Propositions 12

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);

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.

As the divine nature has absolutely infinite attributes (by Def. 6), 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.

Corollary 1: Hence it follows, that God is the efficient cause of all that can fall within the sphere of an infinite intellect.

Corollary 2: It also follows that God is a cause in himself, and not through an accident of his nature. Corollary 3= It follows, thirdly, that God is the absolutely first cause.

17. God acts solely by the laws of his own nature, and is not constrained by anyone.

Proof: We have just shown (in Prop. 16), that solely from the necessity of the divine nature or the laws of his nature, an infinite number of things absolutely follow in an infinite number of ways.

We proved (in Prop. 15), that without God nothing can be nor be conceived but that all things are in God.

For that reason:

• nothing can exist outside himself, whereby he can be conditioned or constrained to act.
• God acts solely by the laws of his own nature and is not constrained by anyone. Q.E.D.

Corollary 1 and 2: It follows that:

• there can be no cause which, either extrinsically or intrinsically, besides the perfection of his own nature, moves God to act
• God is the sole free cause.

For God alone exists by the sole necessity of his nature (by Prop. 11 and Prop. 14, Coroll. 1), and acts by the sole necessity of his own nature.

For that reason, God is (by Def. 7) the sole free cause. Q.E.D.

Note: 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 absurd.

Moreover, I will show below, without the aid of this proposition, that neither intellect nor will appertain to God’s nature. Many people think that they can show, that supreme intellect and free will do appertain to God’s nature. They say they know of nothing more perfect, which they can attribute to God, than that which is the highest perfection in ourselves.

They conceive God as actually supremely intelligent, but they 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 asset:

• 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 have shown clearly (by Prop. 16), 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 flow 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.

For that reason, God’s omnipotence has been displayed from all eternity.

It will remain in the same state of activity for all eternity.

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.

For that reason, 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.

(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 significance 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 (Prop. 16, Coroll. 1).

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.

For that reason, God’s intellect, 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.

Since God’s intellect is the sole cause of the essence and existence of things, 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).

Therefore, the two men may be entirely similar in essence, but must be different in existence.

Hence if the existence of one of them ceases, 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.

For that reason, 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 God’s intellect is the cause both of the essence and the existence of our intellect.

Therefore, God’s intellect. 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.

This reasoning is identical in the case of the will, as anyone can easily see. –>

18. God is the indwelling and not the transient cause of all things.

Proof: All things which are, are in God, and must be conceived through God (by Prop. 15), therefore (by Prop. 16, Coroll. 1) 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 Prop. 14), that is 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.

19. God, and all the attributes of God, are eternal.

Proof: God (by Def. 6) is substance, which (by Prop. 11) necessarily exists, that is (by Prop. 7) existence appertains to its nature, or (what is the same thing) follows from its definition; therefore, God is eternal (by Def. 8).

Further, by the attributes of God we must understand that which (by Def. 4) 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 Prop. vii.); therefore, eternity must appertain to each of the attributes, and thus all are eternal. Q.E.D.

Note.—This proposition is also obvious from the way in which (in Prop. 11) I demonstrated the existence of God.

From that proof, 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 God’s eternity in another way which I do not need to repeat here. –>

20. God’s existence and are one and the same.

Proof: God (by the last Prop.) and all his attributes are eternal, that is (by Def. 8) each of his attributes expresses existence.

Therefore, the same attributes of God which 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.

For that reason, God’s existence and essence are one and the same. Q.E.D.

Coroll. 1 & 2: It follows:

• That God’s existence, like his essence, is an eternal truth.
• That God, and all of God’s attributes, 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. –>

21. All things which follow from the absolute nature of any attribute of God must always exist and be infinite, or, in other words, are eternal and infinite through the said attribute.

Proof: Conceive, if it be possible (supposing the proposition to be denied), that something in some of God’s attributes can follow from the absolute nature of the said attribute, and that at the same time it is finite, and has a conditioned existence or duration.

For instance, the idea of God expressed in the attribute thought.

Thought, as an attribute of God, is necessarily (by Prop. 11) in its nature infinite.

But, in so far as it possesses the idea of God, it is supposed finite.

It cannot, however, be conceived as finite, unless it be limited by thought (by Def. 2).

But it is not limited by thought itself, in so far as it has constituted the idea of God (for so far it is supposed to be finite);

Therefore, it is limited by thought, in so far as it has not constituted the idea of God, which nevertheless (by Prop. 11) must necessarily exist.

Therefore, we have now granted thought not constituting the idea of God.

Accordingly, the idea of God does not naturally follow from its nature in so far as it is absolute thought (for it is conceived as constituting, and also as not constituting, the idea of God), which is against our hypothesis.

For that reason, if the idea of God expressed in the attribute thought, or, anything else in any attribute of God (for we may take any example, as the proof is of universal application) follows from the necessity of the absolute nature of the said attribute, the said thing must necessarily be infinite, which was our first point.

Furthermore, a thing which thus follows from the necessity of the nature of any attribute cannot have a limited duration.

For if it can, suppose a thing, which follows from the necessity of the nature of some attribute, to exist in some attribute of God, for instance, the idea of God expressed in the attribute thought, and let it be supposed at some time not to have existed, or to be about not to exist.

Now thought is an attribute of God.

It must necessarily exist unchanged (by Prop. 11, and Prop. 20, Coroll. 2). Beyond the limits of the duration of the idea of God (supposing the latter at some time not to have existed, or not to be going to exist), thought would perforce have existed without the idea of God.

This is contrary to our hypothesis, for we supposed that, thought being given, the idea of God necessarily flowed therefrom.

Therefore, the idea of God expressed in thought, or anything which necessarily follows from the absolute nature of some attribute of God, cannot have a limited duration, but through the said attribute is eternal, which is our second point.

Bear in mind that the same proposition may be affirmed of anything, which in any attribute necessarily follows from God’s absolute nature. –>