Authors/Thomas Aquinas/posteriorum/L1/Lect41

Lecture 41 Comparison of science to science from the standpoint of certainty and of unity and diversity

Latin	English
	Lecture 41 (87a31-b17) COMPARISON OF SCIENCE TO SCIENCE FROM STANDPOINT OF CERTAINTY AND OF UNITY AND DIVERSITY
lib. 1 l. 41 n. 1 Postquam philosophus comparavit demonstrationes ad invicem, hic agit de comparatione scientiae, quae est demonstrationis effectus. Et dividitur in duas partes: in prima parte comparat scientiam ad scientiam; in secunda, comparat scientiam ad alios modos cognoscendi; ibi: scibile autem et scientia differunt et cetera. Circa primum duo facit: primo, comparat scientiam ad scientiam secundum certitudinem; secundo, secundum unitatem et pluralitatem; ibi: una scientia autem et cetera.	After comparing demonstrations one with another, the Philosopher here treats of the comparison of science, which is the effect of demonstration. And his treatment falls into two parts. In the first he compares science to science. In the second he compares science to other modes of knowing (88b30) [L. 44]. Concerning the first he does two things. First, he compares science to science as to certitude. Secondly, as to unity and multiplicity (87a38).
lib. 1 l. 41 n. 2 Circa primum ponit tres modos, quibus una scientia est alia certior. Primum modum ponit dicens, quod illa scientia est prior et certior quam alia, quae scilicet eadem facit cognoscere et quia et propter quid. Non autem est illa certior, quae est cognoscitiva solum ipsius quia, separatim ab ea quae cognoscit propter quid: haec enim est dispositio scientiae subalternantis ad subalternatam, ut supra dictum est: nam scientia subalternata separatim scit quia, nesciens propter quid. Sicut chirurgicus scit quod vulnera circularia tardius curantur, non autem scit propter quid. Sed huiusmodi cognitio pertinet ad geometram, qui considerat rationem circuli, secundum quam partes eius non appropinquant sibi per modum anguli, ex qua propinquitate contingit quod vulnera triangularia citius sanantur.	Concerning the first (87a31) he lays down three modes whereby one science is more certain than another. Laying down the first mode, he says that that science is prior and more certain than another, which, namely, makes one know the same things both quia and propter quid. However, that science is not more certain which knows only the quia apart from one which knows propter quid. But this is the relation of subalternating science to subalternate, as has been said above, namely, that the subalternate science in isolation knows quia without knowing propter quid: thus a surgeon knows that circular wounds are healed more slowly, but he does not know why. But such knowledge pertains to the geometer who considers that characteristic of a circle according to which its parts do not lie close enough to form an angle, the nearness of whose sides makes triangular wounds heal more quickly.
lib. 1 l. 41 n. 3 Secundum modum ponit dicens, quod illa scientia, quae non est de subiecto, est certior illa quae est de subiecto. Et accipitur hic subiectum pro materia sensibili, quia, ut philosophus docet in II physicorum, quaedam scientiae sunt pure mathematicae, quae omnino abstrahunt secundum rationem a materia sensibili, ut geometria et arithmetica: quaedam autem scientiae sunt mediae, quae scilicet principia mathematica applicant ad materiam sensibilem, sicut perspectiva applicat principia geometriae ad lineam visualem, et harmonica, idest musica, applicat principia arithmeticae ad sonos sensibiles. Unde hic dicit quod arithmetica est certior quam musica et prior: prior quidem, quia musica utitur principiis eius ad aliud; certior autem, quia incertitudo causatur propter transmutabilitatem materiae sensibilis; unde quanto magis acceditur ad eam, tanto scientia est minus certa.	He lays down the second mode when he says that a science which is not concerned with a subject is more certain than one which is. Here “subject” is taken to mean sensible matter because, as the Philosopher teaches in Physics II, some sciences are purely mathematical, those, namely, which abstract according to reason from sensible matter, as geometry and arithmetic; but other sciences are intermediate, namely, those which apply mathematical principles to sensible matter, as optics applies the principles of geometry to the visual line, and harmony, i.e., music, applies the principles of arithmetic to sensible sounds. Hence he says here that arithmetic is both more certain and prior to music: it is prior, because music uses its principles for something non-mathematical; it is more certain, because lack of certitude arises from matter’s changes. Hence the closer one gets to matter, the less certain the science.
lib. 1 l. 41 n. 4 Tertium modum ponit dicens, quod scientia quae est ex paucioribus, est prior et certior ea quae est ex appositione, idest quam illa quae se habet ex additione. Et ponit exemplum. Sicut geometria est posterior et minus certa quam arithmetica: habent enim se ea de quibus est geometria, ex additione ad ea de quibus est arithmetica. Et hoc quidem planum est videre secundum positiones Platonicas, secundum quas hic Aristoteles exponit, utens eis ad propositum ostendendum; sicut frequenter in libris logicae utitur opinionibus aliorum philosophorum ad propositum manifestandum per viam exempli. Posuit autem Plato quod unum est substantia rei cuiuslibet; quia non distinguebat inter unum quod convertitur cum ente, quod significat substantiam rei, et unum quod est principium numeri, quod considerat arithmeticus.	He lays down the third mode when he says that a science which arises from fewer things is prior and more certain than one which arises from an addition, i.e., than one which results from that addition. And he gives the example that geometry is posterior to and less certain than arithmetic: for the things of geometry are the result of adding to the things which pertain to arithmetic. This is easy to see if one admits the postulates of Plato, according to which Aristotle is proceeding here, using them to prove his point (as he frequently uses the opinions of other philosophers as examples in his logical works in order to explain a point). Now Plato laid it down that “one” is the substance of each thing, because he did not distinguish between “one” which is converted with being and signifies the substance of a thing, and the “one” which is the principle of number and which arithmetic considers.
Hoc ergo unum, secundum quod recipit additionem positionis in continuo, accipit rationem puncti. Unde dicebat quod unum est substantia non habens positionem. Punctum autem est substantia habens positionem: et sic punctum supra unitatem addit positionem. Et sicut ex uno causantur omnes numeri non habentes positionem; ita ex puncto, secundum Platonicos, causantur omnes quantitates continuae. Nam punctus motus facit lineam; linea mota facit superficiem; superficies mota facit corpus. Et secundum hoc quantitates continuae, de quibus est geometria, se habent ex appositione ad numeros, de quibus est arithmetica. Unde Platonici posuerunt numeros esse formas magnitudinum, dicentes formam puncti esse unitatem; formam autem lineae esse binarium, propter duo extrema; formam autem superficiei esse ternarium, propter primam superficiem triangularem, scilicet quae tribus angulis terminatur: formam autem corporis ponebant quaternarium, propter hoc quod prima figura corporea est pyramis triangularis, quae quatuor angulos corporales habet, unum scilicet in conum et tres in basim.	Accordingly, this “one,” as receiving the added characteristic of occupying a position in a continuum, takes on the guise of a point. Hence he said that “one” is a substance not occupying a position; but a point is a substance that does have a position. Consequently, a point adds something to the notion of “one,” namely, position. And just as all numbers not having position are caused from “one,” so from the point, according to the Platonists, all continuous quantities are caused. For a point in motion makes a line; a line in motion makes a plane, and a plane in motion, makes a body. According to this, then, continuous quantities (which art~l treated in geometry) are the result of additions made to numbers (which are the concern of arithmetic). Hence the Platonists laid it down that numbers are the forms of magnitudes, saying that the point’s form is “one,” and the line’s form is “two,” because it has two endpoints, while a surface’s form is “three,” owing to the first surface’s being the triangle which is terminated by three angles; but the form of bodies is “four,” on the ground that the first solid figure is the triangular pyramid, which is composed of four (non-plane) solid angles, namely, one at the apex and three at the base.
lib. 1 l. 41 n. 5 Et secundum hoc patet quod comparatio certitudinis scientiarum accipitur hic secundum duo. Nam primus modus accipitur secundum quod causa est prior et certior suo effectu. Alii autem duo modi accipiuntur secundum quod forma est certior materia, utpote quia forma est principium cognoscendi materiam. Est autem duplex materia, ut dicitur in VII metaphysicae: una quidem sensibilis, secundum quam accipitur secundus modus; alia vero intelligibilis, scilicet ipsa continuitas, et secundum hanc accipitur tertius modus. Et quamvis hic tertius modus expositus sit secundum opinionem Platonis, tamen etiam secundum opinionem Aristotelis punctus se habet ex additione ad unitatem. Nam punctum est quoddam unum indivisibile in continuo, abstrahens secundum rationem a materia sensibili; unum autem abstrahit et a materia sensibili et ab intelligibili.	According to this it is obvious that the comparison of the certitude of sciences is here based on two things: for the first mode is taken according to the cause as it is prior to and more certain than the effect; but the other two are taken according to the form as this is more certain than matter, inasmuch as the form is the principle of knowing the matter. But, as it is stated in Metaphysics VII, matter is twofold: one is sensible, according to which the second mode is taken; the other is intelligible, i.e., its continuity, according to which the third mode is taken. And although this third mode was explained according to Plato’s theory, yet even according to Aristotle’s theory, a point results from some addition to “one”: for a point is an indivisible unity in a continuum, abstracting according to reason from sensible matter; but unity abstracts from both sensible and intelligible matter.
lib. 1 l. 41 n. 6 Deinde cum dicit: una autem scientia est etc., comparat scientias ad invicem secundum unitatem et diversitatem. Et circa hoc duo facit: primo enim ostendit unitatem et diversitatem esse in scientiis et secundum subiectum et principia; secundo, prosequitur et de subiectis et de principiis; ibi: eius autem quod est a fortuna et cetera. Circa primum duo facit: primo, ostendit quid faciat ad unitatem vel diversitatem scientiae; secundo, ostendit quoddam necessarium ad cognoscendum quid faciat ad pluralitatem scientiarum; ibi: plures autem demonstrationes et cetera. Circa primum duo facit: primo, ostendit quid faciat unitatem scientiae; secundo, quid faciat scientiarum diversitatem; ibi: altera autem scientia et cetera. Circa primum duo facit: primo enim ponit quod unitas scientiae consideratur ex unitate generis subiecti; secundo, ostendit quale sit genus, quod potest esse subiectum scientiae; ibi: quaecunque ex primis et cetera.	Then (87a38) he compares sciences one to another according to unity and diversity. Concerning this he does two things. First, he shows that there is unity and diversity among sciences both according to subject and according to principles. Secondly, he treats concerning both the subjects and principles (87b19) [L. 42]. Concerning the first he does two things. First, he shows what makes for unity and diversity of sciences. Secondly, he explains something which is needed for understanding what makes for multiplicity of sciences (87b5). Concerning the first he does two things. First, he shows what makes for the unity of a science. Secondly, what makes for diversity of sciences (87a41). Concerning the first he does two things. First, he lays it down that the unity of a science is considered from the unity of its generic subject. Secondly, he describes the genus which can be the subject of a science (87b8).
lib. 1 l. 41 n. 7 Dicit ergo primo quod scientia dicitur una, ex hoc quod est unius generis subiecti. Cuius ratio est, quia processus scientiae cuiuslibet est quasi quidam motus rationis. Cuiuslibet autem motus unitas ex termino principaliter consideratur, ut patet in V physicorum, et ideo oportet quod unitas scientiae consideretur ex fine sive ex termino scientiae. Est autem cuiuslibet scientiae finis sive terminus, genus circa quod est scientia: quia in speculativis scientiis nihil aliud quaeritur quam cognitio generis subiecti; in practicis autem scientiis intenditur quasi finis constructio ipsius subiecti. Sicut in geometria intenditur quasi finis cognitio magnitudinis, quae est subiectum geometriae; in scientia autem aedificativa intenditur quasi finis constructio domus, quae est huiusmodi artis subiectum. Unde relinquitur quod cuiuslibet scientiae unitas secundum unitatem subiecti est attendenda. Sed sicut unius generis subiecti unitas est communior quam alterius, ut puta entis sive substantiae quam corporis mobilis, ita etiam una scientia communior est quam alia. Sicut metaphysica, quae est de ente sive de substantia, communior est quam physica, quae est de corpore mobili.	He says therefore first (87a38) that a science is said to be one from the fact that it is concerned with one generic subject. The reason for this is that the process of science of any given thing is, as it were, a movement of reason. Now the unity of any motion is judged principally from its terminus, as is clear in Physics V. Consequently, the unity of any science must be judged from its end or terminus. But the end or terminus of a science is the genus concerning which the science treats: because in speculative sciences nothing else is sought except a knowledge of some generic subject; in practical sciences what is intended as the end is the construction of its subject. Thus, in geometry the end intended is knowledge of magnitude, which is the subject of geometry; but in the science of building that which is intended as the end is the construction of a house, which is the subject of this art. Therefore, the unity of each science must be considered in terms of the unity of its subject. But just as the unity of one generic subject is more universal than another, for example, being or substance is more common than mobile being, so one science is more general than another. Thus, metaphysics, which treats of being or substance, is more general in scope than physics, which treats of mobile body.
lib. 1 l. 41 n. 8 Deinde cum dicit: quaecunque ex primis etc., ostendit qualia sunt illa genera, de quibus possunt esse scientiae, et ponit duas conditiones. Quarum unam ponit dicens: quaecunque ex primis componuntur; ista scilicet sunt quorum unius generis una scientia est. Ad cuius evidentiam considerandum est quod, sicut iam dictum est, progressus scientiae consistit in quodam motu rationis discurrentis ab uno in aliud: omnis autem motus a principio quodam procedit et ad aliquid terminatur; unde oportet quod in progressu scientiae ratio procedat ex aliquibus principiis primis. Si qua ergo res est, quae non habeat principia priora, ex quibus ratio procedere possit, horum non potest esse scientia, secundum quod scientia hic accipitur, prout est demonstrationis effectus.	Then (87a38) he describes the marks of those genera concerning which there can be sciences: and he lays down two marks. The first of these is stated when he says, “All the subjects constituted out of primary entities,” i.e., of those subjects of which there is one genus, there is one science. To understand this it should be noted that, as has been said, the process of science consists in a certain movement of reason passing from one thing to another. But all movement starts from some principle or beginning and is terminated at something definite; hence in the progress of a science, reason must proceed from certain first principles, Therefore, if there be anything which does not have prior principles from which reason can proceed, there cannot be science of such things, if we take science to mean the effect of demonstration, as we do here.
Unde scientiae speculativae non sunt de ipsis essentiis substantiarum separatarum. Non enim per scientias demonstrativas possumus scire quod quid est in eis; quia ipsae essentiae harum substantiarum sunt intelligibiles per seipsas ab intellectu ad hoc proportionato; non autem congregatur earum notitia, qua cognoscitur quod quid est ipsarum, per aliqua priora. Sed per scientias speculativas potest scire de eis an sint, et quid non sunt, et aliquid secundum similitudinem in rebus inferioribus inventam. Et tunc utimur posterioribus ut prioribus ad earum cognitionem; quia quae sunt posteriora secundum naturam, sunt priora et notiora quoad nos. Et sic patet quod illa, de quibus habetur scientia per ea quae sunt priora simpliciter, sunt composita secundum se ex aliquibus prioribus. Quaecunque vero cognoscuntur per posteriora, quae sunt prima quoad nos, etsi in seipsis sint simplicia, secundum tamen quod in nostra cognitione accipiuntur, componuntur ex aliquibus primis quoad nos.	Thus, speculative sciences are not concerned with the very essences of separated substances: for we cannot, through demonstrative sciences, know the essences in them, because the essences of such substances are intelligible of themselves to an intellect proportionate to such intelligibility, and a grasp of the essences of such substances is not obtained by any prior conceptions. The only thing that can be known through speculative sciences about these substances is whether they exist and what they are not; anything else about them is known in terms of likenesses to lower things. But in that case we are really using subsequent things as though they were prior in order to understand them, because things that are subsequent according to nature are prior and better known to us. And so it is clear that those things concerning which we have science through what is absolutely prior, are of themselves composed of prior items; but things which are known through subsequent items (but prior in reference to us), even though they be simple in themselves, are nevertheless in our knowledge of them composed of things that are first to us.
lib. 1 l. 41 n. 9 Secundam conditionem ponit cum dicit: et partes aut passiones eorum sunt per se; ubi considerandum est quod subiectum alicuius scientiae duplices partes habere potest, scilicet partes ex quibus componitur sicut ex primis, ut dictum est, idest ipsa principia subiecti, et partes subiectivas. Et quamvis de utrisque partibus possit intelligi quod hic dicitur, tamen magis videtur esse intelligendum de primo genere partium. In qualibet enim scientia sunt quaedam principia subiecti, de quibus est prima consideratio; sicut in scientia naturali de materia et forma, et in grammatica de literis. Est etiam in qualibet scientia aliquid ultimum, ad quod terminatur consideratio scientiae, ut scilicet passiones subiecti manifestentur. Sed utrumque horum, scilicet et primae partes et passiones, possunt alicui attribui et per se et non per se. Nam ea quae sunt per se principia et passiones trianguli, non sunt per se principia et passiones isoscelis, in quantum isosceles est, sed in quantum triangulus. Nec etiam sunt per se principia et passiones aeris et albi, quamvis contingat aliquod aes triangulum esse, vel aliquod album. Unde si qua scientia esset, quae ex principiis trianguli manifestaret passiones trianguli, huiusmodi scientiae subiectum non esset isosceles, neque album aut aes, sed triangulus; cuius etiam per se subiectivae partes sunt isosceles, aequilaterus et gradatus. Sed pro tanto dixi de his partibus hic ad praesens non ita convenienter accipi, quia magis accipere possumus documentum qualiter scientia se habeat ad huiusmodi partes subiectivas, ex eo quod se habet aliqualiter ad totum genus, quam e converso.	He lays down the second mark when he says, “The parts of this total subject and their per se properties.” Here it should be noted that the subject of a science can have two types of parts: first, the parts out of which, as out of first things, it is composed, i.e., the very principles of the subject; and secondly, the subjective parts. And although what is stated here can be applied to either of these types of parts, yet it seems to truer of the first type of parts. For in every science there are the principles of its subject, and these must be considered before all else: for example, in natural science the first consideration is about matter and form, and in grammar about the alphabet. But in every science there is also something ultimate, at which the study of that science terminates, namely, that the properties of the subject be manifested. But each of these, namely, the first parts and the properties, can be attributed to something either per se or not per se. For the per se principles and properties of a triangle are not the per se principles and properties of an isosceles triangle precisely as isosceles, but precisely as triangle. Neither are they the per se principles and properties of brass or white, even though the triangle happens to be of brass or be white. Hence, if there were a science which manifests the properties of triangle from the principles of the triangle, the subject of that science would not be isosceles or white or brass, but triangle—whose per se subjective parts would be isosceles equilateral and scalene.
lib. 1 l. 41 n. 10 Deinde cum dicit: altera autem scientia etc., ostendit rationem diversitatis scientiarum. Et primo, ponit hanc rationem; secundo, manifestat eam; ibi: huiusmodi autem signum et cetera. Est autem considerandum circa primum, quod cum rationem unitatis scientiae acceperit ex unitate generis subiecti, rationem diversitatis scientiarum non accipit ex diversitate subiecti, sed ex diversitate principiorum. Dicit enim quod una scientia est altera ab alia, quarum principia sunt diversa; ita quod nec ambarum scientiarum principia procedant ex aliquibus principiis prioribus, nec principia unius scientiae procedant ex principiis alterius; quia sive procederent ex eisdem principiis, sive alia ex aliis, non esset diversa scientia.	Then (87a41) he shows the reason for sciences being diverse. First, he lays down this reason. Secondly, he explains it (87b1). It should be noted in regard to the first point that although he took the reason for the oneness of a science from the oneness of its generic subject, he does not take the reason for their diversity from the diversity of their subject, but from the diversity of principles. For he says (87a41) that one science is distinct from another when their principles are diverse, in the sense that the principles of the two sciences do not proceed from any prior principles, nor the principles of the one science from those of the other; because if both proceed from the same principles, or if one proceeds from those of another, they would not be diverse sciences.
lib. 1 l. 41 n. 11 Ad huius ergo evidentiam sciendum est, quod materialis diversitas obiecti non diversificat habitum, sed solum formalis. Cum ergo scibile sit proprium obiectum scientiae, non diversificabuntur scientiae secundum diversitatem materialem scibilium, sed secundum diversitatem eorum formalem. Sicut autem formalis ratio visibilis sumitur ex lumine, per quod color videtur, ita formalis ratio scibilis accipitur secundum principia, ex quibus aliquid scitur. Et ideo quantumcunque sint aliqua diversa scibilia secundum suam naturam, dummodo per eadem principia sciantur, pertinent ad unam scientiam; quia non erunt iam diversa in quantum sunt scibilia. Sunt enim per sua principia scibilia.	To understand this it should be noted that a material diversity of objects does not diversity habits, but only a formal diversity. Therefore, since something scientifically knowable is the proper object of a science, the sciences will not be diversified according to a material diversity of, their scientifically knowable objects, but according to their formal diversity. Now just as the formality of visible is taken from light, through which color is seen, so the formal aspect of a scientifically knowable object is taken according to the principles from which something is scientifically known. Therefore, no matter how diverse certain scientifically knowable objects may be in their nature, so long as they are known through the same principles, they pertain to one science, because they will not differ precisely as scientifically knowable. For they are scientifically knowable in virtue of their own principles.
Sicut patet quod voces humanae multum differunt secundum suam naturam a sonis inanimatorum corporum; sed tamen, quia secundum eadem principia attenditur consonantia in vocibus humanis et sonis inanimatorum corporum, eadem est scientia musicae, quae de utrisque considerat. Si vero aliqua sint eadem secundum naturam, et tamen per diversa principia considerentur, manifestum est quod ad diversas scientias pertinent. Sicut corpus mathematicum non est separatum subiecto a corpore naturali; quia tamen corpus mathematicum cognoscitur per principia quantitatis, corpus autem naturale per principia motus, non est eadem scientia geometria et naturalis. Patet ergo quod ad diversificandum scientias sufficit diversitas principiorum, quam comitatur diversitas generis scibilis. Ad hoc autem quod sit una scientia simpliciter utrumque requiritur et unitas subiecti et unitas principiorum. Et ideo de unitate subiecti supra fecit mentionem, cum dixit, quae est unius generis; de principiis autem, cum dixit, quaecunque ex primis et cetera.	This is made clear by an example, namely, that human voices differ a great deal according to their nature from the sounds of inanimate bodies; but because the consonance of human voices and of the sounds of inanimate bodies is considered according to the same principles, the science of music, which considers both, is one science. On the other hand, if there are things which have the same nature but are considered according to diverse principles, it is obvious that they pertain to diverse sciences. Thus, the mathematical body is never really distinct from a natural body; yet because the mathematical body is known through the principles of quantity, but a natural body through the principles of motion, the science of geometry and the science of nature are not the same. It is clear, therefore, that for sciences to be diverse it is enough that the principles be diverse, this diversity of principles being accompanied by a diversity of scientifically knowable objects. But in order to have one science absolutely, both are required, namely, unity of subject and unity of principles. That is why above he made mention of unity of subject when he said, “whose domain is one genus,” but made mention of principles when he said, “all the subjects constituted out of the primary entities of the genus.”
lib. 1 l. 41 n. 12 Sed ulterius considerandum est quod secunda principia virtutem sortiuntur a primis. Unde requiritur diversitas primorum principiorum ad diversitatem scientiarum. Quod quidem non erit, si vel diversorum principia ex eisdem principiis fluant, sicut principia trianguli et quadrati derivantur ex principiis figurae; vel principia unius deriventur ex principiis alterius, sicut principia isoscelis dependent a principiis trianguli.	However, it should be further noted that second principles derive their force from the first principles. Hence for diversity of sciences, diversity of first principles is required. But this will not be verified if the principles of diverse things flow from the same principles, as the principles of triangle and square are derived from the principles of figure, or the principles of one are derived from the principles of another, as the principles of isosceles depend on the principles of triangle.
Nec tamen intelligendum est quod sufficiat ad unitatem scientiae unitas principiorum primorum simpliciter, sed unitas principiorum primorum in aliquo genere scibili. Distinguuntur autem genera scibilium secundum diversum modum cognoscendi. Sicut alio modo cognoscuntur ea quae definiuntur cum materia, et ea quae definiuntur sine materia. Unde aliud genus scibilium est corpus naturale et corpus mathematicum. Unde sunt diversa prima principia utriusque generis, et per consequens diversae scientiae. Et utrumque horum generum distinguitur in diversas species scibilium, secundum diversos modos et rationes cognoscibilitatis.	Yet it should not be supposed that for the unity of a science it is enough that there be unity of first principles absolutely, but unity of first principles in some scientifically knowable genus. Now the genera of the scientifically knowable are distinguished according to the diverse modes of knowing: thus things that are defined with matter are known in one mode, and those defined without matter are known in another. Hence the natural body is one genus of the scientifically knowable, and mathematical body is another genus. Hence there are diverse first principles for each of these genera and, consequently, diverse sciences. Furthermore, each of these genera is distinguished into diverse species according to diverse modes and aspects of intelligibility.
lib. 1 l. 41 n. 13 Deinde cum dicit: huiusmodi autem signum est etc., manifestat positam rationem. Et dicit quod signum huius est, quod scientiae sint alterae secundum principia, cum perveniatur resolvendo ad principia prima, quae sunt indemonstrabilia, quae oportet esse eiusdem generis cum his quae demonstrantur; quia, sicut supra ostensum est, non contingit ex alio genere procedentem demonstrare. Ad hoc autem quod principia indemonstrabilia sint unius generis, accipitur ut signum, cum ea quae demonstrantur per ipsa, sint in eodem genere et congenea, idest connaturalia vel proxima secundum genus sibi ipsis; huiusmodi enim habent eadem principia. Et sic patet quod unitas generis scibilis, in quantum est scibile, ex quo accipiebatur unitas scientiae, et unitas principiorum, secundum quae accipiebatur scientiae diversitas, sibi mutuo correspondent.	Then (87b1) he explains the reason he laid down, saying that a sign of the fact that sciences are diversified according to their principles is obtained when one resolves a science into principles that are indemonstrable, for they must be of the same genus as the things demonstrated; because, as stated above, one does not demonstrate by proceeding from an alien genus. Now the reason why the reaching of indemonstrable principles of one genus is taken as a sign is that the facts demonstrated by them are in the same genus and are co-generic, i.e., connatural, or generically proximate to them: for these have the same principles. And so it is clear that the unity of a scientifically knowable genus, precisely as it is the scientifically knowable genus from which was taken the oneness of the science, and the unity of the principles, according to which was taken th diversity among the sciences, mutually correspond.
lib. 1 l. 41 n. 14 Deinde cum dicit: plures autem demonstrationes etc., ostendit quomodo una conclusio per plura principia demonstrari potest. Et hoc quidem contingit dupliciter. Uno quidem modo, quando ponuntur plura media in eadem coordinatione, et in una demonstratione accipitur unum illorum mediorum, et in alia demonstratione accipitur aliud ad eamdem conclusionem: et sic oportet quod accipiatur medium non continuum; ut si sint duo extrema ab, ut puta habere tres et isosceles, et sint eorum duo media coordinata, scilicet d et c, ut puta triangulus et figura talis. Posset ergo demonstrari a de b duabus demonstrationibus, in quarum una accipietur pro medio c, et in alia d, et in neutra accipietur medium continuum extremis, quia in una accipietur medium continuum uni extremo et discontinuum ab altero, in alia vero e converso.	Then (87b5) he shows how one conclusion can be demonstrated through several principles. And this can happen in two ways: in one way, when”, a number of middles are laid down in the same coordination, and one of these middles is used in one demonstration and another one in another, both leading to the same conclusion. This, of course, requires that the middles be non-continuous. Thus, if the two extremes, A and B, are “to have three” and “isosceles” respectively, but the middles, D and Q are coordinate, as “triangle” and “this type of figure,” A could be demonstrated of B with two demonstrations. In the first one, C could be taken as middle, and D in the other, so that in neither demonstration will, there be a middle continuous with the extremes, because in one demonstration a middle continuous with one extreme and not continuous with the other would be taken, and in the other demonstration the converse would be taken.
lib. 1 l. 41 n. 15 Alio modo hoc contingit, quando accipiuntur diversa media ex diversa coordinatione, ut puta si a, quod est maior extremitas, sit transmutari, et b, quod est minor extremitas, sit delectari, et accipiantur diversa media non existentia sub invicem, scilicet e, quod est quiescere, et d, quod est moveri. Secundum hoc enim eadem conclusio potest concludi per diversa media non unius ordinis; et erit una demonstratio talis: omne quod quiescit transmutatur, quia eiusdem est transmutari et quiescere; omne quod delectatur quiescit, quia quies in bono desiderato causat delectationem; ergo omne quod delectatur transmutatur. Alia demonstratio erit: omne quod movetur transmutatur; omne quod delectatur movetur, quia delectatio est quidam motus appetitivae potentiae; ergo omne quod delectatur transmutatur. Vel quod dicit omne quod delectatur movetur, est secundum opinionem Platonis, et habet locum in delectationibus sensibilibus, quae sunt cum motu. Aliud quod dicit, omne quod delectatur quiescit, est verum secundum opinionem Aristotelis, ut patet in VII et X Ethicorum. Et hoc praecipue verificatur in delectationibus intelligibilibus.	Or this can happen in a second way, namely, when diverse middles are taken from diverse coordinations; for example, if A, which is the major extreme, were “to be altered,” and B, which is the minor extreme, were “to be pleased,” and the middles taken were independent, say G would be “to be at rest,” and D “to be in motion.” In this case the same conclusion can be reached through diverse middles that are not of one order. Thus one demonstration would be this: “Whatever is at rest is altered, because it belongs to the same thing to be at rest and to be altered; but whatever is pleased is at rest, because rest in the desired good causes pleasure: therefore, whatever is pleased is altered.” The other demonstration would be: “Whatever is in motion is altered; but whatever is pleased is in motion, because pleasure is a movement of the appetitive faculty [power]: therefore, whatever is pleased is altered.” (Now the statement, “Whatever is pleased is in motion, “ is Plato’s opinion and is verified in sensible pleasures which involve movement. The other statement, “Whatever is pleased is at rest,” is true according to Aristotle’s opinion, as is clear from Ethics VII and X. And this is verified particularly in intellectual pleasures.
lib. 1 l. 41 n. 16 Deinde dicit quod, sicut hoc ostensum est in prima figura, ita etiam potest in aliis figuris de facili considerari, quod eadem conclusio diversis mediis potest syllogizari. Inducit autem hoc philosophus ad ostendendum quod diversum medium demonstrationis quandoque pertinet ad eamdem scientiam, puta cum est ex eadem coordinatione; quandoque autem ad diversas scientias, puta quando est ex alia coordinatione. Sicut terram esse rotundam per aliud medium demonstrat astrologus, scilicet per eclipsim solis et lunae, et per aliud naturalis, scilicet per motum gravium ad centrum, ut dicitur in II physicorum.	Then he says that just as this has been proved in the first figure, so in the other figures it is easy to see that the same conclusion can be syllogized with diverse middles. Now the Philosopher mentioned this to show that diverse middles of demonstration sometimes pertain to the same science, as when they are taken from the same coordination, and sometimes to diverse sciences, when they are taken from a different coordination. Thus, astronomy demonstrates that the earth is round, using one middle, namely, the eclipse of the sun and moon; and natural science uses another middle, namely, the motion of heavy objects tending toward the center, as it is stated in Physics II.