This study is a prolegomenon to a formal theory of the natural growth of conceptual and lexical fields. Negation, in the various forms in which it occurs in language, is found to be a powerful indicator. Other than in standard logic, natural language negation selects its complement within universes of discourse that are, for practical and functional reasons, restricted in various ways and to different degrees. It is hypothesized that a system of cognitive principles drives recursive processes of universe restriction, which in turn affects logical relations within the restricted universes. This approach provides a new perspective in which to view the well-known clashes between standard logic and natural logical intuitions. Lexicalization in language, especially the morphological incorporation of negation, is limited to highly restricted universes, which explains, for example, why a dog can be said not to be a Catholic, but also not to be a non-Catholic. Cognition is taken to restrict the universe of discourse to contrary pairs, splitting up one or both of the contraries into further subuniverses as a result of further cognitive activity. It is shown how a logically sound square of opposition , expanded to a hexagon (Jacoby 1950, 1960, Sesmat 1951, Blanché 1952, 1953, 1966), is generated by a hierarchy of universe restrictions, defining the notion ‘natural’ for logical systems. The logical hexagon contains two additional vertices, one for ‘some but not all’ (the Y-type) and one for ‘either all or none’ (the U-type), and incorporates both the classic square and the Hamiltonian triangle of contraries . Some is thus considered semantically ambiguous, representing two distinct quantifiers. The pragmaticist claim that the language system contains only the standard logical ‘some perhaps all’ and that the ‘some but not all’ meaning is pragmatically derived from the use of the system is rejected. Four principles are proposed according to which negation selects a complement from the subuniverses at hand. On the basis of these principles and of the logico-cognitive system proposed, the well-known nonlexicalization not only of *nall and *nand but also of many other nonlogical cases found throughout the lexicons of languages is analyzed and explained.