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in "half of the slices were eaten" the phrase "half of the slices" is clearly headed by "slices" as the verb the subject took are plural. however, "of" is a preposition which takes "the slices" as its complement, therefore I dont see how the plurality of the word "slices" is projected to the subject.

Trin TA Athigapanich
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    you're analysing "of the slices" as a prepositional phrase, rather than "half of" as a determiner phrase – Tristan Oct 26 '22 at 10:12
  • so is the structure you are suggesting is dp[ dp[ d'[ d[ half ] ] pp[ of ] ] d'[ d[ the ] np[ slices ] ] ] ? or should i make "half of" one lexicon unit? – Trin TA Athigapanich Oct 27 '22 at 02:52
  • also, if "half of" is a determiner phrase then not sure where "the slices" will get its case from. for example, in "half of them", "them" gets its case from "of" the head of prepositional phrase. – Trin TA Athigapanich Oct 29 '22 at 08:13

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In my opinion, “Slices” is not the head. “Half” is the head and is plural here because it semantically refers to multiple things. Compare “Half were eaten” and “One of the slices was eaten.”

I found a paper that discusses the construction:

when they are used in a construction with of (as in All of the people were happy), Quirk et al (1985:258) refer to [all, both and half] as pronouns functioning as NP heads (see Section 3.3.4.1). Huddleston & Pullum (2002:434) consider half to be a noun since it can take a preceding indefinite article or a cardinal number.

("Syntactic variation in English quantified noun phrases with all, whole, both and half", Maria Estling Vannestål, Acta Wexionensia Nr 38/2004 Humaniora. Page 55)

I don’t know how to analyze this structure formally. My feeling is that the grammatical number of the verb or of "half" in these kinds of contexts is not determined by syntax; it is based instead on some kind of extra-syntactic factors such as pragmatics or semantics. For comparison, I think that in many contexts, the selection of an anaphoric or cataphoric pronoun is not determined by syntax, even though the choice of pronoun can be related in various ways to the meaning or even the grammatical properties of another word in the same or a different sentence.

brass tacks
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    wow the reference is very thorough how did i not find it! thank you brass. quick comment, if "half" is the head, then "half of the pie was eaten" cant be explained. – Trin TA Athigapanich Oct 27 '22 at 02:59
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    Why not? "[half [of the pie]] was eaten"--half is singular because it refers to a mass – brass tacks Oct 27 '22 at 05:43
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    hmm.. but for "half" to know whether it is plural or not it has to look at the complement of prepositional phrase "of the pie" which is "the pie" which is singular. is that okay? wont the preposition "of" which heads "the slices" blocks that? sorry i may be confusing myself. – Trin TA Athigapanich Oct 27 '22 at 06:05
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    @TrinTAAthigapanich: I think that whether "half" is plural or not is not based on syntax; or at least, not always. It is (or can be) based on what it means. The word "half" can even occur in a separate sentence from the word that semantically explains what it is half of: "I baked a pie yesterday. Today, half was eaten by my siblings!" "I baked cookies yesterday. Today, half were eaten by my siblings!" There might also be some similarity to how anaphoric pronouns are selected – brass tacks Oct 27 '22 at 06:23