Concepts are highly theoretical entities. One cannot study them empirically without committing oneself to substantial preliminary assumptions. Among the competing theories of concepts and categorization developed by psychologists in the last thirty years, the implicit theoretical assumption that what falls under a concept is determined by description (“descriptionism”) has never been seriously challenged. I present a nondescriptionist theory of our most basic concepts, “substances,” which include (1) stuffs (gold, milk), (2) real kinds (cat, chair), and (3) individuals (Mama, Bill Clinton, the Empire State Building). On the basis of something important that all three have in common, our earliest and most basic concepts of substances are identical in structure. The membership of the category “cat,” like that of “Mama,” is a natural unit in nature, to which the concept “cat” does something like pointing, and continues to point despite large changes in the properties the thinker represents the unit as having. For example, large changes can occur in the way a child identifies cats and the things it is willing to call “cat” without affecting the extension of its word “cat.” The difficulty is to cash in the metaphor of “pointing” in this context. Having substance concepts need not depend on knowing words, but language interacts with substance concepts, completely transforming the conceptual repertoire. I will discuss how public language plays a crucial role in both the acquisition of substance concepts and their completed structure.