Last time we saw that thoughts were for Wolff effects in soul connected with a consciouness of oneself and that sensations or perceptions as consciouness of things were a subspecies of thoughts. A concept, then, is according to Wolff also something in thought, namely, a representation (Vorstellung) of something in thoughts. Wolff's definition thus points out two essential characteristics of a concept: it is a mental event and not, say, an abstract ontological structure, and it is connected to an object that it represents.
Otherwise Wolff allows for quite a variability in concepts. The object of the concept or something represented (Sache) might be either concrete or abstract. Furthermore, the means of representation might differ e.g. from concrete images to mere words. Hence, both a mental image of the Sun and a verbal explanation of virtue fulfil the criteria of Wolffian concepts.
What I find interesting is that Wolff appears to nominate perceptions as the primary causes of our concepts. Sure, Wolff does recognise other ways to generate new concepts, such as abstraction or variation of characteristics in known concepts. Yet, all these other methods appear to demand that we already have some concepts from which to produce new concepts, while only perceptions can create concepts without the help of old concepts. Wolff leaves hence no room for the so-called innate ideas, which Locke had famously argued against. I shall probably comment on this when I shall discuss the relationship of Wolff's philosophy to empiricism.
Wolff does not just define, but also classifies concepts into a hierarchy of more and more perfect kinds of concepts. Wolff's classification was probably not original, but based on the tradition of logic preceding him. Still, Wolff was at least the first to translate these terms to German. As the German logicians used the essentially same classification and even Hegel comments on it, I shall introduce Wolffian hierarchy in more detail.
Descartes had spoken of clearness and distinctness as criteria for the reliability of perceptions, but as far as I know, he had never properly explained what he meant by these terms. Well, Wolff does that for him. Clear (klar) concepts are for Wolff such that they allow us to recognise things that they represent. If a concept is worthless for this purpose, it is obscure (dunckel). Thus, Wolff suggests, if we have seen a plant in a garden, but we cannot say whether we have seen that same plant in another place, our concept of the plant is obscure. Although the difference between obscure and clear concepts appears simple, Wolff suggests that there is actually a continuum of possible levels of clearness. Thus, we might be able to distinguish the forementioned plant from a dandelion, but not from a rose.
In a distinct (deutlich) concept, the level of clarity is so high that we can state what Wolff calls Merckmahle, by which the thing represented by the concpt is recognised. Not all clear concepts are distinct, which is proved by the case of colours. Primary colours are undoubtedly quite clear concepts for anyone with a normal vision, as we have no problem of separating e.g. blue from red. Still, we cannot really say what distinguishes blue from red, apart from one being blue and other red.
The notion of Merckmahle is somewhat undistinct itself, although it was widely used in the later German logical tradition and even by Kant. Yes, we do know that they help to distinguish things, but it is unclear what they are. Now, Wolff says in passing that Merckmahle are nothing more than new concepts. Thus, a distinct concept is such that can be distinguished from other concepts through yet another concept, just as we can distinguish a triangle from other polygons through the concept of three that characterises the number of the angles of a triangle. In other words, a distinct concept can be defined.
The definition in question might be either nominal or real. We have earlier seen how Wolff distinguishes the two: nominal definitions merely analyse the meaning of a phrase, while real definitions tell how a thing described by such a phrase can be generated. It is probably the latter sort of definition Wolff is referring to, when he indicates microscopes as a tool for making our concepts distinct - microscopes cannot be used to analyse the nominal meaning of a word, but they might come in handy, when we want to know what a thing is made of.
The further stages in the hierarchy of concepts merely add more Merckmahle to a concept. In a full (ausführlich) concept, the given Merckmahle allow us to recognise the thing represented in all possible cases. That is, a mere distinct concept characterises a thing, but a full concept will truly define and identify it. Finally, in perfect (vollständig) concepts even the Merckmahle are clear and distinct concepts, that is, even the components of the definition can be further defined.
Wolff is keen to advertise that his writings consists of perfect concepts, while the concepts of his followers are often not even full – like Cartesian concept of matter, which fails to distinguish matter from mere space – and in some cases they are outright obscure. Wolff also provides a number of examples of full concepts. Some of them are rather amusing, like the concept of rain as many drops of water that fall side by side and one after another from a cloud through air. Others are nowadays quite controversial, like Wolff's concept of marriage as a union between a man and a woman for the sake of conceiving and raising children.
Now, it is not difficult to see that just like the notion of clarity, the notion of perfectness comes also in grades, because we can always ask whether the constituents of the definition can also be defined. Thus, a concept that is perfect enough for mathematical purposes might still require more analysis from the viewpoint of ontology. The natural question is then whether the perfectness has any limit, that is, whether there are concepts that can only be clear, but not distinct. Wolff suggests that there must be, in case of both nominal and real definitions. In nominal definitions the limit is reached when we find words that are undefinable, for instance, when we cannot explain anymore what green is, except by pointing out green objects. In case of real definitions, on the other hand, the limit is reached when we find things that cannot be generated – in effect, for Wolff, God.