@KinzleB Hmm... according to my experience, the more I know about something, the fewer words I need to explain it.
If I have to explain the same thing with more words, it's probably to accommodate the listener, but if the listener doesn't need a longer version, I usually prefer to use as few words as possible.
Also, good examples are usually very useful.
Okay, I reviewed that page in CGEL quickly. I think I have a better idea now.
Before checking out the page, these were questions that popped up in my head:
> In the modality chapter of the Cambridge Grammar of the English Language, Huddleston and Pullum et al devote a section to the scope of the perfect. They point out that have, when following a modal auxiliary “may belong semantically in the complement of the modal or [it] may have scope over the modal” (2002: 203).
What is this? What is this scope? What does the scope of the perfect mean? Is it about have? Do they mean "the perfect" by have? Are they the same?
It was unclear until I saw the original sentence, and they write, "Perfect have". That gave me a clearer idea.
> They point out that have, when following a modal auxiliary “may belong semantically in the complement of the modal or [it] may have scope over the modal”
I would read that as "They point out that have, when following a modal auxiliary" are your words, and “may belong semantically in the complement of the modal or [it] may have scope over the modal” are their exact words.
Turns out that is not the case.
I guess unless the reader already reads that section in CGEL and can remember it, they may be not sure what scope, internal perfect, external perfect, etc. are about.
And because you quote two books, another book adds more terms such as counterfactual meaning, communicating anteriority, I'd say it makes it more difficult to understand these terms precisely (again, unless the reader already knows them.)
Now that I (sort of) understand their point in CGEL (just their point, not the whole question, not even what "communicating anteriority" is), if I want to verify how I should internalize these usages (i.e., conceptualize these modal usages in my mind), I may quote their examples and paraphrase them like this.
> From CGEL examples (Chapter 3, section 9.9, page 203, example [61] i and ii), I understand them like this:
> [61] i. She must have saved him. = I think it's the case that she has saved him.
> [61] ii. She could have saved him if she'd tried. = It was possible for her to save him if she tried.
> (Note that in my paraphrase of [61] i. my main clause is "I think it's the case", the tense is in the present, but in [61] ii. the main clause is "It was possible", the tense is in the past.)
> Is my understanding correct?
> He continues, "Like you, I'm a vampire, although I don't know how your son could have known (I'm a vampire) when he asked me to help you."
> Paraphrase 1: "I don't know how it is possible for your son to have known..".
> Paraphrase 2: "I don't know how your son already knew (or had known) that when he asked me".
This sentence in CGEL is a bit strange, I think. What exactly does this follow mean?
> In [ii] the perfect has extended scope, attributable to the fact that can lacks the past participle form that would be needed if it were to follow have.
can follows have because it comes after have (which is not the case)? Or because it follows have to somewhere?
It follows have to have's scope? But when have's scope is internal perfect, the modal's scope is outside!
Maybe this is another typo in the book.
Oh, hmm... this is a bit risky, I think.
> [62] i He needn't / ought to / should / might / could have told her. [deontic]
> The deontic case [i] allows need but not must; ...
It's very important to understand their "deontic" before reading that sentence.
Because He must have told her is perfectly grammatical.