After definitions, Crusius moves on to divisions, in which a more extensive logical concept (genus) is separated into narrower logical concepts contained in it (species and in rare cases even individuals) adequately, in other words, in such a manner that all individuals of the genus belong to one and only one of the divided species. Crusius is clear to distinguish division from mere distinction of concepts in general, which could be applied also to concepts that are not logical (say, when distinguishing cause from effect). He also points out the obvious fact that the divided concept is more undetermined and the narrower concepts go through all the possible determinations that could be attached to the divided concept.
Just like definitions, Crusius divides divisions into nominal and real kinds. By nominal division, he means an account of different meanings an ambiguous word has. In addition to this definition, nominal divisions are not of that much interest to Crusius, who deals more with real divisions, where species or individuals contained in an abstract concept are separated from one another. Crusius notes that real divisions come with four important elements: firstly, we have divided and undetermined general concept, secondly, the narrower concepts, into which the general concept is divided or determined, thirdly, the difference between the different members of the division or the narrower concepts, and finally, the point of division in the undetermined concept, to which the narrower concepts or separated species relate as further determinations. Crusius states that this point of division can be an existential or causal abstraction, and in the former case, an external or internal abstraction.
Crusius points out many reasons why we need to make divisions, first of them being that division brings abstract concepts closer to practical applications. Furthermore, he adds, if we did not have a clear idea of a hierarchy of a general concept dividing into many species, we would have to make do with mere individuals, with no idea of their commonalities, thus being deprived of many important truths. Yet, the main use Crusius envisions for divisions lies in their application in disjunctive deductions.
Crusius goes through the most prominent classifications of real divisions. Thus, real divisions are either divisions of logical oppositions or divisions of real oppositions and also either divisions of contraries or divisions of contradictories. Furthermore, Crusius notes that if we compare divisions applied to the same general concept, these alternative divisions can be subordinated – one division applies the other division and then divides its members further – or coordinated, that is, made according to completely different schema.
Besides these classifications, Crusius hands out some rules, such that the point of division should optimally be essential to the divided general concept and that in choosing from different alternative divisions, we should consider what is the most useful of them. Finally, he shares some methods for finding divisions, such as following experiences of differences or going through possible determinations and causal connections of the general concept to be divided.
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