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I'm reading "Time and Space" by Dainton, and it gives a lengthy discussion on the different views on Newtonian and neo-Newtonian spacetime, arguing that absolutists and relativists (or substantivalists and relationists) have different arguments for the "absolute acceleration" problem in the two cases. Cited examples are from Maudlin, Teller, and Sklar.

Now, while I understand the historical significance of such a debate (Newton vs Leibniz), I can't see why it could be important for modern philosophers: it is now known that there is only one acceleration, and it is absolute, meaning that an accelerating observer can perform experiments that will tell it that it is accelerating. Am I missing something?

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    The point is exactly to clarify the underlying ontology of classical mechanics, and which relational or absolutist interpretations fit it better. This establishes the baseline for comparison to modern physics, see SEP. For example, in special relativity acceleration supervenes on spacetime intervals, so if you replace the classical relationism (which relied on absolute simultaneity) with a special relativistic version it appears to be closer to SR than absolutism.
    – Conifold
    Feb 12 at 18:30
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Modern science doesn't and cannot answer the endless debate of metaphysical preferences of your question, now as 300 years ago, you still can choose Newton's absolute spacetime or Leibnitz's relative spacetime.

Most people implicitly hold Newton's absolute spacetime view as there exists a permanent fixed background stage to start the motion stories, this is such a common experience and if you doubt about it seriously at the metaphysical level, you'll be regarded crazy everywhere.

But relativists like Leibnitz do hold a serious metaphysical ontological image which looks very different from the common. Like in pure clear Math, we require "same space" 3 attributes as follows as mentioned in @Conifold's SEP:

(i) A body comes to the "same place" as another once did, when it comes to stand in the same "relations" to bodies we suppose to be "unchanged".

(ii) Then we can define "a place" to be that which any such two bodies have in common.

(iii) space is all such places put together.

However, Leibnitz also holds that properties are "particular", incapable of being instantiated by more than one individual, even at different times; hence it is impossible for the two bodies to be in literally the same relations to the "unchanged" place. Thus the final "particular" nature of physical properties cannot satisfy requirement (ii) above. Obviously relativists regard "relations" between substances as fundamental properties of physical reality (ie, the definition of physical reality can only defined and thus measured via mathematical relations), just as a circle is NOTHING BUT a plane curve satisfying x^2 + y^2 = r^2 relation along its body.

In conclusion, just like there're no two exactly same leaves in this physical world, there're no two exact same background space when you are talking about different objects moving inside it. Of course, this doesn't mean in our ideal math realm there doesn't exist number "2" or any fixed unchanged space coordinate. The conflict is just the different metaphysical speculations of the underlying ontological world (assuming its existence), however, since metaphysics usually leads and creates any model or theory, the implications of them may be of huge differences...

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  • What about the acceleration problem? That's the point I really don't get: we may still argue on the ontological significance of space itself, but doesn't the evidence of privileged (accelerated) frames of reference refute at least the most Leibnizian relationism, which claims that if there is a single object in the universe no motion can occur whatsoever (and denies the Sklar's "biting the bullet" of an intrinsic acceleration property)? Feb 13 at 8:00
  • There're 2 types of notions at debate of relationism and absolutism. Leibniz famously denied space's ontological existence as mere convenient ideal construct and byproduct of the relations between motions of matter. But he also famously asserts a type of "true" motion exists caused by active force (vis-viva, similar to kinetic energy). Ur confused "absolute acceleration" belongs to this type of "true" absolute motion which is not at conflict at least for Leibniz. He was an idealist who denied even the real existence of matter, his point is what's real is the "vis-viva" from a conscious monad. Feb 16 at 0:37
  • As for "if there is a single object in the universe no motion can occur whatsoever", seems naturally sensible ontological speculation. Physicists used earth/stars as inertial frame to apply Newtonian mechanics at ease based on absolute space ontology belief, but if there's only one real object in the world, where can change originate from? How can any motion be possible?. Modern GR allows non-trivial closed spacetime solution without any matter, most hold spacetime is real structure controlling motion, not just reference frame, but still can't prove it cannot be a byproduct illusion of motion. Feb 16 at 1:03
  • So in summary. there're 4 ontological beliefs about spacetime: Descartes' space as matter, Newton's Absolute Space Substantivalism, Leiniz's Relationism (with modern Dynamic Approach advocates), modern Spacetime Geometric Substantivalism (mainstream). It's a fascinated area for endless metaphysics and science interactions. Which is your personal take? What supports your belief? I personally speculate they're probably all correct in some context, since all seem honest descriptions, though Absolute Space does not sound very democratic, Descartes is too dualistic and unnatural for me... Feb 16 at 1:13

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