Space and Mechanics

1. Space.

· Newton thought that space was something real.  Thus, if you grabbed the universe as a whole and moved it over by a mile, you would be moving it over relative to space.  Incautiously, Newton called space God’s sensorium, sensory organ as it were, and Leibniz criticizes this. 

· But L.’s main criticisms are based on the principle of sufficient reason.  If space is real, then things would be different if everything shifted over by a mile, and yet no reason can be given for why they can be thus shifted, and hence they cannot be thus shifted, since that for which no reason could be given is not possible.  So space is not real.  Space instead is ideal. 

· Moreover, since Newton thought that space itself is real, he thought there was empty space.  L. disagrees since this would be contrary to the goodness of God who would want to fill the voids.

· Clarke allows that maybe space is a property rather than a substance.  But of what?  If of God, then we get theological problems—it starts looking like God’s body, or God starts looking like the soul of the universe, or something else pantheistic.  If of nothing, then this is nonsense.  The remaining option is that space is a property of substances in space.  Leibniz agrees with this, but notes that if this is so, then there can’t be any such thing as empty space.

· Space is nothing but the network of interrelations between objects.  In his Fifth Letter to Clarke, which we did not read, Leibniz constructs space as follows:

o Two things at different times are in the same place provided that they stand in the same relation to “a sufficient number” of “fixed” objects.

o The fixed objects are ones where there is no cause of mutual changes.

o Space is the totality of these places. “an ideal thing”

· Each monad represents all of reality.  For instance, I represent Julia as being two meters away from me, the sun as being one astronomical unit away from me, and Vancouver as being about three thousand miles away.  From the network of these relationships we can mathematically construct space.  We say, then, that one object moves when all the others remain in the same network of mutual distances, but the one object changes in its relations to the others.

· But what are the relations between objects?  It is tempting to think of a relation as something between two objects.  But there is no room for such a thing on L.’s system.  It would be an attribute with one leg in each of two objects, L. quips.  Everything on L.’s system is a substance or an attribute of a single substance.  So the relations between objects—any relations—are simply made up of the attributes of the individual objects.  The only attributes there are that could do this are representations (and also appetitions, but those aren’t what L. will choose to focus on here—rather, they will enter into the theory of time).  So, when I say I am two meters from one of you, I mean simply that I represent one of you as two meters away from me and you represent me thusly.  So space is built up out of these representations.

· L. says that one has clearer representations of what is closer.  So perhaps, and this is speculative, ultimately what makes it the case that you are two meters away from me and Vancouver is three thousand miles away is that you are much more clearly represented by my monad and Vancouver much less so.

· If this is correct, then we might have hope for an answer why there can’t be action at a distance.  Remember that the cause of something has a clearer representation of the effect than the effect of the cause.  But the the clearer your representation of it, the closer you are to it.  So maybe you have to be right up against something in order for your representation of it to be sufficiently clear for you to count as causing it?  There are difficult details to work out in such a conception.

2. Time.

• Just as space was built up out of relations, so is time.  Time is built up out of relations of succession.  What kind of succession?  Again, I speculate, but I think the basic kind of succession is the causation within a monad.  To say that one moment of a monad is earlier than another just is to say that the perceptions at the first moment cause those of the second.  Causation within a monad is built-up out of appetitions.  So just as space had to do with the network of perceptions of a monad, and was to be built up out of this network, time is built up out of the network of appetitions.
• Do different monads have different time series?  Maybe: but we can correlate them.

3. Physics

• Geometry is not enough.
• Metaphysics: a conatus, or internally-driven tendency. A nisus.
• “Force”: this is conserved for metaphysical reasons.
• “Force” is proportional to the square of the velocity—Galilean argument. Lifting the same thing twice is high requires twice as much “force”.
• Principle of invariance or relativity.
• (This principle together with the conservation of energy is sufficient to yield the conservation of momentum.)
• Relativity è action and reaction.
• Deformation. Internal causes of motion.

4. Bipartite.

• As in the case of Parmenides, we have a two-part system: a metaphysical account of reality in terms of monads (except that Parmenides thought there was only one of them) and a physical account of the appearances of things—both agree that things like tables and chairs are mere appearances, figments of perceivers’ perceptions.  However, while in Parmenides there was no connection between the metaphysical reality and the appearances, in Leibniz the latter are grounded in the mutually coordinated perceptions of the monads.  In Leibniz, when I say there is a table there, I am not saying a falsehood: I am talking about the network of monadic perceptions throughout the universe having a perception of the table there.  Physical reality is a figment of perceivers’ perceptions, but not just of the mind: of everything’s perceptions.  The table perceives itself, after all, and is not just a figment of our imagination.