Abstract The ‘Biolinguistics’ program seeks to establish specific neuroanatomical models corresponding to the representations and operations characterizing the species-specific language faculty in human beings. Yet after decades of research, no neural structures corresponding to specific linguistic structures, rules, constraints or principles have ever been identified. A key to biolinguistics’ failure is, I suggest, its long-term adherence to two dubious assumptions: (i) a kind of literalism in envisaging the relationship between neural anatomy and linguistic representations, reflecting a seriously misconstrual of Marr’s (1982) tripartite division of cognition, and (ii) a view of such representations as objects fundamentally different from other components of human cognitive capacity. (ii) rests on the premise that phrase markers are the optimal formal representation of natural language sentences, despite major empirical difficulties that syntactic accounts based hierarchical phrase structure face in handling a wide variety of grammatical patterns, including non-canonical coordinations and ellipsis constructions. In contrast, proof-theoretic approaches such as type-logical grammar do not face these difficulties, and their foundational assumptions link language to the higher-order cognitive functions supporting deductive reasoning. This conclusion suggests a promising alternative to the current, essentially result-free ‘Biolinguistic’ paradigm.