If in the previous chapter Crusius dealt with the application of sensations and experience, he now turns his attention toward abstract ideas, which due to their non-concreteness are prone to confusion and might even not correspond to anything existent. Thus, he argues, abstract concepts should always be defined. By definition Crusius means a method of making objects of an abstract concept distinguishable from other objects. Definition needs therefore not reveal the fundamental essence of a thing. Still, it is something more than mere description, which just collects some distinctly abstracted predicates of a thing, which still are not sufficient to distinguish the thing from others, except perhaps in some limited context.
Crusius goes on to indicate some basic rules about definitions. Definition, he says, should contain only concepts that belong to the defined object always and are thus logically essential to it. This means that the concepts contained in a definition are either genera or propria, which in case of definitions are usually called specific differences. Furthermore, Crusius continues, these logically essential concepts can be either essential as such to the object defined or just natural, which then have to be used sparingly and always with the appropriate restriction that they belong to the object regularly and are lacking only in extraordinary cases. Some of the logically essential concepts, he adds, are essential to the object in themselves, but others only when we suppose the existence of the world.
Parts of a definition, Crusius explains, must be more distinct than the defined object, in other words, obscure concepts should not be defined by other obscure concepts. Especially metaphors and circular definitions should be avoided. Even so, he admits, the parts of the definition need not be fully distinct, just more distinct than the object defined. Crusius adds also that a definition must be adequate in the sense that it contains all the same individuals as the defined concept and nothing more.
Crusius divides definitions according to their purpose: the purpose of a nominal definition is to explain what a word means through an abstract idea separated into its constituents, while the purpose of real definition is to transform an obscure or at least concrete concept into an abstractly distinct and adequate concept. A clear consequence of these explanations is that the same definition can be nominal and real, depending on its purpose.
Starting with nominal definitions, Crusius notes that they should be used to define something possible, because it would be of no use to have a word that refers to something that could not be thought. Indeed, he adds, nominal definitions should in general be useful, which implies that they should not give occasion to error and confusion and should conform as much as possible to ordinary language Crusius emphasises also that nominal definitions can be used only to deduce nominal conclusions, how a word can or must be used.
Crusius divides real definitions into ideal definitions, which define only something possible that need not exist, and real definitions in the strict sense, which transform a concrete idea of an existing thing into an abstract and adequate idea. Beginning with ideal definitions, he notes that they are not to be confused with nominal definitions, which define only a name of something. Still, they are also not yet real definitions in the strict sense, because they cannot be used to deduce what really is or is not, but only hypothetical conclusions: what must be affirmed or denied when we presuppose the existence of objects corresponding to this concept. Of course, if we show that there exists something agreeing with the ideal definition, we have made it a real definition. Crusius also notes that in pure mathematics ideal definitions are always real definitions, since this discipline investigates abstract possible magnitudes with their properties and relations.
Real definitions in the strict sense, finally, are divided by Crusius into fundamental or first concepts and deduced or further definitions. By a first concept he means a definition that we can know without presupposing a proof from another definition. Crusius emphasises that a first concept is thus first only for us and need not be a natural ground for all other properties of a thing. Indeed, he adds, there could well be many first concepts, depending on what characteristics is our starting point for abstractions.
It depends on the thing in question where we should find their first concepts, Crusius explains. With physical, non-artificial entities (e.g. natural bodies and souls), the crucial question, according to him, is whether they are sensuous or not: with the former, the sensations provide us enough first concepts, while with the latter, we must just begin with the most undetermined idea. With artificial entities, the first concept is provided by their method of generation, and if they particularly are mechanical entities, the first concept is given by their immediate purpose and the structure required for this purpose. With moral entities (e.g. obligations and rights), Crusius notes, their first concept is defined by their purpose. Finally, he concludes, God and their activities can be defined only by symbolical concepts, indicating negatively what they are not, or pointing positively to their effects and to very indeterminate abstractions common to all things.
An important point for Crusius is that we should always demonstrate that a first concept does really refer to objects beyond our thought (if we couldn’t do that, it wouldn’t be a real definition, but only nominal or ideal). He does explain that in some cases we might not be speaking of physical, but of moral existence, in other words, that something should be the case (this is evidently what we should prove of moral entities). In any case, the proof can happen a posteriori from experience or a priori from connections between concepts or grounds.
The final type of real definition – that of further or deduced definitions – includes, Crusius says, many useless explanations that really add nothing to the first concept and even confuse what is meant with them. He delineates two useful kinds of deduced definitions, namely explanations of the essence of things, which serve to uncover the fundamental nature of the thing defined, and characteristic definitions, which help to distinguish individuals belonging to the defined class from others.
Starting with the explanations of the essence of things, Crusius notes that they might provide the physical ground – fundamental forces that constitute the defined thing – or the moral ground – explanation why the defined thing should or is allowed to exist (the traditional explanation why God allows the existence of sin is of this kind). In searching for these explanations, he adds, we might either start from a sensuously given first concept and then move to the grounds explaining these sensuous properties, or then we can start from an undetermined first concept of a non-sensuous or a moral thing and determine it in more detail.
Ending his discussion with characteristic definitions, Crusius explains that they are required, whenever the first concepts do not give us enough criteria for deciding how to apply these concepts. Examples of such characteristic definitions are criteria for deciding when something is true or false, criteria for deciding when some law applies, or criteria for recognising the existence of non-sensuous entities from their effects.
