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Conceptual atomists argue that most of our concepts are primitive. I take up three arguments that have been thought to support atomism and show that they are inconclusive. The evidence that allegedly backs atomism is equally compatible with a localist position on which concepts are structured representations with complex semantic content. I lay out such a localist position and argue that the appropriate position for a non-atomist to adopt is a pluralist view of conceptual structure. I show several ways in which conceptual pluralism provides an advantage in satisfying the empirical and philosophical demands on a theory of conceptual structure and content.