Propositions 7-8

7. The order and connection of ideas is the same as the order and connection of things.

Proof: This proposition is evident from Part 1, Ax. 4.

The idea of everything that is caused depends on a knowledge of its cause.

Corollary: Hence, God’s power of thinking is equal to his realized power of action.

Whatever follows from God’s infinite nature in the world of extension (formaliter), follows without exception in the same order and connection from the idea of God in the world of thought (objective).

Note: Whatever that can be perceived by the infinite intellect as constituting the essence of substance, belongs altogether only to one substance.

Consequently, substance-thinking and substance-extended are one and the same substance. These are comprehended now through one attribute, now through the other.

Likewise, a mode of extension and the idea of that mode are one and the same thing, though expressed in two ways.

This truth seems to have been dimly recognized by those Jews who maintained that the following are identical:

• God
• God’s intellect
• the things understood by God.

For instance, the two are one and the same thing displayed through different attributes:

1. A circle existing in nature
2. The idea of a circle existing

We find the same chain of causes whether we conceive nature:

• under the attribute of extension, or
• under the attribute of thought,
• under any other attribute,

That is, the same things follow in either case.

God is the cause:

• of an idea, such as the idea of a circle, as he is a thinking thing.
• of a circle, in so far as he is an extended thing.

This is simply because the actual existence of the idea of a circle can only be perceived as a proximate cause through another mode of thinking.

That mode of thinking is again through another, and so on to infinity.

As long as we consider things as modes of thinking, we must explain the order of the whole of nature, or the whole chain of causes, through the attribute of thought only.

And, in so far as we consider things as modes of extension, we must explain the order of the whole of nature through the attributes of extension only; and so on, in the case of the other attributes.

Wherefore of things as they are in themselves God is really the cause, inasmuch as he consists of infinite attributes.

8. The ideas of particular things or modes that do not exist are within the infinite idea of God

This is in the same way as the formal essences of particular things or modes are contained in God’s attributes.

Proof: This is evident from the last proposition.

It is understood more clearly from the preceding note.

Corollary: As long as particular things do not exist, their thought or ideas do not exist in reality but only exist in the infinite idea of God.

When particular things exist, their ideas also exist.

Note: I am unable to give any example of this.

However, I will try to illustrate it as far as possible.

The nature of a circle is such that if any number of straight lines intersect within it, the rectangles formed by their segments will be equal to one another.

Thus, infinite equal rectangles are contained in a circle. Yet none of these rectangles exist, except in so far as the circle exists.

The idea of any of these rectangles also do not exist, except in so far as they are comprehended in the idea of the circle.

Let us grant that, from this infinite number of rectangles, only two exist.

The ideas of these two exist as they are contained in the idea of the circle, but also as they involve the existence of those rectangles.

Wherefore they are distinguished from the remaining ideas of the remaining rectangles.