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  1. Newton starts his book The Mathematical Principals of Natural Philosophy, 1687

II. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable.

  1. Kant starts his book The Metaphysical Foundations of Natural Science (1786)

EXPLANATION I. Matter is the movable in space; space, which is itself movable, is termed material or relative space; that in which all motion must in the last resort be conceived (which is therefore itself absolutely immovable), is termed pure or absolute space.

  1. My question: Do Kant and Newton use 'absolute space' with the same meaning?

I would appreciate answers which mainly reference the primary source, referring to a lesser degree to later interpretations.

Jo Wehler
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    See [Kant’s Views on Space and Time](https://plato.stanford.edu/entries/kant-spacetime/#BackKantViewCrit) and see [Kant’s criticisms of Newton](https://plato.stanford.edu/entries/kant-spacetime/#KantCritNewt): "he criticizes the Newtonians for holding a transcendental realist position concerning space and time (the Newtonian “subsistence” view of space and time)." For Newton, *space* is the [*sensorium dei*](https://link.springer.com/content/pdf/bfm:978-3-319-72053-1/1.pdf), while for Kant is an *a priori* representation. – Mauro ALLEGRANZA Apr 13 '22 at 12:46
  • What does Kant mean with relative space? What is movable space? – Pathfinder Apr 13 '22 at 13:03
  • @Felicia Please see in the quoted reference, Oberservation II. The reference allows to make a text-search. – Jo Wehler Apr 13 '22 at 13:25
  • I think the difference is that Kant allows movable space. I don't see movable, material, and relative space in Newton. – Pathfinder Apr 13 '22 at 13:32
  • @Felicia - This need historical details: in the same *locus*, Newton defines also "relative space". IMO, at this level of "analysis", Kant is simply Newtonian: we have to assume that Kant had a good understanding of Newtonian mechanics. The difference - if any - regards the metaphysical implications of the basic physical concepts. – Mauro ALLEGRANZA Apr 13 '22 at 14:31
  • @MauroALLEGRANZA What do they mean with movable space? Put it in a box and take it somewhere else? – Pathfinder Apr 13 '22 at 14:43
  • See *Scholium*, page 6 of [Cajori edition of Motte translation](https://www.google.it/books/edition/Sir_Isaac_Newton_s_Mathematical_Principl/lSoJ2tJKfIEC). – Mauro ALLEGRANZA Apr 13 '22 at 14:52
  • If "absolute space" only means "immovable", do you think modern physics allows space to be movable? If so, movable with respect to what? – David Gudeman Apr 13 '22 at 17:59
  • @David Gudeman Both Newton and Kant say the same about absolute space. Expressed in modern language: Absolute space defines a global coordinate system such that any local coordinate system transforms to this distinguished coordinate system. A point in space does not move if and only if its coordinates with respect to absolute space do not depend on time. - Modern physics dismisses the concept of absolute space. – Jo Wehler Apr 13 '22 at 18:29
  • @JoWehler, your expression in modern language is not the same as either of those definitions. For that matter, your definition doesn't do what you seem to want it to do because it allows me to define absolute space as any coordinate system I choose. – David Gudeman Apr 14 '22 at 19:00
  • @David Gudeman I think it is just the opposite: You will not find a single global coordinate system at all. Because coordinate systems are local objects, see the definition of the mathematical concept of a manifold. In general a manifold cannot be covered by one global chart. – Jo Wehler Apr 14 '22 at 20:24
  • @JoWehler, are you suggesting that astronomers don't have a coordinate system that can be used to identify the location of every galaxy? Whatever coordinate system they chose, some galaxies will not be locatable on it? – David Gudeman Apr 14 '22 at 21:58
  • @David Gudeman Yes, even locally at the event horizon of a star one has to change from Schwarzschild coordinates to Kruskal-Szekeres coordinates. Moreover spacetime deviates more and more from Minkowski space when approaching and crossing the event horizon. - At large scale there exist several global spacetime models of the universe. Already due to topological reasons they often differ from Euclidean space R**4 and cannot be covered by a single chart. – Jo Wehler Apr 15 '22 at 06:15
  • @JoWehler, you are talking about spacetime coordinates, not space coordinates. Kant had nothing to say about spacetime, which had not been invented yet. Spacetime is a mathematical abstraction used to solve certain kinds of problems in physics. Space is not a mathematical abstraction. Space is not geometry. Space is the perceptual relationship that geometry attempts to model. Kant was not trying to answer the question, "what is geometry?" but the question, "how is geometry possible?" In the course of answering that, he had to answer the question "what is space?" – David Gudeman Apr 15 '22 at 08:41
  • @David Gudeman I agree, Kant talks about space not about spacetime. But just this fact shows that Kant reasons about the wrong concept: In general, one cannot decompose spacetime in a unique way into space and time. Each chosen decomposition provides a different space component, its properties depending on the type of decomposition. I consider the relativity of the splitting a further argument against the concept of ‚absolute space‘. 1/2 – Jo Wehler Apr 15 '22 at 15:42
  • @David Gudeman You mention the question ‚How is geometry possible?‘. 1. When considered a mathematical question, then the question has been answered by the Euclidean axioms and the rules of logic. With the consequence that propositions from geometry are analytic. 2. When understood as: Why does Euclidean geometry describe physical space?, then the answer is: Euclidean space only approximates physical space. The concept is superseded by the non-Euclidean spacetime-concept of Relativity. 2/2 – Jo Wehler Apr 15 '22 at 15:43
  • "Euclidean space only approximates physical space" I've never seen a sound defense of that position. The mere fact that other formalisms are useful in certain physics problems does not mean that Euclidean geometry is wrong. No one has ever demonstrated a violation of Euclid's Fifth Postulate. All they have done is pick out a set of curves that aren't parallel straight lines, *called* those curves parallel straight lines, and then used this renaming as a counter-example to Euclidean geometry. – David Gudeman Apr 15 '22 at 16:01
  • @JoWehler, "Euclidean space only approximates physical space" I've never seen a sound defense of that position. The mere fact that other formalisms are useful in certain physics problems does not mean that Euclidean geometry is wrong. No one has ever demonstrated a violation of Euclid's Fifth Postulate. All they have done is pick out a set of curves that aren't parallel straight lines, *called* those curves parallel straight lines, and then used this renaming as a counter-example to Euclidean geometry. – David Gudeman Apr 15 '22 at 16:02
  • @David Gudeman To continue the discussion could you open up a new question with focus on a specific issue? - Possibly you sent your last comment two times. – Jo Wehler Apr 15 '22 at 16:16

1 Answers1

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To answer quickly: yes, I think the object ("absolute space") is the same for both (in the Critique of pure reason, A39, Kant seems to almost explicitly criticise the Newtonian view, the view of "mathematical investigators of nature", and this is about "the absolute reality of space and time", the existence of which requires "two eternal and infinite self-subsisting non-entities (space and time)"). But this object, the absolute space, hasn't the same properties in the Newtonian view and in the Kantian one (Kant criticises the Newtonian view). According to Newton, absolute space has empirical reality, but according to Kant, it hasn't.

More details:

If I understood well your question, it seems that Kant gave an answer in the same book you quoted :

[...] a movable [empirical] space, if its motion is to be capable of being perceived, presupposes in turn an enlarged material space, in which it is movable; this latter presupposes in precisely the same way yet another; and so on to infinity.

Thus all motion that is an object of experience is merely relative; and the space in which it is perceived is a relative space, which itself moves in turn in an enlarged space [...]. Absolute space is thus in itself nothing [...] To make this [absolute space] into an actual thing is to transform the logical universality of any space with which I can compare any empirical space, as included therein, into a physical universality of actual extent, and to misunderstand reason in its idea.

(Kant Immanuel, Metaphysical Foundations of Natural Science, eng. M. Friedman, Cambridge University Press, 2004, « First Chapter: Metaphysical Foundations of Phoronomy », « Explanation 1 », « Remark 2 ».)

As I understand this excerpt, there is a difference between Newton's conception of space and time and the Kantian conception of it. The Newtonian one is absolute, and the Kantian one is relative: the absolute space is, according to Newton, real, but it is ideal according to Kant ("Absolute space is thus in itself nothing"). Newton gave the concept (not in the Kantian meaning of "concept" but more in the daily meaning of it) of absolute space an empirical or physical reality (this is why Kant wrote about the transformation of the "logical universality" of the absolute --- Newtonian --- space into an "empirical universality" --- transformation he disagrees with).

On the one hand, you have the empirical, physical, scientifical absolute space, whose substance would be aether, if I'm right (Newton); and on the other hand, you have the perceived space (Kant): for example, I see a book on my shelf, and I can move this book on my shelf: the perceived space filled by my book is relative to --- this means: can be moved compared to --- the perceived space filled by my shelf (and the perceived space filled by my shelf is relative to the perceived space filled by my wall, and so on: this is, if I understood well, the idea that Kant is presenting in the first sentence of the excerpt). This relative space is the only one that has empirical reality, according to Kant (and it is called "empirical space").

Mick
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