Christian August Crusius: Draft of necessary truths of reason, in so far as they are set opposite to contingent ones - Space and time

Crusius begins a new chapter by pointing out that our thinking begins from sensations. This implies that we already implicitly begin with a notion of existence, sensation being its criterion. Crusius admits this, but adds that we must still abstract the notion of existence from our sensations.

We have seen Wolff defining existence as something added to possibility - in effect, this was no real definition of existence, but existence was a combination of various concepts, namely the existences of complex things, simple things and God, some of which we can define and understand, while others we can’t. Crusius does admit Wolff’s point in some sense. What Wolff was trying to do was to define existence in terms of how it is generated (for instance, complex things are generated by combining simpler things), and Crusius accepts that we cannot ultimately know where existence comes from. Yet, he insists that this is a false way to approach the problem and says that we can define existence rather simply as being in space and time.

What then are these space and time for Crucius? Starting from space, he says that space is just where we think all existing substances are and what is left, when we remove all substances in our thought. Space is then independent of all substances in it or absolute.

Crusius defends his notion of space with an argument that clearly inspired Kant’s discussion of space, although the conclusions of both are very different. Indeed, Crusius begins by pointing out that space is not considered to be a substance, since otherwise we would fall into an infinite loop, because all substances are thought to be in space. Then, just like Kant, Crusius considers the possibility that space might be taken as a property of some substance, but decides against it, because space is not thought to be in some subjects, but subjects are thought to be in space.

Finally, Crusius looks upon the idea that space might be a relation. He notes that if space would be a relation, it would have to be a relation of substances being next to one another (here the inclusion of the notion of a substance in the definition is necessary, because e.g. music also has things next to one another, namely, sounds, but space is the only thing, where these beings next to one another are substances). Still, Crusius concludes, even this possibility is unsatisfactory, because even a single substance would have to be thought of as being in space.

Crusius’ argument is meant to show that his notion of space agrees with what everyone thinks space is. There’s still the possibility that space is a kind of collective delusion or mere imagination. Crusius rejects this possibility by referring back to his criteria of truth: since we cannot separate in our thoughts existence from space, they should be accepted as truly connected, unless this incapacity of separation is somehow connected to limitations of our understanding. Kant would later argue that we really can’t say, if it is down to some limitation of our cognition, but Crusius does not consider this possible: otherwise, we would have to reject also the principle of sufficient reason as susceptible.

Crusius admits that some people have rejected the notion of absolute space as something independent of substances and taken it as a mere relation of substances. One reason for this is simply that they assume space must be substance, property or relation, and because the two first options seem impossible, they have assumed that it can only be a relation. Crusius notes that his very point has been that these are not all the options: while notions of substance and property are concepts linked to essences, spatiality is a component of or abstraction from concrete existence.

More concerning for Crusius seems the objection that the absolute space would rival God in dignity, because both would be eternal and necessary. Crusius’ answer is that space is not a complete thing or substance, but a mere abstraction from existence of all substances. Thus, even God is in a sense spatial, because he could be said to exist everywhere. Of course, Crusius thinks that God’s existence is not bodily and so cannot be sensed. Therefore space could be empty in the sense of being without any bodies, even with God present in it. Extrapolating from this, Crusius suggests that all simple substances might be in space in a similar non-sensuous fashion, or as he puts it in terms that Kant was to borrow later, they fill space, but do not extend it.

After defining some concepts related to space, such as location, Crusius turns to discuss time. His main point is similar as with space: time is not a substance nor a property or a relation, but an abstraction out of existence of actual things, and more precisely, their succession following one another. Importantly, Crusius thinks that time is absolute or independent of things and that it is not mere imagination. A point Crusius did not make with space is that although we cannot think of an infinity of time or eternity, this only tells of the limitations of our understanding.

Crusius then returns to the notion of possibility. He suggests that the criteria of possibility earlier considered - that of non-contradiction - delineates only the realm of ideal possibilities or possibilities in thought. A more substantial form of real possibility, he continues, refers to things that do not yet exist. In other words, such a real possibility will at some point come into existence, and its possibility outside thought is guaranteed by causes that will eventually make the possibility actual. Crusius notes that such real possibility is dependent on the existence of something, namely, its cause. Thus, if nothing exists, nothing will be possible.

When the realm of possible is restricted, the realm of impossible grows. Thus, not just contradictions make something impossible, Crusius explains, but anything that prevents something to have causes that would make them existent. Crusius refers especially to the principles he has inherited from Hoffmann that combination or separation of concepts we cannot make are impossible, barring the possibility that our incapacity is due just to our limited understanding.

We already saw earlier a few reasons why the principle should not hold, such as a revelation by some more perfect spirit. Here Crusius outlines a few further reasons, which he has again inherited from Hoffmann. Firstly, although we could not separate something from a negative concept, this might not be true of a more perfect being, for instance, although we cannot abstract things from limits, another being might be able to think infinities. Secondly, although we could not combine things, this might not be impossible, if we are dealing with immaterial entities.