According to Biber et. al. in the Longman Student Grammar of Spoken and Written English:

For each class of lexical word, there is a major phrase type with an example of that class as the head: noun phrase, verb phrase, adjective phrase, adverb phrase, and prepositional phrase. The head is the principal, obligatory word. In fact, each phrase type can often consist of just one word: the head.

In the previous chapter, the author divides the words, as a grammatical unit, into three major 'families': lexical words, function words and inserts.

As silly as the question is, i'd like to know why do we discuss lexical words, such as nouns/verbs/adjectives/adverbs, as the heads of phrases and out of a number of function words only prepositions serve that role?

I apologize if the question is still unclear and/or inane.

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    What is a lexical word? Your question is confusing so please give an example of what you mean. – Lambie Oct 7 '16 at 13:01
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    @Lambie This is a site for linguists! :-) If you want to ask a question on the notional difference between lexical and function words it might make a good post. – Araucaria - Not here any more. Oct 7 '16 at 13:19
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    Do you understand the question? I don't. I AM a linguist. – Lambie Oct 7 '16 at 13:31
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    Prepositions are arguably borderline between lexical words and function words. 'Under' hints at a (restricted) type of mental image that 'than' doesn't. – Edwin Ashworth Oct 7 '16 at 13:52
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    The excerpt you've given (could you give a more specific reference than just “Biber et al.”, by the way?) makes it look like the author considers prepositions lexical words, which renders the main question somewhat null, at least in the context of the quote provided. – Janus Bahs Jacquet Oct 7 '16 at 15:50

Determiners like "the", "a", and "that" are often considered function words. Further, determiners are sometimes considered the heads of what are called determiner phrases.

Many linguists have abandoned the notion of noun phrases in favor of determiner phrases. For example, classically

the dog

would be regarded as a noun phrase with "dog" as its head. But very many synctacticians now classify it as a determiner phrase with "the" as its head.

See the wiki on determiner phrases or google "DP hypothesis" for more information.

So prepositions might not be the only function words that head phrases.

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Function words are in fact considered heads of phrases for many (most?) syntacticians. Complementisers, auxiliary verbs, determiners, tense morphemes, negative particles (in fact particles of many kinds) and more are all heads of phrases. It's more complicated to explain this to learners, so many grammars don't put it that way, and instead have determiners as part of noun phrases and so on. I can't check the Biber et al reference right now so I'm not sure exactly what they say and I don't know what they mean by 'insert', but for a student grammar they almost certainly made this decision (or perhaps it is the theory they subscribe to). As to why prepositions are considered heads even so, it's most likely because as Edwin notes above, they are borderline between functional and lexical items. They are closed class, like functional elements, and many have a purely grammatical function, but many of them do 'have meaning' like lexical elements and so it's easier (for students) to identify them as contributing their category to a phrase.

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