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.
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