Language is infinitely productive because syntax defines dependencies between grammatical categories of words and constituents, so there is interchangeability of these words and constituents within syntactic structures. Previous laboratory-based studies of language learning have shown that complex language structures like hierarchical center embeddings (HCE) are very hard to learn, but these studies tend to simplify the language learning task, omitting semantics and focusing either on learning dependencies between individual words or on acquiring the category membership of those words. We tested whether categories of words and dependencies between these categories and between constituents, could be learned simultaneously in an artificial language with HCE's, when accompanied by scenes illustrating the sentence's intended meaning. Across four experiments, we showed that participants were able to learn the HCE language varying words across categories and category-dependencies, and constituents across constituents-dependencies. They also were able to generalize the learned structure to novel sentences and novel scenes that they had not previously experienced. This simultaneous learning resulting in a productive complex language system, may be a consequence of grounding complex syntax acquisition in semantics.