Book II, lectio XIIQUOMODO IN DEMONSTRATIONE ACCIPIATUR CAUSA QUAE NON EST SIMUL CUM EFFECTU IN IIS QUAE CIRCULARITER FIUNT; ET QUALITER DIVERSIMODE DEMONSTRETUR PER CAUSAM IN HIS QUAE SUNT SEMPER, ET IN HIS QUAE SUNT UT FREQUENTER
Aristotle's text
Quoniam autem videmus in his quae fiunt circulo quamdam generationem esse, et contingit hoc esse si quidem consequantur ad invicem medium et termini; in his enim converti est; ostensum est autem hoc in prioribus, quod convertantur conclusiones: circulo autem esse hoc est. In operibus autem videtur sic. Compluta enim terra, necesse est vaporem fieri; hoc autem facto, nubem; hac vero facta, necesse est terram complutam esse. Hoc autem erat ex principio; quare circulo circuivit: cum enim unum horum quodlibet est, alterum est; et cum illud est, alterum; et cum hoc, primum.
Sunt autem quaedam quae fiunt universaliter, semper quidem, et in omni aut se habent aut fiunt semper: alia vero semper quidem non, sed sicut frequenter sunt, ut non semper omnis homo masculus barbatus, sed est sicut frequenter. Talium igitur necesse est et medium sicut frequenter esse. Si enim A de B praedicatur universaliter et B de C universaliter, necesse est et A de C semper et de omni praedicari; hoc enim erat universaliter et de omni et semper. Sed suppositum est sicut frequenter esse; necesse ergo est medium sicut frequenter esse, quod est in quo est B. Erunt igitur et eorum quae sunt frequenter principia sine medio, quaecunque frequenter sunt sic aut fiunt.
Quomodo quidem igitur quod quid est inter terminos assignatum est, et qualiter demonstratio aut definitio sit ipsius aut non, dictum est prius.
The Latin version St Thomas commented, as the Leonine edition prints it.
The cause of things which are, is the same also as that of things which are generated, which have been generated, and which will be, for the middle is the cause, except that being is the cause to be, what is generated, to those which are generated, what has been, to those which have been, and what will be to those that will be. Thus why was there an eclipse? because the earth was interposed, but an eclipse is generated, because an interposition of the earth is generated, but there will be, because the earth will be, and there is, because it is interposed. What is ice? Let it be assumed to be congealed water; let water be C, congealed A, the middle cause B, a perfect defect of heat; B then is present with C, but with this A, viz. to be congealed, but ice is generated, when B is generated, it was so, when the latter was so, and it will be, when the latter will be.
Hence that which is thus a cause, and that of which it is the cause, are generated at one and the same time, when they are generated; are simultaneously when they are; and in like manner, in respect to the having been, and the will be, generated. In the case of things which are not simultaneous, are there in a continued time, as it seems to us, different causes of different things? for instance, is another thing having been generated the cause of this thing having been generated, and another thing which will be, the cause that this will be, and of this being, something which was generated before? the syllogism however is from what was afterwards generated. And the principle of these are those things which have been generated, wherefore the case is the same as to things which are generated. From the prior indeed there is no (syllogism), as that this thing was afterwards generated, because that thing was generated, it is the same also in regard to the future. For whether the time be indefinite or definite, it will not result that because that thing was truly said to have been generated, this which is posterior is truly said to have been generated, since in the interval it will be false to say this,1 when already another thing2 has been produced. The same reasoning also happens to what will be, nor because that3 was produced, will this be, as the middle must be generated at the same time;4 of things that have been that which has been, of the future the future, of what are produced that which is produced, of things which are that which is, but of what was generated, and of that which will be, the middle cannot possibly be produced at one and the same time. Moreover neither can the interval § be indefinite, nor definite,5 since it will be false to assert it in the interval;6 but we must consider what is connected with it, so that after the having been generated, to be generated may exist in things.7 Or is it evident that what is generated is not connected with what was generated ? for the past does not cohere with what was generated, since they are terms and individuals. As then neither points are mutually connected, those things which have been produced are not so, for both are indivisible; nor for the same reason does that which is, cohere with that which has been generated, for that which is generated is divisible, but that which has been is indivisible. As a line then is to a point, so is that which is to that which was generated, for infinite things which have been, are inherent in that which is;|| we must however enunciate these matters more clearly in the universal discussions about motion. Concerning then the manner in which, when there is a successive generation, the middle cause subsists, let so much be assumed, for in these also it is necessary that the middle and the first should be immediate, thus A was generated because C was so, but C was after, A before. The principle indeed is C, because it is nearer to the now, which is the principle of time, but C was generated if D was, hence from D having been, it is necessary that A should have been. The cause however is C, for from D having been, it is necessary that C should have been generated, but C having been, A must of necessity have been produced before. When however we thus assume the middle, will (the process) at any time stop at the immediate, or on account of the infinity will a medium always intervene? for, as we have stated, what has been generated is not connected with what has been; nevertheless we must commence at least from the immediate8 and from the first now.9 Likewise with regard to the “will be,” for if it is true to say that D will be, it is necessary that, prior to this, it should be true to say that A will be, the cause however of this is C, for if D will be, prior to it C will be, but if C will be, prior to it A will be. Likewise also in these the division is infinite, for things which will be, are not mutually coherent, but an immediate principle must also be assumed in these. It is thus in the case of works, if a house has been built, stones must necessarily have been cut, and formed; and why this? because the foundation must of necessity have been laid, if the house was built, but if the foundation was laid, stones must necessarily have been prepared before. Again, if there shall be a house, in like manner there will be stones prior to this, still the demonstration is in like manner through a medium, for the foundation will have a prior subsistence.
Notwithstanding, since we see in things which are, that there is a certain generation in a circle, this happens when the middle and the extremes follow each other, for in these there is a reciprocation; this however was shown in the first treatise, viz. that the conclusions are converted; but the case of being in a circle is thus. In works it appears after this manner, when the earth has been moistened, vapour is necessarily produced, from the production of this, there is a cloud, from this last, water, and from the presence of this, the earth is necessarily moistened, this however was the (cause) at first, so that it has come round in a circle, for any one of these existing, another is, and if that is, another, and from this, the first.
There are some things which are generated universally, (for always, and in every thing, they either thus subsist, or are generated,) but others not always, but for the most part; thus not every vigorous man has a beard, but this is generally the case, now of such things it is necessary that the medium also should be for the most part; for if A is universally predicated of B, and this of C universally, it is necessary that A also should be predicated always, and of every C, (for the universal is that which is present with every individual and always,) but it was supposed to be for the most part, wherefore it is necessary that the medium also, B, should be for the most part: hence of those which are for the most part, the principles are immediate, as many as thus subsist for the most part, or are generated.
The whole chapters, in the translation of Octavius Freire Owen (London: George Bell & Sons, 1889 (Bohn's Classical Library), vol. I, from the plates of the first edition (London: H. G. Bohn, 1853), same pagination).
Synopsis by the Leonine editors
1. Argumentum primae partis lectionis. — 2. In iis quae circulo generantur, causa syllogizatur a posteriori, si hoc modo accipiantur termini demonstrationis, quod medium et extremi se invicem consequantur: neque tamen haec est demonstratio circularis, quia quod assumitur ut principium et conclusio, non est idem numero, sed solummodo idem specie. — 3. Manifestatur assertum per exempla. — 4. Altera pars lectionis. — Diversitas demonstrationis per causam in iis quae fiunt semper, et in iis quae fiunt sicut frequenter. — 5. Ad concludendum id quod est sicut frequenter, necesse est accipere medium quod est sicut frequenter. — 6. Epilogus eorum quae dicta sunt circa τὸ quod quid est et circa τὸ propter quid.
St Thomas's commentary
1. Postquam Philosophus ostendit quomodo accipiendum sit medium quod est causa in his quae fiunt in rectum, hic ostendit quomodo debeat accipi in his quae fiunt secundum generationem circularem. Et primo, ostendit propositum; secundo, manifestat per exempla; ibi: In operibus autem videtur sic etc.
2. Circa primum considerandum est quod, quia motus caeli circularis causa est generationis in istis inferioribus, ideo dicitur in II De generatione, quod quaedam circulatio in generationibus invenitur, puta quod ex aqua generatur terra, et ex terra iterum aqua. Dicit ergo quod, quia videmus esse quamdam generationem in his quae circulo generantur, in his etiam contingit observari hoc quod supra dictum est, scilicet quod syllogizetur a posteriori, si hoc modo accipiantur termini demonstrationis, quod medium et extremi termini se invicem consequuntur: quia in his quae sic generantur, est quaedam conversio circularis, dum scilicet a primo generato devenitur ad ultimum, et ab ultimo reditur ad primum, non idem numero, sed idem specie, ut patet in II De generatione. Et ita non sequitur quod idem numero sit prius et posterius, effectus et causa. Et hoc ipsum competit processui demonstrationum, eo quod, ut in praecedentibus dictum est, quandoque conclusiones convertuntur, ut scilicet ex eis syllogizentur aliquae praemissarum; hoc enim est circulo demonstrare. Quod quamvis non competat si omnino sit unum et idem quod prius fuit conclusio, et postea est principium respectu eiusdem numero, ne sit idem notius et minus notum; si tamen non sit omnino idem, sicut accidit in his quae circulo generantur, nullum inconveniens est.
3. Deinde cum dicit: In operibus autem videtur sic etc., manifestat quod dixerat per exempla, et dicit quod in ipsis operibus naturae videtur sic evenire, quod sit quidam circularis processus. Quia si terra sit compluta, necesse est quod per actionem solis vapor ex ea resolvatur; quo resoluto et sursum elevato, necesse est quod generetur nubes; et hac generata, necesse est quod generetur aqua pluviae; qua generata, necesse est quod cadens super terram compluat eam. Et hoc est quod accipiebamus quasi primum: non tamen est eadem complutio terrae ad quam ultimo pervenitur, et a qua primo incipiebatur. Et sic manifestum est quod factus est quidam circuitus, inquantum uno eorum existente fit aliud, et illo existente fit aliquod aliud; quo existente reditur ad primum, non idem numero, sed idem specie. Iste tamen causarum circuitus inveniri non potest secundum ordinem qui invenitur in causis per se: sic enim necesse est pervenire ad unum primum in quolibet genere causarum, ut probatur in II Metaphys. Quod autem aqua generetur ex igne, et ignis iterato ex aqua, hoc non est per se, sed per accidens. Non enim ens per se generatur ut ex ente in actu, sed ex ente in potentia, ut dicitur in I Physicor. Procedendo ergo in causis per se non erit circulatio. Nam complutionis terrae causam agentem accipiemus calorem aeris, qui causatur ex sole, et non e converso; causam vero materialem aquam, cuius materia non est vapor, sed materia communis elementorum.
4. Deinde cum dicit: Sunt autem quaedam quae etc., ostendit qualiter diversimode demonstretur per causam in his quae sunt semper, et in his quae sunt ut frequenter. Et circa hoc tria facit: primo, proponit quod intendit; secundo, probat propositum; ibi: Si enim A de B etc.; tertio, epilogat quae dicta sunt; ibi: Quomodo quidem igitur etc. Dicit ergo primo quod quaedam sunt quae universaliter fiunt, et quantum ad tempus, quia semper, et quantum ad subiectum, quia in omnibus, aut se habent, sicut immobilia, quibus non competit proprie fieri, aut fiunt, sicut mobilia quae semper eodem modo se habent, ut patet in motibus caelestibus. Quaedam vero non fiunt sicut semper, sed sicut frequenter. Et ponit de his exemplum. Sicut quod omnis homo masculus efficiatur quandoque barbatus, non accidit semper, sed sicut frequenter. Sicut igitur eorum quae sunt semper, oportet accipere medium quod est semper; ita et talium, quae sunt sicut frequenter, oportet accipere medium sicut frequenter.
5. Deinde cum dicit: Si enim A de B praedicatur etc., probat quod ad concludendum id quod est sicut frequenter, necesse sit accipere medium quod sit sicut frequenter. Detur enim oppositum, quod accipiatur medium quod sit universaliter et semper; puta si A, quae est maior extremitas, praedicetur universaliter de B, quod est medium, et B de C, quod est minor extremitas: ex necessitate sequitur quod A praedicetur de C universaliter, et quantum ad tempus et quantum ad subiectum, quod est semper et de omni praedicari. Unde idem nunc dicimus universaliter praedicari, quod praedicari de omni et semper. Sed suppositum erat quod A praedicaretur de C sicut frequenter. Necesse est ergo quod medium, quod est B, accipiatur sicut frequenter existens. Sic igitur patet quod possunt accipi quaedam immediata principia eorum quae sunt frequenter, ita quod ipsa principia sint aut fiant sicut frequenter. Huiusmodi tamen demonstrationes non faciunt simpliciter scire verum esse quod concluditur, sed secundum quid, scilicet quod sit verum ut in pluribus; et sic etiam principia quae assumuntur, veritatem habent. Unde huiusmodi scientiae deficiunt a scientiis, quae sunt de necessariis absolute, quantum ad certitudinem demonstrationis.
6. Deinde cum dicit: Quomodo quidem igitur etc., epilogat ea quae dicta sunt; et dicit quod iam supra dictum est, quomodo quod quid est, quod est aliqualiter idem ei quod propter quid, assignatur inter terminos syllogisticos, dum ostensum est qualiter singula causarum genera, et in singulis diversitatibus rerum, sint media demonstrationum. Dictum est etiam qualiter eius quod quid est sit vel non sit demonstratio vel definitio.
No English translation of this commentary is in the public domain: the Latin is given here.
Notes of the Leonine editors
α) Quod quia motus etc. — Fl om. quia. — 1: circulariter. — AS: ut dicitur; F et p. m. C: et ideo dic.; C s. m.: et ideo ut dic. — A: (om. quod) ideo quaedam; CEFIKLMNOQST p. m. D et ed. a om. quod. — Quae hic a s. Thoma recitantur ex secundo libro De generatione, ibidem ab eodem s. Doctore ad mentem Aristotelis exponuntur in haec verba: « Si... motus caeli est in circuitu, oportet quod quaecunque sunt passiones huius motus, et quaecunque sunt per hunc motum solum, sicut per causam efficientem, quod etiam illa sint. Si enim quod in circuitu movetur movet elementa, necesse est etiam quod motus horum, quae sunt passiones eius, et quod motus eorum quae sufficienter generantur ab hoc, sint etiam ex necessitate. Verbi gratia, cum allatio superioris, hoc est circuli declivis, sit in circuitu, necesse est quod moveantur etiam alii planetae. Quia vero hoc, idest Sol movetur in circuitu, necesse est etiam horas in circuitu generari et iterari; horis autem in circuitu generatis, necesse est quod omnia quae sunt a causa efficiente, sicut a motu Solis et motu horarum, sint etiam generata ex necessitate et in circuitu. Et hae sunt generationes elementorum, quia ex istorum generatione omnia alia generantur, maxime omnia temporalia » (Lect. xii, cit. in marg.).
β) Medium et extremi termini. — In nostro textu, τὸ μέσον καὶ οἱ κροι, medium et extremi; et est lectio Bekkeri (Ed. Acad. Reg. Boruss., pag. 95, col. 2). Waitz ponit τὸ μέσον καὶ οἱ ὅροι, medium et termini,
et in Comm. super cap. XII, pag. 413, ait: « Dedimus δὶ ὅροι, quod etiam » Boeth. et vet. intp. habuerunt: nam οἱ ἄκροι, quod Bkk. exhibuit, » haud scio an nullo alio loco hoc sensu usurpatum ab Aristotele occur- » rat; quamquam neutrum τὰ ἄκρα saepissime apud eum maiorem et » minorem terminum significet, qui quod hic dicantur οἱ ὅροι offendere » non potest, quia opponuntur τῷ μέσ: hunc enim certis finibus circum- » scribunt (ὁρίζουσι), quos ille, quum latius pateat minore, dum maioris » ambitu superetur ipse, transire nequit. » — Philoponus in II Poster. utrumque ponit, τοὺς ἄκρους ὅρους (Ed. graec. pag. 228). Anonymus in textu, quem refert, Aristotelis, habet οἱ ἄκροι; et οἱ ἄκροι repetit in ipsius textus expositione (ib. pag. 278-9). De significationibus quibus usurpatur ab Aristotele vox ἄκρος cf. Bonitz, Index Aristotelicus.
γ) Ut in praecedentibus dictum est. — BO: sicut in primo; Q: (om. ut) in praecedenti; alii codd.: (om. ut) in praesenti; D. s. m. (om. ut) in praecedentibus dictum est quod quandoque etc. Retinemus in praecedentibus: attamen lectio BO conformior videtur textui, in primis: Διὰ ταῦτα δὲ τοῦτο ἐν τοῖς πρώτοις. De demonstratione circulari actum est in I libro, lect. VIII (Cf. lect. XXXI, seqq.). In citata lect. VII, not. β, duo probavimus, nempe circularem demonstrationem esse impossibilem attenta natura syllogismi demonstrativi, et servato eodem genere demonstrationis; esse autem possibilem circularem demonstrationem, variato eius genere, non simpliciter in omnibus, sed in his quae possunt ad invicem converti. Quae illic asseruimus hic habes expresse confirmata a s. Thoma.