I was just rethinking the homework Part 2, and I realized that there is a small error in the way I described the problem. Here’s the real issue:

In the structure you wind up with for Part 2 (that is, for the sentence #2), one of the following conditions seems to hold: either 1) tense is higher than negation or 2) negation is higher than tense.

I stated that as an ordering restriction (which one you have to raise first), but actually now that I look at the rules, it isn’t really about order. It really is about the outcome. It turns out that order doesn’t really matter, because it is possible while following the rules to raise one to the top of the structure, and then raise the second to a position that is actually below the first one you raised. I had been implicitly assuming that raising tense or negation or quantifiers must necessarily “extend” the structure (by adding the raised element to the very top of the tree), but the rules do not actually encode this requirement.

If you were making the same implicit assumption as I was, then fine, everything is good. But if you noticed that it was possible to “tuck in” a raised quantifier/negation/tense like this, then I just wanted to say explicitly here that the real question isn’t about order, but rather which of tense and negation needs to wind up higher in the structure after all of the transformations are done.

Going into that in just a bit more detail: Here are the rules for Neg raising and Tense raising:

[_S X [ Neg Y ] ] → [_S Neg [_S X Y ] ]
[_S X [ Tense Y ] ] → [_S Tense [_S X Y ] ]

Doing either one of them produces a “new S”. That is, you have your original S, minus the thing you raised, and then you have a new S that contains the thing you raised and the original S.

                 S
    S           / \\
   /_\\  -->  Neg   S
  X  /\\           /_\\
   Neg Y         X   Y

The rule doesn’t strictly speaking really require that the S in the lefthand tree be the topmost one in the whole structure, though. So, if you subsequently applied Tense raising, you could target the lower of the two Ses in the righthand tree. And then you’d have Neg higher than Tense, even though you moved Neg first. (If you instead target the higher S when applying Tense raising, then Tense would end up above Neg.)

The bottom line really is just that even the order in which you do the transformations (Neg raising and Tense raising) doesn’t determine which one will be higher in the end, so you have to interpret the question as being not about the order, but rather about the end result. Or, you could make the assumption I originally made when formulating the problem, and suppose that the S on the lefthand side of the Tense raising and Neg raising rules is the topmost one.