Categorical reasoning is one of the cornerstones of psychological functioning, supporting explanation, induction, and learning in virtually every domain of knowledge, including reasoning about social categories. Dominant theories of social cognition focus on the role of internal/essential characteristics in representations of social kinds. Drawing upon an emerging literature in philosophy, I introduce an alternative to internalist thinking, called "structural thinking", in which observed correlations between social categories and their properties are explained through stable external constraints, rather than derived from the inherent nature of the categories. In a series of studies with children and adults, I examine how people acknowledge dependence of categorical relationships on background variables, and recognize confounds between category membership and social positions. Structural thinking emerges as a distinct, early-developing mode of thought with a unique cognitive, linguistic and behavioral profile which distinguishes it from other types of reasoning focused either on internal or external but non-structural factors. For example, structural thinking promotes an expectation that properties of social kinds are mutable rather than stable; fosters rectification of inequality in resource allocation decisions; and supports formal explanations (“category member has property P due to category membership C”), generic claims (“Cs have P”), and some forms of generalization. This evidence highlights important connections between causal and categorical representations, and invites us to rethink dominant theories of categorical representations and generic language.