Authors/Thomas Aquinas/physics/L3/lect8

Lecture 8 No Sensible Infinite

Latin	English
	LECTURE 8 No Sensible Infinite
lib. 3 l. 8 n. 1 Postquam philosophus removit opinionem antiquorum qui de infinito non naturaliter loquebantur, illud a sensibilibus separantes, hic ostendit non esse infinitum, sicut philosophi naturales ponebant. Et primo ostendit hoc per rationes logicas; secundo per rationes naturales, ibi: physice autem magis et cetera. Dicuntur autem primae rationes logicae, non quia ex terminis logicis logice procedant, sed quia modo logico procedunt, scilicet ex communibus et probabilibus, quod est proprium syllogismi dialectici.	349. After rejecting the opinion of the earlier philosophers who spoke non-naturally of the infinite, separating it from sensible things, the Philosopher now shows there is no infinite even in the sense in which the natural philosophers laid it down. First he shows this by logical reasons; Secondly by natural reasons in 353. The first set of reasons are called “logical,” not because they proceed logically from logical terms, but because they proceed in a logical manner, i.e., from common and probable propositions, which is the characteristic of the dialectical syllogism.
lib. 3 l. 8 n. 2 Ponit ergo duas logicas rationes. In quarum prima ostenditur quod non sit aliquod corpus infinitum. Definitio enim corporis est, quod sit determinatum planitie, idest superficie, sicut definitio lineae est quod eius termini sint puncta. Nullum autem corpus determinatum superficie, est infinitum: ergo nullum corpus est infinitum; neque sensibile, quod est corpus naturale, neque intelligibile, quod est corpus mathematicum. Quod ergo dicit rationabiliter, exponendum est logice: nam logica dicitur rationalis philosophia.	350. He gives therefore [237 204 b4] two logical reasons. In the first of these it is shown that there is no infinite body. For the definition of body is that it is determined by a surface, just as the definition of a line is that its terms are points. But no body determined by a surface is infinite. Therefore, no body is infinite, whether it be sensible, i.e., a natural body, or intelligible, i.e., a mathematical body. (The word “rational” [or dialectical] should be here expounded as “logical” indeed, logic is called “rational philosophy.”)
lib. 3 l. 8 n. 3 Secunda ratio ostendit quod non sit infinitum multitudine. Omne enim numerabile contingit numerari, et per consequens numerando transiri; omnis autem numerus, et omne quod habet numerum, est numerabile; ergo omne huiusmodi contingit transiri. Si igitur aliquis numerus, sive separatus, sive in sensibilibus existens, sit infinitus, sequetur quod possibile sit transire infinitum; quod est impossibile.	351. The second reason shows that there is no infinite multitude. For everything countable can be numbered and consequently passed through by counting. But every number and whatever has a number is countable. Therefore, every such thing can be passed over. If, therefore any number, whether separated or existing in sensible things, be infinite, it follows that the infinite can be passed through, which is impossible.
lib. 3 l. 8 n. 4 Attendendum est autem quod istae rationes sunt probabiles, et procedentes ex iis quae communiter dicuntur. Non enim ex necessitate concludunt: quia qui poneret aliquod corpus esse infinitum, non concederet quod de ratione corporis esset terminari superficie, nisi forte secundum potentiam; quamvis hoc sit probabile et famosum. Similiter qui diceret aliquam multitudinem esse infinitam, non diceret eam esse numerum, vel numerum habere. Addit enim numerus super multitudinem rationem mensurationis: est enim numerus multitudo mensurata per unum, ut dicitur in X Metaphys. Et propter hoc numerus ponitur species quantitatis discretae, non autem multitudo; sed est de transcendentibus.	352. Notice that these reasons are probable and proceed from common premises. For they do not conclude of necessity: in effect, whoever posits an infinite body would not concede that it would of its very nature be terminated by a surface, except perhaps potentially; although this is probable and well-known. Similarly, whoever would posit an infinite multitude would not admit it to be a number or that it has a number. For number adds to multitude the notion of measure, because a number is “multitude measured by unity,” as is said in Metaphysics X. For this reason number is considered to be a species of discrete quantity, but multitude is not; it is, rather, a transcendental.
lib. 3 l. 8 n. 5 Deinde cum dicit: physice autem magis etc., inducit rationes naturales ad ostendendum quod non sit corpus infinitum in actu. Circa quas considerandum est quod, quia Aristoteles nondum probaverat corpus caeleste esse alterius essentiae a quatuor elementis, opinio autem communis suo tempore fuerat quod esset de natura quatuor elementorum, procedit in his rationibus ac si non esset aliud corpus sensibile extra quatuor elementa, secundum suam consuetudinem: quia semper antequam probet id quod est suae opinionis, procedit ex suppositione opinionis aliorum communis. Unde postquam probavit in primo libro de caelo et mundo, caelum esse alterius naturae ab elementis, ad veritatis certitudinem iterat considerationem de infinito, ostendens universaliter quod nullum corpus sensibile est infinitum. Hic autem primo ostendit quod non sit corpus sensibile infinitum, supposito quod sint elementa finita multitudine; secundo ostendit idem universaliter, ibi: oportet autem de omni et cetera. Dicit ergo primo quod procedendo naturaliter, idest ex principiis scientiae naturalis, magis et certius considerari poterit quod non sit corpus sensibile infinitum, ex iis quae dicentur. Omne enim corpus sensibile aut est simplex aut compositum.	353. Then [238 204 b10] he produces natural reasons to show that there is no infinite body in act. In connection with these reasons one must consider that since Aristotle had not yet proved that the heavenly body was of another essence from that of the four elements, and the common opinion of his time was that it was of the same nature as the four elements, he therefore proceeds in these reasonings as though there were no other sensible body outside of the four elements. This is in keeping with his custom, since he always, before proving that which is his own belief, proceeds from what is supposed by the common opinion of others. Hence, after he proved in De Caelo I (l.4) that the heavens are of another nature from the elements, he repeats, for the sake of the certitude of the truth, the consideration of the infinite, showing unqualifiedly that no sensible body is infinite. Here, however, he first shows that there is no sensible infinite body on the supposition that the elements are finite in number; secondly he shows the same thing in a universal way, at no. 358. He says therefore first that when one proceeds “naturally,” i.e., according to the principles of natural science, one is better able, and with more certitude, to consider that there is no sensible infinite body from what will be said. For every sensible body is either simple or composite.
lib. 3 l. 8 n. 6 Primo ergo ostendit quod non sit corpus sensibile compositum infinitum, supposito quod sint elementa finita secundum multitudinem. Non enim potest esse quod unum ipsorum sit infinitum et alia finita: quia ad compositionem alicuius corporis mixti requiritur quod sint plura elementa, et quod contraria aliquo modo adaequentur; alias compositio permanere non posset; quia illud quod esset omnino potentius, destrueret alia, cum elementa sint contraria. Si autem unum elementorum esset infinitum, nulla aequalitas esset, aliis finitis existentibus; quia infinitum improportionaliter excedit finitum. Non ergo hoc potest esse, quod unum tantum eorum quae veniunt in mixtionem, sit infinitum. Posset autem aliquis dicere quod illud infinitum esset debilis virtutis in agendo, et ideo non potest vincere alia, scilicet finita, quae sunt fortioris virtutis, utpote si infinitus sit aer et finitus ignis. Et ideo ad hoc removendum dicit, quod quantumcumque potentia unius corporis quod ponitur infinitum, deficiat a potentia alterius corporis quod ponitur finitum, utpote si ignis sit finitus et aer infinitus; necesse est tamen dicere quod aer quantumcumque duplicatus, idest secundum aliquem numerum multiplicatus, sit aequalis igni in potentia. Si enim potentia ignis est centuplo maior quam potentia aeris eiusdem quantitatis, si aer centuplicetur secundum quantitatem, erit aequalis ei in potentia: et tamen aer centuplicatus est multiplicatus secundum aliquem numerum determinatum, et vincitur a potentia totius aeris infiniti. Unde manifestum est quod etiam potentia ignis vincetur a potentia aeris infiniti; et sic infinitum excellit et corrumpit finitum, quantumcumque potentioris naturae videatur.	354. First therefore he shows that there is no composite sensible body that is infinite, supposing that the elements are finite according to multitude. For it cannot be that one of the elements is infinite and the others finite—because the composition of any compound body requires that there be a number of elements and that the contraries therein be somehow in equilibrium. If this were not so, the composition could not endure—for the strongest would destroy all the others, since the elements are contrary. But if one of the elements were infinite, no equilibrium would ensue as long as the other elements were finite, because there is no proportion between infinite and finite. Therefore it cannot be that only one of the elements in the composite be infinite. But someone could claim that the infinite element might have such weak energy in acting, that it would not destroy the finite elements which are stronger; for example, if the infinite one were air and the finite one fire. And therefore, to remove this objection he says that no matter how much less the energy of that one infinite body is than that of the finite body (for example, if fire be infinite and air finite) nevertheless an infinite accumulation of air would be equal in energy to the fire. For if the energy of the fire is one hundred times greater than an equal quantity of air, then if the air be multiplied a hundredfold, it will equal the fire in energy; and yet air multiplied a hundred times is multiplied according to a finite number and is exceeded by the power of the whole infinite amount of air. Hence, it is clear that even the energy of the fire will be overcome by the energy of infinite air: thus the infinite will excel and corrupt the finite, no matter how powerful its nature.
lib. 3 l. 8 n. 7 Similiter etiam non potest esse quod quodlibet elementorum ex quibus componitur corpus mixtum, sit infinitum: quia de ratione corporis est quod habeat dimensiones in omnem partem, non in longitudinem tantum ut linea, neque in longitudinem et latitudinem solum ut superficies: de ratione autem infiniti est, quod habeat distantias seu dimensiones infinitas; ergo de ratione corporis infiniti est quod habeat dimensiones infinitas in omnem partem. Et sic non potest esse quod ex pluribus corporibus infinitis aliquod unum componatur, quia quodlibet occupat totum mundum; nisi ponantur duo corpora esse simul, quod est impossibile.	355. Similarly, it cannot be that any of the elements out of which a compound body is composed be infinite; because it is a property of a body that it have dimensions in every direction, and not in length only, as in a line, or in length and width only, as on a surface. But the nature of the infinite is to have infinite “distances” or dimensions. Therefore, the infinite body should have infinite dimensions in every direction. Thus, it cannot be that one body result from a number of infinite bodies, because each occupies the whole world, unless you posit that two bodies interpenetrate, which is impossible.
lib. 3 l. 8 n. 8 Sic igitur ostenso quod corpus compositum non potest esse infinitum, ostendit ulterius quod nec etiam corpus simplex, neque unum elementorum, neque aliquod medium inter ea, ut vapor est medium inter aerem et aquam. Quidam enim posuerunt hoc esse principium, ex eo alia generari dicentes. Et hoc dicebant esse infinitum: non autem aerem, aut aquam, aut aliquod aliorum elementorum; quia contingeret alia elementa corrumpi a quocumque ipsorum, quod infinitum poneretur, quia elementa habent contrarietatem ad invicem, cum aer sit humidus, aqua frigida, ignis calidus, terra sicca: unde si unum horum esset infinitum, corrumperet alia, cum contrarium natum sit corrumpi a contrario. Et ideo dicunt aliquid aliud ab elementis esse infinitum, ex quo sicut ex principio elementa causantur. Hanc autem positionem dicit esse impossibilem, non solum quantum ad hoc, quod dicit tale corpus medium esse infinitum, quia de hoc dicetur communis quaedam ratio tam de igne et aere, et aqua, quam etiam de corpore medio; sed ex hoc ipso etiam est impossibilis praedicta positio, quia ponit aliquod principium elementare praeter quatuor elementa. Non enim invenitur aliquod corpus sensibile praeter ea quae dicuntur elementa, scilicet aerem, aquam et huiusmodi: sed hoc oporteret si aliquid aliud praeter elementa veniret in compositionem istorum corporum. Unumquodque enim compositum resolvitur in ea ex quibus componitur. Si igitur aliquid aliud veniret in compositionem istorum corporum quam haec quatuor elementa, sequeretur quod hic apud nos inveniretur aliquod corpus simplex praeter ista elementa, per resolutionem istorum in elementa. Sic igitur patet quod positio praemissa falsa est quantum ad hoc, quod posuit aliquod corpus simplex praeter haec elementa nota.	356. Therefore, having shown that a composite body cannot be infinite, he now proves that neither can a simple body, nor one of the elements, nor any medium among the elements(taking vapor as a medium between air and water) be infinite. For some posited this last as a principle stating other things to be generated from it. And they said that this was something infinite, but not air or water or any of the other elements; because the other elements would be corrupted by whichever one was supposed as infinite. For the elements have contrariety one to the other since air is humid, water cold, fire hot and earth dry. Hence if one of them were infinite, it would destroy the others, since one contrary is disposed to be corrupted by another. And that is why they said that something other than the elements was infinite, from which, as from a principle, the elements arose. Now he states this position to be impossible not only as to its maintaining such a mediate body to be infinite, since there will be applied a same common argument [in no. 35] to fire and air and water and likewise to the mediate body, but also as to its laying down some elemental principle in addition to the elements. For there is found no sensible body outside of those things called the “elements,” namely, air, water, and the like. But this would have to be the case if anything besides the elements should enter into the composition of such bodies. If, therefore, anything else should enter into the composition of those bodies in addition to the four elements, it would follow that we should find here some simple body besides the elements, by the resolution of the above bodies into their elements. It follows therefore that the aforesaid position is false as to its positing of some simple body besides the known elements.
lib. 3 l. 8 n. 9 Ulterius autem ostendit communi ratione, quod nullum elementorum possit esse infinitum: quia si aliquod elementorum esset infinitum, impossibile esset totum universum esse aliud nisi illud elementum; et oporteret quod omnia alia elementa converterentur in ipsum, vel iam essent conversa in ipsum, propter excellentiam virtutis infiniti super alia: sicut Heraclitus dicit quod quandoque futurum est quod omnia convertantur in ignem, propter excellentem ignis virtutem. Et eadem ratio est de uno elementorum et de alio corpore quod faciunt quidam naturales extra elementa. Oportet enim illud aliud habere contrarietatem ad elementa, cum ex eo ponantur alia generari: mutatio autem non fit nisi ex contrario in contrarium, ut ex calido in frigidum, sicut supra ostensum est. Sic igitur et istud corpus medium ratione contrarietatis destruet alia elementa.	357. He further shows by a general argument that none of the elements can be infinite. For if any of the elements were infinite, it would be impossible for the whole universe to be anything but that element. It would likewise be necessary that all the other elements be changed into it, or to have already been changed into it, due to the excess of power of the infinite over other things, as Heraclitus says that at some future time all things will be converted into fire because of the excelling power of fire. And the same reason holds good for one of the elements and for come other body that some natural philosophers create besides the elements. For it is necessary that this other body have contrariety toward the elements, since other things are laid down as being generated from it, and change does not take place except from ;)ne contrary to another, as in the case of going from hot to cold, as shown above (I, l.10). This middle body would therefore in this way destroy, by reason of its contrariety, the other elements.