Authors/Thomas Aquinas/posteriorum/L1/Lect18

Lecture 18 Difference between principles and non-principles, common and proper principles

Latin	English
	Lecture 18 (7646-b22) DIFFERENCE BETWEEN PRINCIPLES AND NON-PRINCIPLES, COMMON AND PROPER PRINCIPLES
lib. 1 l. 18 n. 1 Postquam ostendit quod demonstratio non procedit ex principiis communibus sed ex propriis, hic ad evidentiam praemissorum determinat de principiis propriis et communibus. Et circa hoc duo facit. Primo, ostendit necessitatem huiusmodi determinationis, dicens quod difficile est cognoscere utrum sciamus ex principiis propriis (quod solum est vere scire) aut non ex propriis. Opinantur enim multi se scire, si habeant syllogismum ex aliquibus veris et primis. Sed hoc non est verum: immo oportet, ad hoc quod sciamus, quod principia sint proxima illis quae debent demonstrari (quae hic dicuntur prima, sicut et supra dicebantur extrema); vel oportet proxima esse primis principiis indemonstrabilibus.	After showing that demonstration does not proceed from common but from proper principles, the Philosopher, to elucidate this point, decides questions concerning proper and common principles. With respect to this he does two things. First (76a26), he shows the need for such a determination, saying that it is difficult to discern whether we know from proper principles, which alone is truly scientific knowing, or do not know from proper principles. For many believe that they know scientifically if they possess a syllogism composed of things true and first. But this is not so; indeed, to know in a scientific manner it is required that the principles be proximate to the things to be demonstrated—here they are called “first,” just as above they were called “extremes”—or proximate to the first indemonstrable principles.
lib. 1 l. 18 n. 2 Secundo, ibi: dico autem principia etc., determinat de principiis propriis et communibus. Et circa hoc duo facit: primo enim determinat de principiis propriis et communibus; secundo, ostendit qualiter ad huiusmodi principia se habeant demonstrativae scientiae; ibi: non contingere autem et cetera. Circa primum duo facit: primo, distinguit principia a non principiis; secundo, principia ad invicem; ibi: sunt autem quibus et cetera.	Secondly (76a3l), he determines concerning proper and common principles. And in regard to this he does two things. First he determines concerning common and proper principles. Secondly, he shows how the demonstrative sciences are related to such principles (77a10) [L. 20]. Concerning the first he does two things. First, he distinguishes principles from non-principles. Secondly, he distinguishes the principles from each other (76a37).
lib. 1 l. 18 n. 3 Circa primum duo facit. Primo, ostendit quae sint principia, dicens quod principia in unoquoque genere sunt illa quae, cum sint vera, tamen non contingit ea demonstrare vel simpliciter si sint principia prima, vel ad minus non est demonstrare in illa scientia in qua sumuntur ut principia. Dicit autem, cum sint vera, ad differentiam falsorum, quae non demonstrantur in aliqua scientia.	In regard to the first he does two things. First (76a3l), he shows what the principles are and says that the principles in any genus are those which, since they are true, happen not to be demonstrated, either not at all, if they are first principles, or at least not in that science in which they are accepted as principles. And he says, “the existence of which,” (i.e., whose truth), “cannot be proved,” to distinguish from the false which are not demonstrated in any science.
lib. 1 l. 18 n. 4 Secundo, ibi: quid quidem igitur etc., ostendit convenientiam et differentiam inter principia et non principia. Conveniunt enim principia cum non principiis in hoc, quod de utrisque oportet accipere, quasi supponendo quid significent, et prima, idest principia, et quae sunt ex his, idest quae ex principiis sumuntur: quia quod quid est proprie pertinet ad scientiam quae est de substantia, scilicet ad philosophiam primam, a qua omnes aliae hoc accipiunt.	Secondly (76a32), he shows the points of agreement and of difference between principles and non-principles. For principles agree with non-principles in the fact that with respect to each, i.e., with respect both to the first, namely, the principles, and to the things that proceed from them, i.e., things assumed from the principles, one must accept the supposition signify, because the quod quid est [that which the definition of what they signifies] of a thing pertains properly to the science concerned with substance, i.e., to first philosophy, from which all other sciences accept this.
Sed in hoc differunt principia, et quae sunt ex principiis, quia de principiis oportet accipere supponendo quod sunt; de aliis autem, quae sunt ex principiis, oportet demonstrare quia sunt. Sicut in mathematicis accipitur supponendo et quid est unitas, quae est principium, et quid est rectum, et quid est triangulus, quae non sunt principia, sed passiones: sed quod unitas sit, aut quod magnitudo sit, accipit mathematicus quasi principia; alia vero demonstrat, scilicet quae sunt ex principiis. Demonstrat enim triangulum aequilaterum et angulum rectum, et etiam hanc lineam rectam esse.	But they are unlike in the fact that in regard to the principles one must accept the supposition that they are, whereas in regard to things from principles one is required to demonstrate that they are. Thus in mathematics one accepts by supposing both what unity is (which is a principle) and what straight and triangle are (which are not principles but proper attributes): but the fact that unity is or that magnitude is, the mathematician accepts as principles; but the other things, namely, things that are from principles, he demonstrates. For he demonstrates that a triangle is equilateral, or that an angle is right, or even that this line is straight.
lib. 1 l. 18 n. 5 Deinde cum dicit: sunt autem quibus etc., distinguit principia ad invicem: et primo, principia propria a communibus; secundo, communia ad invicem; ibi: non est autem suppositio et cetera. Prima dividitur in duas; in prima, dividit principia propria et communia; in secunda, manifestat quoddam quod poterat esse dubium; ibi: quasdam tamen scientias et cetera.	Then (76a37) he distinguishes principles from one another. First, the proper from the common. Secondly, the common, one from the other (76b23) [L. 19]. The first is divided into two parts. First, he divides proper and common principles. Secondly, he settles something which might be doubtful (76b16).
lib. 1 l. 18 n. 6 Circa primum tria facit. Primo, ponit divisionem, dicens quod principiorum, quibus utimur in demonstrativis scientiis, alia sunt propria uniuscuiusque scientiae, alia vero communia. Et quia hoc posset videri contrarium ei, quod supra ostensum est, quia scientiae demonstrativae non procedunt ex communibus, ideo subiungit quod communia principia accipiuntur in unaquaque scientia demonstrativa secundum analogiam, idest secundum quod sunt proportionata illi scientiae. Et hoc est quod subdit exponens, quod utile est accipere huiusmodi principia in scientiis, quantum pertinet ad genus subiectum, quod continetur sub illa scientia.	In regard to the first he does three things. First (76a37), he lays down a division, saying that “of the principles which we use in demonstrative sciences, some are proper to each single science but others common.” Then, because this statement might seem contrary to what he established above, namely, that demonstrative sciences do not proceed from common principles, he hastens to add that “the common principles are taken in each demonstrative science according to an analogy,” i.e., as proportionate to that science. And this is what he means when by way of explanation he further states that “it is useful” to accept such principles in the sciences insofar as they pertain to the genus of the subject which is investigated in that science.
lib. 1 l. 18 n. 7 Secundo, ibi: propria principia etc., exemplificat de utrisque, dicens quod propria principia sunt, ut lineam esse huiusmodi, vel rectum. Tam enim subiecti quam passionis definitio in scientiis pro principio habetur. Communia vero principia sunt, ut, si ab aequalibus aequalia demas, quae remanent sunt aequalia, et aliae communes animi conceptiones.	Secondly (76a40), he gives examples of each, saying that proper principles are, for example, that a line or a right angle is such and such. For in the sciences the definitions, both of the subject and of the proper attribute, are held as principles. But common principles are, for example, that if equals be subtracted from equals, the remainders are equal, and other common conceptions in the mind.
lib. 1 l. 18 n. 8 Tertio, ibi: sufficiens autem est etc., ostendit quomodo praemissis principiis scientiae demonstrativae utantur. Et primo quidem de communibus dicit quod sufficiens est accipere unumquodque istorum communium, quantum pertinet ad genus subiectum, de quo est scientia. Idem enim faciet geometria, si non accipiat praemissum principium commune in sua communitate, sed solum in magnitudinibus, et arithmetica in solis numeris. Ita enim poterit concludere geometria, si dicat: si ab aequalibus magnitudinibus aequales auferas magnitudines, quae remanent sunt aequales; sicut si diceret: si ab aequalibus aequalia demas, quae remanent sunt aequalia. Et similiter dicendum est de numeris.	Thirdly (76a42), he shows how the demonstrative sciences use the aforesaid principles. First, in regard to the common principles, he says that “it suffices to accept each of those common ones,” so far as it pertains to the generic subject with which the science is concerned. For geometry does this if it takes the above-mentioned common principle not in its generality but only in regard to magnitudes, and arithmetic in regard to numbers. For the geometer will then be able to reach his conclusion by saying that if equal magnitudes be taken from equal magnitudes, the remaining magnitudes are equal, just as if he were to say that if equals are taken from equals, the remainders are equal. The same must also be said for numbers.
lib. 1 l. 18 n. 9 Secundo, ibi: sunt autem propria etc., ostendit qualiter demonstrativae scientiae utantur propriis principiis, dicens quod propria principia sunt quae supponuntur esse in scientiis, scilicet subiecta, circa quae scientia speculatur ea quae per se insunt eis. Sicut arithmetica considerat unitates, et geometria considerat signa, idest puncta et lineas. Praedictae enim supponunt esse et hoc esse, idest supponunt de eis, et quia sunt et quid sunt. Sed de passionibus supponunt praedictae scientiae quid significet unaquaeque; sicut arithmetica supponit quid est par, et quid est impar, aut quid est numerus quadratus aut cubicus; et geometria supponit quid est rationale in lineis. Dicitur enim linea rationalis, de qua possumus ratiocinari per lineam datam: huiusmodi autem est omnis linea commensurabilis lineae datae; quae vero est ei non commensurabilis, vocatur irrationalis vel surda. Similiter et geometria supponit quid est reflexum aut curvum. Sed praedictae scientiae demonstrant de omnibus praedictis passionibus quod sint per principia communia, et ex illis principiis, quae demonstrantur ex communibus. Et quod dictum est de geometria et arithmetica, intelligendum est etiam de astrologia.	Secondly (76b2), he shows how the demonstrative sciences employ proper principles. And he says that proper principles are things supposed in the sciences as existing, namely, the subjects, whose proper attributes are investigated in the sciences. In this way arithmetic considers unities, and geometry considers “signs,” i.e., points, and lines. For they suppose these things to be and to be this, i.e., they suppose of them that they are and what they are. But in regard to the proper attributes they suppose what each signifies. Thus arithmetic supposes what “even” is and what “odd” is and what a “square or cubic number” is. Similarly, geometry supposes what is rational in lines. (For a rational line is one about which we can reason, the line being given. For example, a rational line is any line commensurable with the given lines; but one which is incommensurable with it is called irrational and surd). In like manner, geometry supposes what a reflex or what a curved line are. However, these sciences demonstrate concerning all the above-mentioned proper attributes that they are, and they do so through common principles and principles demonstrated from the common principles. And what has been said 6f geometry and arithmetic should also be understood of astronomy.
Omnis enim scientia demonstrativa est circa tria: quorum unum est genus subiectum, cuius per se passiones scrutantur; et aliud est communes dignitates, ex quibus sicut ex primis demonstrat; tertium autem passiones, de quibus unaquaeque scientia accipit quid significent.	For every demonstrative science is concerned with three things: one is the generic subject whose per se attributes are investigated; another is the common (axioms) dignities from which, as from basic truths, it demonstrates; the third are the proper attributes concerning which each science supposes what their names signify.
lib. 1 l. 18 n. 10 Deinde cum dicit: quasdam tamen scientias etc., manifestat quoddam, quod poterat esse dubium. Quia enim dixerat quod scientiae supponunt de principiis quia sunt, de passionibus quid sunt, de subiectis autem utrumque, posset aliquis credere quod oporteret specialem fieri mentionem de omnibus istis. Unde hoc removet, dicens quod nihil prohibet quasdam scientias despicere quaedam praedictorum, idest non facere mentionem expressam de praemissis, sicut quandoque non facit mentionem de hoc quod supponat genus subiectum esse, si sit manifestum quod sit, quia non est similiter manifestum de omnibus quod sint, sicut quod sit numerus, et quod sit calidum vel frigidum: quorum unum est propinquum rationi, alterum sensui. Similiter et quaedam scientiae non supponunt de passionibus quid significent, expressam mentionem de eis faciendo. Sicut etiam non oportet quod de communibus principiis semper scientiae faciant mentionem, quia nota sunt. Nihilominus tamen, tria praedicta naturaliter sunt in qualibet scientia supponenda.	Then (76b16) he clarifies something about which there might be doubt. For since he had said that the sciences suppose concerning the principles that they are and concerning the proper attributes what they are, but concerning the subject both that it is and what it is, someone might believe that he should have made special mention of all these. Hence he removes this by saying that nothing hinders certain sciences from neglecting some of the aforesaid, i.e., from making express mention of them, as for example, not mentioning that it takes the existence of its generic subject for granted, if it is already obvious that it does exist. For we not have the same evidence in all cases that they do exist, as we do in the case of number and in the case of hot and cold, the one being close to reason and the other to sense. Again, certain sciences do not suppose what the proper attributes signify in the sense of making express mention of them, just as they do not think it necessary always to make express mention of the common principles, because they are known. Be that as it may, the three above-mentioned items are naturally to be supposed in each science.