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Hereditarians have claimed that recent advances in psychological and psychiatric genetics support their contention that socially important aspects of behavior and cognition in individuals and groups are largely insensitive to environmental context. This has been countered by anti-hereditarians who (correctly) claim that the conclusion of genetic ineluctability is false. Anti-hereditarians, however, sometimes use problematic arguments based on complexity and the ignorance that comes with complexity and a demand for mechanistic, as opposed to variational, explanations for the ways in which genes affect phenotype. I argue here, as a committed anti-hereditarian, that the complexity gambit and the demand for mechanisms open anti-hereditarian arguments to counterattack from hereditarians. Refocusing the argument onto issues about when heritability, genotypic scores, and genome-wide association studies may be appropriately applied and reemphasizing the point that context matters are stronger measures to counter hereditarian claims.