Propositions 1-6

Proposition 1: Thought is an attribute of God, or God is a thinking thing.

Proof: Particular thoughts are modes which express God’s nature, in a certain conditioned manner (Pt. 1, Prop. 25, Coroll.).

God therefore possesses the attribute (Pt. 1, Def. 5) of which the concept is involved in all particular thoughts, which latter are conceived thereby.

Therefore, thought is one of God’s infinite attributes, which express God’s eternal and infinite essence (Pt. 1, Def. 6).

In other words, God is a thinking thing. Q.E.D.

Note: This proposition is also evident from the fact, that we are able to conceive an infinite thinking being.

For, in proportion as a thinking being is conceived as thinking more thoughts, so is it conceived as containing more reality or perfection.

Therefore a being, which can think an infinite number of things in an infinite number of ways, is necessarily infinite, in respect of thinking.

As, therefore, from the consideration of thought alone, we conceive an infinite being, thought is necessarily (Pt. 1, Def. 4 and 6) one of the infinite attributes of God.

Proposition 2: Extension is an attribute of God, or God is an extended thing*.

Proof: The proof of this proposition is similar to the proof of the last.

Proposition 3: In God, there is necessarily the idea of his essence and also of all things which necessarily follow from his essence.

Proof: God (by the Prop. 1 of this Part) can think an infinite number of things in infinite ways.

• He (what is the same thing, by Prop. 16, Part 1) can form the idea of his essence, and of all things which necessarily follow from it.
• All that is in God’s power necessarily is (Pt. 1, Prop. 35).

Therefore, such an idea as we are considering necessarily is, and in God alone. Q.E.D. (Part 1, Prop. 15)

Note: People understand by the power of God, the free will of God and the right over all things that exist, which latter are accordingly generally considered as contingent.

It is said that God has the power to destroy all things and to reduce them to nothing.

God’s power is very often likened to the power of kings. But we have refuted this doctrine (Pt. 1, Prop. 32, Corolls. 1 and 2).

Part 1, Prop. 16 has shown that God acts by the same necessity, as that by which he understands himself.

In other words, as it follows from the necessity of the divine nature, that God understands himself, so also does it follow by the same necessity, that God performs infinite acts in infinite ways.

Part 1, Prop. 34 showed that God’s power is identical with God’s essence in action.

Therefore, it is as impossible for us to conceive God as not acting, as to conceive him as non—existent.

If we pursue this further, it follows that the power we commonly attribute to God (where people often show that God as a man) is a human power, and actually involves a negation of power.

I beg the reader not to confound God’s power with the human power and right of kings.

Proposition 4: The idea of God, from which an infinite number of things follow in infinite ways, can only be one.

Proof: Infinite intellect comprehends nothing except God’s attributes and his modifications (Part 1, Prop. 30).

God is one (Part 1, Prop. 14, Coroll.).

Therefore the idea of God, wherefrom an infinite number of things follow in infinite ways, can only be one. Q.E.D.

Proposition 5: The actual being of ideas has God as its cause, only as he is a thinking thing, not through any other attribute.

That is, the ideas both of the attributes of God and of particular things do not own as their efficient cause their objects (ideata) or the things perceived, but God himself in so far as he is a thinking thing.

Proof: This proposition is evident from Prop. 3 of this Part.

We there concluded that God can form the idea of his essence, and of all things which follow necessarily therefrom, solely because he is a thinking thing, and not because he is the object of his own idea.

Wherefore the actual being of ideas has its cause as God, in so far as he is a thinking thing. It may be differently proved as follows.

The actual being of ideas is a mode of thought.

It is (Part 1, Prop. 25, Coroll.) a mode which expresses the nature of God in a certain way, in so far as he is a thinking thing.

It therefore (Part 1, Prop. 10) involves the conception of no other attribute of God.

Consequently (by Part 1, Ax. 4) it is not the effect of any attribute except thought.

Therefore the actual being of ideas owns God as its cause, as he is considered as a thinking thing. Q.E.D.

Proposition 6. The modes of any given attribute are caused by God, through the mode-ness of those attributes, and not through any other attribute.

Proof: Each attribute is conceived through itself, without any other (Part 1, Prop. 10)

Wherefore the modes of each attribute involve the conception of that attribute, but not of any other.

Thus (Part 1, Ax. 4) they are caused by God, only in so far as he is considered through the attribute whose modes they are, and not in so far as he is considered through any other. Q.E.D.

Corollary: Hence the actual being of things, which are not modes of thought, does not follow from the divine nature, because that nature has prior knowledge of the things.

Things represented in ideas follow, and are derived from their particular attribute, in the same way, and with the same necessity as ideas follow from the attribute of thought.