In a couples of posts ago, I compared Wolffian things or possibilities with coherent lists of predicates or determinations, as Wolff calls them. Now, he also mentions the possibility that such a thing would be fully or in every possible manner determined. Wolff doesn't really explain what this means, but one might put it like this. Think the aforementioned lists as answers to multiple choice questionnaires, in which one can, with each question, choose one among many possibilities or leave the question unanswered. Clearly, there is the distinct possibility that all the questions of the questionnaire would be answered – then the answers would describe a fully determined entity.
This simile undoubtedly hinges on the assumption that all possible predicates in such lists could be ordered in the form of such a questionnaire – in effect, a space of possible predicates a thing can fulfill. Wolff himself just innocently accepts this possibility, and I shall also not pursue the question whether the assumption is as innocuous as it looks. Indeed, there is no need, as the notion of fully determinate list of predicates could be characterised even without the notion of such a questionnaire. Just think what adding a new predicate to a fully determined list would do: either it would contradict some combination of the other predicates in the list or then be deducible from such a combination. One need then only to take this characteristic as the defining feature of a fully determined thing.
Being fully determined is then what defines an individual thing, according to Wolff. In addition, being fully determined is also a necessary characteristic of all actual things, and indeed, one rarely sees e.g. otherwise featureless birds flying around. In effect, Wolff is here showing his nominalist leanings. Then again, Wolff clearly is not committed to the idea that full determination would define actuality, as some of his successors were to do. This leaves open the possibility of merely possible individuals that are not actualised (say, a person just like me, except with red hair).
Now, Wolff notes that one need not list all the predicates of an individual to define him. Just think of a triangle with all angles equal – we do not need to tell anymore that its sides are also equal, because this follows from the equality of its angles. Clearly then we could have a minimal set of predicates defining an individual entity – indeed, we could probably have many of them or it wouldn't be a unique set or list (for instance, in case of the triangle, the implication goes both ways, so we could as well begin with the equality of the sides). Such a minimal list would then define what could be called an individual essence, but which Wolff prefers to call by the medieval name haecceitas.
Just as we can distinguish those questionnaires that are fully completed, we can also talk about incomplete questionnaires or lists of predicates that can still be consistently augmented by truly new predicates. If a complete determination defined individuals, incomplete determination then defines genera and species. Wolff apparently doesn't use the modern idea of genera and species as sets of individuals or extensions of certain concepts. Instead, Wolffian genera might be called ”incomplete individuals”: we add some determinations to our would-be individual, but leave it otherwise hazy and vague. Of course, such a vague entity cannot really exist, just like there's no generic triangle, but it might be actualised in various individuals that have the exact properties this vague object is supposed to have. We might say the generic entities are fictional, but they are useful for bringing out the various groupings of individuals. Such a vague entity then has some essence, just like individual had its haecceitas: essence is similarly a minimal list of predicates for such a generic entity.
The genera and species or universals form then a hierarchy, arranged according to their level of determination. The ultimate bottom of this hierarchy is formed by individuals, the only truly actual aspect of the hierarchy. Furthermore, Wolff suggests that in well-planned hierarchy the genera correspond not just with some accidental combinations of characteristics, but reveal how the things are produced. In other words, individuals corresponding to same generic entity should have a similar genesis, just like two humans share some points as to how they have been generated. Furthermore, belonging to a certain genus should determine not just some determinate characteristics of a thing, but also all the possible manners how the thing can be modified.
So much for individuals, next time we shall consider Wolff's notion of necessity.