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.

Joachim Darjes: Elements of metaphysics 1 - Connecting substances

While in previous post I discussed Darjesian notions of entity and substance, when regarded in abstraction from other entities and substances, now we shall see what happens when entities and substances are connected to one another. Darjes notes that these connections fall into three general classes, depending on whether the connection exists between mere entities, between both mere entities and substances or between substances. In case of the first kind of connection the things connected are regarded as just being impenetrable to one another. Example of a such a connection would be placing many entities into a same space so as to form a figure.

If in addition to or in place of mere entities substances are added to the connection, Darjes notes, we get forces to the equation. Such connections involve either the existence of substances or then their states – for instance, existence of certain substances might be connected with a state of one substance. In other words, such substantial connections concern various interactions between substances, for example, when one substance acts upon a passive substance or when one substance removes obstacles stopping some substance from acting.

All connections involving mere entities are extrinsic in the sense that it doesn't affect entities if we e.g. arrange them to form a figure. Thus, these connections are completely contingent. One might think that the case might be different with substantial connections, but Darjes notes that this is not so – substances can exist independently of one another, so there is no necessity that e.g. a substance affects another substance. Because no connections between entities or substances is necessary, Darjes says, these connections must ultimately be dependent on some necessary entity.

A particular type of connection Darjes mentions is the relationship between cause and what is caused. Like always, Darjes makes interesting divisions rarely seen in previous Wolffian philosophy. Thus,he notes when discussing cause or caused, one can firstly regard cause and caused as mere subjects – that is, as a material cause and caused – secondly as containing a reason for the possibility of something or having a reason of possibility in some other entity – this is what Darjes calls active/passive causating reason – and finally, as containing or having in something else a reason for actuality – active or passive causality. Like many other Wolffians before him, Darjes goes into great lengths in describing various causal notions, such as principal cause and instrumental cause or mediate and immediate cause, and we need not follow him in such a detail.

Just like almost all Wolffians thus far, Darjes defines the notion of space through the spatial relations an entity could have. Indeed, spatial relations are based on certain connections between entities, in which one entity cannot take the place of the other entities. Such space is then no true entity, but merely an abstraction out of real entities and their relationships. While spatial relationships are completely external to the entities or substances, if one adds activities to the equation, the connection becomes at least more internal. Darjes speaks of presence, by which he means the factor of one substance affecting another – the more a substance affects another, the more present it is to that other substance. Darjesian presence is then a much stronger relationship than mere spatial closeness – if one unites entities by bringing them close to one another, the union is merely external, while a union involving substances being present to one another is internal.

Before moving to more particular parts of metaphysics, Darjes finally considers the notions of infinity and finity, which he defines simply through the notion of perfection – finite entity is such that something can be more perfect than it, while an infinite entity is as perfect as is possible. The finity of an entity does not mean it couldn't be also perfect in some measure. It just isn't completely perfect and all perfection it has must belong also to the infinite entity. It is then immediately clear that all passivity, incompleteness and possibility of non-existence are signs of finity.

Already at this place in metaphysics, Darjes introduces Wolffian aposteriori and apriori proofs of God's existence, although he is, of course, not yet speaking of God. He notes, firstly, that since all finite entities are contingent, they must ultimately depend on a necessary infinite entity. Hence, if finite entities exist, an infinite entity surely must exist also (aposteriori proof). Since it is clearly possible that a finite entity would exist, an infinite entity must also be a possibility. Because infinite entity can be only impossible or necessary, it must then exist necessarily (apriori proof). We see here a similar dual role played by the two proofs as in Wolff's theology, the difference being that Darjes has to assume only the possibility of something finite.

Infinite and finite form then the major division of entities. Infinite entity is essentially unique, so no further division of that species is possible. Finite entities, on the other hand, can divide into further subspecies, depending on whether they are simple or complex.

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.

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.