Both Leibniz and Wolff divided cognition into two kinds: intuitive and symbolic. I've had some difficulties clarifying to myself how these two relate to the progression from sensations through imagination and memory to intellectual faculties of understanding and reason, so it feels a bit helpful to see what Bilfinger has to say about the issue.
The basic definitions deriving from Leibniz are pretty straightforward: intuitive cognition is caused by attending the nature of things directly, while symbolic cognition is connected to things only via mediation of signs. Leibniz then had supposed that composite concepts are usually cognized symbolically: after all, analysis of concepts into its constituents happens usually through signs, e.g. if I define square as a rectangle with all sides equal, the definition would be expressed verbally. Primitive concepts, on the other hand, might be cognized either intuitively or symbolically: e.g. point could be defined either by looking at points or by saying what one means when speaking of a point.
Furthermore, all distinct concepts – that is, concepts that can be analysed into clear concepts or into concepts through which we can distinguish objects – must be based on intuitive concepts. In other words, if we had an analysed concept, in which we would know all the constituent concepts only through further linguistic explications, somewhere along the line we would have to use a circular explication, which clearly wouldn't help to distinguish any objects. Thus, an analysis or explication that is successful should at some point meet some cognitions which are directly connected to things. Intuitive cognition is therefore a necessary ingredient of good cognition: if our cognition is not grounded on things, it might well deteriorate into a shamble of contradictions and meaningless expressions.
From the perspective on what Leibniz has to say, intuitive cognition is essential to well-founded science. What good is symbolic cognition then? Bilfinger answers by turning into Wolff's account. While symbolic cognition cannot by itself be a source of true cognition, it can be used in inferring truths from known truths. In particular, symbolic cognition is required whenever we want to move to general truths about classes of objects: we cannot literally be effected by any class of objects, because classes are not real entities. Thus, symbolic cognition makes it also possible that the Leibnizian ideal of an algebraic art of thinking could be one day found. In addition, symbolic cognition is also useful in transmitting cognition from one person to another: we cannot share intuitions, but we can share signs and symbols.
Interesting here is how the division of cognition into intuitive and symbolic kinds corresponds better with Kantian division of sensibility/intuition vs. spontaneity/understanding than Wolff's own division of sensations and concepts. Indeed, Kant's famous statement that intuition without understanding is blind, while understanding without intuition is empty, could be easily translated into the Leibnizian-Wolffian statement that intuitive understanding by itself is blind, because it cannot be generalized, while symbolic understanding by itself is empty, because it fails to connect cognition with actual things. Of course, Kant doesn't call his intuitions and concepts alone cognitions, but reserves this name only for the result of the interplay of the two.
So much for Bilfinger's take on Wolffian psychology, next time I'll discuss his notes on Wolffian natural theology and especially the problem of evil.