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

Concepts of simple and complex substances were of great interest to Wolffians, being one of the primary divisions of substances, and Crusius seems eager to show where Wolffians wen’t wrong with them. He firstly notes that just like the concepts of part and whole, on which the two former concepts are based on, can actually mean very different things. Starting with the parts, these can mean, Crusius says, any group of things we can represent as forming also a one thing, which then is the respective whole. Furthermore, these parts can be actual or such that they can be separated elsewhere than in our thoughts, but they can also be mere thought parts, which can be distinguished in our thinking, but not really separated.

Simple is then for Crusius something that has no parts - in some sense, while complex is something that has parts - again, in some sense. Since the notion of parts was already twofold, this same duality continues with the notions of simple and complex: something may be simple or complex just based on mere thoughts, but also based on something outside our thought.

Even in case of actual simplicity, Crusius notes, there are various levels of simplicity. The epitome of simplicity, he thinks, is God, who is not just a simple substance - that is, something, which cannot be separated into further substances - but also has a simple essence in the sense that no property could be removed from his essence. This is not always the case, Crusius says, because substance can be simple, like a human soul, without having a simple essence. Even a complex substance, like air, Crusius notes, is simpler than, say, a human body, because the former has only integral parts - parts that all have the same essence - but no physical parts - parts that have a different essence from one another.

Crusius also notes that it is a different thing, if something is simple as such or has nothing separable in it, than if something is simple on the condition that the current world exists, Crusius notes that we cannot really distinguish between the two cases and neither can any finite being, but God might be able to do it.

Every force is in some subject, Crusius insists, because no subjectless forces could be thought of. On this basis Crusius argues that in case of complex substances, their force must be determined by forces of their parts. Crusius then concludes that if a complex substance wouldn’t ultimately consist of simple substances, the constituent forces would have no immediate subject where to subsist, which he thinks is absurd. Despite the seeming complexity of the argument, it appears to just assume what it sets out to prove: that the existence of a complex thing must be based on the existence of simple things.

Crusius is especially keen to distance his notion of a simple substance from a mathematical understanding of simplicity. Mathematics, he says, considers only abstract magnitudes, not other determinations of things. In other words, he rephrases, mathematics is only about the concept of space and its possible divisions. Thus, it was natural for mathematicians to assume the existence of points, which should have even no parts that could be thought of as being outside one another. Yet, Crusius states, no true simple substance is simple in the mathematical sense, but is spatial - they just cannot be physically divided further.

Crusius goes thus straight against the Wolffian notion of elements, which are more like non-spatial forces. If we would accept such non-spatial substances, how could we account for spatial matter being generated from them, especially as any concrete matter would require an infinite amount of them? Furthermore, he continues, we couldn’t even say how such pointlike substances could touch one another, as there are always further points between any two points.

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

From the very start of metaphysics, in the book with that name by Aristotle, the concept of one was regarded as an important topic. Thus, it is no wonder that Crusius would consider it. Indeed, he thinks that we have many different notions of one, distinguished by what concepts they are opposed to. First of these is the concept of one thing in contrast to several things. This concept, he insists, cannot really be defined, but can only be exemplified. In essence, a thing, no matter what it is, is always one or a unit, because we can think what it would be like, if it were multiplied into several similar things.

Another concept of one, Crusius continues is that of something unified in contrast to what is disunified. By unification Crusius means a relation where things are so intrinsically related under certain conditions that when one is assumed to exist, the other must be assumed to exist also. Unification can come in many forms, the primary ones of which are unification merely in our thoughts and unification in real existence. Crusius notes that we cannot really know all the subdivisions of unification and mentions only a few examples, such as metaphysical unification of one thing subsisting in another (e.g. property in a substance), existential unification of two perfect things connected so as to become inseparable, such as a hand and a torso, and moral unification where two persons are united by having common goals. In any case, Crusius emphasises, all cases of real existential unification are ultimately based on causal interactions. Thus, he insists that Leibnizian pre-established harmony would be no real unification of body and soul.

A third notion of one is connected with the notion of identity. Crusius defines the concept of identity as the opposite of difference, where two things are different if in one is something that is not in the other - Crusius notes in passing that this notion of “not” or denial is again something simple, which we cannot really define. Identity as the denial of difference can then be just similarity, where things share something, but also identity in a strict sense, where one thing - here is the connection to one - is represented through two concepts, of which one is found to contain nothing that wouldn’t be contained in the other.

Crusius considers the question, when we can know that the objects of two concepts are identical. The criterion he suggests is that one should be able to replace what is thought in one concept with what is thought in the other without any consequence. He also emphasises that mere same essence is no true criterion of identity, since we could have substances that are just numerically different, that is, that would agree in their absolute properties, but would be e.g. in different spaces at the same time.

Although Crusius' definition of identity might seem rather rigid, he does admit that identity can fluctuate according to the viewpoint chosen. For instance, when we are considering whether things at different points of time are the same thing, we might get different results depending on what we focus on: corpse is in a sense different from a living body – they have different essence - but in another sense they can be identical, because they share the same matter. Then again, if an essence of a thing consists of a certain relations of parts, the thing can remain identical, despite its parts being replaced by different, but similar parts.

Crusius chooses at this point to give a list of simplest concepts. This list is a development of a similar one from Hoffmann, and we could consider it to be a precursor of Kant’s list of categories. Crusius' list contains the following concepts:

• Subsistence, that is, the relation between a property and its subject
• Relation of one thing being spatially within or outside of another thing
• Succession
• Causality
• Relation of one thing being figuratively outside of another thing, in the sense of not being its part, property or determination
• Oneness in opposition to plurality
• Relation of things being unified
• Thing’s being somewhere in space.

Crusius also clarifies further the relation of these simple concepts to the seemingly simple concepts of sensation, like colours. Crusius’ idea is that while the above mentioned simple concepts are the ultimate result of analysing more complex concepts for any understanding, it is we humans who are incapable of analysing sensations just because they are caused by unknown activities affecting us in a confused manner, so that we cannot distinguish these causes from one another. Crusius also distinguishes the simple concepts from indeterminate, symbolic concepts, which we cannot really think, but which we can only represent by saying what it is not and what its relations to other things are.