Researchers in the cognitive sciences often seek neural correlates of psychological constructs. In this paper, I argue that even when these correlates are discovered, they do not always lead to reductive outcomes. To this end, I examine the psychological construct of a critical period and briefly describe research identifying its neural correlates. Although the critical period is correlated with certain neural mechanisms, this does not imply that there is a reductionist relationship between this psychological construct and its neural correlates. Instead, this case study suggests that there may be many-to-many psychological-neural mappings, not just one-to-one or even one-to-many relations between psychological kinds and types of neural mechanisms.