Abstract
Jaegwon Kim contends that global supervenience is consistent with non-materialistic cases. Paull and Sider, Horgan, as well as Kim, attempt to defend it from these charges. It is shown here that their defense is only partially successful. Their defense meets one challenge to global supervenience---the hydrogen-atom case---but fails to meet other, ‘local’, cases. It is suggested that the other challenges can be met if global supervenience is combined with weak supervenience. The combination of global and weak supervenience constitutes a viable picture of psychophysical relations, and is especially attractive to nonreductive materialists who are also anti-individualists.