Authors/Thomas Aquinas/posteriorum/L1/Lect20

Lecture 20 Relation between demonstrative sciences and common principles

Latin	English
	Lecture 20 (77a10-35) RELATION BETWEEN DEMONSTRATIVE SCIENCES AND COMMON PRINCIPLES
lib. 1 l. 20 n. 1 Postquam determinavit philosophus de principiis propriis et communibus, hic ostendit qualiter demonstrativae scientiae se habeant ad principia communia et propria. Et dividitur in duas partes: in prima, ostendit qualiter se habeant demonstrativae scientiae circa communia: in secunda, qualiter se habeant circa propria; ibi: si autem idem est interrogatio et cetera. Circa primum duo facit: primo, ostendit qualiter se habeant demonstrativae scientiae circa prima principia inter communia; secundo, quomodo se habeant communiter circa omnia principia communia; ibi: communicant autem omnes scientiae et cetera. Circa primum duo facit: primo, ostendit quomodo se habeant demonstrativae scientiae circa hoc principium, quod, non contingit simul affirmare et negare; secundo, quomodo se habeant circa istud principium, de quolibet est affirmatio vel negatio vera; ibi: omne autem affirmare et cetera. Haec enim duo principia sunt omnium prima, ut probatur in IV metaphysicae.	After determining about proper and common principles, the Philosopher now shows how the demonstrative sciences behave in regard to the common and to the proper principles. His treatment falls into two parts. In the first he shows how the demonstrative sciences are related to common principles. In the second he shows how they are related to proper principles (77a36) [L. 21]. Concerning the first he does two things. First, he shows how the demonstrative sciences are related to the first of the common principles. Secondly, how they are related generally to all the common principles (77a29). Concerning the first he does two things. First, he shows how the demonstrative sciences behave relative to the principle that one should not affirm and deny the same thing. Secondly, how they behave relative to the principle that there is either true affirmation or true negation of each thing, for, as is proved in Metaphysics IV, these two principles are the first of all principles (77a22).
lib. 1 l. 20 n. 2 Dicit ergo primo quod nulla demonstratio accipit hoc principium, quod, non contingit simul affirmare et negare. Si enim aliqua demonstratio eo uteretur ad ostendendum aliquam conclusionem, oporteret quod sic eo uteretur, quod acciperet primum, idest maiorem extremitatem, affirmari de medio et non negari. Quia si acciperet affirmationem et negationem ex parte medii, nihil differret utrum sic vel sic esset; et eadem ratio est de tertio, idest de minori extremitate per comparationem ad medium. Verbi gratia: sit animal primum, homo medium, et Callias tertium. Si quis vellet uti praedicto principio in demonstratione, oporteret sic arguere: omnis homo est animal et non est non animal; Callias est homo; ergo Callias est animal et non est non animal. Cum vero dicat, omnis homo est animal, nihil differt, utrum etiam haec sit vera, non homo est animal, vel non sit vera. Et similiter in conclusione non differt, ex quo Callias est animal, utrum non Callias sit animal, vel non animal.	He says therefore first (77a10) that no demonstration makes use of the principle that one does not affirm and deny at one and the same time. For if a demonstration were to use it to show some conclusion, it would have to use it in such a way as to assert that the first, i.e., the major, extreme is affirmed of the middle and not denied; because if it were to admit affirmation and negation on the part of the middle, it would make no difference whether it was this way or that. And the same reasoning holds for the third, i.e., minor, extreme in relation to the middle. For example, take “animal” as the first, “man” as the middle’ and “Callias” as the third. If someone wished to use this principle in a demonstration, he would have to argue in the following way: Every man is an animal and is not a non-animal; But Callias is a man: Therefore, Callias is an animal and is not a non-animal. For when we say that every man is an animal, it matters not whether it is also true that a non-man is an animal, or whether it is not true. Similarly, in the conclusion it matters not, Callias being an animal, whether nonCallias is an animal or not.
Et huius causa est, quia primum non oportet dici de solo medio, sed potest etiam dici de quodam alio, quod est diversum a medio, quod significatur per negationem medii; propter hoc quod primum dicitur de pluribus quandoque quam medium, sicut animal de pluribus quam homo; unde dicitur de equo, qui est non homo. Unde si accipiatur medium idem et non idem, idest, si accipiatur medium affirmativum et negativum, ut cum dico, homo et non homo est animal, nihil facit ad conclusionem. Cum autem accipitur affirmatio et negatio ex parte maioris extremitatis, differt quidem quantum ad conclusionem et etiam quantum ad veritatem praemissarum. Si enim homo esset non animal, non esset verum quod homo est animal, neque sequeretur quod Callias esset animal. Tamen nihil plus certificatur cum dicitur, homo est animal et non est non animal, quam cum dicitur solum, homo est animal. Idem enim intelligitur per utrumque. Et sic manifestum est quod demonstrationes non utuntur hoc principio, scilicet quod affirmatio et negatio non sint simul vera, neque ex parte praedicati, neque ex parte subiecti.	Now the reason for this is that the first is not limited to being said only *of the middle but can also be said of something else diverse from the middle and described by a negation of the riliddle (since the first is sometimes said of things other than the middle, as “animal” is said of things other than man; for it is said of horse, which is not man). Hence if the middle is taken the same and not the same, i.e., if an affirmative and a negative middle be taken, as when I say, “man” and “non-man” are animals, it contributes nothing to the conclusion. However, if the affirmation and negation are taken on the part of the major extreme, it does make a difference both as to the conclusion and as to the truth of the premises. For if man were not an animal, it would not be true that man is an animal, nor would it follow that Callias is an animal. Yet nothing more is verified by stating that man is an animal and is not a non-animal than by merely stating that man is an animal, for the same thing is conveyed by each. And thus it is clear that demonstrations do not use the principle that affirmation and negation are not simultaneously true, either on the part of the predicate or on the part of the subject.
lib. 1 l. 20 n. 3 Deinde, cum dicit: omne autem affirmare etc., ostendit quomodo demonstrativae scientiae utantur hoc principio, de quolibet est affirmatio vel negatio vera. Et dicit quod hoc principium accipit demonstratio, quae est ad impossibile. In hac enim demonstratione probatur aliquid esse verum per hoc quod eius oppositum est falsum.	Then (77a22) he shows how demonstrative sciences use the principle that “of anything there is either true affirmation or negation.” And he says that this principle is utilized in a demonstration leading to the impossible. For in this demonstration something is proved to be true by the fact that its opposite is false. (This of course would never happen, if it were possible for the two opposites to be false).
Quod nequaquam contingeret, si possibile esset utrumque oppositorum esse falsum. Non tamen semper utitur praedicta demonstratio hoc principio, quia quandoque illud oppositum quod ostenditur esse falsum, non est negatio, sed contrarium immediatum. Sicut si ostenderetur aliquem numerum esse parem per hoc quod falsum est ipsum esse imparem ducendo ad impossibile. Neque etiam utitur hoc principio universaliter, idest in sua universalitate, sub his terminis, ens et non ens, sed quantum sufficiens est in genere aliquo. Et dico de illo genere, circa quod sunt demonstrationes. Sicut si in geometria accipiatur rectum et non rectum; ut cum ostenditur aliqua linea esse recta per hoc quod est falsum eam esse non rectam ducendo ad impossibile.	Nevertheless such a demonstration does not always employ this principle, for sometimes that opposite which is shown to be false is not a negation but an immediate contrary. For example, if a number were shown to be even on the ground that its opposite, namely, “it is odd,” is false, and this were done by leading to the impossible. Neither does it use this principle universally, i.e., in its universality, namely, under the terms “being” and “non-being,” but only so far as is sufficient for a genus or so far as it is narrowed to a generic subject. And I mean the first genus involved in the demonstration. For example, in leading to the impossible in geometry the terms would be “straight” and “non-straight” in the case where it is shown that some line is straight on the ground that it is false to state that it is not straight.
lib. 1 l. 20 n. 4 Deinde, cum dicit: communicant autem etc., ostendit qualiter demonstrativae scientiae se habeant communiter ad omnia principia communia. Et circa hoc duo facit. Primo, dicit quod omnes scientiae in communibus principiis communicant hoc modo, quod omnes utuntur eis, sicut ex quibus demonstrant, quod est uti eis ut principiis: sed non utuntur eis, ut de quibus aliquid demonstrant, ut de subiectis, neque sicut quod demonstrant, quasi conclusionibus.	Then (77a26) he shows how the sciences as a community function relative to all common principles. In regard to this he does two things. First, he says that all the sciences share alike in the common principles in the sense that they all use them as items from which they demonstrate-which is to use them as principles. But they do not use them as things about which they demonstrate something, i.e., as subjects, or as things which they demonstrate, i.e., as conclusions.
lib. 1 l. 20 n. 5 Secundo, ibi: et dialectica de omnibus etc., ostendit quod quaedam scientiae utuntur principiis communibus alio modo quam dictum est. Dialectica enim est de communibus; et aliqua alia scientia est etiam de communibus, scilicet philosophia prima, cuius subiectum est ens et considerat ea quae consequuntur ens, ut proprias passiones entis. Sciendum tamen est quod alia ratione dialectica est de communibus et logica et philosophia prima. Philosophia enim prima est de communibus, quia eius consideratio est circa ipsas res communes, scilicet circa ens et partes et passiones entis. Et quia circa omnia quae in rebus sunt habet negotiari ratio, logica autem est de operationibus rationis; logica etiam erit de his, quae communia sunt omnibus, idest de intentionibus rationis, quae ad omnes res se habent. Non autem ita, quod logica sit de ipsis rebus communibus, sicut de subiectis. Considerat enim logica, sicut subiecta, syllogismum, enunciationem, praedicatum, aut aliquid huiusmodi.	Secondly (77a29), he shows that certain sciences employ the common principles in a manner other than has been described. For dialectics is concerned with common things, and a certain other science is concerned with common things, namely, first philosophy, whose subject is being and which considers the things which follow upon being as the proper attributes of being. Yet it should be noted that dialectics is concerned with common things under an aspect different from logic and first philosophy. For first philosophy is concerned with common things because its consideration is focused on those common things, namely, on being and on the parts and attributes of being. But because reason occupies itself with all things that are, and logic studies the operations of reason, logic will also be concerned with matters common to all things, i.e., with reason’s intentionalities which bear on all things, but not in such a way that logic has these common things as its subject-for logic considers as its subject the syllogism, enunciation, predication, and things of that type.
Pars autem logicae, quae demonstrativa est, etsi circa communes intentiones versetur docendo, tamen usu demonstrativae scientiae non est in procedendo ex his communibus intentionibus ad aliquid ostendendum de rebus, quae sunt subiecta aliarum scientiarum. Sed hoc dialectica facit, quia ex communibus intentionibus procedit arguendo dialecticus ad ea quae sunt aliarum scientiarum, sive sint propria sive communia, maxime tamen ad communia. Sicut argumentatur quod odium est in concupiscibili, in qua est amor, ex hoc quod contraria sunt circa idem. Est ergo dialectica de communibus non solum quia pertractat intentiones communes rationis, quod est commune toti logicae, sed etiam quia circa communia rerum argumentatur. Quaecunque autem scientia argumentatur circa communia rerum, oportet quod argumentetur circa principia communia, quia veritas principiorum communium est manifesta ex cognitione terminorum communium, ut entis et non entis, totius et partis, et similium.	But although the part of logic which is demonstrative is engaged in teaching about common intentionalities, the use of a demonstrative science does not consist in proceeding from common intentionalities to show anything about the things which are the subjects of the other sciences. But dialectics does this, for it goes from common intentions and argues to things that pertain to other sciences, whether they be proper or common things, but mainly common things. Thus, it argues that hatred is in the concupiscible appetite, because love is, on the ground that contraries are concerned with a same thing. Consequently, dialectics is concerned with common things not only because it treats concerning the common intentionalities of reason, which is common to all logic, but also because it argues about common characteristics of things. But any science that argues about the common characteristics of things must argue about the common principles, because the truth of the common principles is made manifest from the knowledge of common terms, as “being” and “non-being,” “whole” and “part” and the like.
Dicit autem signanter: et si aliqua scientia tentet monstrare communia, quia philosophia prima non demonstrat principia communia, sunt enim indemonstrabilia simpliciter; sed aliqui errantes tentaverunt ea demonstrare, ut patet in IV metaphysicae. Vel etiam quia, etsi non possunt demonstrari simpliciter, tamen philosophus primus tentat ea monstrare eo modo, quo est possibile, scilicet contradicendo negantibus ea, per ea quae oportet ab eis concedi, non per ea, quae sunt magis nota.	It is significant that he says, “and any science which might attempt,” because first philosophy does not demonstrate the common principles, since they are absolutely indemonstrable, although some have unwittingly attempted to demonstrate them, as is stated in Metaphysics IV. Or else, because even though they cannot, strictly speaking, be demonstrated, the first philosopher attempts to uphold them in a way that is possible, namely, by contradicting those who deny them, appealing to things that must be conceded by them, though not to things which are more known.
lib. 1 l. 20 n. 6 Sciendum est etiam quod primus philosophus non solum hoc modo demonstrat ea, sed etiam monstrat aliquid de eis, sicut de subiectis; sicut quod, impossibile est mente concipere opposita eorum, ut patet in IV metaphysicae. Cum ergo disputet circa haec principia et philosophus primus et dialecticus, tamen aliter et aliter. Dialecticus enim non procedit ex aliquibus principiis demonstrativis, neque assumit alteram partem contradictionis tantum, sed se habet ad utramque (contingit enim utramque quandoque vel probabilem esse, vel ex probabilibus ostendi, quae accipit dialecticus). Et propter hoc interrogat. Demonstrator autem non interrogat, quia non se habet ad opposita. Et haec differentia utriusque posita est in his, quae de syllogismo sunt, idest in libro priorum. Philosophia ergo prima procedit circa communia per modum demonstrationis, et non per modum dialecticae disputationis.	It should also be noted that the first philosopher demonstrates them not only in this way, but also shows something about them as about subjects: for example, that “it is impossible for the mind to think their opposites,” as is clear from Metaphysics IV. Therefore’ although both the first philosopher and the dialectician debate about these first principles, yet one does so in one way and the other in another way. For the dialectician neither proceeds from demonstrative principles nor takes only one side of a contradiction but is open to both. For each side might happen to be probable or be upheld by probable statements, which the dialectician utilizes: and that is why he asks [his questions in terms of two alternatives]. But the demonstrator does not ask [in that way], because he is not open to opposites. And this is the difference between the two, as was laid down in the treatment of the syllogism, namely, in the beginning of the Prior Analytics. Therefore, first philosophy in treating common principles proceeds after the manner of a demonstration and not after the manner of a dialectical disputation.