In diagramming sentences, I never seem to understand when it's permissible to add an additional X-bar (X') or XP segment to a tree. Is there a rule for knowing when an additional branch of the same X will be necessary and/or is permissible?
Yes, but the rule is determined by the theory that you're assuming. It's never allowed in Current Theory. I don't recall anyone ever positing triple-bar level, except in jest.– user6726Nov 12, 2016 at 20:01
To answer your question, we'd need a theoretical understanding of "bar" and "bar level" (as opposed to a diagrammatic esthetic). One idea is to connect "bar" with the addition of complements, then increasing "bar-level" would accompany adding more complements.
The addition of adjuncts, unlike complements, does not increase bar-level. For instance, the combination of a noun-modifier (a kind of adjunct) with a N' (N-bar that is) gives another N'. Bar-level remains the same. We can tell that, because we can keep on adding noun-modifiers (adjectives, for instance) -- when the category is changed by adding something, you can't generally add another thing of the same type.
Similarly, adding an adverb to a V' produces another V' (not a V''), so you can add several adverbs to a V'.
To test when bar-level changes, we need to look at ways of adding complements. In McCawley's version of bar syntax, we get an N' from a N by adding a complement, as for example getting the N' "father of the bride" by adding to the N "father" the complement "of the bride". Correspondingly, we get the V' "fathered the bride" by combining the V "fathered" with the direct object complement "the bride".
Sometimes S is written V'', because taking subjects to be complements of a V', you'd expect bar-level to be increased.
If we think that verbs can take several complements, then, this would be a place to look for additional bar-levels of V. Perhaps double object verbs are examples, or verbs of movement which take both source and destination PP.
Looking in the other direction, up, a case could be made that addition of a vocative NP to a sentence produces a V'''.
It has been proposed that morphological parts of N and V, such as roots and stems, have negative bar-level.
Are there any diagrams you could add to this, or any concise reading I could do?– Adam_GDec 10, 2016 at 1:42
McCawley's text The Syntactic Phenomena of English has plenty of diagrams, and I believe what I said is consistent with his views. McCawley's version of X-bar "theory" is meant to describe what happens in nominalizations, when V-bar constituents systematically become N-bar constituents. I use scare quotes around "theory", because it all seems to me to be about convenient nomenclature, not syntactic theory.– Greg LeeDec 10, 2016 at 4:17
Here are some remarks by McCawley comparing his bar notation with Chomsky's: books.google.com/…– Greg LeeDec 10, 2016 at 4:18
Great. Thank you!– Adam_GDec 10, 2016 at 12:05