sentences:  Meaningful predicates have both "extension" and "intension", so predicates of predicates get their meanings from at least two sources of information, namely, the classes of relations and the qualities of qualities to which they refer.Considerations like these tend to generate hierarchies of subject matters, extending through what is traditionally called the "logic of second intentions", or what is handled very roughly by "second order logic" in contemporary parlance, and continuing onward through higher intensions, or "higher order logic" and "type theory".Peirce arrived at his own system of three categories after a thoroughgoing study of his predecessors, with special reference to the categories of Aristotle, Kant, and Hegel.