How does the faculty of language relate to rules, axioms, and constraints?

This paper explores the link between rules of grammar, grammar formalisms and the architecture of the language faculty. In doing so, it provides a flexible meta-level theory of the language faculty through the postulation of general axioms that govern the interaction of different components of grammar. The idea is simply that such an abstract formulation allows us to view the structure of the language faculty independently of specific theoretical frameworks/formalisms. It turns out that the system of rules, axioms and constraints of grammar cannot be explicitly represented in a general architecture of the language faculty — which circumvents the ontological mismatch of mental representations and formal/axiomatic properties of language. Rather, the system of rules, axioms, constraints of grammar is intentionally projected by humans, and this projection realizes/instantiates what Dascal (1992) calls ‘psychopragmatics’. Relevant implications for linguistic theory, learnability and (computational) models of language processing are also explored.