Usually simplification of a syntactic system leads to an increase in its expressive power, as the removal of restrictions widens the potential richness of representations. The proposal, within Minimalist Syntax, to reduce the structure building part of the grammar to the operation Merge, has lead to an explosion in the kinds of derivations and representations admitted by the theory. We have External Merge, Internal Merge, Self Merge, Under Merge, Parallel Merge (and its cousin Sideways Move), Late Merge (and its big sister, Wholesale Late Merger), Morphological Merge(r), as well as an increase in the kinds of structure admitted, with Roll Up, Remnant Roll Up, and Head Roll Up. And the field hasn't yet really got its mitts on Pair Merge and various imaginable versions of that.
This lecture points out the problem, and suggests two avenues to reduction of this richness. One is to impose a restriction on the design of the structure building system: syntax builds hierarchical structures that can be mapped to semantic interpretation with no loss of information. That is, the system does not have the capacity to change structure without semantic effect. The other avenue is to reduce the complexity of the structure building operation itself.
I then tackle head movement operations, showing that structures where head movement has applied do not feed more information to the semantics than those where it hasn't applied: head movement phenomena are, as has been often noted, semantically vacuous. I also show that the word building capacity of head movement has to be separated from the positioning of a head with respect to other elements in structure. But this means the structure changing operation of head movement is needed neither for semantics, nor for morphology.