In this paper I argue that the Minimalist syntactic model of Chomsky (1995) may be a suitable vehicle for expressing an 'embodied' model of language, positing that language supervenes strongly on the sensorimotor system. The basic idea is that the principles which define the 'logical form' (LF) of concrete sentences, which Minimalists see as reflecting innate knowledge of language, may in fact have their origin in constraints in sensorimotor processing.