semi-automatic waffle

Sunday, 25 January 2026

Spinoza does reason deductively, but he rarely relies on classic syllogisms (“All A are B; C is A; therefore C is B”). Instead, he deliberately chose a different method.

How Spinoza actually reasons

In works like the Ethics, Spinoza uses what he calls the geometrical method, modeled on Euclid rather than Aristotle. This involves:

Definitions
Axioms
Propositions
Demonstrations
Corollaries and scholia

The demonstrations often function like chains of syllogistic reasoning, but they are:

More formal and cumulative
Spread across multiple propositions
Dependent on earlier definitions and axioms rather than explicit syllogistic forms

So instead of writing:

All substances are X
God is a substance
Therefore God is X

He’ll write a proposition whose proof cites earlier propositions and axioms, producing the same logical effect without syllogistic packaging.

Why he avoided syllogisms

Spinoza was skeptical of traditional scholastic logic. He thought:

Syllogisms often preserve knowledge rather than generate it
True understanding comes from grasping causes, not merely valid inference
The geometrical method better reflects necessity in nature

This aligns with his broader rationalist project: showing that reality unfolds with the same necessity as a mathematical system.

Bottom line

Deductive reasoning? Yes, constantly
Explicit syllogisms? Rarely
Underlying logical structure? Often syllogistic in effect, but not in form

If you want, I can point to specific propositions in the Ethics where a syllogism is basically “hidden” inside the demonstration.

Spinoza’s geometrical method is not just a stylistic choice—it’s meant to enact his metaphysics. I’ll explain it first structurally, then philosophically, and finally with a concrete example.

1. The structure of the geometrical method

Spinoza models the Ethics on Euclid’s Elements. Each part proceeds in a fixed order:

a) Definitions

These fix the meanings of key terms (e.g. substance, attribute, mode).
They are stipulative, not empirical: Spinoza is telling you how the concepts are to be used.

Example: “By substance I understand that which is in itself and is conceived through itself.”

Definitions are not argued for; they are starting points.

b) Axioms (or postulates)

Axioms are general truths Spinoza takes to be self-evident or immediately grasped by reason.

Example: “From a given determinate cause the effect follows necessarily.”

They express basic causal or logical principles rather than facts about the world.

c) Propositions

These are theorems Spinoza wants to establish.

Example: “God necessarily exists.”

Each proposition has a fixed place in the sequence and depends on earlier material.

d) Demonstrations

This is where the real reasoning happens.
A demonstration proves a proposition by explicitly citing:

Definitions
Axioms
Earlier propositions

Each step is supposed to follow with necessity, not probability.

e) Corollaries and scholia

Corollaries: immediate consequences of a proposition
Scholia: explanatory, polemical, or clarifying remarks (often where Spinoza sounds most “human” and least geometric)

2. How this differs from syllogisms

A syllogism is local and self-contained.
Spinoza’s method is global and cumulative.

Instead of:

All substances are eternal
God is a substance
Therefore God is eternal

Spinoza:

Defines substance
Proves propositions about substance in general
Proves that God is substance
Draws conclusions that must apply to God because they apply to substance as such

So the logical force comes not from a single inference, but from the entire system already in place.

3. Why Spinoza thought this method was superior

a) It mirrors causal necessity

For Spinoza, reality itself is a necessary causal order.
The geometrical method is meant to mirror that order in thought.

To understand something is to see how it follows from its cause.

The method forces the reader to follow causes step by step.

b) It blocks appeals to imagination and authority

By eliminating rhetoric, examples, and appeals to tradition, Spinoza aims to:

Prevent emotional persuasion
Prevent theological shortcuts
Force rational assent

You don’t agree with a proposition; you either see that it follows or you don’t.

c) It trains the intellect

Spinoza thinks reading the Ethics properly actually reforms your mind:

You learn to think in terms of necessity
You stop seeing things as contingent or arbitrary
You move from confused ideas to adequate ones

So the method is partly ethical and therapeutic, not just logical.

4. A simple example (compressed)

Very roughly, Part I of the Ethics goes like this:

Definition: Substance is what exists in itself
Axiom: Nothing can be produced by nothing
Proposition: A substance cannot be produced by another substance
Proposition: There can be only one substance with a given attribute
Proposition: God is a substance with infinite attributes
Conclusion: Therefore God necessarily exists and is the only substance

Each step leans on earlier ones; skipping a step breaks the proof.

5. A common criticism (worth noting)

Many critics argue that:

The definitions already smuggle in the conclusions
The axioms are not as self-evident as Spinoza claims
The method gives an illusion of necessity rather than guaranteeing it

Spinoza was aware of this worry—but he thought any rational system has to start somewhere, and his starting points are the clearest possible ones.

In one sentence

Spinoza’s geometrical method is a tightly ordered deductive system designed to make metaphysical necessity visible, not through syllogisms, but through an entire architecture of definitions, axioms, and interlocking proofs.

If you want, I can walk through one specific proposition from the Ethics line by line to show how a demonstration actually works on the page.