Because the world is a complex object, it must ultimately consist of simple substances: we have already seen this statement in the chapter on ontology, although the argument supposedly justifying it was faulty. Just like the world was already characterised by its complexity, these ultimate elements of the world are characterised by their simplicity. They cannot, for instance, have any spatial magnitude and thus differ from Democritean atoms. Yet, they must still be placed within some place – or more likely, remembering the Wolffian notion of space, their relations should constitute space.
Wolffian elements should then be infinitesimally small, just like mathematical points. Then again, they cannot be mere points. Wolff uses as a justification anothe principle he learned from Leibniz – the so-called identity of indiscernibles. This principle is based on the higher principle of sufficient reason. All things must have a reason, thus, there must be a reason why one thing is in one place and another in another place. Because the Wolffian space is relational, he thinks that the reason cannot lie in the space itself – space cannot exist without things and their relations. If now the two separate things are supposed to be completely similar, there cannot be any characteristic causing one to occupy a different place from the other – in other words, they must occupy the same place, and indeed, be identical.
Whatever one thinks of Wolff's attempt to justify the principle, it is clearly against taking mathematical points as true existents: point cannot be distinguished from another point through nothing else, but its position. Wolffian elements resemble then more Leibnizian monads, with the exception that Wolff does not take seriously Leibniz's idea of perception as the essential characteristic of all monads. True, he does pay lip service to the idea, but only in the restricted sense that all the elements reflect the whole world by being in harmony with it, in other words, by being in harmony with one another: the state of one simple thing matches the state of other simple things, e.g.. when one thing is in a state of activity, another is correspondingly in a state of passivity.
We have already seen in a previous text (http://thegermanidealism.blogspot.com/2011/11/units-of-force.html ) what actually individuates Wolffian elements: they are all units of force or activity, each developing independently of all others. What Wolff adds in this chapter is the explanation how bodies are generated out of the elements. Just like states of all the elements are harmonious in general and this general harmony constitutes the world, the states of particular elements might have a stronger harmony and thus form a complex unity or body.
Wolff goes to great lengths in explaining what characteristics all these bodies have: for instance, bodies consist of an essence (the structure of having been assembled in a certain manner from elements), matter (their activity of resisting externally induced movement) and moving force (their activity of moving themselves and mediately also other bodies). This analysis is not very original, but in essentials lidted from Leibniz's physical writings, and not philosophically fruitful, so I shall ignore it.
What interests me more is the relationship of the elements and the bodies. The existence of bodies is dependent on the existence of simple elements: a faulty assumption, perhaps, but one which Wolff endorsed. The divisibility of bodies has then a limit, because the elements cannot be divided anymore. This limit Wolff places outside possible experience, when he once again confirms that elements as simple things cannot be seen. This time he even has a proper argument: elements cannot be affected by movement, hence, light will not interact with them and they are therefore invisible to us.
On the other hand, bodies as spatial must be divisible into further spatial things, that is, further bodies. Wolff appears then to accept both infinite divisibility of bodies and the existence of a limit for that divisibility: indeed, his arguments for both are almost exactly those Kant will use in his second antinomy. Kant's antinomies are based on the assumption that the two arguments are both convincing and that both of their results cannot hold at the same time: Kant can then note that this apparent paradox is avoided by adpoting his own transcendental idealism. We have already seen at least one argument in the second antinomy is far from convincing. If we can also find out a convincing reason how Wolff could accept the two arguments without falling into contradiction, Kant's ”negative argument” for transcendental idealism would fall apart.
The simple solution for the seeming contradiction is that the indivisible elements are not extended, but point-like entities: thus, they are dimensionless and cannot be divided anymore. Analogically, mathematical figures can be divided into further and further figures, but no division leads into anything smaller than indivisible points. In other words, elements are the result of a practically impossible infinite division of bodies: thus, after every finite division we are in a point where the antithesis of Kantian antinomy works, although there is a final limit which no finite division can reach and in which the thesis holds.
This is enough of Wolffian cosmology. Next time we are back with studying human soul in rational psychology.