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.
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