Conceptual structure has been the focus of research in recent years not only in cognitive grammars but also in autonomous syntactic theories concerned with mapping form to meaning. In this paper, we give a sketch of the universal basis of conceptual structure and propose a relativist view of conceptual structures underlying different languages. Spatial expressions in Chinese and English are used to explore this view. Spatial expressions in sign language are also considered to deepen our understanding of conceptual structure. We take issue with the theory of conceptual semantics advocated by Jackendoff for the past two decades. We present a view that "creativity" and "generativity" resides largely in conceptual component, and only derivatively in syntactic component. Thus, the process of "syntacticization" is essentially on a par with lexicalization. We argue that syntactic patterns reflect conceptualizations in different languages and cultures and genuine cases of syntax-semantics mismatch are greatly reduced and hence simpler syntax. We also show how pragmatic inferences can be used to simplify syntactic structure, using word order, argument selection, and contextual expressions in Mandarin Chinese as case studies. We thus propose a sketch to work out a non-autonomous theory of syntax with minimal requirement of tentative innate linguistic structure. (James H.-Y. Tai)