A recipe gives numbered instructions: cut, marinate, heat the pan, stir, serve. Beside them are smaller notes. Keep the heat down. A different cooking wine will do. The first attempt may feel rushed.

The instructions seem to speak without a speaker. In the notes, you hear someone who has actually cooked the dish.

In the Ethics, the proposition is something like the name of the dish, the demonstration its steps, and the scholium the accompanying advice. But here the accompanying remarks occupy more space than the demonstrations.

Counting the parts

There are 130 scholia: fourteen in Part I, twenty-four in Part II, thirty-seven each in Parts III and IV, and eighteen in Part V.

A rough count of the linked Latin transcription gives over twenty-four thousand words in the scholia and over twenty-one thousand in the demonstrations. The proposition statements themselves occupy much less space. The precise boundary and tokenization affect the totals, not the striking difference in scale.

The formal statements of the 259 propositions do not speak as “I.” First-person singular remarks appear occasionally in the demonstrations—an author recalling what he has shown or said—and repeatedly in the scholia. They are not interchangeable kinds of prose.

Where knowledge gets its names

Part II distinguishes three kinds of knowledge. Their names and definitions are laid out in the second scholium to Proposition Forty.

One kind comes from fragmentary sensory experience or from signs, including things heard and read. Spinoza calls these opinion or imagination. A second arises from common notions: reason. A third he calls intuitive knowledge.

To illustrate, he asks for a fourth number that stands to the third as the second stands to the first. A merchant multiplies the second by the third and divides by the first. Perhaps the rule was learned from a teacher without a proof. Perhaps repeated easy cases made it familiar. Perhaps the merchant understands Euclid’s demonstration.

But with one, two and three, one can immediately see the fourth number: six. In this easy case, the relation can be apprehended without going through those other routes.

The next proposition says that knowledge of the first kind is the sole cause of falsity, while the second and third are necessarily true. Its demonstration begins by referring to what was said in the preceding scholium about inadequate and confused ideas.

The scholium is not decorative small print. It names the kinds of knowledge; the next proof takes those names and classifications up as premises.

The donkey

The last proposition of Part II has a corollary identifying will and intellect. After the corollary comes a long scholium in which Spinoza sets out objections and answers them one by one. Here I concede; there I deny.

The fourth objection invokes Buridan’s ass. Without freedom of the will, what would happen to a person placed in a perfect balance between equally urgent alternatives? Would they starve or die of thirst?

Spinoza accepts the consequence under the stipulated conditions: someone aware only of hunger and thirst, with food and drink equally placed, would perish. Asked whether such a being should count as a person or a donkey, he says he does not know—just as he does not know how to classify a person who hangs himself, a child, or those described in the period’s language as fools or madmen.

It is an unsettling answer, not a neat reassurance. Part II ends with this extended scholium. A book of demonstrations also makes space for the author saying what he does not know.

At the end

The recipe comparison needs a correction. There are people in this book’s proofs, too. The plural “we” appears throughout: we have shown, we imagine, we understand.

The singular “I” is heard especially often in the remarks. Small print, but not a small part of the book.