I have always found the concept of
infinity, as used by many historical philosophers, to be rather
confusing. This is probably due to my own background as a student in
mathematics, where by infinity one means a number so great that all
the regular numbers are way little in comparison. Because the
infinities of which these philosophers speak – particularly God –
are supposedly something beyond numbers, I have tried to avoid the
ambiguous term. Indeed, one of my articles was once rejected, because
the reviewer had something against me speaking of perfections,
instead of infinities. Yet, I still feel that the two concepts are
rather close. Infinite substance, for instance, is something ”way
awesome”, superior in all relevant senses compared to a mere finite
substance – shouldn't we then say that it is perfect in comparison
with the finite substances?
Wolff describes infinity of a thing as
a lack of all bounds (Schranke),
and while he never explicitly defines what he means by these bounds,
he in several occasions appears to relate them with how a thing is
determined and classified. The identification of boundaries and
determination resembles Hegel's statement that ”all determination
is negation”; Hegel says that he borrowed the statement from
Spinoza, and it would be interesting to know how widely it had
circulated.
The identification
of boundaries/negations and determinations may be difficult to
understand. With Wolff, we should remember the notion of essence: a
possible structure, which can be actualised in concrete things.
Essence determines then at least some characteristics of an actual
thing, but other characteristics might be determined by its relations
to other things. These relations, then, are what bound the essence
and divide it into different species: if the essence in question
would be a hole in the wall, the windows and the doors would be
differentiated by their differing relations to persons using them.
The word ”boundary” is here used somewhat metaphorically:
boundaries of a figure are also its relations to the things
surrounding it. Essence and all the relations determine then an
individual thing completely, because by knowing the essence of a
thing and its relations to other things we know everything there is
to know about the thing.
Infinite thing is
then something that is not bounded, that is, it is determined only by
its own essence and not by any relations to other things. In other
words, an infinite thing cannot be distinguished from other infinite
things. Instead, it is completely inclassifiable – it cannot be put
into a same class with finite things, because their nature or essence
is too dissimilar. Thus, all we can do to describe an infinite thing
is to use meaningless superlatives – it is beyond anything we can
imagine, or indeed, just ”way awesome”.
How does the
division of infinite and finite things then relate to the earlied
division of simple and complex things? Wolff notes that infinite
things cannot really change, and by change he means specifically a
change of the bounding relations: an essence of a thing cannot be
changed, but at most one can replace a thing having one essence with
another thing having a different essence. Infinite thing is then all
that it is ”at once” and not by going through successive stages.
Then again, a complex thing might change e.g. its spatial
characteristics, which for Wolff are essentially relations to other
things. Thus, an infinite thing, as atemporal, must be simple.
Complex and
infinite things are then two classes with no common members, but are
there any finite simple things? Well, all the complex things, says
Wolff, must be founded on some simple things, the combination of
which has generated the complex thing. Now, a combination of simple
things is undoubtedly a relation of them, and furthermore, a relation
which might change. Thus, the simple things that are the final
constituents of complex things must be capable of change and
therefore finite.
Boundaries of
complex things can be spatial or relate to the number of things it
consists of, but what about boundaries of a simple thing, which is
not spatial and does not consist of other objects? Remember that by
boundary Wolff refers to a non-essential classification caused by the
relations of a thing to other things. He apparently seems to think
that such a classification must at least be analogical with the
relations of magnitudes. A good example of this sort of scale would
be one consisting of temperatures: temperatures do not consist of
smaller temperatures, although they can be related like one number
relates to another. Wolff calls quantities of such scale grades: this
concept was used later by Kant and Hegel.
Wolff shares with
Kant and Hegel also the idea of relating grades to forces (Kraft).
Indeed, beyond numeric and spatial magnitudes, it is rather
difficult to imagine any quantities, but those which measure the
effects of a thing. For instance, temperature can be quantified,
because a certain grade of temperature has a clear effect on the size
of certain substances. Thus, Hegel later suggested that all
grade-scales are not just similarly structured as scales of numeric
and spatial magnitudes, but also essentially connected to such.
Wolff's simple, but
finite things are thus indivisible units of forces. In this Wolff
appears to move beyond Leibnizian monadology, where the ontological
units were characterised by perception, and towards the
identification of activity as the most essential characteristic of
true existence, which is a common theme in German idealists.
By a force,
furthermore, Wolff does not mean a mere capacity, the activation of
which is completely contingent. Instead, force is active and causes
some effects, unless it is countered by a contrary force.
Furthermore, the force of a finite thing is bounded or has a definite
grade. In other words, the activity of a simple, finite thing is
somehow limited. This limitation is not essential, and the simple,
finite thing could well change it, which proves the possibility of
applying temporal terms to these things.
Wolff does not stop
here, but suggests that simple things are constantly striving towards
changing their boundaries. Wolff's only justification for this
statement appears to be the principle of contradiction: a thing
cannot counteract its own actions. The justification appears once
again
somewhat loose:
although the thing itself cannot nullify its own force, other things
might well affect the thing, that is, if the opposing force is strong enough,
the simple thing becomes to a standstill or even starts to become
weaker. Wolff also apparently thinks that static states of standstill
are merely transitory phenomena, which cannot hinder the almost
constant change of the strength of the forces.
We could thus
picture a finite simple substance through a graph where every moment
of time is connected with some grade in the scale measuring the
quantity of the force. The graph goes up, when the force achieves its
goals, and when it goes down, it is hindered by other forces. In the
shadowy distance above, there is the infinity, unreachable by mere
finite things.
Wolff does not say
as much, but it appears reasonable to suppose that it is this
infinity towards which the finite substances probably strive. The
notion of infinity thus produces an objective criteria for making
value judgements in the realm of finite substances: the more the
finite things resemble the infinite thing, the better they are. We
shall see next time what sort of value scale of things Wolff suggests.
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