PART II QUESTION IV: Concerning Those Things That Pertain to the Cause of Plurality
Article 1: Whether Otherness Is the Cause of Plurality
Article 2: Whether Variety of Accidents Produces Diversity According to Number
Article 3: Whether Two Bodies Can Be, or Can Be Conceived of as Being Simultaneously in the Same Place
Article 4: Whether Variety of Location Has Any Influence in Effecting Numerical Difference

Latin	English
Sancti Thomae de Aquino	Thomas Aquinas
Super Boetium De Trinitate	On Boethius on the Trinity
Textum a Bruno Decker Lugduni Batauorum 1959 editum ac automato translatum a Roberto Busa SJ in taenias magneticas denuo recognovit Enrique Alarcón atque instruxit	Questions 1-4, translated by Rose E. Brennan, S.H.N. (Herder, 1946)
Quaestio 4	QUESTION IV
Prooemium
Pars 2 q. 4 pr.
Deinde quaeritur de his quae ad causam pluralitatis pertinent. Et circa hoc quaeruntur quattuor.	Concerning Those Things That Pertain to the Cause of Plurality. Inquiry is made of those things that pertain to the cause of plurality. And this inquiry involves four questions:
Pars 2 q. 4 pr. 1
Primo. Utrum alteritas sit causa pluralitatis.	1. Whether otherness is the cause of plurality.
Pars 2 q. 4 pr. 2
Secundo. Utrum varietas accidentium faciat diversitatem secundum numerum.	2. Whether variety of accidents produces diversity according to number.
Pars 2 q. 4 pr. 3
Tertio. Utrum duo corpora possint esse vel intelligi esse in eodem loco.	3. Whether two bodies can be, or can be thought of as being, simultaneously in the same place.
Pars 2 q. 4 pr. 4
Quarto. Utrum varietas loci aliquid operetur ad differentiam secundum numerum.	4. Whether difference of location exerts some influence as to difference according to number.
Articulus 1	Whether Otherness Is the Cause of Plurality.
Pars 2 q. 4 a. 1 arg. 1
Ad primum sic proceditur. Videtur quod pluralitatis causa non sit alteritas. Ut enim dicitur in arithmetica Boethii, omnia quaecumque a primaeva rerum natura constructa sunt, numerorum videntur ratione esse formata. Hoc enim fuit principale in animo conditoris exemplar. Et huic consonat quod dicitur Sap. 11: omnia in pondere, numero et mensura disposuisti. Ergo pluralitas sive numerus est primum inter res creatas, et non est eius aliqua causa creata quaerenda.	1. It seems that the cause of plurality cannot be otherness. For as is said in the Arithmetica of Boethius, all things whatever of the sum-total of beings that have been established in nature seem to ‘ have been formed by reason of numbers. For this was the principal exemplar in the mind of the builder of the universe: and this is in agreement with what is said in Wis. 11:21, "You have disposed all things in weight and in number and in measure". Therefore plurality or number is first among created things, and no cause of it is to be sought for.
Pars 2 q. 4 a. 1 arg. 2
Praeterea, ut dicitur in libro de causis, prima rerum creatarum est esse. Sed ens primo dividitur per unum et multa. Ergo multitudine nihil potest esse prius nisi ens et unum. Ergo non videtur esse verum, quod aliquid aliud sit eius causa.	2. As said in the book De causis, the first of created things is being; but being is divided at first by one and many; hence nothing can exist as prior to multitude except being and unity. Therefore it does not seem to be true that anything else should be its cause.
Pars 2 q. 4 a. 1 arg. 3
Praeterea, pluralitas vel circuit omnia genera, secundum quod condividitur contra unum, quod est convertibile cum ente, vel est in genere quantitatis, secundum quod condividitur uni quod est principium numeri. Sed alteritas est in genere relationis. Relationes autem non sunt causae quantitatum, sed magis e converso, et multo minus relationes sunt causae eius quod est in omnibus generibus, quia sic essent causae etiam substantiae. Ergo alteritas nullo modo est causa pluralitatis.	3. Plurality either includes all genera according as it is distinguished from unity, which is convertible with being: or it is itself in the genus of quantity, according as it is distinguished from that unity which is the principle of number. But otherness is in the genus of relation, and relations are not causes of quantities, but rather the converse is true. Much less, then, is relation the cause of what is in every genus, because in that case it would be the cause of substance; therefore otherness can in no way be the cause of plurality.
Pars 2 q. 4 a. 1 arg. 4
Praeterea, contrariorum contrariae sunt causae. Sed identitas et diversitas sive alteritas sunt opposita. Ergo habent oppositas causas. Sed unitas est causa identitatis, ut patet in V metaphysicae. Ergo pluralitas vel multitudo est causa diversitatis sive alteritatis. Non ergo alteritas est causa pluralitatis.	4. For contrary things there are contrary causes: but identity and otherness or diversity are opposites; therefore they have opposite causes. But unity is the cause of identity, as is evident in V Metaph.; therefore plurality or multitude is the cause of diversity; and consequently otherness is not the cause of plurality.
Pars 2 q. 4 a. 1 arg. 5
Praeterea, alteritatis principium est accidentalis differentia; huiusmodi enim differentiae secundum Porphyrium faciunt alterum. Sed non in omnibus, in quibus est pluralitas, invenitur accidentalis differentia nec etiam differentia qualiscumque. Quaedam enim sunt quae accidentibus subici non possunt, sicut formae simplices; quaedam vero sunt quae in nullo conveniunt, unde non possunt differentia dici, sed diversa, ut patet per philosophum in X metaphysicae. Ergo non omnis pluralitatis causa est alteritas.	5. The principle of otherness is accidental difference; for differences of this kind, according to Porphyry, make a thing other. But accidental difference is not found in all things in which there is plurality; in fact, in some cases there is no difference of any kind. Certain things, such as simple forms, cannot be subjects of accidents; and there are other things that agree in no way, so that they cannot be called different, but diverse, as is evident by the words of the Philosopher in X Metaph. Therefore otherness is not the cause of all plurality.
Pars 2 q. 4 a. 1 s. c. 1
Sed contra est quod Damascenus dicit quod divisio est causa numeri. Sed divisio in diversitate vel alteritate consistit. Ergo diversitas vel alteritas principium pluralitatis est.	But on the contrary is what Damascene says, that division is the cause of number; but division consists in diversity or otherness; therefore diversity, or otherness, is the principle of plurality.
Pars 2 q. 4 a. 1 s. c. 2
Praeterea, Isidorus dicit quod numerus dicitur quasi nutus, id est signum, memeris, id est divisionis. Et sic idem quod prius.	Again, Isidore says that number is called, as it were, the master of numeration, that is, of division; and so the conclusion is like the first.
Pars 2 q. 4 a. 1 s. c. 3
Praeterea, pluralitas non constituitur nisi per recessum ab unitate. Sed ab unitate non recedit aliquid nisi per divisionem, cum ex hoc aliquid dicatur unum, quod est indivisum, ut patet in X metaphysicae. Ergo divisio pluralitatem constituit, et sic idem quod prius.	Again, plurality is not constituted except by recession from unity; but there is no loss of unity except by division, since a thing is said to be one in that it is undivided, as is evident from X Metaph.; therefore division constitutes plurality, and thus the conclusion is as before.
Pars 2 q. 4 a. 1 co. 1
Responsio. Dicendum quod, sicut dicit philosophus in X metaphysicae, plurale dicitur aliquid ex hoc quod est divisibile vel divisum. Unde omne illud quod est causa divisionis oportet ponere causam pluralitatis.	Response. I answer that it must be said, as the Philosopher states in X Metaph., that a thing is said to be plural (many) from the fact that it is divisible or has been divided. Wherefore anything that is the cause of division ought to be regarded as a cause of plurality.
Causa autem divisionis aliter est accipienda in posterioribus et compositis et in primis et simplicibus. In posterioribus namque et compositis causa divisionis quasi formalis, id est ratione cuius fit divisio, est diversitas simplicium et priorum. Quod patet in divisione quantitatis. Dividitur enim una pars lineae ab alia per hoc quod habet diversum situm, qui est quasi formalis differentia quantitatis continuae positionem habentis. Patet etiam in divisione substantiarum. Dividitur enim homo ab asino per hoc quod habent diversas differentias constitutivas. Sed diversitas, qua dividuntur posteriora composita secundum priora et simplicia, praesupponit pluralitatem priorum simplicium. Ex hoc enim homo et asinus habent diversas differentias, quod rationale et irrationale non sunt una, sed plures differentiae. Nec potest semper dici quod illius pluralitatis sit aliqua diversitas aliquorum priorum et simpliciorum causa, quia sic esset abire in infinitum.	Now, the cause of division cannot be considered the same in posterior and composite beings as in those that are first and simple. For in’posterior and composite things, the cause of division which is, as it were, the formal cause of division by reason of which division comes about, is diversity found in more simple and primary beings, as is made clear in the case of division according to quantity. For one part of a line is divided from another part by the fact that they have each a different place, which is, as it were, the formal difference of a thing of continuous quantity having position. It is also evident in the division of substances. For man is different from an ass because he has diverse constitutive differences: but the diversity by which posterior, composite beings are divided according as prior and simpler beings are, presupposes plurality of these same primary and more simple beings. For the reason why man and ass have diverse differences is that ratipnality and irrationality are not one and the same thing, but differ in many ways. Nor can it be said endlessly that the plurality of one thing is owing to another diversity in another prior and simpler cause, because thus we would go on to infinity.
Pars 2 q. 4 a. 1 co. 2
Et ideo pluralitatis vel divisionis primorum et simplicium oportet alio modo causam assignare. Sunt enim huiusmodi secundum se ipsa divisa.	Therefore it is necessary in some other way to assign a cause of plurality and division in prior and more simple beings.
Non potest autem hoc esse, quod ens dividatur ab ente in quantum est ens; nihil autem dividitur ab ente nisi non ens. Unde et ab hoc ente non dividitur hoc ens nisi per hoc quod in hoc ente includitur negatio illius entis. Unde in primis terminis propositiones negativae sunt immediatae, quasi negatio unius sit in intellectu alterius. Primum etiam creatum in hoc facit pluralitatem cum sua causa, quod non attingit ad eam.	Now, there are some beings of this kind divided in themselves. Nevertheless it cannot be that being is divided from being, inasmuch as it is being: for nothing is divided from being except non-being. Likewise also from this-being, this-being is not divided, unless in this-being there is included negation of the same being. Wherefore in primary termini of thought negative propositions are immediately, as it were, negations, one of the other, in the intellect. For the first thing caused constitutes plurality with its cause, which does not reach to it [so as to be identical with it].
Et secundum hoc quidam posuerunt quodam ordine pluralitatem ab uno primo causari, ut ab uno primo procedat primo unum, quod cum causa pluralitatem constituat, et ex eo iam possunt duo procedere: unum secundum se ipsum, aliud secundum coniunctionem ipsius ad causam. Quod dicere non cogimur, cum unum primum possit aliquid imitari, in quo alterum ab eo deficit, et deficere, in quo alterum imitatur. Et sic possunt inveniri plures primi effectus, in quorum quolibet est negatio et causae et effectus alterius secundum idem vel secundum remotiorem distantiam etiam in uno et eodem.	And according to this, certain philosophers hold that plurality is caused in a certain order from one and the selfsame thing; so that from one thing proceeds, at first, one being, which with its cause constitutes a plurality, and from this plurality, now two things can proceed, one according to the thing itself, and the other according to its conjunction to a cause. But we are not forced to say this, since one thing might be able to imitate the first in some way in which the second would fail to agree with it; and this defect could be imitated in another; and so there can be found many effects of the first cause in any number of which there is both negation of the cause and negation of the effects in the same way, or according to distance separating one from the other.
Pars 2 q. 4 a. 1 co. 3
Sic ergo patet quod prima pluralitatis vel divisionis ratio sive principium est ex negatione et affirmatione, ut talis ordo originis pluralitatis intelligatur, quod primo sint intelligenda ens et non ens, ex quibus ipsa prima divisa constituuntur, ac per hoc plura.	So, therefore, it is evident that the first reason or, principle of plurality or division is from affirmation and negation, as the order of origin of such plurality is understood, because first there must be understanding of being and non-being, by which first divisions are constituted, and by this, there are the many.
Unde sicut post ens, in quantum est indivisum, statim invenitur unum, ita post divisionem entis et non entis statim invenitur pluralitas priorum simplicium. Hanc autem pluralitatem consequitur ratio diversitatis, secundum quod manet in ea suae causae virtus, scilicet oppositionis entis et non entis. Ideo enim unum plurium diversum dicitur alteri comparatum, quia non est illud. Et quia causa secunda non producit effectum nisi per virtutem causae primae, ideo pluralitas primorum non facit divisionem et pluralitatem in secundis compositis, nisi in quantum manet in ea vis oppositionis primae, quae est inter ens et non ens, ex qua habet rationem diversitatis. Et sic diversitas primorum facit pluralitatem secundorum.	Hence, just as first being, inasmuch as it is undivided, is immediately recognized as one, so after division of being and non-being there is immediate recognition of the plurality of first simple beings. The nature of diversity, moreover, follows upon plurality according as there remains in it the virtue of its cause, that is, the opposition of being and nonbeing. Therefore one of many diverse things is said to be related to another because it is not that other. And since a second cause does not produce its effect except by virtue of a first cause, therefore the plurality of first causes does not make division and plurality in secondary, composite beings unless there remains in that plurality the virtue of prime opposition, which is between being and non-being, by reason of which it has the nature of diversity; and thus the diversity of first causes produces the diversity of second.
Pars 2 q. 4 a. 1 co. 4
Et secundum hoc verum est quod Boethius dicit quod alteritas est principium pluralitatis. Ex hoc enim alteritas in aliquibus invenitur, quod eis diversa insunt. Quamvis autem divisio praecedat pluralitatem priorum, non tamen diversitas, quia divisio non requirit utrumque condivisorum esse ens, cum sit divisio per affirmationem et negationem; sed diversitas requirit utrumque esse ens, unde praesupponit pluralitatem. Unde nullo modo potest esse quod pluralitatis primorum causa sit diversitas, nisi diversitas pro divisione sumatur.	According to this, it is true, as Boethius says, that otherness is the principle of plurality. indeed, otherness is to be found in things because there is diversity among them. However, although division precedes plurality of first causes, diversity does not; because ‘ division does not require the being of things divided among themselves, since division is by affirmation and negation, but diversity does require each to be a distinct being; wherefore it presupposes plurality. Hence it is in no way possible that the cause of the plurality of first beings should be diversity, unless diversity is employed as meaning division.
Loquitur ergo Boethius de pluralitate compositorum, quod patet ex hoc, quod inducit probationem de his quae sunt diversa genere vel specie vel numero, quod non est nisi compositorum. Omne enim, quod est in genere, oportet esse compositum ex genere et differentia. Eos autem, qui ponunt patrem et filium inaequales deos, sequitur compositio saltem ratione, in quantum ponunt eos convenire in hoc quod sunt Deus et differre in hoc quod sunt inaequales.	Boethius, therefore, is speaking of the plurality of composite beings, as is evident from the fact that he presents a proof involving those things that are diverse according to genus or species or number, and these kinds of diversity exist only in composite beings. For anything which is in a genus must be composed of genus and difference. Those, therefore, who declare the Father and Son to be unequal make declaration of composition, at least according to reason, inasmuch as they say the Father and Son agree in this, that they are God, but differ in the fact that they are unequal.
Pars 2 q. 4 a. 1 ad 1
Ad primum ergo dicendum quod numerus ex verbis illis ostenditur esse prior rebus aliis creatis, ut elementis et aliis huiusmodi, non autem aliis intentionibus, utpote affirmatione et negatione aut divisione vel aliis huiusmodi. Nec tamen quilibet numerus est prior omnibus rebus creatis, sed numerus qui est exemplar omnis rei, scilicet ipse Deus, qui secundum Augustinum est numerus omni rei speciem praebens.	1. It may be said: In these words, number is shown to be prior to other created things, such as the elements and other such beings; but it is not prior to other notions, such as affirmation and negation or division and the like. Moreover, not every kind of number is prior to all created beings, but only number which is the cause of each thing, namely, God Himself, who, according to Augustine, is Number, giving species to every creature.
Pars 2 q. 4 a. 1 ad 2
Ad secundum dicendum quod pluralitas communiter loquendo immediate sequitur ens, non tamen oportet quod omnis pluralitas. Et ideo non est inconveniens, si pluralitas secundorum causetur ex diversitate priorum.	2. It may be answered: Plurality, commonly speaking, immediately follows upon being; but this is not necessarily true of all plurality, and so it is not unfitting that the plurality of posterior beings should be caused by the diversity of those that are prior.
Pars 2 q. 4 a. 1 ad 3
Ad tertium dicendum quod sicut unum et multa, ita idem et diversum non sunt propria unius generis, sed sunt quasi passiones entis, in quantum est ens. Et ideo non est inconveniens, si aliquorum diversitas aliorum pluralitatem causet.	3. It may be said: As one and many are not properly of one genus, so neither are the same and the diverse, but they are passiones of being inasmuch as it is being, and hence there is no difficulty if the diversity of certain beings causes the plurality of others.
Pars 2 q. 4 a. 1 ad 4
Ad quartum dicendum quod omnem diversitatem praecedit aliqua pluralitas, sed non omnem pluralitatem praecedit diversitas, sed aliquam pluralitatem aliqua diversitas. Unde et utrumque verum est, scilicet quod multitudo diversitatem faciat communiter loquendo, ut philosophus dicit, et quod diversitas in compositis faciat pluralitatem, ut Boethius hic dicit.	4. It may be said: Some kind of plurality precedes all diversity, but diversity does not precede all plurality, yet some kind of diversity precedes certain plurality. Hence two things are equally true: namely, that, commonly speaking, multitude produces diversity, as the Philosopher says; and that diversity in composite things produces plurality, as Boethius here declares.
Pars 2 q. 4 a. 1 ad 5
Ad quintum dicendum quod Boethius accepit alteritatem pro diversitate, quae constituitur ex aliquibus differentiis, sive sint accidentales sive substantiales. Illa vero, quae sunt diversa et non differentia, sunt prima, de quibus hic Boethius non loquitur.	5. It may be answered: Boethius is using "otherness" in place of "diversity," which is constituted by certain differences, whether they are accidental or substantial. But those beings that are diverse yet not different are first beings, and Boethius is here not speaking of them.
Articulus 2	Whether Variety of Accidents Produces Diversity According to Number.
[84570] Pars 2 q. 4 a. 2 arg. 1
Ad secundum sic proceditur. Videtur quod varietas accidentium non possit esse causa pluralitatis secundum numerum. Philosophus enim dicit in V metaphysicae quod numero sunt unum, quorum est materia una. Ergo et numero plura, quorum sunt materiae plures. Ergo diversitatem in numero non facit varietas accidentium, sed magis diversitas materiae.	1. It seems that variety of accidents cannot be the cause of plurality according to number. For the Philosopher says in V Metaph. that those things are numerically one in which the matter is one; therefore they are numerically plural in which the matter is plural; therefore variety of accidents does not produce diversity in number, but rather diversity of matter does so.
[84571] Pars 2 q. 4 a. 2 arg. 2
Praeterea, philosophus dicit in X metaphysicae quod idem est rebus causa substantiae et unitatis. Sed accidentia non sunt individuis causa substantiae, ergo nec unitatis, et ita per consequens nec pluralitatis secundum numerum.	2. As the Philosopher says in IV Metaph., the cause of the substance and of the unity in things is the same; but accidents are not the cause either of the substance or of the unity in the individual; consequently they cannot be the cause of numerical plurality.
[84572] Pars 2 q. 4 a. 2 arg. 3
Praeterea, omnia accidentia, cum sint formae, ex se ipsis sunt communicabilia et universalia. Sed nihil tale potest esse alteri principium individuationis. Ergo accidentia non sunt individuationis principium. Sed aliqua sunt secundum numerum diversa, in quantum in sua individuatione dividuntur. Igitur accidentia non possunt esse principium diversitatis secundum numerum.	3. All accidents, since accidents are indeed forms, are themselves communicable or common and universal: but nothing of this kind can be the cause of individuation in another, or a principle of individuation; therefore accidents cannot be principles of individuation. But certain things are diverse according to number inasmuch as they are divided in their own individuation; therefore accidents cannot be causes of diversity according to number.
[84573] Pars 2 q. 4 a. 2 arg. 4
Praeterea, sicut ea, quae differunt genere vel specie in genere substantiae, differunt secundum substantiam et non solum secundum accidens, ita et ea quae differunt secundum numerum. Sed aliqua dicuntur diversa genere vel specie per id quod est in genere substantiae. Igitur et similiter dicuntur diversa numero per id quod est in genere substantiae et non per accidentia.	4. As those things that are in a genus or a species differ according to their substance, and not only according to an accident, so also those things that differ according to number must do likewise; but certain things are said to be diverse in genus or in species by reason of what is in the genus of substance, and not according to their accidents; therefore, in like manner, things are said to be numerically diverse according to what is in the genus of substance, and not according to accidents.
[84574] Pars 2 q. 4 a. 2 arg. 5
Praeterea, remota causa removetur effectus. Sed omne accidens contingit a subiecto removeri vel actu vel cogitatione. Si ergo accidens est principium identitatis secundum numerum et diversitatis, contingeret actu vel cogitatione eadem quandoque esse unum secundum numerum, quandoque vero diversa.	5. If a cause is removed, so is its effect. Now it happens that every accident is removed from a subject either actually or by thought. If, therefore, an accident were the principle of plurality according to number and diversity, it would happen that the same things would sometimes be numerically one and sometimes diverse, either actually or by thought.
[84575] Pars 2 q. 4 a. 2 arg. 6
Praeterea, posterius numquam est causa prioris. Sed inter omnia accidentia primum locum tenet quantitas, ut dicit Boethius in commento praedicamentorum. Inter quantitates autem naturaliter numerus prior est, cum sit simplicior et magis abstractus. Ergo impossibile est quod aliquod aliud accidens sit principium pluralitatis secundum numerum.	6. What is posterior is never the cause of what is prior. But among all accidents, quantity holds first place, as Boethius says in Lib. praedicam. Among quantities, however, number is prior since it is more simple and more abstract. Therefore an accident cannot be the principle of plurality according to number.
[84576] Pars 2 q. 4 a. 2 s. c. 1
Sed contra est quod dicit Porphyrius quod individuum facit collectio accidentium, quae in alio reperiri non possunt. Sed illud, quod est principium individuationis, est principium diversitatis secundum numerum. Ergo accidentia sunt principium pluralitatis secundum numerum.	On the contrary is the statement made byy Porphyry, that a collection of accidents which are not to be found in another produces the individual. But what is the principle of individuation is the principle of numerical plurality; therefore accidents are the principle of plurality according to number.
[84577] Pars 2 q. 4 a. 2 s. c. 2
Praeterea, in individuo nihil invenitur nisi forma et materia et accidentia. Sed diversitas formae non facit diversitatem secundum numerum, sed secundum speciem, ut patet in X metaphysicae. Diversitatem vero secundum genus facit diversitas materiae. Dicit enim philosophus in X metaphysicae quod genere differunt, quorum non est materia communis nec generatio ad invicem. Ergo diversitatem secundum numerum nihil potest facere nisi diversitas accidentium.	Again, in the individual, there is found nothing except matter, form, and accidents. Diversity of form, however, does not produce diversity according to number, but according to species, as is said in X Metaph. Now, diversity of matter produces diversity of genus. For the Philosopher says in X Metaph. that those things differ in genus in which there is not common matter, or generation of one into the other (mutual generation). Therefore diversity according to number cannot be produced except by diversity of accidents.
[84578] Pars 2 q. 4 a. 2 s. c. 3
Praeterea, illud, quod invenitur commune in pluribus specie differentibus, non est causa diversitatis secundum numerum, quia divisio generis in species praecedit divisionem speciei in individua. Sed materia invenitur communis in diversis secundum speciem, quia eadem materia formis contrariis subditur; alias habentia contrarias formas non transmutarentur invicem. Ergo materia non est principium diversitatis secundum numerum, nec forma, ut probatum est. Ergo relinquitur quod accidentia sint huius diversitatis causa.	Moreover, what is found as common in many things that are specifically different is not the cause of diversity according to number, because the division of genus into species precedes the division of species into individuals; but matter is found to be common in things that are different in species because the same matter is possessed by contrary forms, otherwise beings having contrary forms would not be transmuted one into the other; therefore matter is not the principle of individuation according to number, and neither is form, as has been noted at the beginning. Hence it remains that accidents are the cause of this kind of diversity.
[84579] Pars 2 q. 4 a. 2 s. c. 4
Praeterea, in genere substantiae nihil invenitur nisi genus et differentia. Sed individua unius speciei non differunt genere nec substantialibus differentiis. Ergo non differunt nisi differentiis accidentalibus.	Again, in the genus of substance there is found only genus and difference; but the individuals of one species differ neither in genus, nor by reason of substantial differences; therefore they do not differ except because of accidental differences.
[84580] Pars 2 q. 4 a. 2 co. 1
Responsio. Dicendum quod ad evidentiam huius quaestionis et eorum, quae in littera dicuntur, oportet videre, quid sit causa huius triplicis diversitatis, quae in littera assignatur.	Response. I answer: For the clarification of this question and of those other questions treated of in the text of Boethius, it is necessary to see what may be the cause of the threefold diversity spoken of in the text.
Cum autem in individuo composito in genere substantiae non sint nisi tria, scilicet materia, forma et compositum, oportet ex aliquo horum cuiuslibet harum diversitatum causas invenire. Sciendum est ergo quod diversitas secundum genus reducitur in diversitatem materiae, diversitas vero secundum speciem in diversitatem formae, sed diversitas secundum numerum partim in diversitatem materiae, partim in diversitatem accidentis.	Now, since in the individual composite in the genus of substance there are only three things (matter, form, and the composite), it must be that in each of these things the causes of their diversities are to be found. Accordingly it must be evident that diversity of genus is reduced to diversity of matter; but diversity according to species is reduced to diversity of form; whereas diversity according to number is owing partly to diversity of matter, and partly to accidental diversity.
Cum autem genus sit principium cognoscendi, utpote prima diffinitionis pars, materia autem secundum se sit ignota, non potest secundum se ex ea accipi diversitas generis, sed solum illo modo, quo cognoscibilis est. Est autem cognoscibilis dupliciter. Uno modo per analogiam sive per proportionem, ut dicitur in I physicorum. Hoc est, ut dicamus illud esse materiam quod hoc modo se habet ad res naturales sicut lignum ad lectum. Alio modo cognoscitur per formam, per quam habet esse in actu. Unumquodque enim cognoscitur, secundum quod est in actu, et non secundum quod est in potentia, ut dicitur in IX metaphysicae.	Since, moreover, genus is the principle for knowableness of a thing, inasmuch as it is the first part of a definition, though matter in itself is unknowable, it is not possible that from matter in se diversity of genus should be known, but only according to that mode by which it is knowable. Now, a thing is knowable in two ways. (1) In one way, by analogy, or by comparison, as is said in I Physic. Thus we say that this is matter or that matter is related to natural things as wood is to a couch. (2) In another way, a thing is known by the form because of which it has actual being. For everything is known inasmuch as it is in act, not according as it is in potency, as is said in X Metaph.
[84581] Pars 2 q. 4 a. 2 co. 2
	Now, since in the individual composite in the genus of substance there are only three things (matter, form, and the composite), it must be that in each of these things the causes of their diversities are to be found.
	Accordingly it must be evident that diversity of genus is reduced to diversity of matter; but diversity according to species is reduced to diversity of form; whereas diversity according to number is owing partly to diversity of matter, and partly to accidental diversity.
Et secundum hoc dupliciter sumitur diversitas generis ex materia. Uno modo ex diversa analogia ad materiam, et sic penes materiam distinguuntur prima rerum genera. Id enim, quod est in genere substantiae, comparatur ad materiam sicut ad partem sui; quod vero est in genere quantitatis, non habet materiam partem sui, sed comparatur ad ipsam sicut mensura, et qualitas sicut dispositio. Et his duobus generibus mediantibus omnia alia genera nanciscuntur diversas comparationes ad materiam, quae est pars substantiae, ex qua substantia habet rationem subiecti, secundum quam ad accidentia comparatur. Alio modo penes materiam sumitur diversitas generis, secundum quod materia est perfecta per formam. Cum enim materia sit potentia pura et Deus actus purus, nihil est aliud materiam perfici in actum qui est forma, nisi quatenus participat aliquam similitudinem actus primi, licet imperfecte, ut sic illud, quod est iam compositum ex materia et forma, sit medium inter potentiam puram et actum purum.	According to this aspect, diversity of genus derives from matter in two ways. (1) In one way, by analogous diversity in relation to form, and thus the first genera of things are distinguished according to matter. For what is in the genus of substance is referred to matter as to a part of itself; but what is in the genus of quantity has no matter as a part of itself, but is related to it as its measure, and quality is related as its disposition. And by means of these two genera (namely, quantity and quality), all other genera are diversely related to matter, which is a part of substance; hence substance has the nature of a subject and as such has a certain relation to accidents. (2) In another way, diversity of genus has its, origin in matter inasmuch as matter is perfected by form. And since matter is pure potency, just as God is Pure Act, to say that matter is perfected by act (which is form) is to say nothing else than that in some way it shares in a certain similitude to First Act, imperfectly indeed, since what is composed of matter and form is midway between pure potency and pure act.
[84582] Pars 2 q. 4 a. 2 co. 3
Non autem materia ex omni parte recipit aequaliter similitudinem primi actus, sed a quibusdam imperfecte, a quibusdam vero perfectius, utpote quaedam participant divinam similitudinem secundum hoc tantum quod subsistunt, quaedam vero secundum quod vivunt, quaedam vero secundum quod cognoscunt, quaedam secundum quod intelligunt. Ipsa igitur similitudo primi actus in quacumque materia exsistens est forma eius. Sed forma talis in quibusdam facit esse tantum, in quibusdam esse et vivere, et sic de aliis una et eadem. Similitudo enim perfectior habet omne illud quod habet similitudo minus perfecta, et adhuc amplius. Aliquid ergo invenitur commune in utraque similitudine, quod in una substernitur imperfectioni et in alia perfectioni, sicut materia substernebatur actui et privationi. Et ideo materia simul accepta cum hoc communi est adhuc materialis respectu perfectionis et imperfectionis praedictae.	Moreover, matter does not receive similitude to First Act in an altogether equal way, but in some things it is received imperfectly and in others more perfectly; thus, for example, some beings participate in a divine similitude inasmuch only as they subsist; others, in that they have knowledge; and still others, by possession of intellect. Therefore what is the similitude of First Act in any existing matter is its form. But in some beings this form causes it only to exist, in others to exist and to live, and so, in one and the same being, form may be the cause of other perfections. For what is the more perfect similitude has everything that less perfect similitudes have by way of perfections, and more besides. Something common, therefore, may be found in various similitudes, but possessed more imperfectly in some and more perfectly in cothers; just as matter may be subjected to both act and privation. And so matter, once taken together with this common element, is still material in regard to the aforementioned perfection and imperfection.
[84583] Pars 2 q. 4 a. 2 co. 4
Et ex hoc materiali sumitur genus, differentiae vero ex perfectione et imperfectione praedicta. Sicut ex hoc communi materiali, quod est habere vitam, sumitur hoc genus animatum corpus; ex perfectione vero superaddita haec differentia sensibile; ex imperfectione vero haec differentia insensibile. Et sic diversitas talium materialium inducit diversitatem generis, sicut animal a planta. Et propter hoc dicitur materia esse principium diversitatis secundum genus. Et eadem ratione forma est principium diversitatis secundum speciem, quia a praedictis formalibus, quae habent ad dicta materialia, unde genera sumuntur, comparationem formae ad materiam, sumuntur differentiae quae constituunt species.	From this material element it takes its genus, but its difference is from the perfection or imperfection of which we spoke above. For example, frorp this common material element (namely, having life), there is derived the genus "animated body"; but because of a superadded perfection there derives the difference "sensible," while, on the other hand, from imperfection there is derived the difference "insensible." Thus the diversity of such material things brings about diversity of genus, as that between animal and plant. On this account matter is said to be the principle of diversity according to genus, and in the same way, form is the principle of diversity according to species; because it is by reason of formal qualities which material things possess in addition to those which are the cause of their genus as material things, or by relation of form to matter, that the differences constituting species are derived.
[84584] Pars 2 q. 4 a. 2 co. 5
Sciendum tamen quod cum illud materiale, unde sumitur genus, habeat in se materiam et formam, logicus considerat genus solum ex parte eius quod formale est, unde et eius diffinitiones dicuntur formales, sed naturalis considerat genus ex parte utriusque. Et ideo contingit quandoque quod aliquid communicat in genere secundum logicum, quod non communicat secundum naturalem. Contingit enim quandoque quod illud de similitudine primi actus quod consequitur res aliqua in materia tali, aliud consequatur sine materia et aliud in alia materia omnino diversa. Sicut patet quod lapis in materia, quae est secundum potentiam ad esse, pertingit ad hoc quod subsistat, ad quod idem pertingit sol secundum materiam ad ubi et non ad esse et Angelus omni materia carens. Unde logicus inveniens in omnibus his illud materiae, ex quo genus sumebat, ponit omnia in uno genere substantiae. Naturalis vero et metaphysicus, qui considerant omnia principia rei, non invenientes convenientiam in materia dicunt genere differre secundum hoc quod dicitur in X metaphysicae quod corruptibile et incorruptibile differunt genere et quod illa conveniunt genere, quorum materia est una et generatio ad invicem.	However, it must be borne in mind that this "matter" whence genus is derived has in itself both form and matter. While the logician considers genus only according to its formal aspect, his definitions are said to be formal; but the natural philosopher considers genus from both aspects. Hence it sometimes happens that a thing shares in a logical genus in which it would not be classed according to the natural philosopher. Now, this happens when something by way of similitude to First Act is found in a material thing, and again in one without matter, and again in a being altogether different in matter. Thus it is evident that a stone which is in matter in such a way as to be potential to being, attains to something of similitude to First Act by being subsistent, and the sun also attains to the same similitude, though being in matter which is potential to place, but not any longer to being (having subsistent existence); and an angel likewise, although lacking any kind of matter. Hence the logician, finding in all these beings that from which a genus derives, places them all in the genus of substance; but the natural philosopher and the metaphysician, who considers the principles of things, not finding these all to be in material agreement, says that they differ in genus; as is said in X Metaph.: that corruptible and incorruptible differ generically and that those beings agree in genus whose matter is one and among which there is mutual generation.
[84585] Pars 2 q. 4 a. 2 co. 6
Sic ergo patet, quomodo materia facit diversitatem in genere et forma diversitatem in specie. Inter individua vero unius speciei hoc modo consideranda est diversitas. Secundum philosophum enim in VII metaphysicae sicut partes generis et speciei sunt materia et forma, ita partes individui sunt haec materia et haec forma. Unde sicut diversitatem in genere vel specie facit diversitas materiae vel formae absolute, ita diversitatem in numero facit haec forma et haec materia. Nulla autem forma in quantum huiusmodi est haec ex se ipsa. Dico autem in quantum huiusmodi propter animam rationalem, quae quodammodo ex se ipsa est hoc aliquid, sed non in quantum forma. Intellectus enim quamlibet formam, quam possibile est recipi in aliquo sicut in materia vel in subiecto, natus est attribuere pluribus, quod est contra rationem eius quod est hoc aliquid. Unde forma fit haec per hoc quod recipitur in materia. Sed cum materia in se sit indistincta, non potest esse quod formam receptam individuet, nisi secundum quod est distinguibilis. Non enim forma individuatur per hoc quod recipitur in materia, nisi quatenus recipitur in hac materia distincta et determinata ad hic et nunc.	Thus therefore it is evident in what way matter produces diversity in genus, and form produces diversity in species. But among individuals of the same species diversity should be considered, according to that laid down by the Philosopher (VII Metaph.); namely, that just as parts of genus and species are matter and form, so the parts of the individual are this matter and this form. Therefore, just as diversity of matter causes diversity in genus, or diversity of form causes diversity in species, absolutely, so this form and this matter produce diversity in number: but no form, as such, is of itself. I say, however, "no form, as such," because of the rational soul, which in a manner is this something of itself, but not merely inasmuch as it is a form. Intellect, in truth, since it is a form capable of being received into anything—as its matter, or as its subject—can naturally be attributed to many; a thing which is contrary to the nature of that which is this something; hence it is, made a form by the fact that it is received in matter. But since matter, considered in itself, is indistinct, it is not possible that it would individuate a form received into it, except as it is distinguishable. For no form is individuated by the fact that it is received into’matter, except in so far as it is received into this matter, or it is this distinct form, determined to this, and at this time.
Materia autem non est divisibilis nisi per quantitatem. Unde philosophus dicit in I physicorum quod subtracta quantitate remanebit substantia indivisibilis. Et ideo materia efficitur haec et signata, secundum quod subest dimensionibus.	Moreover, matter is not divisible except by quantity. Therefore the Philosopher says in I Physic., that if quantity were removed, a substance would remain indivisible: hence matter is made to be this matter and is signate inasmuch as it exists under dimensions.
[84586] Pars 2 q. 4 a. 2 co. 7
Dimensiones autem istae possunt dupliciter considerari.	Dimensions, however, can be considered in two ways.
Uno modo secundum earum terminationem; et dico eas terminari secundum determinatam mensuram et figuram, et sic ut entia perfecta collocantur in genere quantitatis. Et sic non possunt esse principium individuationis; quia cum talis terminatio dimensionum varietur frequenter circa individuum, sequeretur quod individuum non remaneret semper idem numero.	1. In one way according to their termination, and I say that they are terminated according to limited measure and figure; and so, as complete beings, dimensions are classed in the genus of quantity, and thus they cannot be the principle of individuation: because such termination of dimensions may frequently vary in regard to the same individual, and in such case it would follow that the individual would not remain numerically the same.
Alio modo possunt considerari sine ista determinatione in natura dimensionis tantum, quamvis numquam sine aliqua determinatione esse possint, sicut nec natura coloris sine determinatione albi et nigri; et sic collocantur in genere quantitatis ut imperfectum. Et ex his dimensionibus indeterminatis materia efficitur haec materia signata, et sic individuat formam, et sic ex materia causatur diversitas secundum numerum in eadem specie.	2. In another way, dimensions may be considered without this certain determination, merely in the nature of dimension, although they never could exist without some kind of determination; just as the nature of color cannot exist without determination to white or black; and according to this aspect dimensions are classed in the genus of quantity as imperfect. And by these indeterminate dimensions matter is made to be this signate matter, and thus gives individuality to a form, and thus also by matter there is caused the numerical diversity of things in the same species.
[84587] Pars 2 q. 4 a. 2 co. 8
Unde patet quod materia secundum se accepta nec est principium diversitatis secundum speciem nec secundum numerum, sed sicut est principium diversitatis secundum genus, prout subest formae communi, ita est principium diversitatis secundum numerum, prout subest dimensionibus interminatis. Et ideo cum hae dimensiones sint de genere accidentium, quandoque diversitas secundum numerum reducitur in diversitatem materiae, quandoque in diversitatem accidentis, et hoc ratione dimensionum praedictarum. Alia vero accidentia non sunt principium individuationis, sed sunt principium cognoscendi distinctionem individuorum. Et per hunc modum etiam aliis accidentibus individuatio attribuitur.	Therefore it is evident that matter, according as it is considered in itself, is not the principle of diversity, either according to species or according to number; but as it is the principle of generic diversity inasmuch as it is considered the subject of a common form, so it is the principle of numerical diversity inasmuch as it is considered as subject to indeterminate dimensions. Therefore also, since these dimensions are in the genus of accidents, diversity according to number is reduced to diversity of matter, or to accidental diversity, according to the nature of the aforesaid dimensions. Other accidents, however, are not principles of individuation, but they are the principle of knowing the individual to be distinct. In this way individuation is also attributed to other accidents.
[84588] Pars 2 q. 4 a. 2 ad 1
Ad primum ergo dicendum quod, cum dicit philosophus quod numero sunt unum, quorum est materia una, intelligendum est de materia signata, quae subest dimensionibus, alias oporteret dicere quod omnia generabilia et corruptibilia sint unum numero, cum eorum sit materia una.	1. It may be said: When the Philosopher says that those things are numerically one in which the matter is one, this must be understood of signate matter which is the subject of dimensions; otherwise it would be necessary to say that all generable and corruptible things are numerically one, since their matter is one.
[84589] Pars 2 q. 4 a. 2 ad 2
Ad secundum dicendum quod dimensiones, cum sint accidentia, per se non possunt esse principium unitatis individuae substantiae; sed materia, prout talibus dimensionibus subest, intelligitur esse principium talis unitatis et multitudinis.	2. It may be answered: Since dimensions are accidents, they cannot per se be the principle of the unity of an individual substance; but matter, inasmuch as it underlies such and such dimensions, is understood to be the principle of this unity and of this multitude.
[84590] Pars 2 q. 4 a. 2 ad 3
Ad tertium dicendum quod de ratione individui est quod sit in se indivisum et ab aliis ultima divisione divisum. Nullum autem accidens habet ex se propriam rationem divisionis nisi quantitas. Unde dimensiones ex se ipsis habent quandam rationem individuationis secundum determinatum situm, prout situs est differentia quantitatis. Et sic dimensio habet duplicem rationem individuationis: unam ex subiecto, sicut et quodlibet aliud accidens, et aliam ex se ipsa, in quantum habet situm, ratione cuius etiam abstrahendo a materia sensibili imaginamur hanc lineam et hunc circulum. Et ideo recte materiae convenit individuare omnes alias formas ex hoc, quod subditur illi formae, quae ex se ipsa habet individuationis rationem, ita quod etiam ipsae dimensiones terminatae, quae fundantur in subiecto iam completo, individuantur quodammodo ex materia individuata per dimensiones interminatas praeintellectas in materia.	3. It may be said: It is according to the nature of an individual thing that it be undivided in itself, and divided from other things by an ultimate division. No accident, however, has in itself the proper nature of division, unless it is quantity; therefore dimensions of themselves have a certain nature of individuation according to a determined place, inasmuch as place is a difference of quantity. Thus there is a twofold meaning of individuation: the one on the part of a subject, and this is the same for any accident; the other meaning, on the part of individuation itself, inasmuch as it has place, by reason of which, in abstracting from sensible matter, we may imagine this line and this circle. Hence it rightly pertains to matter to individuate all other forms, because it gives to this form, which of itself has the nature of individuation, that it also be terminated by those dimensions that are found in a subject now made complete; accordingly they are individuated by matter which is individuated by indeterminate dimensions conceived of as in matter.
[84591] Pars 2 q. 4 a. 2 ad 4
Ad quartum dicendum quod illa, quae differunt numero in genere substantiae, non solum differunt accidentibus, sed etiam forma et materia. Sed si quaeratur, quare differens est eorum forma, non erit alia ratio, nisi quia est in alia materia signata. Nec invenitur alia ratio, quare haec materia sit divisa ab illa, nisi propter quantitatem. Et ideo materia subiecta dimensioni intelligitur esse principium huius diversitatis.	4. It may be said: Things that differ numerically in the genus of substance, differ not dinly because of accidents, but also by reason of form and matter; but if it is asked how this form differs from that, the only reason can be that it is in other signate matter. Nor can there be found another reason why this matter is divided from that except by reason of its quantity. Hence matter subject to dimension is undersiood to be the principle of this kind of diversity.
[84592] Pars 2 q. 4 a. 2 ad 5
Ad quintum dicendum quod ratio illa procedit de accidentibus completis, quae sequuntur esse formae in materia, non autem de dimensionibus interminatis, quae praeintelliguntur ante ipsam formam in materia. Sine his enim non potest intelligi individuum, sicut nec sine forma.	5. It may be said: This reasoning relates to completed accidents which follow upon the existence of a form in matter; but not to those indeterminate dimensions which may be conceived of before the reception of the form in matter. For without these, a thing cannot be understood to be ‘ individual, any more than it can be conceived of without form.
[84593] Pars 2 q. 4 a. 2 ad 6
Ad sextum dicendum quod numerus formaliter loquendo est prius quam quantitas continua, sed materialiter quantitas continua est prior, cum numerus ex divisione continui relinquatur, ut dicitur in III physicorum. Et secundum hanc viam causat diversitatem secundum numerum divisio materiae secundum dimensiones.	6. It may be answered: Number, formally speaking, is prior to continuous quantity: but materially, continuous quantity is prior, since number is the result of the division of a continuum, as is said in IV Physic. In this way, division of matter, according to dimensions, causes numerical diversity.
Rationes autem quae sunt in contrarium patet ex dictis qualiter sunt concedendae et qualiter falsum concludunt.	As to contrary reasons proposed, it is clear what must be conceded and what false conclusions have been deduced.
Articulus 3	Whether Two Bodies Can Be, or Can Be Conceived of as Being Simultaneously in the Same Place.
Pars 2 q. 4 a. 3 arg. 1
Ad tertium sic proceditur. Videtur quod duo corpora possint intelligi esse in eodem loco. Omnis enim propositio videtur esse intelligibilis, in cuius subiecto non includitur oppositum praedicati, quia talis propositio non habet repugnantiam intellectuum. Sed haec propositio duo corpora sunt in eodem loco non est huiusmodi; alias numquam posset miraculose fieri quod duo corpora sint in eodem loco; quod patet esse falsum in corpore dominico quod exivit clauso utero virginis et intravit ad discipulos clausis ianuis. Non enim Deus potest facere quod affirmatio et negatio sint simul vera, ut dicit Augustinus contra Faustum. Ergo potest aliquis saltem intellectu fingere duo corpora esse in eodem loco.	1. It seems that two bodies can be conceived of as being in the same place. For any proposition seems to be intelligible in which there is included no opposition of the predicate to the subject, since such a proposition contains nothing repugnant to understanding. But this proposition, "Two bodies are in the same place," is not a proposition repugnant to the intellect. Otherwise it could not happen miraculously, a thing evidently false regarding the body of our Lord, which came forth from the closed womb of the Virgin, and which entered into the midst of the disciples, the doors being shut. Now, even God cannot cause affirmation and negation to be simultaneously true, as Augustine says in answer to Faustus; therefore one can understand, or at least conceive of in his mind, that two bodies could be in the same place at the same time.
Pars 2 q. 4 a. 3 arg. 2
Praeterea, a corporibus glorificatis non removetur natura corporeitatis, sed solum natura corpulentiae. Sed removetur ab eis ista condicio, quod non possunt esse in eodem loco, per dotem subtilitatis, ut a multis dicitur. Ergo haec condicio non sequitur naturam corporeitatis, sed corpulentiae sive grossitiei cuiusdam. Ergo non est impossibile universaliter duo corpora esse in eodem loco.	2. From glorified bodies there will be removed not the nature of corporeity, but only that of corpulentia (bodily mass). When this is removed, the possibility of being with other bodies in the same place is theirs by reason of the gift of subtlety, as is said by many. Therefore this condition does not follow the nature of corporeity, but that of corpulentia, of a certain mass. Therefore it is not impossible to conceive of two bodies being simultaneously in the same place.
Pars 2 q. 4 a. 3 arg. 3
Praeterea, Augustinus dicit super Genesim ad litteram quod lux in corporibus primum tenet locum. Sed lux est simul in eodem loco cum aere. Ergo duo corpora possunt esse simul in eodem loco.	3. Augustine, in commenting upon the Book of Genesis speaks,of light as holding first place among corporeal things; but light is simultaneously in the same place with air; therefore two bodies can be in the same place at the same time.
Pars 2 q. 4 a. 3 arg. 4
Praeterea, quaelibet species ignis est corpus. Sed lux est quaedam species ignis, ut dicit philosophus in V topicorum. Ergo lux est corpus. Et sic idem quod prius.	4. Any species of fire, as the Philosopher says in V Topic., is a body; and so the conclusion is like the previous one.
Pars 2 q. 4 a. 3 arg. 5
Praeterea, in ferro ignito simul est ignis et ferrum. Utrumque autem est corpus. Ergo possibile est simul esse duo corpora in eodem loco.	5. In glowing iron, the fire and the iron are simultaneous; but each is a body; therefore it is possible for two bodies to be in the same place at the same time.
Pars 2 q. 4 a. 3 arg. 6
Praeterea, elementa in mixto non sunt corrupta, alias mixtum non sequeretur dominantis motum. Sed omnia quattuor elementa sunt corpora et simul in qualibet parte mixti. Ergo possibile est duo corpora esse in eodem loco.	6. Elements in a compound are not corrupted; otherwise a compound would not follow the motion of a dominant element; but all four elements are bodies and are simultaneously in every part of the compound; therefore it is possible for two bodies to be simultaneously in the same place.
Pars 2 q. 4 a. 3 arg. 7
Praeterea, quod duo corpora non sint in eodem loco, hoc non potest convenire corporibus ratione materiae, cum materiae secundum se non debeatur locus, nec ratione formae propter idem nec ratione dimensionis, cum dimensiones non repleant locum, quod patet ex hoc quod quidam locum, ubi erant solae dimensiones, dicebant esse vacuum. Ergo hoc non convenit corpori nisi ratione aliquorum accidentium posteriorum, quae non sunt omnibus corporibus communia et quae possibile est a corporibus separari. Et sic videtur quod duo corpora possint esse in eodem loco.	7. The fact that two bodies are not simultaneously in one place does not occur by reason of the matter of the bodies, since to matter in itself there is no due place; nor does it occur because of the form, for the same reason; nor is it because of dimension, since dimensions do not fill up place, as is evident from the fact that certain philosophers are accustomed to say that the place where there are only dimensions is a vacuum. Therefore this characteristic of a body must arise only from certain posterior accidents, which are not altogether common and which can be separated from the body; and so it seems that two bodies could be simultaneously in the same place.
Pars 2 q. 4 a. 3 arg. 8
Praeterea, secundum astrologos, qui sequuntur Ptolemaeum, sex planetarum corpora moventur in epicyclis, qui sunt circuli intersecantes sphaeras excentricas planetarum. Oportet ergo quod planetae corpus quandoque perveniat ad locum sectionis. Sed non potest dici quod ibi sit aliquid vacuum, cum vacuum natura non patiatur, neque quod substantia sphaerarum sit divisibilis, ut intelligatur cedere corpori planetae quando pervenit illuc, sicut cedit aer lapidi aut alii corpori, cum caeli solidissimi quasi aere fundati sint, ut dicitur Iob 37. Ergo oportet quod corpus planetae sit simul cum corpore sphaerae eius in eodem loco. Et sic falsum est quod dicit Boethius hic quod duo corpora numquam unum obtinent locum.	8. According to the astrologers who follow Ptolemy, the six bod?es of the planets move in epicycles, which are circles intersecting the spheres extrinsic to the planets. Therefore it must be that a body of a planet at some time would arrive at the place of section. But it cannot be said that at that place there is any vacuum, since nature does not suffer this; nor that the substance of the spheres is divisible, so that it might be thought of as giving way when the planetary body had reached it, as air gives way to a stone, for the heavens are most solid, being formed, as it were, of molten brass, as is said in Job, 37:18. Therefore it must be that the body of the planet is simultaneously in the same place as the body of the sphere; and so Boethius falsely says that two bodies cannot occupy one and the same place.
Pars 2 q. 4 a. 3 s. c. 1
Sed contra est, quia si duo corpora sunt in eodem loco, eadem ratione et quotlibet. Sed aliquod corpus quantumcumque magnum potest dividi in parva cuiuscumque quantitatis secundum aliquem numerum. Ergo sequetur quod in loco parvissimo continebitur maximum corpus; quod videtur absurdum.	On the contrary is the fact that if two bodies are in one and the same place, they are the same in nature and in every respect; but any body, however large, can be divided into small bodies of any qqantity, according to any number; therefore, it would follow that in the very smallest place there would be contained the largest body, a thing which appears to be absurd.
Pars 2 q. 4 a. 3 s. c. 2
Praeterea, impossibile est inter duo puncta signata esse plures lineas rectas. Hoc autem sequetur, si duo corpora sint in eodem loco. Signatis enim duobus punctis ex duabus partibus loci oppositis erunt inter ea duae lineae rectae signatae in duobus corporibus locatis. Non enim potest dici quod inter illa duo puncta nulla sit linea neque quod unius locati linea magis sit inter ea quam alia neque quod sit ibi aliqua una linea praeter corpora locata quae sit inter duo puncta loci, quia sic illa linea esset non in subiecto. Ergo impossibile est duo corpora esse in eodem loco.	Again, it is impossible for there to be many straight lines between two given points. But this would follow if two bodies could be in the same place. For then, given two points in two opposite parts of space, there will be between them two straight lines assigned corporeally to two places. Now, it cannot be said that between these two points there will be no lines at all, or that a line of one location would be greater than the other, or that there could be any one line apart from those corporeally located between the two points of given location, for in that case the two lines would not be in a subject. Therefore it is impossible for two bodies to be simultaneously in the same place.
Pars 2 q. 4 a. 3 s. c. 3
Praeterea, demonstratum est in geometria quod duo circuli non se contingunt nisi in puncto. Sed ponamus duo corpora quae sunt in eodem loco; sequetur quod duo circuli signati in eis se secundum totum contingunt. Ergo impossibile est duo corpora esse in eodem loco.	Again, it has been demonstrated in geometry that two circles are tangent only at one point: but if we posit two bodies being simultaneously in the same place, it would follow that two circles could be totally tangent. Therefore it is impossible that two bodies should be in the same place at the same time.
Pars 2 q. 4 a. 3 s. c. 4
Praeterea, quaecumque uni et eidem sunt eadem, sibi invicem sunt eadem. Sed cum oporteat eandem esse dimensionem loci et locati ex eo quod non est ponere dimensiones sine subiecto, si duo corpora sint in eodem loco, sequetur dimensiones utriusque corporis esse easdem dimensionibus loci. Ergo sequetur eas esse easdem ad invicem, quod est impossibile.	Again, whatever things are equal to one and the same thing are equal to each other; but since local dimension must be one with a localized body (since no dimension can be supposed without a subject), if two bodies could be simultaneously in the same place, it would follow that the dimensions of each body would be equal to the dimensions of the place; therefore it would follow that the bodies would be the same, but this is impossible.
Pars 2 q. 4 a. 3 co. 1
Responsio. Dicendum quod in his quae apud nos sunt, quae omnes esse corpora confitentur, ad sensum videmus quod adveniente uno corpore ad locum aliquem aliud corpus a loco illo expellitur. Unde experimento patet talium corporum duo in eodem loco esse non posse.	Response. I answer that it must be said that in those things belonging to our world, all of which are judged to be corporeal, we see from sense experience that when one body arrives at any given place, any other body is expelled from that place; therefore it is experimentally evident that two such bodies cannot be in the same place.
Quidam autem dicunt quod non prohibentur duo horum corporum ab hoc, quod sint simul, propter corporeitatem vel propter aliquid quod sit de ratione corporis, in quantum est corpus; sic enim sequeretur omnino duo corpora prohiberi ab hoc quod est esse simul. Sed dicunt quod ab hoc prohibentur propter corpulentiam ipsorum. Sed quidquid sit hoc quod corpulentiam nominant, sive sit densitas sive impuritas vel corruptibilitas aliquorum corporum vel etiam aliqua natura specialis naturae generali corporeitatis superaddita, non potest esse causa huius prohibitionis.	There are, however, certain philosophers who declare that two bodies are not thus prohibited from simultaneous occupation of the same place on account of their corporeity, or on account of anything else which belongs to the nature of a body, as a body, for thus it would follow that it would be altogether impossible for two bodies to exist simultaneously [in the same place]. But they say that this prohibition is due only to their corpulentia. But whatever this corpulentia may mean—whether density or impurity or corruptibility which attends certain bodies, or even some special nature superadded to the general nature of corporeity—the prohibition can be on account of none of these things.
Pars 2 q. 4 a. 3 co. 2
Invenitur enim duplex comparatio corporis ad locum. Una, secundum quam ponitur in loco hoc vel illo determinato; et haec comparatio sequitur naturam specialem huius vel illius corporis, sicut quod gravia ex natura gravitatis sunt deorsum, levia vero sursum ex natura levitatis.	Now, there is to be found a double relation of a body to place. One is according as it has location in this or that determined place; and this relationship follows upon the specific nature of this or that body, just as heavy things, by the very nature of their gravity, hold a lower place, but light bodies, a higher place.
Alia vero comparatio est, secundum quam dicitur esse in loco simpliciter; et haec comparatio sequitur corpus ex ipsa natura corporeitatis, non propter aliquid additum. Secundum hoc enim corpus est in loco, quod loco se commetitur; hoc autem est, secundum quod est dimensionatum dimensionibus aequalibus et similibus dimensionibus loci. Dimensiones autem insunt cuilibet corpori ex ipsa corporeitatis natura. Esse autem plura corpora in eodem loco vel non esse non respicit locum determinatum, sed locum absolute. Unde oportet quod causa huius impedimenti referatur ad ipsam naturam corporeitatis, ex qua convenit omni corpori quod, in quantum est corpus, natum sit esse in loco.	But another relationship prevails according as a body is said, absolutely, to be in place: and this relationship characterizes a bodily thing by the very nature of its corporeity, not because of anything additional. For according as a particular body is in place, it is commensurate with that place; but this is because it has dimensions that are equal and similar to the dimensions of the place; moreover, dimensions belong to every body by reason of its very corporeity. For, that many bodies should or should not be in the same place, has no relation to a determined place, but regards place absolutely; therefore it must be that the cause of this impediment should be referred to the nature of corporeity, by reason of which every body, inasmuch as it is a body, is destined to be in place.
Et si ultima sphaera non sit in loco, hoc non est nisi quia nihil potest esse extra ipsam, non autem propter defectum aptitudinis praedictae.	And if the last sphere should not be in place, this is so only because nothing can be outside it, but not because it is lacking in the aforesaid aptitude to occupy place.
Pars 2 q. 4 a. 3 co. 3
Et ideo alii concedunt simpliciter quod nulla duo corpora possunt esse in eodem loco et rationem huius referunt ad principia mathematica, quae oportet salvari in omnibus naturalibus, ut dicitur in III caeli et mundi. Sed hoc non videtur esse conveniens, quia mathematicis non competit esse in loco nisi similitudinarie et non proprie, ut habetur in I de generatione. Et ideo ratio praedicti impedimenti non est sumenda ex principiis mathematicis, sed ex principiis naturalibus, quibus proprie locus debetur. Praeterea, rationes mathematicae non sufficienter concludunt in ista materia. Etsi enim mathematica salventur in naturalibus, tamen naturalia addunt aliquid supra mathematica, scilicet materiam sensibilem, et ex hoc addito potest assignari ratio alicuius in naturalibus, cuius ratio in mathematicis non poterat assignari. In mathematicis enim non potest assignari ratio diversitatis harum duarum linearum nisi propter situm. Unde remota diversitate situs non remanet pluralitas linearum mathematicarum et similiter nec superficierum aut corporum. Et propter hoc non potest esse quod corpora mathematica sint plura et sint simul; et similiter de lineis et superficiebus.	Hence there are others who concede that, absolutely, no two bodies can be in the same place at the same time, and they assign the reason for this to mathematical principles, which ought to be observed in all the natural sciences, as is said in III Coel. et mun. But this reason does not seem fitting, because it does not pertain to the objects of mathematics to be in place, except improperly and by similitude, as is said in II De generatione. Hence, the reason for maintaining this impediment should not be derived from mathematical principles, but from the principles of natural things, to which place is properly due. Furthermore, mathematical reasoning is sufficiently conclusive only in regard to its own matter. For, although mathematical truths are preserved in natural sciences, beings of the natural order add something over and above what is possessed by, mathematical beings: namely, sensible matter; and because of this addition it is possible to assign as an explanation of something in the natural order what would not be assigned in explanation of an object of mathematics. For in mathematics no reason for diversity of two given lines can be assigned except because of their situation; wherefore, if diversity of situation is removed, there remains no plurality of mathematical lines, and likewise no diversity of surfaces or of bodies. On this account mathematical bodies cannot be both many and simultaneous, and in like manner neither can lines or surfaces.
Sed in corporibus naturalibus posset ab adversario assignari alia ratio diversitatis, scilicet ex materia sensibili, etiam remota diversitate situs. Et ideo illa, quae probabat duo corpora mathematica non esse simul, non est sufficiens ad probandum duo corpora naturalia simul non esse.	But in regard to corporeal things in nature, it is possible to assign another and different reason for diversity: namely, that of sensible matter, even though diversity of situation were removed. Hence the reasoning which proves that two mathematical bodies cannot be simultaneously in the same place does not suffice for proving that two bodies in the natural order could not be simultaneous.
Pars 2 q. 4 a. 3 co. 4
Et ideo accipienda est via Avicennae, qua utitur in sua sufficientia in tractatu de loco, per quam assignat causam prohibitionis praedictae ex ipsa natura corporeitatis per principia naturalia. Dicit enim quod non potest esse causa huius prohibitionis nisi illud cui primo et per se competit esse in loco; hoc est enim quod natum est replere locum. Formae autem non competit esse in loco nisi per accidens, quamvis aliquae formae sint principium, quo corpus determinatur ad hunc vel illum locum. Similiter nec materia secundum se considerata, quia sic intelligitur praeter omnia alia genera, ut dicitur in VII metaphysicae. Unde oportet quod materia secundum quod subest ei, per quod habet primam comparationem ad locum, hoc prohibeat. Comparatur autem ad locum, prout subest dimensionibus.	And therefore the explanation of Avicenna must be accepted, which he uses in his Sufficientia, in the treatise De loco. In this explanation he assigns as reason of the aforesaid prohibition one which, by natural principles, is owing to the very nature of corporeity itself. For he says there can be no cause of this prohibition except that it pertains, first and per se, to a thing to be in place: but this means that it is destined by its nature to fill a place. Moreover, it does not pertain to a form to be in place, except accidentally; although certain forms are the principles by which a body is inclined to this or that place. Likewise neither does it pertain to matter, considered per se, to be in place, because, as so considered, it is understood apart from all genera, as is said in VII Metaph. Wherefore it must be that matter, according as it is subject to that by which it has primary relation to place, is the cause of this prohibition; but it is related to place inasmuch as it is subject to dimensions:
Pars 2 q. 4 a. 3 co. 5
Et ideo ex natura materiae subiectae dimensionibus prohibentur corpora esse in eodem loco plura.	hence it is by nature of matter subject to dimensions that many bodies are prohibited from being in the same place.
Oportet enim esse plura corpora, in quibus forma corporeitatis invenitur divisa, quae quidem non dividitur nisi secundum divisionem materiae, cuius divisio cum sit solum per dimensiones, de quarum ratione est situs, impossibile est esse hanc materiam distinctam ab illa, nisi quando est distincta secundum situm, quod non est quando duo corpora ponuntur esse in eodem loco. Unde sequitur illa duo corpora esse unum corpus, quod est impossibile. Cum ergo materia dimensionibus subiecta inveniatur in quibuslibet corporibus, oportet quaelibet duo corpora prohiberi ex ipsa natura corporeitatis, ne sint in eodem loco.	For, wherever the form of corporeity is found to be divided, there must be a plurality of bodies; but this division does not take place except by division of matter. Since division of matter is only by dimensions, because of which matter has situation, it is impossible that this matter should be distinct from that unless it is distinct according to situation. But this would not be the case if two bodies were posited as being in the same place; for then they would not be two bodies but one body, a thing which is impossible. Since, therefore, matter subject to dimensions is found in all corporeal things, it must be by reason of the very nature of corporeity that any two bodies are prohibited from being in the same place at the same time.
Pars 2 q. 4 a. 3 ad 1
Ad primum ergo dicendum quod dupliciter aliqua propositio potest dici non intelligibilis. Uno modo ex parte intelligentis qui deficit intellectu, sicut haec propositio: in tribus personis divinis est una essentia. Et huiusmodi propositio non oportet quod implicet contradictionem.	1. It may be said: A proposition may be called not-intelligible in two ways. In one way, it may be on the part of the one understanding, because of the deficiency of his intellect, as is the case in relation to this proposition: "In the three divine Persons there is one essence." In a proposition of this kind, there can be, indeed, no contradiction.
Alio modo ex parte ipsius propositionis. Et hoc dupliciter. Uno modo implicat contradictionem absolute, sicut rationale est irrationale et similia; et huiusmodi nullo miraculo verificari possunt. Alia vero implicant contradictionem aliquo modo, sicut ista: mortuus redit ad vitam. Implicat enim contradictionem, secundum quod intelligitur redire ad vitam propria virtute, cum ponatur per hoc quod dicitur mortuum omni vitae principio destitutum. Et talia possunt verificari per miraculum superiori virtute operante. Et similiter est in proposito. Non enim in duobus corporibus in eodem loco positis potest aliqua naturalis causa diversitatis inveniri. Sed divina virtus potest ea, quamvis sint unita in situ, in sua distinctione conservare. Et sic miraculose fieri potest quod duo corpora sint in eodem loco.	In another way, non-intelligibility may be on the part of the proposition, and this again for two reasons. In one way because it implies a contradiction, absolutely, as for example, "The rational is irrational"; and not even by a miracle can propositions of this sort be made true. In another way, because they imply a contradiction in a certain manner, as this proposition: "The dead man rose to life by his own (proper) power"; for, by the fact that he is said to be "dead," it is posited that he is destitute of every principle of life. Propositions of this kind can be made true by the miraculous operation of a superior power; and such is the case in regard to this proposition. For just as there can be found no natural cause of diversity for two bodies in the same place, so, by divine power, it is possible that two bodies be in the same place and that, although united in situation, their, distinction be conserved, as does miraculously happen.
Pars 2 q. 4 a. 3 ad 2
Ad secundum dicendum quod quidquid sit illa corpulentia quae ponitur removeri a corporibus gloriosis, tamen planum est quod corporeitas ab eis numquam removebitur et ideo nec causa naturaliter prohibens aliquod eorum simul esse cum alio corpore in eodem loco. Sed solum miraculose hoc esse poterit quod sint simul cum aliis corporibus in eodem loco.	2. It may be said: Whatever may be this corpulentia, which is said to be removed from glorified bodies, nevertheless it is evident that corporeity will not be removed from them; therefore, neither will the cause which naturally prohibits any one of them from simultaneously occupying the same place with another; but only by a miracle is it possible that a glorified body be in the same place simultaneously with other bodies.
Pars 2 q. 4 a. 3 ad 3
Ad tertium dicendum quod lux non est corpus, sed qualitas quaedam, ut Damascenus dicit et etiam Avicenna. Augustinus autem lucem nominat ipsum ignem, quod patet ex hoc quod condividit lucem contra aerem, aquam et terram.	3. It may be answered: Light is not a body, but a certain quality, as Damascene says, and Avicenna also. But Augustine gives light the same name as fire, as is evident from the fact that he speaks of light as contradistinguished from air, water, and earth.
Pars 2 q. 4 a. 3 ad 4
Ad quartum dicendum quod tres species ignis a philosopho assignatae sic sunt intelligendae, ut per lucem intelligatur ignis in propria materia exsistens, dato etiam, ut quidam dicunt, quod ignis in propria sphaera non lucet. Lucis enim non est lucere, sed quod ex eius participatione alia luceant. Et similiter ignis, etsi in propria materia non luceat, tamen eius participatione alia lucentia fiunt. Per flammam autem intelligitur ignis exsistens in materia aerea, per carbonem in materia terrea. In materia autem aquea non potest ignis convalescere in tantum quod ignis nomen habeat, quia aqua habet omnes qualitates oppositas igni.	4. It may be answered: The three species of fire spoken of by the Philosopher are to be understood in such a way that by "light" is understood fire existing in its proper matter, and granted also, as some say, that fire in its own proper sphere emits no light. For it does not belong to the nature of light to be luminous, but by participation in it other things become so. The same is true of fire: for, although in its own sphere it emits no light, nevertheless, by participation in it, other things become refulgent. By flame, however, is to be understood fire in the air; and by carbo, fire in terrestrial matter. In aqueous matter, however, fire cannot continue in such a way as to have the nature of fire, because water has qualities which are altogether opposed to fire.
Pars 2 q. 4 a. 3 ad 5
Ad quintum dicendum quod in ferro ignito non sunt duo corpora, sed unum corpus habens quidem speciem ferri, sed aliquas proprietates ignis.	5. It must be said: In iron which has become ignited there are not two bodies, but one body having indeed the species of iron, but certain properties of fire.
Pars 2 q. 4 a. 3 ad 6
Ad sextum dicendum quod etsi ponantur elementa in corpore mixto remanere secundum suas formas substantiales, non tamen ponuntur esse plura corpora in actu, alias nullum corpus mixtum esset vere unum, sed est unum in actu et multa in potentia.	6. It may be answered: Although elements in a compound are supposed to remain according to their substantial forms, nevertheless it is not supposed that there are then many bodies in act, for otherwise no compound would be truly one; but while it is potentially many, it is one in act.
Probabilior tamen videtur esse opinio Commentatoris in III caeli et mundi, qui hanc opinionem Avicennae improbans dicit elementorum formas in mixto non remanere nec totaliter corrumpi, sed fieri ex his unam mediam formam, in quantum suscipiunt magis et minus. Sed cum formae substantiales magis et minus suscipere sit absonum, videtur eius dictum esse intelligendum hoc modo, quod formae elementorum suscipiant magis et minus non secundum se, sed secundum quod manent virtute in qualitatibus elementaribus quasi in propriis instrumentis, ut sic dicatur quod formae secundum se non remanent, sed solum prout sunt virtute in qualitatibus, ex quibus fit una media qualitas.	Nevertheless the opinion of the Commentator, III Coel. et mun., seems the more probable. In rejecting the opinion of Avicenna, he says that the forms of elements neither remain in a compound nor are altogether corrupted, but that from them there comes to be one common or neuter form inasmuch as they comprise it, more or less. But since to give rise to a substantial form "more or less" seems an improbability, it appears that this saying ought to be understood in this way: that the forms of the elements are receptive of more or less (or comprise the form of the compound, more or less), not secundum se, but according as they remain in elementary qualities, as it were in their proper instruments. And thus it is said: Forms remain virtually in the qualities of the elements certain instrumental properties, as it were. Forms secundum se, do not remain, but only according as they remain virtually in their qualities, out of which there is made one, median, or common quality.
Pars 2 q. 4 a. 3 ad 7
Ad septimum dicendum quod quamvis dimensiones per se non possent replere locum, tamen corpus naturale ex hoc quod eius materia intelligitur subiecta dimensionibus habet quod repleat locum.	7. It may be said: Although dimensions of themselves cannot fill out a place, nevertheless a natural body, because of the fact that its matter is understood to be subject to dimensions, has the natural characteristic of filling a place.
Pars 2 q. 4 a. 3 ad 8
Ad octavum dicendum quod opinio Ptolemaei de epicyclis et excentricis non videtur consonare principiis naturalibus quae Aristoteles ponit; et ideo illa opinio sectatoribus Aristotelis non placet. Si tamen sustineatur, nulla necessitas erit quod duo corpora sint in eodem loco, quia secundum tenentes illam opinionem triplex substantia distinguitur in caelestibus corporibus, scilicet substantia stellarum, quae est luminosa, et substantia sphaerarum, quae est diaphana et solida non divisibilis, et substantia alia quae est inter sphaeras, quae est divisibilis et inspissabilis ad modum aeris, quamvis sit incorruptibilis. Et per hanc substantiam defenduntur, ne oporteat eos ponere substantiam sphaerarum dividi aut duo corpora esse in eodem loco.	8. It may be said: The opinion of Ptolemy regarding epicycles and eccentrics does not seem consonant with principles of natural philosophy which Aristotle holds; hence this opinion is not acceptable to the followers of Aristotle. If, however, it should be sustained, no necessity arises for supposing two bodies to be in the same place since, according to those who hold this opinion, the substances of heavenly bodies are distinguished as of three kinds: namely, the substance of the stars, which is luminous; the substance of the spheres, which is diaphanous and solid, but not divisible; and another kind of substance, which is between the spheres, and which is divisible and of resisting density, after the manner of the air, although this substance is incorruptible. And thus those who hold the theory of this third substance have no need to say that the substance of the spheres is divided or that two bodies occupy the same place simultaneously.
Articulus 4	Whether Variety of Location Has Any Influence in Effecting Numerical Difference.
Pars 2 q. 4 a. 4 arg. 1
Ad quartum sic proceditur. Videtur quod loci varietas nihil faciat ad diversitatem secundum numerum. Causa enim diversitatis secundum numerum est in ipsis quae numero differunt. Sed locus est extra locata. Ergo ex diversitate locorum non potest esse causa diversitatis secundum numerum.	1. It seems that variety of location effects nothing as regards diversity according to number. For the cause of diversity according to number is in those things which differ numerically; but place is outside things that are located; therefore diversity of place cannot be the cause of numerical diversity.
Pars 2 q. 4 a. 4 arg. 2
Praeterea, res non est completa in esse nisi secundum quod est ab aliis distincta. Sed locus advenit post esse completum, unde etiam motus ad locum est motus perfecti secundum substantiam, ut dicitur in VIII physicorum. Ergo non potest ex loco sumi aliqua causa distinctionis in corporibus locatis.	2. A thing is not complete in being unless it is distinct from others; but place comes after complete being; therefore motion to a place is the motion of that which is perfect according to substance, as is said in IX Physic. Therefore it is not possible that any cause of the distinction of bodies occupying space should be derived from place.
Pars 2 q. 4 a. 4 arg. 3
Praeterea, distinctio secundum numerum est invariabilis circa ipsa distincta. Sed a causa variabili non procedit effectus invariabilis. Ergo cum locus varietur circa locatum, non potest esse quod diversitas secundum locum sit causa diversitatis secundum numerum.	3. Numerical distinction is invariable as regards things that are distinct: but an invariable effect cannot proceed from a variable cause; therefore, since place varies in regard to that having location, it is not possible for diversity according to place to be the cause of numerical diversity.
Pars 2 q. 4 a. 4 arg. 4
Praeterea, remota causa removetur effectus. Sed aliquando a duobus corporibus removetur per miraculum distinctio secundum locum, ut prius dictum est, et tamen non removetur distinctio secundum numerum. Ergo distinctio secundum locum non est causa diversitatis secundum numerum.	4. If a cause is removed, so also is its effect: but it sometimes happens by a miracle that distinction of place is removed in respect to two bodies, as has been previously said; yet distinction according to number is not removed; therefore distinction according to place is not the cause of numerical diversity.
Pars 2 q. 4 a. 4 arg. 5
Praeterea, diversitas secundum numerum non solum invenitur in corporibus, sed etiam in substantiis incorporeis. Sed in eis diversitas locorum non potest esse causa diversitatis secundum numerum, cum incorporalia in loco non sint, ut dicit ipsemet in libro de hebdomadibus. Ergo diversitas secundum locum non potest poni causa diversitatis secundum numerum universaliter, ut ipse videtur dicere.	5. Diversity according to number is found not only in corporeal things, but even in incorporeal substances; but in these latter, diversity according to place cannot be the cause of numerical diversity, since incorporeal beings are not in a place, as Boethius himself says in his book, De hebdomadibus; therefore diversity according to place cannot be taken as the cause of diversity according to number, that is, as its cause by very reason of its nature, as he himself seems to say.
Pars 2 q. 4 a. 4 s. c. 1
Sed contra est quod ea, quae differunt secundum numerum, differunt accidentibus. Sed nullius accidentis diversitas ita inseparabiliter se habet ad diversitatem in numero, sicut diversitas loci. Ergo diversitas in loco maxime videtur facere ad diversitatem in numero.	On the contrary is the fact that things differing according to number differ by reason of their accidents: but the diversity of no other accident is so inseparablv related to diversity in number as is diversity of location; therefore diversity in place seems especially to influence diversity in number.
Pars 2 q. 4 a. 4 s. c. 2
Praeterea, diversitas locorum secundum speciem concomitatur diversitatem corporum secundum speciem, sicut patet in gravibus et levibus. Ergo et diversitas locorum secundum numerum indivisibiliter concomitatur diversitatem corporum secundum numerum, et sic idem quod prius.	Again, diversity of location according to the species of things is concomitant with the diversity of bodies according to their species, as is evident in the case of heavy and light bodies. Therefore also diversity of places according to number is indivisibly concomitant with diversity of bodies according to number, and so the conclusion is the same as before.
Pars 2 q. 4 a. 4 s. c. 3
Praeterea, sicut tempus est mensura motus, ita locus est mensura corporis. Sed motus dividitur numero secundum tempus, ut dicitur in V physicorum. Ergo et corpus dividitur numero secundum locum.	Again, as time is the measure of motion, so place is the measure of a body: but motion is divided numerically according to time, as is said in V Physic.; therefore also what is corporeal is divided numerically according to place.
Pars 2 q. 4 a. 4 co.
Responsio. Dicendum quod, sicut ex supra dictis patet, diversitas secundum numerum causatur ex divisione materiae sub dimensionibus exsistentis. Ipsa etiam materia, secundum quod sub dimensionibus exsistit, prohibet duo corpora esse in eodem loco, in quantum oportet duorum corporum distinctas secundum situm esse materias. Et sic patet quod ex eodem causatur diversitas secundum numerum, ex quo causatur necessitas diversitatis locorum in diversis corporibus. Et ideo ipsa diversitas locorum in se considerata est signum diversitatis secundum numerum, sicut et de aliis accidentibus praeter dimensiones primas interminatas supra dictum est. Sed si diversitas loci consideretur secundum suam causam, sic planum est quod diversitas loci est causa diversitatis secundum numerum. Et ideo Boethius quod varietas accidentium facit diversitatem secundum numerum omnibus aliis remotis in locorum diversitate hic inevitabiliter verificari constituit, quia scilicet nullum aliud accidentium, quae exterius apparent completa, est ita propinquum ad causam diversitatis secundum numerum sicut diversitas locorum.	Response. I answer: It must be said that, as is evident from previous statements, diversity according to number is caused by division of matter existing under dimensions. Now, matter itself, according as it exists under dimensions, prohibits two bodies from being in the same place, inasmuch as in each of the two bodies there must be matter distinct in its situation. And thus it is evident that diversity according to number is caused by the same thing as diversity of location in diverse bodies. Hence diversity of location, considered in itself, is a sign of the diversity which exists according to number—just as is also true of other accidents, except the first indeterminate dimensions which have been previously discussed. But if diversity of place is considered according to its own cause, then it is clear that diversity of place is the cause of diversity according to number. Therefore Boethius says it is variety of accidents that produces diversity according to number. But if all other accidents are removed, numerical diversity still remains verifiable by reason of the diversity of things in place; since, indeed, no other of those accidents which appear as extrinsic to a complete being is so closely related to the cause of diversity according to number as is diversity of location.
Pars 2 q. 4 a. 4 ad 1
Ad primum ergo dicendum et secundum et tertium quod rationes illae concludunt quod diversitas loci non est causa diversitatis individuorum secundum se. Sed per hoc non removetur, quin causa diversitatis locorum sit causa diversitatis secundum numerum.	Answers to objections. 1-3. To the first, second, and third objections it may be said: These reasons show conclusively that diversity of place is not the cause of diversity of individuals, secundum se., but this does not refute the fact that the cause of diversity of locations is the cause of diversity according to number.
Pars 2 q. 4 a. 4 ad 4
Ad quartum dicendum quod omnes effectus causarum secundarum magis dependent a Deo quam etiam ab ipsis causis secundis, et ideo etiam remotis causis secundis ipse miraculose potest producere effectus quos voluerit.	4. It may be answered: All effects of second causes depend more on God than on secondary causes, since either with these second causes, or without them, He is able to produce miraculously whatever effects He wills.
Pars 2 q. 4 a. 4 ad 5
Ad quintum dicendum quod in substantiis incorporeis diversitas secundum numerum sequitur diversitatem secundum speciem excepta anima rationali, quae sequitur divisionem materiae sibi dispositae. Hic autem Boethius loquitur de diversitate secundum numerum, ubi est eadem species.	5. It may be said: In corporeal substances diversity according to species follows diversity according to number, except in the case of the rational soul, which follows division of matter disposed for it. Here, however, Boethius is speaking of diversity according to number where the species is the same.
Pars 2 q. 4 a. 4 ad s. c. 1
Ad primum vero eorum quae in contrarium obiciuntur dicendum quod varietas aliorum accidentium praeter dimensiones interminatas non facit diversitatem in numero sicut causa, sed dicitur facere sicut signum demonstrans, et sic maxime diversitas loci facit, in quantum est propinquius signum.	Further answers. 1. In contradiction to the first objection, it may be said: Variety of accidents, because of indeterminate dimensions, does not produce diversity in number after the manner of a cause, but this variety is said to produce, a sign indicating numerical diversity; and diversity of place does this in a special way, inasmuch as it is the sign, most closely related to numerical diversity.
Pars 2 q. 4 a. 4 ad s. c. 2
Ad secundum dicendum quod diversitas locorum secundum speciem est signum diversitatis corporum secundum speciem, sed non causa.	2. To the second, it may be answered: Diversity of locations according to species is a sign of diversity of bodies according to their species, but not a cause of specific diversity.
Pars 2 q. 4 a. 4 ad s. c. 3
Ad tertium dicendum quod, cum divisio temporis causetur ex divisione motus, diversitas etiam temporis non est causa diversitatis motus, sed signum. Et similiter est de loco ad corpora.	3. To the third, it may be said: Although division of time is caused by division of motion, diversity, even diversity of time is not the cause of diversity of motion, but a sign of it; and the same is true of location in its relation to a body.

THE LOGIC MUSEUM Copyright (html and introduction only) (C) E.D.Buckner 2010.