In the following passage, Kant discusses the infinite divisibility of matter:

Matter is impenetrable, through its original expansive force…But this is only a consequence of the repulsive forces of each point in a space filled with matter. Now the space filled by matter is mathematically divisible to infinity, that is, its parts can be distinguished to infinity, although they cannot be moved, and thus cannot be divided (according to geometrical proofs). But in a space filled with matter, every part of it contains repulsive force, so as to counteract all the rest in all directions, and thus to repel them and to be repelled by them, that is, to be moved a distance from them.

Proposition 4, Metaphysical Foundations of Natural Science

What is Kant saying?

  • 3
    It's from Metaphysical foundations of natural science (1786), proof of Proposition 4, which proposes that "Matter is divisible to infinity, and, in fact, into parts such that each is matter in turn." Dec 24, 2023 at 10:54
  • Can the OP provide a link to the text? Can the OP add details on what they do and do not understand about the passage; for example, do they have an inkling about why Kant wishes to claim matter is infinitely divisible, or do they not know why Kant brings this up? It may be that a longer excerpt will make it clear what Kant is attempting to establish. Dec 26, 2023 at 14:07
  • Physics from 100 years ago shows it to be false. Why continue to pursue it?
    – Scott Rowe
    Dec 26, 2023 at 15:21
  • 1
    Thank you for this explanation. The sentence I most have difficulty with is "Now the space filled by matter is mathematically divisible to infinity, that is, its parts can be distinguished to infinity, although they cannot be moved, and thus cannot be divided (according to geometrical proofs).." I'm confused because of course the parts of a thing are moveable, that's what it means to be parted. So what is here that he says is immoveable? Is he distinguishing immoveable parts of space, points, from parts of matter, which of course is moveable?
    – Gerry
    Dec 27, 2023 at 21:22
  • These are some links that may help anyone to investigate the question further: PDF Wikisource Wikipedia SEP Dec 28, 2023 at 16:42

2 Answers 2


The point is to distinguish between

  1. the mathematical (geometrical), infinite divisibility of space, where every point can be distinguished between either being occupied by matter or not, and
  2. actual, physical divisibility of matter into infinity.

As a background, now, we need to know about two propositions:

  1. Physical matter can only be divided so far (atomic theory) and
  2. Space can only be occupied by a single object comprised of matter (Law of Excluded Middle, basically Aristotelian physics).

Thus, it follows that every infinitely small "geometrical" point occupied by matter "defends" its place against other matter (repelling force, forbidding infinitely close distance (=equity)), even if matter cannot actually be infinitely divided.

  • 2
    The answer can be improved by contextualizing the exposition of the passage with an analysis of why Kant wants to make these propositions. Dec 26, 2023 at 14:10
  • We've seen that although matter can't be infinitely divided, it can be infinitely crushed, which is not something Kant really thought about.
    – Scott Rowe
    Dec 26, 2023 at 15:23
  • @JuliusH. Are you able to offer such contextualization in your own answer?
    – J D
    Dec 26, 2023 at 17:23
  • @JD I need extended discussion, research and contemplation to attempt to do so, so I would appreciate anyone joining me here: chat.stackexchange.com/rooms/150550/… Thanks. Dec 28, 2023 at 17:07
  • @JuliusH. Confident and articulate response. I'll have a look-see after the airport. Kant is a constant source of fascination.
    – J D
    Dec 28, 2023 at 21:12
  1. I understand the sentence quoted above as follows:

    Kant states that space, an object of geometry, is mathematically divisible without end. That’s correct, because any non zero volume of in space contains a proper volume which is less.

    But this division is only in thought, because one cannot cut physically space into pieces. Hence one cannot divide space physically and one cannot move the pieces apart.

    But I cannot follow Kant’s "proof" of proposition 4.

  2. The whole attempt to derive fundamental properties of space from philosophical argumentation seems totally outdated to me. The investigation of space is an object of physics.

    It is to expect that below a certain scale (e.g., the Planck scale) space has a totally different structure than we register in the mesocosmos. The structure of space and time, and hence of spacetime, is currently an open question of science. E.g., see Carlo Rovelli: What is time? What is space.

  • Yes, for an explanation to be meaningful, it must transcend the terms it was explaining and describe it in completely different, opposite, terms. That is what an 'explanation' requires to not be vacuous. Kant would have been closer to the truth to say, "and then a miracle occurs", since that is what we must always say until we know more.
    – Scott Rowe
    Dec 26, 2023 at 15:25

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