On The Geometric Method of Spinoza's Ethics

Spinoza’s Ethics is infamous for it’s utilization of Euclid’s geometric method, a compounding list of definitions, axioms, propositions, and the like as a means to elucidate the nature of God. In the context of the Ethics, the method has been accused of being a cold, mathematical reduction of the world and pointlessly complicated to the point of incomprehensibility. In this paper I will attempt to show some of Spinoza’s theoretical foundations for adopting the method, and the pedagogic power it allows for the exploration of the philosophical terrain Spinoza is interested in.

Before I can begin to divulge why I believe the geometric method is so important, it is best to explain the concept of common notions. According to Spinoza, knowledge is acquired in four ways. The first two are inadequate by definition: “knowledge from casual experience” and “knowledge from symbols”, these both being what he calls “opinion” or “imagination”. The third and only kind of knowledge we should strive for is the knowledge of “common notions and adequate ideas of the properties of things”, or “reason”. The fourth kind of knowledge is that which follows from these adequate ideas of God we gain from reason, or “intuition”¹. The common notions that we are to strive to create and encounter are not common sense, but rather “something common to bodies, either to all bodies . . . or to some bodies (at least two, mine and another)”². To have true knowledge of oneself as being a body without interactions with other bodies is impossible. Interactions between bodies that share something in common allow them to perceive that commonality adequately, which they would be unable to do by simply trying to perceive themselves. The knowledge of bodies leads to our knowledge of the ideas of our bodies and selves within the intellect, as “the idea of what is caused [in the attribute of thought] depends on the knowledge of the cause [in the attribute of extension]” and as such “the order and connection of ideas is the same as the order and connections of things”³. Put more simply, when one body interacts with other bodies, it gives them the idea of this interaction and with it an understanding of the commonalities between these bodies. For Spinoza, this is the entire basis of reason.