Substance, nature, and necessity › What the geometric method asks of a reader

The Ethics presents definitions, axioms, propositions, proofs, corollaries, and explanatory notes usually called scholia. Its sequence encourages the reader to trace a disputed conclusion back to the claims on which it rests. If proposition 14 is unconvincing, we can ask whether the problem lies in its inference, the account of attributes, or an earlier proposition invoked by the proof.

This is more useful than treating the conclusions as detached pronouncements. It is also more demanding than assuming that a proof-shaped passage must work like an accepted mathematical theorem. A clear chain of references can still contain a premise we reject or an inference that needs more explanation. The method makes an argument inspectable; accepting the argument requires assessing what the references actually establish.

The prose appendices and prefaces help explain its purpose. In the appendix to Part I, Spinoza criticizes the habit of interpreting nature through human purposes. People know their appetites but are often ignorant of the causes determining them; they then imagine purposes in nature through the model of their own goal-directed conduct. This is Spinoza's diagnosis of a way of thinking, rather than an empirical psychology established by the book's method.

Suppose someone explains a storm by saying that it happened to punish a community. The illustration shows what an appeal to purpose adds to an event. Understanding atmospheric conditions would be one task; establishing a punishing intention would require a further argument. Spinoza rejects the projection of human purposes onto God or nature. That rejection does not prevent a person from acting toward a purpose within nature.