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The book is worth reading.

How to parse the sentence constituents? How to parse "worth doing"? What kind of constituent it is?

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Doing is the complement of the adjective worth, so called because it completes the sense of the adjective.

Just like verbs, many adjectives—happy, reluctant, confident, likely, for instance— require or can take complements. And just like verbs, each adjective licenses specific kinds of complements. Worth can take phrases headed by nouns or gerunds:

The book is worth reading carefully.
The book is worth a trip to the library.
The book is worth $60.
The book is worth my entire library.

The adjective and its complement together constitute an Adjective Phrase acting as the complement of the verb is, which predicates the AP of the subject, The book.

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Phrases which fit the pattern:

worth + [verb]-ing

create an adjective phrase which attributes some noun with the quality that performing the gerund action on it is beneficial, relative to the effort put in: profitable in some way.

So "worth reading", is an adjective which means "beneficial to read": the worth of the information obtained from the book exceeds the worth of the time and effort put into reading it.

The opposite is "not worth reading": a book not worth reading is a complete waste of time. The time spent reading is valuable (has worth), and the value of the content of the book is lower: it has a lower worth than the time spent.

Phrases in the pattern:

worth + [noun phrase]

Can all be derived from the example "worth one dollar". It's an adjective phrase which indicates that the value of something meets or exceeds the value of the given [noun phrase]. If something is "worth one dollar" that means we are appraising it to have a value of exactly one dollar, or in some cases more than one dollar.

This tool saves me so much time, it was worth the three hours I spent making it. [Because it saves me time, the value of the tool exceeds the value of the three hours I spent making it. The tool has saved me more than three hours already.]

The special phrase

worth it

is used in a general way as a substitute for worthwhile. The "it" pronoun vaguely refers to whatever effort is required which brings about the benefit. This can give rise to a sentence with multiple "it":

It is worth it to study hard in school.

The first "it" is an anticipatory subject, which basically refers to "to study hard in school", since we can rewrite the sentence like this, and eliminate that "it":

To study hard in school is worth it.

Then "worth it" essentially just means "worthwhile" or "beneficial". A child might ask the question "Worth ... it? Worth what? What is it?" The answer would have to be something like: "worth the extra time and effort that it takes to study hard; those are what 'it' refers to".

Notes:

1. "Worth one dollar" can also be expressed using the gerund form (from, for instance, a buyer's perspective) as "worth paying one dollar".

2. "Worth + [verb]-ing" uses positive verbs. "Worth not [verb]-ing" does not make sense, because it takes no time, effort or other resources to not do something.

So, the following is incorrect, or possibly a deliberate joke:

That book is worth not reading. *

It says that the value we obtain from the book's content has a worth which exceeds the worth of effort of not reading it, which is nonsensical, since not reading takes no effort, and moreover, if the book is not read, then whatever benefit it provides is not obtained!

3. Worth is not just about resources like time, effort or money but, abstractly, about any kind of suffering, inconvenience, or anything that might be superfluous if it has no benefit. It can also

Fasting for a week was worth it; I feel great! [I had to endure fasting, but the benefit is greater than the suffering.]

When you're sewing pants, extra length is worth leaving; if they are too long for the wearer, the pants can easily be hemmed, whereas it is inconvenient to add material to pants which are too short! [A few inches if extra cloth hardly cost anything, and take no extra time to add to the design. Yet it is a negative surplus (pants are too long in their unaltered state), which has a potential benefit.]

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