulars are corruptible, in that they are subject to corruption as to their individual principles, although not as to the formality of the species, which is common to all and conserved through generation. And so in regard to that which pertains to their formality, the universals are beings to a higher degree than particulars. Nevertheless, in regard to natural subsistence the particulars, which are called the first and chief substances, have more being.
lib. 1 l. 37 n. 9 Tertiam rationem solvit ibi: amplius neque una necessitas etc., et dicit quod quamvis in propositionibus vel demonstrationibus universalibus significetur aliquid unum secundum se, puta triangulus, nulla tamen necessitas est quod propter hoc aliquis opinetur quod triangulus sit quoddam unum praeter multa; sicut in his quae non significant substantiam, sed aliquod genus accidentis, cum ea absolute significamus, puta dicendo albedinem, vel paternitatem, non propter hoc cognoscimus aliquem opinari quod huiusmodi sint praeter substantiam. Intellectus enim potest intelligere aliquid eorum, quae sunt coniuncta secundum rem, sine hoc quod actu intelligat aliud, nec tamen intellectus est falsus. Sicut si album sit musicum, possum intelligere album et aliquid attribuere ei et demonstrare de ipso, puta quod sit disgregativum visus, nulla consideratione habita de musico. Si tamen aliquis intelligeret album non esse musicum, esset intellectus falsus. Sic igitur cum dicimus aut intelligimus quod albedo est color, nulla mentione facta de subiecto, verum dicimus. Esset autem falsum si diceremus, albedo, quae est color, non est in subiecto. Et similiter cum dicimus homo est animal, vere loquimur, non facta mentione de aliquo particulari homine. Esset tamen falsum si diceremus, homo est animal, existens separatus a particularibus hominibus. Si autem hoc est, ergo sequitur quod demonstratio non sit causa falsae opinionis, qua quis opinatur universale esse extra singularia, sed audiens, qui male intelligit. Unde ex hoc nihil derogatur universali demonstrationi.	Then (85b18) he answers the third reason, saying that although in propositions or demonstrations that are universal, something which is one according to itself, say “triangle,” is signified, nevertheless there is no need for anyone to suppose on this account that “triangle” is some one thing apart from the many, any more than there is need in the case of things which do not signify substance but some genus of accident (when we signify them absolutely, as when we say “whiteness” or “fatherhood”), to suppose that such things exist apart from the substance. For the intellect is able to understand one of the things which are joined in reality without actually thinking of some other one; yet the intellect is not false. Thus, if something white is musical, I am able to think of the white and attribute something to it and demonstrate something of it, say, that it disperses the vision, without adverting at all to musical. However, if one were to understand that the white one is not musical, then the intellect would be false. And so when we say or understand that whiteness is a color, no mention being made of the subject, we are saying something true. But it would be false, were we to say that the whiteness which is a color is not in a subject. In like fashion, when we say that every man is an animal, we are speaking truly, even though no particular man is mentioned. But it would be false were we to say that man is “an animal existing apart from particular men.” And if this is so, it follows that demonstration is not the cause of the false opinion according to which someone supposes that the universal is some thing outside the singulars, but it is rather the hearer who understands incorrectly. Hence this does not detract at all from universal demonstration.