Crusius divides existential subordination into five classes, corresponding to kinds of abstraction. Firstly, he says, we have external subordination, where one idea or concept is externally abstracted from the other, like a place where a person lives is abstracted from that person. Secondly, we have metaphysical subordination, where an abstraction subsists in something concrete, like a figure in a body. Thirdly, we have mathematical subordination where an abstraction relates to something concrete as its integral part, being either continuous or discrete quantity, like 10 is a part of 100. Fourthly, we have a qualitative or physical subordination, where an abstraction relates to something concrete as a part that is not regarded as a magnitude or figure, but as a substance or a physical quality. Finally, we have logical subordination, where one individual is comprehended under another, like a human is related to a substance.
Crusius takes a closer look at logical subordination, because all other cases of existential subordination can be turned into logical subordination. Thus, he says, one should investigate whether logical subordination is such in itself or only contingently: for instance, when we say “human has a head”, this is not a case of logical subordination, but we can turn it into a logical subordination by saying “human is something that has a head”. Furthermore, Crusius is adamant that the difference of various kinds of subordination is important and therefore other kinds should not be transformed into logical subordinations: if I say that a soul has an understanding (metaphysical subordination), I do not mean that soul is an understanding (which would be logical subordination, if it were true).
What the elements of logical subordination or logical abstractions are, Crusius explains, is representations of a set of individuals ignoring their individuality and showing them as similar: in other words, they are names of similar individuals. Such a logical abstraction, he adds, does not designate only a part of a concrete individual, but the whole individual. Furthermore, although only a part of its properties is selected to designate the whole, these properties are not regarded as independent, but as attached to a subject: for instance, Crusius suggests, in a concept of a scholar one thinks of a subject according to a certain quality, but when I say scholarship, I regard the same quality in abstraction from any individual subject. Hence, I can say that many people are scholars, but not that they are scholarships.
Crusius notes that logical abstraction can be regarded in two ways. Firstly, it can be regarded essentially or materially in regard to its essential content, that is, in regard to ideas thought under it. Secondly, Crusius adds, it can be regarded in relation to extension, that is, in regard to the set of individuals, which can be named by it. The more extensive a logical abstraction becomes, the less ideas one thinks in it, since otherwise it couldn’t name so many things that are dissimilar in many respects.
Logical subordinates, Crusius continues, either comprehend all individuals belonging to each other or then one or the other is more extensive than the other. In the latter case, he continues, the more extensive is called genus, while the other must then be species. A genus, Crusius divides, is either an essential genus by itself or contingent genus by accident. In the first case, all individuals subordinated to the genus belong to it essentially, even when regarded without particular purpose, as when substance is a genus of humans. In the second case, he compares, some contingent property is chosen arbitrarily and changed into a genus: for instance, when I say that all scholars are either sick or healthy, this does not mean that all sick people would be scholars, but only that sick individuals known to be scholars are scholars.
Crusius goes on making distinctions by noting that a genus is either a distant one, where there is always a possibility for an even closer genus, or a closest or proximate genus, where there isn’t such a possibility. Since the series of distant genera cannot be infinite, Crusius argues, there must also be the highest genus (thing in the most extensive sense of the word), and in relation to it all others are middle or subaltern genera.
Genus can be either a pure or an impure abstraction, Crusius muses. Furthermore, it is either homogenous or heterogeneous concept. A homogenous concept belongs to all its species or individuals in a completely same sense, for instance, human is animal in the same sense as dog, because both have body and soul. A heterogenous concept, on the other hand, does not belong to all its species or individuals in a completely same sense. Thus, although a certain similar part of concept might be a reason why the concept belongs to species or individuals, some species or individuals might add new circumstances and modifications of the same general concept: for instance, snowing in winter is said to be possible because of natural causes, but golden mountain is said to be possible, because it contains nothing contradictory.
Crusius notes that what holds of a genus, must hold also of species and individuals under it. He makes this statement more accurate by noting that its message concerns actually just pure genera: others it concerns only under the conditions, in which they are genera. Crusius also insists that before applying heterogenous genera to some individuals, these genera should be divided and their heterogeneity should be recognised, because otherwise one could apply to some of its individuals what could be said only of others – for instance, golden mountains could be called possible without explaining what type of possibility is meant.
Species is generated from a genus by adding an accident to the concept of genus. This accident, Crusius explains, can be either something that is in itself a determination, like the sameness of all sides in a triangle, or something that is made contingently into it, like clothes in a human being. The accident in question, Crusius continues, can be something that is found in all individuals belonging to it, like reason in a soul, or it is an external abstract, like time.
Crusius divides accidents into proper and common accidents. A proper accident does not belong to all existing individuals generally or at all times, but still cannot belong to individuals or species under other genera: in this sense, Crusius insists, virtue is a proper accident of entities with reason. A common accident, on the other hand, can also belong to individuals of other genus, just like being sick is a common accident of humans, because other beings beyond humans might be sick.
When a species is made by adding an accident to a genus, Crusius explains, either to each species is added another positive accident (say, when thinking and moving are suggested as species under the concept of action) or it is added only to one, while others are assumed to lack it, just like in the case of passive and active matter.
Crusius notes finally that an accident might imply in individuals no other difference but such that consists only in another state of the essence and depends on the different grade and direction of its forces and on the different relations of things toward another. He calls such an accident natural, because nature itself has made it into an accident, like speed or slowness of movement. On the other hand, Crusius points out, the accident might not be enough for distinguishing subordinated things: this he calls an arbitrary accident.
