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In monadology, Liebniz describes monads as the true atoms, that which cannot be broken into parts, and enters into compounds. They are simple substances. Nor can they have shape, extension or divisibility.

Now take spacetime itself; this obviously has extension & shape, so cannot be a monad: it must be a compound of them.

(So, if I'm right, Liebniz is going much further than the greek atomists as his atoms build spacetime).

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  • Monad is qualia. O mighty Leibniz where are you now !?
    – Asphir Dom
    Jul 26 '14 at 16:11
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I'm not certain quite how to respond to this question. It strikes me that the way it is asked tries to force an answer out of Leibniz's thought which it is not equipped to give.

First, it is important to ask what the status of space and time are in Leibniz's own words. A helpful text in this regard is Leibniz's correspondence with Samuel Clarke, which may be found here (PDF). Here in Leibniz's third paper we find the passage (§4, p. 9 of the linked document):

For my part, I have said several times that I hold space to be something merely relative, as time is, taking space to be an order of coexistences, as time is an order of successions. For space indicates... an order of things existing at the same time, considered just as existing together, without bringing in any details about what they are like. When we see a number of things together, one becomes aware of this order among them.

The instance here on space and time being "an order of things" is repeated throughout the correspondence. The meaning of this phrase itself and it's implications might be debatable, but what it is meant to oppose is quite clear. Leibniz is here concerned with objecting to two views (1) that space is a thing (this he does in §5 of the third paper and again in §10 of the fourth paper albeit for difference reasons) or (2) that space is a property of a thing (the objection here is more clear-cut: which thing is it a property or an attribute of? -- see §8 and §9 of the fourth paper).

Leibniz gives us a further hint here when he writes (fourth paper, §41):

[S]pace doesn’t depend on this or that particular spatial lay-out of bodies, but it is the order that makes it possible for bodies to be situated, and by which they have a lay-out among themselves when they exist together, just as time is that order with respect to their successive position.

So, for Leibniz, space and time are orders among bodies, which I suppose means their positioning vis-à-vis other bodies. In this sense, space and time are constituted by a multiplicity of bodies (an infinity, as we find out in §61-69 of the Monadology). If this sense is what your are asking, then it is true, but only in the trivial sense that the very notion of space and time for Leibniz are such that they are comprised of nothing other than the multiplicity of bodies.

However, it still seems to me wrong to suppose that, for Leibniz, there is a "space" or "time" out there (whatever that would mean) containing bodies. Rather, it bears paying attention to something Leibniz says about the relation between bodies and monads, viz.:

And as this body expresses all the universe through the interconnection of all matter in the plenum, the soul also represents the whole universe in representing this body, which belongs to it in a particular way.

(Monadology, §62)

"Space" and "time" therefore might best be seen as orders internal to the monad corresponding to how the monad represents it's body among the rest of the bodies. And such an order, for Leibniz, only exists in the mind of God.

All that said (and I'm not sure it's entirely clear), where Leibniz more radically diverges from the atomists is in his notion of le plein -- translated in the version I've linked above as plenum -- i.e. the notion that there is no void. For the early atomists, the universe consisted in atoms and void between those atoms. For Leibniz, it is quite clear that there is no void. The universe is composed entirely of monads.

Again, as with space and time this would be trivially true for Leibniz as a universe "containing" void or that was "larger" than all monads would be undifferentiable from a universe consisting of all monads -- Leibniz here takes the "nothingness" of the void quite literally. What is operating here is what called "the law of identity of indiscernibles", a statement of which can be found in §9 of the Monadology:

Each monad, indeed, must be different from every other monad. For there are never in nature two beings which are exactly alike, and in which it is not possible to find a difference either internal or based on an intrinsic property.

Since a universe consisting of monads and void has "nothing" distinguishing it from a universe consisting of only monads the two are one and the same, and hence, there cannot be any void at all.

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  • You're right in thinking that I'm perhaps shoehorning concepts into Liebniz that aren't there. Its interesting to me that people were arguing that space/time could be seen as a thing, do you know who were pushing that point of view? Jun 26 '12 at 9:11
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    The SEP, has Samuel Clarke stating, 'Although space is not sensible, Clarke rejected its identification with nothingness, since space has some properties, for example, quantity and dimensions. One might add other properties he accepted, such as homogeneity, immutability, and continuity. Space, then, is an entity in which things are, and not mere absence of matter.', and then' Space is also not an aggregate of its parts but presumably an essential whole preceding all it parts' Jun 26 '12 at 9:27
  • @MoziburUllah Clarke is right except space IS sensible. And the only muscle which can sense/create/be it is - mind/soul/monad/god.
    – Asphir Dom
    Jul 26 '14 at 16:08

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