Authors/Ockham/Summa Logicae/Book I/Chapter 44

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[CAP. 44. DE PRAEDICAMENTO QUANTITATIS] [Chapter 44. On the category of quantity]
Sequitur nunc disserere de praedicamento quantitatis. Circa quod est primo sciendum quod hoc commune ‘quantitas’ est quaedam intentio animae, habens sub se multa contenta ordinata secundum superius et inferius. Et quia communiter ponitur a modernis quod quaelibet quantitas est quaedam res distincta realiter et totaliter a substantia et qualitate, ita quod quantitas continua est unum accidens medium inter substantiani et qualitatem, quae ponitur esse subiective in substantia et esse subiectum qualitatum. Similiter ponitur quod quantitas discreta est quaedam res distincta realiter a substantiis, et idem ponitur de loco et tempore. Ideo de ista opinione perscrutandum est. It follows now to discuss the category of quantity. About this it should first be known that the common term "quantity" is a certain intention of the soul, having many things subordinated to it, ordered according to superior and inferior. And because it is commonly supposed by the moderns that every quantity is a certain thing really and totally distinct from substance and quality, so that continuous quantity is an accident in between substance and quality, which is supposed to be subjectively in substance and to be the subject of qualities, similarly it is supposed that discrete quantity is a certain thing really distinct from substance, and same it is supposed of place and time. Therefore that opinion should be examined.
Primo autem volo ostendere quod ista opinio est contra mentem Aristotelis. Secundo ponam aliquas rationes contra eam. Tertio recitabo opinionem contrariam, quae mihi videtur esse de mente Aristotelis, sive sit vera sive falsa, sive catholica sive haeretica. But first I wish to show that this opinion is against the thinking of Aristotle. Secondly, I will give some reasons against it. Third, I will cite a contrary opinion, which to me seems to be the view of Aristotle, whether it be true or false, catholic or heretical.
Quod autem ista opinio sit contra mentem Aristotelis, ostensum est in praecedenti capitulo, quia secundum eum, sicut dictum est ibi, nullum accidens distinctum realiter a substantia est susceptivum contrariorum per sui mutationem. Si autem quantitas esset accidens et subiectum qualitatum, manifestum est quod mutaretur in recipiendo qualitatem, et ita per mutationem sui in se reciperet contraria, quod est contra mentem Aristotelis. But that this opinion is against the thinking of Aristotle, was shown in the chapter above because, according to him, just as was said there, no accident really distinct from a substance is receptive of contraries by its change. But if quantity were an accident and the subject of qualities, it is manifest that it would be changed in receiving the quality, and so through its change would itself receive contraries, which is against the thinking of Aristotle.
Item, de mente Aristotelis est, sicut patet IV Physicorum, quod aer potest condensari sine mutatione omnium qualitatum vel aliquarum. Unde quando aer condensatur, non oportet quod deperdat aliquam qualitatem, vel saltem non oportet quod amittat omnem qualitatem quam habuit prius. Ex quo arguo: quando aer condensatur, aut manet tota quantitas praecedens, et praecise illa quae prius, aut non. Si sic, igitur eadem quantitas est nunc minor quam prius per hoc solum quod partes quantitatis propinquius iacent nunc quam prius; igitur cum partes substantiae sint eodem modo propinquius iacentes nunc quam prius, et propter aliud non ponitur quantitas, videtur quantitas esse superflua. Si autem non manet tota quantitas quae prius, igitur aliqua pars deperditur; et cum ad corruptionem subiecti immediati corrumpatur accidens eius, sequitur quod non omnis qualitas manet, quod est contra Aristotelem. Likewise, it is of the thinking of Aristotle (as is clear in Physics IV)[1] that air can be condensed without all or some of its qualities, changing. Hence, when air is condensed, it does not have to lose any quality, or at least it does not have to lose every quality which it had before. From which I argue that when air is condensed, either the whole preceding quantity remains, and precisely that which [was there] before, or not. If so, then the same quantity is now less than before only because the parts of quantity lie closer now than before. Therefore since the parts of the substance are in the same way lying closer now than before, and quantity is not supposed to exist for any other reason, it seems quantity is superfluous. But if the whole quantity which was there before does not remain, therefore some part is lost, and since from the corruption of the immediate subject there some accident of it is corrupted, it follows that not every quality remains, which is against Aristotle.
Item, de mente Aristotelis est quod omne accidens est in aliquo subiecto primo, ita quod si sit accidens partibile, una pars illius accidentis est in una parte subiecti et alia pars accidentis in alia parte subiecti, sicut tota albedo est in toto corpore et pars albedinis est in parte corporis. Si autem sit accidens indivisibile, est in aliquo subiecto indivisibili primo. Ex quo arguo quod punctus non sit alia res a linea, nec linea alia res a superficie, nec superficies alia res a corpore; et eadem ratione corpus non est alia res a substantia et qualitate secundum eum. Quod autem ex praedicto principio sequatur quod punctus non sit alia res a linea, probo sic. Moreover, the thinking of Aristotle is that every accident is primarily in some subject, and so if it is a divisible accident, one part of that accident is in one part of the subject and another part of the accident is in another part of the subject, just as all of a whiteness is in all of a body, and part of a whiteness is in part of a body. If on the other hand it is an indivisible accident, it is in the subject indivisibly. From which I say that a point is not another thing from a line, nor is a line another thing from a surface, nor is a surface another thing from a body; and by the same token a body is nothing different from a substance and from a quality (according to him). Moreover, that from the previous principle it follows that a point is not different from a line, I show as follows.
Si punctus sit accidens absolutum, distinctum a substantia, igitur est in aliquo subiecto primo. Tunc quaero: aut in substantia aut in linea. Non in substantia, quia aut in substantia divisibili, quod est impossibile, quia tunc pars esset in parte, et ita punctus esset accidens divisibile, quod negant. Aut est in substantia indivisibili, quod est impossibile, quia secundum Aristotelem in genere substantiae non est nisi materia et forma et compositum, quorum quodlibet, secundum eum, est divisibile. If a point is an absolute accident, distinct from a substance, then it is in some subject first. Then I ask, whether in the substance or in the line. Not in the substance, because either [it is] in a divisible substance, which is impossible, because then a part would be in a part, and so a point would be a divisible accident, which they deny. Or it is an indivisible substance, which is [also] impossible, since according to Aristotle there is nothing in the genus of substance except material both formed and aggregated, of which any [part], according to him, is divisible.
Sic igitur punctus non est accidens indivisibile exsistens subiective in aliqua substantia immediate tamquam in subiecto primo. Nec est primo in linea, nec in parte lineae, tamquam in subiecto primo, quia linea, et quaelibet pars lineae, est divisibilis, et per consequens non est subiectum primum accidentis indivisibilis. Thus, accordingly, a point is not an indivisible accident existing subjectively in some substance immediately, as though in a primary subject. Nor is it primarily in the line, nor in a part of the line, as though in a primary subject, because the line, and any part of the line, is divisible, and as a consequence is not the primary subject of an indivisible accident.
Sic igitur patet quod de mente Aristotelis est quod punctus non est accidens indivisibile; et eadem ratione linea non est accidens indivisibile secundum latitudinem distinctum realiter a superficie; et eadem ratione nec superficies est accidens indivisibile secundum profunditatem distinctum realiter et totaliter a corpore. Et Aristoteles non plus ponit corpus, quod est quantitas, esse distinctum realiter a substantia quam ponit lineam et superficiem distingui a corpore. Propter quod mihi videtur quod de intentione Aristotelis est quod quantitas continua non est res absoluta realiter et totaliter distincta a corpore. Thus it is clear that the thinking of Aristotle is that a point is not an indivisible accident, and by the same reasoning a line is not an indivisible accident really distinct in width from a surface, and by the same reasoning neither is a surface an indivisible accident really and wholly distinct in depth from a body. And Aristotle no more supposes that body, which is quantity, is distinct really from substance than he supposes that a line or a surface is distinct from body. Because of this, it seems to me that, concerning the intention of Aristotle it is that continuous quantity is not an absolute thing really and wholly distinct from body.
Ideo contra istam opinionem communem modernorum intendo aliquas rationes, etiam theologicas, recitare, sive concludant sive non, saltem valeant quantum valere possunt.Unde arguo sic primo: omnem rem absolutam, priorem alia, potest Deus conservare sine mutatione locali eiusdem et rem posteriorem destruere. Cum igitur, secundum opinionem communem, hoc lignum sit quaedam substantia habens partes, quarum una est sub parte quantitatis inhaerentis toti et alia pars substantiae ligni sub alia parte quantitatis, et ista res substantialis est prior natura illa quantitate inhaerente sibi, poterit Deus sine mutatione locali istis substantiae conservare eam et destruere illam quantitatem. Therefore, against that common opinion of the moderns, I intend to list out some reasons, also theological, whether conclusive or not, at least they are valid as much as they can be valid. Hence I first argue thus. God can preserve any absolute thing, prior to others, without local change of that thing, and can destroy the thing that comes after it. Therefore - since according to that common opinion this wood is a certain substance having parts, of which one is under the part of quantity inhering in the whole, and another part of the substance of the wood under another part of quantity, and that substantial thing is prior by nature to the quantity inhering in it - then without local change of that substance God could preserve it and destroy the quantity.
Quod si sit possibile, ponatur in esse. Quo facto quaero: aut ista substantia habet partem distantem a parte aut non. Si sic, igitur est quanta sine quantitate addita, igitur illa superfluit. Si non habet partem distantem a parte et prius distabant illae partes, igitur sunt mutatae localiter, quod est contra hypothesim. If this is possible, let it be the case. With this done, I ask: either that substance has a part distant from part or not. If so, then it is a quantum without added quantity, therefore it is superfluous. If it does not have a part distant from part, and before those parts were distant, then they are locally changed, which is against the hypothesis.
Item, omne quod per se ipsum et per partes suas intrinsecas est praesens alicui quanto, ita quod totum est praesens toti et partes partibus, per se ipsum et per partes suas intrinsecas habet partem distantem a parte; omne autem tale per se et per partes suas est quantum, sed substantia materialis per se ipsam et per partes suas est praesens alicui toti quanto, puta saltem illi quantitati informanti eam, si sit talis quantitas informans eam. Igitur per se ipsam et per partes suas habet partem situaliter distantem a parte; igitur per se ipsam et per partes suas est quanta. Likewise, everything which exists though itself, and is present in some quantum through its instrinic parts, so that the whole is present in the whole, and the parts in the parts, has part distant from part though itself and through its intrinsic parts. But every such thing though itself and through its parts is a quantum. But material substance though itself and through its parts is present in some whole quantum (e.g. at least in that quantity informing it, if there be some such quantity informing it). Therefore though itself and through its parts it has a part distinct in situation from part. Therefore through itself and through its parts it is a quantum.
Item, quod quantitas non sit tale accidens medium inter substantiam et qualitatem et subiectum qualitatum, potest probari per sacramentum Altaris. Quia si sic, qualitates remanentes in sacramento Altaris essent in quantitate subiective. Consequens videtur falsum multis, igitur antecedens. Falsitatem consequentis probo. Primo, quia tunc illae qualitates non essent per se subsistentes, quod est contra Magistrum, libro IV Sententiarum, ubi loquens de colore, sapore, pondere et huiusmodi qualitatibus, dicit quod talia accidentia sunt ibi per se subsistentia. Likewise, by the sacrament of the altar it can be proved that quantity is not such an accident, intermediate between substance and quality, and the subject of qualities. For if so, the qualities remaining in the sacrament would be in quantity subjectively. The consequent seems false to many, therefore also the antecedent. I prove the falsity of the consequent. First, because then those qualities would not be per se subsisting, which is against the Master [2] (Sentences IV), where, speaking of colour, taste, weight and other such qualities, he says that such accidents are per se subsisting there.
Similiter, si quantitas esset subiectum illarum qualitatum, illa quantitas vere esset ponderosa et alba et sapida. Consequens est contra Glossam, De consecratione, distinctione secunda, super illud capitulum ‘Si per negligentiam’, ubi dicit Glossa quod ‘ponderositas remanet ibi cum aliis accidentibus, tamen nihil est ibi ponderosum’. Similarly, if quantity were a subject of those qualities, that quantity truly would be weighty, and white, and savoury. The consequent is against the gloss (On Consecration, second distinction, on the chapter ‘if through negligence’, where the gloss says that ‘weight remains there with the other accidents, yet nothing is heavy there’).
Istae rationes probant quod quantitas longa, lata et profunda non est res distincta a substantia et qualitate. Quod autem linea non sit distincta a superficie, probo. Quia si linea esset talis res alia, continuans superficies ad invicem, dividatur illa superficies. Qua divisa, quaero: aut est aliqua linea nova aut solum linea prior manet. Si est aliqua linea nova, erunt infinitae novae, quia diviso corpore infinitae superficies erunt, habentes infinitas lineas, sicut divisa superficie erunt infinita puncta terminantia infinitas lineas. Si nulla linea sit nova, igitur remanet illa quae praefuit, et non magis cum una parte superficiei quam cum alia. Igitur vel remanebit per se vel remanebit in distinctis locis cum utraque superficie; quorum utrumque est absurdum, igitur et illud ex quo sequitur. These reasonings prove that the quantity of length, width and depth is not a thing distinct from substance and quality. But that a line is not distinct from a surface, I prove. For if a line were some other thing, continuing surfaces amongst one another, let that surface be divided. With it divided, I ask whether there is some new line, or only the line before remains. If it is some new line, there will be infinitely many new lines, because with the body divided there will be infinitely many surfaces, having infinite lines, just as when a surface is divided there will be infinitely many points terminating infinitely many lines. If there is no new line, then there will remain the one which was there before, and no more with one part of the surface than with another. Therefore either it will remain per se or it will remain in distinct places with both surfaces. Both of these are absurd, therefore what follows from them is also absurd.
Item, si linea sit alia res a superficie et punctus a linea,igitur poterit Deus conservare lineam et destruere punctum. Quo facto, quaero: aut linea est finita aut infinita. Non infinita, manifestum est, igitur finita, et tamen sine puncto. Igitur frustra ponitur punctus terminans lineam. Likewise, if the line is some thing other than the surface, and the point something other than the line, then God could preserve the line and destroy the point. With this done, I ask whether the line is finite or infinite. Not infinite, it is manifest, therefore finite, and yet without a point. Therefore it is vain to suppose there is a point terminating a line.
Similiter, posset Deus conservare lineam destruendo omnia puncta. Quo facto adhuc linea esset linea, et per consequens quantitas; et non quantitas discreta, igitur continua; igitur vere esset continua, quamvis non esset ibi aliqua alia res a partibus lineae copulans partes ad invicem. Frustra igitur ponuntur talia puncta distincta a linea. Et eadem ratione frustra ponuntur lineae distinctae a superficiebus, et eadem ratione frustra ponuntur superficies distinctae a corporibus. Similarly , God could preserve the line by destroying all points. With this done, the line would still be a line, and as a consequence a quantity, and not discrete quantity, therefore continuous. Therefore it would be truly continuous, although there would not be there some other thing from the parts of the line joining the parts to one another. Therefore it is vain to suppose there are points distinct from the line. And by the same reasoning it is vain to suppose there are lines distinct from surfaces, and by the same reason it is vain to suppose there are surfaces distinct from bodies.
Ideo est alia opinio de quantitate, quae mihi videtur esse de mente Aristotelis, sive sit haeretica sive catholica, quam volo nunc recitare, quamvis nolim eam asserere. Et ideo quando istam opinionem posui et scripsi super philosophiam, non scripsi eam tamquam meam sed tamquam Aristotelis, quam exposui ut mihi videbatur, et eodem modo nunc sine assertione recitabo eam. [3] Therefore there is another opinion about quantity, which seems to me to be the thinking of Aristotle, whether it be heretical or catholic, which I now wish to give, although I do not wish to assert it. And therefore when I posited that opinion and wrote about philosophy, I did not write it as if mine, but as if Aristotle’s, which I have set out as it seemed to me, and in the same way I will now recite it without asserting [it].
Est autem ista opinio, quam etiam multi theologi tenent et tenuerunt, scilicet quod nulla quantitas est realiter distincta a substantia et qualitate, sive tales propositiones ‘substantia est quantitas’, ‘qualitas est quantitas’ sint concedendae sive non. Et de quantitate quidem continua permanente tenetur per istum modum, scilicet quod quantitas continua permanens nihil aliud est nisi res una habens partem situaliter distantem a parte, ita quod ista duo ‘quantitas continua permanens’ et ‘res una habens partem distantem a parte’ sint aequivalentia in significando, in tantum quod erunt termini convertibiles, nisi aliquis modus syncategorematicus vel aliqua determinatio inclusa aequivalenter in uno impediat convertibilitatem et praedicationem unius de alio. Et ideo, cum substantia habeat partem situaliter distantem a parte, et similiter qualitas, aliqua quantitas non erit alia res a substantia, et aliqua quantitas non erit alia res a qualitate. Now it is that opinion, which many theologians also hold (and have held), namely that no quantity is really distinct from substance and quality, whether such propositions as "substance is quantity", "quality is quantity" are conceded or not. And of course concerning permanent continuous quantity, it is held in this way: namely that permanent continuous quantity is nothing other than a single thing having one part at a distance from another part, so that the two expressions "permanent continuous quantity" and "a single thing having part distant from part" are equivalent in signifying , inasmuch as they are convertible terms, unless some syncategorematic mode or some equivalent determination included in one prevents convertibility and predication of one of the other. And therefore, when a substance has part distant from part, and similarly quality, a quantity is not some thing other than substance, and a quantity will not be some thing other than quality.
Nec videtur multum consonum theologiae dicere quod Deus non possit facere istas partes substantiae distare situaliter nisi rem aliam absolutam coniungat eisdem. Quod si potest facere, vere ista substantia habebit partem distantem a parte sine re absoluta addita eis, et per consequens erit quanta sine alia re absoluta. Et idem argumentum fieri potest de qualitate. Et ideo, cum substantia possit esse quanta sine quantitate quae sit alia res, et similiter qualitas, quantitas talis media inter substantiam et qualitatem videtur omnino superfluere. Nor does there seem to be much agreement with theology in saying that God could make those parts of a substance stand apart spatially unless he joined another absolute object to them. Which, if he can do, truly that substance will have part distant from part, without some absolute thing added to them, and as a consequence there will be a quantum without another absolute thing. And the same argument can be made about quality. And for that reason, when a substance could be a quantum without a quantity which is another thing, and similarly for quality, such a quantity intermediate between substance and quality would seem altogether superfluous.
Propter quod dicunt quod nulla quantitas est alia a substantia et qualitate, sicut nulla est res habens partem situaliter distantem a parte nisi substantia et qualitas. Unde et de sacramento Altaris dicunt quod post consecrationem corporis Christi una quantitas, quae praecessit, erat eadem realiter cum substantia panis, et illa non manet; sed praeter illam manet una quantitas quae est eadem cum qualitate, in qua tamen quantitate non est aliqua qualitas subiective, sed omnia accidentia remanentia post consecrationem remanent simul cum corpore Christi sine omni subiecto, quia per se subsistentia. Sic igitur dicunt de quantitate continua. Because of this, they say that no quantity is different from substance and quality, just as nothing is a thing having one part distant from another part except substance and quality. Hence, concerning the sacrament of the Altar they say that after the consecration of the body of Christ, a quantity, which existed before, was really the same as the substance of the bread, and that does not remain; but beyond that there remains a quantity which is the same as the quality, in which quantity, nonetheless, there is not some quality subjectively, but all accidents remaining after the consecration remain together with the body of Christ without any subject, because they are per se subsistent. In this way, then, they speak of continuous quantity.
De quantitate autem discreta dicunt quod numerus nihil aliud est quam ipsae res numeratae. Unde dicunt quod sicut unitas rei non est aliquod accidens additum illi rei quae est una, ita numerus non est aliquod accidens additum illis rebus quae sunt numeratae. Quod autem unitas non sit aliquod accidens additum rei quae est una, potest ostendi, quia si sit accidens, secundum omnes oportet quod sit respectivum vel absolutum. Non respectivum, quia nullum terminum realem habere potest. Unde ad hoc quod aliquid sit unum, non oportet quod sit alicuius unum, nec quod sit alicui unum, et sic de aliis casibus sub quibus aliquid dicitur ad aliud. Nec est accidens absolutum, quia tunc vel esset qualitas, quod evidenter patet esse falsum, vel est quantitas, et tunc vel continua vel discreta, quorum utrumque patet esse falsum. Reliquitur igitur quod unitas non est aliquod accidens realiter distinctum ab illo quod est unum et additum sibi in re extra. Et eadem ratione nec numerus erit accidens additum rebus numeratis. De loco etiam et tempore dicunt quod non sunt res aliae distinctae. Sed de hoc in libro Physicorum perscrutatum est. Now concerning discrete quantity they say that number is nothing other than the numbered things themselves. Hence they say that just as the unity of a thing is not some accident added to that thing which is one, so also number is not some accident added to those things which are numbered. And that unity is not some accident added to a thing which is one can be shown, because if it were an accident, it has to be relative or absolute, according to all persons. Not relative, because it can have no real term. Hence, for something to be one, it does not have to be one of something, nor one in relation to something, and so on for the other cases where something is said to be related 'to' something. Nor is it an absolute accident, for then it would either be a quality, which is obviously false, or it is a quantity, and then either continuous or discrete, of which either is clearly false. It remains, therefore, that unity is not some accident really distinct from that which is one, and added to it in external reality. And by the same reasoning, nor will number be an accident added to the numbered things. Of space and time, they also say that they are not other distinct things. But this was examined in detail in the Physics.
De oratione autem dicunt quod non est nisi ipsae voces prolatae. Istis visis consequenter habent positores praedictae opinionis ponere quod punctus, linea, superficies et corpus et numerus non sunt res totaliter distinctae et realiter nec inter se nec a substantia et qualitate. Verumtamen, secundum eos, non obstante identitate illorum quae importantur per omnia ista, tamen ista praedicabilia sunt distincta et sunt distinctae species quantitatis. Aliquando enim praedicabilia habent eadem significata et tamen in tantum distinguuntur quod praedicatio unius de alio est impossibilis. Isti enim termini ‘homo’ et ‘homines’ idem significant, et tamen haec est impossibilis ‘homo est homines’. Ita est in proposito quod omnia ista easdem res significant et tamen sunt distinctae species et distincta praedicabilia. But about a sentence they say that it is nothing except the uttered words themselves. Given this, consequently, the proponents of the opinion above have to suppose that point, line, surface and body and number are not things that are totally and really distinct either from each other or from substance and quality. Nevertheless, according to them, notwithstanding the identity of all those things which are conveyed by all this, still these predicables are distinct, and are distinct species of quantity. For sometimes the predicables have the same significates and yet they are distinguished inasmuch as the predication of one of the other is impossible. For the terms 'man' and 'men' signify the same, and yet 'a man is men' is impossible. So it is in the case at hand: that all these terms signify the same, and yet are distinct species and distinct predicable.

Notes

  1. 216 b22, see also Thomas' commentary on the same passage.
  2. i.e. Peter Lombard
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