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can TP dominate CP, for example: BILL WANTS ROBERT TO BOLDLY EAT THE CHILI-PEPPER. That's a CP embedded in a CP or a TP? in other words, is the maximal projection 'CP' or TP.

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For the most part, any type of phrase can dominate any other type of phrase, because of the recursive structure of syntax. Since a CP can be dominated by a VP, and a VP can be dominated by a CP, you can prove mathematically that any two phrase types that can go in a CP can dominate each other.

For your specific example, though, entire sentences are usually taken to be CPs, because the specC position is needed to explain topic fronting and question fronting. I would say that this whole sentence is a CP (headed by the invisible declarative-sentence marker), which contains a TP (headed by the present tense on "wants"), which contains a TP (headed by "to").

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    Dec 23, 2022 at 19:38

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