Christian Wolff: Reasonable thoughts on God, world, and human soul, furthermore, of all things in general - Relational view of space and time

In the years 1715 and 1716 a philosophically significant correspondence occurred between Leibniz and Samuel Clarke, a proponent of Isaac Newton. Particularly Leibniz attacked the Newtonian idea of an absolute space and an absolute time that exist independently of any things within them. Leibniz based his criticism on the principle of sufficient reason: if there would be an absolute space, God might have created world few meters away from its actual place in the absolute space, but since all the places in an absolute space are completely similar, He would have had no reason to create it in any particular place and would thus have been unable to create the world anywhere.

Instead of an absolute space and time, Leibniz suggested a relational view of them: space and time are nothing but orders of things – space an order of coexistent things and time an order of successive things. An important consequence of this view is that it becomes meaningless to speak of space and time without any things. (Note that this view is not relativistic: spatial and temporal magnitudes are still stable, despite the differences in the velocity or the effects of gravity.)

Leibniz's view was accepted by Wolff, and indeed, it appears to have been in favour throughout the German idealism. Kant, for instance, appears to take Leibniz's view more seriously than Newtonian absolute space: Kant attacks in Critique of pure reason the relational view more vigorously and also appears to apply a modified relational theory of space in his metaphysical foundations of natural science. Indeed, presupposing an absolute space and time adds to an ontological system two rather strange entities, which are not things as such, but also not based on things.

Now, if one would take Leibniz's description of relational view literally, one could instantly derive all sorts of absurdities. For instance, if space was nothing more than an order of things, space would change at once, when the order of things changes: space would become larger, if a thing went farther from all other things than any thing before. As Leibniz himself appears to have been aware, these problems could be avoided by defining space and time through possible, rather than actual order of things. Thus, space could continue beyond the actual positions of things, because the things have the capacity to or at least could be conceived to move further than they are.

Wolff, on the other hand, seems not to be aware of the possible problems and suggests that space and time could be defined as the actual order of things. Thus, he is able to say that even a single thing by itself would be non-spatial or that spatiality required at least two things and their actual relation.

Because Wolff's simple things should have no things as their constituents, their internal constitution could not be spatial, because it would involve no actual relation of several objects. As we noticed in the previous text, Wolffian notion of a simple thing is ambiguous, because it leaves out the possibility of Aristotle's potentially divisible and still actually unified substances. Similar problems arise with Wolff's notion of space. According to Wolff's definition, the Aristotelian divisible substance without any actual parts would be non-spatial, which is clearly absurd, when we think of e.g. a portion of water. Here we should obviously add some modalities to Wolffian account of space: Aristotelian substance is spatial, because it can be divided into parts that have spatial relations.

Even this correction might not be sufficient. Democritean atoms were supposedly indivisible substances, but still spatial. Wolff notes – consistently with his own definition of space – that this atomist notion is contradictory. Yet, it seems quite possible to imagine that a thing would be physically indivisible and still have some spatial magnitude: spatiality is here not connected to a capacity to divide a thing, but to a possibility of conceiving the division of a thing.

For Wolff, spatiality is something connected with the inner consitution of complex things. What sort of characteristics are then left for simple things? I shall return to this question in the next blog text.