Authors/Thomas Aquinas/posteriorum/L1/Lect38

Lecture 38 Universal demonstration is stronger than particular demonstration

Latin	English
	Lecture 38 (85b22-86a32) UNIVERSAL DEMONSTRATION IS STRONGER THAN PARTICULAR DEMONSTRATION
lib. 1 l. 38 n. 1 Postquam philosophus solvit rationes, quae sunt ad partem falsam, hic inducit rationes ad partem veram, scilicet ad ostendendum quod demonstratio universalis sit potior. Et circa hoc ponit septem rationes, annectens eas praemissis solutionibus, ex quibus etiam propositum concludi potest, ut supra patuit.	After answering the arguments which favored the false side, the Philosopher now introduces arguments for the true side, namely, to show that universal demonstration is the more powerful. In regard to this he sets down seven reasons, adding them to the previous solutions from which the proposition can also be concluded, as was clear from the above.
lib. 1 l. 38 n. 2 Prima ergo ratio talis est. Demonstratio est syllogismus ostendens causam et propter quid: sic enim contingit scire, sicut supra habitum est. Sed universale est magis tale quam particulare. Iam enim ostensum est in prima solutione quod universali magis inest per se aliquid quam particulari. Illud autem cui inest aliquid per se, est causa eius: subiectum enim est causa propriae passionis, quae ei per se inest. Universale autem est primum cui propria passio inest, ut ex supra dictis patet: unde patet quod proprie causa est id quod est universale. Ex quo concludit propositum, scilicet quod demonstratio universalis sit dignior, utpote magis declarans causam et propter quid.	The first reason (85b22), is this: Demonstration is a syllogism showing the cause and propter quid: for this is the way scientific knowing takes place, as stated above. But the universal does this better than the particular. For as was shown in the first solution, something is per se in the universal more than in the particular. But that in which something is per se is the cause of this something: for the subject is the cause of the proper attribute which is in it per se. However, the first thing in which the proper attribute is present is the universal, as is clear from what has been stated above. Hence it is plain that, properly speaking, the cause is that which is universal. From this he concludes the proposition, namely, that universal demonstration is more valuable as better declaring the cause and propter quid.
lib. 1 l. 38 n. 3 Secundam rationem ponit ibi: amplius usque ad hoc etc., et sumitur haec ratio a causis finalibus. Ubi considerandum est quod aliquid est finis alterius et quantum ad fieri, et quantum ad esse: quantum ad fieri quidem, sicut generatio est propter formam; quantum ad esse autem, sicut domus est propter habitationem.	Then (85b28) he gives the second reason. This reason is taken from the final causes. Here it should be pointed out that something is the end of another thing both in regard to becoming and in regard to being: in regard to becoming, as generation is for the sake of form; in regard to being, as a house is for the sake of habitation.
Dicit ergo quod usque ad illum terminum quaerimus propter quid fiat aliquid, aut propter quid sit aliquid, quousque non sit aliquid aliud assignare quam hoc ad quod perventum est, propter quod fiat vel sit illud, de quo quaeritur propter quid. Et quando hoc invenimus, tunc opinamur nos scire propter quid; et hoc ideo quia illud quod iam sic est ultimum ut non sit aliquid aliud ulterius quaerendum, est id quod est vere finis et terminus, qui quaeritur cum quaerimus propter quid. Et ponit exemplum, puta si quaeramus cuius causa aliquis venit, et respondeatur, ut accipiat argentum: hoc autem propter quid? Ut scilicet reddat debitum: et hoc propter hoc aliud, ut scilicet non iniuste agat. Et sic semper procedentes, quando iam non erit amplius propter aliquid aliud sicut propter finem, puta cum pervenerimus ad ultimum finem, qui est beatitudo, dicemus quod propter hoc venit sicut propter finem. Et similiter est in omnibus aliis, quae sunt vel fiunt propter finem, et quando ad hoc pervenerimus, sciemus propter quid venit.	He says, therefore, that we search for the “reason why” something is done or why something is, until we reach the point where there is nothing further to assign, beyond the point reached, as the reason why that comes to be or is, whose reason why is sought. And when we find this we think that we know the propter quid: the reason being that that which is ultimate in this way, i.e., leaving nothing further to be sought, is truly the end and terminus which is being sought when we seek the propter quid. And he gives this example: if we should ask why someone went out, and the answer is given, “to get money,” and this in order to pay a debt, and “this for this other reason,” namely, lest he be guilty of injustice; and we continue in this way until there is nothing further for the sake of which as for an end—as when we arrive at the ultimate end, which is happiness—we will say that it was for this, as for an end, that he went. And it is the same in all other things that are or are done for the sake of an end: when we arrive at it, we will know the reason why he went.
Si igitur ita se habet in aliis causis sicut in causis finalibus, quod tunc maxime scimus quando ad ultimum fuerit perventum; ergo in aliis tunc maxime sciemus, quando perveniemus ad hoc, quod hoc inest huic non amplius propter aliquid aliud: et hoc contingit cum pervenerimus ad universale.	Now if things are so related in the other causes as they are in the final cause, namely, that we know fully when the last one has been reached, then we will know best in the others, when we shall have arrived at the fact that “this is in this” no longer because of something further. And this happens when we shall have reached the universal.
Et hoc manifestat in tali exemplo. Si enim quaeramus de isto triangulo particulari, quare anguli eius extrinseci sunt aequales quatuor rectis; respondebitur quod hoc contingit huic triangulo quia est isosceles; isosceles autem est talis quia est triangulus; triangulus autem est talis quia est figura rectilinea talis. Si ergo amplius non possit procedi, tunc maxime scimus: hoc autem est, quando pervenitur ad universale. Ergo universalis demonstratio potior est particulari.	To elucidate this he offers the following example: If we should ask concerning this particular triangle, why its exterior angles are equal to four right angles, the answer will be that this happens to this triangle because it is isosceles; and it is so for the isosceles, because it is a triangle; and it is so for a triangle, because it is such and such a rectilinear figure. If no further step can be taken, then we know in the best way. But this happens when the universal has been reached. Therefore the universal demonstration is stronger than the particular.
lib. 1 l. 38 n. 4 Tertiam rationem ponit ibi: amplius quantocumque etc., et dicit quod quanto magis proceditur versus particularia, tanto magis itur versus infinitum; quia, ut dicitur in III Physic., infinitum congruit materiae, quae est individuationis principium. Sed quanto magis proceditur versus universale, tanto magis itur in aliquid simplex et in ipsum finem; quia ratio universalis sumitur ex parte formae, quae est simplex, et habet rationem finis, in quantum terminat infinitatem materiae. Manifestum est autem quod infinita in quantum huiusmodi non sunt scibilia, sed in quantum aliqua sunt finita in tantum sunt scibilia; quia materia non est principium cognoscendi rem, sed magis forma. Manifestum est ergo quod universalia sunt magis scibilia quam particularia. Ergo etiam sunt magis demonstrabilia, quia demonstratio est syllogismus faciens scire. Sed magis demonstrabilium est potior demonstratio: simul enim intenduntur ea, quae dicuntur ad invicem; demonstratio autem ad demonstrabile dicitur. Et sic cum universalia sint magis demonstrabilia, demonstratio universalis erit potior.	Then (86a3) he gives the third reason, saying that the more one proceeds toward particulars, the nearer one gets to what is infinite; because, as it is stated in Physics III, the infinite is appropriate to matter which is the principle of individuation. On the other hand, the more one proceeds toward the universal, the nearer he gets to what is simple and to the end itself; because the universal reason is taken on the part of the form, ic is simple and which has the character of an end insofar as it terminates the infinitude of matter. Now it is obvious that infinite things as such are not scientifically knowable; rather to the extent that they are finite, to that extent are they knowable; because the principle of knowing a thing is not the matter but the form. Therefore, it is obvious that universals are scientifically more knowable than particulars. Consequently, they are also more demonstrable, because a demonstration is a syllogism that makes one know scientifically. But a demonstration of the more demonstrable is more powerful; for things which are described one in terms of the other grow apace. But demonstration is described in terms of the demonstrable. Consequently, since universals are more demonstrable, universal demonstration will be more powerful.
lib. 1 l. 38 n. 5 Quartam rationem ponit ibi: amplius si magis praeponenda etc., quae talis est. Cum demonstrationis finis sit scientia, quanto demonstratio plura facit scire, tanto potior est. Et hoc est quod dicit, quod magis praeferenda est demonstratio, secundum quam homo cognoscit hoc et aliud, quam illa secundum quam homo cognoscit unum solum. Sed ille qui habet cognitionem de universali, cognoscit etiam particulare, dummodo sciat quod sub universali contineatur particulare; sicut qui cognoscit omnem mulam esse sterilem, scit hoc animal, quod cognoscit esse mulam, esse sterile: sed ille qui cognoscit particulare, non propter hoc cognoscit universale. Non enim si cognosco hanc mulam esse sterilem, propter hoc cognosco omnem mulam esse sterilem. Relinquitur ergo quod demonstratio universalis, per quam cognoscitur universale et particulare, sit potior quam particularis, per quam cognoscitur solum particulare.	Then (86a11) he gives the fourth reason and it is this: Since the end of demonstration is scientific knowledge, the more things a demonstration enables one to know, the more powerful it is. And this is what he states, namely, that a demonstration, according to which a man knows one thing and something additional, is preferable to one according to which a man knows only the one. But a man who has knowledge of the universal knows also the particular, so long as he knows that the particular is contained under the universal. Thus, one who knows that every mule is sterile, knows that this animal, which he recognizes to be a mule, is sterile. But one who knows the particular does not on that account know the universal. For if I know that this mule is sterile, I do not on that account know that every mule is sterile. It remains, therefore, that universal demonstration, through which the universal is known, is stronger than particular, through which the particular is known.
lib. 1 l. 38 n. 6 Quintam rationem ponit ibi: amplius autem et sic etc., quae talis est. Quanto medium demonstrationis est propinquius primo principio, tanto demonstratio est potior. Et hoc probat, quia si illa demonstratio, quae procedit ex principio immediato, est certior ea quae non procedit ex principio immediato, sed ex mediato, necesse est quod quanto aliqua demonstratio procedit ex medio propinquiori principio immediato, tanto sit potior. Sed universalis demonstratio procedit ex medio propinquiori principio, quod est propositio immediata. Et hoc manifestat in terminis. Si enim oporteat demonstrare a, quod est universalissimum, de d, quod est particularissimum, puta substantiam de homine, et accipiantur media b et c, puta animal et vivum, ita quod b sit superius quam c, sicut vivum quam animal; manifestum est quod b, quod est universalius, erit immediatum ipsi a, et per hoc magis cognoscetur quam per c, quod est minus universale. Unde relinquitur quod demonstratio universalis potior sit quam particularis.	Then (86a14) he gives the fifth reason, and it is this: The nearer to the first principle the middle of a demonstration is, the more powerful is the demonstration. He proves this on the ground that if a demonstration which proceeds from an immediate principle is more certain than one which does not proceed from an immediate, but from a mediate, principle, then it is necessary that to the extent that a demonstration proceeds from a middle nearer an immediate principle, the more powerful it is. But a universal demonstration proceeds from a middle nearer the principle which is an immediate proposition. And he exemplifies this with terms. For if one is required to demonstrate A, which is the most universal, of B, which is the most particular, say “substance” of man, and B and C, say “living” and “animal” be taken, such that B is more general than C, as “living” than “animal,” it is obvious that B, which is the more universal, will be immediate to A; consequently, more will be known through it than through C, which is less universal. Hence it remains that universal demonstration is more powerful than particular.
Addit autem quasdam praedictarum rationum logicas esse: quia scilicet procedunt ex communibus principiis, quae non sunt demonstrationi propria; sicut praecipue tertia et quarta, quae accipiunt pro medio id quod est commune omni cognitioni. Aliae vero tres praedictarum rationum, scilicet prima, secunda et quinta, magis videntur esse analyticae, utpote procedentes ex propriis principiis demonstrationis.	But he remarks that some of the above reasons are “logical,” because, namely, they proceed from common principles which are not proper to demonstration; especially the third and fourth, which take as their middle something which is common to all knowledge. However, the other three, namely, the first, second and fifth, seem to be more analytic, proceeding as they do from principles proper to demonstration.
lib. 1 l. 38 n. 7 Sextam rationem ponit ibi: maxime autem manifestum est etc., et dicit quod maxime evidens est universalem demonstrationem principaliorem esse ex ipsis propositionibus, ex quibus utraque demonstratio procedit. Nam universalis demonstratio procedit ex universalibus propositionibus. Particularis autem demonstratio procedit ex aliqua particulari propositione. Propositionum autem universalis et particularis talis est comparatio, quod ille qui habet cognitionem de priori, scilicet de universali, cognoscit quodammodo posteriorem, scilicet in potentia. Nam in universali sunt in potentia particularia, sicut in toto sunt in potentia partes. Puta si aliquis cognoscit quod omnis triangulus habet tres angulos aequales duobus rectis, iam in potentia cognoscit hoc de isoscele. Sed ille qui cognoscit aliquid in particulari, non propter hoc cognoscit in universali, neque in actu neque in potentia. Non enim universalis propositio continetur in particulari, neque in actu neque in potentia. Si igitur demonstratio est potior, quae ex potioribus propositionibus procedit, sequitur quod demonstratio universalis sit potior.	Then (86a21) he gives the sixth reason and says that the primacy of universal demonstration over particular is evident from the very propositions from which the two demonstrations proceed. For the universal demonstration proceeds from universal propositions, whereas the particular demonstration proceeds from a particular proposition. Now the comparison between universal and particular propositions is such that one who has knowledge of the former, i.e., of the universal, somehow knows the latter, namely, in potency. For the particulars are potentially in the universal, as the parts are potentially in a whole. Thus, if one knows that every triangle has three angles equal to two right angles, he already knows it potentially of isosceles. But one who knows something in a particular way does not on that account know it universally either potentially or actually. For the universal proposition is neither potentially nor actually contained in the particular. Therefore, if that demonstration is more powerful which proceeds from stronger propositions, it follows that universal demonstration is more powerful.
Est autem attendendum quod haec ratio non differt a quarta supraposita, nisi quod ibi fiebat comparatio conclusionum, quae cognoscuntur per demonstrationem, hic autem fit comparatio propositionum, ex quibus demonstratio procedit.	It should be noted that this reason does not differ from the fourth one given above, except that in the fourth one the comparison was made between the conclusions which are known through demonstration, whereas here the comparison is between the propositions from which the demonstration proceeds.
lib. 1 l. 38 n. 8 Septimam rationem ponit ibi: et universalis quidem etc., quae talis est. Universalis demonstratio intelligibilis est, idest in ipso intellectu terminatur, quia finitur ad universale, quod solo intellectu cognoscitur. Sed demonstratio particularis in intellectu incipiens terminatur ad sensum, quia concludit particulare, quod directe per sensum cognoscitur; et per quamdam applicationem, seu reflexionem, ratio demonstrans usque ad particulare producitur. Cum igitur intellectus sit potior sensu, sequitur quod demonstratio universalis potior sit quam particularis. Ultimo epilogando concludit hoc esse manifestum per omnia supra dicta.	Then (86a28) he gives the seventh reason and it is this: The universal demonstration is intelligible, i.e., is terminated in the intellect, because it finishes in”a universal which is known only by the intellect. On the other. hand, a particular demonstration, although it begins in the intellect is terminated in sense, because it concludes a particular which is directly known by sense, and the reason demonstrating reaches out to the particular through a certain application or reflexion. Now since intellect is more powerful than sense, it follows that universal demonstration is stronger than particular. Finally, he concludes that this is clear in virtue of all that has been said above.