Spinoza’s Geometric Ontology

Geometric ontology is an ontology used by Baruch Spinoza  (later Benedict de Spinoza), one of the Great Philosophers, to establish and elaborate elements of the Ethics, his principal work.

The Ethics is divided into five parts. Each part begins with a set of definitions and axioms. They are followed by series of propositions and their related demonstrations. Each demonstration relies on previously introduced definitions and axioms and previously demonstrated propositions.

By using Geometric ontology Spinoza demonstrated his philosophy regarding the truth about God, nature and ourselves. The crucial message of the Spinoza’s Ethics is that our well-being is not in passions and transitory goods, nor in the religion, but rather in the life of reason.

Steven Nadler, Professor of Philosophy from the University of Wisconsin-Madison, is the author of  book Spinoza’s Ethics: An Introduction. This book is a great philosophical commentary about Spinoza’s Ethics. While reading the The Geometric Method chapter, I came up with an idea to present a short overview of Spinoza’s Geometric ontology.

The concepts of Spinoza’s Geometric ontology are:

  • Definition
  • Axiom
  • Proposition
  • Demonstration
  • Corollary
  • Scholia


A definition of a thing is such that “when it is considered alone without any others conjoined, all the thing’s properties can be deduced from it”. Definitions must be simple and basic, relative to the rest of the system. Understanding a definition must not require understanding of any other element of the system.

Axioms are general principles about things.  Axioms sometimes require definitions. While a definition may or may not be true, an axiom must be true. Spinoza believes that the truth of an axiom should be self-evident.

A proposition is a theorem about a basic claim. Propositions are core elements of the Spinoza’s Ethics philosophical conclusions about God, Nature and the human being.

Spinoza uses demonstrations to establish truth for each proposition. When a proposition is demonstrated it is used as a premise in the demonstrations of the subsequent propositions. Some propositions are also followed by corollaries and scholias.

A corollary is a theorem related to a proposition. Each corollary has a respective demonstration.

A scholia is an informal discussion in which Spinoza explains particular themes.