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Historically, opponents of realism have managed to slip beneath a key objection which realists raise against them. The opponents say that some element of the world is constructed by our cognitive practices; realists retort that the element would have existed unaltered, had our practices differed; the opponents sometimes agree, contending that we construct in just such a way as to render the counterfactual true. The contemporary instalment of this debate starts with conventionalism about modality, which holds that the borders of the world's kinds and the careers of individuals in those kinds obtain only relative to our conventions of individuation. Realists object that the kinds and careers in nature would still have obtained, had our conventions been different, but conventionalists claim to be able to agree. I argue that this claim is false, and that conventionalism contradicts itself.