Head-movement is something of a conundrum in modern syntactic theory. At the beginning of the 1990s, it fit beautifully into the system of assumptions that were gradually coalescing into the Minimalist Program. The Head Movement Constraint of Travis 1984 was unified with other constraints on movement as an instance of Rizzi’s 1990:11 Relativized Minimality, the first overarching vision of how economy principles might restrict move-α. The extremely elegant account of the relative positioning of verbs, auxiliaries, negation, tense and C° in English, French and German that head-movement affords is a paradigm case for Principles and Parameters theory, included in essentially every modern syntax textbook (e.g. Haegeman 1991:522-30, Radford 1997:216-34, Carnie 2002:189-210). Nonetheless, getting the structural mechanism of head-movement to interact properly with the other fundamentals of the theory was a headache even within X-bar theory (Rizzi 1991:117 n. 19 decided that it must be substitution, rather than adjunction; Chomsky and Lasnik 1993: ex. 51, 58, concluded the opposite). When Chomsky 1994 introduced Bare Phrase Structure as a fundamental part of the Minimalist Program, it became essentially impossible. In Bare Phrase Structure, the notion ‘segment of X°’ becomes incoherent, since ‘head’ is equivalent to ‘terminal node’ and an X° is simply a terminal element with something adjoined to it, so that it projects; anything dominating a branching node is not an X°. Consequently, within BPS, an adjunction-to-X° account of head-movement violates not only Extend Target (since adjunction is to a non-root node), but also Chain Uniformity, as outlined by Chomsky 1995: 321:
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