Explaining rigidity Wolfram Hinzen Abstract: I argue that both the 'rigid' and 'non-rigid' or 'descriptive' interpretations of the reference of nominals have an explanation in the structure or linguistic form of these nominals, hence are conditioned broadly syntactically. This seems desirable under assumptions of a 'transparent' and compositional syntax-semantics mapping. Two ways in which nominal reference is conditioned on syntactic complexity are analyzed. The first is based on a traditional DP (and N-to-D movement) analysis and its plausible semantic effects. The second appeals to namehood as a property of atomic (unstructured) lexical concepts as such. It explains rigidity as the trivial effect of syntactic atomicity, in which case rigidity has nothing specifically to do with either names or grammatical categories. I defend the second proposal, on both theoretical and cross-linguistic grounds. I argue specifically that the basis of human reference is the reference of conceptual atoms, which are as such lexically unspecified for name, noun, count or mass properties. The discussion traces out the effects of this proposal for a long tradition of philosophical argument, where name-reference is standardly explained in externalist (causal) or semantic, rather than internalist and syntactic, terms.