As I understood it Spinoza claims everything has Extension, it occupies space. But in physics there are things called point particles which are zero dimensional, they don't occupy space.

So for example photons do not have Extension therefore Spinoza is wrong, have I misunderstood something?

Thank you!

  • 7
    Not on this score. Photons are called point particles, but they are neither particles nor literally point-like, they are "quantum particles" whose wave functions extend over the entire universe. Not that it matters, Spinoza was well familiar with dimensionless geometric points, he modeled Ethics after Elements after all. Zero extension is still extension. It is much more mysterious how extension applies to God and abstractions, but to Spinoza somehow it does.
    – Conifold
    Commented Oct 6, 2021 at 18:41
  • 2
    "In quantum mechanics, the concept of a point particle is complicated by the Heisenberg uncertainty principle, because even an elementary particle, with no internal structure, occupies a nonzero volume." en.wikipedia.org/wiki/Point_particle Point-like refers to not having internal structure, rather than truly being located at a point
    – CriglCragl
    Commented Oct 14, 2021 at 8:07
  • Quote, please (I don't recall such statement). Anyway, common things have 3d features (as CriglCragl states, "internal structure"), while protons have 0d features; within a 0-dimensional context, the pure existence of a point already implies an extension in such context.
    – RodolfoAP
    Commented Jun 5 at 9:34

4 Answers 4


I'm not a physicist, but I actually look into the Physics of Descartes and Spinoza.

  • "Extension" is Descartes-speak for metaphysical space.
  • "Space" is physical space.

Spinoza's assertions are based on Descartes who proposed that God is Everything, both physical and metaphysical. This everythingness manifests as metaphysical extension and physical space. "There is no Void" simply means "God is Everywhere".

Everything is just space that has modes. For example, an atom is 99% space and 1% particles. The particles are then modes of space or extension, just as space and extension is a mode of the aether, which is the substance of God.

So Spinoza was way ahead of everyone by saying everything is space.

This space in Descartes' Physics is the 2nd Element (which is spacetime or gravitons in modern Physics).

In Hinduism, this substance is called citta or mind-stuff. Descartes' did not expound on this new aethereal God, fearing the Church response. So Spinoza did it for him.

In a nutshell, photons do not occupy physical space as point-particles in modern Physics. They do so as a wave. But in both cases, they have extension, since the basis of the extension is the aether which is a theory from Descartes and not Spinoza.

Spinoza's best assertions that have been proven by particle physics are:

  1. Atoms are divisible - this has been proven by particle colliders
  2. Everything is mostly space - atoms are 99% empty space
  3. Local Motion - this is now proven by Relativity

First, point particles occupy space. The point particle at (1,1,1) in a 3D coordinate system occupies the space precisely at (1,1,1). Points are 0-dimensional, with a physical volume, surface area, and perimeter of 0. They, and any countable collection of them, have a measure of 0 under a standard measure but can have other measures under other choices.

Secondly, whether or not point particles exist in modern theories of physics is not entirely clear. It is true that, according to the wave/particle duality of quantum mechanics, Heisenberg’s Uncertainty Principle, and the fact that particles have a calculable de Brogle wavelength, particles seem to act as if they are not entirely point-like.

On the other hand, electrons, for example, have no internal structure and behave like point particles in other ways. Traditional interpretations of the collapse of the wave function conclude electrons are point particles after a measurement or observation. The details get hazy, dependent upon interpretation, and even philosophical very quickly. (Eg. For how long after? Decoherence anyone? How does this not violate the Uncertainty Principle and is the Uncertainty Principle epistemic or ontological?)

Nonetheless, modern theories of physics are so radically different from what anyone could have predicted before about 1870 (to be safe) that every philosopher who philosophized about physics was proven incorrect in countless foundational ways.

Update in response to other posted answers

“Dimensionless point particles do not exist in physics” is false.

After all, a particle, by its nature, is localized at a point, whereas the wave function (as it’s name suggests) is spread out in space (it’s a function of x, for any given time t). How can such an object represent the state of a particle? The answer is provided by Born’s statistical interpretation of the wave function, which says that [|psi| squared] gives the probability of finding a particle at point x at time t

Introduction to Quantum Mechanics, Second Edition. David J. Griffiths.

The electron (as far as we know) is a structureless point

Introduction to Quantum Mechanics, Third Edition. David J. Griffiths. (This was published in 2018.)

This is a canonical standard-bearer for quantum mechanics. Many other places in the text explicitly refer to a particle as being a point (in the collapse of the wave function).

  • -1: The Griffiths quote isn't going into the ontology of the a particle point. A particle localised around a point means that it's extension is negligible and not that it's extension is zero. Ask what localised means in Math.SE. Commented Oct 14, 2021 at 10:03
  • 1
    I do not need to, I teach the subject. Griffiths is quite clear, and the mathematics is as well. But having philosophical outliers is common for us. “Extension” is not a mathematical or physical concept, but a philosophical one. I will not comment on it. Commented Oct 14, 2021 at 12:03
  • And I have studied maths and physics upto masters level at well respected institutions. Like I have already explained above, physical extension is usually understood as spatial. A particle localised around a point is one that has neglible spatial extension. Commented Oct 14, 2021 at 17:07
  • Moreover, a point, mathematically and physically speaking, indicates position. Commented Oct 14, 2021 at 18:01
  • The equation and interpretation Griffiths discusses would still be an excellent approximation for all current real-world experiments even in theories where the particle had non-zero extension near the Planck scale, like string theory. Also note that the book is about nonrelativistic quantum mechanics rather than relativistic quantum field theory (the latter incorporates special relativity but not general relativity, which would require a theory of quantum gravity), so that's already enough grounds for showing that the model he's discussing is only meant to be approximate rather than exact.
    – Hypnosifl
    Commented Oct 14, 2021 at 19:06

First, dimensionless point particles do not exist in physics. They are simply a way of speaking about a particle whose extension is negligible for the effects that are bring modelled.

Secondly, physics is generally geometric in myriad ways and hence about extension in myriad ways. This tallies with what Spinoza says about the physical world, it is a mode of extension. In fact, extension is simply a mode of the absolute substance, thought is another and there are infinitely many other unobservable modes.

Thus, Spinoza's theology is compatible with modern physics and hasn't been disproved by it.

  • are you nick land?
    – user56815
    Commented Nov 28, 2021 at 18:04

One way he was proven wrong is the discovery of truly random behavior in quantum mechanics (edit: apparently it's not settled, see comments below). For Spinoza events necessary follow from their causes and are entirely determined by them.

Note that it does not have much consequence on his views, as our mind have no control over the results of quantic measurements, and our behavior is still determined by the laws of physics. In Ethics Spinoza states that dualists don't have the faintest idea of how a spaceless mind could affect our material body's behavior, and AFAIK it is still true to this day.

Photons don't occupy space but they are in space, they manifest their existence under the Extension attribute of Nature. When a photon goes from the Sun to our eye, both of those locations and the distance between them are part of the Extension. Of course, we can also have an idea of a photon and that's why they also exist under the Idea attribute (not sure of the correct English word, sorry), like everything else.

On the other hand, Antonio Samasio, who is not a physicist but a brain surgeon, wrote a very interesting book, Looking for Spinoza: Joy, Sorrow, and the Feeling Brain, where he explains how many intuitions of Spinoza about the human mind have been confirmed by modern neurology.

  • 3
    Whether quantum mechanics is truly random is unknown, both Bohmian mechanics and the various flavors of the Everett interpretation (including the many-worlds interpretation) are fully deterministic interpretations of quantum mechanics, but all interpretations make identical predictions so they are untestable. It's possible a future theory of quantum gravity might settle the issue, though.
    – Hypnosifl
    Commented Oct 14, 2021 at 2:34
  • @hypnosifl thanks. I added a note in the answer. Anyway, as I say above wether its truly random or not does not radically change Spinozas system.
    – armand
    Commented Oct 14, 2021 at 2:44

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