|E1: PROP. 12. No attribute of substance can be conceived from which it would follow that substance can be divided.|
|Proof.--The parts into which
substance as thus conceived would be
divided, either will retain the nature of substance, or they will not. If
the former, then (by E1P8) each part will
(by E1P6) self-caused, and
(by E1P5) will perforce consist of a
so that, in that case, several substances could be
formed out of one substance,
which (by E1P6)
is absurd. Moreover, the
parts (by E1P2) would have nothing in common
with their whole, and the
whole (by E1D4 and E1P10)
could both exist and be conceived without
its parts, which everyone will admit to be absurd.
If we adopt the second alternative namely, that the parts will not retain the nature of substance then, if the whole substance were divided into equal parts, it would lose the nature of substance, and would cease to exist, which (by E1P7) is absurd.
|Referenced in: E1P13, - E1P15N|
|E1: PROP. 13. Substance absolutely infinite is indivisible.|
|Proof.--If it could be divided, the parts into which it was divided would either retain the nature of absolutely infinite substance, or they would not. If the former, we should have several substances of the same nature, which (by E1P5) is absurd. If the latter, then (by E1P7) [E1P12] substance absolutely infinite could cease to exist, which (by E1P11) is also absurd.|
|E1: PROP. 13, Corollary.--It follows, that no substance, and consequently no extended substance, in so far as it is substance, is divisible.|
|Referenced in: E1P15N|
|E1: PROP. 13, Corollary, Note. --The indivisibility of substance may be more easily understood as follows. The nature of substance can only be conceived as infinite, and by a part of substance, nothing else can be understood than finite substance, which (by E1P8) involves a manifest contradiction.|
|E1: PROP. 14. Besides God no substance can be granted or conceived.|
|Proof.--As God is a being absolutely infinite, of whom no attribute that expresses the essence of substance can be denied (by E1D6), and he necessarily exists (by E1P11); if any substance besides God were granted, it would have to be explained by some attribute of God, and thus two substances with the same attribute would exist, which (by E1P5) is absurd; therefore, besides God no substance can be granted, or, consequently, be conceived. If it could be conceived, it would necessarily have to be conceived as existent; but this (by the first part of this proof) is absurd. Therefore, besides God no substance can be granted or conceived. Q.E.D.|
|Referenced in: E1P15, - E1P15N,- E1P18|
|E1: PROP. 14, Corollary 1.--Clearly, therefore: 1. God is one, that is (by E1D6) only one substance can be granted in the universe, and that substance is absolutely infinite, as we have already indicated (in the note to E1P10N).|
|Referenced in: E1P17C2,- E1P24C,- E1P29N,- E1P30,- E1P33,- E2P4|
|E1: PROP. 14, Corollary 2.--It follows: 2. That extension and thought are either attributes of God or (by E1A1) accidents (affectiones) of the attributes of God.|
|E1: PROP. 15. Whatsoever is, is in God, and without God nothing can be, or be conceived.|
|Proof.--Besides God, no substance is granted or can be conceived (by E1P14), that is (by E1D3) nothing which is in itself and is conceived through itself. But modes (by E1D5) can neither be, nor be conceived without substance; wherefore they can only be in the divine nature, and can only through it be conceived. But substances and modes form the sum total of existence (by E1A1), therefore, without God nothing can be, or be conceived. Q.E.D.|
|Referenced in: E1P17,- E1P18,- E1P23,- E1P25,- E1P25C,- E1P28N,- E1P29,- E1P30,- E1P31,- E2P3,- E2P10C,- E2P33,- E2P36,- E2P45,- E4P28,- E4P37,- E5P14,- E5P36CN|
| E1: PROP. 15, Note.
--[A.] 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
But meanwhile by the 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 (E1P6C, and E1P8N2), that no substance can be produced or created by anything other than itself. Further, I showed (in E1P14), 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:--
[B.] 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.
[C.] 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, in so far as it is divisible, is passive. It follows, therefore, that extended substance does not appertain to the essence of God.
[D.] 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 (E1P12, and E1P13C) 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 E1P12). 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 centre, from which all lines drawn to the circumference are equal. For, taking extended substance, which can only be conceived as infinite, one, and indivisible (E1P8, E1P5, E1P12) 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 also that the parts cannot be really distinguished, and that extended substance in so far as it is substance cannot be divided.
[E.] If anyone asks me the further question, Why are we naturally 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.
[F.] 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 E1P14) 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.
|Referenced in: E2P13L1|
|E1: PROP. 16. From the necessity of the divine nature must follow an infinite number of things in infinite ways--that is, all things which can fall within the sphere of infinite intellect.|
|Proof.--This proposition will be clear to everyone, who remembers that from the given definition of any thing the intellect infers several properties, which really necessarily follow therefrom (that is, from the actual essence of the thing defined); and it infers more properties in proportion as the definition of the thing expresses more reality, that is, in proportion as the essence of the thing defined involves more reality. Now, as the divine nature has absolutely infinite attributes (by E1D6), of which each expresses infinite essence after its kind, it follows that from the necessity of its nature an infinite number of things (that is, everything which can fall within the sphere of an infinite intellect) must necessarily follow. Q.E.D.|
|Referenced in: E1P17,- E1P17N,- E1P25N,- E1P26,- E1P29,- E1P33,- E1P34,- E1P36,- E1APND,- E2PREF,- E2P3,- E2P3N,- E2P44C2,- E2P45N,- E4PREF,- E4P4,- E5P22|
|E1: PROP. 16, Corollary 1.--Hence it follows, that God is the efficient cause of all that can fall within the sphere of an infinite intellect.|
|Referenced in: E1P17N,- E1P18,- E1P34|
|E1: PROP. 16, Corollary 2.--It also follows that God is a cause in himself, and not through an accident of his nature.|
|Referenced in: E1P34|
|E1: PROP. 16, Corollary 3.--It follows, thirdly, that God is the absolutely first cause.|
|E1: PROP. 17. God acts solely by the laws of his own nature, and is not constrained by anyone.|
|Proof.--We have just shown (in E1P16), that solely from the necessity of the divine nature, or, what is the same thing, solely from the laws of his nature, an infinite number of things absolutely follow in an infinite number of ways; and we proved (in E1P15), that without God nothing can be nor be conceived; but that all things are in God. Wherefore nothing can exist outside himself, whereby he can be conditioned or constrained to act. Wherefore God acts solely by the laws of his own nature, and is not constrained by anyone. Q.E.D.|
|Referenced in: E1P17C2|
|E1: PROP. 17, Corollary 1.--It follows: 1. That there can be no cause which, either extrinsically or intrinsically, besides the perfection of his own nature, moves God to act.|
|E1: PROP. 17, Corollary 2.--It follows: 2. That God is the sole free cause.|
|For God alone exists by the sole necessity of his nature (by E1P11 and E1P14C1), and acts by the sole necessity of his nature [E1P17], wherefore God is (by E1D7) the sole free cause. Q.E.D.|
|Referenced in: E1P29N,- E2P48|
| E1: PROP. 17, Note.
--[A.] Others think that God is a free cause, because he can, as they think,
bring it about, that those things which we have said follow from his
nature--that is, which are in his power, should not come to pass, or
should not be produced by him. But this is the same as if they said, that
God could bring it about, that it should follow from the nature of a
triangle, that its three interior angles should not be equal to two right
angles; or that from a given cause no effect should follow, which is
Moreover, I will show below, without the aid of this proposition, that neither intellect nor will appertain to God's nature. I know that there are many who think that they can show, that supreme intellect and free will do appertain to God's nature; for they say they know of nothing more perfect, which they can attribute to God, than that which is the highest perfection in ourselves.
Further, although they conceive God as actually supremely intelligent, they yet do not believe, that he can bring into existence everything which he actually understands, for they think that they would thus destroy God's power. If, they contend, God had created everything which is in his intellect, he would not be able to create anything more, and this, they think, would clash with God's omnipotence; therefore, they prefer to assert that God is indifferent to all things, and that he creates nothing except that which he has decided, by some absolute exercise of will, to create.
However, I think I have shown sufficiently clearly (by E1P16), that from God's supreme power, or infinite nature, an infinite number of things--that is, all things have necessarily flowed forth in an infinite number of ways, or always follow from the same necessity; in the same way as from the nature of a triangle it follows from eternity and for eternity, that its three interior angles are equal to two right angles. Wherefore the omnipotence of God has been displayed from all eternity, and will for all eternity remain in the same state of activity. This manner of treating the question attributes to God an omnipotence, in my opinion, far more perfect.
For, otherwise, we are compelled to confess that God understands an infinite number of creatable things, which he will never be able to create, for, if he created all that he understands, he would, according to this showing, exhaust his omnipotence, and render himself imperfect. Wherefore, in order to establish that God is perfect, we should be reduced to establishing at the same time, that he cannot bring to pass everything over which his power extends; this seems to be a hypothesis most absurd, and most repugnant to God's omnipotence.
[B.]Further (to say a word here concerning the intellect and the will which we attribute to God), if intellect and will appertain to the eternal essence of God, we must take these words in some significations quite different from those they usually bear. For intellect and will, which should constitute the essence of God, would perforce be as far apart as the poles from the human intellect and will, in fact, would have nothing in common with them but the name; there would be about as much correspondence between the two as there is between the Dog, the heavenly constellation, and a dog, an animal that barks. This I will prove as follows.
If intellect belongs to the divine nature, it cannot be in nature, as ours is generally thought to be, posterior to, or simultaneous with the things understood, inasmuch as God is prior to all things by reason of his causality (E1P16C1). On the contrary, the truth and formal essence of things is as it is, because it exists by representation as such in the intellect of God.
Wherefore the intellect of God, in so far as it is conceived to constitute God's essence, is, in reality, the cause of things, both of their essence and of their existence. This seems to have been recognized by those who have asserted, that God's intellect, God's will, and God's power, are one and the same. As, therefore, God's intellect is the sole cause of things, namely, both of their essence and existence, it must necessarily differ from them in respect to its essence, and in respect to its existence. For a cause differs from a thing it causes, precisely in the quality which the latter gains from the former. For example, a man is the cause of another man's existence, but not of his essence (for the latter is an eternal truth), and, therefore, the two men may be entirely similar in essence, but must be different in existence; and hence if the existence of one of them cease, the existence of the other will not necessarily cease also; but if the essence of one could be destroyed, and be made false, the essence of the other would be destroyed also.
Wherefore, a thing which is the cause both of the essence and of the existence of a given effect, must differ from such effect both in respect to its essence, and also in respect to its existence. Now the intellect of God is the cause of both the essence and the existence of our intellect; therefore, the intellect of God in so far as it is conceived to constitute the divine essence, differs from our intellect both in respect to essence and in respect to existence, nor can it in anywise agree therewith save in name, as we said before. The reasoning would be identical in the case of the will, as anyone can easily see.
|Referenced in: E1P33N2|
|E1: PROP. 18. God is the indwelling [immanens] and not the transient cause of all things.|
|Proof.--All things which are, are in God, and must be conceived through God (by E1P15), therefore (by E1P16C1) God is the cause of those things which are in him. This is our first point. Further, besides God there can be no substance (by E1P14), that is [E1D3] nothing in itself external to God. This is our second point. God, therefore, is the indwelling and not the transient cause of all things. Q.E.D.|
|E1: PROP. 19. God, and all the attributes of God, are eternal.|
|Proof.--God (by E1D6) is substance, which (by E1P11) necessarily exists, that is (by E1P7) existence appertains to its nature, or (what is the same thing) follows from its definition; therefore, God is eternal (by E1D8). Further, by the attributes of God we must understand that which (by E1D4) expresses the essence of the divine substance --in other words, that which appertains to substance: that, I say, should be involved in the attributes of substance. Now eternity appertains to the nature of substance (as I have already shown in E1P7); therefore, eternity must appertain to each of the attributes, and thus all are eternal. Q.E.D.|
|Referenced in: E1P20, - E1P23|
|E1: PROP. 19, Note. --This proposition is also evident from the manner in which (in E1P11) I demonstrated the existence of God; it is evident, I repeat, from that proof, that the existence of God, like his essence, is an eternal truth. Further (in Prop. 19. of my " Principles of the Cartesian Philosophy"), I have proved the eternity of God, in another manner, which I need not here repeat.|
|E1: PROP. 20. The existence of God and his essence are one and the same.|
|Proof.--God (by the last Prop E1P19) and all his attributes are eternal, that is (by E1D8) each of his attributes expresses existence. Therefore the same attributes of God which [E1D4] explain his eternal essence, explain at the same time his eternal existence --in other words, that which constitutes God's essence constitutes at the same time his existence. Wherefore God's existence and God's essence are one and the same. Q.E.D.|
|E1: PROP. 20, Corollary 1.--Hence it follows that God's existence, like His essence, is an eternal truth.|
|E1: PROP. 20, Corollary 2.--Secondly, it follows that God, and all the attributes of God, are unchangeable.|
|For if they could be changed in respect to existence, they must also be able to be changed in respect to essence-- that is, obviously, be changed from true to false, which is absurd.|
|Referenced in: E1P21,- E5P17|