Greenberg's (1963) Universal 34 states that "No language has a trial number unless it has a dual. No language has a dual unless it has a plural." We present an associative model of the acquisition of grammatical number based on the Rescorla-Wagner learning theory (Rescorla & Wagner, 1972) that predicts this generalization. Number as a real-world category is inherently structured: higher numerosity sets are mentioned less frequently than lower numerosity sets, and higher numerosity sets always contain lower numerosity sets. Using simulations, we demonstrate that these facts, along with general principles of probabilistic learning, lead to the emergence of Greenberg’s Number Hierarchy.