E1P15S
Scholium — Part I
Latin
Sunt qui Deum instar hominis corpore et mente constantem atque passionibus obnoxium fingunt sed quam longe hi a vera Dei cognitione aberrent, satis ex jam demonstratis constat. Sed hos mitto : nam omnes qui naturam divinam aliquo modo contemplati sunt, Deum esse corporeum negant. Quod etiam optime probant ex eo quod per corpus intelligimus quamcunque quantitatem longam, latam et profundam, certa aliqua figura terminatam, quo nihil absurdius de Deo, ente scilicet absolute infinito, dici potest. Attamen interim aliis rationibus quibus hoc idem demonstrare conantur, clare ostendunt se substantiam ipsam corpoream sive extensam a natura divina omnino removere atque ipsam a Deo creatam statuunt. Ex qua autem divina potentia creari potuerit, prorsus ignorant; quod clare ostendit illos id quod ipsimet dicunt, non intelligere. Ego saltem satis clare meo quidem judicio demonstravi (vide corollarium propositionis 6 et scholium II propositionis 8) nullam substantiam ab alio produci vel creari. Porro propositione 14 ostendimus præter Deum nullam dari neque concipi posse substantiam atque hinc conclusimus substantiam extensam unum ex infinitis Dei attributis esse. Verum ad pleniorem explicationem adversariorum argumenta refutabo quæ omnia huc redeunt primo quod substantia corporea quatenus substantia constat ut putant partibus et ideo eandem infinitam posse esse et consequenter ad Deum pertinere posse negant. Atque hoc multis exemplis explicant ex quibus unum aut alterum afferam. Si substantia corporea aiunt est infinita, concipiatur in duas partes dividi; erit unaquæque pars vel finita vel infinita. Si illud, componitur ergo infinitum ex duabus partibus finitis, quod est absurdum. Si hoc, datur ergo infinitum duplo majus alio infinito, quod etiam est absurdum. Porro si quantitas infinita mensuratur partibus pedes æquantibus, infinitis talibus partibus constare debebit ut et si partibus mensuretur digitos æquantibus ac propterea unus numerus infinitus erit duodecies major alio infinito. Denique si ex uno puncto infinitæ cujusdam quantitatis concipiatur duas lineas ut AB, AC, certa ac determinata in initio distantia in infinitum protendi, certum est distantiam inter B et C continuo augeri et tandem ex determinata indeterminabilem fore. Cum igitur hæc absurda sequantur ut putant ex eo quod quantitas infinita supponitur, inde concludunt substantiam corpoream debere esse finitam et consequenter ad Dei essentiam non pertinere. Secundum argumentum petitur etiam a summa Dei perfectione. Deus enim inquiunt cum sit ens summe perfectum, pati non potest : atqui substantia corporea quandoquidem divisibilis est, pati potest; sequitur ergo ipsam ad Dei essentiam non pertinere. Hæc sunt quæ apud scriptores invenio argumenta quibus ostendere conantur substantiam corpoream divina natura indignam esse nec ad eandem posse pertinere. Verumenimvero si quis recte attendat, me ad hæc jam respondisse comperiet quandoquidem hæc argumenta in eo tantum fundantur quod substantiam corpoream ex partibus componi supponunt, quod jam (per propositionem 12 cum corollario propositionis 13) absurdum esse ostendi. Deinde si quis rem recte perpendere velit, videbit omnia illa absurda (siquidem omnia absurda sunt, de quo non jam disputo) ex quibus concludere volunt substantiam extensam finitam esse, minime ex eo sequi quod quantitas infinita supponatur sed quod quantitatem infinitam mensurabilem et ex partibus finitis conflari supponunt; quare ex absurdis quæ inde sequuntur, nihil aliud concludere possunt quam quod quantitas infinita non sit mensurabilis et quod ex partibus finitis conflari non possit. Atque hoc idem est quod nos supra (propositione 12 etc.) jam demonstravimus. Quare telum quod in nos intendunt, in se ipsos revera conjiciunt. Si igitur ipsi ex suo hoc absurdo concludere tamen volunt substantiam extensam debere esse finitam, nihil aliud hercle faciunt quam si quis ex eo quod finxit circulum quadrati proprietates habere, concludit circulum non habere centrum ex quo omnes ad circumferentiam ductæ lineæ sunt æquales. Nam substantiam corpoream quæ non nisi infinita, non nisi unica et non nisi indivisibilis potest concipi (vide propositiones 8, 5 et 12) eam ipsi ad concludendum eandem esse finitam, ex partibus finitis conflari et multiplicem esse et divisibilem concipiunt. Sic etiam alii postquam fingunt lineam ex punctis componi, multa sciunt invenire argumenta quibus ostendant lineam non posse in infinitum dividi. Et profecto non minus absurdum est ponere quod substantia corporea ex corporibus sive partibus componatur quam quod corpus ex superficiebus, superficies ex lineis, lineæ denique ex punctis componantur. Atque hoc omnes qui claram rationem infallibilem esse sciunt, fateri debent et imprimis ii qui negant dari vacuum. Nam si substantia corporea ita posset dividi ut ejus partes realiter distinctæ essent, cur ergo una pars non posset annihilari manentibus reliquis ut ante inter se connexis? et cur omnes ita aptari debent ne detur vacuum? Sane rerum quæ realiter ab invicem distinctæ sunt, una sine alia esse et in suo statu manere potest. Cum igitur vacuum in natura non detur (de quo alias) sed omnes partes ita concurrere debent ne detur vacuum, sequitur hinc etiam easdem non posse realiter distingui hoc est substantiam corpoream quatenus substantia est, non posse dividi. Si quis tamen jam quærat cur nos ex natura ita propensi simus ad dividendam quantitatem? ei respondeo quod quantitas duobus modis a nobis concipitur, abstracte scilicet sive superficialiter prout nempe ipsam imaginamur vel ut substantia, quod a solo intellectu fit. Si itaque ad quantitatem attendimus prout in imaginatione est, quod sæpe et facilius a nobis fit, reperietur finita, divisibilis et partibus conflata; si autem ad ipsam prout in intellectu est, attendimus et eam quatenus substantia est, concipimus, quod difficillime fit, tum ut jam satis demonstravimus, infinita, unica et indivisibilis reperietur. Quod omnibus qui inter imaginationem et intellectum distinguere sciverint, satis manifestum erit, præcipue si ad hoc etiam attendatur quod materia ubique eadem est nec partes in eadem distinguuntur nisi quatenus materiam diversimode affectam esse concipimus, unde ejus partes modaliter tantum distinguuntur, non autem realiter. Exempli gratia aquam quatenus aqua est, dividi concipimus ejusque partes ab invicem separari; at non quatenus substantia est corporea; eatenus enim neque separatur neque dividitur. Porro aqua quatenus aqua generatur et corrumpitur; at quatenus substantia nec generatur nec corrumpitur. Atque his me ad secundum argumentum etiam respondisse puto quandoquidem id in eo etiam fundatur quod materia quatenus substantia divisibilis sit et partibus confletur. Et quamvis hoc non esset, nescio cur divina natura indigna esset quandoquidem (per propositionem 14) extra Deum nulla substantia dari potest a qua ipsa pateretur. Omnia inquam in Deo sunt et omnia quæ fiunt per solas leges infinitæ Dei naturæ fiunt et ex necessitate ejus essentiæ (ut mox ostendam) sequuntur; quare nulla ratione dici potest Deum ab alio pati aut substantiam extensam divina natura indignam esse tametsi divisibilis supponatur dummodo æterna et infinita concedatur. Sed de his impræsentiarum satis.
English (Elwes 1883)
Some assert that God, like a man, consists of body and mind, and is susceptible of passions. How far such persons have strayed from the truth is sufficiently evident from what has been said. But these I pass over. For all who have in anywise reflected on the divine nature deny that God has a body. Of this they find excellent proof in the fact that we understand by body a definite quantity, so long, so broad, so deep, bounded by a certain shape, and it is the height of absurdity to predicate such a thing of God, a being absolutely infinite. But meanwhile by other reasons with which they try to prove their point, they show that they think corporeal or extended substance wholly apart from the divine nature, and say it was created by God. Wherefrom the divine nature can have been created, they are wholly ignorant; thus they clearly show, that they do not know the meaning of their own words. I myself have proved sufficiently clearly, at any rate in my own judgment (Coroll. Prop. vi, and note 2, Prop. viii.), that no substance can be produced or created by anything other than itself. Further, I showed (in Prop. xiv.), that besides God no substance can be granted or conceived. Hence we drew the conclusion that extended substance is one of the infinite attributes of God. However, in order to explain more fully, I will refute the arguments of my adversaries, which all start from the following points:----
Extended substance, in so far as it is substance, consists, as they think, in parts, wherefore they deny that it can be infinite, or consequently, that it can appertain to God. This they illustrate with many examples, of which I will take one or two. If extended substance, they say, is infinite, let it be conceived to be divided into two parts; each part will then be either finite or infinite. If the former, then infinite substance is composed of two finite parts, which is absurd. If the latter, then one infinite will be twice as large as another infinite, which is also absurd.
Further, if an infinite line be measured out in foot lengths, it will consist of an infinite number of such parts; it would equally consist of an infinite number of parts, if each part measured only an inch: therefore, one infinity would be twelve times as great as the other.
Lastly, if from a single point there be conceived to be drawn two diverging lines which at first are at a definite distance apart, but are produced to infinity, it is certain that the distance between the two lines will be continually increased, until at length it changes from definite to indefinable. As these absurdities follow, it is said, from considering quantity as infinite, the conclusion is drawn, that extended substance must necessarily be finite, and, consequently, cannot appertain to the nature of God.
The second argument is also drawn from God's supreme perfection. God, it is said, inasmuch as he is a supremely perfect being, cannot be passive; but extended substance, insofar as it is divisible, is passive. It follows, therefore, that extended substance does not appertain to the essence of God.
Such are the arguments I find on the subject in writers, who by them try to prove that extended substance is unworthy of the divine nature, and cannot possibly appertain thereto. However, I think an attentive reader will see that I have already answered their propositions; for all their arguments are founded on the hypothesis that extended substance is composed of parts, and such a hypothesis I have shown (Prop. xii., and Coroll. Prop. xiii.) to be absurd. Moreover, anyone who reflects will see that all these absurdities (if absurdities they be, which I am not now discussing), from which it is sought to extract the conclusion that extended substance is finite, do not at all follow from the notion of an infinite quantity, but merely from the notion that an infinite quantity is measurable, and composed of finite parts therefore, the only fair conclusion to be drawn is that: infinite quantity is not measurable, and cannot be composed of finite parts. This is exactly what we have already proved (in Prop. xii.). Wherefore the weapon which they aimed at us has in reality recoiled upon themselves. If, from this absurdity of theirs, they persist in drawing the conclusion that extended substance must be finite, they will in good sooth be acting like a man who asserts that circles have the properties of squares, and, finding himself thereby landed in absurdities, proceeds to deny that circles have any center, from which all lines drawn to the circumference are equal. For, taking extended substance, which can only be conceived as infinite, one, and indivisible (Props. viii., v., xii.) they assert, in order to prove that it is finite, that it is composed of finite parts, and that it can be multiplied and divided.
So, also, others, after asserting that a line is composed of points, can produce many arguments to prove that a line cannot be infinitely divided. Assuredly it is not less absurd to assert that extended substance is made up of bodies or parts, than it would be to assert that a solid is made up of surfaces, a surface of lines, and a line of points. This must be admitted by all who know clear reason to be infallible, and most of all by those who deny the possibility of a vacuum. For if extended substance could be so divided that its parts were really separate, why should not one part admit of being destroyed, the others remaining joined together as before? And why should all be so fitted into one another as to leave no vacuum? Surely in the case of things, which are really distinct one from the other, one can exist without the other, and can remain in its original condition. As, then, there does not exist a vacuum in nature (of which anon), but all parts are bound to come together to prevent it, it follows from this that the parts cannot really be distinguished, and that extended substance in so far as it is substance cannot be divided.
If anyone asks me the further question, Why are we naturally so prone to divide quantity? I answer, that quantity is conceived by us in two ways; in the abstract and superficially, as we imagine it; or as substance, as we conceive it solely by the intellect. If, then, we regard quantity as it is represented in our imagination, which we often and more easily do, we shall find that it is finite, divisible, and compounded of parts; but if we regard it as it is represented in our intellect, and conceive it as substance, which it is very difficult to do, we shall then, as I have sufficiently proved, find that it is infinite, one, and indivisible. This will be plain enough to all who make a distinction between the intellect and the imagination, especially if it be remembered, that matter is everywhere the same, that its parts are not distinguishable, except in so far as we conceive matter as diversely modified, whence its parts are distinguished, not really, but modally. For instance, water, in so far as it is water, we conceive to be divided, and its parts to be separated one from the other; but not in so far as it is extended substance; from this point of view it is neither separated nor divisible. Further, water, in so far as it is water, is produced and corrupted; but, in so far as it is substance, it is neither produced nor corrupted.
I think I have now answered the second argument; it is, in fact, founded on the same assumption as the first--namely, that matter, in so far as it is substance, is divisible, and composed of parts. Even if it were so, I do not know why it should be considered unworthy of the divine nature, inasmuch as besides God (by Prop. xiv.) no substance can be granted, wherefrom it could receive its modifications. All things, I repeat, are in God, and all things which come to pass, come to pass solely through the laws of the infinite nature of God, and follow (as I will shortly show) from the necessity of his essence. Wherefore it can in nowise be said, that God is passive in respect to anything other than himself, or that extended substance is unworthy of the Divine nature, even if it be supposed divisible, so long as it is granted to be infinite and eternal. But enough of this for the present.
Modern English
Some imagine that God, like a human being, consists of body and mind and is subject to passions. How far they have strayed from a true knowledge of God is clear enough from what has been demonstrated, so I set them aside. Everyone who has reflected on the divine nature at all denies that God is corporeal, and they prove it well: by body we understand any quantity with length, breadth, and depth, bounded by some definite shape — and nothing more absurd could be said of God, an absolutely infinite being.
At the same time, the further reasons they give for the same conclusion clearly show that they remove corporeal, that is, extended, substance from the divine nature altogether, and hold that it was created by God. Out of what divine power it could have been created, they have no idea, which clearly shows that they do not understand what they themselves are saying. I have shown clearly enough, at least in my own judgment (see (E1P6C) and (E1P8S2)), that no substance can be produced or created by another. And by (E1P14) I showed that no substance can exist or be conceived besides God, and from this concluded that extended substance is one of God's infinite attributes.
For a fuller account I will now refute my opponents' arguments. They all come down to this. First: corporeal substance, taken as substance, consists, they suppose, of parts; so they deny it can be infinite, and consequently deny it can belong to God. They illustrate this with many examples; I will mention one or two. If corporeal substance is infinite, they say, suppose it divided into two parts: each part will be either finite or infinite. If finite, an infinite is composed of two finite parts, which is absurd. If infinite, then one infinite is twice as great as another infinite, which is also absurd. Again: if an infinite quantity is measured in parts each a foot long, it must consist of infinitely many such parts; and if measured in parts each an inch long, also infinitely many, so one infinite number would be twelve times greater than another. Finally: suppose, from a single point within some infinite quantity, two lines AB and AC are drawn, starting at a definite and determinate distance apart, and extended to infinity. It is certain that the distance between B and C will continually increase and at last become indeterminable instead of determinate. From these absurdities, said to follow from supposing quantity to be infinite, they conclude that corporeal substance must be finite, and therefore does not belong to God's essence.
Their second argument is taken from God's supreme perfection. God, they say, since he is a supremely perfect being, cannot be acted on; but corporeal substance, since it is divisible, can be acted on; so it does not belong to God's essence.
These are the arguments I find in the writers on this subject, by which they try to show that corporeal substance is unworthy of the divine nature and cannot belong to it. But anyone who looks closely will find I have already answered them, since these arguments all rest on supposing corporeal substance to be composed of parts, which I have already shown to be absurd (E1P12) and (E1P13C). Anyone who weighs the matter rightly will see that all those absurdities (if they are absurdities, which I am not now disputing), from which they want to conclude that extended substance is finite, do not follow at all from supposing quantity to be infinite. They follow from supposing infinite quantity to be measurable and to be put together from finite parts. So from the absurdities that follow they can only conclude that infinite quantity is not measurable and cannot be put together from finite parts, exactly what we proved earlier (E1P12). The weapon they aimed at us, they have in fact thrown at themselves.
If from this absurdity of theirs they still want to conclude that extended substance must be finite, they are doing nothing more than someone who, having imagined a circle with the properties of a square, then concludes that the circle has no center from which all lines drawn to the circumference are equal. For corporeal substance, which can only be conceived as infinite, only as unique, and only as indivisible (E1P8), (E1P5), and (E1P12), they conceive as finite, composed of finite parts, multiple, and divisible, so they can conclude it is finite. Just so, others, after imagining a line composed of points, find no shortage of arguments to show that a line cannot be infinitely divided. And it is no less absurd to claim that corporeal substance is composed of bodies or parts than that a solid is composed of surfaces, surfaces of lines, and lines of points.
Everyone who knows clear reason to be infallible must concede this, and especially those who deny that there is a vacuum. For if corporeal substance could be divided in such a way that its parts were really distinct, why could one part not be annihilated while the rest remained connected as before? And why must they all be so fitted to one another that no vacuum is left? Things really distinct from one another can certainly exist one without the other, and remain in their own state. Since, then, there is no vacuum in nature (about which elsewhere), and all parts must come together in such a way that no vacuum is left, it follows that they cannot really be distinguished, that is, corporeal substance, taken as substance, cannot be divided.
If anyone now asks why we are by nature so inclined to divide quantity, my answer is that quantity is conceived by us in two ways: abstractly or superficially, as we imagine it, or as substance, which only the intellect does. So if we attend to quantity as it is in the imagination, which is what we usually and more easily do, it will be found finite, divisible, and made of parts; but if we attend to it as it is in the intellect, and conceive it as substance, which is very difficult, then, as I have already shown well enough, it will be found infinite, unique, and indivisible. This will be clear enough to anyone who can distinguish between intellect and imagination, especially if it is also kept in mind that matter is everywhere the same, and that parts are distinguished in it only insofar as we conceive matter as differently affected, so that its parts are distinguished only modally, not really. For example, we conceive that water, as water, is divided, and that its parts are separated from one another; but not as it is corporeal substance; in that respect it is neither separated nor divided. Again, water as water is generated and destroyed; but as substance, it is neither generated nor destroyed.
With this, I think, I have answered the second argument as well, since it too rests on supposing matter, as substance, to be divisible and made of parts. And even if it were not so, I do not see why it would be unworthy of the divine nature, since outside God no substance exists (E1P14) from which God could be acted on. All things, I say, are in God, and all things that happen, happen by the laws alone of God's infinite nature and follow from the necessity of his essence (as I will shortly show). So there is no way of saying that God is acted on by anything else, or that extended substance is unworthy of the divine nature, even if it is supposed divisible, provided it is granted to be eternal and infinite. But enough of this for now.