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Melamed and Lin contend that for Leibniz,

Leibniz thinks that space and time cannot be substances or anything else absolute and must ultimately be a system of relations that obtain between bodies. (e.g., LC, L, 3.5) This is because if space, for example, were absolute, then there would be space points and such points would be indiscernible from one another. God would treat these space points differently from each other insofar as he orients his creation in space one way rather than another. This would have to be an arbitrary decision for the reasons outlined above. So, space and time are not absolute (SEP entry on Sufficient Reason).

Is this compatible with Leibniz's Identity of Indiscernibles? Doesn't this contradict the existence of indiscernible Space Points?

More importantly, aren't these Space Points are by definition distinct since they are different Points of the Absolute Space, so being treated differently would not contradict the Principle of Sufficient Reason since they are actually inherently different.

Am I misunderstanding something?

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    I've brought more of the quote into play here and made clearer who is saying what. I've also modified the way the question is asked to make it on-topic ("am I right?" questions are off-topic here).
    – virmaior
    May 7, 2016 at 5:51

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In what sense:

distinct points are "different" points of the Absolute Space ?

The argument used by Leibniz to “confute the fancy” of those who take space to exist independently of spatially related things, is the following:

if space was an absolute being, something would happen for which it would be impossible to give a sufficient reason – which is against my axiom [the Principle of Sufficient Reason]. And I prove it thus: Space is something absolutely uniform, and without the things placed in it, one point of space absolutely does not differ in any respect whatsoever from another point of space. Now from this it follows (supposing space to be something in itself, besides the order of bodies among themselves) that it is impossible there should be a reason why God, preserving the same situation of bodies among themselves, should have placed them in space after one certain particular manner and not otherwise.

Physical things are located by way of "measuring" them (through coordinates) against some reference frame.

If we assume the existence of points in the absolute space, they have no intrinsic properties that can differentiate them from one another: we cannot "measure" them against the Absolute Space because they are the absolute space (we cannot measure our height comparing us with ourself...).

Thus, distinct "real" points cannot be discerned [here he use the priciple of Identity of Indiscernibles] and all the purported distinct points must collapse into a sort of "singualrity".

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  • "Points in the absolute Space have no intrinsec properties that can differentiate them from one another", then how do you argue that they're distinct (which is implied by the use of points)?
    – user2268997
    May 7, 2016 at 15:48
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    if "one point of space absolutely does not differ in any respect whatsoever from another point of space" then how could there be an absolute space, (that objects can be measured against)? i.e: doesn't that contradict the definition of absolute space?
    – user2268997
    May 8, 2016 at 15:37
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    @user2268997 But aren't the two things you object to implied by the notion of substance? The atoms of mercury are mercury by being alike. The idea that one is here and the other is there has to do with space, and not mercury. It is like Feynman's notion that there could really be only one electron, all electrons being identical, but it is somehow reflected into apparent duplicates by travel through time or space. We like the idea of electrons, but we can't be sure.
    – user9166
    May 8, 2016 at 17:11
  • @jobermark, and you conclude that...?
    – user2268997
    May 14, 2016 at 12:00
  • @user2268997 I don't really like this notion of substance, property etc. But within that framework, his logic holds. Space is something different from a collection of objects identified by their properties. Location is not a property of a point, because it can be specified only relative to the other points, and that leads us to a circular reference. Nothing absolute should devolve into circularity in this way. But location is all a point has, so the point has no usable properties. Since the properties of an object are what make it an object, points are something different.
    – user9166
    May 14, 2016 at 18:37

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