Authors/Thomas Aquinas/metaphysics/liber4/lect5

Lecture 5

Latin	English
lib. 4 l. 5 n. 1 Hic solvit aliam quaestionem in tertio motam; scilicet utrum ad istam scientiam pertineat considerare prima principia demonstrationis. Et dividitur in duo. Primo ostendit, quod eius est considerare universaliter de omnibus his principiis. Secundo specialiter de primo eorum ibi, congruit autem et cetera. Circa primum tria facit. Primo movet quaestionem, quae est, utrum unius scientiae sit considerare de substantia et de principiis quae in scientiis mathematicis vocantur dignitates, aut est alterius et alterius scientiae considerare. Appropriat autem ista principia magis mathematicis scientiis, quia certiores demonstrationes habent, et manifestius istis principiis per se notis utuntur, omnes suas demonstrationes ad haec principia resolventes.	588. Here he answers another question raised in Book III (387): whether it belongs to this science to consider the first principles of demonstration. This is divided into two parts. In the first he shows that it belongs to this science to make a general study of all these principles; and in the second (596) he shows that it also belongs to it to make a special study of the first of these principles (“And it is fitting”). In regard to the first he does three things. First, he raises the question whether it belongs to one or to different sciences to consider substance and the principles which are called axioms in the mathematical sciences. He assigns these principles more to the mathematical sciences because such sciences have more certain demonstrations and use these self-evident principles in a more manifest way inasmuch as they refer all of their demonstrations to them.
lib. 4 l. 5 n. 2 Palam autem secundo solvit: quae quidem solutio est, quia una scientia intendit de utrisque praedictis: et haec est philosophia, quae prae manibus habetur.	589. Now it is evident (320). Second, he answers this question by saying that a single science investigates both of the foregoing things, and that this is the philosophy with which we are now concerned.
lib. 4 l. 5 n. 3 Omnibus enim tertio probat solutionem propositam: et circa hoc duo facit. Primo probat propositum. Secundo conclusionem principalem inducit, ibi, quoniam igitur et cetera. Probat autem solutionem propositam dupliciter. Primo per rationem. Secundo per signum, ibi, unde nullus et cetera. Ratio talis est. Quaecumque insunt omnibus entibus, et non solum alicui generi entium separatim ab aliis, haec pertinent ad considerationem philosophi: sed praedicta principia sunt huiusmodi: ergo pertinent ad considerationem philosophi. Minorem sic probat. Illa, quibus utuntur omnes scientiae, sunt entis inquantum huiusmodi: sed prima principia sunt huiusmodi: ergo pertinent ad ens inquantum est ens.	590. For these principles (321). Third, he proves his proposed answer, and in regard to this he does two things. First, he proves it. Second (595), he introduces his main conclusion (“It is evident”). Now he proves his proposed answer in two ways. He does this, first, by an argument; and second (592), by an example (“Hence no one”). The argument is as follows: whatever principles pertain to all beings, and not just to one class of beings distinct from the others, belong to the consideration of the philosopher. But the above-mentioned principles are of this kind. Therefore they belong to the consideration of the philosopher. He proves the minor premise as follows. Those principles which all sciences use pertain to being as being. But first principles are principles of this kind. Therefore they pertain to being as being.
lib. 4 l. 5 n. 4 Rationem autem, quare omnes scientiae eis utuntur, sic assignat; quia unumquodque genus subiectum alicuius scientiae recipit praedicationem entis. Utuntur autem principiis praedictis scientiae particulares non secundum suam communitatem, prout se extendunt ad omnia entia, sed quantum sufficit eis: et hoc secundum continentiam generis, quod in scientia subiicitur, de quo ipsa scientia demonstrationes affert. Sicut ipsa philosophia naturalis utitur eis secundum quod se extendunt ad entia mobilia, et non ulterius.	591. The reason which he gives for saying that all sciences use these principles is that the subject genus of each science has being predicated of it. Now the particular sciences do not use the foregoing principles insofar as they are common principles, i.e., as extending to all beings, but insofar as they have need of them; that is, insofar as they extend to the things contained in the class of beings which constitutes the subject of a particular science about which it makes demonstrations. For example, the philosophy of nature uses them insofar as they extend to changeable beings and no further.
lib. 4 l. 5 n. 5 Deinde cum dicit unde nullus probat quod dixerat, per signum. Et primo inducit probationem. Secundo excludit quorumdam errorem, ibi, sed quoniam est adhuc. Dicit ergo primo, quod nullus intendens primo tradere scientiam alicuius particularis entis, conatus est aliquid dicere de primis principiis utrum sint vera aut non: nec geometra, aut arithmeticus, qui tamen istis principiis plurimum utuntur, ut supra dictum est. Unde patet quod consideratio dictorum principiorum ad hanc scientiam pertinet.	592. Hence no one (322). Then he proves what he had said by using an example. First, he introduces the proof; and second (593), he rejects a false notion held by some men (“However, some”). He accordingly says, first, that no one whose chief intention is to hand down scientific knowledge of some particular being has attempted to say anything about the truth or falsity of first principles. Neither the geometer nor the arithmetician does this even though they make the greatest use of these principles, as was said above (588). Hence it is evident that the investigation of these principles belongs to this science.
lib. 4 l. 5 n. 6 Deinde cum dicit nisi physicorum excludit errorem quorumdam: et circa hoc duo facit. Primo excludit errorem eorum, qui de praedictis se intromittebant, cum ad eos non pertineret. Secundo eorum, qui de eis alio modo volebant tractare quam de eis sit tractandum, ibi, quicumque autem utuntur et cetera. Dicit ergo primo, quod quamvis nulla scientiarum particularium de praedictis principiis se intromittere debeat, quidam tamen naturalium de his se intromiserunt; et hoc non sine ratione. Antiqui enim non opinabantur aliquam substantiam esse praeter substantiam corpoream mobilem, de qua physicus tractat. Et ideo creditum est, quod soli determinent de tota natura, et per consequens de ente; et ita etiam de primis principiis quae sunt simul consideranda cum ente. Hoc autem falsum est; quia adhuc est quaedam scientia superior naturali: ipsa enim natura, idest res naturalis habens in se principium motus, in se ipsa est unum aliquod genus entis universalis. Non enim omne ens est huiusmodi: cum probatum sit in octavo physicorum, esse aliquod ens immobile. Hoc autem ens immobile superius est et nobilius ente mobili, de quo considerat naturalis. Et quia ad illam scientiam pertinet consideratio entis communis, ad quam pertinet consideratio entis primi, ideo ad aliam scientiam quam ad naturalem pertinet consideratio entis communis; et eius etiam erit considerare huiusmodi principia communia. Physica enim est quaedam pars philosophiae: sed non prima, quae considerat ens commune, et ea quae sunt entis inquantum huiusmodi.	593. However, some (323). Here he rejects the false notion held by some men, and in regard to this he does two things. First, he rejects the false notion of those who occupied themselves with these principles even though they did not concern them. Second, (594), he rejects the false notion of those who wanted to deal with these principles in a different way than they should be dealt with. He accordingly says, first, that even though none of the particular sciences ought to deal with the above-mentioned principles, nevertheless some of the natural philosophers have dealt with them; and they did so not without reason. For the ancients did not think that there was any substance besides the changeable corporeal substance with which the philosophy of nature is concerned. Hence they believed that they alone established the truth about the whole of nature and therefore about being, and thus about first principles, which must be considered along with being. But this is false, because there is still a science which is superior to the science of nature. For nature itself, i.e., natural being, which has its own principle of motion, constitutes in itself one class of universal being. But not every being is of this kind, because it has been proved in the Physics, Book VIII, that an unchangeable being exists. Now this unchangeable being is superior to and nobler than changeable being, with which the philosophy of nature is concerned. And since the consideration of common being belongs to that science which studies the primary kind of being, then the consideration of common being belongs to a different science than the philosophy of nature. And the consideration of common principles of this kind will also belong to this science. For the philosophy of nature is a part of philosophy but not the first part, which considers common being and those attributes which belong to being as being.
lib. 4 l. 5 n. 7 Deinde cum dicit quicumque vero excludit alium errorem circa modum tractandi huiusmodi principia. Quidam enim tractabant de istis principiis volentes ea demonstrare: et quaecumque isti dixerunt de veritate praedictorum principiorum, quomodo oporteat ea recipere per vim demonstrationis, vel quomodo oporteat contingere veritatem in omnibus istis ita se habere, hoc fecerunt propter ignorantiam, vel propter imperitiam analyticorum, idest illius partis logicae, in qua ars demonstrandi traditur: quia oportet scientes de his pervenire, idest omnis scientia per demonstrationem acquisita ex his principiis causatur. Sed non oportet audientes, idest discipulos instruendos in aliqua scientia, quaerere de his sicut de aliquibus demonstrandis. Vel secundum aliam literam oportet de his pervenire scientes, idest oportet, quod qui acquirunt scientiam per demonstrationem perveniant ad cognoscendum huiusmodi principia communia, et non quod quaerant ea sibi demonstrari.	594. And whatever (324). Then he rejects the other false notion, which concerns the way in which such principles should be treated. For some men investigated these principles with the aim of demonstrating them. And whatever they said about the truth of these principles, i.e., how they must be accepted as true by force of demonstration, or how the truth found in all these principles must be reached, they did through ignorance of, or lack of skill in, “analytics,” which is that part of logic in which the art of demonstration is treated. For “they must know these principles in order to attain scientific knowledge”; i.e., every science acquired by demonstration depends on these principles. But “those who are learning,” i.e., the pupils who are being instructed in some science, must not seek these principles as something to be demonstrated. Or, according to another text, “those who have scientific knowledge must attain science from these principles”; i.e., those who attain knowledge by demonstration must come to know common principles of this kind and not ask that they be demonstrated to them.
lib. 4 l. 5 n. 8 Deinde cum dicit quoniam igitur concludit conclusionem principaliter intentam: scilicet quod philosophi erit considerare de omni substantia inquantum huiusmodi, et de primis syllogismorum principiis. Ad huius autem evidentiam sciendum, quod propositiones per se notae sunt, quae statim notis terminis cognoscuntur, ut dicitur primo posteriorum. Hoc autem contingit in illis propositionibus, in quibus praedicatum ponitur in definitione subiecti, vel praedicatum est idem subiecto. Sed contingit aliquam propositionem quantum in se est esse per se notam, non tamen esse per se notam omnibus, qui ignorant definitionem praedicati et subiecti. Unde Boetius dicit in libro de hebdomadibus, quod quaedam sunt per se nota sapientibus quae non sunt per se nota omnibus. Illa autem sunt per se nota omnibus, quorum termini in conceptionem omnium cadunt. Huiusmodi autem sunt communia, eo quod nostra cognitio a communibus ad propria pervenit, ut dicitur in primo physicorum. Et ideo istae propositiones sunt prima demonstrationum principia, quae componuntur ex terminis communibus, sicut totum et pars, ut, omne totum est maius sua parte; et sicut aequale et inaequale, ut, quae uni et eidem sunt aequalia, sibi sunt aequalia. Et eadem ratio est de similibus. Et quia huiusmodi communes termini pertinent ad considerationem philosophi, ideo haec principia de consideratione philosophi sunt. Determinat autem ea philosophus non demonstrando, sed rationes terminorum tradendo, ut quid totum et quid pars et sic de aliis. Hoc autem cognito, veritas praedictorum principiorum manifesta relinquitur.	595. It is evident (325). He draws the conclusion primarily intended, namely, that it will be the function of the philosopher to consider every substance as such and also the first syllogistic principles. In order to make this clear it must be noted that self-evident propositions are those which are known as soon as their terms are known, as is stated in Book I of the Posterior Analytics. This occurs in the case of those propositions in which the predicate is given in the definition of the subject, or is the same as the subject. But it happens that one kind of proposition, even though it is self-evident in itself, is still not self-evident to all, i.e., to those who are ignorant of the definition of both the subject and the predicate. Hence Boethius says in De Hebdomadibus that there are some propositions which are self-evident to the learned but not to all. Now those are self-evident to all whose terms are comprehended by all. And common principles are of this kind, because our knowledge proceeds from common principles to proper ones, as is said in Book I of the Physics. Hence those propositions which are composed of such common terms as whole and part (for example, every whole is greater than one of its parts) and of such terms as equal and unequal (for example, things equal to one and the same thing are equal to each other), constitute the first principles of demonstration. And the same is true of similar terms. Now since common terms of this kind belong to the consideration of the philosopher, then it follows that these principles also fall within his scope. But the philosopher does not establish the truth of these principles (~) by way of demonstration, but (+) by considering the meaning of their terms. For example, he considers what a whole is and what a part is; and the same applies to the rest. And when the meaning of these terms becomes known, it follows that the truth of the above-mentioned principles becomes evident.