During the Root Infinitive (RI) stage of acquisition, children use non-finite verb forms in matrix clauses that require a finite form. Cross-linguistic work has demonstrated that the length and frequency of the RI stage is related to the "richness" of the verbal morphological paradigm, suggesting that RIs are closely intertwined with morphological acquisition. How exactly these phenomena are related, however, remains an open question. I argue that RIs emerge as a consequence of the acquisition of inflectional categories. Specifically, I propose that children learn which morphosyntactic features are marked in their language via a process of recursive subdivision, and that RIs emerge before the child has learned that tense is marked. I introduce the Sufficient Contrast Learner (SCL), a computational model of inflectional category acquisition. A mathematical consequence of this model is that in languages with rich φ-agreement morphology, the resulting subdivisions will entail that tense marking is learned more quickly and the RI stage is thus shorter. Using English, French, and Spanish as test cases, I demonstrate that SCL correctly predicts the relevant cross-linguistic differences in the length of the RI stage, while matching well with developmental findings regarding order of acquisition and vocabulary size.