I would like to pose a set of fundamental questions regarding the constraints we can place on the structure of our concepts, particularly as revealed through language. I will outline a methodology for the construction of ontological types based on the dual concerns of capturing linguistic generalizations and satisfying metaphysical considerations. I discuss what “kinds of things” there are, as reflected in the models of semantics we adopt for our linguistic theories. I argue that the flat and relatively homogeneous typing models coming out of classic Montague Grammar are grossly inadequate to the task of modeling and describing language and its meaning. I outline aspects of a semantic theory (Generative Lexicon) employing a ranking of types. I distinguish first between natural (simple) types and functional types, and then motivate the use of complex types (dot objects) to model objects with multiple and interdependent denotations. This approach will be called the Principle of Type Ordering. I will explore what the top lattice structures are within this model, and how these constructions relate to more classic issues in syntactic mapping from meaning.