Complex extension

A clear difference between Wolff's Latin and German books of philosophy is that the more extensive Latin books have also a more detailed structure than their German counterparts. This is also true of Latin ontology. The book began with a section detailing the two basic principles of contradiction and sufficient reason. The second section was then dedicated to explicating the central notion of essence and some related concepts. Finally, the third section dealt with several characteristics common to all entities, such as identity, quantity and truth. Together, these three sections then formed the first part of Wolff's ontology, dealing with things in general.

The second and final part of Wolffian ontology is then about a general classification of things into simple and complex things. The second part contains, quite naturally, one section dedicated to complex entities and another dedicated to simple entities. In addition to these, there's also a section investigating relations between things, probably just because there was no better place for it.

Schematics of Wolff's Latin ontology

Wolff does not add considerable novelties to his account of complex entities in German metaphysics – the important fact is that the essence of a complex or composite entity is based on the essences of its parts and their mutual relations. Parts are then more essential than their combinations, in which they still retain their independence.

Now, when we are conscious of such a combination of several mutually extrinsic things, we see the combination as extended. In fact, we can abstract from all other features of the complex things, but this extension, as we do in geometry. Geometrically we can then define such notions as continuity (when you cannot put anything else between any two parts of a single thing) and contiguity (when you cannot put anything between surfaces of two different things). If two things are not contiguous, one can also define distance as the shortest line between them.

Extension and related notions can then be used to define space. As I've said earlier, Wolff follows Leibniz in accepting the idea of a relational nature of space – space is determined by certain relations between extended objects (distance etc.), so that space wouldn't exist without extended things having those relations. Here Wolff goes even so far to say that absolute space is just a useful fiction that we abstract from the concrete relations of complex things – and same goes for absolute time.

A novelty in Wolff's treatment of space and time in comparison with German metaphysics is that he extends his account to motion. On the one hand, this means just an extension of mathematical treatment of space or extended things to moving things. Lines can be used to describe not just extension, but also motion – Wolff is here expounding basics of vector calculation.

On the other hand, Wolff also suggests that if both absolute space and time are fictions, so must absolute motion be at least partially fictitious. Still, he is not willing to say that motion is completely imaginary. What is imaginary is the idea of motion happening in some absolute coordinate system with fixed places. Instead, motion is just change in the relations of things – a falling ball is, say, coming closer to the ground.

Furthermore, movement is something that is sustained by the moving entity – falling ball has impetus for moving in constant velocity towards the ground. In addition relations to external things can change the status of movement a thing has – a ball is constantly accelerated by something in its fall, and once it has hit the ground, it will stop moving towards the ground.

So much for complex things and their characteristics, next time I'll have something to say about simple things.