Authors/Thomas Aquinas/posteriorum/L1/Lect5

Lecture 5 First and immediate propositions

Latin	English
	Lecture 5 (72a8-24) FIRST AND IMMEDIATE PROPOSITIONS
lib. 1 l. 5 n. 1 Quia superius philosophus dixerat quod demonstratio est ex primis et immediatis, et haec ab ipso nondum manifestata erant, ideo intendit ista notificare. Et dividitur in partes tres: in prima, ostendit quid sit propositio immediata; in secunda vero ostendit quod oporteat huiusmodi propositiones esse notiores conclusione; ibi: quoniam autem oportet credere et scire etc.; in tertia, excludit quosdam errores, qui ex praedictis occasionem habebant; ibi: quibusdam quidem igitur et cetera. Circa primum duo facit: primo, ostendit quid sit propositio immediata; secundo, dividit ipsam; ibi: immediati autem principii et cetera.	Because the Philosopher had stated above that demonstration is from “first and immediate principles,” but had not yet identified them, he now sets out to identify them. And this is divided into three parts. In the first part he shows what an immediate proposition is. In the second part he shows that such propositions must be better known than the conclusion (72a25) [L. 6]. In the third part he excludes certain errors which arose from the foregoing (72b5) [L. 7]. Concerning the first he does two things. First, he shows what an immediate principle is. Secondly, h divides them (72a15).
Circa primum hoc modo procedit. Primo namque, resumit quod supra dictum erat, scilicet quod principium demonstrationis sit propositio immediata: nam et supra dixerat quod demonstratio est ex primis et immediatis.	With respect to the first he proceeds this way. First (72a8), he recall, what has been said above, namely, that a principle of demonstration I, an immediate proposition, for he had also stated above that a demonstration is composed of things which are first and immediate.
lib. 1 l. 5 n. 2 Secundo, ibi: immediata autem etc., definit immediatam propositionem, et dicit quod immediata propositio est qua non est altera prior. Cuius quidem notificationis ratio ex praedictis apparet. Dictum est enim supra quod demonstratio est ex prioribus. Quandocunque igitur aliqua propositio est mediata, idest habens medium per quod demonstretur praedicatum de subiecto, oportet quod priores ea sint propositiones ex quibus demonstratur: nam praedicatum conclusionis per prius inest medio quam subiecto; cui etiam per prius inest medium quam praedicatum. Relinquitur ergo quod illa propositio, qua non est altera prior, sit immediata.	Secondly (ibid.), he defines the immediate proposition and says that a immediate proposition is one which has no other one prior to it. the reason underlying this description is clear from what has been said. For it has been said above that demonstration is composed of things that, are prior. Accordingly, whenever a proposition is mediate, i.e., has a middle through which the predicate is demonstrated of its subject, it is required that there be prior propositions by which this one is demonstrated. For the predicate of a conclusion is present in the middle previously to being present in the subject; in which, however, the middle is present before the predicate is. Therefore, it follows that that proposition which does not have some other one prior to it is immediate.
lib. 1 l. 5 n. 3 Tertio, ibi: propositio autem est etc., ostendit quid sit propositio, quae ponitur in definitione immediatae propositionis. Et circa hoc tria facit. Primo namque definit propositionem simpliciter, dicens quod propositio est altera pars enunciationis, in qua praedicatur unum de uno. Habet enim enunciatio duas partes, scilicet affirmationem et negationem. Oportet autem quod omnis syllogizans alteram earum proponat, non autem utramque: hoc enim est proprium eius, qui a principio quaestionem movet. Unde per hoc separatur propositio a problemate. Sicut etiam in uno syllogismo non concluditur nisi unum, ita oportet quod propositio, quae est syllogismi principium, sit una. Una autem est in qua est unum de uno. Unde per hoc quod philosophus dicit unum de uno, separatur propositio ab enunciatione, quae dicitur plures, in qua plura de uno vel unum de pluribus praedicatur.	Thirdly (720), he shows what is the nature of the proposition which is mentioned in the definition of an immediate proposition. Concerning this he does three things: First, he defines absolutely what a proposition is, saying that it is one or the other part of an enunciation in which one thing is predicated of one thing. For the enunciation has two parts, namely, affirmation and negation. For anyone who syllogizes must propose one or the other of these parts but not both, for this latter procedure is characteristic of one who first raises a question. (Hence it is on this basis that proposition is distinguished from a problem). For just as one and only one thing is concluded in one syllogism, so the proposition which is a principle of the syllogism should be one—and it is one if one thing is stated of one thing. Hence in asserting that it is “one of one,” he distinguishes the proposition from the enunciation which is said to be “of several,” whether sundry things are said of one thing or of one thing sundry.
lib. 1 l. 5 n. 4 Secundo, ibi: dialectica etc., ponit differentiam inter dialecticam propositionem et demonstrativam, dicens quod cum propositio accipiat alteram partem enunciationis, dialectica indifferenter accipit quancunque earum. Habet enim viam ad utranque partem contradictionis, eo quod ex probabilibus procedit. Unde etiam et in proponendo accipit utramlibet partem contradictionis et quaerendo proponit. Demonstrativa autem propositio accipit alteram partem determinate, quia nunquam habet demonstrator viam, nisi ad verum demonstrandum. Unde etiam semper proponendo accipit veram partem contradictionis. Propter hoc etiam non interrogat, sed sumit, qui demonstrat, quasi notum.	Secondly (72a10), he lays down the difference between the dialectical and the demonstrative proposition, saying that whereas the demonstrative proposition takes one definite side of a question, the dialectical takes either side indifferently. For since dialectic begins with the probable, it can lead to each side of a contradiction. Hence when it lays down its propositions, it employs both parts of a contradiction and presents them in the form of a question [Is an animal that walks on its feet a man, or not?]. But a demonstrative proposition takes one side definitively, because a demonstrator never has any other alternative but to demonstrate the truth. Hence in forming its propositions he always assumes the true side of a contradiction [An animal which walks on two feet is a man, is it not?]. On this account he does not ask but posits something as known in the demonstration.
lib. 1 l. 5 n. 5 Tertio, ibi: enunciatio autem etc., definit enunciationem quae ponitur in definitione propositionis, dicens quod enunciatio complectitur utranque partem contradictionis, ut ex dictis patet. Quid autem sit contradictio consequenter ostendit, dicens quod contradictio est oppositio, cuius non est medium secundum se. Quamvis enim in privatione et habitu, et in contrariis immediatis non sit medium circa determinatum subiectum, tamen est medium simpliciter, nam lapis neque caecus, neque videns est, et albedo neque par, neque impar est. Et hoc etiam quod habent de immediatione circa determinatum subiectum, habent in quantum aliquid participant contradictionis: nam privatio est negatio in subiecto determinato. Et alterum etiam contrariorum habet aliquid privationis. Sed contradictio simpliciter in omnibus caret medio; et hoc non habet ab alio, sed ex seipsa; et propter hoc dicit quod eius non est medium secundum se.	Thirdly (72a11), he defines the term, “enunciation,” which appeared in the definition of a proposition, saying that an enunciation embraces both sides of a contradiction, as is clear from what has been said. Then he shows what contradiction is, saying that contradiction is a form of opposition between whose parts there is of itself no middle. For although between privation and possession and between immediate contraries there is no middle in a given subject, nevertheless, absolutely speaking, there is one; for a stone is neither blind nor seeing, and something white is neither even nor odd. Furthermore, whatever immediacy they have in relation to a definite subject is traced to their participation in contradiction, for privation is negation in a definite subject; and of two things that are immediately contrary, one has some of the marks of privation. But contradiction in the full sense lacks a middle in all cases. And this belongs to it of its very nature and not in virtue of something else. Hence he says that of itself it has no medium.
Exponit etiam consequenter quid sit pars contradictionis: est enim contradictio oppositio affirmationis et negationis. Unde altera pars eius est affirmatio, quae praedicat aliquid de aliquo; altera vero negatio, quae removet aliquid ab aliquo.	He then explains what the parts of a contradiction are. For contradiction is an opposition of affirmation and negation; hence one of its parts is affirmation, which asserts something of something, and the other is negation, which denies something of something.
lib. 1 l. 5 n. 6 Deinde cum dicit: immediati autem etc. dividit immediatum principium. Et circa hoc duo facit: primo dividit; secundo subdividit; ibi: positiones autem quaedam et cetera. Dicit ergo primo quod immediatum principium syllogismi duplex est. Unum est quod dicitur positio, quam non contingit demonstrare et ex hoc immediatum dicitur; neque tamen aliquem docendum, idest qui doceri debet in demonstrativa scientia, necesse est habere, idest mente concipere sive ei assentire. Aliud vero est, quod dicitur dignitas vel maxima propositio, quam necesse est habere in mente et ei assentire quemlibet, qui doceri debet. Et manifestum est quod quaedam principia talia sunt ut probatur in IV metaphysicae de hoc principio, quod affirmatio et negatio non sunt simul vera, cuius contrarium nullus mente credere potest etsi ore proferat. Et in talibus utimur nomine praedicto, scilicet dignitatis vel maximae propositionis, propter huiusmodi principiorum certitudinem ad manifestandum alia.	Then (72a15) he divides immediate principle. Concerning this he does two things. First, he divides. Secondly, he subdivides (72a19). He says therefore first (7205), that there are two types of immediate principles of a syllogism: the first is called a “position” [thesis] and is said to be immediate because one does not demonstrate (neither is it required that the student, i.e., the one being instructed in the demonstrative science, have it, i.e., advert to it or assent to it); the other is called a “dignity” or “maxim,” which anyone who is to be instructed must have in his mind and assent to. That there are such principles is clear from Metaphysics IV, where it is proved that one such is the principle that “affirmation and negation are not simultaneously true,” for no one can believe the contrary of this in his mind ‘ even though he should state it orally. To such principles we give the aforesaid name of “dignity” or “maxim” on account of their certainty in manifesting other things.
lib. 1 l. 5 n. 7 Ad huius autem divisionis intellectum sciendum est quod quaelibet propositio, cuius praedicatum est in ratione subiecti, est immediata et per se nota, quantum est in se. Sed quarundam propositionum termini sunt tales, quod sunt in notitia omnium, sicut ens, et unum, et alia quae sunt entis, in quantum ens: nam ens est prima conceptio intellectus. Unde oportet quod tales propositiones non solum in se, sed etiam quoad omnes, quasi per se notae habeantur. Sicut quod, non contingit idem esse et non esse; et quod, totum sit maius sua parte: et similia. Unde et huiusmodi principia omnes scientiae accipiunt a metaphysica, cuius est considerare ens simpliciter et ea, quae sunt entis.	To clarify this division it should be noted that any proposition whose predicate is included within the notion of its subject is immediate and known in virtue of itself as it stands. However, in the case of some of these propositions the terms are such that they are understood by everyone, as being and one and those other notions that are characteristic of being precisely as being: for being is the first concept in the intellect. Hence it is necessary that propositions of this kind be held as known in virtue of themselves not only as they stand but also in reference to us. Examples of these are the propositions that “It does not occur that the same thing is and is not” and that “The whole is greater than its part,” and others like these. Hence all the sciences take principles of this kind from metaphysics whose task it is to consider being absolutely and the characteristics of being.
Quaedam vero propositiones sunt immediatae, quarum termini non sunt apud omnes noti. Unde, licet praedicatum sit de ratione subiecti, tamen quia definitio subiecti non est omnibus nota, non est necessarium quod tales propositiones ab omnibus concedantur. Sicut haec propositio: omnes recti anguli sunt aequales, quantum est in se, est per se nota sive immediata, quia aequalitas cadit in definitione anguli recti. Angulus enim rectus est, quem facit linea recta super aliam rectam cadens, ita quod ex utraque parte anguli reddantur aequales. Et ideo, cum quadam positione recipiuntur huiusmodi principia.	On the other hand, there are some immediate propositions whose terms are not known by everyone. Hence, although their predicate may be included in the very notion of their subject, yet because the definition of the subject is not known to everyone, it is not necessary that such propositions be conceded by everyone. (Thus the proposition, “All right angles are equal,” is in itself a proposition which is immediate and known in virtue of itself, because equality appears in the definition of a right angle. For a right angle is one which a straight line form when it meets another straight line in such a way that the angles on each side are equal). Therefore, such principles are received as being posited or laid down.
Est et alius modus, quo aliquae propositiones suppositiones dicuntur. Sunt enim quaedam propositiones, quae non possunt probari nisi per principia alterius scientiae; et ideo oportet quod in illa scientia supponantur, licet probentur per principia alterius scientiae. Sicut a puncto ad punctum rectam lineam ducere, supponit geometra et probat naturalis; ostendens quod inter quaelibet duo puncta sit linea media.	There is yet another way, and according to it certain propositions are called “suppositions.” For there are some propositions which can be proved only by the principles of some other science; therefore, they must be supposed in the one science, although they are proved by the principles of the other science. Thus the geometer supposes that he can draw one straight line from one point to another, but the philosopher of nature proves it by showing that there is one straight line between any two points.
lib. 1 l. 5 n. 8 Deinde cum dicit: positionis autem quae est etc., subdividit alterum membrum primae divisionis, scilicet positionem: dicens quod quaedam positio est, quae accipit aliquam partem enunciationis, scilicet affirmationem vel negationem; quod significat cum dicit: ut dico aliquid esse aut non esse. Et haec positio suppositio dicitur, quia tanquam veritatem habens supponitur. Alia autem positio est, quae non significat esse vel non esse, sicut definitio, quae positio dicitur. Ponitur enim ab arithmetico definitio unitatis, tanquam quoddam principium, scilicet quod unitas est indivisibile secundum quantitatem. Sed tamen definitio non dicitur suppositio: illud enim proprie supponitur, quod verum vel falsum significat. Et ideo subdit quod non idem est, quod quid est unitas, quod neque verum, neque falsum significat, et esse unitatem, quod significat verum vel falsum.	Then (72a19) he subdivides a member of the original division, namely, “position,” and says that there is one type of position which takes one side of an enunciation, namely, either affirmation or negation. He refers to this type when he says, “i.e., asserts either the existence or non-existence of a subject.” Such a position is called a “supposition” or “hypothesis,” because it is accepted as having truth. Another type of position is the one which does not signify existence or non-existence: in this way a definition is a position. For the definition of “one” is laid down in arithmetic as a principle, namely, that “one is the quantitatively indivisible.” Nevertheless a definition is not called a supposition, for a supposition, strictly speaking, is a statement which signifies the true or the false. Consequently, he adds that “the definition of ‘one,”’ inasmuch as it signifies neither the true nor the false, “is not the same as ‘to be one,”’ which does signify the true or the false.
lib. 1 l. 5 n. 9 Sed potest quaeri: cum definitio non sit propositio significans esse vel non esse, quomodo ponatur in subdivisione immediatae propositionis. Sed dicendum quod in subdivisione non resumit immediatam propositionem ad subdividendum, sed immediatum principium. Principium autem syllogismi dici potest non solum propositio, sed etiam definitio. Vel potest dici quod licet definitio in se non sit propositio in actu, est tamen in virtute propositio quia cognita definitione, apparet definitionem de subiecto vere praedicari.	Now it might be asked how it is that definition is set down as a member of the subdivision of immediate proposition, if a definition is not a proposition signifying either existence or non-existence. One might answer that in this subdivision he was not subdividing immediate proposition but, immediate principle. Or one might answer that although a definition as such is not an actual proposition, it is one virtually, because once a definition is known, it becomes clear that it is truly predicated of the subject.