Under a Minimalist conception, syntax builds (possibly multi-dominant) phrase structure trees, and at certain points during the structure-building process chunks are processed by the operations Transfer-PF and Transfer-LF and sent off to the interfaces. As Chris Collins lamented in his guest post, the technical details of these operations have never been fully spelled out in the literature. It is usually assumed that they apply every time a phase is completed, but the mechanisms for determining which occurrences of an LI should be pronounced or how quantifier scope should be determined are left open. These are not trivial issues. As a matter of fact, a whopping 9 pages of Collins and Stabler are dedicated to getting the system off the ground and figuring out what pieces are indispensable for it to work.
The MG perspective Greg presents is a lot simpler on a technical level while actually doing more work.
- First of all, it operates directly on derivation trees, with no reference to phrase structure trees (as Greg will be quick to point out, though, we could just as well state it over multidominant phrase structure trees if we wanted to because they are so similar to derivation trees). So this is yet another instance where derived trees turn out to be redundant, they serve no function that can't be taken care of by derivation trees.
- Second, MG Transfer is more local than its Minimalist conception because the former applies at every step of the derivation but the latter does not. This addresses a problem that as far as I know was first raised by Michael Brody: If Transfer applies to entire CPs, then it operates on very elaborate tree representations. So Minimalism is both derivational and representational, which isn't all that minimal. The MG perspective shows that Transfer doesn't have to wait for full CPs to be assembled, it can apply at every point in the derivation. Minimalism without representations is possible after all.
- Third, the procedure Greg describes is precise, yet general. It handles standard phrasal movement just as easily as head movement, roll-up movement or remnant movement. And it gives an exact translation from derivations to logical formulas, including a simple treatment for scope ambiguities.