Infinite Modes and Finite Modes
Modes: "affections of a substance, or that which is in something else and is conceived through something else" (p. 158)
Anything that requires something else for its existence, or requires somethig else for it to be conceived (to be intelligible) is a mode. Since the only thing that does not require anything else for its existence is substance, it will follow that everything that exists is either a substance or a mode of a substance.
Thus, anything 'less' than a substance is a mode. A mode is "conceived through something else" in the sense that the concept of it requires the concept of something else. Modes of substance are "in" substance in the sense that they are dependent upon substance for their existence.
The most important difference between a 'mode' in Spinoza and a 'mode' in another philosopher, such as Descartes, is as follows. What we normally think of as (finite) substances -- e.g. mountains, cars, souls, angels, dirt, the Milky Way galaxy -- are not substances at all for Spinoza. For they fail to meet the necessary criteria -- they can't exist on their own, they can't be understood on their own, they do not exist because of their natures, and they are not infinite. All of these things are dependent on something else (substance) for their existence and in order to be understood (the reason why they exist, etc.), and are finite. So all of these things are modes.
We may say that modes are modifications of substance. But more properly, modes are modifications of attributes of substance, and come in two kinds: infinite modes, and finite modes.
Now, each mode, whether infinite or finite, is a modification of each attribute of substance. So for every mode of the attribute of thinking, there is a mode of the attribute of extension. This applies to infinite modes as much as finite modes.
The infinite mode of the attribute of extension applies to all finite modes of extension. The example that Spinoza provides is motion (or rest). The way to think of this is think of this infinite mode as a law or laws. Thus, each finite mode of extension is in motion (or rest), and hence, the law(s) of motion (or rest) applies to it.
The infinite mode of the attribute of thinking applies to all finite modes of thought. The example that Spinoza provides is "infinite intellect", which is not very helpful. If we think of this as a law or laws, however, then it is the law(s) of thinking, i.e. the law(s) of logic. Thus, each finite mode of thinking (i.e. each idea) is in the infinite intellect, and hence, the law(s) of logic applies to it.
(Note: some interpreters talk about 'psychological laws' instead of laws of logic. But whatever laws we are talking about, they are laws of thinking.)
Now, the infinite mode of the attribute of extension that is the law(s) of motion, and the infinite mode of the attribute of thought that is the law(s) of logic, are actually one and the same infinite mode. We simply conceive the infinite mode first under the attribute of extension, and then under the attribute of thinking.
Infinite modes are still modes, of course, and hence, are dependent upon substance for their existence. Without substance, there would be no law(s) of motion (or rest), and no law(s) of logic.
"Particular things" are actually finite modes of attributes of substance. We only know of two attributes, extension and thought. So each "particular thing" is a finite mode of the attribute of extension (looked at one way) and a finite mode of the attribute of thought (looked at another way).
"Particular things are nothing but affections of the attributes of God, that is, modes wherein the attributes of God find expression in a definite and determinate way."(Part I, Proposition 25, Corollary; p. 169)
In the case of the attribute of extension, finite modes of the attribute of extension will be, e.g. Albert Einstein's body, a rock's body, a bird's body, the body of Notre Dame Cathedral, the body of the Milky Way galaxy.
However, finite modes of the attribute of thinking will be, e.g. the idea-of-Albert Einstein's-body, the idea-of-a-rock's-body, the idea-of-a-bird's-body, the idea-of -Notre-Dame-Cathedral, the idea-of-the-Milky-Way-galaxy.
Now, in the case of human beings at least, we have a name for the "idea-of-Albert-Einstein's-body". The name for it is "Albert Einstein's mind".
Thus Albert Einstein is a particular thing, conceived of one way as a body, and conceived of another way as an idea (a mind).
Particular things are said to be "in" God, or infinite substance.
Proposition 15: "Whatever is, is in God, and nothing can be or be conceived without God." (p. 163)
This means that Albert Einstein's body is "in" God conceived under the attribute of extension, and the idea-of-Albert-Einstein's-body, or Albert Einstein's mind, is "in" God conceived under the attribute of thought. Perhaps we can say here that Albert Einstein's body is "in" God's body, and the idea of Albert Einstein's body, or his mind, is "in" God's intellect.