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.