1. The relation between thought and extension
Remember that thought and extension are both attributes of substance, i.e. both express the essence of substance. Remember also that it’s one and the same essence that thought and extension express in their different ways. The language of modes of extension and the language of modes of thinking are just different languages which express the very same thing, much as the same novel (Anna Karenina, say) can be expressed both in Russian and in English.
In this connection, proposition 7 is illuminating: “The order and connection of ideas is the same as the order and connection of things.” “Ideas” of course are modes of thought, while “things” in Spinoza’s sense are modes of extension (not substances: see proposition 10, “substance does not constitute the form of man,” and its corollary, “the essence of man is constituted by definite modifications of the attributes of God”). So the idea seems to be that whenever one event causes another, the idea of the first event logically implies the idea of the second; studying the course of events and studying the logical connections of ideas amounts to the very same thing. (Notice how neatly this fits into Spinoza’s idea that causal explanation and logical explanation are really the same thing.) Similarly, in the scholium to prop. 7, Spinoza writes that “a mode of extension and the idea of that mode are the same thing, expressed in two ways.”
Since the story of causal connections among extended things is the very same story as the story of logical connections among ideas, only differently expressed, it would be a confusion to think that ideas have effects on things or vice versa. Spinoza points this out toward the end of pr. 7, scholium: “as long as things are considered as modes of thought, we must explicate the order of the whole of Nature, or the connection of causes, through the attribute of Thought alone,” and similarly for Extension. (An analogy may be helpful. I’m about to change the font of this document from Palatino to Times. I’ll do that by highlighting the whole document and then using my mouse to select “Times” from a pull-down menu. The very same sequence of events may be described in terms of the transmission of electrical impulses and the opening and closing of circuits. But it wouldn’t really be right to say that my highlighting the whole document caused a series of electrical impulses, or that a series of electrical impulses caused the document to change fonts. A series of electrical impulses caused a series of further electrical impulses; these further impulses constitute the changing of fonts, but do not stand in any sort of causal relation to that change.)
This general point about the relation between thought and extension carries over to the relation between mind and body. Thus we get prop. 13: “The object of the idea constituting the human mind is the body.” It may seem odd to say that all the ideas we have are really ideas of our own body. What about ideas of trees, other people, etc.? But Spinoza will say we don’t so much have the idea of a tree, period, as we have the idea of the effect of a tree on our own body: our idea is the idea of the impact of the tree on our sense organs, not of the tree as it might be “in itself.” (Compare prop. 16: “The idea of any mode wherein the human body is affected by external bodies must involve the nature of the human body together with the nature of the external body.” See also prop. 26.) Because we only understand the tree by way of its effects on our body, our understanding of the tree is inadequate and incomplete (prop. 25: “The idea of any affection of the human body does not involve an adequate knowledge of an external body”).
2. Adequate and inadequate ideas
Here is a puzzle for Spinoza. (It’s a worry for Berkeley, too.) On Spinoza’s view, God’s mind includes our minds along with a lot more (see the corollary to proposition 11). Our ideas are just a part of the mind of God. But Spinoza agrees with traditional theology that God doesn’t have any false ideas. God is omniscient in a sense; God’s mind includes all possible ideas, along with all their connections to one another. But we have all sorts of false beliefs. How can it be that our false ideas are in God’s mind, and yet God has no false ideas?
Spinoza’s solution to this problem is quite ingenious. (See especially propositions 32-35.) The only sort of falsity ideas are capable of is incompleteness. Our ideas are false to the extent that we don’t perceive all their connections to other ideas. But the very ideas which are incomplete in our minds are complete in the mind of God, since God’s mind includes all our ideas and more besides. An idea that is incomplete in us may be completed by other ideas in God’s mind. (Spinoza uses the example of our mistaken views about freedom to explain this in the scholium to prop. 35.)
3. Three kinds of knowledge
The second scholium to prop. 40 is interesting because of its typology of knowledge, which is divided into opinion, reason, and intuition. Intuition is the most basic of these; it corresponds to Descartes' “clear and distinct perception,” or things we perceive “by the natural light.” Things we know by way of reason are things we prove on the basis of the starting points which we intuit. Opinion is the only source of error; we can’t be wrong about what we intuit, or about what we carefully prove on the basis of what we intuit.
4. More on free will
Descartes thought that ideas and volitions were two different things, and correspondingly that having an idea and having a belief were two different things: belief = idea plus affirmation, where affirmation is a free act. Spinoza thinks that’s completely mistaken; a volition is nothing but a certain kind of idea; thus “the will and the intellect are one and the same” (prop. 49, corollary).
5. The cause of error
The scholium to proposition 49, which concludes part II, rejects Descartes' analysis of the possibility of error, which depends on a notion of the will that Spinoza cannot accept.