 It is clear that strong individual supervenience entails global supervenience (see Kim 1984). The question that has attracted attention is the converse—whether global supervenience entails strong individual supervenience. In this section, we describe the initial stages of this debate, which took place when the going notion of global supervenience was that outlined just above. In Section 4.3.2, we explain how that notion has been replaced by a family of more precise notions, and explore how it affects the question of whether global supervenience entails strong individual supervenience. (Most of the reminder of this section paraphrases McLaughlin 1995, 55–56.)