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Some philosophers (like Kevin Scharp) have proposed that concepts themselves—not just the propositions or beliefs they figure into—can be inconsistent, and thereby defective. Others (like Herman Cappelen) have rejected this proposal for relying on inferentialism. I argue that what's needed for the proposal is not inferentialism, but rather bilateralism. This means that even those of us are not inferentialists can take this kind of inconsistency to be a source of conceptual defectiveness. However, I also argue that we are left with a puzzle for explaining what would make this kind of inconsistency a defect.