I assumed that extension in Spinoza, means the geometrisation of the phenomenal world; but possibly - probably this is wrong. After all, how does one geometrise something like matter? (There is, in this case, the speculative notion of Lord Kelvin, an atom as a vortex, a knot of pure geometry ie pure extension, and its mass indicated by how it knots).

But, this on the face of it, seems merely a speculation of my own. Ungrounded in any texts. How then should one theorise extension? What did Spinoza mean by it? How have other philosophers used it?

  • space? as in taking up space?
    – user6917
    Jan 4, 2015 at 5:03
  • i mean that's obvious, but don't we share an intuitive sense of the meaning of "space", whether or not it can be refined in the course of an argument
    – user6917
    Jan 4, 2015 at 6:16

2 Answers 2


The geometrization of matter is a large issue, and is very relevant in present day physics (through General Relativity theory).

Spinoza in this issue, as in many others, stood on the shoulders of Descartes.

Descartes officially identified matter with geometrical (three dimensional) extension. For example, he wrote:

In this way we will discern that the nature of matter or body, considered in general, does not consist in its being hard, or ponderous, or coloured, or that which affects our senses in any other way, but simply in its being a substance extended in length, breadth, and depth. (Principles P.II-IV)

On the other hand, many assertions of Descartes' imply that matter, for him, was more than mere geometrical extension. For example, he notes that a body may get condensed, or rarefied. And that

The body, however, when condensed, has not, therefore, less extension than when the parts embrace a greater space. (Principles P.II-VI)

That is, a condensed body, though smaller in spatial extension, is not smaller in (material) extension. Which implies that (material) extension for Descartes is not simply identical with spatial, geometrical extension. It is not simply identical with the space that the body occupies.


To understand extension I do not believe you need to understand his idea of geometric being (or objects as conceived geometrically). Geometric being would be an attribute as perceived by intellect or mind, as a mental aid in measure. Or to use his terminology, as an "imagining" and not a comprehension (understanding the composition of relations constituting a body). Thus one is not in the same plane of discussion as with simple bodies in extension. One would be thinking in images of existence instead of being in relation to the existent. It sounds minor but he wrests a lot on establishing a sort of isomorphic non-causal interaction between these two separate planes of modality. He wrestles the most and fleshes out his thinking on this topic mostly in the Treatise on the Intellect.

Anyhow, starting from the beginning of the Ethics:


Proposition 1 establishes that God thinks; and

Proposition 2 establishes that God exists in extension.

then, this parallelism runs throughout all attributes of substance. Bodies exist. Thinking exists. All deriving from God as modes of extension and modes of thinking. And more importantly, this parallelism exists in complex relationships of reciprocity (e.g. "The mind is therefore the idea of the corresponding body" Book II Prop 11)

All bodies thus refer to the other finite existing modes that determines it. Put another way, all extension is determined by its extensive parts/relations. Any type of body presupposes an existence which exists in extension and which can be affected by and can affect other bodies.

I think there is the extent to which he postulates on the quality of extension-in-and-of-itself. The Kelvin knot type of idea is interesting but I don't think he would see that type of qualification as necessary for defining the essential character of extensionality, which he aligned more to the idea of Power of action (i.e. what it could do in affectus, affectio or essence).

Measures (such as geometrization), numbers, signs, images are all occurring in mind or thinking, not in extension itself.

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