 Because Kant’s terminology is not always consistent, it is difficult to provide a definitive characterization of the various types of purposiveness. However, the following simplified scheme may serve as a guide. The notion of purposiveness is divided in the first instance into subjective and objective purposiveness. Both kinds of purposiveness are in turn divided into formal and material (or real). The most important kinds of purposiveness for the concerns of the Critique of Judgment are (i) subjective formal purposiveness and (ii) objective material purposiveness. Subjective formal purposiveness corresponds both to the “aesthetic” purposiveness displayed by beautiful objects (or by the activity of our cognitive faculties in the perception of them) and to the “logical” purposiveness displayed by nature as a whole in so far as it is comprehensible to human beings (see  Section 3.2).  Objective material purposiveness corresponds to the purposiveness displayed both by organisms qua “natural purposes” (see  Section 3.3)  and by arrangements of natural things or processes which stand to one another in means-end relations (see  Section 3.5).  But Kant also allows for subjective material purposiveness, which is the kind of purposiveness exhibited by an agreeable object, i.e., one which pleases our senses (FI VIII, 224); and for objective formal purposiveness, which is exhibited by geometrical figures in virtue of their fruitfulness for solving mathematical problems (§62).