Authors/Thomas Aquinas/metaphysics/liber11/lect4

Lecture 4

Latin	English
lib. 11 l. 4 n. 1 Postquam philosophus ostendit quomodo consideratio huius scientiae est circa entia, et ea quae consequuntur ens inquantum huiusmodi; hic ostendit quomodo consideratio huius scientiae est de primis principiis demonstrationis. Et dividitur in duas partes. In prima ostendit quod ad hanc scientiam pertinet considerare de his. In secunda determinat de quodam principio demonstrationis quod est inter alia primum, ibi, est autem quoddam et cetera. Circa primum duo facit. Primo ostendit propositum ex consideratione scientiae mathematicae. Secundo ex consideratione scientiae naturalis, ibi, eodem autem. Utitur autem in prima parte tali ratione. Quaecumque communia a scientiis particularibus accipiuntur particulariter, et non secundum quod sunt in sua communitate, pertinent ad considerationem huius scientiae. Sed prima principia demonstrationis accipiuntur a mathematica et ab aliis particularibus scientiis particulariter tantum: ergo eorum consideratio secundum quod sunt communia, pertinet ad hanc scientiam, quae considerat de ente inquantum est ens.	2206. Having shown how the investigations of this science are concerned with beings and with the attributes which belong to being as being, the Philosopher now shows how the investigations of this science are concerned with the first principles of demonstration. This is divided into two parts. In the first (932)C 2206) he shows that it is the office of this science to consider these first principles of demonstration. In the second (934:C 2211) he draws his conclusions about one principle of demonstration which is prior to the others (“There is a principle”). In regard to the first he does two things. First (932:C 2206), he clarifies his thesis by considering the science of mathematics; and second (933:C 2209), by considering the philosophy of nature (“Now what applies”). In the first part he uses the following argument: all the common axioms which are used by the particular sciences in a way peculiar to themselves and not in their common aspect belong to the consideration of this science. But the first principles of demonstration are used by the science of mathematics and by other particular sciences in a way peculiar to themselves. Therefore an investigation of these principles insofar as they are common belongs to the science which considers being as being.
lib. 11 l. 4 n. 2 Dicit ergo quod mathematicus utitur principiis communibus proprie, idest secundum quod appropriantur suae materiae. Oportet autem quod ad primam philosophiam pertineat considerare principia huiusmodi secundum suam communitatem. Sic enim accepta sunt principia suiipsorum secundum quod sunt alicui materiae particulari appropriata. Et hoc quod dixerat manifestat per exemplum.	2207. He accordingly says that, since the mathematician uses “the common axioms in a particular way,” i.e., insofar as they are adapted to his subject matter, it must be the function of first philosophy to consider such principles in their common aspect. For these principles are taken as principles of the sciences insofar as they are adapted to some particular subject matter. He clarifies his statement by an example.
lib. 11 l. 4 n. 3 Nam hoc principium: si ab aequalibus aequalia demas, quae relinquuntur aequalia sunt, est commune in omnibus quantis, in quibus inveniuntur aequale et inaequale. Sed mathematica assumunt huiusmodi principia ad propriam considerationem circa aliquam partem quanti, quae est materia sibi conveniens. Non est enim aliqua mathematica scientia, quae consideret ea quae sunt quantitatis communia, inquantum est quantitas. Hoc enim est primae philosophiae. Sed considerant mathematicae scientiae ea quae sunt huius vel illius quantitatis, sicut arithmetica ea quae sunt numeri, et geometria ea quae sunt magnitudinis. Unde arithmeticus accipit praedictum principium, secundum quod pertinet ad numeros tantum; geometra autem secundum quod pertinet ad lineas vel ad angulos. Non autem considerat geometra hoc principium circa entia inquantum sunt entia; sed circa ens inquantum est continuum, vel secundum unam dimensionem ut linea, vel secundum duas ut superficies, vel secundum tres ut corpus. Sed philosophia prima non intendit de partibus entis inquantum aliquid accidit unicuique eorum; sed cum speculatur unumquodque communium talium, speculatur circa ens inquantum est ens.	2208. The principle that “when equals are subtracted from equals the remainders are equal” is common to all instances of quantity which admit of equality and inequality. But the science of mathematics presupposes principles of this kind in order to make a special study of that part of quantity which constitutes its proper subject matter; for there is no mathematical science which considers the attributes common to quantity as quantity, because this is the work of first philosophy. The mathematical sciences rather consider those attributes which belong to this or to that quantity; for example, arithmetic considers the attributes that belong to number, and geometry considers those that belong to continuous quantity. Thus the arithmetician uses the above-mentioned principle only inasmuch as it has to do with numbers, and the geometer uses it inasmuch as it has to do with lines and with angles. The geometer, however, does not consider this principle inasmuch as it relates to beings as beings but inasmuch as it relates to being as continuous, whether it is continuous in one dimension, as a line; or in two, as a surface; or in three, as a body. But first philosophy does not study the parts of being inasmuch as each has certain accidents; but when it studies each of these common attributes, it studies being as being.
lib. 11 l. 4 n. 4 Deinde cum dicit eodem autem ostendit idem ex consideratione naturalis scientiae; dicens, quod eodem modo se habet naturalis scientia quantum ad hoc sicut et mathematica; quia naturalis scientia speculatur accidentia entium, et principia, non inquantum sunt entia, sed inquantum sunt mota. Sed prima scientia est de his secundum quod sunt entia, et non secundum aliquid aliud. Et ideo naturalem scientiam et mathematicam oportet partes esse primae philosophiae, sicut particularis scientia pars dicitur esse universalis.	2209. Now what applies (933). Then he makes the same thing clear by considering the philosophy of nature. He says that what applies in the case of the science of mathematics is also true of the philosophy of nature; for while the philosophy of nature studies the attributes and principles of beings, it does not consider beings as beings but as mobile. The first science, on the other hand, deals with these inasmuch as they are being, and not in any other respect. Hence, the philosophy of nature and the science of mathematics must be parts of first philosophy, just as any particular science is said to be a part of a universal science.
lib. 11 l. 4 n. 5 Quod autem huiusmodi principia communia pertineant ad considerationem primae philosophiae, huius ratio est quia cum omnes primae propositiones per se sint, quorum praedicata sunt de ratione subiectorum; ad hoc quod sint per se notae quantum ad omnes, oportet quod subiecta et praedicata sint nota omnibus. Huiusmodi autem sunt communia, quae in omnium conceptione cadunt; ut ens et non ens, et totum et pars, aequale et inaequale, idem et diversum, et similia quae sunt de consideratione philosophi primi. Unde oportet, quod propositiones communes, quae ex huiusmodi terminis constituuntur, sint principaliter de consideratione philosophi primi.	2210. The reason why common principles of this kind belong to the consideration of first philosophy is this: since all first self-evident propositions are those of which the predicate is included in the definition of the subject, then in order that propositions may be self-evident to all, it is necessary that their subjects and predicates should be known to all. Common notions of this type are those which are conceived by all men, as being and non-being, whole and part, equal and unequal, same and different, and so on. But these belong to the consideration of first philosophy; and therefore common propositions composed of such terms must belong chiefly to the consideration of first philosophy.