Structural equation modelers judge multi-item constructs against three requirements: (a) multiple items converge in a single dimension; (b) individual-level patterns of item convergence are invariant across countries; (c) aggregate-level patterns of item convergence replicate those at the individual level. This approach involves two premises: Measurement validity hinges solely on a construct's internal convergence, and convergence patterns at the individual level have priority over those at the aggregate level. We question both premises (a) because convergence patterns at the aggregate-level exist in their own right and (b) because only a construct's external linkages reveal its reality outreach. In support of these claims, we use the example of emancipative values to show that constructs can entirely lack convergence at the individual level and nevertheless exhibit powerful and important linkages at the aggregate level. Consequently, we advocate a paradigm shift from internal convergence toward external linkage as the prime criterion of validity.