The Ethics begins by defining a cause of itself: by this, Spinoza understands something whose essence involves existence, or whose nature can be conceived only as existing.

The first verb in the main text of a book demonstrated in geometrical order is a first-person verb. I understand.

Eight definitions

Part I has eight definitions. Six follow this pattern: name a term, then say what I understand by it. Cause of itself, substance, attribute, mode, God and eternity all enter in this manner.

The other two use a different construction: something is called finite in its kind if another thing of the same nature can limit it; something is called free if it exists solely through the necessity of its own nature and is determined to act by itself alone.

After defining God, Spinoza adds an explanation. Again there is a speaker: I say absolutely infinite, not merely infinite in its kind.

Compare the opening of Euclid’s Elements. A point is that which has no part. That definition does not introduce itself through an “I.”

When the speaker falls quiet

Seven axioms follow Spinoza’s definitions. The first-person singular falls away.

Then comes the first proposition: substance is prior in nature to its modifications. The demonstration is one sentence, referring us to Definitions Three and Five.

Sentences originally introduced as what I understand have become numbered premises. Definition Three. Definition Five. Subsequent proofs refer to definitions, axioms and propositions in turn. Through the first eight propositions, the singular speaker does not return in that earlier manner.

The statement has not vanished. It has changed its role in the page’s machinery.

When he returns

Proposition Eight has two scholia. At the beginning of the second, the first person returns. Spinoza does not doubt that readers who judge things confusedly, and are unused to knowing them through their first causes, will find the demonstration of Proposition Seven difficult.

Proposition Seven says that existence belongs to the nature of substance. Spinoza describes the confusions of people ignorant of causes: they imagine trees speaking like people, or people arising from stones as readily as from seed.

Then he says that if people attended to the nature of substance, they would not doubt the proposition at all. It would be an axiom for them, because they would understand substance as what is in itself and conceived through itself.

At the beginning: what I understand. Here: what they would understand.

In the same scholium he explains what a true definition should contain. It expresses nothing beyond the nature of what is defined. A triangle’s definition expresses the nature of a triangle, not the existence of a particular number of triangles.

In a classroom

A physics teacher begins a lesson: for the constant force we are considering, by work I mean force multiplied by the displacement in its direction.

The lesson proceeds on that basis. The teacher need not keep saying what I mean at every calculation. The “I” appeared at the beginning; what it established continues to support later steps.

At a difficult point the teacher pauses: I know this is not easy to see. The voice returns where an anticipated reader or listener needs attention.

At the end

The opening speaker tells us how he understands his terms. Returning in the scholium, he says that anyone attending properly would understand them in that way.

A proposition must be followed by its demonstration. That latter statement is not presented as another proposition. It is written in a scholium.