Volume 2 · pp. 200–202

Chapter IV. On those things which are demonstrated through several causes.

Latin (Borgnet)English

pp. 200–202

CAPUT IV. De his quae per plures causas demonstrantur. Contingit autem idem et unum in conclusione vel effectu demonstrari, et per quid est, hoc est, per formam: et propter quid est, hoc est, per finem: et ex necessitate, hoc est ex materia, quae est necessitas demonstrati: sicut est exemplum in hoc effectu vel conclusione per lucernae pellem lumen transire: et hoc patet: et namque ex necessitate disgregitur, quod in parva est partibilius, et per majores poros, hoc est, per majores poros disgregitur ex materiae necessitate, quod partibilius est, hoc est, valde partibile. Et hoc potest esse necessitate pellis per quam egreditur lumen, vel ex necessitate materiae luminis, vel forte ex necessitate utriusque. Et melius exponitur si ex necessitate pellis: quia pellis dividitur per majores poros, quam terrestres soliditates poris interpositae: ita quod majores habet poros, quam sint continuitates interpositae: et ideo luminis emissionem non impediunt, sed pori transducunt lumen emissum. Ex parte luminis sic, quod lumen propter suae substantiae subtilitatem divisibile in subtiliores radios a luminoso corpore (quod in lucerna est) emissos, quam sint pori pellis: et ideo radiales lineae ubique pertranseunt poros: et sic egreditur lumen, et lumen sic emissum disgregitur et late illuminat: quia a quolibet puncto luminosi protractum, a quolibet poro egrediens disgregitur in figuram pyramidis, cujus conus est in puncto luminosi vel in poro pellis: basis autem locus illuminatus: radius enim inferius adveniens a luminoso, ascendit sursum: et radius superius a luminoso ad porum veniens, descendit deorsum: et a dextro veniens, vadit ad sinistrum: et a sinistro veniens, vadit ad dextrum: et sic efficitur pyramis latior, quo magis distat a luminoso vel a poro: siquidem ignis luminosus plus et plus fit disgrediendo, hoc est, per reflexiones ad porosum se spargendo. Hoc est de forma et natura luminosi, quod sic spargitur et multiplicatur ad porosum. Hoc est commentum. <marginal-label>Opinio quorundam de luce et lumine.</marginal-label> Quidam autem dicunt quod lumen vel lux est substantia, cujus natura formalis est se multiplicare per emissionem partis a parte: sed hoc nunquam aliquis dixit auctor: sed fictiones sunt quorumdam ita dicentium. Et sic conjunctae sunt duae causae: formalis, et materialis ad idem ostendendum, ut sic per aliquod genus causae vel per aliquot numero plura unum ostendamus effectum. Siquidem per materiam arguitur, tunc talis erit demonstratio: omne corpus divisibile per poros majores, quam sint soliditates interpositae poris, transducit luminis transitum. Per causam autem formalem sic: omne corpus ex sua forma penetrativum et reflexibile, pertransit pellem lucernae ad majorem illuminationem: forma ignis vel alterius lucentis est talis: ergo pellem lucernae pertransit ad majorem illuminationem. Propter aliquid autem et propter finem sic: quod est conservativum vel contentivum luminis, faciens ne ambulans offendatur, luminis permittit transitum: tale est lucerna: ergo permittit et multiplicat transitum luminis. Et sic idem per tres causas demonstratur. In talibus autem si esse contingit (hoc est, demonstrari) aliquid per plures causas secundum esse: tunc etiam contingit fieri, hoc est, demonstrari per plures causas secundum fieri. Hoc autem patet in alio exemplo praehabito (hoc enim exemplum quod jam induximus, fuit in perspectivis) sicut si tonat extincto igne in nube aquosa, sicut dixit Democritus: tunc enim sonus tonitru probatur per ignis extinctionem sicut per causam efficientem: extincto enim igne in nube aquosa necesse extinctum et ignitum sisinire et sonare: sisinum enim vocatur strepitus et sonus quem ignis extinctus facit in humido: sic ergo demonstratur per causam efficientem. Et si quemadmodum Pythagorici dicunt, tonitru fit minarum et terroris causa his qui sunt in Tartaro, quatenus timeant illi qui sunt in Tartaro juxta fluvios/infernales: tunc potest demonstrari per causam finalem: quia tunc tonat Jupiter quatenus timeant illi qui in Tartaro sunt. Plurima autem hujusmodi sunt, quae sic efficiente et fine et materia demonstrata sunt in his quae natura dicuntur subsistere. In his enim et efficiens et materia et forma et finis sunt in natura constantibus: hoc quidem (hoc est, quaedam) propter hoc determinatum scilicet finem natura fecit: illa vero fiunt ex necessitate. <marginal-label>Necessitas dupliciter, scilicet naturae, et violentiae.</marginal-label> Necessitas autem duplex: haec quidem secundum naturam, sicut est necessitas materiae: et alia secundum motum alicujus exterioris violenter moventis, sicut lapis ex necessitate violentiae fertur sursum, et ex necessitate materiae fertur deorsum. Sed non sic sit propter eamdem et unius rationis necessitatem: quia illa quae est secundum violentiam, est necessitas efficiens. In naturalibus autem est necessitas materiae. Sed in his quae fiunt ab intelligentia agente sive a proposito, alia quidem, hoc est, quaedam nequaquam fiunt ab eo quod est per se frustra (hoc est, sine causa finali) ita quod fiant frustra, sicut artificialia in quibus vel actio ipsa vel opus factum finis est, ut domus effigies (hoc est, imago vel idolum) quod fit ut repraesentet absentem. Neque ex necessitate materiae fiunt: quia materiae necessitas non est nisi ad naturalia, quae potentia sic sunt in materia, quod motore naturali educuntur de illa: sed sunt talia propter hoc quod determinant finem: et ideo talia per finem habent demonstrari. Alia vero talium sunt a fortuna vel casu quae sunt per accidens, ut sanitas aliquando, et salus aliquando: ut qui non intendens sanari ambulavit, et ambulando sanatus est: et qui intendit exire de domo non ut salvetur, domo postea cadente salvatus est exeundo. Maxime autem attenditur finis in quibusdam naturalibus et artificialibus in quibuscumque possibile est fieri et sic et aliter: quia contingentia sunt, in quibus fortuna non est causa: quia in illis non intenditur finis in quibus generationis (hoc est, effectus) fortuna est causa: in illis enim non est finis. Propter quod patet, quod finis bonus (hoc est, finis qui est bonum) semper est in eo quod propter aliquid fit: et fit tale quid aut natura aut arte: et in talibus est demonstratio ex efficiente vel fine: a fortuna autem nihil propter aliquid: et ideo in talibus nihil per finem demonstratur.

CHAPTER IV. On those things which are demonstrated through several causes. But it happens that the same and one thing in the conclusion or effect is demonstrated both through what it is, that is, through form, and through on account of what it is, that is, through the end, and from necessity, that is, from matter, which is the necessity of the demonstrated thing. An example is in this effect or conclusion: that light passes through the covering of a lamp. And this is clear; for from necessity it is dispersed, because in a small thing it is more divisible, and through the greater pores, that is, it is dispersed through greater pores from the necessity of matter, because it is more divisible, that is, very divisible. And this can be from the necessity of the covering through which the light goes out, or from the necessity of the matter of light, or perhaps from the necessity of both. And it is better expounded if from the necessity of the covering, because the covering is divided by greater pores than the earthy solidities interposed between the pores, so that it has greater pores than the interposed continuities are; and therefore they do not impede the emission of light, but the pores lead through the emitted light. On the part of light it is thus, that light, because of the subtlety of its substance, is divisible into subtler rays emitted from the luminous body which is in the lamp than are the pores of the covering; and therefore radial lines everywhere pass through the pores. And thus light goes out, and light thus emitted is dispersed and illuminates broadly, because, drawn from any point of the luminous body and going out from any pore, it is dispersed into the figure of a pyramid, whose cone is at the point of the luminous body or in the pore of the covering, but whose base is the illuminated place. For a ray coming from the luminous body lower down ascends upward; and a ray coming from the luminous body above to the pore descends downward; and one coming from the right goes to the left; and one coming from the left goes to the right; and thus the pyramid is made broader the more it stands apart from the luminous body or from the pore. Indeed the luminous fire becomes more and more by being dispersed, that is, by spreading itself through reflections toward the porous thing. This belongs to the form and nature of the luminous thing, that it is thus spread and multiplied toward the porous thing. This is the commentary. <marginal-label>Opinion of certain persons concerning light and illumination.</marginal-label> But certain people say that lumen or lux is a substance whose formal nature is to multiply itself through the emission of part from part; but no authoritative writer ever said this, but these are fictions of certain people speaking thus. And so two causes are joined, formal and material, for showing the same thing, so that thus through some genus of cause or through several things greater in number we may show one effect. If indeed one argues through matter, then the demonstration will be such: every body divisible through pores greater than the solidities interposed to the pores leads through the passage of light. But through the formal cause thus: every body penetrative and reflective from its form passes through the covering of the lamp for greater illumination; the form of fire or of another shining thing is such; therefore it passes through the covering of the lamp for greater illumination. But on account of something and on account of the end thus: that which is preservative or containing of light, making it so that one walking may not be struck, permits the passage of light; the lamp is such; therefore it permits and multiplies the passage of light. And thus the same thing is demonstrated through three causes. But in such things, if something happens to be, that is, to be demonstrated, through several causes according to being, then it also happens to come to be, that is, to be demonstrated, through several causes according to coming-to-be. But this is clear in another example previously had, for this example which we have now introduced was in optics: as if it thunders when fire has been extinguished in a watery cloud, as Democritus said; then the sound of thunder is proved through the extinction of fire as through the efficient cause. For when fire has been extinguished in a watery cloud, it is necessary that the extinguished and kindled thing hiss and sound; for `sisinium` is called the crash and sound which extinguished fire makes in moisture. Thus therefore it is demonstrated through the efficient cause. And if, in the way the Pythagoreans say, thunder comes to be for the sake of threats and terror for those who are in Tartarus, so that those who are in Tartarus near the infernal rivers may fear, then it can be demonstrated through the final cause, because then Jupiter thunders so that those who are in Tartarus may fear. But very many things of this sort are demonstrated thus by efficient cause and end and matter in those things which are said to subsist by nature. For in these things both efficient cause and matter and form and end exist in things standing firm in nature. This indeed, that is, certain things, nature made on account of this determinate thing, namely an end; but those other things come to be from necessity. <marginal-label>Necessity in two ways, namely of nature and of violence.</marginal-label> But necessity is twofold: this according to nature, as is the necessity of matter; and another according to the motion of some exterior thing moving violently, as a stone from the necessity of violence is borne upward and from the necessity of matter is borne downward. But it should not so be on account of the same necessity and a necessity of one account, because that which is according to violence is efficient necessity; but in natural things there is necessity of matter. But in those things which come to be from an acting intelligence or from purpose, some, that is, certain things, in no way come to be from that which is per se in vain, that is, without a final cause, so that they come to be in vain, as artificial things in which either the action itself or the work made is the end, as a likeness of a house, that is, an image or idol, which is made so that it may represent one absent. Nor do they come to be from the necessity of matter, because the necessity of matter belongs only to natural things, which are potentially in matter in such a way that by a natural mover they are drawn out from it. But such things exist on account of this, that they determine the end; and therefore such things have to be demonstrated through the end. But other things of such things are from fortune or chance, which are per accidens, as health sometimes and safety sometimes; as one who, not intending to be healed, walked and by walking was healed, and one who intended to go out of the house not in order to be saved was saved by going out when the house afterward fell. But the end is most greatly attended to in certain natural and artificial things, in whatever things it is possible to come to be both thus and otherwise, because they are contingent things, in which fortune is not the cause, because in those things the end is not intended in which fortune is the cause of generation, that is, of the effect; for in those things there is no end. For this reason it is clear that the good end, that is, the end which is a good, is always in that which comes to be on account of something; and such a what comes to be either by nature or by art; and in such things there is demonstration from the efficient cause or from the end. But from fortune nothing is on account of something; and therefore in such things nothing is demonstrated through the end.