Authors/Thomas Aquinas/posteriorum/L1/Lect12

Lecture 12 How error occurs in understanding the universal

Latin	English
	Lecture 12 (74a4-b4) HOW ERROR OCCURS IN TAKING THE UNIVERSAL
lib. 1 l. 12 n. 1 Postquam notificavit Aristoteles quid sit universale, hic ostendit quomodo in acceptione universalis errare contingat. Et circa hoc tria facit: primo, dicit quod aliquando circa hoc peccare contingit; secundo, assignat quot modis; ibi: oberramus etc.; tertio, dat documentum quomodo possit cognosci utrum vere acceptum sit universale; ibi: utrum autem secundum quod et cetera.	After specifying what the universal is, the Philosopher here shows how one might err in understanding the universal. In regard to this he does three things. First, he says that sometimes one might err in this matter. Secondly, he tells in how many ways (74a6). Thirdly, he gives the criterion for knowing whether the universal is being employed correctly (74a35).
lib. 1 l. 12 n. 2 Dicit ergo primo quod ad hoc, quod non accidat in demonstratione peccatum, oportet non latere quod multoties videtur demonstrari universale, non autem demonstratur.	He says therefore first (74a4), that in order to avoid mistakes in demonstrating, one should be aware of the fact that quite often something universal seems to be demonstrated, which is not being demonstrated.
lib. 1 l. 12 n. 3 Deinde cum dicit: oberramus autem etc., assignat modos quibus circa hoc errare contingit. Et circa hoc duo facit. Primo, enumerat ipsos modos, dicens quod tripliciter contingit decipi circa acceptionem universalis. Primo quidem, cum nihil aliud sit accipere sub aliquo communi cui primo competit universale, quam hoc singulare, cui inconvenienter assignatur. Sicut si sensibile, quod primo et per se inest animali, assignaretur ut universale primum homini, nullo alio animali existente. Unde notandum quod singulare hic large accipitur pro quolibet inferiori, sicut si species dicatur singulare sub genere contentum. Vel potest dici quod non est possibile invenire aliquod genus, cuius una tantum sit species. Genus enim dividitur in species per oppositas differentias; oportet autem, si unum contrariorum invenitur in natura, et reliquum inveniri, ut patet per philosophum in II de caelo et mundo; et ideo si una species invenitur, invenitur et alia. Una autem species dividitur in diversa individua per divisionem materiae. Contingit autem totam materiam alicui speciei proportionatam, sub uno individuo comprehendi, et tunc non est nisi unum individuum sub una specie. Unde et signanter de singulari mentionem facit.	Secondly (74a6), he indicates the ways in which this mistake can occur. And in regard to this he does two things. First, he enumerates these ways and says that there are three possible errors in understanding a universal. The first is likely to occur when under some common genus there is nothing else to take as the thing to which the universal initially applies than this singular, to which it is incorrectly applied. For example, if man were the only animal existing, and “sensible,” which is initially and per se in animal, were to be assigned as a primary universal to man. (It should be noted that singular is being used here in a wide sense for any inferior, in the way that a species might be called a singular contained under a genus). Or we might say that it is not possible to find a genus with only one species: for a genus is divided into species through opposing differences. But if one contrary is found in nature, so must the other, as the Philosopher explains in On the Heavens II. Therefore, if one species is found, another will be found. However, one species is divided into distinct individuals by the division of matter. But it sometimes happens that all the matter proportionate to a given species is comprehended under one individual, so that in that case there is only one individual under one species. Hence it is significant that he did say, “singular.”
lib. 1 l. 12 n. 4 Secundus modus est, quando est quidem accipere sub aliquo communi multa inferiora, sed tamen illud est commune innominatum, quod invenitur in rebus differentibus specie. Sicut si animali non esset nomen impositum, et sensibile, quod est proprium animalis, assignaretur ut universale primum his quae sub animali continentur, vel divisim vel coniunctim.	The second way is when it is possible to take several inferiors under something common which is verified in things that differ in species, but that common item has no name. For example, if “animality” had no name, and “sensibility,” which is proper to animal, were to be assigned to the inferiors of animal (either collectively or distributively) as their primary universal.
lib. 1 l. 12 n. 5 Tertius modus est, quando illud de quo demonstratur aliquid, ut universale primum, se habet ad id quod demonstratur de eo, sicut totum ad partem. Sicut si posse videre assignaretur animali ut universale primum. Non enim omne animal potest videre. Inest enim his, quae sunt in parte, idest quae particulariter et non universaliter alicui subiecto conveniunt, demonstratio, idest quod demonstrari possint, et erit quidem demonstratio de omni, non tamen respectu huius de quo demonstratur. Posse enim videre demonstratur quidem de aliquo universaliter, non tamen universaliter de animali, sicut de eo cui primo insit. Et exponit quid sit primum, secundum quod demonstratio fertur, quod est universale primum.	The third way is when that of which something is demonstrated to be its primary universal is related to what is demonstrated of it, as a whole is related to a part. For example, if the power to see were assigned as a primary universal to animal: for not every animal can see. In this case the demonstration, i.e., what should have been demonstrated, is “in those things which are in part,” i.e., in some but not all of the things included under the subject; furthermore, it will be a demonstration “of all,” but not of all that the demonstration mentions. For the power to see can indeed be demonstrated universally of something, but not of animal universally, as of that to which it belongs primarily. And he explains why he says, “primarily,” namely, because a demonstration bears on what is both universal and first.
lib. 1 l. 12 n. 6 Secundo; ibi: si igitur etc., subiungit exempla ad praedictos modos, et primo ad tertium, dicens quod, si quis demonstret de lineis rectis quod non intercidant, idest non concurrant, videbitur huiusmodi esse demonstratio, scilicet universalis primi, propter hoc quod non concurrere inest aliquibus lineis rectis. Non autem ita quod hoc fiat, nisi lineae rectae sint aequales, idest aeque distantes. Sed si lineae fuerint aequales, idest aeque distantes, tunc non concurrere convenit eis in quolibet, quia universaliter verum est quod lineae rectae aeque distantes, etiam si in infinitum protrahantur, in neutram partem concurrent.	Secondly (74a13), he gives examples of each of these ways. First, of the third way, saying that if someone were to demonstrate of two straight lines that they do not intersect, i.e., that they do not meet, it might seem that we have a demonstration of this sort, i.e., one that bears on a primary universal, on the ground that “not to meet” is true of certain straight lines, and not that this happens only because the straight lines are equal, i.e., equally distant. But if the lines should be equal, i.e., equidistant, then “not to meet” belongs to any and all of them, because it is universally true that lines which are straight and equally distant, even should they be lengthened ad infinitum, will not meet.
lib. 1 l. 12 n. 7 Secundo; ibi: et si triangulus etc., ponit exemplum ad primum modum, dicens quod si non esset alius triangulus, quam isosceles, qui est triangulus duorum aequalium laterum, quod est trianguli in quantum huiusmodi, videretur esse isoscelis secundum quod est isosceles: nec tamen hoc esset verum.	Secondly (74a17), he gives an example of the first way, saying that if there were no triangle but the isosceles which is a triangle having two equal sides, it might seem that what is true of triangle as triangle should be true of isosceles as isosceles. But this would not be so.
lib. 1 l. 12 n. 8 Tertio; ibi: et proportionale etc., exemplificat de secundo modo. Et videtur hoc ultimo ponere, quia circa hoc diutius immoratur. Et circa hoc tria facit: primo, ponit exemplum; secundo, inducit quoddam corollarium ex dictis; ibi: propter hoc nec si aliquis etc.; tertio, assignat rationem dictorum; ibi: quando igitur non novit et cetera.	Thirdly (74a18), he gives an example of the second way. Now it seems that he saved this for last because he wished to spend more time on it. Concerning it he does three things. First, he gives the example. Secondly, he draws a corollary from what he has said (74a25). Thirdly, he gives a reason for the aforesaid (74a33).
Circa primum sciendum est quod proportio est habitudo unius quantitatis ad alteram, sicut sex ad tria se habent in proportione dupla. Proportionalitas vero est collatio duarum proportionum. Quae, si sit disiuncta, habet quatuor terminos; ut hic: sicut se habent quatuor ad duo, ita sex ad tria: si vero sit coniuncta, habet tres terminos: nam uno utitur ut duobus; ut hic: sicut se habent octo ad quatuor, ita quatuor ad duo.	Concerning the first it should be noted that a ratio is a relation of one quantity to another, as 6 is related to 3 in the ratio of 2 to 1. The com. paring of one ratio to another is a proportion, which, if it is disjoint, has four terms: for example, as 4 is to 2, so 6 is to 3. But if it is joint, it has three terms, one of which is used twice: for example, as 8 is to 4, so 4 is to 2.
Patet autem quod in proportione duo termini se habent ut antecedentia; duo vero ut consequentia; ut hic: sicut se habent quatuor ad duo, ita se habent sex ad tria; sex et quatuor sunt antecedentia: tria vero et duo sunt consequentia. Permutata ergo proportio est quando antecedentia invicem conferuntur, et consequentia similiter. Ut si dicam: sicut se habent quatuor ad duo, ita se habent sex ad tria; ergo sicut se habent quatuor ad sex, ita se habent duo ad tria.	Now it is obvious that in a proportion two terms are antecedents and two are consequents. For example, in the proportion that 6 is to 3 as 4 is to 2, 6 and 4 are the antecedents, 3 and 2 the consequents. Again, a proportion is alternated by bringing the antecedents together and the consequents together. For example, when I say: As 4 is to 2, so 6 is to 3; therefore, as 4 is to 6, so 2 is to 3.
Dicit ergo quod esse proportionale commutabiliter convenit numeris, et lineis, et firmis, idest corporibus, et temporibus. Sicut autem de singulis determinatum est aliquando seorsum, de numeris quidem in arithmetica, de lineis et firmis in geometria, de temporibus in naturali philosophia vel astrologia, ita contingens est, quod de omnibus praedictis commutatim proportionari una demonstratione demonstretur. Sed ideo commutatim proportionari, de singulis horum seorsum demonstratur, quia non est nominatum illud commune, in quo omnia ista sunt unum. Etsi enim quantitas omnibus his communis sit, tamen sub se et alia, praeter haec, comprehendit, sicut orationem et quaedam, quae sunt quantitates per accidens.	What he is saying, therefore, is that alternate proportion is verified in lines, numbers, solids, (i.e., bodies), and times. But just as this is established separately for each of them, namely, for numbers in arithmetic, for lines and solids in geometry, and for times in natural philosophy or astronomy, so it is possible to prove it of all of them in a single demonstration. But the reason why a separate demonstration was employed to prove alternation for each was that the one feature they had in common was unnamed. For although quantity is a feature common to all of them, quantity includes other things besides them; for example, speech and other things that are accidentally quantitative.
Vel melius dicendum quod commutatim proportionari non convenit quantitati in quantum est quantitas, sed in quantum est comparata alteri quantitati secundum proportionalitatem quandam. Et ideo dixerat etiam in principio proportionale esse quod commutabiliter est. Omnibus autem istis, in quantum sunt proportionalia, non est nomen commune positum. Cum autem demonstratur commutatim proportionari de singulis praedictorum divisim, non demonstratur universale. Non enim commutatim proportionari inest numeris et lineis, secundum quod huiusmodi, sed secundum quoddam commune. Demonstrantes autem de lineis seorsum vel de numeris ponunt hoc, quod est commutabiliter proportionari, esse quasi quoddam universale praedicatum lineae secundum quod linea est, aut numeri secundum quod numerus.	Or, better still, it was because alternate proportion does not belong to quantity precisely as quantity, but as compared to another quantity according to a fixed ratio. That is why at the very start he spoke of alternate proportion. But there is no general name for the aforesaid things precisely as they are proportional. Furthermore, when alternate proportion is demonstrated separately for each of them, it is not a universal that is being demonstrated. For “to be alternately proportional” is not in numbers and lines according to what each of them is, but according to something common. Besides, those who demonstrate alternate proportion of lines look upon this attribute as a universal predicate of line precisely as it is a line, or of number precisely as it is number.
lib. 1 l. 12 n. 9 Deinde cum dicit: propter hoc nec si aliquis etc., inducit quoddam corollarium ex dictis, dicens quod eadem ratione, qua non demonstratur universale cum de singulis speciebus aliquid demonstratur, quod est universale praedicatum communis innominati; nec etiam demonstratur universale modo praedicto, si sit commune nomen positum. Sicut si aliquis aut eadem demonstratione aut diversa demonstret de unaquaque specie trianguli, quod habet duos rectos, seorsum scilicet de isoscele et seorsum de gradato, idest de triangulo trium laterum inaequalium, non tamen propter hoc cognovit quod triangulus tres angulos habeat aequales duobus rectis, nisi sophistico modo, idest per accidens: quia non cognovit de triangulo secundum quod est triangulus, sed secundum quod est aequilaterus, aut duorum aequalium laterum, aut trium inaequalium.	Then (74a25), he draws a corollary from the above and says that for the same reason that something universal is not being demonstrated when a common unnamed attribute is proved to be a universal predicate of each species, so too when something is demonstrated this way of a common attribute which does have a name. For example, if someone uses the same demonstration for each species of triangle and proves that each has three angles equal to two right angles, or if he uses different demonstrations, say one for isosceles and another for scalene, even then he does not on that account know that a triangle has three angles equal to two right angles except in a sophistical way, i.e., per accidens: for he does not know it of triangle as triangle, but as equilateral or as having two equal sides or as having three unequal sides.
Neque etiam demonstrans cognovit universale trianguli, idest habet cognitionem de triangulo in universali, etiamsi nullus alius triangulus esset praeter illos, de quibus cognovit. Et hoc ideo, quia non cognovit de triangulo secundum quod est triangulus, sed sub ratione specierum eius. Unde neque cognovit, per se loquendo, omnem triangulum: quia et si secundum numerum cognovit omnem triangulum (si nullus est, quem non novit), tamen secundum speciem non cognovit omnem. Tunc enim cognoscitur aliquid universaliter secundum speciem, quando cognoscitur secundum rationem speciei. Secundum numerum autem et non universaliter, quando cognoscitur secundum multitudinem contentorum sub specie. Nec est differentia quantum ad hoc si comparemus species ad individua vel genera ad species. Nam triangulus est genus aequilateri et isoscelis.	Furthermore, one who demonstrates in this way does not know the universal of triangle, i.e., he does not have a knowledge of triangle in a universal way (even if there happens to be no other triangle besides those of which he knew this: and this because he had not the knowledge of triangle as triangle but under the aspect of its various species). Again, strictly speaking, he did not know every triangle: for although he knew every triangle according to number (if there was none he did not know), yet according to species he did not know each one. For something is known universally according to species, when it is known according to the notion of the species, but according to number and not universally, when it is known according to the multifarious things contained under the species. And in this matter there is no difference whether we compare species to individuals or genera to species. For triangle is the genus of equilateral and isosceles.
lib. 1 l. 12 n. 10 Deinde cum dicit: quando igitur non novit etc., assignat rationem praedictorum, quaerens quando aliquis cognoscat universaliter et simpliciter, ex quo praedicto modo cognoscens non cognoscit universaliter. Et respondet manifestum esse quod, si eadem esset ratio trianguli in communi et uniuscuiusque specierum eius seorsum acceptae aut omnium simul acceptarum, tunc universaliter et simpliciter nosceret de triangulo, quando sciret de aliqua specie eius vel de omnibus simul. Si vero non est eadem ratio, tunc non erit idem cognoscere triangulum in communi et singulas species eius; sed est alterum. Et cognoscendo de speciebus, non cognoscitur de triangulo secundum quod est triangulus.	Then (74a33) he assigns the reason for the aforesaid, first asking when does one know universally and absolutely, if one who knew in the aforesaid way did not know universally. And he answers that obviously if the essence of triangle in general and of each of its species (each taken sepai-ately or all taken together) were the same, then one would know universally and absolutely about triangle, when he knew about any one species of it separately or about all of them together. But if the essence is not the same, then it will not be the same but something different to know triangle and to know its several species. And by knowing something of the species one does not know it of triangle precisely as triangle.
lib. 1 l. 12 n. 11 Deinde cum dicit: utrum autem etc., dat documentum quo proprie possit accipi universale, dicens quod, utrum aliquid sit trianguli secundum quod est triangulus, aut isoscelis, secundum quod est isosceles, et quando id cuius est demonstratio sit primum et universale, secundum hoc, idest secundum aliquod subiectum positum; manifestum est ex hoc quod dicam.	Then (74a35) he gives the rule on how the universal can be properly understood, saying that whether something belongs to triangle precisely as triangle or to isosceles precisely as isosceles, and when it is that what is demonstrated is first and universal in the given subject precisely as this, i.e., precisely according to the subject—all this will be clear from what I shall say.
Quandocumque enim, remoto aliquo, adhuc remanet illud quod assignatur universale, sciendum est quod non est primum universale illius. Sicut, remoto isoscele vel aeneo triangulo, remanet quod habeat tres angulos, scilicet duobus rectis aequales. Unde patet quod habere tres angulos aequales duobus rectis non est universale primum, neque isoscelis, neque aenei trianguli. Remota autem figura non remanet habere tres, nec etiam, remoto termino, qui est superius ad figuram, cum figura sit, quae termino vel terminis clauditur; sed tamen non primo convenit neque figurae, neque termino, quia non convenit eis universaliter.	For whenever some item is removed from the subject and the original universal still applies to what remains, then it is not the first universal of that subject. For example, upon the removal of isosceles or of brazen there still remains the triangle which has three angles equal to two right angles; hence the possession of three angles equal to two right angles is not a first universal of isosceles or of brazen triangle. But if the item “figure” be removed, nothing which has three angles equal to two right angles remains, nor again if you remove “bounded” which is more universal than figure, since a figure is something enclosed by a bound or bounds. Nevertheless, the attribute in question [namely, having three angles equal to two right angles] does not belong first to figure or to bounded, because it does not belong to either of them universally.
Cuius ergo erit primo? Manifestum est quod trianguli, quia secundum triangulum inest aliis, tam superioribus, quam inferioribus: ideo enim competit figurae habere tres, quia triangulus est quaedam figura; et similiter isosceli, quia triangulus est, et de triangulo habere tres universaliter demonstratur. Unde eius est universale primum.	To what then will it be first? Obviously to triangle, because it belongs to the others (both superiors and inferiors) precisely as they are triangles For it belongs to figure to have three angles equal to two right angles only because a triangle is some figure, and similarly to isosceles, only because it is a triangle, and it is of triangle that “having three...” is demonstrated. Hence, it is to triangle that it belongs as a first universal.