The Baldwin effect has been explicitly used by Pinker and Bloom as an explanation of the origins of language and the evolution of a language acquisition device. This article presents new simulations of an artificial life model for the evolution of compositional languages. It specifically addresses the role of cultural variation and of learning costs in the Baldwin effect for the evolution of language. Results show that when a high cost is associated with language learning, agents gradually assimilate in their genome some explicit features (e.g., lexical properties) of the specific language they are exposed to. When the structure of the language is allowed to vary through cultural transmission, Baldwinian processes cause, instead, the assimilation of a predisposition to learn, rather than any structural properties associated with a specific language. The analysis of the mechanisms underlying such a predisposition in terms of categorical perception supports Deacon's hypothesis regarding the Baldwinian inheritance of general underlying cognitive capabilities that serve language acquisition. This is in opposition to the thesis that argues for assimilation of structural properties needed for the specification of a full-blown language acquisition device.