Authors/Thomas Aquinas/posteriorum/L1/Lect25

Lecture 25 demonstration “quia” differs from demonstration “propter quid” when the former pertains to one science and the latter to another

Latin	English
	Lecture 25 (78b34-79a16) HOW DEMONSTRATION “QUIA” DIFFERS FROM DEMONSTRATION “PROPTER QUID” WHEN THE FORMER PERTAINS TO ONE SCIENCE AND THE LATTER TO ANOTHER
lib. 1 l. 25 n. 1 Postquam ostendit philosophus qualiter demonstratio quia differt a demonstratione propter quid in eadem scientia; hic ostendit quomodo differt in diversis scientiis. Et circa hoc duo facit. Primo, proponit intentum, dicens quod alio modo a praedictis differt propter quid ab ipso quia, propter hoc quod in diversis scientiis considerantur, idest quod ad unam scientiam pertinet scire propter quid, et ad aliam scientiam pertinet scire quia.	After showing how demonstration quia differs from demonstration propter quid in the same science, the Philosopher shows how they differ in sciences that are diverse. And he does two things: First, he states his proposition, saying (78b34) that in a way other than the above the propter quid differs from the quia due to the fact that they are considered in diverse sciences, i.e., that the propter quid pertains to one science and the quia to another.
Secundo cum dicit: huiusmodi autem sunt etc., manifestat propositum. Et circa hoc duo facit: primo, manifestat propositum in scientiis, quarum una est sub altera; secundo, in scientiis, quarum una non est sub altera; ibi: multae autem non sibi et cetera. Circa primum duo facit: primo, ostendit qualiter se habeant scientiae ad invicem, quarum una est sub altera, ad quarum unam pertinet propter quid, ad alteram autem quia; secundo, ostendit quomodo in praedictis scientiis ad unam earum pertinet quia, et ad aliam propter quid; ibi: hoc enim ipsum et cetera. Circa primum duo facit: primo, ostendit quomodo praedictae scientiae se habeant ad invicem secundum ordinem; secundo, ostendit qualiter se habeant ad invicem secundum convenientiam; ibi: fere autem univocae et cetera.	Secondly (78b34) he elucidates his proposition. First, he elucidates it in sciences one of which is under the other. Secondly, in sciences one of which is not under the other (79a13). Concerning the first he does two things. First, he shows how those sciences are related, one of which is under the other and to one of which pertains the quia and to the other the propter quid. Secondly, he shows how in these sciences the quia pertains to one and the propter quid to the other (790). Concerning the first he does two things. First, he shows how such sciences relate to one another as to order. Secondly, how they relate to one another as to agreement (79a1).
lib. 1 l. 25 n. 2 Dicit ergo primo quod huiusmodi scientiae sunt (scilicet ad quarum unam pertinet quia, ad aliam autem propter quid) quaecunque sic se habent ad invicem, quod altera est sub altera. Sed intelligendum est unam scientiam esse sub altera dupliciter. Uno modo, quando subiectum unius scientiae est species subiecti superioris scientiae; sicut animal est species corporis naturalis, et ideo scientia de animalibus est sub scientia naturali. Alio modo, quando subiectum inferioris scientiae, non est species subiecti superioris scientiae; sed subiectum inferioris scientiae comparatur ad subiectum superioris, sicut materiale ad formale. Et hoc modo accipit hic unam scientiam esse sub altera, sicut speculativa, idest perspectiva, se habet ad geometriam. Geometria enim est de linea et aliis magnitudinibus: perspectiva autem est circa lineam determinatam ad materiam, idest circa lineam visualem. Linea autem visualis non est species lineae simpliciter, sicut nec triangulus ligneus est species trianguli: non enim ligneum est differentia trianguli. Et similiter machinativa, idest scientia de faciendis machinis, se habet ad stereometriam, idest ad scientiam quae est de mensurationibus corporum. Et haec scientia dicitur esse sub scientia per applicationem formalis ad materiale. Nam mensurae corporum simpliciter comparantur ad mensuras lignorum et aliarum materierum, quae requiruntur ad machinas, per applicationem formalis ad materiale. Et similiter se habet harmonica, idest musica, ad arithmeticam. Nam musica applicat numerum formalem (quem considerat arithmeticus) ad materiam, idest ad sonos. Et similiter se habet apparentia, idest scientia navalis, quae considerat signa apparentia serenitatis vel tempestatis, ad astrologiam, quae considerat motus et situs astrorum.	He says therefore first (78b35) that these sciences (i.e., to one of which pertains quia and to the other propter quid) are the ones so related that one is under the other. But this occurs in two ways: in one way, when the subject of one science is a species of the subject of the higher science, as animal is a species of natural body—consequently, the science of animals is under natural science; in another way, when the subject of the lower science is not a species of the subject of the higher science but is compared to the latter as material to formal. An example of this latter way of one science being under another is the way “specular,” i.e., optics, is under geometry. For geometry is concerned with lines and other magnitudes, whereas optics is concerned with a line determined to matter, i.e., the visual line. Now the visual line is not, strictly speaking, a species of line any more than wooden triangle is a species of triangle: for wooden is not a difference in respect to triangle. In like manner mechanical engineering, i.e., the science of making machines, is related to stereometry, i.e., the science of measuring bodies. This science is said to be under the other as applying the formal to the material. For the measures of bodies’ absolutely are compared to the measures of wood and other material required for machines as the application of the formal to the material. In like manner, harmonics, i.e., music, is related to arithmetic: for music applies formal number, which arithmetic considers, to matter, i.e., to sounds. And the same is true of “appearance,” i.e., nautical science (which considers the signs indicative of calm or storm), as compared to astronomy, which considers the motions and positions of the stars.
lib. 1 l. 25 n. 3 Deinde cum dicit: fere autem univocae etc., ostendit qualiter se habent praedictae scientiae ad invicem secundum convenientiam, dicens quod fere huiusmodi scientiae sunt univocae ad invicem. Dicit autem fere, quia communicant in nomine generis, et non in nomine speciei. Dicuntur enim omnes praedictae scientiae mathematicae; quaedam quidem quia sunt de subiecto abstracto a materia, ut geometria et arithmetica, quae simpliciter mathematicae sunt; quaedam autem per applicationem principiorum mathematicorum ad res materiales, sicut astrologia dicitur mathematica et etiam navalis scientia, et similiter harmonica, idest musica, dicitur mathematica, et quae est secundum auditum, idest practica musicae, quae cognoscit ex experientia auditus sonos. Vel potest dici quod sunt univocae, quia etiam in nomine speciei conveniunt. Nam et navalis dicitur astrologia, et practica musicae dicitur musica. Dicit autem fere, quia hoc non contingit in omnibus, sed in pluribus.	Then (79a1) he shows how the aforesaid sciences relate to one another in point of agreement. And he says that these sciences are almost mutually univocal. And he says, “almost,” because they agree in the name of their genus and not in the name of their species. Thus, all the sciences mentioned above are called mathematical: some, indeed, because they are concerned with a subject which is abstracted from matter, as geometry and arithmetic, which are absolutely mathematical; but others are so through applying mathematical principles to material things, as astronomy is called mathematical and as nautical science is. Similarly, harmonics, i.e., music, is called mathematical and so is acoustics, i.e., practical music, which knows sounds through experience based on hearing. Or it might be said that they are univocal because they also agree in the name of their species, for we speak of nautical astronomy as astronomy and of practical music as music. But because this is not so in all but only in some, he says “almost.”
lib. 1 l. 25 n. 4 Deinde cum dicit: hoc enim ipsum etc., manifestat quomodo in praedictis scientiis ad unam scientiam pertinet quia, et ad aliam propter quid.	Then (79a3) he shows how in these sciences the quia pertains to the one science and the propter quid to the other.
Et circa hoc duo facit: primo, ostendit quomodo scientiae, quae sub se continent alias, habent dicere propter quid; secundo, quomodo scientiae, quae sub eis continentur, habent dicere propter quid respectu aliarum scientiarum; ibi: habet autem se et cetera.	In regard to this there are two points. First, he shows how those sciences which contain others under them state the propter quid. Secondly, how sciences which are contained under another one state the propter quid of some others (79a10).
Sciendum ergo est circa primum quod in omnibus praenominatis scientiis, illae quae continentur sub aliis, applicant principia mathematicae ad sensibilia. Quae autem sub se continent alias sunt magis mathematicae. Et ideo dicit primo philosophus quod scire quia est sensibilium, idest scientiarum inferiorum, quae applicant ad sensibilia: sed scire propter quid est mathematicorum, idest scientiarum, quarum principia applicantur ad sensibilia. Huiusmodi enim habent demonstrare ea, quae assumuntur ut causae in inferioribus scientiis.	One should note, therefore, with respect to the first point that in all the above-mentioned sciences, the ones which are contained under others apply mathematical principles to sensible things, while the ones which contain others under them are more mathematical. Accordingly, the Philosopher first of all says (79a3) that to know the quia pertains to the sensible, i.e., to the lower sciences, which make application to sensible things; but to know the propter quid pertains to the mathematical, i.e., to those sciences whose principles are not applied to sensible things. For these latter sciences are concerned with demonstrating matters which are accepted as causes in the lower sciences.
Et quia posset aliquis credere quod qui sciret propter quid, sciret etiam de necessitate quia, consequenter hoc removet dicens quod multoties illi, qui sciunt propter quid, nesciunt quia. Et hoc manifestat per exemplum: sicut considerantes universale, multoties nesciunt quaedam singularia, propter hoc, quod non intendunt per considerationem; sicut qui scit omnem mulam esse sterilem, nescit de ista, quam non considerat. Et similiter mathematicus qui demonstrat propter quid, nescit quandoque quia, quia non applicat principia superioris scientiae ad ea, quae demonstrantur in inferiori scientia.	But because someone might suppose that whoever knows the propter quid also necessarily knows the quia, he dismisses this, saying that very frequently those who know the propter quid do not know the quia. And he gives as an example of this those who, when considering the universal often take no account of the singulars precisely because their speculation does not consider them: thus, one who knows that every mule is sterile, does not know this of the one he does not consider. In like manner, a mathematician who demonstrates propter quid, now and then does not know the quia, because he does not apply the principles of the higher sciences to matters demonstrated in the lower science.
Et quia dixerat quod scire propter quid est mathematicorum, vult ostendere cuiusmodi genus causae a mathematicis sumatur. Unde dicit quod istae scientiae, quae accipiunt propter quid a mathematicis, sunt alterum quiddam, idest differunt ab eis secundum subiectum, scilicet in quantum applicant ad materiam. Unde huiusmodi scientiae utuntur speciebus, idest formalibus principiis, quae accipiunt a mathematicis. Mathematicae enim scientiae sunt circa species. Non enim earum consideratio est de subiecto, idest de materia; quia quamvis ea, de quibus geometria considerat, sint in materia, sicut linea, superficies et huiusmodi; non tamen considerat de eis geometria, secundum quod sunt in materia, sed secundum quod sunt abstracta. Nam geometria ea, quae sunt in materia secundum esse, abstrahit a materia secundum considerationem. Scientiae autem ei subalternatae e converso accipiunt ea, quae sunt considerata in abstractione a geometra, et applicant ad materiam. Unde patet quod geometra dicit propter quid in istis scientiis secundum causam formalem.	And because he had said that it belongs to mathematics to know the propter quid, he proposes to indicate which genus of cause is used by mathematics. Hence he says that those sciences which receive the propter quid from mathematics “are something else,” i.e., they differ from the mathematical according to subject, i.e., insofar as they make application to matter. Hence these latter “use forms’ “ i.e., formal principles, which they receive from mathematics: “for the mathematical sciences concern forms.” For their considerations do not bear on the subject, i.e., on matter, because although the items which geometry considers exist in matter, for example, the line, plane and so on, nevertheless geometry does not consider them precisely as they are in matter, but as abstracted. For those things that are in matter according to existence, geometry abstracts from matter according to consideration. Conversely, the sciences subalternated to it accept those things which were considered in the abstract by geometry and apply them to matter. Hence it is plain that it is according to the formal cause that geometry states the propter quid in those sciences.
lib. 1 l. 25 n. 5 Deinde cum dicit: habet autem se etc., ostendit quod etiam scientia subalternata dicit propter quid, non respectu subalternantis, sed respectu cuiusdam alterius. Perspectiva enim subalternatur geometriae. Et si comparemus perspectivam ad geometriam, perspectiva dicit quia et geometria propter quid. Sed sicut perspectiva subalternatur geometriae, ita scientia de iride subalternatur perspectivae. Applicat enim principia, quae perspectiva tradit simpliciter, ad determinatam materiam. Unde ipsius physici, qui tractat de iride, est scire quia; sed perspectivi est scire propter quid. Dicit enim physicus conversionem visus ad nubem, aliquo modo dispositam ad solem, esse causam iridis. Propter quid autem sumit a perspectivo.	Then (79a10) he shows that even the subalternated sciences state the propter quid, not of its subalternating science but of some other science. Thus, optics is subalternated to geometry, so that if we compare the one with the other, optics states the quia and geometry the propter quid. But just as optics is subalternated to geometry, so the science of the rainbow is subalternated to optics, for it applies to a determinate matter the principles which optics hands down absolutely. Hence it belongs to the naturalist who treats of the rainbow to know the quia, but to the expert in optics to know the propter quid. For the naturalist says that the cause of the rainbow is the convergence of a visual line at a cloud arranged in some relation to the sun; but the propter quid he takes from optics.
lib. 1 l. 25 n. 6 Deinde cum dicit: multae autem et non sub etc., ostendit quomodo quia et propter quid differunt in diversis scientiis non subalternatis, dicens quod multae scientiarum, quae non sunt sub invicem, sic se habent ad invicem, scilicet quod ad unam pertinet quia, et ad alteram pertinet propter quid. Sicut patet de medicina et geometria. Non enim subiectum medicinae sumitur sub subiecto geometriae, sicut subiectum perspectivae; sed tamen ad aliquam conclusionem, in medicina consideratam, applicabilia sunt principia geometriae. Sicut quod vulnera circularia tardius sanentur, medici est scire quia, qui hoc experitur, sed propter quid scire est geometrae, ad quem pertinet cognoscere quod circulus est figura sine angulo. Unde partes circularis vulneris non appropinquant sibi, ut possint de facili coniungi. Sciendum autem est quod illa differentia quia et propter quid, quae est secundum diversas scientias, continetur sub altero praedictorum modorum, scilicet quando fit demonstratio per causam remotam.	Then (79a13) he shows how quia and propter quid differ among sciences that are diverse but not subalternate. And he says that many sciences which are not subalternate are nevertheless related, i.e., in such a way that one states the quia and the other the propter quid. This is true of medicine and geometry. For the subject of medicine is not subsumed under the subject of geometry as the subject of optics is. Nevertheless, the principles of geometry are applicable to certain conclusions reached in medicine: for example, it belongs to the man of medicine who observes it to know quia that circular wounds heal rather slowly; but to know the propter quid belongs to the geometer, whose business it is to know that a circle is a figure without corners. Hence the edges of a circular wound are not close enough to each other to allow them to be easily joined. It should also be noted that this difference of quia and propter quid between sciences that are diverse is contained under one of the modes previously discussed, namely, when the demonstration is made through a remote cause.