Authors/Thomas Aquinas/posteriorum/L1/Lect13

Lecture 13 Demonstration proceeds from necessary things

Latin	English
	Lecture 13 (74b5-75a17) DEMONSTRATION PROCEEDS FROM NECESSARY THINGS
lib. 1 l. 13 n. 1 Postquam determinavit philosophus de dici de omni, et per se, et universali quibus utimur in demonstratione, hic iam incipit ostendere ex quibus demonstratio procedit. Et dividitur in duas partes: in prima, ostendit ex quibus procedat demonstratio propter quid; in secunda, ex quibus procedat demonstratio quia; ibi: sed quia differt et propter quid et cetera. Prima in duas: in prima, ostendit qualia sint ex quibus demonstratio procedit; in secunda, docet quae sint demonstrationis principia; ibi: quid quidem igitur prima significent et cetera. Prima in tres: in prima, ostendit quod demonstratio est ex necessariis; in secunda, quod est ex his, quae sunt per se; ibi: accidentium autem etc.; in tertia, quod procedat ex principiis propriis; ibi: non ergo est ex alio genere et cetera. Circa primum duo facit: primo, ostendit quod demonstratio procedat ex necessariis; secundo, probat quaedam quae supposuerat; ibi: quod autem oporteat ex necessariis et cetera. Circa primum tria facit: primo, continuat se ad praecedentia; secundo, probat propositum; ibi: quae autem sunt per se etc.; tertio, infert ex dictis quandam conclusionem; ibi: manifestum autem ex his et cetera.	Having finished his treatment of that which is said “of all” and “per se” and “universally,” all of which we use in demonstration, the Philosopher now begins to discuss the items from which demonstration proceeds. And there are two parts. In the first he shows what demonstration of the reasoned fact [demonstration propter quid] proceeds from. In the second what demonstration of the fact [demonstration quia] proceeds from (78a22) [L. 23]. The first is divided into two parts. In the first he shows the sort of things from which a demonstration proceeds. In the second, what the principles of demonstration are (76a26) [L. 18]. The first is divided into three parts. In the first he shows that demonstration issues from necessary things. In the second that it issues from things that are per se (76a26) [L. 14]. In the third that it proceeds from proper principles (75a38) [L. 15]. Concerning the first he does two things. First, he shows that demonstration should proceed from necessary things. Secondly, he proves certain things he had presupposed (74b27). In regard to the first he does three things. First, he makes a connection with what went before. Secondly, he proves his proposition (74b6). Thirdly, he draws a conclusion from the aforesaid (74b22).
Dicit ergo primo, ex praedictis inferens, quod si est demonstrativa scientia, idest si scientia per demonstrationem acquiritur, oportet quod sit ex necessariis principiis. Cuius illationis necessitas ex hoc apparet, quia quod scitur impossibile est aliter se habere, ut habitum est in definitione eius quod est scire.	He says therefore first (74b5), as an inference from what has already been established, that if there be demonstrative science, i.e., if science is acquired through demonstration, it must issue from necessary principles. The necessity of this inference is clear, because that which is known scientifically cannot be otherwise than it is, as was pointed out in the definition of scientific knowing.
lib. 1 l. 13 n. 2 Deinde cum dicit: quae autem per se sunt etc., ostendit quod demonstratio sit ex necessariis; et primo, per rationem; secundo, per signum; ibi: signum autem est et cetera. Circa primum ponit duas rationes: quarum prima talis est. Ea, quae per se praedicantur, necessario insunt. Et hoc manifestat in duobus modis per se. In primo quidem, quia ea, quae per se praedicantur, insunt in eo quod quid est, idest in definitione subiecti. Quod autem ponitur in definitione alicuius, necessario praedicatur de eo. In secundo vero, quia quaedam sunt subiecta, quae ponuntur in quod quid est praedicantibus de ipsis, idest in definitione suorum praedicatorum. Quae quidem si sint opposita, necesse est quod alterum eorum subiecto insit; sicut par vel impar numero, ut superius ostensum est. Sed manifestum est quod ex quibusdam principiis huiusmodi, scilicet per se, fit syllogismus demonstrativus: quod probat per hoc, quod omne quod praedicatur, aut praedicatur per se aut per accidens; et ea, quae praedicantur per accidens, non sunt necessaria: ex his autem, quae sunt per accidens, non fit demonstratio, sed magis sophisticus syllogismus. Unde relinquitur quod demonstratio sit ex necessariis.	Then (74b6) he shows that demonstration issues from necessary things. First, with a reason. Secondly, with a sign (74b19). With respect to the first he gives two reasons. The first (74b6) is this: Things predicated per se are in a thing necessarily. (And he manifests this in two of the modes of predicating per se: in the first mode, because the things predicated per se are “in that which is what,” i.e., in the definition of the subject. But whatever is put in the definition of anything is predicated of it necessarily. In the second mode, because certain subjects are put in “that which is the what of things predicated of them,” i.e., in the definition of their predicates. And if these are opposites, one or other of them is necessarily in the subject: thus, either “odd” or “even” is in number, as we showed above). Now it is clear that it is from principles of this kind, namely, per se, that a demonstrative syllogism proceeds. (And this is proved by the fact that whatever is predicated, is predicated either per se or per accidens, and that things predicated per accidens are not necessary). Therefore, since it is not a demonstration but rather a sophistic syllogism that issues from things that are per accidens, it follows that demonstration proceeds from necessary things.
lib. 1 l. 13 n. 3 Sciendum autem est quod cum in demonstratione probetur passio de subiecto per medium, quod est definitio, oportet quod prima propositio, cuius praedicatum est passio et subiectum est definitio, quae continet principia passionis, sit per se in quarto modo; secunda autem, cuius subiectum est ipsum subiectum et praedicatum ipsa definitio, in primo modo. Conclusio vero, in qua praedicatur passio de subiecto, est per se in secundo modo.	Furthermore, it should be noted that, since in a demonstration a proper attribute is proved of a subject through a middle which is the definition, it is required that the first proposition (whose predicate is the proper attribute, and whose subject is the definition which contains the principles of the proper attribute) be per se in the fourth mode, and that the second proposition (whose subject is the subject itself and the predicate its definition) must be in the first mode. But the conclusion, in which the proper attribute is predicated of the subject, must be per se in the second mode.
lib. 1 l. 13 n. 4 Secundam rationem ponit; ibi: aut igitur sic etc.: quae talis est. Demonstratio circa necessarium est et demonstratum, idest demonstrationis conclusio, non potest aliter se habere. Et hoc accipiendum est tanquam principium ad ostendendum propositum, scilicet quod demonstratio ex necessariis procedat; cuius quidem principii veritas ex praemissis apparet, ut iam dictum est. Ex hoc autem principio sic argumentatur. Conclusio necessaria non potest sciri nisi ex principiis necessariis; sed demonstratio facit scire conclusionem necessariam; ergo oportet quod sit ex principiis necessariis.	Then (74b14) he sets forth the second reason and it is this: “Demonstration is concerned with the necessary and the demonstrated,” i.e., the conclusion of the demonstration cannot be other than it is. This statement is to be taken as the principle proving our proposition that demonstration proceeds from necessary things. And from what has been said, the truth of this principle is obvious. From this principle one argues thus: a necessary conclusion cannot be scientifically known save from necessary principles; but a demonstration makes a necessary conclusion scientifically known: therefore, it must proceed from necessary principles.
In quo differt demonstratio ab aliis syllogismis: sufficit enim in aliis syllogismis quod syllogizetur ex veris. Nec est aliquod aliud genus syllogismi, in quo oporteat ex necessariis procedere, sed in demonstratione tantum oportet hoc observare. Et hoc est proprium demonstrationis, scilicet ex necessariis semper procedere.	Herein lies the difference between a demonstration and other syllogisms. For in the latter it is enough if one syllogizes from true principles. Nor is there any other type of syllogism in which it is required to proceed from the necessary: in a demonstration alone must this be observed. And this is proper to a demonstration, i.e., to proceed from the necessary.
lib. 1 l. 13 n. 5 Deinde cum dicit: signum autem etc., probat idem per signum hoc modo. Contra rationem aliquam non infertur instantia, nisi per hoc quod deficit aliquid eorum, quae in ratione illa observanda sunt; sed contra eum, qui opinatur se demonstrare, ferimus instantiam quod non sit necesse ea, ex quibus procedit, esse vera: sive opinemur ea contingere aliter se habere, sive talem instantiam feramus rationis, idest disputationis causa; ergo demonstratio debet procedere ex necessariis.	Then (74b18) he proves the same thing in the following way, using a sign: Suit is brought against an argument solely on the ground that something is wanting that should have been observed in that argument. But against one who believes that he has demonstrated, we bring the charge that the things from which he proceeded are not necessarily true, whether we are convinced that they could be otherwise than stated, or whether we bring a charge of reason, i.e., for the sake of disputing. Therefore, demonstration should proceed from necessary things.
lib. 1 l. 13 n. 6 Deinde cum dicit: manifestum autem etc., infert conclusionem ex dictis: dicens quod manifestum est, ex hoc quod oportet demonstrationem ex necessariis concludere, quod stulti sunt illi, qui opinati sunt bene se principia demonstrationis accipere, si solum propositio accepta sit probabilis vel vera, ut sophistae faciunt, idest illi, qui apparent scientes et non sunt. Nam scire non est nisi per hoc quod scientia habetur, scilicet ex demonstratione; ex hoc autem quod aliquid est probabile vel improbabile non habetur quod sit primum vel non primum: sed tamen oportet illud circa quod fit demonstratio esse primum in genere aliquo et esse verum. Non tamen omne primum accipit demonstrator, sed primum proprium illi generi, circa quod demonstrat; sicut arithmeticus non accipit primum, quod est circa magnitudinem, sed circa numerum.	Then (74b22) he draws a conclusion from the foregoing, saying that “this,” namely, the fact that a demonstration must conclude from necessary things, “shows” that they are obtuse who assumed that they rightly chose the principles of demonstration, if the proposition they chose was probable or true, as the Sophists do, i.e., those who appear wise but are not. For scientific knowing consists in nothing less than having science, namely, from demonstration. But when something is probable or improbable, it is not certain whether it is first or not first, whereas that on which a demonstration bears must be first in some genus and be true. This does not mean that a demonstrator may take anything that is first: it must be first in that genus with respect to which he is demonstrating. Thus, arithmetic does not choose what is first in regard to magnitude, in regard to number.
lib. 1 l. 13 n. 7 Attendendum est autem quod sophistae non sumuntur hic sicut in libro elenchorum, qui procedunt ex his quae videntur probabilia et non sunt, aut videntur syllogizare, non tamen syllogizant. Sicut enim tales sophistae dicuntur, idest apparentes et non existentes, in quantum deficiunt a dialectica argumentatione; ita dialecticae argumentationes si appareant demonstrative probare et non probent, sophisticae sunt, in quantum videntur sua argumentatione scientes, et non sunt.	It should be noted that Sophists are not taken here as they are in the book of Sophistical Refutations, i.e., who proceed from things that seem probable but are not, or seem to syllogize but do not. For just as some are called Sophists, i.e., seeming to be wise but not really so, inasmuch as they appear by their arguments to be scientific knowers but are not, so dialectical arguments, if they seem to prove demonstratively but do not, are sophistic.
lib. 1 l. 13 n. 8 Deinde cum dicit: quod autem ex necessariis etc., ostendit quod supposuerat. Et circa hoc duo facit: primo, ostendit quod conclusio necessaria non potest sciri ex principiis non necessariis; secundo, quod licet non possit sciri necessarium ex non necessariis, tamen syllogizari potest; ibi: cum quidem igitur conclusio et cetera. Primum ostendit duabus rationibus, quarum prima talis est. Si quis non habeat rationem propter quid ostendentem, non efficitur sciens, etiam demonstratione habita: quia scire est causam rei cognoscere, ut supra dictum est. Sed ratio, quae infert conclusionem necessariam ex non necessariis principiis, non ostendit propter quid.	Then (74b27) he proves something he had presupposed. And concerning this he does two things. First, he shows that a necessary conclusion cannot be scientifically known from non-necessary principles. Secondly, that although the necessary cannot be scientifically known from the nonnecessary, it can nevertheless be syllogized (75al). He proves the first with two reasons, one of which (74b27) is this: If one does not have an argument which shows the cause why [i.e., propter quid], he does not know scientifically, even though a syllogism be had; because to know scientifically is to know the cause of a thing, as we stated above. But an argument which infers a necessary conclusion from nonnecessary principles does not show the cause why.
Quod exemplificat in terminis communibus. Ponatur enim quod haec conclusio sit necessaria: omne c est a; et demonstretur per hoc medium b, quod non sit necessarium medium, sed contingens, puta quod haec propositio sit contingens, omne b est a, vel omne c est b, aut utraque; constat quod per hoc medium contingens, quod est b, non potest sciri de conclusione necessaria, quae est, omne c est a, propter quid. Quod sic probatur. Remota causa propter quam est aliquid, oportet quod removeatur effectus; sed hoc medium cum sit contingens, contingit removeri, conclusionem autem removeri non contingit cum sit necessaria; relinquitur ergo quod non potest sciri conclusio necessaria per medium contingens.	To clarify this he gives an example, using general terms. Assume that the conclusion, “Every C is A,” is necessary, and that it is demonstrated by a middle, B, which is not a necessary middle but a contingent one, so that, for example, one of the propositions, “Every B is A,” and “Every C is B,” or both, are contingent. Now it is obvious that through this contingent middle, namely, B, one cannot obtain scientific knowledge propter quid of the necessary conclusion, “Every C is A.” For if the cause on which something depends is removed, the effect must be removed. But this middle, being contingent, can be withdrawn, whereas the conclusion, since it is necessary, cannot be withdrawn. It follows, therefore, that a necessary conclusion cannot be scientifically known through a contingent middle.
lib. 1 l. 13 n. 9 Secundam rationem ponit; ibi: amplius si etc., quae talis est. Si aliquis nunc nescit, cum tamen habeat eandem rationem, quam prius habuit, et salvatus est, idest non desiit esse, salva re, idest etiam re scita non corrupta, et iterum ipse non est oblitus; manifestum est quod etiam neque prius scivit. In hoc autem philosophus innuit quatuor modos, quibus aliquis amittit scientiam, quam prius habuit. Unus modus est quando excidit a mente eius ratio, per quam prius sciebat. Alius modus est per corruptionem ipsius scientis. Tertius per corruptionem ipsius rei scitae, sicut si sciam te sedere, dum sedes, te non sedente, haec scientia perit. Quartus est per oblivionem. Unde nullo istorum modorum existente, si aliquis modo nesciat aliquid, nec prius scivit. Sed ille, qui habet conclusionem necessariam per medium contingens, corrupto medio contingenti, nescit, medio non existente, et tamen eandem rationem habet, et salvus est, et salva est res, et non est oblitus. Ergo neque prius scivit, quando medium non erat corruptum.	The second reason (74b32) is this: “If a man is without scientific knowledge now, then even though he possesses the same argument he had up to now, and he has been kept sound,” i.e., has not ceased to be, “and the thing known has not changed; and if he has not forgotten, then obviously he has not known scientifically.” In this passage the Philosopher mentions four ways in which a person loses the science he once had: one way is when there slips from his mind the argument through which he formerly knew scientifically. Another is through the destruction of the knower. A third is by a change occurring in the thing known: thus if, while you are sitting, I know that you are sitting, this knowledge perishes when you are not sitting. The fourth way is by forgetting. Hence if none of these ways has occurred, then, if a person does not know a thing scientifically now, he never did know it. Now one who holds a necessary (onclusion in virtue of a contingent middle, no longer knows it scientifically when the middle ceases to be, for the middle no longer exists, cven though he retains the same argument and the fact remains the same, and he has not forgotten anything. Therefore, even when the middle had not ceased to be, he did not know scientifically.
Quod autem medium, quod est contingens, corrumpatur, probat, quia id quod non est necessarium, oportet quod aliquando corrumpatur. Si autem dicatur quod medium nondum est corruptum: quia tamen non est necessarium, manifestum est quod contingit ipsum corrumpi.Posito autem contingenti, illud quod accidit non est impossibile, sed possibile et contingens. Quod autem sequebatur erat impossibile, scilicet, quod aliquis scientiam haberet alicuius, quod postea nesciret, manentibus conditionibus supra positis: quod tamen sequitur ex hoc quod est medium esse corruptum; quod et si non sit verum, est tamen contingens, ut dictum est.	But that a contingent middle is liable to perish he proves by the fact that whatever is not necessary must at some time perish. And even though the middle has not perished, nevertheless, because it is not necessary, it is obvious that it is liable to perish. Now when something contingent is put forward, its result is not impossible but possible and contingent. But what followed in our case was impossible, namely, that one should have had science of something and later not have had it, all the conditions described above prevailing. And this follows from the fact that a contingent middle has perished, which, although it may not be true [that it has], is nevertheless liable to, as has been said.
lib. 1 l. 13 n. 10 Deinde cum dicit: cum quidem igitur etc., ostendit quod licet per medium contingens non possit sciri conclusio necessaria, tamen potest syllogizari conclusio necessaria ex medio non necessario. Dicit ergo quod nihil prohibet, cum conclusio necessaria est, medium non necessarium esse per quod ostenditur, syllogismo tamen dialectico, non demonstrativo, qui facit scire. Contingit enim necessarium syllogizari ex non necessariis, sicut contingit syllogizari verum ex non veris: non tamen contingit e converso; quia cum medium est necessarium et conclusio necessaria erit, sicuti ex veris praemissis semper concluditur verum.	Then (75a1) he shows that although a necessary conclusion cannot be scientifically known through a contingent middle, nevertheless a necessary conclusion can be syllogized from a non-necessary middle. Hence he says that nothing hinders a necessary conclusion from being obtained through a non-necessary middle, as witness the case in which something is syllogized with a dialectical syllogism, although not with a demonstrative syllogism which causes science. For the necessary happens to be syllogized from the non-necessary, just as the true happens to be syllogized from the untrue—although the converse does not occur. For when the middle is necessary, the conclusion too will be necessary; similarly, from true premises something true is concluded.
Quod autem ex necessariis semper concludatur necessarium, sic probat: sit enim a de b ex necessitate, idest sit haec propositio necessaria: omne b est a; et hoc de c, idest sit haec etiam necessaria: omne c est b; ex his autem duabus necessariis sequitur tertia necessaria, scilicet conclusio, quod, omne c est a. Ostensum est enim in libro priorum quod ex duabus propositionibus de necessitate sequitur conclusio de necessitate.	But that the necessary is always concluded from necessary premises he proves thus: “Let A be necessary of B,” i.e., let this proposition, “Every B is A,” be necessary, “and the latter of C,” i.e., let “Every C is B” also be necessary. Now from these two necessary things follows a third necessary thing, namely, the conclusion, “Every C is A.” For it has been proved in the Prior Analytics that “from two propositions of necessity follows a’ conclusion of necessity.”
Ostendit etiam consequenter quod si conclusio non esset necessaria, nec medium posset esse necessarium. Ponatur enim quod haec conclusio, omne c est a, sit non necessaria, praemissae autem duae sint necessariae; secundum id quod praeostensum est, sequitur quod conclusio sit necessaria, cum tamen contrarium sit positum, scilicet quod conclusio sit non necessaria.	Then by way of consequence he shows that if the conclusion were not necessary, the middle could not be necessary. For example, suppose that this conclusion, “Every C is A,” is not necessary, but that the two premises are necessary. According to our previous doctrine it follows that the conclusion is necessary—which is contrary to the supposition in our example, namely, that the conclusion not be necessary.
lib. 1 l. 13 n. 11 Deinde cum dicit: quoniam igitur etc., infert conclusionem principaliter intentam ex omnibus praedictis, dicens quod quia oportet necessarium esse aliquid, si demonstratione sciatur, manifestum est ex praemissis quod oportet demonstrationem haberi per medium necessarium: alioquin nesciretur quod conclusio sit necessaria, neque propter quid, neque quia, cum necessarium non possit sciri per non necessarium, ut ostensum est. Sed si aliquis habeat rationem per medium non necessarium, dupliciter potest esse dispositus. Aut enim cum ipse sit non sciens, opinabitur tamen se scire, si accipiat in sua opinione medium non necessarium, tanquam necessarium; aut etiam non opinabitur se scire, si scilicet credat non se habere medium necessarium. Et hoc universaliter intelligendum est, tam de scientia quia, qua scitur aliquid per mediata, quam de scientia propter quid, qua scitur aliquid per immediata. Horum autem differentia posterius ostendetur.	Then (75a13) he infers from the aforesaid the conclusion originally intended, saying that since a thing must be necessary if it is made known by way of demonstration, it is clear from the foregoing that a demonstration must rest on a necessary middle. For otherwise it would not be scientifically known that the conclusion is necessary, neither propter quid nor quia, since the necessary cannot be known through the non-necessary, as we have shown. But if someone rests on an argument based on a non-necessary middle, he will be in one of two states. For since he does not actually know in a scientific way, he will either believe that he does know in a scientific way, if he assumes a non-necessary middle as necessary, or he will not presume that he knows in a scientific way, i.e., if he believes that he does not have a necessary middle. And this is to be universally understood both of scientific knowledge quia, in which something is known through mediate principles, and of science propter quid, in which something is known through immediate principles. The difference between these two will be explained later.