Each of us as language learners had different language experiences, yet somehow we have converged upon broadly the same language system. From diverse, often noisy samples, we have attained similar linguistic competence. How so? What mechanisms channel language acquisition? Could our linguistic commonalities possibly have converged from our shared psychology of learning as applied to the evidence of similar-enough language experience? This article outlines a research program to investigate whether there are sufficient constraints in the dynamics of language to promote robust induction by means of statistical learning over limited samples. It illustrates the approach with regard to English verbs, their grammatical form, semantics, and Zipfian patterns of usage. It explores the emergence of structure from experience using methods from cognitive linguistics, corpus linguistics, learning theory, complex systems, and network science.